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Thread: The Standard Model: where are we now?

  1. #1 The Standard Model: where are we now? 
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    The Standard Model has been very successful, accounting for a very wide range of observations and experiments, especially if one counts emergent effects like macroscopic structures. But there is reason to think that it is incomplete.

    Observational problems:
    • Gravity. It's hard to quantize, and it's hard to connect it to the Standard Model.
    • Neutrino masses. The Standard Model makes them massless.
    • Matter/antimatter asymmetry. It requires baryon-number violation.
    • Dark matter. Likely some particles left over from the early Universe that then became much of the masses of galaxies and galaxy clusters.
    • Dark energy. Something or other with (pressure) ~ - (mass density)*c^2 (yes, negative pressure)
    • The inflaton (no second i), whatever had caused cosmic inflation.

    The Standard Model makes neutrinos massless because before the last decade or so, there were only upper limits of neutrino masses. However, there was no theoretical reason that neutrinos have to be massless, as there is for the photon.

    Theoretical problems:
    • The hierarchy problem: why are Standard-Model particles much less massive than the Planck mass?
    • Higgs-particle instability at high energies, like near the Planck energy.
    • The small masses of neutrinos, much smaller than the masses of the charged elementary fermions.
    • The "strong CP problem", how to keep QCD from getting CP violation without fine tuning.
    • The generations of elementary fermions fit Grand Unified Theory multiplets rather well, without needing a lot of extra particles.
    • Extrapolation of the QCD and the two electroweak couplings to high energies gives convergence at energies not much less than the Planck mass.

    Supersymmetry solves some of them, especially TeV-scale SUSY with the Minimal Supersymmetric Standard Model or the Next-to-MSSM. It makes much better convergence of the QCD and electroweak couplings, to a few percent at about 2*10^(16) GeV, the presumed GUT symmetry-breaking energy scale. It also stabilizes the Higgs particle, all the way up to GUT energies, and it approximately predicts the Higgs particle's mass. However, the Large Hadron Collider's experimenters have discovered some rather disappointingly high lower bounds for the masses of some of the SUSY partners of Standard-Model particles.

    The neutrino's low mass could be do the something called the seesaw mechanism. It would have a "Dirac mass", like the charged elementary fermions, a mass due to the Higgs mechanism. But its right-handed part would also have a "Majorana mass" that would be only a little less than the GUT energy scale. These two effects would then combine to give our observed neutrinos very low masses.

    Dark matter could be due to the Lightest Supersymmetric Particle, and there are various other particles that it could be, like the axion, which would suppress strong CP violation. All these would-be dark-matter particles are electrically neutral and QCD colorless, properties necessary for being a good one. There are several experiments in progress for detecting dark-matter particles, both directly and indirectly.

    We have much less of a clue about the natures of the inflaton and dark energy, however.

    Including gravity is very difficult. String theory offers a way to do it, but string theory has problems of its own, like rather extreme non-uniqueness of its low-energy limit.
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  2. #2  
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    A few comments:

    Gravity. It's hard to quantize, and it's hard to connect it to the Standard Model.

    You have to start by knowing how gravity works, and then you need to know that "a field is a state of space". How many fields has an electron got? One.

    Neutrino masses. The Standard Model makes them massless.

    Check out photon effective mass. If the speed drops below c, some of the energy-momentum is exhibited as mass. If the speed drops to zero, all of it is.

    Matter/antimatter asymmetry. It requires baryon-number violation.

    You can "melt" baryons in a quark-gluon plasma. Baryon asymmetry is matched by lepton asymmetry. Matter is labelled as such by convention. Positronium is an exotic atom which is comprised of both matter and antimatter. And it's like "light hydrogen".

    Dark matter. Likely some particles left over from the early Universe that then became much of the masses of galaxies and galaxy clusters.

    Space expands between the galaxies but not within. It has its vacuum energy which has a mass equivalence.

    Dark energy. Something or other with (pressure) ~ - (mass density)*c^2 (yes, negative pressure)

    Tension is negative pressure. Look to the bag model and think of the balloon analogy for the expanding universe, but make it a bubble-gum balloon. As it expands the skin gets thinner and the tensile strength reduces. So it expands faster and the skin gets thinner and the tensile strength reduces. And repeat.

    The inflaton (no second i), whatever had caused cosmic inflation.

    Cosmic inflation is a dead man walking. Forget it.
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  3. #3  
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    (Me: Gravity. It's hard to quantize, and it's hard to connect it to the Standard Model.)
    Quote Originally Posted by Farsight
    You have to start by knowing how gravity works, and then you need to know that "a field is a state of space".
    It is not, and how many times must we explain that to you?

    (Me: Matter/antimatter asymmetry. It requires baryon-number violation.)
    Quote Originally Posted by Farsight
    You can "melt" baryons in a quark-gluon plasma. ...
    I marvel at this display of irrelevance.

    (other such babbling snipped)
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  4. #4  
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    There's a further problem with the Standard Model. Its rather sizable number of free parameters: 19. This is in addition to its rather complicated gauge-multiplet structure and symmetry group, SU(3) * SU(2) * U(1).

    SU(3) - QCD
    SU(2) - Weak isospin
    U(1) - Weak hypercharge

    The second and third are mixed by electroweak symmetry breaking. Each of them has one coupling constant, and to these three is added a fourth: the strong-CP parameter. The gauge part and its interactions with the other parts are all well-determined.

    The Higgs particle has two parameters: its mass and its self-interaction.

    The elementary fermions have 9 masses and the quarks have 3 CP-preserving mixing angles and 1 CP-violating phase.

    This gives a grand total of 19.

    -

    Neutrinos being massive adds 3 more masses, 3 more CP-preserving mixing angles, and 1 more CP-violating phase. This may also add 2 Majorana phases. So we get a total of 26 or 28 parameters.

    Though unbroken supersymmetry will not add parameters, SUSY is broken, and its breaking adds about 100 parameters to the Minimal Supersymmetric Standard Model. Many of these make neutral currents that are not observed, and imposing flavor independence cuts that number by a large fraction. In fact, one can get the MSSM down to as few as 5 extra parameters.
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  5. #5  
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    Quote Originally Posted by lpetrich
    It is not, and how many times must we explain that to you?
    You haven't explained anything. A field is a state of space. You can't separate a field from the space it's in. I'm not just making this stuff up. Have a read of this and note the section entitled "Expanding the Theory". Einstein is talking about the electromagnetic field and the gravitational field, and says this: "It can, however, scarcely be imagined that empty space has conditions or states of two essentially different kinds, and it is natural to suspect that this only appears to be so because the structure of the physical continuum is not completely described by the Riemannian metric." But I'll suppose you'll just dismiss that, along with the "melting" which means baryon-number conservation is not sacrosanct.

    I'm sorry Loren, but with respect you seem to be astonishingly ignorant of both historical and contemporary physics, and moreover you seem to have something of an attitude problem when it comes to learning about something you don't already know. By the way, you might want to read up on how supersymmetry is a busted flush, see for example this: The Rise and Fall of Supersymmetry – Starts With A Bang
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    (Einstein-thumping snipped)
    Quote Originally Posted by Farsight
    But I'll suppose you'll just dismiss that, along with the "melting" which means baryon-number conservation is not sacrosanct.
    Except that quarks have nonzero baryon number B. Ordinary ones have B = 1/3, while antiquarks have B = -1/3. So a quark-gluon plasma does not violate baryon number, except from some extremely literal-minded standpoint.
    Quote Originally Posted by Farsight
    I'm sorry Loren, but with respect you seem to be astonishingly ignorant of both historical and contemporary physics, ...
    I don't see how I'm supposed to be ignorant when I can easily do much of the math behind many important physical theories.
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  7. #7  
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    This is in addition to its rather complicated gauge-multiplet structure and symmetry group, SU(3) * SU(2) * U(1).
    Yes, this is the core issue - the symmetry group is a very complicated one. If gravity can be formulated as a QFT and hence included in the SM ( which is by no means certain ! ), it is reasonable to assume that the above symmetry group is only a sub-group of an even more complicated arrangement. We would find ourselves in a situation where we can formally write down a Lagrangian, but not do anything with it due to its sheer complexity.

    I have another issue too - while we are in a position to make our laws of nature diffeomorphism invariant, little attention seems to be paid to the topology of the underlying space-time, specifically in terms of connectedness. What if it turns out that the microscopic structure of the vacuum has a non-trivial topology and is multiply connected in some way ? Is the SM Lagrangian invariant under changes in topology ? If not, what impact would such a change have ? And is there a way to formulate laws of nature so that they are invariant both to changes in geometry and changes in topology ?
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    Actually, most Grand Unified Theories feature simpler gauge groups, though larger ones. I've seen SU(5), SU(6), SU(4)*SU(2)*SU(2) ~ SO(6)*SO(4), SU(3)^3, SO(10), E6, and E8.

    The multiplet structure also gets simplified.

    But the price of this simplification is GUT-scale symmetry breaking and rather complicated symmetry breaking at that. Though the Standard-Model Higgs particles are rather small multiplets, GUT Higgs particles are often rather large ones, larger than most other particles' ones. Compactification of additional dimensions offers other possibie ways of symmetry breaking, though they still look rather complicated.

    As to the multiplet structure and interactions, they rather nicely simplify in the more-discussed models.

    I'll consider the MSSM, and use the higgsino's chirality. The multiplet structure is (QCD multiplicity, weak-isospin multiplicity, weak hypercharge, chirality: L, R, or -) A * will include a conjugate rep.

    Gauge particles are always in the adjoint rep:
    gluon: (8,1,0,-), W (1,3,0,-), B (1,1,0,-)

    The elementary fermions: quarks and leptons, including right-handed neutrinos
    Q (3,2,1/6,L), Q* (3*,2,-1/6,R), U (3,1,2/3,R), U* (3*,1,-2/3,L), D (3,1,-1/3,R), D* (3*,1,1/3,L)
    L (1,2,-1/2,L), L* (1,2,1/2,R), N (1,1,0,R), N* (1,1,0,L), E (1,1,-1,R), E* (1,1,1,L)
    The Higgs particle (up and down Higgs):
    Hu (1,2,1/2,L), Hu* (1,2,-1/2,R), Hd (1,2,-1/2,L), Hd* (1,2,1/2,R)

    Interactions, indexed over elementary-fermion generations. Left-handed parts here only; right-handed parts are their Hermitian conjugates. I'll include the seesaw-mechanism mass term for the right-handed neutrinos.
    yuij.Qi.U*j.Hu + ydij.Qi.D*j.Hd + ynij.Li.N*j.Hu + yeij.Li.E*j.Hd + mrij.N*i.N*j + mh.Hu.Hd

    The y's are EF-Higgs Yukawa-coupling matrices, mr is a mass matrix for the right handed neutrinos, and mh is the μ term in the MSSM. mr is symmetric and near GUT scales, while mh is near electroweak scales.

    The Standard Model looks rather horribly baroque, it must be said.
    Last edited by lpetrich; 07-01-2014 at 07:03 PM. Reason: Added some tidbits
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    Here's the Georgi-Glashow SU(5) model:

    Gauge particles:
    G(24) = gluon + W + B + (3,2,-5/6,-) + (3*,2,5/6,-)

    Elementary fermions:
    F(1,L) = N*
    F(5,R) = L* + D
    F(10,L) = Q + U* + E*
    F(10*,R) = Q* + U + E
    F(5*,L) = L + D*
    F(1,R) = N
    Nice pattern.

    Higgs particles:
    H(5,L) = Hu + (3,1,-1/3,L)
    H(5*,L) = Hd + (3*,1,1/3,L)
    H(5*,R) = Hu* + (3*,1,1/3,R)
    H(5,R) = Hd* + (3,1,-1/3,R)

    Interactions:
    yuij.F(10,L)i.F(10,L)j.H(5,L) + ydij.F(10,L)i.F(5*,L)j.H(5*,L) + ynij.F(5*,L)i.F(1,L)j.H(5,L) + mrijF(1,L)i.F(1,L)j + mh.H(5,L).H(5*,L)
    yu is symmetric, and ye = transpose(yd). Thus predicting bottom-tau mass unification at GUT energies.

    There are some extra gauge and Higgs multiplets, and all of them must be given GUT-scale masses by symmetry breaking to keep isolated protons from decaying faster than their observed lower limit.
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    Quote Originally Posted by lpetrich View Post
    Except that quarks have nonzero baryon number B. Ordinary ones have B = 1/3, while antiquarks have B = -1/3. So a quark-gluon plasma does not violate baryon number, except from some extremely literal-minded standpoint.
    It violates it totally. You start with a proton and an antiproton. Then you can melt the antiproton. It's gone. The quark-gluon plasma isn't actually a seething mass of quarks and gluons. Gluons in ordinary hadrons are virtual particles. And we've never seen a free quark. Think in terms of pea soup. There aren't actually any peas in pea soup.

    Quote Originally Posted by lpetrich View Post
    I don't see how I'm supposed to be ignorant when I can easily do much of the math behind many important physical theories.
    Being able to do some math isn't the same as knowing about the physics. When I give you bona-fide references to tell you about something that isn't in your textbook bible, you reject it out of hand. Don't.
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    Quote Originally Posted by Farsight View Post
    Being able to do some math isn't the same as knowing about the physics.
    It is exactly the same when the details of the physics are the mathematics.
    When I give you bona-fide references to tell you about something that isn't in your textbook bible, you reject it out of hand. Don't.
    Given that you have so often been mistaken about your references in a way that doesn't stain your character, the wise move is to assume that you are mistaken about your references, perhaps in a way that doesn't stain your character.
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    Quote Originally Posted by Markus Hanke View Post
    ...What if it turns out that the microscopic structure of the vacuum has a non-trivial topology
    That's what particles are. We can diffract electrons. The wave nature of matter is not in doubt. And what's waving? The vacuum. Space. We make structures out of waves in it, these waves displacing themselves into closed paths. We call these structures electrons and protons and so on. And they don't call it topological quantum field theory for nothing.
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    Here is the Fritzsch-Minkowski-Glashow SO(10) model:

    This is Peter Minkowski, not Hermann Minkowski.

    I'll break it down to GG SU(5), with SO(10) -> SU(5) * U(1)

    This gives an additional quantum number which is related to B - L: (baryon number) - (lepton number)

    Gauge:
    G(45) -> G(24,0) + G(1,0) + G(10,-1) + G(10*,1)

    Elementary fermions:
    F(16,L) -> F(1,5/4,L) + F(10,-3/4,L) + F(5*,5/4,L)
    F(16*,R) -> F(1,-5/4,R) + F(10*,3/4,R) + F(5,-5/4,R)

    Higgs:
    H(10,L) -> H(5,-1/2,L) + H(5*,1/2,L)
    H(10,R) -> H(5*,1/2,R) + H(5,-1/2,R)

    Interactions:
    yij.F(16,L)i.F(16,L)j.H(10,L) + mh.H(10,L).H(10,L)
    yu = yd = yn = ye = y, which is symmetric. This mass unification is too successful: it eliminates cross-generation decay. So that sort of decay, and also right-handed-neutrino masses, must be generated by breaking of SO(10).


    The SU(5) reps are:
    24 = adjoint = (vector).(conjugate vector) - (scalar)
    1, 5, 10, 10*, 5*, 1 -- antisymmetric tensors with 0, 1, 2, 3, 4, 5 indices. Each one is the conjugate of the one in the same position from the opposite in. 5* is the conjugate of 5, 5 is the conjugate of 5*, etc.

    The SO(10) reps are:
    45 = adjoint = antisymmetric 2-tensor
    10 = vector
    16 = spinor
    16* = conjugate spinor
    Last edited by lpetrich; 07-01-2014 at 08:25 PM. Reason: Fixed a typo
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    Quote Originally Posted by Farsight
    The quark-gluon plasma isn't actually a seething mass of quarks and gluons.
    Except for this: Explained: Quark-gluon plasma | MIT News Office
    For a few millionths of a second after the Big Bang, the universe consisted of a hot soup of elementary particles called quarks and gluons. A few microseconds later, those particles began cooling to form protons and neutrons, the building blocks of matter.

    Over the past decade, physicists around the world have been trying to re-create that soup, known as quark-gluon plasma (QGP), by slamming together nuclei of atoms with enough energy to produce trillion-degree temperatures.
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    Ipetrich, it all looks very impressive, but what does it signify?
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    There's some further unification that one can do.

    E6 -> SO(10) * U(1)

    adding a quantum number whose significance is far from clear to me.

    It makes some more GUT gauge particles:
    78 -> (45,0) + (1,0) + (16,-1) + (16*,1)

    It also has the elementary fermions and the Higgs particles in the same kind of multiplet:
    27 -> (16,1/3) + (10,-2/3) + (1,4/3)
    27* -> (16*,-1/3) + (10*,2/3) + (1,-4/3)

    The EF-Higgs interaction terms take the form (27).(27).(27)

    The Higgs mass term can take this form if we replace mh with S, a SO(10) singlet. So we'd get
    g.Hu.Hd.S
    g.H(5,L).H(5*,L).S
    g.H(10,L).H(10,L).S

    This S may survive down to electroweak energies, where it would be part of the NMSSM, the Next-to-Minimal Supersymmetric Standard Model. SO(10) and subsets could also have interaction term S^3, but it would be a consequence of E6 breaking.

    So X -> F + H + S
    with X.X.X -> F.F.H + H.H.S


    Finally, we get to E8, a part of some string models. It would break down
    E8 -> E6 * SU(3)

    and its fundamental / adjoint rep would break down
    248 -> (78,1) + (1,8) + (27,3) + (27*,3*)

    So according to some string-based hypotheses, *all* the Standard Model's particles, and then some, fit into one gauge-particle multiplet.
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    Quote Originally Posted by Jilan
    Ipetrich, it all looks very impressive, but what does it signify?
    The structure of the Standard Model's particle multiplets suggests Grand Unified Theories that unify them. But while one can indeed get a lot of unification, the price for that is complicated symmetry breaking. The more unification a theory has, the more symmetry breaking the theory needs.
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    lpetrich, please can you explain symmetry breaking? In your own words.
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    Quote Originally Posted by Farsight
    lpetrich, please can you explain symmetry breaking? In your own words.
    Here's a common analogy.

    Consider a bowl on a table. It is axially symmetric, with its axis of symmetry being vertical and going through its center. One can rotate it horizontally around its center and it will look the same.

    Drop a marble into it. The marble will come to rest in its center. The system will still be axially symmetric around its center.

    Now consider a bowl with a hump in the middle, something like a juice squeezer. But even with the hump, the bowl is still axially symmetric around its center.

    Drop a marble into it. The marble will come to rest in the trough. However, when you rotate the bowl with the marble, the marble's position changes relative to your coordinates, and the system's axial symmetry is lost. It has been broken by that marble's presence.

    But if one shakes that bowl back and forth vigorously enough, the marble will move over the center hump and the symmetry will be restored. This shaking corresponds to temperature, more shaking is higher temperature.
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    I've found John Ellis's presentation Outlook for Supersymmetry, for a particle-physics conference. In the last slide, he pointed out a long history of inventing particles to solve particle-physics problems. I'll list them with some paraphrasing and description and extra ones, along with the years of proposal and discovery.

    The successes so far:
    • Reconciling quantum mechanics and special relativity. Charged particles have antiparticles with opposite charge. 1928. 1932.
    • Masses of nuclides. Approximate multiples of a proton's mass, with some different-mass nuclides having the same electric charge. Neutron. 1920. 1932.
    • Beta decay has continuous spectrum. Energy and angular momentum being lost. Neutrino. 1930. 1956.
    • Lepton number not violated. Separate electron and muon neutrinos. Late 1940's. 1962.
    • Flavor SU(3) symmetry. Omega-minus baryon completes spin-3/2 light-baryon multiplet. 1962. 1964.
    • Flavor SU(3) symmetry. Quarks. 1962. 1968 - early 1970's.
    • Flavor-changing neutral currents. Like the neutral kaon changing to its antiparticle and back. Charm quark. 1970. 1974.
    • CP violation. Third generation of quarks: bottom, top. 1973. 1977 and 1995.
    • Strong-interaction dynamics. Gluon, QCD. 1972. 1979.
    • Weak interactions. W+-, Z0. 1968. 1983.
    • Electroweak renormalizability. Higgs particle. 1964. 2012.
    All of them are inside the Standard Model.

    Between proposal and discovery, the number of years is very variable.

    Some well-known proposed particles:
    • Various criteria, like naturalness. Supersymmetry. 1971.
    • Strong CP problem. It seems very fine-tuned. Axion. 1977.
    • Dark matter. WIMP: Weakly Interacting Massive Particle. ?
    • Cosmic inflation. Inflaton. 1980.
    • Dark energy. Quintessence. ?
    All of them are outside the Standard Model.
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    Quote Originally Posted by lpetrich View Post
    Here's a common analogy.

    Consider a bowl on a table...
    I appreciate the effort, but can you give me a description that's more relevant to the Standard Model? The bowl analogy is a bit of a non-answer I'm afraid.

    I'd take John Ellis with a pinch of salt if I were you. Have a read of what Peter Woit has said about him.
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    Why is that analogy supposed to be irrelevant to the Standard Model? It's a good nonmathematical analogy, and a commonly-used one. If you find it unsatisfactory, would you want for me to show you the mathematics involved?

    As to Peter Woit on John Ellis, I will read it when you give us a proper link. Search-engine result pages are not proper links. For my part, I think that John Ellis is essentially correct about the history of positing new particles.
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    Quote Originally Posted by Farsight View Post
    I appreciate the effort, but can you give me a description that's more relevant to the Standard Model? The bowl analogy is a bit of a non-answer I'm afraid.

    I'd take John Ellis with a pinch of salt if I were you. Have a read of what Peter Woit has said about him.
    Symmetry breaking is a simple idea at heart. The precise statement would obscure the essential details (and in any case, you can find it online in many places), so I will offer an analogy which sits somewhere between the bowl picture and full QFT.

    Imagine you had a complex scalar field throughout space, and suppose that you want to find the lowest energy state of that field (i.e. the vacuum state). You'd start by considering uniform states of the field such that is constant everywhere, since non-uniformities would tend to increase the energy. Suppose, for the sake of example, that the energy per unit volume of such states is given by some expression like


    (I'm taking to be dimensionless, just to keep things uncluttered.) In such a case, as you can verify by differentiating , the the lowest energy uniform field is not the "symmetry-respecting" state , but any of the states for which . There is an entire unit circle of possibilities to choose from in the complex plane, but the system must pick one. Thus, like a pencil balanced on its tip, or spontaneous magnetisation of a ferromagnet, or the marble in lpetrich's analogy, the field must transition to one of the non-symmetric states in order to minimise its energy. The result is that the physical vacuum has a non-zero field everywhere.

    There are a couple of interesting consequences to this.

    1. If we imagine writing for real fields and , we see that spontaneous symmetry breaking has forced to be 0, but allowed to be any (constant) value from 0 to . In reality, the fields won't be exactly constant, and will be able to undergo small oscillations about the vacuum state, so we should see two species of particle corresponding to oscillations in the and "directions". If you picture lpetrich's bowl and relate it to the function above, our vacuum state is somewhere in the circular "valley", and you can see that oscillations in the direction are "radial" modes which must climb the potential in each direction; they have an effective potential term (EDIT: which may remind you of the simple harmonic oscillator), and therefore appear to us like massive modes. On the other hand, the "tangential" modes in the direction will not have to climb the potential, and will appear to us like massless modes (called Goldstone bosons).

    2. If there is some massless field which is coupled to , then as a result of acquiring its non-zero vacuum expectation value (VEV) as described above, excitations of acquire an additional amount of energy proportional to the VEV and the strength of the coupling. If the form of the coupling term is just right, this additional energy looks exactly like rest mass for the excitations.
    Last edited by btr; 07-04-2014 at 08:00 PM. Reason: Added comment in parentheses (marked with EDIT)
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    Btr, given that symmetry is already broken would that explain why weird quantum effect disappear once a particle interacts with the universe?
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    Quote Originally Posted by Jilan View Post
    Btr, given that symmetry is already broken would that explain why weird quantum effect disappear once a particle interacts with the universe?
    Do you mean the fact that quantum effects don't tend to be evident on large scales? There are a couple of ways of looking at that, which gets us into the various interpretations of quantum mechanics, but it is really a separate phenomenon from the symmetry breaking we're talking about here.

    Symmetry breaking is something which only happens to one special field that we know of (the Higgs field), or at least so it seems. What I think you're alluding to is something which affects quantum systems quite generally, even outside of quantum field theory.
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    No I don't think so. It seems to be related to systems that haven't yet reacted with another one, hence the question. Such systems appear to have a symmetry that they lose though interactions (decoherence). Big or small doesn't matter. I have just had this evening a compelling leaning towards this view, but I am finding hard to put it into words. Sorry, I need to think this through more carefully. Although perhaps not on a Friday night after the week I've had -lol.
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    Quote Originally Posted by btr View Post
    Symmetry breaking is a simple idea at heart. The precise statement would obscure the essential details (and in any case, you can find it online in many places), so I will offer an analogy which sits somewhere between the bowl picture and full QFT...
    Thanks for this, btr. But I'm still struggling to get any understanding out of it. I'll try to explain why.

    Quote Originally Posted by btr View Post
    Imagine you had a complex scalar field throughout space, and suppose that you want to find the lowest energy state of that field (i.e. the vacuum state). You'd start by considering uniform states of the field such that is constant everywhere, since non-uniformities would tend to increase the energy.
    No problem with a field throughout space.

    Quote Originally Posted by btr View Post
    Suppose, for the sake of example, that the energy per unit volume of such states is given by some expression like


    (I'm taking to be dimensionless, just to keep things uncluttered.) In such a case, as you can verify by differentiating , the the lowest energy uniform field is not the "symmetry-respecting" state , but any of the states for which . There is an entire unit circle of possibilities to choose from in the complex plane, but the system must pick one. Thus, like a pencil balanced on its tip, or spontaneous magnetisation of a ferromagnet, or the marble in lpetrich's analogy, the field must transition to one of the non-symmetric states in order to minimise its energy. The result is that the physical vacuum has a non-zero field everywhere.
    I don't have an issue with the physical vacuum and a non-zero field everywhere, but where does the expression come from?

    Quote Originally Posted by btr
    There are a couple of interesting consequences to this.

    1. If we imagine writing for real fields and , we see that spontaneous symmetry breaking has forced to be 0, but allowed to be any (constant) value from 0 to .
    We've somehow gone from a field to two fields. This jars, because I consider a field to be "a state of space". I cannot conceive of space having two states at the same time.

    Quote Originally Posted by btr
    In reality, the fields won't be exactly constant, and will be able to undergo small oscillations about the vacuum state, so we should see two species of particle corresponding to oscillations in the and "directions".
    I can get some meaning out of this. If you've got a washing line, sight your eye down its length, and twang it. You will see a transverse wave move along it. This is an analogy for a photon. Alternatively twist it with a pair of pliers and let go quickly. A rotational wave moves down the washing line. This is an analogy for a neutrino, a "Weyl spinor" L.

    Quote Originally Posted by btr
    If you picture lpetrich's bowl and relate it to the function above, our vacuum state is somewhere in the circular "valley", and you can see that oscillations in the direction are "radial" modes which must climb the potential in each direction; they have an effective potential term (EDIT: which may remind you of the simple harmonic oscillator), and therefore appear to us like massive modes.
    Neutrinos oscillate, but I'm just not getting this bowl.

    Quote Originally Posted by btr
    On the other hand, the "tangential" modes in the direction will not have to climb the potential, and will appear to us like massless modes (called Goldstone bosons).
    It's not as if we see them flying around like we see photons.

    Quote Originally Posted by btr
    2. If there is some massless field which is coupled to , then as a result of acquiring its non-zero vacuum expectation value (VEV) as described above, excitations of acquire an additional amount of energy proportional to the VEV and the strength of the coupling. If the form of the coupling term is just right, this additional energy looks exactly like rest mass for the excitations.
    Again the multiple fields leaves me saying huh? But no problem with energy having a mass equivalence. Although I seem to be none the wiser about symmetry-breaking. Sorry.

    Quote Originally Posted by btr
    Symmetry breaking is something which only happens to one special field that we know of (the Higgs field), or at least so it seems.
    Noted. I'm not a fan of the Higgs mechanism myself.
    Last edited by Farsight; 07-07-2014 at 02:53 PM. Reason: superfluos quotebrackets
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    Quote Originally Posted by Farsight
    We've somehow gone from a field to two fields. This jars, because I consider a field to be "a state of space". I cannot conceive of space having two states at the same time.
    There are more things in Heaven and Earth than are dreamt of in such conceptions. That includes multiple fields. Which, BTW, are *not* "states of space".
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    That's what Einstein said in this field theory article dating from 1929. See the Expanding the Theory section where he was talking about electromagnetic and gravitational fields. This is the bit:

    "The two types of field are causally linked in this theory, but still not fused to an identity. It can, however, scarcely be imagined that empty space has conditions or states of two essentially different kinds, and it is natural to suspect that this only appears to be so because the structure of the physical continuum is not completely described by the Riemannian metric".

    Think of the electron as having one field. We typically call it an electromagnetic field rather than an electric field or a magnetic field. Then put the electron next to a proton. The two opposite electromagnetic fields largely cancel, but not quite. What's left over is what we call a gravitational field. The "state of space" around a hydrogen atom isn't the same as for an electron, so it's reasonable to talk about two different fields. But go back to the electron, and it isn't reasonable to claim it's got an electromagnetic field which is something totally different to its gravitational field. The moot point being that electroweak notwithstanding, the multiple fields of the Standard Model represents a backward step which isn't in line with unification.
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    That's some great theology.
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    I agree that it's just like theology.

    On the History of Unified Field Theories (1914 - 1933), On the History of Unified Field Theories. Part II. (ca. 1930 – ca. 1965) That's something that Albert Einstein had worked on for the later part of his life, though without much success. We now know that there is no way that it could have worked in that form, because of the great success of quantum electrodynamics and electroweak unification.

    Quote Originally Posted by Farsight
    The moot point being that electroweak notwithstanding, the multiple fields of the Standard Model represents a backward step which isn't in line with unification.
    Much of the Standard Model was empirically motivated, and although it looks ugly and baroque, it seems simple and elegant compared to some of what it explains.

    Consider the case of the muon, discovered in 1936. It at first seemed like a proposed nucleon-nucleon interaction particle, but it was soon discovered to behave just like an electron, but almost 207 times more massive. Physicist I.I. Rabi famously asked "Who ordered that?" In "UFO's: A Scientific Debate" (Sagan, Page eds), page 259, one of the contributors mentioned that someone posted something at a conference called "The Moon as a Giant Electron". It turned out to be a typo: "The Muon as a Giant Electron". Not only was it a sort of different flavor of electron, it turned out to have its own flavor of neutrino, distinct from what electrons have. In 1975, the tau lepton was discovered, and it turned out to be yet another flavor of electronlike particle, complete with its own flavor of neutrino.

    In the Standard Model, the electron, muon, and tau form a flavor triplet with those states being mass eigenstates of it. Neutrinos form a massless flavor triplet in it, though they have been observed to be massive. Their oscillations are due to their mass states not being orthogonal to those of the charged leptons.

    Lepton physics is fairly simple compared to hadron physics, and before the emergence of the Standard Model, hadron physics was a horrible mess. The early quark model tamed some of it, but it had problems of its own, like quarks having spin 1/2, but behaving in bosonic fashion in baryons. But by the mid 1970's, such problems were resolved, with the partial exception of color confinement. Baryons' valence quarks have an antisymmetric color wavefunction, thus making them behave in fermionic fashion.

    Electroweak unification helps keep the W and Z particles well-behaved at interaction energies of more than a few hundred GeV, something that is otherwise a big problem.

    So dismissing the Standard Model as a retrogression is just plain dumb.
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    Quote Originally Posted by Farsight View Post
    Thanks for this, btr. But I'm still struggling to get any understanding out of it. I'll try to explain why.

    No problem with a field throughout space.

    I don't have an issue with the physical vacuum and a non-zero field everywhere, but where does the expression come from?
    It's just an illustrative toy example, one among many, of an expression which is rotationally symmetric, but with a minimum that's not at the origin. There exists a particularly simple scalar field theory which gives rise to an expression of much the same form as this, as it happens, but that's really a side-issue; for now, I'm just saying that perhaps such a thing is possible. If this were a real theory, the next step would be to puzzle out the observable behaviour and ask the experimentalists whether it corresponds to reality.

    Quote Originally Posted by Farsight View Post
    We've somehow gone from a field to two fields. This jars, because I consider a field to be "a state of space". I cannot conceive of space having two states at the same time.

    I can get some meaning out of this. If you've got a washing line, sight your eye down its length, and twang it. You will see a transverse wave move along it. This is an analogy for a photon. Alternatively twist it with a pair of pliers and let go quickly. A rotational wave moves down the washing line. This is an analogy for a neutrino, a "Weyl spinor" L.

    Neutrinos oscillate, but I'm just not getting this bowl.
    You just have a field , which is described by a complex number at each point of spacetime. Because it is complex-valued, it can oscillate in two independent ways at each point in space; either in such a way that its modulus varies, or in such a way that its argument varies.

    I'd suggest that it is not helpful to view every field as being a state of space in quite the way you are picturing; there is no geometric distortion of density fluctuation or twist or whatever associated with (or at least, none that is required by the example). You could just about picture it as being density fluctuations in two overlapping "aethers", but that would obscure the fact that is invariant under Lorentz transformations (and the word "aether" comes with a great deal of baggage that isn't needed here).

    Regarding Goldstone bosons:

    Quote Originally Posted by Farsight View Post
    It's not as if we see them flying around like we see photons.
    In the Standard Model, that's due to some other stuff which goes on, beyond the simple mechanism I've described here. In the "toy" complex scalar model I've been outlining, you would indeed see both of the spin-zero particle species flying around (one massive, one massless).

    The massless ones wouldn't look quite like photons, however, due to having the wrong spin.

    Quote Originally Posted by Farsight View Post
    Again the multiple fields leaves me saying huh? But no problem with energy having a mass equivalence. Although I seem to be none the wiser about symmetry-breaking. Sorry.

    Noted. I'm not a fan of the Higgs mechanism myself.
    Just let me know if you have any more questions.
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    Thanks for getting back to me btr. I have to go now, but for now: methinks there is much work to be done here.

    lpetrich: I'll get back to you, but if lepton physics is fairly simple compared to hadron physics, how come there's no electron model in the Standard model? How can people like Ellis propose a selectron when he doesn't even know what an electron is? The electron is a fundamental particle, pah. It's like HEP marches to the drumbeat, and is heading for a cliff. See RIP Portuguese science.
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    Quote Originally Posted by Farsight View Post
    ... if lepton physics is fairly simple compared to hadron physics, how come there's no electron model in the Standard model?
    Farsight, what would you consider an acceptable electron model? Some diagram drawn with crayons in a kiddie coloring book?

    How can people like Ellis propose a selectron when he doesn't even know what an electron is? The electron is a fundamental particle, pah.
    What makes you so sure that physicist John Ellis doesn't know what an electron is?
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    Quote Originally Posted by lpetrich View Post
    Farsight, what would you consider an acceptable electron model?
    An updated/completed version of Williamson and van der Mark's proposal. Something that tied in nicely with both classical electromagnetism and QED.

    Quote Originally Posted by lpetrich
    What makes you so sure that physicist John Ellis doesn't know what an electron is?
    He's an advocate of SUSY and the selectron. Going back to your previous post:

    Quote Originally Posted by lpterich
    Much of the Standard Model was empirically motivated, and although it looks ugly and baroque, it seems simple and elegant compared to some of what it explains.
    I'd say some parts are better than others.

    Quote Originally Posted by lpetrich
    Consider the case of the muon, discovered in 1936. It at first seemed like a proposed nucleon-nucleon interaction particle, but it was soon discovered to behave just like an electron, but almost 207 times more massive. Physicist I.I. Rabi famously asked "Who ordered that?" In "UFO's: A Scientific Debate" (Sagan, Page eds), page 259, one of the contributors mentioned that someone posted something at a conference called "The Moon as a Giant Electron". It turned out to be a typo: "The Muon as a Giant Electron". Not only was it a sort of different flavor of electron, it turned out to have its own flavor of neutrino, distinct from what electrons have. In 1975, the tau lepton was discovered, and it turned out to be yet another flavor of electronlike particle, complete with its own flavor of neutrino.
    The big difference is that the muon isn't stable, and nor is the tau. IMHO the Standard Model just doesn't say enough about that. On top of not saying enough about the electron.

    Quote Originally Posted by lpetrich
    In the Standard Model, the electron, muon, and tau form a flavor triplet with those states being mass eigenstates of it. Neutrinos form a massless flavor triplet in it, though they have been observed to be massive. Their oscillations are due to their mass states not being orthogonal to those of the charged leptons.
    Neutrinos are a another issue for the Standard Model. They're classed as leptons along with electrons, but actually they're more like photons than they're like electrons. And mass is a big issue for the Standard Model. There's no concept of effective mass, wherein the photon has an effective mass if you reduce its speed below c. And the Higgs mechanism contradicts E=mc². It's as if it doesn't tie in with non-standard-model physics which is utterly robust and solid as a rock.

    Quote Originally Posted by lpetrich
    Lepton physics is fairly simple compared to hadron physics, and before the emergence of the Standard Model, hadron physics was a horrible mess. The early quark model tamed some of it, but it had problems of its own, like quarks having spin 1/2, but behaving in bosonic fashion in baryons. But by the mid 1970's, such problems were resolved, with the partial exception of color confinement. Baryons' valence quarks have an antisymmetric color wavefunction, thus making them behave in fermionic fashion.
    I think there are problems still here which could be improved by thinking in terms of "partons".

    Quote Originally Posted by lpetrich
    Electroweak unification helps keep the W and Z particles well-behaved at interaction energies of more than a few hundred GeV, something that is otherwise a big problem.
    Electroweak unification seems a bit of s sham coming from you lpetrich. You reject electromagnetic unification.

    Quote Originally Posted by lpetrich
    So dismissing the Standard Model as a retrogression is just plain dumb.
    The multiple fields is definitely a backward step. It needs fixing. For example, where does the gluon field go in low-energy proton-antiproton annihilation to gamma photons? And what is it that keeps those photons moving at c? There's low-handing fruit hidden in plain view, rich pickings for scientific progress. But only for those who will concede that the Standard Model is not perfection.
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    Quote Originally Posted by Farsight View Post
    An updated/completed version of Williamson and van der Mark's proposal.
    Worthless tripe. It does not explain what keeps a photon confined in its path. It would require a superstrong interaction that is not observed. It also cannot explain electrons' having spin 1/2.

    (John Ellis)
    He's an advocate of SUSY and the selectron.
    I'm sure that he has a good understanding of what an electron is.

    The big difference is that the muon isn't stable, and nor is the tau. IMHO the Standard Model just doesn't say enough about that.
    Their instability is in full agreement with the Standard Model.

    Neutrinos are a another issue for the Standard Model. They're classed as leptons along with electrons, but actually they're more like photons than they're like electrons.
    Abysmal tripe. Neutrinos are elementary fermions and closely related to charged leptons.

    And the Higgs mechanism contradicts E=mc².
    That's abysmally stupid.

    (hadron physics)
    I think there are problems still here which could be improved by thinking in terms of "partons".
    Whatever those are supposed to be.

    You reject electromagnetic unification.
    News to me.

    The multiple fields is definitely a backward step. It needs fixing.
    For what reason?

    For example, where does the gluon field go in low-energy proton-antiproton annihilation to gamma photons?
    I've never heard of a law of conservation of gluon field. Furthermore, that is not a very common proton-antiproton annihilation outcome. It's usually about 3 to 5 pions.

    And what is it that keeps those photons moving at c?
    That's well understood.
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    Quote Originally Posted by lpetrich View Post
    Worthless tripe. It does not explain what keeps a photon confined in its path. It would require a superstrong interaction that is not observed.
    It is observed. Pair production happens. Surely you don't still believe the canard that one photon magically morphs into an electron and a positron with which the other photon interacts? That pair production occurs because pair production occurs? That's worthless tripe. And I've told you, it's displacement current that keeps the photon confined on its path.

    Quote Originally Posted by lpetrich
    It also cannot explain electrons' having spin 1/2.
    It absolutely does. Au contraire, the tripe that says the electron is a fundamental particle doesn't.

    Quote Originally Posted by lpetrich
    (John Ellis) I'm sure that he has a good understanding of what an electron is.
    If he did, he wouldn't be pimping SUSY, even though it's a busted flush. That guy isn't doing HEP any favours Loren.

    Quote Originally Posted by lpetrich
    Their instability is in full agreement with the Standard Model.
    Oh yes? Care to point out where that's given? You won't. Because not only is there no electron model, and there's no muon model either.

    Quote Originally Posted by lpetrich
    Abysmal tripe. Neutrinos are elementary fermions and closely related to charged leptons.
    Photons have no mass and no charge and travel at c. Neutrinos have no mass and no charge to speak of and travel at c. Electrons have plenty of mass and charge and don't travel at c. And you can convert photons into electrons (and positrons) and vice versa via pair production and annihilation. It's patently obvious that the electron is a self-trapped photon, and absolutely nothing like a neutrino. Only a child could confuse the two.

    Quote Originally Posted by lpetrich
    That's abysmally stupid.
    Oh no it isn't. The Higgs mechanism really does contradict E=mc². The former says the electron gets its mass from interacting with a space-filling field. The latter says mass is a measure of a body's energy content, and the electron is a body. The brutal truth is that photon momentum is a measure of resistance-to-change-in-motion for a wave propagating linearly at c, while electron mass is a measure of resistance-to-change-in-motion for a wave going round and round at c. The sooner this goes into the Standard Model the better.

    Quote Originally Posted by lpetrich
    (hadron physics) Whatever those are supposed to be.
    Partons are supposed to be parts. Like we've never seen a quark because they are the parts of a proton. Like the loops are parts of a trefoil knot. The sooner elements of TQFT go into the Standard Model the better.

    Quote Originally Posted by lpetrich
    News to me.
    I keep telling you about the electromagnetic field, you keep evading it and refusing to depict it. You're in denial about it. Don't be. The sooner aspects of classical electromagnetism go into the Standard Model the better.

    Quote Originally Posted by lpetrich
    For what reason?
    A field is a state of space. Not some abstract mathematical thing. When two magnets repel each other or when you drop your pencil, it's because the space there has a certain state. Not because of anything else.

    Quote Originally Posted by lpetrich
    I've never heard of a law of conservation of gluon field.
    Thing bag-model. Think elastic. Think ripple in a rubber sheet.

    Quote Originally Posted by lpetrich
    Furthermore, that is not a very common proton-antiproton annihilation outcome. It's usually about 3 to 5 pions.
    Which last for hardly any time at all.

    Quote Originally Posted by lpetrich
    That's well understood.
    Then explain it. What does keep photons moving at c?
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    Quote Originally Posted by Farsight View Post
    And mass is a big issue for the Standard Model. There's no concept of effective mass, wherein the photon has an effective mass if you reduce its speed below c.
    What, where did this come from? Did you mean water would effectively burn if flammable?

    Are you saying a photon bends space and time when "it slows down" in different positions?
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    (What confines a photon to a circular path in an electron?)
    Quote Originally Posted by Farsight View Post
    It is observed. Pair production happens. Surely you don't still believe the canard that one photon magically morphs into an electron and a positron with which the other photon interacts?
    It's not a canard when it's the truth. Farsight, what you find incredulous is not the last word in physics. Why don't you write down the Lagrangian for this interaction and get various observed quantities from it?

    And I've told you, it's displacement current that keeps the photon confined on its path.
    Except that the numbers don't work out. Photons aren't gluons.

    (how a circling photon can't explain electrons' spin 1/2)
    It absolutely does.
    Prove it mathematically.

    (Me about the muon and the tau: Their instability is in full agreement with the Standard Model.)
    Oh yes? Care to point out where that's given? You won't. Because not only is there no electron model, and there's no muon model either.
    A muon decays into a virtual W and a muon neutrino, and the virtual W then makes an electron and and electron antineutrino. This decay can happen because the muon has enough rest mass to make it happen.

    It's patently obvious that the electron is a self-trapped photon, and absolutely nothing like a neutrino.
    Maybe to you, Farsight, but not to the scientific community.

    The Higgs mechanism really does contradict E=mc². The former says the electron gets its mass from interacting with a space-filling field. The latter says mass is a measure of a body's energy content, and the electron is a body.
    These are not mutually exclusive. E = mc^2 is automatically satisfied in any theory consistent with special relativity, as the Standard Model is.

    Partons are supposed to be parts. Like we've never seen a quark because they are the parts of a proton. Like the loops are parts of a trefoil knot.
    Except that quarks are electronlike particles.

    The sooner aspects of classical electromagnetism go into the Standard Model the better.
    As if classical electromagnetism is not already present as the classical limit of the electromagnetic part of it.

    A field is a state of space.
    I don't know how often I'll have to correct this rather gross error.

    (pions)
    Which last for hardly any time at all.
    So what?
    I repeat, so what?

    What does keep photons moving at c?
    Their having zero rest mass.
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    I'll now consider the prospects for discovering and observing and understanding various Beyond-Standard-Model particles and effects.

    Particle Data Group is a good place to go for the current state of affairs about searches for new particles and the like.

    Matter-antimatter asymmetry It has only one parameter, a Universe-wide ratio of baryons to photons. That makes it difficult to deduce details of the mechanism that produced it, details beyond Sakharov's conditions. There are several proposed mechanisms of "baryogenesis", as it's called, taking place at energy scales from electroweak symmetry breaking to GUT symmetry breaking. But whatever caused it must have happened after cosmic inflation ended, because inflation would have diluted a baryon-number imbalance to unobservability.

    WIMP dark matter There are active research projects for detecting it, both directly and indirectly. The latter is from the particles that the WIMP's would make if they run into each other. Still only upper limits, but the experiments are starting to get into interesting ranges of masses and cross sections for various sorts of WIMP's.

    Dark energy It has one Universe-wide parameter, its mass density, and possibly two, its ratio of pressure to density, though it is close to cosmological-constant-like behavior. Same problem as with matter-antimatter asymmetry.

    The inflaton Since its energy scale is around GUT energies, it is unlikely that we'd see any manifestation of it at accelerator-accessible energies. From primordial fluctuations, we can find clues about its potential energy, but that won't tell us about how it's related to other particles.

    Axions Electroweak-scale interactions have been ruled out, though not GUT-scale ones.

    Neutrino masses and mixing The favorite hypothesis there is the seesaw model, but that requires very massive right-handed neutrinos, with masses near GUT energy scales. But getting improved values of masses and mixings will still be good. Neutrino mixing angles are rather curiously large, unlike quark ones. It may even be possible to probe neutrino-mass effects by observing neutrinoless double beta decay.

    More CP violation This gives electric dipole moments to several elementary particles, notably the neutron. Measured upper limits are starting to approach interesting values, though still well above Standard-Model predictions.

    Proton decay Observed mean-life lower limits are starting to press against various GUT predictions. Successful observation could permit tests of GUT hypotheses, tests not otherwise possible because GUT energies are well out of reach of accelerators.

    Departures from general relativity, like the Generalized Brans-Dicke model. This is essentially GR + an extra scalar field. Observations give strong upper limits, however.

    Supersymmetry There is a big range of supersymmetric models, but the ones most interesting here are the simpler supersymmetric extensions of the Standard Model where the supersymmetry (SUSY) is broken at about 1 to 10 TeV. The Minimal Supersymmetric Standard Model (MSSM) and the Next-to-MSSM (NMSSM) have the nice property of successful gauge unification at about 2*10^(16) GeV. This suggests that that is the energy for GUT symmetry breaking.

    It is difficult to get SUSY breaking out of the (N)MSSM itself, and it's usually posited to happen in some "hidden sector" with it getting transmitted to (N)MSSM particles by gravitational interactions or some other such mechanism. But one may be able to distinguish different mechanisms by different patterns of SUSY breaking. In the (N)MSSM, SUSY breaking is necessary for electroweak symmetry breaking, pointing to a constraint on SUSY-breaking energy scales.

    There's a sizable zoo of superpartners of Standard-Model particles, and also some additional Higgs particles.

    The MSSM has a Standard-Model-Like neutral Higgs particle with two additional neutral ones and a charged one. The NMSSM adds two more neutral ones.

    The (N)MSSM has spin-1/2 superpartners of the SM gauge particles, the gluon, the W, and the B, called the gluino, the wino, and the bino. The Higgs particles have spin-1/2 superpartners called higgsinos. Electroweak symmetry breaking mixes the wino, bino, and higgsinos, making in the MSSM four neutralinos and two charginos, with the NMSSM adding a fifth neutralino.

    The (N)MSSM has spin-0 superpartners of the elementary fermions, called sparticles, s being short for scalar. Thus, there are squarks and sleptons, with the superpartners of the more massive ones being stau, sbottom, and stop.

    Supersymmetry applied to gravity yields supergravity. The graviton or gravitational field has spin 2, and its superpartner, the gravitino, has spin 3/2.

    These particles act just like their "originals", to within their masses and spins being different.

    It must be pointed out that the first run of the LHC has been disappointing.

    The easiest of these particles to make in it are the gluino and the squarks, because of their QCD colors. But from that LHC run, the lower limits on their masses is at least a TeV. The sleptons, charginos, and neutralinos are more difficult to make, and the limits on these are not as strong.

    But by next year, the LHC will be running at nearly twice its previous energy, and will have more of a chance to make some of these particles.
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    Quote Originally Posted by Beer w/Straw View Post
    What, where did this come from? Did you mean water would effectively burn if flammable?
    Huh? You burn hydrogen, it combines with oxygen, and water is the result. Haven't you ever heard of photon effective mass? Go and look it up.

    Quote Originally Posted by Beer w/Straw
    Are you saying a photon bends space and time when "it slows down" in different positions?
    No. I'm saying when you trap a photon in a mirror-box it increases the mass of that system. Then when you open the box it's a radiating body that loses mass. That's what Einstein's E=mc² paper is all about. The mass of a body is a measure of it's energy-content. And he even refers to the electron on that page. The electron is a body. Its mass is a measure of its energy content. Not a measure of its interaction with some field. The Higgs mechanism contradicts E=mc². Only lpetrich won't admit it.
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    Quote Originally Posted by lpetrich View Post
    It's not a canard when it's the truth. Farsight, what you find incredulous is not the last word in physics. Why don't you write down the Lagrangian for this interaction and get various observed quantities from it?
    It isn't the truth, it's specious garbage. Gamma-gamma pair production does not occur because one of the photons magically spontaneously transforms into a fermion pair like worms from mud. That's a cargo-cult tautology. Pair production occurs because pair production occurs! Geddoutofit, how stupid do you think people are? How can you peddle such trash?

    Quote Originally Posted by lpetrich View Post
    Except that the numbers don't work out. Photons aren't gluons.
    No they aren't. Because gluons are virtual. Nobody has ever seen a gluon.

    Quote Originally Posted by lpetrich View Post
    Prove it mathematically.
    I can't. The hard scientific evidence proves it. You know what that is don't you? And that we're talking about electron diffraction, Einstein-de Haas, et cetera?

    Quote Originally Posted by lpetrich
    A muon decays into a virtual W and a muon neutrino, and the virtual W then makes an electron and and electron antineutrino. This decay can happen because the muon has enough rest mass to make it happen.
    A trash non-explanation.

    Quote Originally Posted by lpetrich
    These are not mutually exclusive. E = mc^2 is automatically satisfied in any theory consistent with special relativity, as the Standard Model is.
    The Higgs mechanism contradicts E=mc², end of story. The cosmic treacle is yet more trash.

    Quote Originally Posted by lpetrich
    Except that quarks are electronlike particles.
    Only we've never seen one. Funny that.

    Quote Originally Posted by lpetrich
    As if classical electromagnetism is not already present as the classical limit of the electromagnetic part of it.
    Well let's see now, the electron has its electromagnetic field like Minkowski said. Only in the standard model it's an excitation of the electron field. Which is a different field to the photon field. Ho hum.

    Quote Originally Posted by lpetrich
    I don't know how often I'll have to correct this rather gross error.
    Don't try, because Einstein said it, and it's true.

    Quote Originally Posted by lpetrich
    So what? I repeat, so what?
    It's a vapid waste of time to study ephemera whilst totally dismissing electron models.

    Quote Originally Posted by lpetrich
    Their having zero rest mass.
    Yet more trash.
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    Farsight, I didn't say Hydrogen. I said water.

    Why are you referring to mass when the stress-energy tensor would be the explanation for a gravitational field in GR?

    You can ignore me if you want. It's not going to break my heart.
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    Quote Originally Posted by Farsight View Post
    I'm saying when you trap a photon in a mirror-box it increases the mass of that system.
    So freaking what?
    Its mass is a measure of its energy content. Not a measure of its interaction with some field. The Higgs mechanism contradicts E=mc². Only lpetrich won't admit it.
    I won't "admit" it because your claims here are just plain wrong. Wrong, wrong, wrong, wrong, wrong.

    Quote Originally Posted by Farsight View Post
    It isn't the truth, it's specious garbage. Gamma-gamma pair production does not occur because one of the photons magically spontaneously transforms into a fermion pair like worms from mud. That's a cargo-cult tautology. Pair production occurs because pair production occurs! Geddoutofit, how stupid do you think people are? How can you peddle such trash?
    Farsight, I will use one of your favorite arguments here. It is written in the Book of Feynman. In particular, his book of lectures on quantum electrodynamics for a graduate-level course in quantum mechanics. So if you deny that, you deny Feynman.
    Nobody has ever seen a gluon.
    So what about never observing a free one?

    (proving that the circling-photon theory of the electron proves that it has spin 1/2...)
    Quote Originally Posted by Farsight
    I can't. The hard scientific evidence proves it.
    Farsight, that's not how you make predictions from a theory. What you do is take the circling-photon theory or the Dirac-field theory or whatever and work out mathematically what they predict.

    (muon -> mu-nu + W, W -> e + e-nu)
    A trash non-explanation.
    That's the mainstream one, like in muon decay, Applications of Feynman Diagrams, etc.

    (quarks)
    Only we've never seen one. Funny that.
    So what about never observing a free one?

    (correcting a gross error: a field as a state of space)
    Don't try, because Einstein said it, and it's true.
    While denying Einstein and Minkowski and Feynman when they state things contrary to your theories.

    (fast-decaying particles...)
    It's a vapid waste of time to study ephemera whilst totally dismissing electron models.
    The Standard Model already has an electron model, so what are you complaining about?

    (photons having zero rest mass)
    Yet more trash.
    Thus dismissing Einstein and Feynman and others.
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    I'll now hunt down limits on BSM physics.

    First, gravity.

    A big review: The Confrontation between General Relativity and Experiment by Clifford Will. Part of the problem is definition. What qualifies as gravity? Is some departure from GR to be called gravity or something else?

    Let us first consider the Einstein Equivalence Principle. It likely has the consequences that space-time has a symmetric metric, that freely-falling objects fall in geodesics, and that in a freely-falling reference frame, the nongravitational laws of physics locally satisfy special relativity. So a theory that satisfies EEP likely also has
    (metric tensor) = some function of (energy-momentum tensor)

    The EEP's three parts are the Weak Equivalence Principle, Local Lorentz Invariance, and Local Position Invariance.

    The Weak Equivalence Principle states that gravity is independent of nongravitational composition. That has been tested with objects with different composition, like with different ratios of neutrons to protons. It has also been tested with several source masses: laboratory ones, the Earth, the Sun, and our Galaxy. The result: zero difference to within experimental accuracy. For instance, [1207.2442] Torsion-balance tests of the weak equivalence principle finds upper limits of about 10-13 for the Earth (10[sup]7 m), 4*10-13 for the Sun (1011 m), and 5*10-5 for galactic dark matter (1020 m). Results | The Eöt-Wash Group has more upper limits, like 4*10-4 for 1 m to 1 km, and 10-2 for 1 mm.

    Local Lorentz Invariance states that the laws of nature are locally invariant under Lorentz boosts. Some extra interactions could cause apparent LLI violations. Modern searches for Lorentz violation - Wikipedia is surprisingly comprehensive. Experimental results are often very good, like 10-12 for variations in the vacuum speed of light with direction.

    Local Position Invariance states that the laws of nature are locally independent of position in space-time. As with LLI, some extra interactions could cause apparent LPI violations. Gravitational-redshift LPI violations are at most about 10-6, and variations in time are less than 10-16/year for the fine-structure constant, 10-11/year for the weak-interaction strength, and 3*10-15/year for the electron-proton mass ratio.

    So we get some strong upper limits on long-range nongravitational Beyond the Standard Model interactions.

    Let's now look at metric theories of gravity. Physicists have invented a whole lot of them, but they have also attempted to sort them out. In particular, they have invented the Parametrized Post-Newtonian (PPN) formalism for expressing metrics in the weak-field, slow-motion, long-distance limit. The lowest order ought to be Newtonian gravity, of course, and with a few simple assumptions, the next order of expansion, the post-Newtonian order, is ten perameters multiplying ten terms. Thus, the parametrized bit.

    Newtonian limit: time curvature only
    Post-Newtonian:
    γ = (space curvature) / (time curvature)
    β = amount of superposition in second-order time curvature
    ξ = preferred-location effects.
    α1, α2, α3 -- preferred-frame effects
    α3, ζ1, ζ2, ζ3, ζ4 -- violation of total momentum conservation

    From most theories, one can calculate the values of these ten parameters, and one can measure them with various observations. General relativity predicts γ = β = 1, all the rest 0. Upper limits:

    |γ - 1|:
    Optical deflection by the Sun: 10-3 (Hipparcos)
    Optical deflection by various galaxies: 0.1
    Radio deflection by the Sun: 10-4 (VLBI)
    Radio delay by the Son: 10-5 (Cassini)

    |β - 1|:
    Perihelion precession of Mercury: 10-4 (Messenger)
    Perihelion precession of Mars: 2*10-4 (Mars Reconnaissance Orbiter)
    All these are excesses over their Newtonian values due to perturbations by other planets and the Sun's oblateness

    The Strong Equivalence Principle states that the EEP is true and that an object's self-gravity makes the same amount of gravity as any other mass. One can assemble several PPN parameters to make one for departures from the SEP:
    η = 4β - γ - 3 - (10/3)ξ - α1 + (2/3)α2 - (2/3)ζ1 - (1/3)ζ2

    Departure from the SEP produces the "Nordtvedt effect". The Earth and the Moon orbit each other, and they are both pulled on by the Sun. Departure from the SEP means that the Sun's pull on the Earth and the Moon are (1 - η*E/m) for each object, where E = - (grav self-energy) and m = mass. E/m is about 4*10-10 for the Earth and 2*10-11 for the Moon. If η is nonzero, that makes some additional perturbations of the Earth's and the Moon's motions.

    In GR, η = 0; GR satisfies the SEP.

    Earth-Moon: |η| has upper limit 5*10-4
    Some white-dwarf-neutron-star binaries: similar upper limits

    The other parameters:
    |ξ| has upper limit 4*10-9 from millisecond-pulsar spin precession, and |α2| likewise has upper limit 2*10-9
    1| has upper limit 10-4 from its polarization of the Moon's orbit, and a similar bound for a binary pulsar
    3| has upper limit 4*10-20 from pulsar acceleration
    1| has upper limit 0.02 from other PPN bounds
    2| has upper limit 4*10-5 from the acceleration of a binary pulsar
    3| has upper limit 10-8 from Newton's third law and the Moon's orbit
    ζ4 is not independent, from a connection between gravity by kinetic energy, gravity by internal energy, and gravity by pressure
    4 = 3α3 + 2ζ1 - 3ζ3

    Finally, the rate of variation of the gravitational "constant" over time. It's less than about 10-14 from tracking of Mars-orbiting spacecraft, and about 4*10-13 from Big-Bang nucleosynthesis.

    I won't get into gravitational radiation, because it's harder to parametrize. But this should be enough to test many theories of gravity.

    The survivors

    General relativity and the Generalized Brans-Dicke theory. The others usually require some complicated cancellation to make α1 = α2 = 0, and sometimes also γ = β = 1.

    The GBD is GR with an additional scalar field that controls the value of the gravitational "constant" and that does not couple to Standard-Model matter. It has

    where ω and λ are parameters of the theory in the weak-field limit.

    In the GBD, one can make ω arbitrarily large, making the gravitational "constant" vary very little with the scalar field, thus making it GR + that scalar field.


    So there are strong upper limits on additional long-range fields that couple to Standard-Model particles or to gravity.
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    Now, axions.

    Axions in Theoretical Physics by Ann Nelson
    Axions in QCD and Cosmology by George K. Fanourakis
    Axions: A Clean Solution to Strong CP and Dark Matter? by ? Moore
    Astrophysical and Cosmological Axion Limits by Georg G. Raffelt

    The axion was first proposed in 1977 by Roberto Peccei and Helen Quinn as a solution to the strong CP problem. Here it is.

    The two fundamental Lorentz invariants that one can form from the electromagnetic field are
    F.F ~ E2 - B2 (even parity)
    F.(*F) ~ F.ε.F ~ E.B (odd parity)

    The electromagnetic Lagrangian contains the even-parity invariant. The odd-parity invariant can be turned into a 4-vector divergence, and it thus drops out. Doing the action integral gives an integral over the surface of the domain of integration.

    The QCD Lagrangian is similar, containing the corresponding even-parity gluon-field invariant, but it's much harder to eliminate the odd-parity one. It violates CP, and it makes nonzero-spin hadrons have electric dipole moments. The upper limit on the neutron's electric dipole moment is about 10-9 of what one would expect with the odd-parity invariant contributing at full strength. As it turns out, this requires some fine tuning of that invariant's coefficient, which is awkward.

    Enter the axion, a pseudoscalar particle (spin 0, with negative parity). Its field multiplies the gluon-field odd-parity invariant, and its interaction with the gluon makes that invariant's coefficient effectively zero. Thus eliminating that troublesome electric-dipole moment and solving the strong-CP problem. This interaction also yields

    (axion mass) ~ (QCD energy scale)2 / (axion interaction energy)
    An interaction energy of 107 GeV gives an axion mass around 0.6 eV.

    Axions likely have a similar interaction with the electromagnetic field, and that interaction is what's used by most axion searches.
    Interaction term in Lagrangian ~ (axion field) * (E.B) / (axion interaction energy)

    It was quickly discovered that (axion interaction energy) >> (electroweak symmetry-breaking energy scale), but beyond that, there is still plenty of unexplored parameter space. Here are some of the bounds that have been found so far.


    Red-giant cores would emit lots of axions, and if the axions' interactions are strong enough, that would make enough energy loss to significantly affect their structure and evolution. Closer to home, the CERN Axion Solar Telescope attempted to observe axions emitted by the Sun, but without success. Both sets of observations yield this limit:
    Axion interaction energy >= 10^10 GeV

    From Supernova 1987a, that recent nearby one, one gets a limit from the time over which it emitted high-energy neutrinos. If it also emitted lots of axions, it may cool down faster than what was observed.
    Axion mass <= 10-2 - 10-3 eV

    The axion can also be a dark-matter particle. Though axions have very low mass, their interactions with other particles are very weak, and after they are formed, their momenta get redshifted in proportion to the Universe's size parameter, like photons' energies. They thus become much colder than the other particles around them, cold enough to be nonrelativistic when the Universe's large-scale structures start to form.
    Axion mass >= 10-6 - 10-5 eV

    Resonant-cavity searches. These involve axions getting turned into radio-frequency and microwave photons, and back again, in resonant cavities with magnetic fields applied to them. From (energy) = h*(frequency),
    4.18*10-6 eV = 1 GHz

    The ADMX search got down to interaction energy > 1015 GeV for masses 2 - 3.5 * 10-6 eV
    The RBF and UF searches got down to {5*1013 GeV, 5*10-6 eV} to {2*1012 GeV, 1.5*10-5 eV}


    So there's still a way to go for axions, whether to find them or to exclude them.
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    Particle Data Group -- I'll look at the elementary fermions' masses and mixings.

    Masses of charged elementary fermions in GeV, with the mass scale for each quark's mass
    up 0.0023 (2 GeV) charm 1.275 (onsh) top 173.07 (onsh)
    down 0.0049 (2 GeV) strange 0.095 (2 GeV) bottom 4.18 (onsh)
    electron 0.000511 muon 0.106 tau 1.78
    onsh = on shell (measured at its own value -- effectively the case for leptons)

    Neutrinos' masses:
    |m22 - m12| = (0.009 eV)2
    |m32 - (m12 + m22)/2| = (0.05 eV)2

    Quark mixing-matrix magnitudes:
    d s b
    u 0.974 0.225 0.004
    c 0.225 0.973 0.04
    t 0.009 0.04 0.9991

    Neutrino mixing angles:
    sin(θ12) = 0.55, sin(θ23) = 0.62, sin(θ13) = 0.16

    Leptons are much more off-diagonal than quarks, for whatever odd reason.

    Overall, it's a big mess.
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    Your posts on gravity, axions, and particles noted, lpetrich. I know we disagree about certain things, but nevertheless I do think it's good that you're making a positive contribution to the forum.

    Quote Originally Posted by lpetrich View Post
    So freaking what?
    The mass of a body is a measure of its energy content. The electron is a body. Its mass is not a measure of its interaction with the Higgs field, it's a measure of its energy content. So the Higgs sector of the Standard Model needs to be thrown out.

    Quote Originally Posted by lpetrich View Post
    Farsight, I will use one of your favorite arguments here. It is written in the Book of Feynman. In particular, his book of lectures on quantum electrodynamics for a graduate-level course in quantum mechanics. So if you deny that, you deny Feynman.
    Let me reiterate: pair production does not occur because pair production occurs. If Feynman said that he's wrong. Please give a reference.

    Quote Originally Posted by lpetrich
    So what about never observing a free one?
    They're partons. That's what Feynman called them. They don't actually exist as particles. They're just the parts of a proton. Take a look at the Topological Quantum Field Theory Club webpage. See those blue trefoil knots at the top? Pick one, start at the bottom left, and trace around it anticlockwise calling out the crossing-over directions: up down up. When you smash protons you don't see quarks and gluons spilling out like beans from a bag.

    Quote Originally Posted by lpetrich
    The Standard Model already has an electron model, so what are you complaining about?
    Then write about it next. When you can't maybe you'll appreciate all the more that overall, it's a big mess. There's a lot of work to do on the Standard Model, Loren.
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    Quote Originally Posted by Duffield

    So the Higgs sector of the Standard Model needs to be thrown out.

    Let me reiterate: pair production does not occur because pair production occurs. If Feynman said that he's wrong.

    See those blue trefoil knots at the top? Pick one, start at the bottom left, and trace around it anticlockwise calling out the crossing-over directions: up down up. When you smash protons you don't see quarks and gluons spilling out like beans from a bag.
    A few more "pearls of wisdom" from John Duffield.
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    Quote Originally Posted by Farsight View Post
    The mass of a body is a measure of its energy content. The electron is a body. Its mass is not a measure of its interaction with the Higgs field, it's a measure of its energy content. So the Higgs sector of the Standard Model needs to be thrown out.
    You appear to be missing the point that the question isn't "Why do electrons have mass?", but "Why do electrons have the particular value of mass that they do?"

    On a side note, the particular value of mass of the electron is a numerical value, and as such requires a mathematical theory to explain it.
    A tensor equation that is valid in any coordinate system is valid in every coordinate system.
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    Quote Originally Posted by Farsight View Post
    Let me reiterate: pair production does not occur because pair production occurs. If Feynman said that he's wrong. Please give a reference.
    Richard Feynman, Quantum Electrodynamics, "Relativistic Treatment of the Interaction of Particles with Light", "Pair Production", p. 111.

    (Quarks...)
    They're partons. That's what Feynman called them. They don't actually exist as particles. ...
    Demonstrably false. It's asymptotic freedom - Wikipedia. It's even been more-or-less observed, because quarks and gluons separating at high energies turn into jets of hadrons: Jet (particle physics) - Wikipedia.

    (Electron model in the Standard Model...)
    Then write about it next. When you can't maybe you'll appreciate all the more that overall, it's a big mess. There's a lot of work to do on the Standard Model, Loren.
    You didn't notice what I called a "big mess". It was the masses and mixings taken together. By comparison, the Standard Model's electron model is rather simple. I'll simplify the SM here to get the essential features.

    Each component of these is a massless Majorana-spinor field, a 2-component field.
    ψL = {N, EL} -- left-handed lepton, weak-isospin doublet
    ψE = {ER} -- right-handed electron, weak-isospin singlet
    Each component of this one is a complex scalar field, a 2-component field.
    H = {H0, HX} -- Higgs particle, weak-isospin doublet

    The Lagrangian's interaction term is g*(H.ε.ψL).ψE = g*(H0*EL - HX*N)*ER
    where g is a constant.

    This gives equations of motion

    D(N) = - g*HX*ER
    D(EL) = g*H0*ER
    D(ER) = g*H0*EL - g*HX*N
    where D is an appropriate differential operator.

    Electroweak symmetry breaking gives the Higgs particle this field value: {v,0}. Plugging it in gives
    D(N) = 0
    D(EL) = m*ER
    D(ER) = m*EL
    where mass m = g*v.

    Thus, the neutrino is a massless Majorana particle and the electron two massless Majorana particles coupled together by a mass term, thus making the electron a massive Dirac particle.
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    Quote Originally Posted by KJW View Post
    You appear to be missing the point that the question isn't "Why do electrons have mass?", but "Why do electrons have the particular value of mass that they do?"
    The Standard Model doesn't answer this because it doesn't include an electron model. lpetrich has said nothing above. The electron does not consist of two neutrino-like particles.

    Quote Originally Posted by KJW View Post
    On a side note, the particular value of mass of the electron is a numerical value, and as such requires a mathematical theory to explain it.
    Sure, no problem. But that mathematics has to tie in with the rest of physics. Things like electron diffraction and magnetic moment and Einstein-de Haas and atomic orbitals wherein electrons exist as standing waves, and with Planck's constant. Take a look at some pictures of the electromagnetic spectrum and ask yourself this: what's the same regardless of frequency?
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    Quote Originally Posted by lpetrich View Post
    Richard Feynman, Quantum Electrodynamics, "Relativistic Treatment of the Interaction of Particles with Light", "Pair Production", p. 111.
    Ah, but he doesn't say pair production occurs because pair production occurs. Does he? Instead he says this:

    "It is easily shown that a single photon of energy greater than 2m cannot create an electron positron pair without the presence of some other means of conserving momentum and energy. Two photons could get together and create a pair, but the photon density is so low that this process is extremely unlikely. A photon can, however, create a pair with the aid of a field, such as that of a nucleus, to which it can impart some momentum. As with bremsstrahlung, there are two indistinguishable ways in which this can happen: (a) The incoming photon creates a pair and subsequently the electron interacts with the field of the nucleus; or (b) the photon creates a pair and the positron interacts with the field of the nucleus. The diagrams for these alternatives are shown in Fig. 22-3..."

    There's an online copy here. And you've been caught out.

    Quote Originally Posted by lpetrich
    Demonstrably false. It's asymptotic freedom - Wikipedia. It's even been more-or-less observed, because quarks and gluons separating at high energies turn into jets of hadrons: Jet (particle physics) - Wikipedia.
    Phoooey. We have never ever seen a free quark or a free gluon. Ever.

    Quote Originally Posted by lpetrich
    You didn't notice what I called a "big mess". It was the masses and mixings taken together. By comparison, the Standard Model's electron model is rather simple. I'll simplify the SM here to get the essential features.

    Each component of these is a massless Majorana-spinor field, a 2-component field.
    ψL = {N, EL} -- left-handed lepton, weak-isospin doublet
    ψE = {ER} -- right-handed electron, weak-isospin singlet
    Each component of this one is a complex scalar field, a 2-component field.
    H = {H0, HX} -- Higgs particle, weak-isospin doublet

    The Lagrangian's interaction term is g*(H.ε.ψL).ψE = g*(H0*EL - HX*N)*ER
    where g is a constant.

    This gives equations of motion

    D(N) = - g*HX*ER
    D(EL) = g*H0*ER
    D(ER) = g*H0*EL - g*HX*N
    where D is an appropriate differential operator.

    Electroweak symmetry breaking gives the Higgs particle this field value: {v,0}. Plugging it in gives
    D(N) = 0
    D(EL) = m*ER
    D(ER) = m*EL
    where mass m = g*v.

    Thus, the neutrino is a massless Majorana particle and the electron two massless Majorana particles coupled together by a mass term...
    Ah, but we've never seen these massless Majorana particles though have we? And pray do tell, is a photon made of two neutrinos too? Only we make electrons and positrons in gamma-gamma pair production and reverse the process in electron-positron annihilation.
    Last edited by Farsight; 07-15-2014 at 07:02 PM.
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    Quote Originally Posted by Farsight View Post
    The Standard Model doesn't answer this because it doesn't include an electron model.
    Empty assertion, and contradicted by my description of how the electron emerges from electroweak symmetry breaking.
    lpetrich has said nothing above. The electron does not consist of two neutrino-like particles.
    Another empty assertion.

    Things like electron diffraction and magnetic moment and Einstein-de Haas and atomic orbitals wherein electrons exist as standing waves, and with Planck's constant.
    All of which is 100% in agreement with the mainstream theory, the theory that you reject out of hand, that an electron is described with a 4-component Dirac-spinor wavefunction. Furthermore, the mainstream theory successfully *predicts* the value of the electron's magnetic moment, while the circling-photon theory can't even explain the electron's spin.

    Take a look at some pictures of the electromagnetic spectrum and ask yourself this: what's the same regardless of frequency?
    Those are schematic diagrams. They are not intended to be literal depictions. Farsight, that style of interpretation makes a fundie creationist look sensible.
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    What's it to be lpetrich? A Dirac-spinor wavefunction, or two massless Majorana particles?
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    Quote Originally Posted by Farsight View Post
    Ah, but he doesn't say pair production occurs because pair production occurs. Does he?
    Instead, he stated the very thing that you dismiss out of hand, that a photon splits into an electron and a positron, and then that one of those two then interacts with the nucleus's virtual-photon field.

    (hadron jets at high energies...)
    Phoooey. We have never ever seen a free quark or a free gluon. Ever.
    So what? How do you explain the jets? Especially jets whose statistics are consistent with them being made by approximately-free high-energy quarks and gluons.

    Ah, but we've never seen these massless Majorana particles though have we?
    It's not necessary to do so.

    And pray do tell, is a photon made of two neutrinos too?
    Of course not.

    Only we make electrons and positrons in gamma-gamma pair production and reverse the process in electron-positron annihilation.
    Yawn.
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    Quote Originally Posted by Farsight View Post
    What's it to be lpetrich? A Dirac-spinor wavefunction, or two massless Majorana particles?
    When the two massless Majorana particles are coupled with a mass term, those two possibilities are mathematically equivalent.
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    Quote Originally Posted by lpetrich View Post
    Instead, he stated the very thing that you dismiss out of hand, that a photon splits into an electron and a positron, and then that one of those two then interacts with the nucleus's virtual-photon field.
    You've got this totally wrong. Gamma-gamma pair production is said to occur because pair production occurs spontaneously like worms from mud. Feynman said a single photon of energy greater than 2m cannot create an electron positron pair without the presence of some other means of conserving momentum and energy. He backs me up. When he's talking about a photon splitting into an electron and a positron he's talking about pair production where a photon gets split over a nucleon. Not gamma-gamma pair production.

    Quote Originally Posted by lpetrich View Post
    So what? How do you explain the jets? Especially jets whose statistics are consistent with them being made by approximately-free high-energy quarks and gluons.
    Call them jets of energy or wavefunction or flux. But remember they aren't literally made out of gluons, because gluons are virtual. And they aren't made out of quarks either, because quarks are just partons. Loops. Crossing points. Topological features, take your pick. That's why we don't see quarks when we do proton-antiproton annihilation. They aren't little billiard ball things. Matt Strassler got into a tangle with this when he tried to describe a proton. See the snapshot of a proton image on this web page. He says imagine all of the quarks (up,down,and strange -- u,d,s), antiquarks (u,d,s with a bar on top), and gluons (g) zipping around near the speed of light, banging into each other, and appearing and disappearing. I say don't. Particles don't spontaneously appear and disappear like magic. That's cargo-cult physics.

    Quote Originally Posted by lpetrich
    It's not necessary to do so.
    What makes me laugh about you Loren, is the way you dismiss patent evidence for something obvious, and shrug when there's no evidence whatsoever for some woo.

    Quote Originally Posted by lpetrich
    When the two massless Majorana particles are coupled with a mass term, those two possibilities are mathematically equivalent.
    The problem being that mass is a measure of energy-content, and electrons and positrons annihilate to photons. Not Majorana particles. Oh, and let's not forget that Majorana fermions remain hypothetical.
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    Quote Originally Posted by Farsight View Post
    You've got this totally wrong. Gamma-gamma pair production is said to occur because pair production occurs spontaneously like worms from mud. ...
    While not considering this quote from Feynman: "a) The incoming photon creates a pair and subsequently the electron interacts with the field of the nucleus; or (b) the photon creates a pair and the positron interacts with the field of the nucleus." What he described was exactly what you dismissed as worms-from-mud spontaneous generation.

    (Jets of hadrons...)
    Call them jets of energy or wavefunction or flux. But remember they aren't literally made out of gluons, because gluons are virtual. And they aren't made out of quarks either, because quarks are just partons. Loops. Crossing points. Topological features, take your pick.
    Empty blathering about energy doesn't prove anything. If anything, it's a mark of woo-woo.

    Does your model of hadron jets predict any features of them? Like this: Evidence for a spin-1 gluon in three-jet events - University of Huddersfield Repository Interpreting 3-jet events as production of an ordinary quark, an antiquark, and a gluon, the authors worked out their expected angular distributions and compared them to what was observed. Farsight, can you repeat that work using your "jets of energy" model?

    Here's how to get two coupled Majorana particles out of a Dirac particle.

    Add in γ5:

    Add and subtract:

    The + one is left-handed and the - one is right-handed:
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    So the Standard Model has two sorts of complexity:
    1. Gauge-symmetry multiplet structure
    2. Values of masses and mixings
    The first of them suggests Grand Unified Theory structure, though it requires some complicated symmetry breaking. Three of the simpler ones were proposed back in 1974, as the Standard Model was taking shape:
    Georgi-Glashow SU(5)
    Fritzsch-Minkowski-Glashow SO(10)
    Pati-Salam SU(4)*SU(2)*SU(2) ~ SO(6)*SO(4)

    Some others are later, like this one from 1984:
    Glashow-Georgi-de-Rujula SU(3)*SU(3)*SU(3) -- trinification

    I can't find out when E6 was proposed.

    -

    The second of them has been *very* difficult to untangle. A common approach has been to experiment with various "textures" of mass matrices, imposing various symmetries and setting various values to zero, and then seeing if one can get the observed masses and mixings. There is no clear success there, as far as I can tell.

    Let's see how it works. L = left-handed part, R = right-handed part, Lc and Rc are charge conjugates of L and R.

    The Dirac-mass interaction is Lc.m.R + Rc.m+.L where m is an arbitrary mass matrix and m+ is its Hermitian conjugate, the transpose of the complex conjugate. Notice that the interaction overall is real: (Lc.m.R)* = L.m*.Rc = Rc.mT.L

    The equations of motion:
    D(L) = m.R
    D(R) = m+.L -- Hermitian conjugate
    D(Lc) = m*.Rc -- complex conjugate
    D(Rc) = mT.Lc -- transpose
    with differential operator D() = i*(γ.d)()

    Combining them gives
    D2(L) = m.m+.L
    This equation is much like the spin-0 Klein-Gordon equation, complete with a mass-squared matrix: m.m+. It has a complete set of nonnegative real eigenvalues: the squares of the masses.

    We also get mixing out of it. m.m+ can be diagonalized as V.msq.V-1 where msq is the mass-squared diagonal matrix and V is the eigenvector matrix. Thus,
    D2(V-1.L) = msq.(V-1.L)

    If one wants to go from up-like quarks to down-like ones, Lweak = Vup.L[sub]up[/sup], Ldown = Vdown-1.Lweak, giving
    Ldown = (Vdown-1.Vup).Lup

    This getting the Cabibbo-Kobayashi-Maskawa matrix for cross-generation quark mixing.

    There's a very serious ambiguity problem. The up and down quark mass matrices have a total of 36 parameters, while observables derived from them have only 10 parameters. Making those mass matrices Hermitian gives a total of 18 parameters, still too many.
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    I'll now consider neutrino masses.

    First what the charged-elementary-fermion masses correspond to in Higgs couplings. Their range:
    Electron: 2*10-5
    Top quark: 0.7

    But for neutrinos, unless their masses are nearly degenerate, one finds a maximum mass of 0.05 eV, corresponding to a Higgs coupling of 2*10-13.

    This is bizarre, because one would expect neutrinos to be comparable in mass to charged leptons.

    A solution to this problem is the "seesaw model", where neutrinos have Dirac masses from coupling to the Higgs particle, and also Majorana masses. In particular, the right-handed ones have huge, nearly-GUT Majorana masses. The right-handed neutrinos' mass terms:

    Rc.M.Rc + R.M*.R

    where M is a mass matrix that is symmetric but that could be complex. Here also, the overall term is real.

    Let's first look at the equations of motion for them:
    D(R) = M.Rc
    D(Rc) = M*.R
    D(R) = M.M*.R
    D(Rc) = M*.M.R
    Here also, we find the sort of mass-squared matrix that we found for Dirac particles.

    The combined Dirac-Majorana equations of motion:
    D(L) = m.R
    D(R) = m+.L + M.Rc
    D(Lc) = m*.Rc
    D(Rc) = mT.Lc + M*.R

    D(R + M*-1.mT.Lc + ...) = (M + O(m2/M)).(Rc + M-1.mT.L + ...)
    D(Rc + M-1.mT.L + ...) = (M* + O(m2/M)).(R + M*-1.mT.Lc + ...)
    D(L - m.M*-1.Rc + ...) = - m.M*-1.mT.(Lc - m*.M-1.R + ...)
    D(Lc - m*.M-1.R + ...) = - m*.M-1.m+.(L - m.M*-1.Rc + ...)

    The result is two sets of Majorana particles. One of them is mostly right-handed and has masses very close to the original right-hand-mass terms. The other is mostly left-handed and has masses of about O(m2/M). For m ~ 10 GeV and M ~ 1012 GeV, one gets a mass of about 0.1 eV, about the right size.


    Like GUT stuff in general, it may not be possible to observe seesaw-effect right-handed neutrinos. But experiments like double-beta decay may eventually make it possible to test Dirac vs. Majorana and find neutrinos' mass scale.
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    Quote Originally Posted by lpetrich View Post
    While not considering this quote from Feynman: "a) The incoming photon creates a pair and subsequently the electron interacts with the field of the nucleus; or (b) the photon creates a pair and the positron interacts with the field of the nucleus." What he described was exactly what you dismissed as worms-from-mud spontaneous generation.
    Again you've got it totally wrong. He previously said A photon can, however, create a pair with the aid of a field, such as that of a nucleus. Again he was talking about pair production over a nucleus, not gamma-gamma pair production.



    Quote Originally Posted by lpetrich View Post
    Does your model of hadron jets predict any features of them? Like this: Evidence for a spin-1 gluon in three-jet events - University of Huddersfield Repository Interpreting 3-jet events as production of an ordinary quark, an antiquark, and a gluon, the authors worked out their expected angular distributions and compared them to what was observed. Farsight, can you repeat that work using your "jets of energy" model?
    I haven't got a "jets of energy" model. And I repeat: the gluons in ordinary hadrons are virtual. So don't talk to me about woo-woo.

    Quote Originally Posted by lpetrich
    Here's how to get two coupled Majorana particles out of a Dirac particle...
    Trash. The electron is one particle. Get used to it.

    Quote Originally Posted by lpetrich
    I'll now consider neutrino masses...
    You absolutely don't understand mass. It's a measure of "the energy content of a body". Or better still it's "how much energy is not moving in aggregate at c with respect to you". And there's two aspects to this. One is how much energy. Another is how much less than c it's going. If you slow down a photon to less than c it exhibits an effective mass. If you slow it to a zero aggregate speed by trapping it in a mirror box, all of the energy-momentum is exhibited as mass. I kid ye not, this is what E=mc² is all about. The wave nature of matter is not in doubt. Photon momentum is a measure of resistance to change-in-motion for a wave propagating linearly at c. The increased mass of the mirror-box is a measure of resistance to change-in-motion for a wave going round and round at c. It's that simple. Don't think the electron is any different.
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    I must add that the seesaw model adds additional parameters. 12 for the most general right-handed-neutrino mass matrix, 6 for a real one.

    Quote Originally Posted by Farsight View Post
    Again you've got it totally wrong. He previously said A photon can, however, create a pair with the aid of a field, such as that of a nucleus.
    It does so by doing the worms-from-mud action of turning into an electron and a positron, with one of them then interacting with the nucleus's field. If nothing else, it is written in the Book of Feynman that that's how it happens.

    (hadron jets from high-energy collision...)
    I haven't got a "jets of energy" model.
    A most commendable confession. By comparison, mainstream particle physicists do have a model of energetic quarks and gluons making jets of hadrons as they separate.

    (the electron as two Majorana particles coupled together...)
    Trash. The electron is one particle. Get used to it.
    Says who? What I was describing was a consequence of electroweak symmetry breaking, and you can find it in any graduate-level textbook of the Standard Model.

    (neutrino masses...)
    You absolutely don't understand mass.
    Think of the masses that I describe as sort of like self-interactions.
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    Quote Originally Posted by lpetrich View Post
    ...It does so by doing the worms-from-mud action of turning into an electron and a positron, with one of them then interacting with the nucleus's field. If nothing else, it is written in the Book of Feynman that that's how it happens....
    Er, no. The photon interacts with the nucleus and is split into an electron-positron pair. Go read the actual book instead of pretending it backs up the cargo-cult nonsense that has snuck into QED since Feynman's time. Pair-production does not occur because pair production occurs. Spontaneously, like worms from mud! It's a tautology, it's abject nonsense. Don't defend it out of some misplaced sense of loyalty towards what you've been taught. It's wrong. Capiche?

    After that go and read what Einstein actually wrote about gravity, and what Maxwell and Minkowski actually wrote about electromagnetism. Do your own research, and when you find that what they said doesn't square with what you've been taught, dig deeper. Think for yourself.

    Quote Originally Posted by lpetrich
    By comparison, mainstream particle physicists do have a model of energetic quarks and gluons making jets of hadrons as they separate.
    Only the model says the gluons are virtual. That they aren't real particles. So they don't really separate, do they?

    Quote Originally Posted by lpetrich
    What I was describing was a consequence of electroweak symmetry breaking, and you can find it in any graduate-level textbook of the Standard Model.
    It's still wrong. The electron is not two neutrinos. You might say it has two orthogonal spins, but we make the electron (and the positron) out of one or two photons, not by sticking neutrinos together. Electron-positron annihilation is of course the opposite process, and we typically get two photons, not four neutrinos.

    Quote Originally Posted by lpetrich
    Think of the masses that I describe as sort of like self-interactions.
    I don't have a problem with a wave suffering a self-interaction that keeps it in a closed path. Then instead of talking about energy E=hf we say momentum p=hf/c is resistance to change-in-motion for a wave on a linear path, then we divide by c again and say mass m=hf/c² is resistance to change-in-motion for a wave in a closed path. But when you say think of the masses that I describe as sort of like self-interactions I think huh? Masses aren't self-interactions. The self-interaction is where a wave of displacement current displaces itself, and keeps on displacing itself into and in its closed path. It's just bog-standard classical electromagnetism, which seems to be totally absent from the Standard Model. It needs to go in for the electron model, and then maybe HEP will start to bloom again.
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    Quote Originally Posted by Farsight View Post
    Er, no. The photon interacts with the nucleus and is split into an electron-positron pair. Go read the actual book ...
    I did, and Farsight, you are just plain wrong about what Richard Feynman had stated. He clearly stated that the incoming photon does *not* directly interact with the EM field of the nucleus, but instead does what you reject, turn into an electron-positron pair.
    After that go and read what Einstein actually wrote about gravity, and what Maxwell and Minkowski actually wrote about electromagnetism.
    In other words, "Read the Bible."
    The electron is not two neutrinos.
    Two neutrino-ish particles, but not two neutrinos themselves.
    I don't have a problem with a wave suffering a self-interaction that keeps it in a closed path.
    Work out how strong its self-interaction has to be for that. I want numbers, not blather.
    The self-interaction is where a wave of displacement current displaces itself, and keeps on displacing itself into and in its closed path.
    The etymological fallacy about "displacement current". Electromagnetism doesn't work that way.
    It's just bog-standard classical electromagnetism, which seems to be totally absent from the Standard Model.
    It's already in the Standard Model as the classical-field limit of the photon.
    It needs to go in for the electron model, and then maybe HEP will start to bloom again.
    Except that there aren't big discrepancies between observed electron behavior and the Standard Model.

    Write a paper explaining your theories and submit it to some mainstream journals. Or show up at a conference.
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    Quote Originally Posted by Ipetrich
    Write a paper explaining your theories and submit it to some mainstream journals. Or show up at a conference.
    He already wrote a book. It is famous.
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    I'll now consider the question of compositeness. More specifically, whether particles are bound states of other particles as opposed to being mixed fields, a result of electroweak symmetry breaking.

    An early version of the issue appeared in 1896, when J.J. Thomson showed that matter contains particles over a thousand times less massive than even the lightest ions. Electrons. Thus making atoms misnamed. He and others proposed various versions of the "plum pudding model", where electrons in atoms were spread out over an atom-sized positively-charged matrix. In 1909, Ernest Rutherford, Hans Geiger, and Ernest Marsden decided to test these hypotheses by sending alpha particles from radioactive decay through some gold foil. They found something startling. An atom's positive charge is concentrated in a region much smaller than the atom itself. Thus atomic nuclei were discovered.

    Nuclei themselves could be made from other nuclei, as was apparent from radioactivity and directly-observed nuclear reactions. In 1920, Ernest Rutherford proposed that they contain neutral protonlike particles in addition to protons, the lightest nuclei. They were discovered in 1932 by James Chadwick and named neutrons.

    The proton and neutron were the first of numerous hadrons discovered, and in the late 1950's and early 1960's, it became evident that they had some sort of order. The quark model explained much of it, but it had plenty of problems. In the late 1960's, experimenters at the Stanford Linear Accelerator Center started shooting electrons at protons. They found evidence that the proton was composite, and that some of its parts had the properties of those earlier-proposed quarks. So hadrons were composite.

    How about Standard-Model particles?

    The LEP smashed electrons and positrons together with energies up to 110 GeV, and found *no* evidence of compositeness or other departures from Standard-Model behavior. This is about 200,000 times an electron's rest mass.

    Likewise, the LHC has smashed up and down quarks into each other with energies of typically around 1 TeV per quark, with a similar lack of evidence of non-SM behavior. Rest masses of those quarks have been difficult to determine, but here also, their energies are around 200,000 times their rest masses to within a factor of 2.

    This is odd behavior for bound states.
    • For atoms, electrons' binding energies range from 10-8 (hydrogen) to around 3*10-6 (estimate for uranium).
    • For nuclei, nucleons' binding energies range from 0.001 (hydrogen-2) to 0.009 (iron-56).
    • For hadrons, quarks' binding energies range from 0.1 (bottomonium) to ~ 1 (up and down quark hadrons), as far as color confinement allows it to be meaningful.
    So for electrons and up and down quarks, being bound states requires that their binding energies cancel out nearly all of their constituents' masses to at least 1 part in 200 thousand.

    Thus, it's unlikely that any Standard-Model particles are bound states.
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    Quote Originally Posted by lpetrich View Post
    I did, and Farsight, you are just plain wrong about what Richard Feynman had stated. He clearly stated that the incoming photon does *not* directly interact with the EM field of the nucleus, but instead does what you reject, turn into an electron-positron pair.
    I'm not plain wrong. You are. Here's what Feynman said again:

    "It is easily shown that a single photon of energy greater than 2m cannot create an electron positron pair without the presence of some other means of conserving momentum and energy. Two photons could get together and create a pair, but the photon density is so low that this process is extremely unlikely. A photon can, however, create a pair with the aid of a field, such as that of a nucleus, to which it can impart some momentum. As with bremsstrahlung, there are two indistinguishable ways in which this can happen: (a) The incoming photon creates a pair and subsequently the electron interacts with the field of the nucleus; or (b) the photon creates a pair and the positron interacts with the field of the nucleus. The diagrams for these alternatives are shown in Fig. 22-3..."

    And again, there's an online copy here.

    Quote Originally Posted by lpetrich View Post
    Two neutrino-ish particles, but not two neutrinos themselves.
    So, what we're talking about is something that has no mass or charge but which travels at c and has a helicity. Only there's two of them, and we might take the word "bispinor" to indicate some kind of orthogonal helicity, or chirality. Now what does that remind you of Loren? This.

    Quote Originally Posted by lpetrich
    Work out how strong its self-interaction has to be for that. I want numbers, not blather.
    I'll give it some thought. It's really strong. Strong force strong. Imagine the electron is made of elastic, it resists being pulled apart like the bag-model proton.

    Quote Originally Posted by lpetrich
    The etymological fallacy about "displacement current". Electromagnetism doesn't work that way.
    It does!

    Quote Originally Posted by lpetrich
    Write a paper explaining your theories and submit it to some mainstream journals. Or show up at a conference.
    They aren't my theories, but I'll think about writing a paper. I could maybe do with a co-author to open some doors for me.


    Quote Originally Posted by lpetrich
    I'll now consider the question of compositeness. More specifically, whether particles are bound states of other particles...
    Some good stuff here.

    Quote Originally Posted by lpetrich
    The proton and neutron were the first of numerous hadrons discovered, and in the late 1950's and early 1960's, it became evident that they had some sort of order. The quark model explained much of it, but it had plenty of problems...
    It still does. We've never seen a free quark, and gluons are virtual. However these and other issues tend to get brushed under the carpet with vapid excuses like "we've never seen a free quark because of quark confinement".

    Quote Originally Posted by lpetrich
    Likewise, the LHC has smashed up and down quarks into each other
    No it hasn't. They've smashed protons into each other, and heavy ions.

    Quote Originally Posted by lpetrich
    Rest masses of those quarks have been difficult to determine
    You betchya. There's no problem determining the electron's rest mass, but not a quarks. Funny that.

    Quote Originally Posted by lpetrich
    Thus, it's unlikely that any Standard-Model particles are bound states.
    Fair enough. Now tell me again about those two "neutrino-ish" particles that you said make up the electron. Oops!
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    Quote Originally Posted by Farsight View Post
    I'm not plain wrong. You are. Here's what Feynman said again: ...
    (mined quote snipped...)

    Conveniently ignoring his discussion of virtual electrons/positrons.

    (what keeps the circling photon confined...)
    It's really strong. Strong force strong. Imagine the electron is made of elastic, it resists being pulled apart like the bag-model proton.
    There is not even a speck of experimental evidence for such a force. It would have shown up long ago in particle-physics experiments if it existed.

    They aren't my theories, but I'll think about writing a paper. I could maybe do with a co-author to open some doors for me.
    Let's see if you get anywhere.

    (The LHC as a quark collider...)
    No it hasn't. They've smashed protons into each other, and heavy ions.
    Particles that contain quarks -- mostly up and down ones. Ask those who make predictions about what particles the LHC can make. I've read some of their papers. They don't model protons as photons circling in trefoil patterns but as a probability distribution of various approximately-free particles: quarks and gluons. Quarks -- much like electrons. Gluons -- much like photons.

    (Standard-Model particles not being bound states...)
    Fair enough. Now tell me again about those two "neutrino-ish" particles that you said make up the electron. Oops!
    That's a mixed state, not a bound state.
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    Quote Originally Posted by lpetrich View Post
    There is not even a speck of experimental evidence for such a force. It would have shown up long ago in particle-physics experiments if it existed.
    There is. Electrons and positrons are created in pair production, and electrons remain as electrons until you annihilate them with positrons. They don't fall apart.

    Quote Originally Posted by lpetrich
    ...I've read some of their papers. They don't model protons as photons circling in trefoil patterns but as a probability distribution of various approximately-free particles: quarks and gluons.
    Only we've never seen a free quark and gluons in protons are virtual. So there's an interpretational issue to be addressed.

    Quote Originally Posted by lpetrich
    That's a mixed state, not a bound state.
    Unconvincing. You might want to have a read of the turning light into matter thread.
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    Only we've never seen a free quark
    That's hardly a surprise, considering that free quarks don't exist. Having said that, one can come pretty close by considering quark-gluon plasmas, in which both the quarks and the gluons almost achieve asymptotic freedom; the RHIC data from 2003 and onwards is fully consistent with that :

    Heavy ions and quark-gluon plasma | CERN
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    (Me earlier: There is not even a speck of experimental evidence for such a force. It would have shown up long ago in particle-physics experiments if it existed.)
    Quote Originally Posted by Farsight View Post
    There is. Electrons and positrons are created in pair production, and electrons remain as electrons until you annihilate them with positrons.
    That's not evidence of a force that keeps photons circling to make electrons and other such particles.

    I will now quote from the Book of Feynman on how pair production happens:
    (a) The incoming photon creates a pair and subsequently the electron interacts with the field of the nucleus; or (b) the photon creates a pair and the positron interacts with the field of the nucleus.
    (Richard Feynman, Quantum Electrodynamics, page 111)

    So if you deny that, you deny Richard Feynman. Farsight, you have yet to acknowledge that he stated that.

    (modeling quarks and gluons as electronlike and photonlike particles...)
    Quote Originally Posted by Farsight
    Only we've never seen a free quark and gluons in protons are virtual. So there's an interpretational issue to be addressed.
    Interpretation. Oh how convenient.

    (Electrons as a mixed state...)
    Unconvincing.
    Maybe to you, Farsight. I understand the math behind it, so that's why I have no trouble with it.
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    Quote Originally Posted by Markus Hanke View Post
    That's hardly a surprise, considering that free quarks don't exist. Having said that, one can come pretty close by considering quark-gluon plasmas, in which both the quarks and the gluons almost achieve asymptotic freedom; the RHIC data from 2003 and onwards is fully consistent with that:
    Heavy ions and quark-gluon plasma | CERN
    You should look more closely at this Markus. Remember what I said about gluons being virtual? Pay attention to this:

    "This forms a miniscule fireball in which everything “melts” into a quark-gluon plasma..."

    Everything has melted, so everything has lost its individuality. Think pea soup. What don't you find in pea soup? Peas. There are no individual peas in pea soup. Likewise there are no individual quarks or gluons in a quark-gluon plasma. Note the next section suggests that this is not the case:

    "The fireball instantly cools, and the individual quarks and gluons (collectively called partons) recombine into a blizzard of ordinary matter that speeds away in all directions. The debris contains particles such as pions and kaons, which are made of a quark and an antiquark; protons and neutrons, made of three quarks; and even copious antiprotons and antineutrons, which may combine to form the nuclei of antiatoms as heavy as helium. Much can be learned by studying the distribution and energy of this debris".

    But then we've got this:

    "An early discovery was that the quark-gluon plasma behaves more like a perfect fluid with small viscosity than like a gas, as many researchers had expected".

    It's like a perfect fluid, not something "lumpy". It isn't a collection of quarks and gluons, like the depiction of the proton on Matt Strassler's web site. See the this physicsworld article about the same subject, where you can read this:

    "In the aftermath of the discoveries at RHIC (see, for example, K Adcox et al. 2005 Nucl. Phys. A757 184), there has been a raging debate about just what exactly is interacting inside the quark–gluon plasma. It is not clear whether the matter consists of individual gluons, pure gluonic fields or perhaps multi-gluon objects that continually split and re-form. The task at RHIC now is to upgrade the accelerator and experiments to provide new probes of the matter to differentiate between these scenarios".

    I say they're "pure gluonic fields" rather than individual gluons.
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    Quote Originally Posted by lpetrich View Post
    That's not evidence of a force that keeps photons circling to make electrons and other such particles.
    You start with two photons moving linearly at c. You do your pair production and then you've got two somethings with a wave nature and spin and not moving at c, then they annihilate and you've got your two photons moving at c again. It ain't magic Loren. And nowhere did you get four neutrino-like particles.

    Quote Originally Posted by lpetrich
    I will now quote from the Book of Feynman on how pair production happens:

    (Richard Feynman, Quantum Electrodynamics, page 111)

    So if you deny that, you deny Richard Feynman. Farsight, you have yet to acknowledge that he stated that.
    Here's the full quote:

    "It is easily shown that a single photon of energy greater than 2m cannot create an electron positron pair without the presence of some other means of conserving momentum and energy. Two photons could get together and create a pair, but the photon density is so low that this process is extremely unlikely. A photon can, however, create a pair with the aid of a field, such as that of a nucleus, to which it can impart some momentum. As with bremsstrahlung, there are two indistinguishable ways in which this can happen: (a) The incoming photon creates a pair and subsequently the electron interacts with the field of the nucleus; or (b) the photon creates a pair and the positron interacts with the field of the nucleus. The diagrams for these alternatives are shown in Fig. 22-3..."

    The incoming photon can't create a pair on its own. Feynman said it. Stop pretending he said something else, it's getting tedious.

    Quote Originally Posted by lpetrich View Post
    Maybe to you, Farsight. I understand the math behind it, so that's why I have no trouble with it.
    My hard scientific evidence trumps your attempt to hide behind mathematics.
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    Stop feeding the Farsight troll.
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    Quote Originally Posted by x0x View Post
    Stop feeding the Farsight troll.
    LOL, in my experience this is the classic troll-type sentence.
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    Quote Originally Posted by Farsight View Post
    You should look more closely at this Markus. Remember what I said about gluons being virtual? Pay attention to this:

    "This forms a miniscule fireball in which everything “melts” into a quark-gluon plasma..."

    Everything has melted, so everything has lost its individuality. Think pea soup. What don't you find in pea soup? Peas. There are no individual peas in pea soup. Likewise there are no individual quarks or gluons in a quark-gluon plasma. ...
    According to these sources, quarks and gluons are well-defined entities in a quark-gluon plasma:
    Quark-Gluon Plasma
    Heavy ions and quark-gluon plasma | CERN
    Explained: Quark-gluon plasma | MIT News Office
    Quark Gluon Plasma
    Physics of the Quark-Gluon Plasma
    Quark-Gluon Plasma and the Early Universe

    "Baryon number" is nowadays a misnomer. "Quark number" would be better, but the old name has stuck, like so much other misleading terminology. In any case, it's conserved in quark-gluon plasma as well as in hadrons.

    I searched in scholar.google.com, and I found references to "baryon number" as far back as 1956, well before when the quark model was proposed. Back then, another name for it was "baryonic charge".
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    The first article says this:

    "A millionth of a second after the Big Bang, the universe was an incredibly dense plasma, so hot that no nuclei nor even nuclear particles could exist. The plasma consisted of quarks, the particles that compose nucleons and some other elementary particles, and gluons, the massless particles that “carry” the force between quarks (See Nuclei Knockdown). Gluons are the particles that quarks exchange as they interact, or, in the language of modern physics, gluons “mediate” the strong force between quarks. Since quarks make up protons and neutrons, this leads to the force that holds protons and neutrons together in a nucleus."

    It sounds reasonable enough, until you remember that the gluons in a proton or neutron are virtual. There are no actual gluons flying around, just as there are no photons flying back and forth between the proton and the electron inside a hydrogen atom. So instead of thinking of gluons as individual things, you should think of them as "gluonic field". Then you remember that you've never seen a free quark and apply more of the same kind of logic. Particularly because the MIT article says this:

    "They also want to delve further into the very surprising similarities that have been seen between QGP and ultracold gases (near absolute zero) that MIT’s Martin Zwierlein and others have created in the laboratory."

    Now have a look at Zweirlein's Ultracold Quantum Gases Group and note the mention of Bose-Einstein condensates. A BEC is where the atoms have lost their individuality. You should think of a QGP in similar vein. NB: note the mention of a solitonic vortex! Also note the mention of evanescent and partons in the CERN article. The last three articles were very bulky, I didn't read them all. The powerpoint presentation certainly gave the impression of individual quarks and gluons, like a panful of garden peas and marrowfat peas instead of the "pea soup" I was telling you about. By the by, the last item started by saying this: There is now considerable evidence that the universe began as a fireball, the so called “Big-Bang”. I think there's an issue there in that the QGP is like a BEC. I think the very early universe was motionless and cold with very high pressure, but not actually hot. That's one for another day, and another thread.
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    I had a quick look at the last article and read this:

    "Quarks are spin-1/2 point particles, very much like electrons..."

    Groan. It's quantum field theory. Everything is fields and waves. It isn't quantum point-particle theory. An electron isn't a point particle, and neither is a quark. Yes, Frank Wilczek along with David Gross and Hugh David Politzer shared a Nobel Prize for "asymptotic freedom". But when guys like this make mistakes like that, Houston we have a problem.
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    A minor kvetch about a common oversimplification.

    Frank Wilczek has some nice articles, and he avoids math in most of them. But in some of them, he has a nice table of how the elementary fermions fit into a SO(10) spinor representation. A SO(10) spinor is an outer product of five 2-component spinors, giving 32 components. It splits into two complex-conjugate 16-dimensional parts, enough for each generation of elementary fermion and a right-handed neutrino. However, nobody seems to have found anything similar for the masses, any simplified form that gives us the known masses and mixings.

    As to asymptotic freedom, it means that quarks and gluons are nearly free particles if they are much closer to each other than the QCD size scale of about 10-15 m. When they separate by that much, their interactions become superstrong, and if they have enough energy, it then becomes energetically favorable to make quark-antiquark pairs between them and make multiple hadrons. That's what makes jets of hadrons from energetic quarks and gluons.
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    It isn't a "minor kvetch", lpetrich. It's cargo-cult trash, and a reminder of just how much work is required on the Standard Model.

    But come to think of it, maybe it would be better to throw it away and start again. That's kind of what Alexander Unzicker was saying in The Higgs Fake.
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    Quote Originally Posted by Farsight View Post
    It isn't a "minor kvetch", lpetrich. It's cargo-cult trash, and a reminder of just how much work is required on the Standard Model.
    What work is necessary? What major observational or theoretical discrepancies do you think there are in the Standard Model?

    Calling elementary fermions pointlike is certainly misleading, but there are alternatives to both that and the circling-photon theory of them. Alternatives which include the mainstream theories of them.

    Here is what an elemenetary-particle field is. It's a function of space-time, space-time-multiplet index, gauge-multiplet index, flavor index, ... Each index value of it can itself be treated as a field. Thus, one can treat electrons, muons, and tau leptons as components of a charged-lepton field. This field can then be decomposed by flavor index into the electron field, the muon field, and the tau-lepton field. If you've ever worked with multidimensional arrays, you should not find this idea very difficult.

    From what space-time multiplet a particle is in, one can find its spin or intrinsic angular momentum.

    The trivial case is a single function. That makes the field a singlet or scalar one, and it thus has spin 0.

    The simplest nontrivial case is a vector, like what the photon and other gauge particles are. Under rotations and boosts, the field's components transform like the offset between two space-time points, or alternately like the gradient of a function of space-time. Rotations and boosts turn components into linear mixtures of them. A field that transforms like that has 4 components and spin 1.

    Measuring the Angular Momentum of Light – Uncertain Principles describes an experiment that successfully measured the angular momentum carried by circular polarization of light. The light in the apparatus is effectively a plane wave, but its electric and magnetic vectors continually change direction as if they were pointing to something going in circles around the beam. However, nothing is macroscopically rotating. Nothing. As a further indication that this is a field effect, one can calculate the angular momentum in the classical limit, and one gets the right result.

    A spinor is more complicated, but the principle is the same. Rotations and boosts turn a spinor's components into a linear mixture of them. A Majorana spinor has 2 components, and it can have either of 2 chiralities: left-handed or right-handed. A Dirac spinor is a left-handed spinor alongside a right-handed spinor, thus having 4 components. Both Majorana and Dirac spinors have spin 1/2.

    One can make additional kinds of space-time multiplets by combining two vectors, combining a vector and a spinor, etc., but I won't get into those. As one might expect, they have additional spin values.

    No circling photons in sight, and there is no Standard-Model interaction that can make a photon make itself go in circles. The closes thing is a glueball state, of gluons that confine themselves by their self-interactions, but glueballs exist because the QCD interaction becomes superstrong at large distances. The photon's interactions are not strong enough to create a photon version of the glueball.
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    Quote Originally Posted by Farsight View Post
    But come to think of it, maybe it would be better to throw it away and start again. That's kind of what Alexander Unzicker was saying in The Higgs Fake.
    That's an incredibly stupid idea. Very successful theories are typically not replaced but turned into special cases of other theories. That's what had happened to Newtonian mechanics.

    As to what Alexander Unzicker thinks about the Higgs particle, I've found this paper at viXra, the alternative arXiv: viXra.org e-Print archive, viXra:1212.0100, The Discovery of What? Ten Questions About the Higgs to the Particle Physics Community

    What were the predictions? About the Higgs particle's mass, it is a function of the free parameters of various Beyond the Standard Model theories, like the Minimal Supersymmetric Standard Model.

    Two photons. So what? True, there is plenty of energetic two-photon background, but it has a continuous spectrum of center-of-mass energies, the masses that one would get if one treats each pair of photons as one particle. The Higgs particle, however, makes a spectrum with a spike in it at its mass, and that's how it was observed. That's rather elementary data analysis for elementary-particle-physics work.

    Is this a triumph of the standard model? The Higgs particle had some hints that it did not quite fit the Standard Model. However, those hints seem to have gone away, and they seem to have been statistical artifacts. But even if the Higgs particle is not an exact fit, it is still very close.

    How is radiation damping controlled? This is from extrapolation of classical-limit radiation damping. However, one runs into quantum-mechanical effects well before one runs into problems with that extrapolation. So it's a non-issue.

    How do you remove a background of one trillion pairs? Because most of them don't look anything near like a Higgs particle's decay products.

    Is the lifetime of the Higgs irrelevant? The observed width of the Higgs-particle state seems much higher than one would expect from its Standard-Model mean life. However, that is a result of experimental error and/or statistics.

    Is this an explanation of masses? He argues that it puts the problem back a step, from the masses to the Higgs-particle couplings. While one can predict those couplings for the W and Z particles, one cannot for the elementary fermions, and one must concede that there is an explanatory gap here.

    How many numbers are in the game? The Standard Model makes predictions of the Higgs particle's interactions from parameters whose values can be found from other observations, like masses of other Standard-Model particles.

    What are the model-independent results? So he wants some purely phenomenological modeling without attempting to fit to the Standard Model? That's in part what the detector teams have been doing, finding branching ratios and the like.

    Why not public data? He ought to ask the detector teams about their data-retention policies. A big problem with the LHC is that it produces huge amount of data, most of which are irrelevant for what many particle physicists are looking for. So one gets (say) all muons with energies more than 10 GeV, or all pairs of muons with center-of-mass energies greater than 10 GeV.

    Most of those objections can easily be answered by someone who works in high-energy physics, and AU complained that arXiv had rejected it.
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    Alexander Unzicker had written a book on particle physics, Vom Urknall zum Durchknall (my translation: "From the Big Bang to the Big Crack-up", lit. madness), and he's published an English translation as How Today's Top Scientists are Gambling Away Their Credibility with journalist Sheilla Jones.

    In Bankrupting Physics | Not Even Wrong, Peter Woit:
    I just spent a depressing and tedious few hours reading through Bankrupting Physics ...

    When I started reading the thing I wasn’t expecting much, but figured it would be some sort of public service to take the time to identify what Unzicker had to say that made sense and what didn’t, and then write something distinguishing the two here. After a while though, it became clear that Unzicker is just a garden-variety crank, of a really tedious sort. ...

    Unzicker’s obsessive idea, shared with innumerable other cranks, is that any scientific theory beyond one intuitively clear to them must be nonsense. Similarly, any experimental result beyond one where they can easily understand and analyze the data themselves is also nonsense.
    That seems very familiar.

    He also complained that general relativity needs fixing for small accelerations, that cosmology has too many free parameters, and that dark matter and dark energy show how ignorant cosmologists are.
    When he gets to particle physics, we learn that things went wrong back when physicists started invoking a symmetry that wasn’t intuitively obvious, isospin symmetry. According to Unzicker, symmetries in particle theory are all a big mistake, “the standard model barely predicts anything”, “the standard model can actually accommodate every result”, and endless other similar nonsense. ...

    High energy physics experiments are all just a big scam, with the physicists involved unwilling to admit this, since they’ve wasted so much money on them.
    Toward the end of his book, he states
    Woit does a great job in debunking the string and SUSY crap. Unfortunately, he has pretty mainstream opinions with respect to the Standard Model.
    PW conceded
    Well, maybe he does get something right…
    What would he prefer? I've found
    Unzicker interview about "Bankrupting Physics" - YouTube

    Toward the end, he states that we ought to revisit some old ideas by Einstein and Dirac.
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    Quote Originally Posted by lpetrich
    That's an incredibly stupid idea. Very successful theories are typically not replaced but turned into special cases of other theories.
    The whole point of The Higgs Fake is that it isn't a successful theory at all. And that it isn't just the Higgs "discovery" that's questionable. Unzicker also writes about the neutral current that dates back to 1973, and how data analysers cherry-picked 100 out of 290,000 photographs. He refers to How Experiments End by Peter Galison about the contradictory paper that was never submitted to a journal. He tells us about the W boson which dates back to 1983 with its lifetime of 10^-25 seconds, and what was actually detected was an electron. He says stuff like "Rubbia urged his collaborators to work day and night before his visit to various institutions in the USA. He took a picture of a 'W-event' with him. There, Steven Weinberg, Abdus Salam and Sheldon Glashow all happily agreed that it was the long sought-after W boson (which confirmed their theory, by the way)…". Unzicker says the official announcement was given in a common seminar of groups UA1 and UA2, which reminds you of 4th July 2012. He says CERN management provided Rubbia with the UA2 results privately, and that believing in independent analysis is like believing in Santa Claus.

    He also talks about the top quark which dates back to 1995. He tells us it has a lifetime of 10^-25 seconds, and had to exist because: "the bottom quark needed a partner, as the Ws and Zs had to exist because otherwise the standard model was wrong". We’ve never seen a free quark, remember? This top quark was seen to decay into a bottom quark and a W boson. But we’ve never actually seen a top quark, or a bottom quark, or a W boson. The top quark was inferred from particles that were inferred. And after that "something had to be found in the theoretical boxroom to inspire the next round of high energy experiments". In a nutshell, he's saying Standard Model physicists have got form. That they're engaged in scientific fraud and standing four-square in the way of scientific progress.

    You know, I'm coming to the conclusion that he's right, and that it's useless to try to talk to particle physicists about the work required to the Standard Model. I'm now thinking the best thing is to talk to the public and politicians instead. And that I should change my views about physics funding cuts.

    PS: You should read some of the other reviews of Bankrupting Physics.
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    (The Standard Model)
    Quote Originally Posted by Farsight View Post
    The whole point of The Higgs Fake is that it isn't a successful theory at all. And that it isn't just the Higgs "discovery" that's questionable.
    If Alexander Unzicker's viXra paper on the Higgs particle is typical of his work, then his case is mostly specious and easily answered.

    Unzicker also writes about the neutral current that dates back to 1973, and how data analysers cherry-picked 100 out of 290,000 photographs.
    How else does one look for rare events?

    He also talks about the top quark which dates back to 1995. He tells us it has a lifetime of 10^-25 seconds, and had to exist because: "the bottom quark needed a partner, as the Ws and Zs had to exist because otherwise the standard model was wrong".
    For good theoretical reasons, I may add.

    You know, I'm coming to the conclusion that he's right, and that it's useless to try to talk to particle physicists about the work required to the Standard Model. I'm now thinking the best thing is to talk to the public and politicians instead. And that I should change my views about physics funding cuts.
    That's what pseudoscientists often do -- appeal to some population other than the scientific community.
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    Another issue in the Standard Model is are there any additional generations of elementary fermions?

    Let's recap the history of the discovery of the elementary fermions.

    The electron was discovered by J.J. Thomson in 1897, and its spin discovered by Samuel Goudsmit and George Uhlenbeck in 1925, explaining an additional quantum number proposed by Wolfgang Pauli in 1924. In 1928, Paul Dirac proposed a relativity-friendly theory of it, a theory that explained its magnetic moment to about 1 part in a thousand. Quantum electrodynamics, the quantum field theory of electromagnetism, was developed over the next few decades, and it successfully explained that discrepancy. Dirac's theory also predicted that the electron has a sort of mirror image or antiparticle with positive electric charge. Was it the proton? It was nearly 2000 times more massive, among other things, and Dirac's theory predicted the same mass as the electron. In 1932, Carl Anderson discovered the positron, and it had the right mass and various other properties for the electron's antiparticle.

    The muon was discovered in 1936, also by Carl Anderson. It was about the right mass to be Hideki Yukawa's proposed carrier of the strong nuclear interaction, but it turned out to be just like an electron, but about 207 times more massive. Another such particle, the tau lepton, was discovered in 1975 by a team led by Martin Lewis Perl. It is also just like an electron, but nearly 3500 times more massive.

    The neutrino was proposed by Wolfgang Pauli in 1930, as a way of explaining how beta decays lost energy and violated angular-momentum conservation. He proposed a particle he called the neutron that carried off the missing energy and angular momentum. But in 1932, James Chadwick discovered Ernest Rutherford's 1920 neutral proton, and he also called it a neutron. In 1933, Enrico Fermi proposed renaming Pauli's neutron the neutrino ("little neutral one" in Italian), and the name stuck.

    In 1956, Frederick Reines, Clyde Cowan, and their collaborators observed neutrinos coming from a nuclear reactor. In 1962, Leon M. Lederman, Melvin Schwartz and Jack Steinberger showed that muons make a kind of neutrino distinct from what electrons make. In 2000, the DONUT collaboration at Fermilab showed that tau leptons also made their own kind of neutrino. Since then, it has been discovered that these flavors of neutrino oscillate among themselves, due to their masses not being orthogonal with their weak interactions.

    So we have made in the lab 3 flavors of charged leptons and 3 flavors of neutrinos.

    Now to quarks and hadrons.

    The first ones discovered were the proton and the neutron. They have very close masses, and their strong interactions were very similar. In 1932, Werner Heisenberg proposed that they were sort of like two states of the same particle, like the two spin states of a spin-1/2 particle. Proton = up, neutron = down. This symmetry was named isospin in 1937 by Eugene Wigner; that name is short for isotopic spin or isobaric spin. The "spin" part is from that mathematical analogy.

    As they were discovered, other hadrons were discovered to have well-defined isospin values. But some hadrons had the strange property of decaying much more slowly than what one would expect of a strongly-interacting particle. In the late 1950's, Murray Gell-Mann and Kazuhiko Nishijima proposed that there is an additional quantum number, which they named "strangeness". It was conserved by the strong interaction but not by the weak interaction, thus being like isospin. Murray Gell-Mann also noted that isospin, with its symmetry group SU(2), could be combined with strangeness to give a larger symmetry group, SU(3). That one has 8 generators, and he called it the Eightfold Way, after the eight things to do in the fourth of Buddhism's Four Noble Truths. The longer-lived mesons and spin-1/2 baryons formed octets in that group, but there ought to have been ten relatively long-lived spin-3/2 baryons. Only nine of them were known, and in 1962, Gell-Mann and Yuval Ne'eman predicted the tenth one. It was found in 1964 at Brookhaven National Laboratory and named the omega baryon.

    Also in 1964, Murray Gell-Mann and George Zweig proposed the quark model. The name is Gell-Mann's; Zweig preferred to call them aces. In the early years, some people called the three flavors proton, neutron, and lambda, but up, down, and strange, from isospin and strangeness, stuck.

    In 1963, Nicola Cabibbo proposed that hadrons' weak interactions were a mixture of strangeness-preserving and strangeness-changing ones, with their relative sizes determined by an angle that got known as the Cabibbo angle. Their total size was about the size of the electrons' and muons' weak interactions. This was quickly adapted to the quark model, and James Bjorken and Sheldon Glashow, among others, speculated that there may be an additional quark that decays into the opposite mixture of down and strange quarks.

    A serious problem with the original quark model was that double-strangeness-changing interactions are very weak. They were known, however, as interactions that change neutral kaons to their antiparticles and back again. In 1970, Sheldon Lee Glashow, John Iliopoulos and Luciano Maiani proposed that a fourth quark could suppress these interactions. I haven't been able to find out who proposed the name charm quark for it.

    In late 1974, Burton Richter at the Stanford Linear Accelerator Center discovered a particle he called psi, and Samuel Ting at the Brookhaven National Laboratory discovered a particle he called J. They were one and the same, and in their honor, it's called J/psi. This particle had been missed in some earlier searches, because its decay width is about a thousandth of what one would naively expect from the strong interaction.

    The J/psi turned out to be a heavy quark and its antiparticle orbiting each other, much like positronium, an electron and a positron orbiting each other. That quark turned out to be the charm quark. Two years later, a particle with a charm quark without its antiquark was discovered, the D meson. The relatively long life of the J/psi turned out to be a consequence of quantum chromodynamics; the charm and anticharm annihilate into three gluons and not one, and from there to light hadrons. However, they can easily annihilate into one photon, which then produces either an electron pair or a muon pair, and those processes are not much slower than the gluon/hadron one.

    The charm quark also suppressed some additional trouble, the "triangle anomaly". It's a quantum-mechanical inconsistency involving a loop of elementary fermions or similar particles with 3 gauge particles coming off of it. The only way to get rid of it is to have a spectrum of particles that have interactions that make it cancel out. Each complete generation of Standard-Model elementary fermions makes the triangle anomaly cancel, but an incomplete one will not.

    More quarks?

    In 1964, James Cronin, Val Fitch, and their collaborators discovered that neutral kaons have decays that violate CP, charge (matter-antimatter) and parity (space reflection) together. Though weak interactions had earlier been discovered to violate parity, the earlier observed ones' violation of charge symmetry made them conserve CP.

    In 1973, Makoto Kobayashi and Toshihide Maskawa proposed that one could explain CP violation by supposing that there is at least one additional generation of quarks. Here is how it works. The mixing of up-like and down-like quarks is expressed by a mixing matrix, called the Cabibbo-Kobayashi-Maskawa or CKM matrix. It is unitary, meaning that it equals its Hermitian conjugate, the transpose of its complex conjugate. For n generations, that gives it n2 parameters. Some of them go into the particles' wavefunctions' phases, making them unobservable. That removes 2*n-1 of them, giving (n-1)2 parameters with observable effects. If quarks' weak interactions preserve CP, then the matrix will be real, giving it (1/2)*n*(n-1) parameters: mixing angles. The remaining parameters are (1/2)*(n-1)*(n-2) CP-violating phases. For n = 2, the quarks' weak interactions preserve CP, while for n >= 3, they can violate CP.

    In 1975, Haim Harari proposed names for a third generation of quarks: bottom and top. Others have called them beauty and truth, but Harari's names have stuck.

    In 1977, Leon Lederman, heading the E288 collaboration at Fermilab, discovered the upsilon meson. It is a bottom quark and its antiquark orbiting each other, much like the J/psi and other quarkonium hadrons. It showed up as a spike in the pair production of muons, from the quark-antiquark annihilation. Soon after, the B meson was discovered, much like the D meson, with a bottom quark and another flavor of antiquark.

    But the top quark proved elusive, with lower limits on its mass getting pushed upward as the years went on. But in the early 1990's, the detector teams at the Fermilab Tevatron started seeing positive evidence for the top quark, and they announced their discovery in 1995. It's mass is about 173 GeV, about 340,000 times the electron's mass, and more massive than any other known particle, including the Higgs particle at 125 GeV. Not surprisingly, it decays very fast, usually into a W and another quark that is usually a bottom quark.

    Are there more generations of elementary fermions?

    Particle Data Group has some discussion of searches for various possible particles. Here are those relevant to possible additional generations of elementary fermions:

    Additional charged lepton: mass > 100.8 GeV
    Number of light neutrino flavors from the Z decay width: 2.92 +- 0.05
    Addition down-like quark (b'): mass > 190 GeV
    Additional up-like quark (t'): mass > 685 GeV

    So it is unlikely that a fourth generation exists.
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    I'll now discuss triangle anomalies and the like. The triangle anomaly arises from a Feynman diagram that contains a loop with spin-1/2 particles in it: elementary fermions or similar. From it come three gauge particles, and if the fermion loop's lines are drawn straight, that loop looks like a triangle. The anomaly comes about when the interactions with the left-handed parts and the right-handed parts differ. It only comes about in even space-time dimensions, and there is an analogous anomalous polygon with D/2 - 1 vertices for D dimensions. Thus, string theory has a hexagon anomaly.

    These anomalies create troublesome inconsistencies, and the only way to keep them from causing trouble is to make them cancel. This constrains the possible interactions of particle-physics theories. A complete generation of Standard-Model elementary fermions will have canceling anomalies, but not an incomplete one. Likewise, the Minimal Supersymmetric Standard Model has Higgs particles whose higgsinos have canceling anomalies.

    Not just gauge particles but also gravitons can create anomalies, and one must taken them into account.

    I'll give how to calculate the interaction part, since that's how one determines whether or not the anomaly cancels. For a triangle anomaly with gauge particles a, b, and c, the matrices for interaction with the fermions are Ta, Tb and Tc. One must calculate for each chirality or handedness

    Tabc = Tr(Ta.{Tb,Tc}) = Tr(Ta.Tb.Tc) + Tr(Ta.Tc.Tb)
    Tr means "trace", and Tr(A) = sum over i of Aii It comes from integrating over a loop and counting all possible fermions.

    One then calculates Tabc = Tabc,left - Tabc,right

    A non-chiral theory, like QCD or electromagnetism, thus has canceling anomalies. But the weak interactions are chiral, because of their parity violation, thus potentially producing anomalies.

    Here are some crude calculations that one can do. They are proportional to the gauge group's Lie-algebra invariants, and if one can find an invariant with the appropriate number of generators, then an anomaly may exist. Otherwise, it will cancel. Thus, for the triangle anomaly, one must find an invariant with three generators multiplying each other.

    For the Standard Model, the symmetry group is SU(3)color * SU(2)weak isospin * U(1)weak hypercharge * SO(3,1)space-time: gravity That last one can be handled by considering its close relative SO(4).

    Here are the sizes of the irreducible invariants for various Lie algebras. All others can be reduced to products of these.
    • U(1): 1
    • A(n): SU(n+1): 2, 3, ..., n+1
    • B(n): SO(2n+1): 2, 4, ..., 2n
    • C(n): Sp(2n): 2, 4, ..., 2n
    • D(n): SO(2n): 2, 4, ..., 2n-2, n
    • G2: 2, 6
    • F4: 2, 6, 8, 12
    • E6: 2, 5, 6, 8, 9, 12
    • E7: 2, 6, 8, 10, 12, 14, 18
    • E8: 2, 8, 12, 14, 18, 20, 24, 30
    For U(1), the invariant is the particle's U(1) interaction strength or "charge".

    Let's go through the possibilities for the triangle anomaly and the Standard Model.

    QCD: 2, 3
    Weak isospin: 2
    Weak hypercharge: 1, 2, 3
    Gravity: 2

    So we get (QCD)3, (QCD)2*(WHC), (WIS)2*(WHC), (gravity)2*(WHC), (WHC)3 to check. All the others automatically cancel. One can avoid calculating most of the individual groups' invariants, since their values are usually shared.

    (QCD)3:
    Left-handed quark: 6 * (Quark^3)
    Right-handed up: - 3 * (Quark^3)
    Right-handed down: -3 * (Quark^3)
    Leptons: 0

    (QCD)2*(WHC):
    Left-handed quark: 6 * (Quark^2) * (1/6)
    Right-handed up: - 3 * (Quark^2) * (2/3)
    Right-handed down: - 3 * (Quark^2) * (-1/3)
    Leptons: 0

    (WIS)2*(WHC):
    Left-handed quark: 6 * (Weak^2) * (1/6)
    Lef-thanded lepton: 2 * (Weak^2) * (-1/2)
    Right-handed EF's: 0

    (gravity)2*(WHC):
    (sum of all left-handed weak hypercharges) - (sum of all right-handed weak hypercharges)
    (Gravity^2) * (6*(1/6) + 2*(-1/2) - 3*(2/3) - 3*(-1/3) - 1*(-1))

    (WHC)3:
    Left-handed quark: 6 * (1/6)3
    Right-handed up: - 3 * (2/3)3
    Right-handed down: - 3 * (-1/3)3
    Left-handed lepton: 2 * (-1/2)3
    Right-handed electron: - 1 * (-1)3

    For the quarks alone and the leptons alone, all the anomalies would cancel except for the (WIS)2*(WHC) one, the one associated with charged weak interactions. Likewise, weak-singlet quarks and leptons would have all anomalies canceling.


    Some extensions of the Standard Model feature a right-handed neutrino. It does not contribute because it's a Standard-Model gauge singlet.

    MSSM Higgs sector:
    Two left-handed doublets with hypercharges 1/2 and -1/2
    (QCD)3: 0
    (QCD)2*(WHC): 0
    (WIS)2*(WHC): 2 *(Weak^2) * ((1/2) + (-1/2))
    (gravity)2*(WHC): (Gravity^2) * (2*(1/2) + 2*(-1/2))
    (WHC)3: 2*(1/2)3 + 2*(-1/2)3


    One can also verify triangle-anomaly cancellation for the SU(5) Grand Unified Theory, and it is automatic for the SO(10) and E6 ones.


    For the low-energy limit of string theory, one has to do the calculations in 10 space-time dimensions, requiring calculation of hexagon anomalies. One gets pure gravitational anomalies in it, in addition to gauge and mixed ones. It's anomaly cancellation that constrains heterotic superstrings to have gauge groups SO(32) and E8*E8.


    [0802.0634] Lectures on Anomalies is extremely technical, and it goes into very gory detail, but I've gotten some results from there. Harish-Chandra isomorphism - Wikipedia gives the sizes of the irreducible invariants of the various simple Lie algebras.
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  90. #90  
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    Quote Originally Posted by lpetrich View Post
    That's what pseudoscientists often do -- appeal to some population other than the scientific community.
    Au contraire, lpetrich. What Unzicker is saying, is that particle physics is now a pseudoscientific community. And when you think of the woo and nonsense and the propaganda and censorship and all the opprobrium in physics these days, the guy really seems to have a point. I mean, there's Max Tegmark talking about a universe made of mathematics, and everybody sucks up to him because he's scientific director at fqxi. And there's Joy Christian trying to dispel quantum mysticism, and he got roasted. Not good. Not good at all. Especially when bona-fide physicists can't put a paper up on the arXiv. Especially when there's been no real scientific progress for decades, and when the fabulous Higgs boson contradicts E=mc².

    The public have lost faith, and interest, and so have politicians. Which is why we're seeing funding cuts I suppose. I always voiced my opposition to them, but you know what lpetrich? Maybe Unzicker is right. Cut all funding for theoretical physics. Have a clear out. I mean, why should my tax dollars pay for quacks to peddle woo and call people names and get in the way of scientific progress?

    By the way, I wasn't quite clear what you thought of my review of his book. I don't write for Bogpaper any more, but maybe I'll write elsewhere.
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    Quote Originally Posted by Farsight View Post
    Especially when there's been no real scientific progress for decades, and when the fabulous Higgs boson contradicts E=mc².
    Hmm... another claim from Farsight that he disagrees with mainstream physics. Yet will Farsight try to defend these claims in the area of the forum where such claims belong? Probably not. He will simply cry and say that he's taking his toys home.
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  92. #92  
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    Quote Originally Posted by Farsight View Post
    I mean, there's Max Tegmark talking about a universe made of mathematics, and everybody sucks up to him because he's scientific director at fqxi.
    I consider that a speculation on his part, not something to be treated as well-established.
    And there's Joy Christian trying to dispel quantum mysticism, and he got roasted.
    ???
    Especially when bona-fide physicists can't put a paper up on the arXiv.
    Like who?
    Especially when there's been no real scientific progress for decades,
    What hooey. Maybe not progress in accepting Farsight physics, but certainly plenty of progress.
    and when the fabulous Higgs boson contradicts E=mc².
    Demonstrably false.
    The public have lost faith, and interest, and so have politicians. Which is why we're seeing funding cuts I suppose. I always voiced my opposition to them, but you know what lpetrich? Maybe Unzicker is right. Cut all funding for theoretical physics. Have a clear out. I mean, why should my tax dollars pay for quacks to peddle woo and call people names and get in the way of scientific progress?
    So you are objecting to the politicians' not financing Farsight physics?
    By the way, I wasn't quite clear what you thought of my review of his book.
    I was responding to Alexander Unzicker's bellyaching about the Standard Model, bellyaching that you seem to endorse. Most of his criticisms are baseless, and I think that Peter Woit was right about him. To repeat,
    Unzicker’s obsessive idea, shared with innumerable other cranks, is that any scientific theory beyond one intuitively clear to them must be nonsense. Similarly, any experimental result beyond one where they can easily understand and analyze the data themselves is also nonsense.
    Farsight, that seems awfully familiar...
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    Quote Originally Posted by lpetrich View Post
    I consider that a speculation on his part, not something to be treated as well-established.
    If I came up with stuff like that you'd rip me to shreds.

    Quote Originally Posted by lpetrich
    ???
    Look up Joy Christian. He featured in New Scientist years back in Quantum untanglement: Is spookiness under threat?. Basically he was saying rotations do not commute, and when you take this into account, spookiness evaporates. He's been subject to heavy personal criticism, do your own research

    Quote Originally Posted by lpetrich
    What hooey. Maybe not progress in accepting Farsight physics, but certainly plenty of progress.
    Scientific progress has been scant. There's a growing list of books saying so.

    Quote Originally Posted by lpetrich
    So you are objecting to the politicians' not financing Farsight physics?
    No, I've always objected to HEP funding cuts in the past.

    Quote Originally Posted by lpetrich
    I was responding to Alexander Unzicker's bellyaching about the Standard Model, bellyaching that you seem to endorse. Most of his criticisms are baseless, and I think that Peter Woit was right about him...
    Woit's criticism was baseless. He shirked the issues, and attacked the man. It was a hatchet job, not an honest review.
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    Quote Originally Posted by Farsight View Post
    Woit's criticism was baseless. He shirked the issues, and attacked the man. It was a hatchet job, not an honest review.
    Compare that to the behavior of someone who ignores Einstein's actual physics work and instead presents him as some sort of authority figure who can do no wrong in his out-of-context statements.
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  95. #95  
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    (a Universe made of math...)
    Quote Originally Posted by Farsight View Post
    If I came up with stuff like that you'd rip me to shreds.
    Boo hoo hoo hoo hoo.

    Look up Joy Christian. He featured in New Scientist years back in Quantum untanglement: Is spookiness under threat?. Basically he was saying rotations do not commute, and when you take this into account, spookiness evaporates. He's been subject to heavy personal criticism, do your own research
    I'm not going to follow that search-engine-result link. As to Joy Christian being some sort of martyr, he is being criticized because he's wrong about something. Shtetl-Optimized » Blog Archive » Bell’s-inequality-denialist Joy Christian offers me $200K if scalable quantum computers are built, Quantum Randi Challenge: Help Perimeter Physicist Joy Christian To Collect The Nobel Prize

    Scientific progress has been scant. There's a growing list of books saying so.
    News to me.

    Woit's criticism was baseless. He shirked the issues, and attacked the man. It was a hatchet job, not an honest review.
    I don't see how he shirked the issues. He seems to have found AU's criticisms too silly to be worth going into detail about. In any case,
    Unzicker’s obsessive idea, shared with innumerable other cranks, is that any scientific theory beyond one intuitively clear to them must be nonsense. Similarly, any experimental result beyond one where they can easily understand and analyze the data themselves is also nonsense.
    seems like it also applies to Farsight physics.
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  96. #96  
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    Look at what you've said above, Loren. It's all ad-hominems. Not sincere logical discussion of the physics and the evidence. Think about it. In order to defend the standard model, you're just slinging mud. Don't think the public and politicians don't notice that sort of thing. Don't think they don't notice what Unzicker and others have been saying. Don't think they're stupid.

    But you do, don't you?
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    I've made plenty of non-ad-hominem criticisms of Alexander Unzicker's claims. What more do you want?

    I think that Peter Woit is right about AU, and he notes that AU claims that modern physics went astray when it started embracing less-than-obvious symmetries like isospin. Space-time symmetries are apparently OK and electromagnetic gauge symmetry might be OK, but the other Standard-Model ones are not OK. What does he propose instead of quark flavor symmetries and QCD and electroweak gauge symmetries? It's hard to tell.
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  98. #98  
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    I don't think Peter Woit is right about AU, I think he's been dishonest about him. Woit is very critical of string theory, but he won't permit criticism of the standard model. Like the people he criticises, he's into propaganda and censorship too. Sadly this sort of thing is going to catch up with HEP. It already is, which is why there's funding issues in the USA. It's like a long slow Hari-Kiri.
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    There is a difference between not permitting criticism of something and thinking that some criticisms of it are erroneous. I don't see any evidence that Peter Woit is trying to suppress criticism of the Standard Model.
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    Because he's deleted it!

    Propaganda and censorship is rife, Loren. And it's getting worse. What's incredible is that the people doing it don't seem to know that nowadays we have this thing called the internet.
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