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Thread: 1/h as a coupling constant

  1. #1 1/h as a coupling constant 
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    I had an odd thought this morning in my car on the way to work. Would the inverse of Planks constant represent a sort of coupling constant between the micro and macro worlds. As h tends to zero the coupling becomes infinite so to speak. I got as far as finding that the fine structure constant is indeed inversely proportional to it and that that it also comes into gravity type equations. Can anyone shed more light on this? If it does represent a coupling constant, what between?
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    I don't know how 1/h represents a coupling constant. Planck's constant of action h features in photon energy E=hf or momentum p = h/λ, but I don't know how either it or its reciprocal is much like the fine structure constant α = e²/2ε0hc.

    It is interesting though. I don't know if you ever saw Leonard Susskind giving a Higgs lecture, but he was talking about Planck's constant and angular momentum, and he rolled his finger round and round. It makes me think of this ocean-wave animation. For a high-frequency wave you roll your finger round fast, for a low-frequency wave you roll your finger round slow. But you roll it round the same path. The dimensionality of action can be stated as momentum x distance, as if there's a set distance which is something to do with the quantum nature of light. I'm not sure what. But it's like the waves are all the same height, no matter what their wavelength. And lummee, when you look at pictures of the electromagnetic spectrum, that's what you see. A height is a distance, and the reciprocal of distance is the diopter which makes me think of the optical Fourier transform which makes me think of the dual slit experiment. But like I said I can't see how 1/h represents a coupling constant. Maybe somebody else can say something.
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    Thanks for giving it some thought. My point about the fine structure constant was only that 1/h appears in it and I am wondering how many constants in it you can set to be equal to 1 at the same time.
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  4. #4  
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    Quote Originally Posted by Jilan View Post
    Thanks for giving it some thought. My point about the fine structure constant was only that 1/h appears in it and I am wondering how many constants in it you can set to be equal to 1 at the same time.
    The constraint is that alpha (the fine structure constant), being a fundamental dimensionless constant, has the same value in all systems of units. So, you can pick any three from the set ε0, c, ħ and e, and fix them at whatever values you prefer; the fourth is then fixed by alpha.
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    Thanks btr, it's pretty clear when you put it like that. So any one of them could be a fundamental coupling constant?
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  6. #6  
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    Quote Originally Posted by Jilan View Post
    Thanks btr, it's pretty clear when you put it like that. So any one of them could be a fundamental coupling constant?
    Yep, basically. The simplest and most common choice in theoretical and particle physics is to keep e around as the photon-to-electrons coupling constant, and then get rid of the other constants by adopting some flavour or other of natural units. There's no problem in principle with making a different choice, but there's no advantage either.
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    Cough. I forgot to mention something: the fine structure constant is a "running" constant. Which means it isn't constant. It's often given like this:



    But see NIST:

    "...at an energy corresponding to the mass of the W boson (approximately 81 GeV, equivalent to a distance of approximately 2 x 10-18 m), α(mW) is approximately 1/128 compared with its zero-energy value of approximately 1/137. Thus the famous number 1/137 is not unique or especially fundamental."

    Note though that conservation of charge ought to tell you that e does not vary. And if e doesn't vary, then ε0, c, and/or ħ has to vary. Sounds novel I know, but have a look at this: Can GPS find variations in Planck's constant? - physicsworld.com .
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    Farsight, I have come across this too. What does it actually mean? Is this generally accepted?
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    Then there is the strange equivalence between the information in a black hole and the area of the event horizon with the number of bits equivalent to the area of the event horizon when it's measured in Planck units. How on earth does that fit into it? Farsight, you were reminded of waves, I am reminded of ROM and RAM.
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    I don't know Jilan. I'd say that the running of the fine structure constant is accepted and correct. I'd also say that variations measured by Webb et al (see Changes spotted in fundamental constant - physicsworld.com ) are correct but are disputed. Then I'd say variations in c (see arXiv) are correct but hotly disputed. Then since you could claim that ε0 varies. But as for h varying, E=hf and conservation of energy suggest to me it doesn't. But don't quote me on that.

    Quote Originally Posted by Jilan
    Then there is the strange equivalence between the information in a black hole and the area of the event horizon with the number of bits equivalent to the area of the event horizon when it's measured in Planck units. How on earth does that fit into it? Farsight, you were reminded of waves, I am reminded of ROM and RAM.
    I'm an IT guy. I'm not moved by physicists and cosmologists talking about information. Especially when it comes to black holes and "the information paradox". There are no paradoxes.
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    Btr, for some reason I cannot quote your post #6. Thanks for that. I see exactly what you are saying. I guess the only advantage might be in how it allows us see things from a different angle. My instinct is that h is more fundamental than e as it also appears in other places that e doesn't.
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    Uhh, I edited my post Jilan. You might not like it any more.
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    I still like it, you can explain it to me then!
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    It's the sort of thing that takes a while Jilan. Have a peek at the Hawking radiation thread and then see the time travel thread. The explanation needs to cover time, then the coordinate speed of light, then gravity, then black holes, then Friedwardt Winterberg's firewall. Then the information paradox isn't a paradox any more. Paradoxes never are. And apart from that, I've got to go. Nice talking to you. Interesting stuff this physics, isn't it?
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    Quote Originally Posted by Jilan View Post
    Farsight, I have come across this too. What does it actually mean? Is this generally accepted?
    It is predicted by theory and confirmed experimentally. The simplest way of putting it is that the apparent charge of a particle increases very slightly if you get really close to it, as though it were partially shielded at long distances. This means that if you collide two electrons at very high energies, so they approach each other more closely, you'll get a higher effective coupling constant than at low energies. For everyday energies, i.e. anything you'll ever come across, alpha = 1/137.04 is perfectly OK. At energies of around 80 GeV (at which point the electrons would collide at a tiny fraction under the speed of light), you find that the value of alpha you need to use is about 1/128.95 (less than 10% higher).

    I have to disagree with Farsight about e not varying as a result of conservation of charge, as that is a bit of a non sequitur. You can of course choose to adopt a system of units, as we saw above, in which e has some fixed value by definition, and since alpha varies whatever the units you'd have to make either Planck's constant, the speed of light or the vacuum permittivity vary. Any of those would be a valid choice, and equivalent to the others in terms of observable physics. However, by near-universal convention, we keep all of those fixed and say that e varies instead.

    I should clarify something: conservation of charge, in quantum field theories at least, is (a bit loosely) the statement that the number of elementary particles with +1 units of charge minus the number with -1 units of charge is constant. It is a statement about whole numbers, and does not care about units invented by humans. It certainly doesn't care if we choose to use the natural units in which e varies, as in such units e is simply a measure of how strongly a particle with charge +1, say, will couple to a photon, not anything to do with how many positive or negative charges there are.
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    Quote Originally Posted by Jilan View Post
    Btr, for some reason I cannot quote your post #6. Thanks for that. I see exactly what you are saying. I guess the only advantage might be in how it allows us see things from a different angle. My instinct is that h is more fundamental than e as it also appears in other places that e doesn't.
    That itself is just an artefact of our unit conventions. If you put everything in terms of Planck units, you eliminate all such arbitrary factors and are left only with truly fundamental constants, such as alpha, or the ratios of elementary particle masses.
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    Thanks btr, the shielding effect - is that due to virtual particles?
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    Farsight, thanks I have been following these threads, but they don't mention how h is related to information which is what I'm trying to understand better.
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    I am making some progress. 1/h is the maximum processing speed per joule of energy, the Bremermann limit. I think this is what I was looking for. This is a nice short paper that discusses a correction to it.
    http://arxiv.org/pdf/0910.3424.pdf
    I would understand this to mean that you cannot make a processing platform run faster than the one that it is running on ( if you get my drift).
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    Quote Originally Posted by Jilan
    Farsight, thanks I have been following these threads, but they don't mention how h is related to information which is what I'm trying to understand better.
    OK noted. I looked at that short paper. I can't offer anything re this information I'm afraid.
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    Quote Originally Posted by Jilan View Post
    Thanks btr, the shielding effect - is that due to virtual particles?
    You can describe it in those terms, and people usually do. There's certainly nothing wrong with looking at it in that way.

    Alternatively, you can avoid speaking about virtual particles and say that when you have an electron sitting there in space, it's electromagnetic field causes a slight polarisation of the charge-carrying quantum fields in the space around it - i.e. the lepton fields, quark fields, etc. - rather like a charged particle does when it's sitting in an ordinary dielectric material, and this partially cancels the effects of the bare charge at long distances.

    As crazy as this sounds, this vacuum polarisation phenomenon is what the standard model demands, and the predicted size of the effect at various distance/energy scales is in very good agreement with experiment.
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    Thanks btr. What determines the strength of these fields and the strength of this effect? Is there any relation to the dielectric permittivity of the vacuum? I have been unsuccessfully trying to find an answer to this for a while.

    I am thinking this morning that if the Et uncertainty is related to processing speed does the px uncertainty relate to anything too? Maybe storage capacity?
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    Quote Originally Posted by jilan
    I am thinking this morning that if the Et uncertainty is related to processing speed does the px uncertainty relate to anything too? Maybe storage capacity?
    I'm an IT guy by trade. I like to think I know my stuff when it comes to IT. And that I know a fair bit of physics. But I have to say that the "forced marriage" of information and physics leaves me cold.

    Quote Originally Posted by jilan
    Thanks btr. What determines the strength of these fields and the strength of this effect? Is there any relation to the dielectric permittivity of the vacuum? I have been unsuccessfully trying to find an answer to this for a while.
    Yes there is. See the vacuum polarization article that btr linked to? It says this:

    "In quantum field theory, and specifically quantum electrodynamics, vacuum polarization describes a process in which a background electromagnetic field produces virtual electron–positron pairs..."

    And do you recall the NIST article I linked to? It says this:

    "According to quantum electrodynamics (QED), the relativistic quantum field theory of the interaction of charged particles and photons, an electron can emit virtual photons that can then emit virtual electron-positron pairs (e+, e-). The virtual positrons are attracted to the original or "bare" electron while the virtual electrons are repelled from it. The bare electron is therefore screened due to this polarization..."

    This is dreadfully misleading. Virtual particles are virtual. They aren't real particles. An electron doesn't emit photons which emit electrons and positrons. Have a look at Matt Strassler's blog: and note this: "A virtual particle is not a particle at all. It refers precisely to a disturbance in a field that is not a particle". Then see Einstein talking about field theory and note that he refers to a field as "a state of space". So these virtual particles are really a disturbance in space. They are caused by the electron, which has the charge that it has. The electron's charge doesn't change just because you move around. If you move away from it and perceive the charge to change it's because of something to do with the space you're in. Notwithstanding what btr said above about near-universal convention, conservation of charge means e does not vary. And of course conservation of energy and E=hf means h isn't in the frame. But α = e²/2ε0hc and c = √(1/ε0μ0) means vacuum permittivity is in the frame.
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    Farsight, there is no "forced marriage". Entropy and information (or lack of it) are closely related. I can appreciate your lack of enthusiasm if you have it as a job (I don't like crunching numbers when I get home, guess what I do all day!)

    Someone explained once, (perhaps on here ?) that a particle is neither completely virtual nor completely real, but that there is a continuum between the two with the distinction really depending on how short lived or how stable the disturbance is. Further more a "real" particle needs to slightly virtual to be able to interact with another one.
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    I have a lack of enthusiasm for information in a physics context because it isn't something that has any fundamental existence. It's essentially a "pattern" in something that does. In similar vein entropy is essentially "sameness". Check out the heat death of the universe. The energy density is the same everywhere, so there's no available energy.

    See what Matt Strassler said about virtual particles. Particles like photons are completely real. Virtual photons aren't short-lived real photons. They're "field quanta". Like you divide the electromagnetic field up into little squares and say each is a virtual particle.
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    Photons would represent the limiting case I guess. Would not all photons be virtual anyway as their lifetime in their frame of reference is zero?
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  27. #27  
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    Quote Originally Posted by Farsight View Post
    I have a lack of enthusiasm for information in a physics context because it isn't something that has any fundamental existence.
    Maybe information is the only thing that does have a fundamental existence.
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    Quote Originally Posted by Jilan
    Would not all photons be virtual anyway as their lifetime in their frame of reference is zero?
    No. A real photon is a real thing that propagates through space at the speed of light. A virtual photon isn't a photon. Read Matt Strassler's article. Or have a look at the near and far field on wiki and note the bit that says this:

    "In the quantum view of electromagnetic interactions, far field effects are manifestations of real photons, while near field effects are due to a mixture of real and virtual photons".

    Or dig up some old paper such as Evanescent modes are virtual photons. The evanescent wave is essentially a "standing" electromagnetic wave that isn't going anywhere. You divide it up into little chunks and say each one is a field quantum. It's a bit like the virtual photons are the accounting units for your calculations. Like pennies are the accounting units of your financial calculations. If you pay a cheque into your bank account, there isn't some hailstorm of real pennies flying into some vault somewhere.

    Quote Originally Posted by KJW
    Maybe information is the only thing that does have a fundamental existence.
    And maybe you'll let me know when somebody discovers some fundamental particles of information.
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    Quote Originally Posted by Farsight View Post
    And maybe you'll let me know when somebody discovers some fundamental particles of information.
    Sure, but you may know them as "photons", "electrons", etc. Here's a challenge for you: Pick any fundamental particle and tell me what it truly is in the deepest sense.
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    Quote Originally Posted by Jilan View Post
    Thanks btr. What determines the strength of these fields and the strength of this effect?
    The simplest way of answering your question is that the strength of the effect depends on how influential virtual particle/antiparticle pairs of various types are in the Standard Model vacuum, which in turn depends on the energy scales we are probing in relation to the masses of those particle types.

    For example, at "medium" momenta which are large compared to the electron mass but smaller than the muon mass, the amount by which the "effective" fine structure constant αeff differs from the low-energy limit α0 is a function of the momentum scale involved, and the mass me of the electron (by which I mean the mass we measure at low energies). If the momentum transfer in a scattering process is p, you have something like this (in natural units):


    (That's very approximate, by the way; it's a "one-loop" correction.)

    At higher momenta, higher-mass leptons and even quarks start to enter into the equation. You could say that we are probing such tiny distance scales that we begin to "see" the effects of higher-energy virtual particle-antiparticle pairs.

    Quote Originally Posted by Jilan View Post
    Is there any relation to the dielectric permittivity of the vacuum? I have been unsuccessfully trying to find an answer to this for a while.
    Yes, you can view it that way. If you want to adopt units in which the coupling constant e, the speed of light and Planck's constant are all fixed, you would have to describe the running of alpha as a scale-dependent vacuum permittivity. There are authors who have done so.

    Quote Originally Posted by Jilan View Post
    I am thinking this morning that if the Et uncertainty is related to processing speed does the px uncertainty relate to anything too? Maybe storage capacity?
    Maybe some argument could be made along those lines. However, as I understand it, the Bremermann limit for processing speed, mentioned in the paper you linked to, is derived from an information density limit to begin with (the Bekenstein bound, which is a fascinating topic).

    Incidentally, I had a (admittedly brief) read of Gorelik's paper. For now I've got my doubts about the argument presented there; just because N operations per unit time are happening in a certain lump of matter, it doesn't follow that the duration of any particular operation is 1/N (since operations can happen in parallel). Perhaps their conclusion is correct, but I'm not convinced. I'll have to go back and read it properly at some point though.
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    Thanks btr, that's a good explanation. I'll find out about the Bekenstein bound, cheers!

    Edit, a bit later.... Wow, that's bang,on topic! There's that 1/h again! The equation looks very much like the px uncertainty relation doesn't it?
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    Quote Originally Posted by KJW
    Sure, but you may know them as "photons", "electrons", etc. Here's a challenge for you: Pick any fundamental particle and tell me what it truly is in the deepest sense.
    Hmmmn. A photon is a soliton pulse of four-potential that propagates through space without dissipating. Note that it isn't localised, just as a seismic wave isn't localised. A seismic wave might run from A to B, but houses well away from the A-B line fall down. In similar vein the photon takes many paths. See post #5 on this thread where Markus and I were talking about field being derivative of potential. I referred to Percy Hammond and curvature too. I've referred to LIGO somewhere too wherein space waves, and I've said that an electromagnetic wave isn't all that different to a gravitational wave in that respect. See [0803.2596] How Long Is a Photon? and physicsworld for the "lemon" shape. But it's important to note that it isn't some billiard-ball particle shaped like a lemon. It's more like you start with a stiff lattice representing the photon field, then climb into it, grab it, and push up like a weightlifter. The lattice now has a lemon-like distortion in it, and there is no outer edge or surface to this distortion. There was some CERN animation that showed this kind of thing, but it had a "billiard ball" as well as a bulge in the lattice and I can't find it any more. Maybe btr can point to some lattice animations.
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    Farsight, if a seismic wave doesn't run under a house, what makes it fall down?
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    Farsight, sorry but I'm full of questions tonight. If virtual particles are just mathematical constructs how would you classify the Z and W bosons, real or virtual?
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    Quote Originally Posted by Jilan
    Farsight, if a seismic wave doesn't run under a house, what makes it fall down?
    Could you rephrase that? What I was trying to get demonstrate was the way a photon isn't local. Another way is think of an ocean wave. It's say 1m high. But what lies beneath demonstrates its non-local nature. Have a look at this.

    Quote Originally Posted by Jilan
    Farsight, sorry but I'm full of questions tonight. If virtual particles are just mathematical constructs how would you classify the Z and W bosons, real or virtual?
    I don't know what to say about that. Sorry.
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  36. #36  
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    Quote Originally Posted by Farsight View Post
    A photon is a soliton pulse of four-potential that propagates through space without dissipating.
    Thank you for accepting the challenge.

    Now, what is a "four-potential"? (What is it truly in the deepest sense?)
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    Energy.
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  38. #38  
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    Quote Originally Posted by Farsight View Post
    Energy.
    So, what you're saying is that photons are soliton pulses of energy. Photons travel at a fixed speed of , but most objects we see around us travel at rather slow variable speeds. Are they also soliton pulses of energy? If so, then you have the problem of manifestly different objects being the same thing.

    Also, what is "energy"? (What is it truly in the deepest sense?)

    So far, I've asked you what things are "truly in the deepest sense", yet your replies haven't been "truly in the deepest sense" because I've found it necessary to enquire deeper than what you are implying is deepest. Where do you think this enquiry is going to end? Do you really think there is a physical notion that is truly fundamental in the deepest sense?
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    Quote Originally Posted by KJW
    So, what you're saying is that photons are soliton pulses of energy. Photons travel at a fixed speed of c, but most objects we see around us travel at rather slow variable speeds. Are they also soliton pulses of energy?
    In a way. You might prefer some other choice of words, involving wavefunction or spin or the wave nature of matter. But don't forget that you can diffract electrons, and neutrons, and buckyballs.

    Quote Originally Posted by KJW
    If so, then you have the problem of manifestly different objects being the same thing.
    It doesn't seem like a big problem. A photon is a wave propagating linearly at c, an electron is a wave going round and round at c. That sort of thing.

    Quote Originally Posted by KJW
    Also, what is "energy"? (What is it truly in the deepest sense?)
    Space.

    Quote Originally Posted by KJW
    So far, I've asked you what things are "truly in the deepest sense", yet your replies haven't been "truly in the deepest sense" because I've found it necessary to enquire deeper than what you are implying is deepest.
    I'm sorry KJW. I've tried to give it to you step by simple step.

    Quote Originally Posted by KJW
    Where do you think this enquiry is going to end? Do you really think there is a physical notion that is truly fundamental in the deepest sense?
    Yes I do. Space is the end of the line. It isn't nothing, instead it something that can sustain fields and waves. It isn't made out of anything, instead things are made of waves in it. Only potential is more fundamental than field, which is the derivative of potential, so we talk about a pulse of potential. Which is like a propagating region of higher-pressure space in space. Look at the stress-energy-momentum tensor on Wikipedia. See the depiction on the right? See the energy-pressure diagonal? Space has its innate pressure and it has a volume. The dimensionality of energy is pressure x volume. A gravitational field is like a pressure gradient in space. A photon has a gravitational field. If you have a region of space, how do you increase the pressure? See the shear stress in the stress-energy-momentum tensor? Shear stress! Think elastic continuum. Or just think ghostly elastic jelly, then think hypodermic. How do you increase the pressure? You inject more jelly. You're adding energy, only the jelly is space too. So at the fundamental level I can't distinguish space and energy. It's the end of the line. It's where I hit the buffers.
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    Quote Originally Posted by Farsight View Post
    Space is the end of the line. It isn't nothing, instead it something that can sustain fields and waves. It isn't made out of anything, instead things are made of waves in it.
    I can still ask: What is space? Intuitively, space is like a theatre in which everything happens, whereas energy is like the things that happen within the theatre of space. So it makes no sense at the intuitive level to say that energy is space. Different locations within the space differ by the amount of energy-density there. But how does that difference manifest itself given that to invoke differences in "energy-density" would be to create a meaningless circularity?

    The point is that terms like: stress, energy, momentum, pressure, force, mass, gravitation, etc, have to be precisely and non-circularly defined in order for those terms to be in any way meaningful. The claim I am making is that the only way to do that is to take ourselves out of the realm of physics and put ourselves in the realm of mathematics where physical notions can be properly defined in terms of the information they provide to the observer.
    A tensor equation that is valid in any coordinate system is valid in every coordinate system.
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    Quote Originally Posted by KJW
    I can still ask: What is space? Intuitively, space is like a theatre in which everything happens
    You already know about curved spacetime, so you shouldn't be too surprised to hear Einstein saying space is not nothing. See his 1920 Leyden Address:

    "According to this theory the metrical qualities of the continuum of space-time differ in the environment of different points of space-time, and are partly conditioned by the matter existing outside of the territory under consideration. This space-time variability of the reciprocal relations of the standards of space and time, or, perhaps, the recognition of the fact that "empty space" in its physical relation is neither homogeneous nor isotropic, compelling us to describe its state by ten functions (the gravitation potentials gmn), has, I think, finally disposed of the view that space is physically empty".

    Then there's his 1929 History of Field Theory where he says a field is "a state of space". Space is a thing, not just the place where things are. A gravitational field is where a concentration of energy usually in the guise of matter has "conditioned" the surrounding space. It hasn't curved it, because space and spacetime aren't the same thing, but that's not the point. It has conditioned it, it has altered it, it has changed it, and the effect diminishes with distance. Because space isn't nothing. There's a shear-stress term in the stress-energy-momentum tensor. Space waves. And the closest you can get to imagining what it's like, is a gin-clear ghostly elastic jelly.

    Quote Originally Posted by KJW
    whereas energy is like the things that happen within the theatre of space.
    Go back to curved spacetime. How do you curve it? You insert a concentration of energy. Imagine your space is some kind of gin-clear ghostly elastic jelly marked out with lattice lines. Now slip a needle into the middle, and inject more jelly. The jelly bulges outward. Your lattice lines are curved, aren't they? As it happens this isn't quite the right analogy, but it gets the point across.

    Quote Originally Posted by KJW
    So it makes no sense at the intuitive level to say that energy is space. Different locations within the space differ by the amount of energy-density there.
    But you can't say this is the space and this is the energy. You just can't separate the two. You might just as well call it the space-density.

    Quote Originally Posted by KJW
    But how does that difference manifest itself given that to invoke differences in "energy-density" would be to create a meaningless circularity?
    I don't think it's some meaningless circularity, it's just admitting you've reached the end of the line.

    Quote Originally Posted by KJW
    The point is that terms like: stress, energy, momentum, pressure, force, mass, gravitation, etc, have to be precisely and non-circularly defined in order for those terms to be in any way meaningful. The claim I am making is that the only way to do that is to take ourselves out of the realm of physics and put ourselves in the realm of mathematics where physical notions can be properly defined in terms of the information they provide to the observer.
    There's no harm in using mathematical definitions. But don't forget the physics. Think about what words like stress and pressure are telling you. It's space that being stressed. It's space that's under pressure and has the radial length contraction. Because it's elastic! Have a look at G S Sandhu's Elastic Continuum Theory of Nature. I wouldn't say it's all right, but I would say it's worth looking at. Space is elastic. Space waves. We call that light. We can make matter out of it. And all the rest is just details.
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    I can make a far simpler idea of curved space:

    Take two apples, put them high up in the atmosphere some distance apart and drop them, they don't fall straight down, but move closer together because they are both falling to the center of the Earth.
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    Replace the Earth with a long rod of matter and that doesn't work any more. You have confused curved space with the spherical Earth.
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    Um, like... gravity... center of mass... Earth?


    I could have shown a picture for gravitational lensing, but I preferred apples.

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    Quote Originally Posted by Farsight View Post
    You already know about curved spacetime
    Yes I do. So when I ask what spacetime curvature is, I'm not just looking for a regurgitation of its definition, or a link to such. Indeed, I'll save you the trouble and get to the point. In its standard form, Riemann curvature is a particular expression in terms of the metric tensor and its partial derivatives up to second order. The metric is an expression of distance between nearby points of spacetime. But what is "distance"? Distance (in spacetime) is what is measured by rulers and clocks. A measurement is information obtained about the subject of interest. However, rulers and clocks are physical objects made of the same notion that we are ultimately measuring: spacetime curvature and hence the metric. Because we are using physical objects to measure physical objects, the only information we can gain about the object being measured is how they relate to other objects. A relationship is an abstract notion that is ultimately nothing more than information.


    Quote Originally Posted by Farsight View Post
    Go back to curved spacetime. How do you curve it? You insert a concentration of energy.
    But given that energy is the curvature of spacetime, saying that you insert a concentration of energy is saying nothing more than you curve spacetime by curving spacetime, a meaningless circularity.


    Quote Originally Posted by Farsight View Post
    Imagine your space is some kind of gin-clear ghostly elastic jelly marked out with lattice lines. Now slip a needle into the middle, and inject more jelly. The jelly bulges outward. Your lattice lines are curved, aren't they? As it happens this isn't quite the right analogy, but it gets the point across.
    I'm not looking for a mere analogy. I'm looking for a precise meaningful description.


    Quote Originally Posted by Farsight View Post
    There's no harm in using mathematical definitions. But don't forget the physics.
    What I'm saying goes beyond simply having a mathematical definition. What I'm talking about is having a truly meaningful ontology.
    A tensor equation that is valid in any coordinate system is valid in every coordinate system.
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    KJW, you said that "given energy is the curvature of space-time". I have not come across this before, though I have wondered if this might be the case due to the nice symmetry that would result. Do you have a good suggestion of where to read about this?
    Thanks. Jilan.
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    Quote Originally Posted by Beer w/Straw View Post
    The apple certainly is easier to relate to. So to an outside observer two apples would be seen to approach each other because the space between the shrinks? One might equally conclude that there was a force pushing them together...maybe?
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    Two objects falling freely near Earth converge toward the center of Earth because of the curvature of space near Earth. Far from Earth (and other masses) , space is flat and parallel paths remain parallel. Close to Earth , the parallel paths begin to converge because space is curved by Earth's mass.

    ~Fundamentals of Physics 8th Edition.

    In general relativity, a geodesic generalizes the notion of a "straight line" to curved spacetime. Importantly, the world line of a particle free from all external, non-gravitational force, is a particular type of geodesic. In other words, a freely moving or falling particle always moves along a geodesic.

    In general relativity, gravity can be regarded as not a force but a consequence of a curved spacetime geometry where the source of curvature is the stress–energy tensor (representing matter, for instance). Thus, for example, the path of a planet orbiting around a star is the projection of a geodesic of the curved 4-D spacetime geometry around the star onto 3-D space.
    Geodesics in general relativity - Wikipedia, the free encyclopedia


    :EDIT:

    Sorry if it looks like spam, but I felt a need to be thorough. My posts are generally one sentence or two
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    Thanks for the clarification, though I did understand your original post ( my posts are really short too , sorry !). I was just thinking about how you could differentiate between the two alternatives.
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    You might be interested in Gravity Probe B

    GB-B 14-Minute VIdeo Overview
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    Quote Originally Posted by Jilan View Post
    KJW, you said that "given energy is the curvature of space-time". I have not come across this before, though I have wondered if this might be the case due to the nice symmetry that would result. Do you have a good suggestion of where to read about this?
    Thanks. Jilan.
    I'm assuming you are familiar with the Einstein equation, so I guess the issue is whether energy-momentum causes spacetime curvature or is spacetime curvature. The way I see it, energy-momentum is the physical quantity that is represented mathematically by the Einstein tensor field. One thing to consider is what the Einstein tensor field looks like viewed from inside the spacetime. The notion that energy-momentum causes spacetime curvature seems to require extra explanation compared to simply being spacetime curvature. After all, how does anything cause spacetime curvature? Also, the notion implies that energy-momentum is distinct from spacetime curvature. That is, if energy-momentum isn't spacetime curvature itself, then what is 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 Beer w/Straw View Post
    You might be interested in Gravity Probe B

    GB-B 14-Minute VIdeo Overview
    Oh, this is great, many thanks!

    Perfectly smooth gyroscopes sent into orbit to measure frame dragging. The spheres are as smooth as the earth would be if the mountains were only 8 foot high! The best bit is how the probe protects the gyros from the cosmic rays and then tracks the motion of one of them so it can follow it on its perfect orbit. Very clever stuff.
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    KJW, Would that require that every tiny particle was actually a very large spatially extended sort of entity. Now why does this ring a bell somewhere? Oh yes quantum mechanics!
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