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Thread: What is position?

  1. #1 What is position? 
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    Stationary particles are prohibited by the uncertainty principle otherwise both position and momentum would be precisely determined together. So everything must always move. This means there is no way to measure a fixed position! The particle and measuring device both move before the measurement is completed. Neither can there be any lengths since there is no way to measure the positions at the ends. So what does "position" in the uncertainty principle mean then if there is no such thing as position and everything always must move? The uncertainty principle appears to be self-contradictory.
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    Quote Originally Posted by JohnMiddlemas View Post
    Stationary particles are prohibited by the uncertainty principle otherwise both position and momentum would be precisely determined together. So everything must always move. This means there is no way to measure a fixed position! The particle and measuring device both move before the measurement is completed. Neither can there be any lengths since there is no way to measure the positions at the ends. So what does "position" in the uncertainty principle mean then if there is no such thing as position and everything always must move? The uncertainty principle appears to be self-contradictory.
    You are confusing what is and how accurately things can be measured.
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  3. #3 Cartesian coordinate assumption 
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    Quote Originally Posted by mathman View Post
    You are confusing what is and how accurately things can be measured.
    Another way of looking at it. The Schrodinger wave equation, from which the uncertainty principle is derived, assumes and uses the time dimension and the cartesian coordinate system applied to space as we know it. E.g. 3D coordinates like (2,1,4). An object at this point must be able to remain there for at least a small amount of time for (2,1,4) to have meaning. But according to the uncertainty principle no object can ever be stationary and so (2,1,4) cannot have meaning. Objects simply cannot have coordinates if everything always must move. So the cartesian system is seen to be a false assumption of the wave equation.

    The idea of a coordinate is derived from the macroscopic illusion of stationary points and objects, and cannot apply to a reality where everything must always move.
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    Quote Originally Posted by JohnMiddlemas View Post
    Stationary particles are prohibited by the uncertainty principle otherwise both position and momentum would be precisely determined together. So everything must always move. This means there is no way to measure a fixed position! The particle and measuring device both move before the measurement is completed. Neither can there be any lengths since there is no way to measure the positions at the ends. So what does "position" in the uncertainty principle mean then if there is no such thing as position and everything always must move? The uncertainty principle appears to be self-contradictory.
    You are thinking along the right lines, but the conclusion is not so bleak. In quantum mechanics, particles don't have positions. "Position" isn't a property of a particle at all, it is an operator which acts on quantum states, which allows us to determine the probabilities of experimental outcomes. The same goes for all observable quantities in quantum mechanics, including momentum.

    By projecting a quantum state onto sharply-localised position eigenstates (i.e. by construction the position wavefunction), you can, with a small amount of mathematics, determine the probability that a position measurement will have an outcome in any given range (i.e. you can determine the probability density distribution for position measurements). Similarly, you can construct a momentum-space wavefunction by projecting the very same state onto momentum eigenstates (which look like plane waves), and determine the probability density distribution for momentum measurements.

    The two equivalent ways of looking at a state - either as a sum of sharply-localised Dirac delta functions, or as a sum of plane waves - are related mathematically by a Fourier transform. It follows, from completely general properties of Fourier transforms, that the spread (more precisely, the standard deviation) of the probability distribution in position space is inversely proportional to the spread of the momentum distribution, which is where Heisenberg's position-momentum uncertainty principle comes from.
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    Quote Originally Posted by btr View Post
    You are thinking along the right lines, but the conclusion is not so bleak. In quantum mechanics, particles don't have positions. "Position" isn't a property of a particle at all, it is an operator which acts on quantum states, which allows us to determine the probabilities of experimental outcomes. The same goes for all observable quantities in quantum mechanics, including momentum.

    By projecting a quantum state onto sharply-localised position eigenstates (i.e. by construction the position wavefunction), you can, with a small amount of mathematics, determine the probability that a position measurement will have an outcome in any given range (i.e. you can determine the probability density distribution for position measurements). Similarly, you can construct a momentum-space wavefunction by projecting the very same state onto momentum eigenstates (which look like plane waves), and determine the probability density distribution for momentum measurements.

    The two equivalent ways of looking at a state - either as a sum of sharply-localised Dirac delta functions, or as a sum of plane waves - are related mathematically by a Fourier transform. It follows, from completely general properties of Fourier transforms, that the spread (more precisely, the standard deviation) of the probability distribution in position space is inversely proportional to the spread of the momentum distribution, which is where Heisenberg's position-momentum uncertainty principle comes from.
    Thank you very much for the comprehensive and interesting reply. I had a look at the points you mentioned but I still can't clear the problem. You agree that particles don't have positions but also say that there are position measurements. I presume this is the collapse of the wavefunction idea, i.e. with no measurement there is no particle position but when measured then the wavefunction collapses and a position is marked.

    So I think that by position you mean measured position, e.g. the mark an electron makes when striking a detector.

    The trouble is that if a second measurement is done which hits the same mark it might not be the same position because everything must always move including the mark. Thus the term "position" becomes undefinable and cannot be used in any wavefunction in the first place. Even if you try and say the mark must be in a certain position range it still won't work because any range is undefinable if its end positions are undefinable.

    If everything must always move according to the uncertainty principle then there can be no notion of position at all. Any measurement is just a moving mark not a position. Maybe the wavefunction LHS needs rewriting as ih*d/dt(Psi(moving marks, t)).
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    Quote Originally Posted by JohnMiddlemas View Post
    Thank you very much for the comprehensive and interesting reply. I had a look at the points you mentioned but I still can't clear the problem. You agree that particles don't have positions but also say that there are position measurements. I presume this is the collapse of the wavefunction idea, i.e. with no measurement there is no particle position but when measured then the wavefunction collapses and a position is marked.
    Wavefunction collapse is the simplest way of looking at it, so let's go with that.

    Quote Originally Posted by JohnMiddlemas View Post
    So I think that by position you mean measured position, e.g. the mark an electron makes when striking a detector.
    Yes, precisely.

    Quote Originally Posted by JohnMiddlemas View Post
    The trouble is that if a second measurement is done which hits the same mark it might not be the same position because everything must always move including the mark.
    The position measurement I described is somewhat idealised, so the issue didn't arise. In practise, though, what you say is true; if we imagine that our position-detector is, say, some photographic film, and the particle detected is a photon, then the resolution of the detector is limited by the quantum uncertainty of the positions of the light-sensitive molecules embedded in the film. As it happens, the resolution is limited much more by the thermal motions of those molecules, their finite density on the film, whatever optics are involved, and so on.

    Quote Originally Posted by JohnMiddlemas View Post
    Thus the term "position" becomes undefinable and cannot be used in any wavefunction in the first place.
    The only issue we've really run into is the very important practical one that position measurements cannot be made with infinite precision. That doesn't mean that we can't define a purely mathematical position operator based on an abstract, mathematical notion of space, which acts on a bunch of other mathematical objects we call quantum states, and in this way build up an entirely mathematical theory (we need some other operators too, but that's just detail). We can most definitely do that! We can construct all of quantum mechanics on these seemingly abstract, mathematical foundations, with no problems whatsoever. The only remaining questions, from a pragmatic standpoint, are these:

    1. Does the theory, as a mathematical model, generate contradictions? No, it does not.
    2. Is it unambiguous how we should apply it to predict the result of any particular real-life experiment? Yes (although it is sometimes difficult), and we can even say what we should obtain from finite-resolution, noisy apparatus.
    3. Does the theory agree with what we actually measure? So far, it does so amazingly well.

    Could there be an even better theory in which the uncertainty of position measurements plays a deeper role (e.g. a theory which models spacetime in a fundamentally different way, using inherently "fuzzy" points or something)? Absolutely! However, so far there are no truly compelling candidates.
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    Quote Originally Posted by btr View Post
    Does the theory, as a mathematical model, generate contradictions? No, it does not.
    The theory LHS is ih*d/dt(Psi(x,y,z,t)). This assumes the existence of a cartesian space (x,y,z) of stationary points with a stationary origin and stationary axes. Call this axiom1. The uncertainty principle is then derived from the theory and seen to prohibit anything stationary, in theory or practice, so falsifying axiom1. Stationary items both exist by axiom1 but also cannot exist by the uncertainty principle.

    So the theory generates falsification of one of its own axioms and is therefore a contradictory theory.

    Maybe a contradictory theory can still give all those successful predictions you mention.
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    Quote Originally Posted by JohnMiddlemas View Post
    The theory LHS is ih*d/dt(Psi(x,y,z,t)). This assumes the existence of a cartesian space (x,y,z) of stationary points with a stationary origin and stationary axes. Call this axiom1.
    OK, so axiom 1 tells us that we have a flat, infinite, 4-dimensional spacetime (that's good enough for now).

    Quote Originally Posted by JohnMiddlemas View Post
    The uncertainty principle is then derived from the theory and seen to prohibit anything stationary, in theory or practice, so falsifying axiom1. Stationary items are both confirmed by axiom1 but also denied by the uncertainty principle.
    The uncertainty principle only concerns itself with the outcomes of measurements on quantum systems, and does not say anything about the underlying spacetime at all. Contrariwise, axiom 1 does not say anything about items (stationary or otherwise), it is just about spacetime. Spacetime points are not physical particles, and are not subject to quantum mechanics.

    Spacetime provides the domain for the single-particle wavefunction, and the position-momentum uncertainty principle tells us about certain properties of that wavefunction (in fact, it is virtually just a restatement of the theorem that a function and its Fourier transform cannot both be localised).
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    As I understand it the uncertainty principle is derived from the wave equation and one form is Dx * Dp >= h/2 where Dx is the standard deviation of position in the x direction and Dp is standard deviation of momentum in the x direction. From what I can assess the item modelled could be an electron, a photon, any other particle, a molecule or whatever physical item in the real world whatsover since everything is a wave.

    The principle is different from the observer effect, where a measurement of x affects p or vice versa, in that it is a fundamental property of all wave-like systems. It comes straight from the mathematics of the theory which is based on a Hilbert space rather than the cartesian system that I thought.

    For an item to be stationary momentum must be continually zero so Dp must be zero. That breaks the uncertainty principle. So every item must always move (an infinite Dx is undefinable).

    Hilberts axiom of Incidence (2) says "For every two points there exists no more than one line that contains them both".

    But if the origin point of the Hilbert space must always move then there are many lines between it and the item at point x.

    However, you are saying that the origin point is not an item, not a real thing, so it can be stationary right? According to Hilbert a point is a primitive concept which is not defined. This is a highly unsettling notion. If points remain undefined then the whole theory is undefined. To find x in reality you have to measure x relative to a physical origin which is a real thing and which must move.

    To me everything in the imagination like a Hilbert space for example should have a defined physical meaning otherwise it is just dreaming and could be a mental error. The only way the concept of a point can mean anything real is when it is a real item in the real world. Otherwise what is a Hilbert point?

    So I will say instead that the theory is contradictory or undefined. Either way it looks very shaky.

    The mystery of entangled particles supposedly having instantaneous communication on measurement, could be a mystery of the understanding of position. So I think it is well worth looking carefully at what is meant by position. So far it is not clear. It may be that a pointfree geometry is needed rather than a Hilbert space.

    I also look at it like this: I see motion and I see objects, but I do not see position nor do I see time, so I wonder if the latter two even exist. The best definitions seem to be position is what rulers measure, and time is what clocks measure. So position comes from objects and time comes from motion, just derived ideas not basic quantities.
    Last edited by JohnMiddlemas; 05-31-2014 at 04:37 PM.
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    Quote Originally Posted by JohnMiddlemas View Post
    As I understand it the uncertainty principle is derived from the wave equation and one form is Dx * Dp >= h/2 where Dx is the standard deviation of position in the x direction and Dp is standard deviation of momentum in the x direction.
    Strictly speaking, the uncertainty principle is more fundamental than the wave equation. It is derived from the fact that the position and momentum operators fail to commute. The wave equation comes about from writing SchrŲdinger's equation in terms of the position eigenstate basis for the space of states of the system.

    There are several other "uncertainty relations" which apply to other pairs of operators which fail to commute.

    Quote Originally Posted by JohnMiddlemas View Post
    From what I can assess the item modelled could be an electron, a photon, any other particle, a molecule or whatever physical item in the real world whatsover since everything is a wave.
    The basic model we've been talking about so far could describe any non-relativistic system with only positional degrees of freedom (or where we don't care about the other degrees of freedom). Photons need a properly relativistic theory, but slow-moving electrons are fine if we don't care about spin (and in any case, we could easily incorporate spin if we wanted to).

    Quote Originally Posted by JohnMiddlemas View Post
    The principle is different from the observer effect, where a measurement of x affects p or vice versa, in that it is a fundamental property of all wave-like systems.
    Yes. It does have something do to with measurements, in that it constrains what you can achieve with them (and is expressed explicitly in terms of what you can achieve with them). What it really says is that if you have an ensemble of systems prepared in the same state and measure momentum on some of them, and position on others, the product of the standard deviations of the momentum and position measurements will be greater than or equal to ħ/2.

    Quote Originally Posted by JohnMiddlemas View Post
    It comes straight from the mathematics of the theory which is based on a Hilbert space rather than the cartesian system that I thought.
    The states of the theory live in a (generally infinite-dimensional) complex Hilbert space.

    In any concrete problem you will find yourself referring to other spaces too (e.g. the 3-dimensional configuration space of a single non-relativistic particle without internal degrees of freedom, which in turn is derived from the 3-dimensional physical space we live in).

    Things like the position and momentum operators are still based on Cartesian coordinates in physical space (so, for example, px really does relate to momentum in the familiar x direction), but the things on which they operate live in the Hilbert space of states.

    Quote Originally Posted by JohnMiddlemas View Post
    For an item to be stationary momentum must be continually zero so Dp must be zero. That breaks the uncertainty principle. So every item must always move (an infinite Dx is undefinable).
    In practice, yes, although in theory there's no problem with considering momentum eigenstates with infinite uncertainty in position (these are basically plane waves). In fact, it is a very useful basis for the Hilbert space of states just mentioned. Switching between this basis and the position eigenstate basis is basically a Fourier transform (or inverse transform).

    Quote Originally Posted by JohnMiddlemas View Post
    Hilberts axiom of Incidence (2) says "For every two points there exists no more than one line that contains them both".

    But if the origin point of the Hilbert space must always move then there are many lines between it and the item at point x.
    The origin point of the Hilbert space of states never moves!

    First, make sure you keep totally separate in your mind (a) the three-dimensional space we live in, (b) the configuration space of the system, which is the domain for the wavefunction, and (c) the complex Hilbert space in which state vectors live (and which is isomorphic to the space of all possible unnormalised wavefunctions for the system).

    Second, points in the configuration space do not move either, and neither do points in the physical three-dimensional space we live in. You are still trying to apply the uncertainty principle - which is a statement about measurements on quantum systems - to points in space, which are not quantum systems.

    A little more on the space of states: For the system we're considering here (a particle moving along the x-axis) the Hilbert space is infinite dimensional. Each point in the space corresponds to a possible wavefunction of the particle, not a point in our ordinary space, and not a point in configuration space. The origin of the Hilbert space is the zero vector, which cannot correspond to a physical state (since the corresponding wavefunction could not be normalised). If we're being really precise, we should take into account that scaling a state vector by some constant does not alter the observable properties of the state. That is, if |A> represents some physical state, then 2|A> and (1 + 3i)|A> represent the same state as far as all measurements go. Therefore it is often said that the quantum mechanical states of a system actually live in a projective Hilbert space.
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    Quote Originally Posted by btr View Post
    The origin point of the Hilbert space of states never moves!
    How exactly do you define "never moves"?
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    Quote Originally Posted by JohnMiddlemas View Post
    How exactly do you define "never moves"?
    We're not talking about a physical particle, or even something which represents the location of a physical particle; we're talking about the origin (properly, the zero vector) in an infinite-dimensional complex vector space, the points of which correspond to unnormalised wavefunctions rather than physical locations. The zero vector "never moves" in precisely the same sense that the constant function mapping its entire domain to zero never moves. The very idea of movement doesn't even apply in this context.
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    Quote Originally Posted by btr View Post
    We're not talking about a physical particle, or even something which represents the location of a physical particle; we're talking about the origin (properly, the zero vector) in an infinite-dimensional complex vector space, the points of which correspond to unnormalised wavefunctions rather than physical locations. The zero vector "never moves" in precisely the same sense that the constant function mapping its entire domain to zero never moves. The very idea of movement doesn't even apply in this context.
    Thanks for your patience.

    I had a look at the position operator in the Hilbert space. It is simply the position x itself, the distance of x from the fixed Hilbert origin. So it looks like in the case of position, the Hilbert space and origin behave just the same as for usual space with the same idea of points.

    I know what you are saying. That the theory comes out of the mind and abstract mathematical ideas rather than being directly physically based. I guess I just believe that all theories should always be physically based throughout since that's where the evidence comes from. Using undefined ideas of points and lines which have no basis in reality goes against that. Hilbert chose not to define what a point is so how can his space be trusted.

    Measurements confirm that Dx * Dp >= h/2. So a fixed particle with no momentum has Dp=0 because there is no spread in values, but Dx would be positive since it is a real particle with size. Now let the particle size tend to zero. Not only will Dp=0 but also Dx will tend to 0 too and that greatly violates uncertainty. The idea of a fixed point in space looks like the worst possible violation of the uncertainty principle. So what justification is there to assume fixed points in any mathematical structure when the physical evidence suggests otherwise?

    There is another problem with points. In short, they cannot even be an idea. When you imagine a point it always has size. It is impossible to imagine a point with no size because there is nothing to imagine. A point in space is equally undefinable. To say it is three coordinates is meaningless, coordinates of what? So the idea of a small blob with real size is all that makes sense, rather than a point, and that's exactly what you find in nature. There are no points and the concept of a point is a mental error.
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    The problem as I see it is that define a point exactly takes an infinite number of decimal places, infinite information if you like. There seems to be a natural limit to how much information you can gain from a system that is related the it's energy. If the particle is small this problem becomes more apparent.
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    Quote Originally Posted by Jilan View Post
    The problem as I see it is that define a point exactly takes an infinite number of decimal places, infinite information if you like. There seems to be a natural limit to how much information you can gain from a system that is related the it's energy. If the particle is small this problem becomes more apparent.
    So the more precisely you make a real object approach a zero size point the more energy required until it passes some limit and starts to form a black hole or something. A true point is never attainable. I agree with that. That's also why I don't believe the concept of points is a correct one in physics. Ok for games in Mathematics only.

    I believe infinity is also a false Mathematical concept. Like a no size point the term "infinity" is not even an idea. We can't say what it is otherwise it would be finite. It is impossible to imagine an infinitely large or small quantity. An unmeasurably large distance is a mental error, because you never can know if you will later find a final limit greater than your current measured value. This is the same reason they can never say a photon has zero rest mass but only that it has been measured down to such and such a tiny value.

    Then there is the Mathematical concept of zero or nothing. It is undefinable otherwise it would be something. If you think carefully about zero you will discover that you don't know what you are thinking about.

    All throughout Mathematics and Physics are the undefinable concepts of 0, infinity, and points, all of which are simply mental errors and cause a lot of trouble.
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    Quote Originally Posted by btr View Post
    The origin point of the Hilbert space of states never moves!

    First, make sure you keep totally separate in your mind (a) the three-dimensional space we live in, (b) the configuration space of the system, which is the domain for the wavefunction, and (c) the complex Hilbert space in which state vectors live (and which is isomorphic to the space of all possible unnormalised wavefunctions for the system).

    Second, points in the configuration space do not move either, and neither do points in the physical three-dimensional space we live in. You are still trying to apply the uncertainty principle - which is a statement about measurements on quantum systems - to points in space, which are not quantum systems.
    Permit me to rewrite the logical sequence which implies a contradiction in quantum theory (QT), using directly the idea of position. This avoids all the different spaces and states involved and gets right to the issue.

    1) QT assumes the concept of position as denoted in the uncertaintly principle by x.
    2) The standard deviation of x multiplied by that of momentum is >= h/2
    3) The position x is the distance of x from an origin point fixed in time and position.
    4) The origin point must exist for distance to exist.
    5) A point with no size cannot exist.
    6) The origin point exists and so has size, and so is a real thing.
    7) A continual zero momentum gives a zero standard deviation of momentum and violates 2).
    8) So all real things must always have some momentum.
    9) So the origin point has momentum and axiom 3 is falsified. The origin point is not fixed.
    10) QT is contradictory since the origin point cannot be both fixed and moving.

    Seems concrete to me.

    Uncertainty generates a physical world where everything in existence must always move and this falsifies the concept of position. If nothing is ever fixed then position can never be known. Position requires a fixed origin.

    Since QT assumes the concept of position x then it has falsifed itself since there is no such concept.

    In the mathematical world of zero size non-existent points, position is defined as the distance between a fixed origin point and the other point. Even here the concept of position is seen to be a mental error because you can't have a distance (or anything else) between non-existent points.

    The uncertainty principle may be basically OK but they need to drop the concept of position, i.e. there are only moving objects.

    Alternatively, the other option is to keep the concept of position and allow fixed objects (drop uncertainty).
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    Quote Originally Posted by JohnMiddlemas View Post
    Thanks for your patience.

    I had a look at the position operator in the Hilbert space. It is simply the position x itself, the distance of x from the fixed Hilbert origin. So it looks like in the case of position, the Hilbert space and origin behave just the same as for usual space with the same idea of points.
    The position operator is not simply a real number, but a linear operator on the Hilbert space which maps state vectors into other state vectors. If we're talking about simple single-particle systems in one dimension, we can write a general "point" of the Hilbert space, i.e. some state vector , as a sum over the basis of eigenstates of like so:


    where the function gives the "components" of the vector in this basis and the vector is an eigenvector of with eigenvalue . In other words, satisfies the eigenvalue equation


    The function is what gets called the "wavefunction", and it is normally written as . The argument of the wavefunction would ordinarily be denotes by rather than , but I wanted to make the distinction between operators and eigenvalues clearer.

    Now, if we operate on with we will get a new vector. It is pretty easy to figure out the components in the basis we've been using:


    Since is a linear operator, we can move it past the integral sign and :


    But is an eigenvector of , so this is equivalent to:


    So, if the vector has components in the position eigenstate basis given by the mapping , the vector has components given by the mapping . If you like, the position operator represents the operation "take the wavefunction f(x) and convert it into the function xf(x)".

    But there is more! As with all vector spaces, we have a choice over which basis to use; there is no reason why we have to use position eigenstates. We could equally well have expanded the exact same state vector in a basis of momentum eigenstates:


    where denotes the state with momentum eigenvalue , and are the components of the vector in this new basis. What happens when we operate on this with the position operator? After some tedious algebra you can show that the result is:


    So, when we expand in terms of the momentum eigenvectors, the operator does not correspond to multiplication of the wavefunction by x. It corresponds to multiplication by -i combined with differentiation!


    Quote Originally Posted by JohnMiddlemas View Post
    I know what you are saying. That the theory comes out of the mind and abstract mathematical ideas rather than being directly physically based. I guess I just believe that all theories should always be physically based throughout since that's where the evidence comes from. Using undefined ideas of points and lines which have no basis in reality goes against that. Hilbert chose not to define what a point is so how can his space be trusted.
    These ideas are not undefined in the slightest. They have extremely precise definitions. If you want to know what those are, you are going to have to invest some serious effort into learning things like real/complex analysis, linear algebra and topology.

    Nor is it true to say they have no basis in reality. The theories we use are tested very carefully against physical reality, continually. The fact that they involve difficult and abstract mathematics is not due to a whim of some theoretical physicists, it is due to the fact that simple and obvious mathematics simply does not work. We started off fairly simple, about 400 years ago, but as experiments probed further and further we were forced to make the models more and more sophisticated. They could not be more rooted in reality.

    Quote Originally Posted by JohnMiddlemas View Post
    Measurements confirm that Dx * Dp >= h/2. So a fixed particle with no momentum has Dp=0 because there is no spread in values, but Dx would be positive since it is a real particle with size.
    Dx measures the standard deviation of position measurements on an ensemble of identically prepared systems; that is clear enough. But what does "size" mean? There are several notions of "size" to choose from, but for virtually all of them it does not have anything to do with the uncertainty in the particle's position. For example, the "size" of a hydrogen atom is often taken to be the Bohr radius (this being the mean distance between the proton and electron in the ground state), but the uncertainty in the position of a hydrogen atom could be a thousand times less than that, or it could be a thousand times more than that.

    Quote Originally Posted by JohnMiddlemas View Post
    There is another problem with points. In short, they cannot even be an idea. When you imagine a point it always has size. It is impossible to imagine a point with no size because there is nothing to imagine.
    Just because something has zero size does not mean there is nothing to imagine; there are properties besides size. Personally, I have absolutely no problem imagining a point with zero size, but I accept that different minds work in different ways (some people are naturally geometric thinkers, others are more analytic etc.). Fortunately, mathematicians have developed a very powerful language and toolkit to get around these differences between people's mental characteristics. The truth of a theorem or the consistency of a theory does not hinge on whether individuals can visualise the objects being discussed; it is instead decided by the careful and verifiable application of logic.

    I would also caution strongly against relying on personal intuition as a guide for what is and is not definable, and what is and is not real. If you glean just one thing from twentieth century physics, it should be this: human intuition is almost useless outside the domain of everyday life, and almost all of nature lies outside that domain.
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    Quote Originally Posted by JohnMiddlemas View Post
    Permit me to rewrite the logical sequence which implies a contradiction in quantum theory (QT), using directly the idea of position. This avoids all the different spaces and states involved and gets right to the issue.

    1) QT assumes the concept of position as denoted in the uncertaintly principle by x.
    2) The standard deviation of x multiplied by that of momentum is >= h/2
    3) The position x is the distance of x from an origin point fixed in time and position.
    4) The origin point must exist for distance to exist.
    5) A point with no size cannot exist.
    6) The origin point exists and so has size, and so is a real thing.
    7) A continual zero momentum gives a zero standard deviation of momentum and violates 2).
    8) So all real things must always have some momentum.
    9) So the origin point has momentum and axiom 3 is falsified. The origin point is not fixed.
    10) QT is contradictory since the origin point cannot be both fixed and moving.
    The main problem with the above argument is this: you are again trying to treat a point in configuration space (the origin) as though it were a particle, which is a major category error.

    The outcomes of position and momentum measurements on a physical particle are subject to the uncertainty principle because the position and momentum observables are non-commuting Hermitian operators in the Hilbert space in which the particle's quantum state vector lives.

    There are no position or momentum operators defined for points in configuration space, because points in configuration space do not have quantum state vectors which live in a Hilbert space. There is no way to even begin to apply the uncertainty principle to points in configuration space, including the origin.
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    Quote Originally Posted by btr View Post
    The main problem with the above argument is this: you are again trying to treat a point in configuration space (the origin) as though it were a particle, which is a major category error.
    position x is the distance from an origin. To have a distance you need to have two physical objects. Without those there is no distance and x is meaningless. It's indisputable.

    The outcomes of position and momentum measurements on a physical particle are subject to the uncertainty principle because the position and momentum observables are non-commuting Hermitian operators in the Hilbert space in which the particle's quantum state vector lives.
    An observable is the physical quantity namely position in the commonly understood sense.

    There are no position or momentum operators defined for points in configuration space, because points in configuration space do not have quantum state vectors which live in a Hilbert space. There is no way to even begin to apply the uncertainty principle to points in configuration space, including the origin.
    I am applying the uncertainty principle to the objects required for the concept of position x as used by the principle. Those objects are an origin and the particle. How else can you talk about a position x of a particle without a physical origin. You cannot have a distance without two physical objects. Whether the physical origin is the same or different from the configuration space origin is irrelevant because the contradiction still holds.
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    Quote Originally Posted by JohnMiddlemas View Post
    position x is the distance from an origin. To have a distance you need to have two physical objects. Without those there is no distance and x is meaningless. It's indisputable.

    An observable is the physical quantity namely position in the commonly understood sense.
    You do not need physical objects to define distance (you just need a manifold with a metric), and "position in the commonly understood sense" is decidedly different from the type of thing called an "observable" in quantum mechanics; an "observable" is a self-adjoint (i.e. Hermitian) linear operator on the Hilbert space of states (see here).

    Quote Originally Posted by JohnMiddlemas View Post
    I am applying the uncertainty principle to the objects required for the concept of position x as used by the principle.
    First, your argument conflates observables (Hermitian operators) and the outcomes of individual measurements. Second, it conflates points and physical particles (both of which you refer to as "objects"); points are simply elements of the configuration space (which is typically a finite-dimensional real manifold), particles are things with states in a Hilbert space (which is typically an infinite-dimensional complex vector space). What you are doing makes literally no sense at all in the context of the theory, which is why you are arriving at a nonsensical conclusion.

    You could construct an equally nonsensical argument in Newtonian physics. In Newtonian physics, no stationary objects can be massless (they'd experience infinite acceleration in reponse to the slightest perturbation) and all massive objects attract each other with a gravitational force. Therefore, since points are objects and there are a continuum of them, space has infinite density and has already undergone an infinitely rapid gravitational collapse. I am guessing that the flaw in that argument is obvious to you, and yet is is not a million miles away from the flaw in your own.
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    What I am trying to understand is "what is position" being the title of the thread. I am no closer to that. One cannot explain a physical thing like position with mathematical symbols and equations. Position seems to require the idea of a fixed point but then the uncertainty principle says nothing is fixed and a zero size point is obviously nonsense so the concept of a point also defies definition. The only thing that appears to work is how we think of position commonly, namely the measured distance between a physical object origin and a physical object and neither of these two are zero size points. Whether they can be fixed is another question. The uncertainty principle seems to suggest they can't. You use a ruler to measure the position and the ruler is also a physical object. So where does that leave us. It must be that position is a property of objects and not of space.
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    Quote Originally Posted by btr View Post
    Just because something has zero size does not mean there is nothing to imagine; there are properties besides size. Personally, I have absolutely no problem imagining a point with zero size, but I accept that different minds work in different ways (some people are naturally geometric thinkers, others are more analytic etc.). Fortunately, mathematicians have developed a very powerful language and toolkit to get around these differences between people's mental characteristics. The truth of a theorem or the consistency of a theory does not hinge on whether individuals can visualise the objects being discussed; it is instead decided by the careful and verifiable application of logic.

    I would also caution strongly against relying on personal intuition as a guide for what is and is not definable, and what is and is not real. If you glean just one thing from twentieth century physics, it should be this: human intuition is almost useless outside the domain of everyday life, and almost all of nature lies outside that domain.
    The only way to define a point with zero size is using coordinates.

    So a point could be defined as (0,0,0) + (x,y,z) = (x,y,z) where x,y,z are the distances from the origin (0,0,0) along the respective 3 axes. Of course you have to define the axes too but we'll skip that.

    The origin is a point too so it's definition must be (0,0,0) + (0,0,0) = (0,0,0). All we get is that the origin = the origin so that didn't help.

    Any definition of points in general hinges on a definition of the origin but there isn't one using coordinates.

    The zero size point itself is nothing at all, and is invisible in the containing space, so cannot be defined directly.

    This means there is no way to define a zero size point. If you know of one please say.

    Logical conclusion: All points must have size.
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    good explanation!
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    Quote Originally Posted by btr View Post
    You do not need physical objects to define distance (you just need a manifold with a metric)
    Please state the definition.

    "position in the commonly understood sense" is decidedly different from the type of thing called an "observable" in quantum mechanics; an "observable" is a self-adjoint (i.e. Hermitian) linear operator on the Hilbert space of states (see here).

    First, your argument conflates observables (Hermitian operators) and the outcomes of individual measurements.
    I do not use the term observable in my argument (1-10) above, just the position x as referred to in the uncertainty principle.

    Second, it conflates points and physical particles (both of which you refer to as "objects");
    A point without size cannot be defined. There is no such thing. Please see my other comment about this. If you think there is something with size that is not an object and relevant here then please say what it is.

    points are simply elements of the configuration space (which is typically a finite-dimensional real manifold).
    Define element. Hilbert didn't, so the term point is also undefined for the configuration space and therefore the whole theory is based on quicksand. See The Foundations of Geometry, page 2.

    In addition a point in a vector space defined by coordinates requires a definition of the origin but there is none except "the origin=the origin". Please see my other comment about this.

    particles are things with states in a Hilbert space (which is typically an infinite-dimensional complex vector space).
    I agree a particle is a thing, a real thing, but states in a Hilbert space are just theory. Also, the term "infinite" is undefinable otherwise it would be finite.

    What you are doing makes literally no sense at all in the context of the theory, which is why you are arriving at a nonsensical conclusion.
    If it's nonsensical then given what I wrote above, which of the lines 1-10 do you still object to and why.

    What actually is nonsensical are zero size points that defy definition, and vector spaces with an undefinable origin, and such are the foundations of quantum theory.
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    JohnMiddlemas - apologies for the late reply, and for the upcoming lengthy post.

    Quote Originally Posted by JohnMiddlemas View Post
    The only way to define a point with zero size is using coordinates.
    Not so; logically, points come first and coordinates come later (if at all). Consult a text on topology for more details.

    I'm going to skip ahead a little...

    Quote Originally Posted by JohnMiddlemas View Post
    Please state the definition.
    (Requesting the definition of "distance".)

    See a text on Riemannian geometry for the complete definition, as it is not something that will fit conveniently into a forum post (or even several such posts); I will give an outline.

    In a Riemannian manifold , you have a metric tensor field on the manifold (which is simply a symmetric, positive-definite bilinear function from pairs of vectors to real numbers). That gives you an inner product on the tangent space at each point, and thus the "length" of vectors at each point; specifically, for each vector the "length" is just .

    Now, given a curve , you can use the metric to compute the length of the curve like so


    If you want, you can now define the distance between two points that can be joined by a curve in terms of the length of the shortest curve joining them; that is, if is the set of all curves joining two given points then the distance between them is


    I do not use the term observable in my argument (1-10) above, just the position x as referred to in the uncertainty principle.
    No, but you used it elsewhere. In particular, you used it in the post I was actually responding to; you said "an observable is the physical quantity namely position in the commonly understood sense," which is mistaken.

    I'm going to skip ahead again, as many of your remaining points are based on the sort of misunderstanding exemplified by this statement:

    In addition a point in a vector space defined by coordinates requires a definition of the origin but there is none except "the origin=the origin". Please see my other comment about this.
    A vector space satisfies certain axioms, by definition. There are various logically equivalent ways of doing this, but in all of them the existence of a unique "zero vector" (i.e. an additive identity) is a direct consequence of them. If your space does not have an additive identity, it is not a vector space in the first place.

    At the level we were discussing things, the Hilbert space in question was the space of unnormalised wavefunctions. You can prove this has a zero vector; it is simply the function (call it ) which maps every point of the configuration space to the zero of the complex plane:


    That function is the "origin" of the Hilbert space, because it acts as the additive identity; for any other wavefunction , it is trivial to prove that


    I want to use this as a jumping-off point to make a more general statement, though. The way that quantum mechanics is structured is that we start with axioms and rules of inference, and from those make deductions. The axioms and rules may seem strange, or may seem intuitive; it doesn't matter one bit. If you want to show that the model is wrong, you must do one or both of the following:

    1. Show that the model makes contradictory statements, by rigorously applying the rules of inference to the axioms of the model.
    2. Show that the model's experimentally testable predictions do not match experiment.

    In the present case, you are trying to argue for the first option, but it is hopeless; despite your objections, you have not provided any rigorous demonstration that the axioms of quantum mechanics together with its rules of inference lead to any contradiction. You have only made informal verbal arguments, in which you have fallen into the error of attempting to apply Heisenberg's uncertainty principle to points of space.

    If it's nonsensical then given what I wrote above, which of the lines 1-10 do you still object to and why.
    OK, line by line:

    1) QT assumes the concept of position as denoted in the uncertaintly principle by x.
    OK. Note that the quantity x used in the uncertainty principle is a random variable denoting the outcome of measurements made on an ensemble of identically-prepared systems.

    2) The standard deviation of x multiplied by that of momentum is >= h/2
    OK. Note that the "momentum" referred to in the uncertainty principle, and therefore here, is a random variable denoting the outcome of measurements made on an ensemble of identically-prepared systems.

    3) The position x is the distance of x from an origin point fixed in time and position.
    False. The quantity x is a random variable, not the distance of anything to anything. The quantity x does not even have a specific real-numbered value. You have committed an equivocation fallacy here. You may think I am being picky, but it is just this sort of lack of precision in your argument which allows it to reach its nonsensical conclusion.

    4) The origin point must exist for distance to exist.
    False. First, you can easily construct coordinates in ordinary 3-dimensional space such that there is no point with coordinates (0, 0, 0), but in which distance is perfectly well defined; where is the origin in such coordinates? Second, you can define distance without appealing to some origin point as a reference (see the definition I gave earlier in terms of the integral along curves).

    5) A point with no size cannot exist.
    False (consult any decent book on topology). Even if you choose to ignore topology this is, at best, an unsupported premise.

    6) The origin point exists and so has size, and so is a real thing.
    That is based on the previous point, and so need not trouble us.

    However, note that even granted the previous point, it is a dubious (and maybe even circular) argument - what, exactly, is the distinction between something that "exists" and something which is a "real thing", and why does having "size" promote the origin from something which merely "exists" to being "a real thing"?

    This is another example of where the lack of precision allows the argument to go in strange directions (later, we will see a key error based on the vagueness of the phrase "real thing").

    7) A continual zero momentum gives a zero standard deviation of momentum and violates 2).
    This is actually a very delicate point. If you demand that the standard deviations in point (2) are finite (as I suppose you do), then you need to be aware that the uncertainty principle, thus restricted, is pretty much silent on the matter of states of definite momentum (or of definite position). To find out what such states are like, we need to go back to the principles underlying the uncertainty principle; that is, we need to go back to the basic axioms of the theory. When we do so, we find that such states are indeed permitted, and in the position basis are the plane wave states (for definite momentum) or the delta function states (for definite position).

    An alternative, but equivalent, way of looking at it is to drop the restriction that the standard deviations must be finite.

    This is, as I said, a delicate point; fortunately, it is far from central to the argument.

    8) So all real things must always have some momentum.
    This is the key step I alluded to earlier.

    With the "so" qualifier, this statement is false (because it does not follow from the preceeding statements), unless you are defining "real thing" as "the sort of thing which can have momentum". However, all we know about "real things" from your previous points is that they are the sorts of thing which can (but needn't) have size.

    Worse, depending on what you mean, precisely, by "real thing" (a term which, despite being key to your argument, you have not defined), the statement without the "so" qualifier may also be false. There are a variety of "things" in physics, and not all of them are the sorts of "things" which to which momentum may be ascribed.

    9) So the origin point has momentum and axiom 3 is falsified. The origin point is not fixed.
    This is based on several previous errors, namely that the origin is a "real thing", that the term "real thing" is even meaningful, and so on.

    10) QT is contradictory since the origin point cannot be both fixed and moving.
    Likewise, this is based on several previous errors.
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    That's a long post, so let me simplify matters by just highlighting where the first problem with your argument cropped up:

    3) The position x is the distance of x from an origin point fixed in time and position.
    Recall that this was false because (as a consequence of point (1) of your argument) the quantity x is a random variable, not a real-valued distance.

    Once you've fixed that, or reformulated your argument so it doesn't rely on it, we can move onto the next point.
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    A true point is never attainable
    So why do you use the word "point" then ? Point does not exist apparently, it is a "false concept". By using it in that real phrase, you made de facto no-sense.


    I agree with that
    No you don't. You still don't understand that concepts are real, and that physical reality is only attainable trough rational concept, however awkward and however precise the uncertainty of that process is.




    That's also why I don't believe the concept of points is a correct one in physics
    Nobody does. Only, you, again and again, mix the correct concept of position (not point) in the description of the model, with the actual measurement made with physical things (called, for lack of a better word, "reality")


    Ok for games in Mathematics only.


    I believe infinity is also a false Mathematical concept
    Games ? Yes, why not. You are even closer to the truth than you know.
    I don't like infinity either. Anyway, that does not preclude it to be the most powerful shortcut to avoid me to fill the entire universe with ink when I want to right it down. Nor the concept of Zero, which, in total agreement with you, is also non-existent in reality.
    Anyway it exists, here is one:0


    This means there is no way to define a zero size point. If you know of one please say.
    (x,y,z,0).
    Your are welcomed.






    Back to games. The computer you are writing those posts on, is filled with matrices of 3 coordinate positions. We rarely refer to them as points, generally as vertices. Most likely, a couple of them define a line, and a triplet define a triangles. I hope you will accept that computers really process those points some billionth times per second. And that all that mathematics is real.


    But, if I may argue in the same direction as you, saying that the sun (which has some size, you'll agree) have a "position" is much more "incorrect" then giving a position to a particle. Which part of the sun ? Where does "the sun" starts, where does it ends ? Anyway, a good old 3(more like 4) set of coordinates (not forgetting an origin) will help you once lost in space.


    And when I look at (x,y,z) I see 3 infinite quantities, or 3 finite 64bit floats, depending if I am in physics vs reality, math vs game (vs operator also do not commute ;-)
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    Quote Originally Posted by Boing3000 View Post
    So why do you use the word "point" then ? Point does not exist apparently, it is a "false concept". By using it in that real phrase, you made de facto no-sense.
    By true point I refer to the standard concept of a zero size point in geometry. This is purely coordinates relative to a non-existent origin with no coordinates and no size. True in the sense of the accepted view, but contradictory in my view because anything relative to non-existence is non-existent itself. The explanation is simple, standard geometric points are just a mental error, and a real geometry must be discrete using points of size. A "quantum" geometry if you like.


    Nobody does. Only, you, again and again, mix the correct concept of position (not point) in the description of the model, with the actual measurement made with physical things (called, for lack of a better word, "reality")
    The "points" I refer to there are classic zero size points. Points which have size are acceptable and based on reality but are not used in physics. This is where a discrete geometry is required rather than the usual continuous geometry. Some work has been done on this.

    Nor the concept of Zero, which, in total agreement with you, is also non-existent in reality.
    By its usual definition as nothingness, zero is non-existence, so yes it is non-existent. If you give it a symbol 0 then that is a contradiction since the symbol represents a non-existence which cannot be represented. You won't find it anywhere in reality because there is no such thing.
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    Quote Originally Posted by btr View Post
    JohnMiddlemas - apologies for the late reply, and for the upcoming lengthy post.
    Apologies for an even later reply.

    In a Riemannian manifold , you have a metric tensor field on the manifold (which is simply a symmetric, positive-definite bilinear function from pairs of vectors to real numbers).
    You are defining distance in a Riemannian manifold not physical distance as we know it. For example your definition assumes the real numbers for which there is no evidence are a genuine concept. Also it uses the concept of smooth continuous functions also for which there is no physical evidence. On the contrary even quantum physics implies that real things come discretely rather than continuously so that should apply to space, time and motion also. If you consider space as infinitely divisible and continuous it leads to contradictory conclusions. A particle in motion from A to B must complete an infinite number of sub-motions to get to B, i.e. 1/2 the motion + 1/4 + 1/8 + ... At some stage logically it must finally jump to B to escape the continuity trap. In jumping this means motion must be discontinuous not continuous. Distance and motion are "quantum" too.

    There must come a tiny length which is indivisible. It may or may not be the Planck length, but all space must be composed of these units unless there is no space at all. Distance is a positive integer multiple of the 1 indivisible length, or more precisely distance is simply a positive integer. If you wish to call 1 meter one of those positive integers then fine but that is just a scaling thing, the foundation is still the positive integers.

    Any definition of physical distance cannot involve continuums. It means that the positive integers must be used in mathematical physics not the real numbers. The same will likely apply to all other physical quantities too. A discrete (quantum) geometry is needed not a continuous one.

    I'll have a crack at the rest of your comments later. It's a lot to go through.
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    This is purely coordinates relative to a non-existent origin with no coordinates and no size

    Why do you keep making that error ? It has been pointed to you already. An origin is totally existent it is written (0,0,0)
    True in the sense of the accepted view, but contradictory in my view because anything relative to non-existence is non-existent itself

    The accepted view about fallacies is that they are build uppon false assumption. Origins exist, I have seen them personally.
    The explanation is simple, standard geometric points are just a mental error

    Qualifying "standard geometry" has a "mental error" is a mental error. I suppose you meant : unfruitful waste of time. But even that would be an error.
    , and a real geometry must be discrete using points of size. A "quantum" geometry if you like.

    Why not ? Although I would NOT call it "real" geometry, just "another" geometry. Given the number of math freak I am pretty sure that a manifold of such geometries already exists.
    If it allows you to do better and easier computation in QM, I bet all physicists will embrace it.
    And to sheer you up, string theory use size-full piece on continuous things to model reality. Maybe 10+ dimensions mathematics will have your liking.

    But, unlike moth drawn by the light, scientists would not start to think that this particular geometry/description/model/math actually means anything other that what it is.
    Maybe you only look too much of the world trough your pixel'ized screen. The "reality" is not made of pixel. And if QM deals sometimes in quanta, and particle, it also deals in waves.

    You won't find it anywhere in reality because there is no such thing

    But, incidentally, you've just find it. Isn't it ironic ?
    Nobody forbids you to use other mathematics with no zero, nor infinities, nor point nor coordinates. Just integers and your fingers to count. Go on, and have fun.

    My personal take on that matter is that going backward is no the right direction forward. So any quantities should have recursive dimensions, like non-linear/fractal mathematics try to model, and like reality clearly seem to be.
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    A vector space satisfies certain axioms, by definition. There are various logically equivalent ways of doing this, but in all of them the existence of a unique "zero vector" (i.e. an additive identity) is a direct consequence of them. If your space does not have an additive identity, it is not a vector space in the first place.
    But there is no such thing as (0,0,0). It has zero's for coordinates and no physical size. Pure nothingness. An impossible concept. As is zero itself. I must conclude that the axiom of additive identity is wrong based on the undefinability of zero as nothingness and the zero vector.

    I know that must sound strange to you but I have considered it at length. Sure you can create a system with any axioms you like but if one of them is an obvious contradiction then it's not a very good start is it. I realise you will dispute that.

    Here's a bit of reasoning about zero as nothingness.

    Nothingness is undefinable otherwise it would be something. This means nothingness is not even an idea even though you think it is. You can't say what it is. It must be a mental error. This is the same as the infinity argument and indeed they are linked since zero is supposedly the ultimate destination of an infinitely shrinking quantity. Yet zero is not even a quantity and not a number since it is nothingness. In fact the infinitely shrinking quantity never actually gets to zero and is always still a quantity. "Undefinable" and "quantity" are different categories and cannot be related.

    Now let's look at zero in arithmetic. 1+0=1 right, 0 is the additive identity, and 0 is defined as a natural number. But zero is not a number because it is not a quantity of anything. If you subtract 1 from both sides of the equation you get +0=

    So +0 is equivalent to "blank" or doing nothing. This means that if 0 is anything at all then it is an operator, not a number. It is an operator which deletes the operator on its left hand side (+) and then deletes itself. This leaves us with 1+0=1 is equivalent to 1=1. Being an operator it cannot then be included in any number line or be part of a zero vector. It cannot exist on its own like a number, it always requires another operator to its left to delete.

    However, this definition when applied to multiplication gives 1x0=1 which I'm sure they won't like, but actually makes sense if you think that multiplying by nothing means the operation of doing nothing. Then the multiplicand just stays the same. Dividing by 0 is tidier, 1/0=1, no infinities. I wonder what sort of maths that might lead to.

    In the present case, you are trying to argue for the first option, but it is hopeless; despite your objections, you have not provided any rigorous demonstration that the axioms of quantum mechanics together with its rules of inference lead to any contradiction. You have only made informal verbal arguments, in which you have fallen into the error of attempting to apply Heisenberg's uncertainty principle to points of space.
    I don't think I'm trying to provide a rigorous demonstration. If I could do that I guess I would be world famous. It is just informal as you say, and QT seems contradictory that's all. I'm not applying the uncertainty principle to unoccupied points of space but to points in space containing an object. Space can't move, only objects and by uncertainty all objects must move.

    False. The quantity x is a random variable, not the distance of anything to anything. The quantity x does not even have a specific real-numbered value. You have committed an equivocation fallacy here. You may think I am being picky, but it is just this sort of lack of precision in your argument which allows it to reach its nonsensical conclusion.
    Here I was just stating the usual understanding of "position x", i.e. the distance from the origin, obviously otherwise how else can it be a position? I don't see how this is an equivocation fallacy. None of the material I have read about the uncertainty principle mentions x is a random variable. Randomness cannot have a standard deviation or any property at all other than randomness.

    Perhaps you mean position x must refer to a number of measurements of x. For example a microscope measuring the position and momentum of an electron. Under the same conditions say repeat the measurement of position 100 times, and then do the momentum 100 times. Then the product of the standard deviations of position and momentum measurements is approximately >=h/2

    But for each measurement of x a number is recorded which is the distance of the electron from the origin of the microscope. Maybe marks on a ruler I guess. This fits with what I said so what is the equivocation fallacy? The standard deviation is then calculated from those 100 numbers.

    My point is simply this, that if you then apply the uncertainty principle to the microscope origin itself and every atom in the experiment, they must all be moving. Thus between measurements the origin is different and the ruler is different if there is one. Therefore the concept of position itself has lost its meaning and the 100 measurements are not referred to the same origin so do not measure position. These additional uncertainties need to be incorporated in the theory at least.

    The 100 measurements could be unrelated numbers. Maybe it is the moving microscope atoms that cause the standard deviation and not the electrons themselves.

    You might say that the movement is very small but how do you quantify that if the very concept of position is gone?

    Position requires a fixed origin to be a definable concept.

    False. First, you can easily construct coordinates in ordinary 3-dimensional space such that there is no point with coordinates (0, 0, 0), but in which distance is perfectly well defined; where is the origin in such coordinates? Second, you can define distance without appealing to some origin point as a reference (see the definition I gave earlier in terms of the integral along curves).
    Your prior definition used the zero vector as origin didn't it?

    False (consult any decent book on topology). Even if you choose to ignore topology this is, at best, an unsupported premise.
    Why not discuss this issue rather than dismiss it? It is a very important one. I have already supported it.

    Well, I am saying standard topology and geometry are wrong. I don't believe in continuums and zero size points, I believe in discrete geometry and sized points. Indivisible unit lengths, indivisible objects, and indivisible jumping motions. What is the support for the premise of a zero size point? It is never justified, just stated without support, like Hilbert elements. The foundations of quantum theory are based on such nothingness and experimental evidence strongly indicates reality is discrete not continuous. That QT is based on the real numbers and continuums is a throwback to the old days of geometry from which Hilbert space originates. It needs updating to a discrete geometry based on positive integers. Maybe that would help with unification.

    However, note that even granted the previous point, it is a dubious (and maybe even circular) argument - what, exactly, is the distinction between something that "exists" and something which is a "real thing", and why does having "size" promote the origin from something which merely "exists" to being "a real thing"?
    Having shown the origin point has size from 4) and 5) it could exist as an empty block of space or a filled one i.e. occupied by a material object. In the latter case I would call it a "real thing". Having size does not promote it to being a real thing so my conclusion there was wrong.

    However, you cannot measure a distance to an object where the origin is an empty block of space since you can't find the origin. So the only practical possibility for an origin is to be a real thing like a part of the testing microscope or a ruler.

    This is actually a very delicate point. If you demand that the standard deviations in point (2) are finite (as I suppose you do), then you need to be aware that the uncertainty principle, thus restricted, is pretty much silent on the matter of states of definite momentum (or of definite position). To find out what such states are like, we need to go back to the principles underlying the uncertainty principle; that is, we need to go back to the basic axioms of the theory. When we do so, we find that such states are indeed permitted, and in the position basis are the plane wave states (for definite momentum) or the delta function states (for definite position). An alternative, but equivalent, way of looking at it is to drop the restriction that the standard deviations must be finite.
    The main issue is that no physical object can be stationary. This is confirmed by David Gross in the video David Gross: Frontiers of Fundamental Physics - YouTube at around 19:39 where he says a stationary pendulum is inconsistent with the uncertainty principle because it has a definite position and no momentum. If stillness is thus prohibited then all physical objects must always move which is my conclusion at 8) even if not justified by 7).

    Thanks. If you reply please make it a bit shorter since that was murder going through it all.
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    John, there are so many errors in what you wrote that I must ask you some contextual information so as to be able to fill some gap here.
    How old are you, or more specifically since when have you been introduced to basic mathematics ?
    Is English you first language (me no, so keep that in mind too).


    From the informal start of this thread, where you speak about self-contradiction in QM, and post #2 where the source of your confusion have been point out to you, you have failed to acknowledge any of the precise responses given to you, on so may level.

    I cannot start quoting separately every mistake, so I'll condense them in inline brackets:

    1.[But there is no such thing as (0,0,0)] <- an obvious contradiction
    2.[It has zero's for coordinates and no physical size] <- correct, coordinate do not have size
    3.[Pure nothingness] <- fallacy, because of 2.
    4.[An impossible concept. As is zero itself] <- now we enter the domain of mental error. You only appear to like positive integers, but not the first of them. So start counting the unicorn tap dancing on your keyboard, or the shrinking quantity that is you bank account, and just spell out loud and clear what that "impossible" number is.
    5.[I must conclude that the axiom of additive identity is wrong based on the undefinability of zero as nothingness and the zero vector.] Repeating fallacies does not make them more correct. Here you should try to explain what is the force that make you do that. Not logic, that is a fact.
    6.[
    I realise you will dispute that] Not at all. Nobody dispute the fact that [obvious contradiction] is bad. *You* are disputing it by making so many obvious contradictions and never disputing it.

    (Pause) That's only 10 % of you post, and it is entirely filled with error. Jumping to conclusions, the reason is because you try to avoid to acknowledge your first formal mistake by hiding it behind others, and now you try bad informal philosophy:

    7.[Nothingness is undefinable otherwise it would be something.] Nothing(ness) is the absence of thing. *It is perfectly defined*. Something is the presence of thing
    8.[This means nothingness is not even an idea even though you think it is. You can't say what it is] Only you think it is not an idea, even though you have started a thread about that idea. Contradiction again ?
    9.[since zero is supposedly the ultimate destination of an infinitely shrinking quantity] Utterly wrong. A shrinking quantity associated with division X * 0.1 -> X guarantees that there will always be something left. If it is associated to another operation (you don't like it, it is subtraction) then zero is met in a blink of an eye.


    (Pause) and now you start making up your own rule for equation (this was not an equation btw).


    10.[But zero is not a number because it is not a quantity of anything] can you stop doing that mental error ?
    11.[If you subtract 1 from both sides of the equation you get +0=] No, you get : 1+0 -1 = 1 -1 (the real rule of 8 year old mathematics can now be applied in many ways here) Here is one: 1 + -1 = 0
    12.[+0=] Following *your personal and new mathematics* where subtracting -1 is find-and-replacing them with void/empty (NOT ZERO !), leads to a perfectly sound result. Adding zero to nothing is nothing. Adding zero to anything is anything. Adding zero to unicorn is unicorn.
    13.[
    So +0 is equivalent to "blank" or doing nothing] hu ? It is adding the additive identity (zero) that is why it is written "+" (adding) "0" (zero)
    14.[This means that if 0 is anything at all then it is an operator, not a number] Wrong. The operator is the addition, symbolized by a sort a plus, that little cross before the 0. And 0 is the number you can add to anything to gave you an identical anything.

    I'll stop there, and hope you'll be able to express some kind of willingness to stop making self-contradiction on the level of the description/symbolic itself, before delving into how it could be relevant to observing/experimenting with reality.
    If you like pixel-like "theory" maybe you'll like this or that

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    Quote Originally Posted by Boing3000 View Post
    John, there are so many errors in what you wrote that I must ask you some contextual information so as to be able to fill some gap here.
    How old are you, or more specifically since when have you been introduced to basic mathematics ?
    Is English you first language (me no, so keep that in mind too).
    It's so easy to insult people on the internet isn't it. That's one reason many steer clear, for fear of people like you. I am not inclined to reply to insulting messages.
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    I am sorry you feel that way, it was a genuine interrogation. My personal weakness in English probably make my message insulting for you, but believe me, it is not my intention (because there are zero insults anyway).

    But you don't have to respond to any of my questions, as I don't have to waste my time responding to yours. Take care
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    OK, I'll take it as a genuine interrogation then, but it would help me if you avoided personal criticisms like "your confusion", "so many errors", "failed to acknowledge", "*You*", "every mistake", "so many obvious contradictions", "Jumping to conclusions", "hiding it behind others", etc, etc. It is very difficult to have a discussion with all that in there and makes you look hostile.

    Just stick to the issues themselves please.

    So let's see if we can sensibly discuss the first of your points before going on to any more.

    Quote Originally Posted by Boing3000 View Post
    1. But there is no such thing as (0,0,0) <- an obvious contradiction
    I can think of three meanings of "thing" here. Which do you refer to if any please?

    1) The characters (0,0,0) as written
    2) A physical origin
    3) The consistent idea of (0,0,0) as an origin

    If you mean 1) then yes it is a contradiction, but that's like me saying "there is no such thing as a pink elephant", and you saying yes there is because the characters "pink elephant" have been written. I did not mean this one.

    2) Physically, you must be able to find an origin, so it must be a physical object. For example the origin of a ruler is a piece of material. Since (0,0,0) has no size then it cannot represent a physical object. It cannot represent a thing nor be a thing. As soon as you even mark an origin then the mark is composed of atoms and has size.

    3) The idea of a point (0,0,0) with size 0 is inconsistent because it contains the inconsistent idea of the number 0 as nothingness. This is my personal belief and I am entitled to it, and which I arrived at by various considerations.

    There is more than one use of 0 in mathematics. The 0 in 105 is not the same use as in 1+0=1. The first is called a "placeholder" and signifies an empty column or an empty box in that position. 0 is not necessary in 105 as roman numerals demonstrate. The second represents nothingness because you must add nothingness to 1 to get 1. The first must come with the column, the second is alone. As you may be aware 0 was introduced well after the roman system. It is the use of 0 as nothingness that I object to.

    So what is nothingness? I have already been over this. I see you try later to define it as the absence of anything. But where is that absence? What is that absence? Nowhere and nothing, that's all that can be said. Nothingness is nothingness. Your definition is circular.

    However hard you try you will not be able to say what nothingness is. This is the inconsistency of 0. We don't know what it is we are talking about, but we think we do.

    If your bank account is a deposit box and you find it empty it is still a box, but never nothingness. Hope you can see the difference.

    Option 2) was my main meaning in writing "there is no such thing as (0,0,0)", but I believe it is also true for option 3).
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    I am sorry John, but there is no conversation here. And now your feel entitled to decide what kind of words or expressions I can use to express myself. It's kind of very rude.

    People have bounce of yours idea in a polite way, even after you called them retards (doing mental error), they have granted you that privilege. That's how values and properties can be assigned to ideas. Until you don't do that, by responding to their questions, instead of making up the questions, and the answers, then there is no conversation. All there is is "This is my personal belief and I am entitled to it". That is your axiom, and certainly not one used in science.

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    Please note the following article. It demonstrates an equivalent decimal number system with no zero, and states:-

    "The foregoing manipulations indicate that the 0-less system has substantially the elasticity of the conventional decimal system, and as a consequence challenges the assertion that modern science, in industry, or commerce would be inconceivable without the zero symbol"

    A Number System without a Zero-Symbol
    James E. Foster
    Mathematics Magazine
    Vol. 21, No. 1 (Sep. - Oct., 1947), pp. 39-41

    This system is also known as The Bijective Base-10 System.
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    In reply to JohnMiddlemas, re: all of your posts this thread.

    All I can say to you is...HUZZAH!!! You have presented all of your posts w/ excellent logic...and unfortunately, this is why you will ALWAYS "fail" in attempting to dislodge the facades

    of modern "physics theory". (Can it be you are not aware of the "castle doctrine" defense systems in-place? That for every error in QM...for every bit of illogical "logic" there exists a

    a maths based answer to "verify" EVERYTHING!!!) How do you think to defeat or dislodge the "system in-place?", given that no one wants anything "modified" "altered" "thrown-out" nor

    in any way disputed. This is the truth of theory (post Einstein)

    ......

    You ask too much, "John". The "system" is in place, and no one dares tamper w/ it...for fear the entire "castle in the air" of modern theory will come crashing down!

    (does it not occur to you that engaging in debate w/ the Pope regarding the "supernatural" state of being of "Christ the Redeemer" is moot? You will NEVER convince the "Vicar of Christ" that

    anything is "wrong" with "Gospel"...he will tell you to "wait, and have faith' and "all you need know will be revealed unto you")

    These are the only things you read regarding "physics theory" from the "High Bishoprics" of QM.

    No one admit will admit anything "just might be wrong" w/ regard to observations and assumptions...they dare not. There is simply too much to lose.

    .....

    Thank you for some of the best posts I have ever read on any site. Period.
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    Quote Originally Posted by Gerry Nightingale View Post
    In reply to JohnMiddlemas, re: all of your posts this thread.

    All I can say to you is...HUZZAH!!! You have presented all of your posts w/ excellent logic...and unfortunately, this is why you will ALWAYS "fail" in attempting to dislodge the facades

    of modern "physics theory". (Can it be you are not aware of the "castle doctrine" defense systems in-place? That for every error in QM...for every bit of illogical "logic" there exists a

    a maths based answer to "verify" EVERYTHING!!!) How do you think to defeat or dislodge the "system in-place?", given that no one wants anything "modified" "altered" "thrown-out" nor

    in any way disputed. This is the truth of theory (post Einstein)

    ......

    You ask too much, "John". The "system" is in place, and no one dares tamper w/ it...for fear the entire "castle in the air" of modern theory will come crashing down!

    (does it not occur to you that engaging in debate w/ the Pope regarding the "supernatural" state of being of "Christ the Redeemer" is moot? You will NEVER convince the "Vicar of Christ" that

    anything is "wrong" with "Gospel"...he will tell you to "wait, and have faith' and "all you need know will be revealed unto you")

    These are the only things you read regarding "physics theory" from the "High Bishoprics" of QM.

    No one admit will admit anything "just might be wrong" w/ regard to observations and assumptions...they dare not. There is simply too much to lose.

    .....

    Thank you for some of the best posts I have ever read on any site. Period.
    Astounding reply. Thank you. I was lately thinking the same myself that the "tower" cannot be shaken, and moreso since my other post regarding zero here.

    By having the contradiction zero in their theories they open the door to any form of manipulation they require (supposedly). This possibly explains the maths based answer to "verify" EVERYTHING!!! you refer to.

    Although blatantly apparent that the mathematical definition of zero (by Frege) is a contradiction my educated counterpoints refuses to accept it. They want to believe in "nothing" like you suggest.

    So I wonder if as you say it is a better idea to let it be. God allowed the system as it is for a reason.

    The zero post is better than this one here since I get down to the nitty gritty of a real definition. However, even with that said I agree it will be monstrous to try and remove their little zero from their system. After all they define the positive integers using the zero as start point. All based on contradiction. { {}, {{}}, {{},{{}}} } is the number 3 where {} is the empty set. Of course the empty set is a contradiction too since you cannot locate the unlocatable emptiness between two braces. Unless of course there is no such thing as location which is an interesting point by itself. I'm not currently sure. That is the title of this post, "what is position". It's not at all obvious what it is if anything.

    The truth is a lot worse than the zero problem though.

    All of logic is certainly wrong too. The use of the negative "NOT" is highly dubious and a whole book has been written about the character of negation. I haven't quite got to showing it an illusion yet though. To do that would be to remove the concept of contradiction itself and Aristotle's Law on non-contradiction. It is clearly tied to zero. If you say I found zero apples in the box it means you did "NOT" find any apples in the box. So I am highly confident "not" is an illusion like zero is. This means the English language needs amending throughout too.

    I can still do something with the ideas though, but in secret.

    As it is these ideas are leading to a new form of logic, much simpler, and integrating all ideas of location, space, time, and numbers, all being "things". So time is a thing too and in packets. There is no intersection as in A & B. An object can't half merge with another! Then there would be three objects anyway. A either externally touches B or A is apart from B and that's about it, like 3 touches 2 and 4 but is apart from 5. Using touching and apart, you should be able do all of reality. So a time blob touches an object which touches a piece of space etc without overlaps. Any idea whatsover can be added to the system except that the idea of choice may require XOR as well. Early days though.

    As regards this topic of "what is position" it still seems concrete to me that the uncertainty principle must bring uncertainty to position measurement and so to position itself. It makes "position" an undefinable concept and therefore destroys its own foundation from the quantum theory. Since the quantum theory uses mathematics containing the contradiction which is zero then the whole theory is invalid anyway. Why it seems to match up to experimental "evidence" is an entirely different topic. Maybe the Devil is fiddling the results, who knows. All we know is that the theory doesn't stack up because of the zero.

    Thanks for your encouraging reply, it cheered me up no end after so much resistence.
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    Quote Originally Posted by JohnMiddlemas
    Stationary particles are prohibited by the uncertainty principle otherwise both position and momentum would be precisely determined together.
    There are various forms of the uncertainty principle and what uncertainty means in modern quantum mechanics. However the one used exclusively in modern quantum mechanics textbooks and journal papers is the one where the uncertainty in a variable is the standard deviation in an ensemble of measurements or of a collection of single measurements from identically prepared systems.
    As such itís very possible to measure a particle at rest. All it means is that the measured value for the momentum is zero. Youíre using the uncertainty principle wrong. The Heisenberg Uncertainty Principle (HUP) is an inequality between the standard deviations of two observables and is a function of the wave function only. Measurement of any other variable before it has no relationship on the measurement of an observable. That means that you can measure the momentum to be exactly zero and then you can measure the position and get an exact value.
    Quote Originally Posted by JohnMiddlemas
    So everything must always move.
    Given what I said about thatís not true at all. Have you ever read about the meaning of uncertainty from anything other than a book written for the layman or a freshman/sophomore student? If not then please see the following
    The Uncertainty Principle (Stanford Encyclopedia of Philosophy)
    Heisenberg - Quantum Mechanics, 1925-1927: The Uncertainty Relations
    Quote Originally Posted by JohnMiddlemas
    So what does "position" in the uncertainty principle mean then if there is no such thing as position and everything always must move? The uncertainty principle appears to be self-contradictory.
    Even if what I said was wrong there is nothing wrong with the idea of measure the position of a moving object. Otherwise youíd be unable to measure the speed of an object.
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    In reply to Johnmiddlemas, re: your #39 post.

    You're welcome!

    Go ahead and read the more advanced books on theoretical physics as "Physicist" suggests (this is a very "hard slog" for me, as my math skills are poor...still, I understand given time)

    .....

    What I will never agree to is the premise that "numbers trump reality, or any theory of reality"...this is what has happened w/ regard to modern physics, at least in QM!

    Debating physics theory now is an exercise in futility, as in "every posit from Hawking is infallible". (I think Hawking is brilliant...and completely wrong w/ regard to his extrapolations

    of gravity theory! There is NO "ultimate gravity" regarding mass...yet his calculus "proves" there is! (Yes, based on a false premise from faulty observations)

    .....

    I would offer you a suggestion? Perhaps you could try posting your stuff as a "presentation" on Youtube...something w/ graphics and illustrations so others can "see what you mean?"

    (I am going to do this myself at some point w/ my own "interpretations", as soon as I am able to figure-out the "hows"...I never had access to a computer prior to 10/13!!! so, I must learn

    as I go...not easy for an old man) I had to "teach myself" and it shows!

    (Thanks for reading!)
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    Hey Gerry, maths is a noble endeavour, if you ever need any help with it you know where we are.
    Kind Regards
    Jilan
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    Gerry, your post is completely wrong in so many ways.

    Making it simple: Newton described the effects of gravity with an inverse square law. It did not mean he knew why gravity does what it does!

    And your rantings about quantum mechanics is ludicrous. Just because something is not to your liking does not mean experimental evidence is disregarded solely on opinion.
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    In reply to Beer w/Straw, re: your #43 post.

    (1) What is so "completely wrong in so many ways?" As far as Newton is concerned, I'm familiar w/ his writing and the principles of an "inverse sq." Since I am familiar w/ "inverse sq." as

    it pertains to "the density/volume of a given body in a given gravimetric-field " will demonstrate the following characteristics "as it falls", et. al. Please tell me the "how" of these mechanisms

    as they apply to a singular "ultra-dense entity" in a "supposedly" non-gravitational environment? What gravity, other than it's OWN, is the "dense-body" inter-acting WITH???

    Just "how" does the density of a mass give rise to an "inverse square of gravity" that has now acquired the ability to "square ITSELF FROM ITSELF!

    Where does Newton...or Einstein, "fit" into this hypothesis?

    .....

    (2) By your criteria...anything I write is either a "rant" or "fools errand" if it does not conform to "standards of doctrine". What I "like" or "dislike" has no bearing on what I think! For instance,

    there is an Administrator whom I despise (another "Site") on a personal basis...yet I can find no flaw in any of his "posts" w/ regard to calculus theory. He's extremely good, and writes very

    elegant formulas. His knowledge of modern theory would likely put anyone here in the "closet"...and yet he knows NOTHING of theory itself, only what he has read! (ask Jilan)

    He has no "intuition" nor any idea of "how to question" anything...yet knows everything pertaining to physics theory.

    ......

    Since when is "experimental evidence" enough to form a hypothesis that is valid...when there is no "counter" even considered? As in..."Let's give him a fair trial...and then hang him".

    Since when is a "mathematical formula" a "proof" of anything more than "mathematical formula?" This is not experimentation, not when "only the parameters of what we expect to find"

    are allowed as "guidelines!" To me...this is NOT "valid science".


    (Thanks for reading!)
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    I believe you have misconceptions.

    It was never a secret that physics has not proved things, and that mathematics is simply the language used to try and describe the workings of the universe.
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    Quote Originally Posted by Gerry Nightingale View Post
    In reply to Johnmiddlemas, re: your #39 post.

    You're welcome!

    Go ahead and read the more advanced books on theoretical physics as "Physicist" suggests (this is a very "hard slog" for me, as my math skills are poor...still, I understand given time)

    .....

    What I will never agree to is the premise that "numbers trump reality, or any theory of reality"...this is what has happened w/ regard to modern physics, at least in QM!

    Debating physics theory now is an exercise in futility, as in "every posit from Hawking is infallible". (I think Hawking is brilliant...and completely wrong w/ regard to his extrapolations

    of gravity theory! There is NO "ultimate gravity" regarding mass...yet his calculus "proves" there is! (Yes, based on a false premise from faulty observations)

    .....

    I would offer you a suggestion? Perhaps you could try posting your stuff as a "presentation" on Youtube...something w/ graphics and illustrations so others can "see what you mean?"

    (I am going to do this myself at some point w/ my own "interpretations", as soon as I am able to figure-out the "hows"...I never had access to a computer prior to 10/13!!! so, I must learn

    as I go...not easy for an old man) I had to "teach myself" and it shows!

    (Thanks for reading!)
    I'm really interesting with news theories. Can you write more about this?
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    Quote Originally Posted by Beer w/Straw View Post
    I believe you have misconceptions.

    It was never a secret that physics has not proved things, and that mathematics is simply the language used to try and describe the workings of the universe.
    There's a very definite sense in which it can be said that physics does prove things.

    Recall the meaning of the term proof - to demonstrate the truth or existence of (something) by evidence or argument.

    In our case we use arguments. All arguments start off with propositions which are taken to be true. Such things are called Axioms, Postulates or Laws. One then presents a series of logical steps until one arrives at the proposition trying to be proved by the argument. Such a proposition is called the conclusion of the argument.

    All proofs follow this process. So it's quite legitimate to say that physics has proved many things. What it hasn't proved is the axioms since, by definition, an axiom can't be proven. Sometimes the physics is better understood to the point where a law of physics ends up being able to be proved, i.e. is able to be proved by an argument based on more basic axioms.

    As an example: If the two postulates of relativity are true then it can be proven that move clocks run slower.
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    Your post appears very philosophical.

    I was more thinking as opposed to a mathematical proof that scientific proofs are always disprovable.
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    Quote Originally Posted by Beer w/Straw View Post
    Your post appears very philosophical.

    I was more thinking as opposed to a mathematical proof that scientific proofs are always disprovable.
    That post wasn't very philosophical but insofar as it was philosophical it was regarding the philosophy of science which applies here since we're talking about what can and what can't be proved. Mathematical proofs can be disproved too if they axioms they're based on turned out to be wrong. Consider the Euclid's fifth postulate which proved out to be wrong, i.e. it had to be modified to take into account the curvature of space in the presence of a gravitational field. Math proofs can be proven wrong just as much as scientific ones can. They're just much more reliable that scientific ones are. So if you thought that mathematical proofs weren't disprovable then you were mistaken, because they are.

    Think about what would happen if Peano's postulates were wrong - Peano axioms - Wikipedia, the free encyclopedia
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    Doesn't Euclid's 5th postulate explicitly state that it is for two dimensional geometry?

    Are you going to debate that 1+1 does not equal 2?

    I am starting to like this forum less and less.
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    Quote Originally Posted by Beer w/Straw
    Doesn't Euclid's 5th postulate explicitly state that it is for two dimensional geometry?
    No.

    Quote Originally Posted by Beer w/Straw
    Are you going to debate that 1+1 does not equal 2?
    Why on earth would I do something outrageously wrong like that? All I said was that both math and physics are both based on axioms and that the validity of the proofs that are logically deduced in both fields is based on the validity of the axioms. So just because I said that you can in no way assert that I meant that any axiom was wrong or something as wrong as 1 + 1 does not equal 2.

    Quote Originally Posted by Beer w/Straw
    I am starting to like this forum less and less.
    Perhaps it's because you're learning that physics is not what you thought it was. It's quite correct to say that you can't prove a scientific theory. You might have confused that fact with what I wrote.

    I find it strange that you so impatient (or whatever it is that makes you want to quit a site for such a purpose)? This isn't the first time I've seen you act like this either. In both cases it's not a pretty site. Please try to keep more of an open mind.

    Please see Can Science Prove Anything?
    One consequence of Popper's work with falsifiability is the understanding that you never really prove a theory. What scientists do is instead come up with implications of the theory, make hypotheses based on those implications, and then try to prove that specific hypothesis true or false through either experiment or careful observation. If the experiment or observation matches the prediction of the hypothesis, the scientist has gained support for the hypothesis (and therefore the underlying theory), but has not proven it. It's always possible that there's another explanation for the result.
    which is quite true but not what I was talking about. But I think this is what you had in mind. However it wasn't what I Had in mind. I was talking about the theorems that physicists work out based on postulates. Here is an example of a proof in physics using the correct structure of a logical argument.

    We're going to use Newton's expression for the gravitational force as an example. Here's how the proof of such a theorem works

    If Newtonian's theory of gravity is correct then Newton's shell theorem is correct. Newton's shell theorem defined as follows
    Shell theorem - Wikipedia, the free encyclopedia

    1.A spherically symmetric body affects external objects gravitationally as though all of its mass were concentrated at a point at its centre.
    2.If the body is a spherically symmetric shell (i.e., a hollow ball), no net gravitational force is exerted by the shell on any object inside, regardless of the object's location within the shell.

    The proof is given in the URL above.
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    According to wiki it states two dimensional.

    You came very close to saying 1+1 does not equal two with that Peano axiom link. Is it you are trying to say 0 is not a real number?

    I'm not learning anything but that it is passed my nap time.

    And everyone already knows Einstein's theory of gravity is a better description, but harder to use than Newton's.
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    In reply to Physicist, re: your #47 post.

    "Clocks run slower" means that a given object will react to any change of condition (I'm assuming you're referencing a relativistic "FoR") I have never argued against this...what I do argue

    against is the idea that a "change of tick-rate" serves as a mandate that "time ITSELF changed" in relation to the clocks' FoR. I cannot accept this...a mathematical construct may imply

    otherwise, for it can do nothing else! "Math" does not think, and to enumerate "time" conditions and then state "here is proof" that "time changed" is an ab initio false proposition.

    "Matter and Mass possess the ability to alter...time has no such ability".

    (Thanks for reading!)
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    Quote Originally Posted by Beer w/Straw View Post
    According to wiki it states two dimensional.
    I'm not interested in that. I'll I was saying was that at one time Euclid's fifth axiom was one time not questioned then GR came along and that changed. Now what used to be an axiom that was never wrong, changed.

    As far as GR versus newton, also not the point. I was saying that given Newton's expression for the force being true (i.e. accepting it as an axiom) then the shell theorem is proven.

    Please go to bed and get some sleep. You don't appear to be ready for this.
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    Well, how exactly was the 5th postulate modified, other than calling it specifically Euclidean?

    Quote Originally Posted by Physicist View Post
    I'm not interested in that.
    That's the crux, isn't it? For two thousand years no one noticed that it could be wrong in an infinite amount of ways in three dimensions?

    And the 5th postulate was never proven in the first place, so bringing it up is a false premise.
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    Quote Originally Posted by Physicist View Post
    There are various forms of the uncertainty principle and what uncertainty means in modern quantum mechanics. However the one used exclusively in modern quantum mechanics textbooks and journal papers is the one where the uncertainty in a variable is the standard deviation in an ensemble of measurements or of a collection of single measurements from identically prepared systems.
    As such itís very possible to measure a particle at rest. All it means is that the measured value for the momentum is zero. Youíre using the uncertainty principle wrong. The Heisenberg Uncertainty Principle (HUP) is an inequality between the standard deviations of two observables and is a function of the wave function only. Measurement of any other variable before it has no relationship on the measurement of an observable. That means that you can measure the momentum to be exactly zero and then you can measure the position and get an exact value.

    Given what I said about thatís not true at all. Have you ever read about the meaning of uncertainty from anything other than a book written for the layman or a freshman/sophomore student? If not then please see the following
    The Uncertainty Principle (Stanford Encyclopedia of Philosophy)
    Heisenberg - Quantum Mechanics, 1925-1927: The Uncertainty Relations

    Even if what I said was wrong there is nothing wrong with the idea of measure the position of a moving object. Otherwise youíd be unable to measure the speed of an object.
    You cannot measure a zero momentum or any other quantity as zero because if you could then you wouldn't have measured anything.
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    Quote Originally Posted by Gerry Nightingale View Post
    Go ahead and read the more advanced books on theoretical physics.

    Perhaps you could try posting your stuff as a "presentation" on Youtube...something w/ graphics and illustrations so others can "see what you mean?
    There's little point reading such books since I have demonstrated that Frege's definition of zero, on which mathematics is based, is wrong and a contradiction. Therefore the whole of science is under suspicion since it uses mathematics. One contradiction in the system invalidates the whole system by the principle of explosion.

    I would love to do a Youtube presentation but have little experience in that. If you wish to form a collaboration I am interested if we can show common ground. I have a possible partner who may be able to sort out the video.
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    Quote Originally Posted by JohnMiddlemas View Post
    You cannot measure a zero momentum or any other quantity as zero because if you could then you wouldn't have measured anything.
    That's not true at all. Where did you ever get an idea like that from? If particle of mass m and charge q is moving at constant velocity in an inertial frame (which means there's no gravitational field present) and it moves in a straight line then you've measured the value of the force on the particle to be zero since F = ma = 0. You've also measured the value of the electric field at that point to be zero since E = F/q = 0/q = 0. If the particle is not moving then v = 0 and therefore p = mv = 0. Zero is merely one of an infinite possible values that can possibly result when a measurement is made. It doesn't mean that you're not measuring it whatsoever.
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    [QUOTE=Gerry Nightingale;18115What I will never agree to is the premise that "numbers trump reality, or any theory of reality"...this is what has happened w/ regard to modern physics, at least in QM![/QUOTE]

    That is so very true! But it's worse, numbers defy definition unless you use a contradiction. Numbers in set theory (basis of modern mathematics) are defined using the empty set {}. It can also be denoted by a single zero like symbol ō. In number theory 0 is defined to be {}. 1 is {{}}, 2 is {{}, {{}}}, etc. So the number 1 is taken to be zero surrounded by brackets, i.e. 1 = {0}. Just the idea of that should set alarm bells ringing worldwide! Obvious nonsense. How can an idea like "one" which may refer to a real object like 1 apple possibly be defined by "nothing" surrounded by ghostly brackets. The brackets themselves are figurative and have no meaning except to locate the 0. Well, the 0 locates itself anyway just by being written or thought about. So the brackets are doubly useless. As well, how can 1 thing (which is what 1 is), be defined by three (or four) things, i.e. {0} xor {{}}?

    By the way I studies Mathematics.

    I use 'xor' because 'or' tries to include the options of both xor neither which is a highly confusing concept. For 'both' we already have 'and'. Neither is 'none' which is the contradictory zero again!

    So there is no sense here saying 1 = {0}. I am sure even physicists may agree this one.

    There is only 1 definition of 1. Here it is:-

    1 is 1.

    Even that is problematic because I just wrote two 1's? Which 1 is the 1? Let me try again...

    1 is itself.

    xor just

    1

    That's really all you need to say about 1. There's also a clue there as to why not only mathematics is wrong but logic also. To say x=x is to say x is the same with itself. The law of identity states "ďeach thing is the same with itself and different from another". That is wrong. My simpler version above is more correct.

    "x is the same with itself"

    should be:-

    "x is itself"

    Why add to the confusion with "the same". Then you require a definition of "same", which they don't give.

    To the physicists who can see the truth here then question hard why you accept the mathematical and logical nonsense they give you and which perverts your science so badly.

    Although trained in mathematics, also studying philosophy and logic, I have realised that the only true discipline is physics. What you see is what you get just about sums it up. I'm not saying there is no logic but it needs redoing completely from a physical perspective only. In effect there is only one scientific discipline and it is PHYSICS. All the mathematics has to go. We don't want it, we just need a new logic, physics logic.

    1st task: Get rid of the zero.

    2nd task: Get rid of negatives. Physics is a positive discipline. We see things, we are things. You are getting anti-particles because you permit -ve numbers in the mathematics nonsense. The square root of -1 has to go quickly. There will be another way to code it.

    3rd task: Realise that all numbers are unary. To write decimal 7 is to write 1111111 in unary. 7 is just another name for the unary number.

    As for computers and programming I'm not sure yet but I've got a very bad feeling about it. Full of negatives, full of 0's, must be full of ****. The reason why things appear to work may be other than what you think.

    Even numbers are a debatable issue. There are things, things touching things. Does everything touch everything else xor is there such a thing as separation of things? Could such a separation be a "space" thing touching each of the separated things, in which case is reality just a huge line of things which can swap direction? Alternatively, is it groups of touching thing? How many things can a thing touch? These are the type of questions to be solved. Do I need to count at all? What is counting? What is 1? So far the definition of 1 is hidden. Is it one thing?
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    This thread should be moved to alternative theories.




    "My hero, zero Such a funny little hero But till you came along We counted on our fingers and toes Now you're here to stay And nobody really knows How wonderful you are Why we could never reach a star Without you, zero, my hero How wonderful you are."

    Zero -- from Wolfram MathWorld
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    Quote Originally Posted by Gerry Nightingale View Post
    Debating physics theory now is an exercise in futility, as in "every posit from Hawking is infallible". (I think Hawking is brilliant...and completely wrong w/ regard to his extrapolations of gravity theory! There is NO "ultimate gravity" regarding mass...yet his calculus "proves" there is! (Yes, based on a false premise from faulty observations)
    I agree that gravity is a silly idea. It could be about touch instead. In one case touch the earth. In another case we are separated from it by touching a space which touches the earth. We swapped position with the space. Why should space be one thing, it might come in loads of packets. Time too. Everything really, you, me, even God could be a packet. The whole shebang is a kid's building kit!

    The law of touching comes from examining logic and it's fallacies. For example the idea of intersection of two sets. If you draw the Venn diagram for this you get two overlapping circles. As if some of one set had merged together with some of the other. Physically though two objects are either touching or separate. So the Venn logic is false physically. Things stay in one piece protected by their borders. An object underwater is still the object. Oil on water stays together. It is hard to find a case of half merging. The logicians will say immediately, yes but the sets are collections of objects rather than just objects. For example Men with a blue garment and Men with a yellow garment. Then the intersection is Men with both a blue garment and a yellow garment. But the intersection is a third set rather than any merging. So really there are just three touching sets. Men with both a blue and a yellow garment are different from Men with a blue garment. The definition of "Men with a blue garment" failed to state whether it was "ONLY" a blue garment therefore the definition was ambiguous and invalid. Anyway, you could argue the point with them a lot more but suffice it to say that we could start a better system of physical logic by ruling out intersections are redefining AND as follows:-

    Theory of Physical Logic
    ------------------------------

    1) Intersections are prohibited.

    2) A AND B means A minimally separated from B

    3) A OR B means A separated from B.

    Minimally separated (touching) means there is a space between A and B of size 1. However even though separated we call them touching. They could be minimally separated in only one tiny place but elsewhere separated by a large distance. This explains the theory of quantum entanglement. Distance is irrelevant for physical logic, just another thing, or property of a thing.

    Separated means any space between A and B is always greater than 1 in size.

    Choosing 1 as the minimum space is optional and you could make it 8 or whatever depending on the application.

    The idea in physical logic is that we always use the real world as a reference point rather than trying abstract methods.

    So we know what touching means from physical examples. To be separated is what you might call not touching but since negatives are to be eliminated then the word "not" is barred.

    Gravity is silly. Why should masses thousands of miles away affect another mass. Very messy idea. Everything happens locally of course. Nice and simple. Pardon me but I'm not a physicist, my worst grade at school but I'm trying.

    So how could I explain the falling of an object using the touch theory? The world is a thing. I am a thing. Space is many things. If I drop an apple then it is separated from me I lose control of it. It falls under the control of the particular space it touches. That space has rules of selection we don't know. Assume it chooses the nearest large object, the world. The space passes control of the apple to the world. The apple stores its own mass, as does the world store its. All large objects with mass contain the laws of gravity and there is some calculation process going on to drag the apple closer to the Earth. The apple is too small to effect a gravity itself.

    So the idea that gravity is "issued out" continually from Earth is wrong. It only occurs when something like an apple requires it. In occuring, it is just a calculation process. The Earth stores its gravity and mass just like a freely moving object must store its velocity. These physical quantities are just properties of the things rather than independent of the things.
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    Quote Originally Posted by Beer w/Straw View Post
    Gerry, your post is completely wrong in so many ways.

    Making it simple: Newton described the effects of gravity with an inverse square law. It did not mean he knew why gravity does what it does!

    And your rantings about quantum mechanics is ludicrous. Just because something is not to your liking does not mean experimental evidence is disregarded solely on opinion.
    Are you sure you even know what 1+1 is? In unary we say 1 + 1 is 11. In decimal you call it 2. Why different names? Oh yes, you will say because decimal notation is more compact. As a physicist one would better consider the physics rather than the numbers.

    Now, 11 looks much more like two particles. Here is 1, and here is the other 1. This gives 11. You call it 2 and you confuse the physics. Well, actually it's the mathematicians who call it 2, sorry.

    So given we don't even know what is going on with numbers, and their definition of numbers is completely bogus, as I have shown here above, then why should we believe an inverse square law either? Oh yes, because it fits experimental facts and evidence you may say. The whole of that premise depends on a proper definition of numbers, but theirs is a sham. To measure anything requires numbers. I cast doubt on the whole measurement philosophy until they provide me with a concrete definition of numbers and with zero prohibited unless they can first say what it is too.

    Quantum mechanics is ludicrous. It uses all the mathematical errors and lies provided by the concept of zero.
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    Quote Originally Posted by JohnMiddlemas View Post
    I agree that gravity is a silly idea...


    I can't fall flat on my face -it would be silly!

    But some how I managed.
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    Quote Originally Posted by Gerry Nightingale View Post
    In reply to Beer w/Straw, re: your #43 post.

    (1) What is so "completely wrong in so many ways?" As far as Newton is concerned, I'm familiar w/ his writing and the principles of an "inverse sq." Since I am familiar w/ "inverse sq." as

    it pertains to "the density/volume of a given body in a given gravimetric-field " will demonstrate the following characteristics "as it falls", et. al. Please tell me the "how" of these mechanisms

    as they apply to a singular "ultra-dense entity" in a "supposedly" non-gravitational environment? What gravity, other than it's OWN, is the "dense-body" inter-acting WITH???

    Just "how" does the density of a mass give rise to an "inverse square of gravity" that has now acquired the ability to "square ITSELF FROM ITSELF!

    Where does Newton...or Einstein, "fit" into this hypothesis?

    .....

    (2) By your criteria...anything I write is either a "rant" or "fools errand" if it does not conform to "standards of doctrine". What I "like" or "dislike" has no bearing on what I think! For instance,

    there is an Administrator whom I despise (another "Site") on a personal basis...yet I can find no flaw in any of his "posts" w/ regard to calculus theory. He's extremely good, and writes very

    elegant formulas. His knowledge of modern theory would likely put anyone here in the "closet"...and yet he knows NOTHING of theory itself, only what he has read! (ask Jilan)

    He has no "intuition" nor any idea of "how to question" anything...yet knows everything pertaining to physics theory.

    ......

    Since when is "experimental evidence" enough to form a hypothesis that is valid...when there is no "counter" even considered? As in..."Let's give him a fair trial...and then hang him".

    Since when is a "mathematical formula" a "proof" of anything more than "mathematical formula?" This is not experimentation, not when "only the parameters of what we expect to find"

    are allowed as "guidelines!" To me...this is NOT "valid science".


    (Thanks for reading!)
    Gerry, you are talking very very much sense I believe. Keep it up please. They will always hate anything which might damage their comfort zone of belief. Actually, it's worse than that and it might even apply to you and me too, because as we approach the "real truth" how far are we prepared to go? What if it could be shown that almost everything or indeed even everything entirely that we believe in is false, even the concept of false itself. That is what I really think is going on. In centuries to come, this time will be looked back upon as one of the darkest times in history, where the whole world followed a pack of lies worse than anything previously concocted.

    As for your gravity question it is interesting. The density of a mass must first be defined. That requires definitions of mass and density. However this contradicts "Touch theory" since density and mass can only touch or be separate. One thing is one thing. Also, they try and say density is a collection of masses divided by the volume of space they occupy. Wow, what a load of stuff. To say that you need to be concrete certain of your definitions of:-

    mass
    numbers
    space
    division
    volume

    Each one of those is currently a mystery and all definitions have failed.

    Forget density. Impossible to define it.
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    Quote Originally Posted by "John&Gerry
    -He has no "intuition" nor any idea of "how to question" anything...
    -Each one of those is currently a mystery and all definitions have failed
    Each of you have failed to even begin to make sense. That's a pity, because there maybe a lot of general things to say about position, without even making complicated math, that you loath, for obvious reason.

    I have not 16 fingers, but I still use hexadecimal to talk to my computer, or binary, and way more abstract representation that you'll probably loath also, even if they entertain you on a daily basis. Using unary would be such a waste of time, especially that you don't understand that "space" is part of your unary number.

    We do measure time by using clock, in GR or in my microwave oven. Whatever you think about what "we" think, it is false. Please understand that.
    We need the zero to represent some value. For example your willingness to participate honestly to a conversation is ZERO 0 #0 unary"".

    Scientist love to challenge their comfort zone, that is their craft. That's why science is somewhat a huge house of card. And they all hope it will fall apart, because the actual one is actually kind of stuck in a dead end.

    You are the ones that fail to challenge your comfort zone, the ranting zone.
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    QUOTE=Boing3000]
    Each of you have failed to even begin to make sense.
    [/quote]
    That's far from the truth. I have you the correct answer in my post. Just because you disagree with it/don't understand it is not my fault. In a two way conversation one must have a student and a teacher. In this thread I'm playing the role of teacher and you the role of student. You simply need to be a better student and not blame your failure to get an answer you like on the teacher. We know our business, you don't. You can't sincerely got to a physics forum, ask a question because you don't understand something and expect to the answer to be whatever you want it to be. Sometimes you're going to be so wrong in your expectations of an answer that it will blow your mind in that it was something you never expected and find it hard to understand. But blaming it on the teacher is a severe problem on your side of the student/teacher relationship.
    Let me retrace what I said from the start. When you got here you made the following claim
    Stationary particles are prohibited by the uncertainty principle Ö
    which is quite wrong, i.e. stationary particles are not prohibited by the Heisenberg Uncertainty Principle (HUP). Like most beginners in QM, and even some professionals, you made the common mistake of thinking that the HUP holds for single measurements. It doesnít. Since uncertainty is defined as the standard deviation of an ensemble of repeated runs of an experiment or multiple executions of a single run by a large number of single runs of a single duplicate system. Itís quite possible to measure the momentum of a particle to be zero. Nothing prohibits it since itís one of the eigenvalues of a wave packet of a Gaussian wave for a single free particle traveling in one dimension. Thereís nothing preventing you from measuring the momentum from being zero. What do you think can be said about a particle whose momentum was measured to be zero?
    Before moving on forward it needs to be made clear that speed and velocity are not well defined terms in quantum mechanics. There really no such thing as a speed operator speed eigenvalue. Same with velocity. Thereís something actually called that but it has to do with canonical momentum over mass rather than linear mechanical momentum over mass, i.e. v = p/m.
    Öare prohibited by the uncertainty principle otherwise both position and momentum would be precisely determined together.
    That too is not true and is also based on your misunderstanding of quantum mechanics. Itís very possible to measure the position of the particle and get an exact value and then measure the momentum of the particle right after that and get an exact value right after that. What is happening is that when you measure the position the wave function collapses into an eigenstates of position. Then the momentum has a uniform probability distribution, i.e. one value of momentum is just as likely to be measured as any other. When you again measure position immediately after that nothing changes. Then when you measure the momentum the system collapses into an eigenstate of momentum. Then the position has a uniform probability distribution, i.e. one value of position is just as likely to be measured as any other. This way there is no reasonable way to say what the position and momentum are at the same time, i.e. together.
    For example your willingness to participate honestly to a conversation is ZERO 0 #0 unary"".
    Are you saying that for real and not as example? If so then what has anybody ever said to you to make you be so rude to them?
    Scientist love to challenge their comfort zone, that is their craft. That's why science is somewhat a huge house of card. And they all hope it will fall apart, because the actual one is actually kind of stuck in a dead end.
    You are the ones that fail to challenge your comfort zone, the ranting zone.
    Who are you referring to? Thatís total nonsense.
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    Quote Originally Posted by JohnMiddlemas
    Another way of looking at it. The Schrodinger wave equation, from which the uncertainty principle is derived, ...
    That is incorrect. The Schrodinger equation is not used in the derivation of the uncertainty principle at all. See Introduction to Quantum
    Mechanics
    by David Griffiths, Section 3.5 The Uncertainty Principle at Introduction to Quantum Mechanics | David J. Griffiths | digital library BookOS
    or
    https://www.physics.ohio-state.edu/~jay/631/uncert1.pdf
    http://www.pa.msu.edu/~mmoore/Lect23_HeisUncPrinc.pdf

    Quote Originally Posted by JohnMiddlemas
    ..assumes and uses the time dimension and the cartesian coordinate system applied to space as we know it.
    That's not necessarily true. The uncertainty principle is an inequality between canonical coordinates and canonical momentum. They can be any valid well be have system of coordinates such as polar coordinates, spherical coordinates, cylindrical coordinates, etc.

    Quote Originally Posted by JohnMiddlemas
    An object at this point must be able to remain there for at least a small amount of time for (2,1,4) to have meaning.
    Not true. The concept of a particle being instantaneously at rest is a well-known one in classical mechanics.

    So far all your conclusions which you've used to disparage us are derived using arguments with logical errors in them.
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    Quote Originally Posted by Physicist
    Quote Originally Posted by Boing3000
    Quote Originally Posted by Physicist
    Quote Originally Posted by Boing3000
    Quote Originally Posted by John&Gerry
    -He has no "intuition" nor any idea of "how to question" anything...
    -Each one of those is currently a mystery and all definitions have failed
    Each of you have failed to even begin to make sense.

    That's far from the truth

    Physicist, I think you've got even more technical problem with the site then we have. Those two quote are not from you, but from Gerry Nightingale and JohnMiddlemas.

    The other quotes are not from me (but the last two), so maybe you can address them to whoever you want to teach some lesson (which are pretty good and informative)
    Quote Originally Posted by Physicist
    Quote Originally Posted by Physicist
    Quote Originally Posted by me
    You are the ones that fail to challenge your comfort zone, the ranting zone

    Who are you referring to? Thatís total nonsense.



    Maybe not clicking on "post" at this position would have saved us some time.
    Physicist likes this.
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    Quote Originally Posted by Boing3000
    Physicist, I think you've got even more technical problem with the site then we have.
    Please accept my most humble apologies. Were they useful as far as they were on the right track?
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  70. #70  
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    Quote Originally Posted by Beer w/Straw View Post
    You came very close to saying 1+1 does not equal two with that Peano axiom link. Is it you are trying to say 0 is not a real number?
    To define 1 + 1 you first must define 1, and +. These are both very difficult to define.

    In set theory they attempt to define 1 by using 0, a.k.a the empty set. 0 = {}, 1 = {0} or {{}}.

    This first requires a definition of 0 which they attempt to give using the axiom of the empty set:-

    ∃x ∀y ¨(y∈x)

    In words: there exists a set x such that for all sets y it is not the case that y is a member of x, i.e. x = {}, and x=0.

    However ¨(y∈x) means "not (y is a member of x)" which means (y is not a member of x) which means (it is false that y is a member of x) which means simply false(y∈x) or "(y∈x) is false". So we get:-

    ∃x ∀y ¨(false) which is:-

    ∃x ∀y true

    In words: There exists a set x such that for all sets y it is true.

    Is that a suitable axiom for an empty set? All it says is that there exists a set x. It says nothing about the contents of x. So it is not the case that x={} as they claim.

    Set theory is wrong. Since set theory is wrong then they have no basis for the rest of mathematics. They can't even define the number 1!!

    What is the real definition of 1? Well, I have an idea which is to do with the concept of indivisibility but I'll leave that for now. As for defining '+' that is a huge bag of worms. Are you joining, moving, concatenating or what? I'll skip that too for now. I have less of an idea about how to define it properly but I think it can be done.
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  71. #71  
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    Quote Originally Posted by Physicist
    Please accept my most humble apologies. Were they useful as far as they were on the right track?
    No problem. As about the usefulness of they, I fail to locate that entity. Probably a FoR problem ;-)
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    Quote Originally Posted by Boing3000 View Post
    We need the zero to represent some value.
    Zero cannot represent a value. It is nothing. No properties, no location, no nothing, no value. A ghost.
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    Quote Originally Posted by Physicist View Post
    All it means is that the measured value for the momentum is zero.
    A measured value cannot be zero. There is nothing to measure. All measured values are something, no matter how small, they are still something, otherwise they would not be a value.

    You need to start thinking properly about what you are saying.
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    Quote Originally Posted by JohnMiddlemas
    A measured value cannot be zero. There is nothing to measure. All measured values are something, no matter how small, they are still something, otherwise they would not be a value.
    As I explained already that's quite wrong and repeating your same claim without modifying it after flaws were pointed out doesn't make it any more valid. As I explained already that's quite wrong and repeating your same claim without modifying it after flaws were pointed out doesn't make it any more valid. What you've shown here is your lack of understanding of what "zero" is and means. It's defined as the lack of something. E.g. if you have a barrel which is only to contain apples and you open it up and see that it's empty then we have a word for that, i.e. there are "zero apples in the barrel". That's what it means to "measure" something and have the result be zero. I.e.

    Zero -- from Wolfram MathWorld
    Zero is the integer denoted 0 that, when used as a counting number, means that no objects are present.
    But you've totally missed that because you never stopped to learn how the term "zero" is defined or what it means. However since one of my degrees is in mathematics I've always known that to be true and that's why I know what I'm talking about and you don't.

    Quote Originally Posted by JohnMiddlemas
    You need to start thinking properly about what you are saying.
    And you need to be less rude when you think you have a point. I know exactly what I'm talking about since I have a great deal of experience both in a lab and theoretically over a period of several decades that what I said is precisely right and how wrong your claim is.

    So far you've been unable to understand the difference between not making a measurement and having the numerical value of the answer being zero. Everything you've based your poor argument on is rooted in your invalid claim that There is nothing to measure. which you're unable to grasp is not the same thing as measuring something and getting zero as a result. Even more so is that you really don't know what the number zero is. The word "zero" refers to a number and that has the literal meaning of "there's nothing to measure." That's why "nothing to measure" and "the result of the measurement is zero" are the exact same thing.

    Being both a physicist and a mathematician means that I know a great deal about math than you've demonstrated so far when it comes to the meaning of numbers and their relationship to reality and physics.

    And I know very well that if you tried to pull this nonsense on any physics exam which had zero as an answer then you'd have failed that question. No physicist in their right mind would tell their student than the result of their calculation can't be measured in the lab if that result is zero. That's just crazy talk. That'd be like saying that it's not meaningful to say that the electric field inside a spherical conductor is zero. If you tried to claim to any physicist that you can't talk about the gravitational field inside a hollow spherically symmetric shell just because its zero and you don't think an instrument reading zero means anything then they'd laugh you out the door. We have instruments for which the value of zero is a very legitimate measurement. I could go on and on and cover all the examples I've run across over the last 30 years of being a physicist but it's clear to me that you wouldn't be able to understand it.

    Please do me a favor. Open up your desk draw and tell us how many pineapples are in it. Lol! Never mind.

    I don't react well to people who are rude to the point where the make comments like You need to start thinking properly about what you are saying. so welcome to my ignore list.
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  75. #75  
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    Quote Originally Posted by John
    Zero cannot represent a value. It is nothing. No properties, no location, no nothing, no value. A ghost.
    Zero can represent a value.
    No-thing == Zero thing.
    No-properties == Zero properties == void.
    No-location == Zero coordinates (not 3/4 coordinates == 0, which is One location)
    No-Nothing == One thing or more
    No-value == Zero value (not One Value == 0, which is One value)
    A ghost == One Ghost (you are right, Zero cannot be used to represent A ghost, unless he have a ghostly T-shirt with a Zero printed on it)

    I doubt you understand why "void" is a different word then "space".
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    Quote Originally Posted by Physicist View Post
    What you've shown here is your lack of understanding of what "zero" is and means.
    Insults are a waste of your time (lack of understanding). Consequently I will cherry pick one of your points only and ignore the rest until you cease to insult.

    Zero is the integer denoted 0 that, when used as a counting number, means that no objects are present.
    Completely invalid definition since he didn't define what 'no' means. Present where?
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  77. #77  
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    Quote Originally Posted by Boing3000 View Post
    Zero can represent a value.
    No-thing == Zero thing.
    Define 'No-thing'. What does it mean to you without mentioning the zero?
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  78. #78  
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    [QUOTE=JohnMiddlemas]Define 'No-thing'. What does it mean to you without mentioning the zero?[QUOTE]
    No-thing is the absence of thing. No-thing <-> there is not a thing

    Do you also want me to define "absence" "is" "no" "there" "thing" without saying "beetlejuice" 3 times ?
    D'ya want an example ?

    Quote Originally Posted by JohnMiddlemas
    Quote Originally Posted by Physicist
    What you've shown here is your lack of understanding of what "zero" is and means.
    Insults are a waste of your time (lack of understanding). Consequently I will cherry pick one of your points only and ignore the rest until you cease to insult.
    I can count the number of insult in Physicist post. I will use my fingers ... wait, I am still counting, I am a slow reader...
    ...Ok. now I look at my hand, and guess how many of them finger/thing are up ? Not one, not two, not tree, not four, not five, not six, not seven, not eight, not nine, not ten.
    So now, you still don't now how many insults I have counted, you miss an important clue ... I have counted less then ten insults.

    Can you say how many insult have I counted ? without using the number-who-cannot-be-named ?

    This site may help you in this difficult endeavor.
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