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Harriman on the Crisis in Physics

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Vik

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If you haven't heard his lecture yet and you are ignorant of what QM and relativity say, you may misunderstand what Harriman is trying to say about them.

I have some comments and questions.

1) Some of QM's pioneers said some nutty things, but the popular press tends to misrepresent QM as well. We should separate *real* nuttiness from *misunderstandings* and *misconceptions* on the part of an ignorant layperson.

In QM, people do NOT "cause wave collapse". "Observer" refers to the measuring apparatus, whose particles can interact with what you're trying to measure and change their behavior.

Harriman makes a comment on Schrodinger's cat. Please be aware that Schrodinger's thought experiment was intended to illustrate the absurdity of taking the Copenhagen interpretation literally. Schrodinger did NOT mean that the cat is REALLY in an indeterminate state until we look.

He wasn't the only one who felt the interpretation was inadequate. Einstein, Podolsky and Rosen wrote a paper on one of the issues. De Broglie thought the wave-particle duality was inadequate and proposed something similar to a standing wave.

Heck, Feynman explicitly stated that if you shine a light on an electron to figure out which slit it's passed through, you lose the interference pattern because photons interact with electrons.

2) I don't see anything in GR that claims that space exists apart from physical entities. GR is founded on SR, which assumes Galilean relativity. If I'm reading Galilean relativity correctly, space is NOT an entity.

It is my understanding that it was Newton who claimed that space was absolute and that it was Einstein who rejected that claim. Google "Newton's buckets". It is my understanding that Einstein REJECTED absolute space and came up with a different explanation for the behavior of the buckets (the rest of the universe).

3) SR claims that space will *appear* to contract to an outside observer.

So why do some people think SR says that space *actually* contracts? I'm pretty sure that's the fault of Lorentz Ether Theory. While Einstein claims that contraction is APPARENT, Lorentz claims that contraction is REAL. AFAIK, both LET and SR make the same predictions. However, SR led to GR, which gave us a correct prediction for Mercury and GPS navigation systems. LET dead-ended.

I wonder what Harriman's thoughts are on the matter.

4) Harriman doesn't like the phrase "time dilation". It is a cold hard fact that fewer seconds pass on a shuttle accelerated into orbit and brought back than a shuttle parked on earth. Why is it wrong to call this "time dilation"? Does he suggest a better phrase?

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In QM, people do NOT "cause wave collapse". "Observer" refers to the measuring apparatus, whose particles can interact with what you're trying to measure and change their behavior.

This is something that's always bugged me, from my layman's perspective: what is a "measurement"? I see only two possibilities. Either a measurement is an interaction between existence and consciousness, or it's an interaction between one part of existence and another. The first model is the "people cause wave collapse" approach and would require building consciousness into the foundations of quantum mechanics -- something that is not the case as far as I know.

The second model sounds like what you're describing, the "what you're trying to measure" and the "measuring apparatus" being the two parts of existence in question. But that raises the question of what makes the measuring apparatus a measuring apparatus? Is it something inherent in its nature? If so, what? Or is is just that when we're doing the calculations we decide to treat the measuring apparatus using the principles of classical physics and the "what you're trying to measure" using the principles of quantum mechanics? (A non-Objectivist former co-worker of mine, who had a Ph.D in theoretical physics from Cambridge, once described the measurement process to me in essentially those terms.) I find that explanation unsatisfying because it still ultimately reduces to consciousness -- in this case, a decision by consciousness to label part of existence as a measuring apparatus and to crank the mathematical formalisms accordingly.

I don't know if I'm missing something obvious here or if this is a real lacuna in the theory, but I've asked a number of knowledgeable people this question, Objectivist and non, and have yet to receive an answer that makes any sense to me -- and this doesn't look like something you can ignore if your goal is to describe and explain what is actually physically happening in reality.

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One other thing:

I am not sure what Harriman means when he claims that Einstein made physics observer-dependent.

Copernicus once said that the laws of the universe are the same everywhere. Einstein integrated this idea with Galilean relativity to develop the principle of general covariance: The laws of physics are the same in all inertial frames of reference. This suggests to me that coordinate system transformations are a way to ensure that the laws remain applicable REGARDLESS of the observer's state of motion.

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This is something that's always bugged me, from my layman's perspective: what is a "measurement"? I see only two possibilities. Either a measurement is an interaction between existence and consciousness, or it's an interaction between one part of existence and another. The first model is the "people cause wave collapse" approach and would require building consciousness into the foundations of quantum mechanics -- something that is not the case as far as I know.

Nope. Just a common misrepresentation on the part of "science" writers.

The second model sounds like what you're describing, the "what you're trying to measure" and the "measuring apparatus" being the two parts of existence in question. But that raises the question of what makes the measuring apparatus a measuring apparatus? Is it something inherent in its nature? If so, what? Or is is just that when we're doing the calculations we decide to treat the measuring apparatus using the principles of classical physics and the "what you're trying to measure" using the principles of quantum mechanics? (A non-Objectivist former co-worker of mine, who had a Ph.D in theoretical physics from Cambridge, once described the measurement process to me in essentially those terms.) I find that explanation unsatisfying because it still ultimately reduces to consciousness -- in this case, a decision by consciousness to label part of existence as a measuring apparatus and to crank the mathematical formalisms accordingly.

I do not see how we can avoid labeling something as measuring apparatus and something as measured.

First, when measuring anything with any device, it is necessary to account for possible errors due to the setup of the device or some other fact about how the device works.

Second, a double-slit surface is huge in comparison to a photon. So huge that the old equations for interference are "good enough" to predict the locations of bright and dark fringes. But if you try to figure out "which" slit a SPECIFIC photon went through, you have to throw something big at the poor tiny photon so you can say "here it is". Once the photon interacts, it will do something DIFFERENT than what it would have done if you hadn't thrown something at it. This has to be accounted for.

It has been suggested to me that if we applied quantum to all the little particles of the measuring device and tried to figure out how to describe the device as a whole, we'd end up with the classical description of the device. So apparently the "choice" is simply a way to avoid unnecessary math.

I don't know if I'm missing something obvious here or if this is a real lacuna in the theory, but I've asked a number of knowledgeable people this question, Objectivist and non, and have yet to receive an answer that makes any sense to me -- and this doesn't look like something you can ignore if your goal is to describe and explain what is actually physically happening in reality.

What do you think of Richard Feynman's explanation of the electron double slit?

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I do not see how we can avoid labeling something as measuring apparatus and something as measured.

Perhaps I should ask a different question. In quantum mechanics, is the 'collapse of the wave function' an actual physical phenomenon? Is it the case that at time T there is a waveform, and at some later time T+n the wave has 'collapsed' into a fully determinate state? If so, then my question is what triggers or causes this event, out there in reality? It can't be triggered by any event that reduces to a choice or identification by consciousness for reasons I think we agree on.

It has been suggested to me that if we applied quantum to all the little particles of the measuring device and tried to figure out how to describe the device as a whole, we'd end up with the classical description of the device. So apparently the "choice" is simply a way to avoid unnecessary math.

Hmm. I'll have to chew that one a bit -- it's after midnight here so Deep Thinking is, at the moment, Right Out.

What do you think of Richard Feynman's explanation of the electron double slit?

I haven't read it. I'm not a physicist; I'm a software engineer with a bunch of eclectic intellectual interests.

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The second model sounds like what you're describing, the "what you're trying to measure" and the "measuring apparatus" being the two parts of existence in question. But that raises the question of what makes the measuring apparatus a measuring apparatus? Is it something inherent in its nature? If so, what?

A measurement of a quantum mechanical system is an example of the interaction of that system with its environment. We now know that interactions with the environment lead very quickly to decoherence of the QM system. This is also an explanation of the classical behavior of macroscopic systems and also why there cannot exist a superposition of an alive and a dead cat in Schrödinger's thought experiment (it isn't the observer/a consciousness that destroys the superposition of the quantum system, but the environment in that box, such as the apparatus that triggers the breaking of the glass). A measurement apparatus is just one particular example of a macroscopic environment that decoheres the QM system, decoherence can also occur due to gas molecules in the atmosphere or even due to the cosmic background radiation.

Or is is just that when we're doing the calculations we decide to treat the measuring apparatus using the principles of classical physics and the "what you're trying to measure" using the principles of quantum mechanics?

That was in fact the pragmatic solution of Bohr at the time, as he didn't know the mechanism of decoherence, so he made a divide between the quantum system and the classical measurement apparatus, which allowed people to use all the machinery of quantum mechanics, while ignoring what exactly happened in the "black box" between the quantum system and the classical measurement apparatus. For most applications that wasn't a problem, you could do all the calculations. But it was of course theoretically unsatisfying, which prompted Schrödinger to come up with his cat example, which lead people to think that it was somehow a consciousness that caused the collapse of the wavefunction. Now we know that this is not true, that it is the mechanisme of decoherence that is responsible for the transition between the quantum system and the classical, macroscopic world (like the measurement apparatus).

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Perhaps I should ask a different question. In quantum mechanics, is the 'collapse of the wave function' an actual physical phenomenon?

Different interpretations say different things:

http://en.wikipedia.org/wiki/Interpretations_of_quantum_mechanics#Comparison

I believe there is not sufficient information at present for a meaningful answer.

Is it the case that at time T there is a waveform, and at some later time T+n the wave has 'collapsed' into a fully determinate state?

You can have a state of knowledge such that you know a particle could end up in a handful of locations but you don't know enough to say which. So you draw up a waveform. When you know enough, you can calculate a determinate state and dispense with the waveform.

But before you're tempted to call the waveform a mathematical artifact, you should consider something.

If you fire electrons, one after another, through a double slit, you will get an interference pattern--a wavelike pattern alternating bands of high concentrations of electrons separated by "bands" where there are no electrons. If you want to know which slit the electron passed through, you could shine a light on it to find out. However, this interaction changes the behavior of the electrons so that they all pile up in one place. So we have reason for thinking there WOULD HAVE BEEN a wavelike pattern if we hadn't violated the condition(s) that made it possible.

Why is there a wavelike pattern in the first place? Do electrons interfere with themselves? Maybe. But if they do, why should the interference pattern disappear when photons interact with electrons? Obviously the interaction caused it. But WHY?

What if electrons normally interact with virtual particles? What if shining a light overwhelms the electrons so they all go one way?

There are several problems with this conjecture.

First, I don't know any way for testing it.

Second, Feynman diagrams, which employ virtual particles, were originally intended to aid memory for the purpose of calculation. It's a bit like saying "Ok I don't know enough about the particle to know what it's been interacting with. But I know enough to say that there is a certain probability that there will be an interaction with A. But there is also a certain probability for interacting with B. And there is another probability for interacting with C, but only if D does X. Given all these probabilities and a list of many others, here is what I predict the measurement will be".

What's interesting about this approach is that the more possibilities you consider, the closer your prediction will be to reality.

Thus Feynman's Path Integral is a tool for summing over all possible histories to arrive at the probability for a particular event. It is a very reliable tool in that it enables you to calculate the probabilities to an arbitrary accuracy. (By "possible histories" I mean that we don't know enough to say which one happened.)

Feynman's approach sidesteps the observer problem, but it doesn't say why the interference pattern goes away. Furthermore, the Feynman diagrams are horrifically messy in QCD. This suggests severe limitations on using the diagrams to get a feel for what's really going on.

The QCD messiness reminds me of the era of astronomy between heliocentric-ism and Kepler, when astronomers used a complicated system of circles to approximate planetary orbit because they didn't think of an ellipse. There is a crucial difference though. In the case of astronomy, it was eventually found that you could NOT approximate the orbit with circles. No such problem exists with the Feynman path integral. That device remains shockingly useful.

If so, then my question is what triggers or causes this event, out there in reality? It can't be triggered by any event that reduces to a choice or identification by consciousness for reasons I think we agree on.

AFAIK, no serious physicist believes that consciousness causes collapse.

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  • 2 months later...

This is something that's always bugged me, from my layman's perspective: what is a "measurement"? I see only two possibilities. Either a measurement is an interaction between existence and consciousness, or it's an interaction between one part of existence and another. The first model is the "people cause wave collapse" approach and would require building consciousness into the foundations of quantum mechanics -- something that is not the case as far as I know.

Measurement is the province of conscious, conceptual beings, like me and you. However, that is NOT what QM means by "measurement" (in the context of Heisenberg's conversion of the equations of motion from representing trajectories to representing states, using Planck's equation to set scale). QM means what you say: to measure a property of an entity, you must associate it with another entity, your measuring device; if the entity is a table, then your eyes will do as device, but in the case of electrons, you need something special. But the idea is the same: you use some form of "sensory" apparatus to bring Existence into the scope of your consciousness. When that occurs, both the entity and the measuring device change quantum state, and it is the state change in your measuring device that is recorded and used to generate the conceptual theory linking your observations into a harmonious package.

- ico

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Perhaps I should ask a different question. In quantum mechanics, is the 'collapse of the wave function' an actual physical phenomenon? Is it the case that at time T there is a waveform, and at some later time T+n the wave has 'collapsed' into a fully determinate state? If so, then my question is what triggers or causes this event, out there in reality? It can't be triggered by any event that reduces to a choice or identification by consciousness for reasons I think we agree on.

It's a misnomer. The reality is spectroscopic data, scattering patterns, and nuclear/chemical reaction products -- the rest is just a fancy model, good as far as it goes, but ripe for replacement should a clever person come up with a better one, thus the progress of science.

The visualization of a "collapsing wave" does not contradict QM's model per se, but neither does it elucidate it unless the process of wave collapse is incrementally observable as it happens, as an objective, reproducible, experimental fact. However, such is not the case. It's a visualization -- and, FWIW, I think it irrelevant and not worth wasting time on.

Bottom line: no cognitive value in the analogy, in my experience.

I haven't read it. I'm not a physicist; I'm a software engineer with a bunch of eclectic intellectual interests.

Hey, me too -- albeit, I do have a background in physics, enough to know what I am saying to the extent I haven't crossed up any wires over the years.

- ico

Edited by icosahedron
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  • 2 weeks later...

Perhaps I should ask a different question. In quantum mechanics, is the 'collapse of the wave function' an actual physical phenomenon? Is it the case that at time T there is a waveform, and at some later time T+n the wave has 'collapsed' into a fully determinate state? If so, then my question is what triggers or causes this event, out there in reality? It can't be triggered by any event that reduces to a choice or identification by consciousness for reasons I think we agree on.

I think it is more appropriate to ask "is the wave function physical?".

While it may seem somewhat plausible in the case of a single particle "system" where the wave function is a function of 3 spatial dimensions, it seems highly implausible as soon as one considers two or more particle systems. It may seem logical that, for multi-particle systems, each particle "gets" a 3D wave function but, according to standard QM, multi-particle systems have a wave function that, for an N particle system, "lives" in a 3N dimensional "space", i.e., there are 3 spatial degrees of freedom for each particle.

So, for example, a two particle QM system has a 6D wave function, i.e., the wave function is a function of the coordinates of both particles.

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I think it is more appropriate to ask "is the wave function physical?".

While it may seem somewhat plausible in the case of a single particle "system" where the wave function is a function of 3 spatial dimensions, it seems highly implausible as soon as one considers two or more particle systems. It may seem logical that, for multi-particle systems, each particle "gets" a 3D wave function but, according to standard QM, multi-particle systems have a wave function that, for an N particle system, "lives" in a 3N dimensional "space", i.e., there are 3 spatial degrees of freedom for each particle.

So, for example, a two particle QM system has a 6D wave function, i.e., the wave function is a function of the coordinates of both particles.

Why can't it be the case that there is a 3N-dimensional wavefunction, which pushes all the particles around? I don't see a conceptual problem there, at least not necessarily. No one is saying it is a physical wave in space, but rather that it is a representation of a real interaction among all the particles (like a path through a 3N+1 dimensional phase space in Hamiltonian mechanics - something I'm learning about in my Classical Mechanics II course right now).

As for Lorentz Aether Theory- don't knock it. It does NOT say that space or time actually contracts. What it says is that we measure everything, ultimately, with massless particles (like photons and the like), and that all massless particles travel at a single constant speed in the absolute rest frame- the speed of light in a vacuum. Since all measurements are ultimately based on massless particles (even yardsticks are made of atoms, which are held together by electromagnetism- i.e. photons), then when you are moving all your measurements are going to be different then before. Do a little simple algebra and out pops time dilation and length contraction and the increase in apparent mass (i.e. that it takes more of a momentum change in order to produce the same change in velocity), etc., as well as all the usual translational relations between any two reference frames. And it turns out that the absolute rest frame can never be observed, and any inertial frame is just as good as any other inertia frame. In short, you get all the results of special relativity, with no room for wishy-washiness about space or time contracting.

Properly understood however, space and time are relational, and since the relations can change, so can space and time. If our measuring stick is light, and light travels in a curved path, then the fastest possible path between the two points is a curve. But the fastest path is a "straight-line", therefore space is curved. The two views are basically identical.

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  • 1 month later...

There is nothing unacceptable in having a function, such as the psi-function, containing all the states of a system, which can be revealed only through measurement; that is, through applying an operator (representing an observable) on it -- the psi-function contains all the possible eigenvectors and whether or not a given eigenvector will be the result of the collapse of that function (the result of the measurement) is only a matter of probability.

All is well and good so far. The problems begin when the state function contains eigenvalues that are non-physical. In this respect the example with the cat enclosed in a box with a decaying radioactive atom does not reflect at all the essence of the problems in quantum mechanics because both states of the cat are physical -- the cat can indeed be either alive or dead and that depends on the probability of the radioactive element to decay. Thus, Schroedinger's cat is just a good illustration of what quantum mechanics would be if everything were OK in it. In quantum mechanics, as mentioned, however, the state function sometimes contains also non-physical eigenvalues which have non-zero probability of appearing after collapsing the state function (after doing the experiment) and that has to be corrected if we want the quantum theory to be a truly physical theory. The correction most likely will come from studying the physical limitations of the Hilbert space which so far is taken as unbridled with regards to its physicality. That limitless perception of Hilbert space as fully representing reality is at the bottom of all kinds of non-physical paradoxes, some of which seem very appealing to more than just a few people. These paradoxes can be enjoyable and entertaining as science fiction read but have nothing to do with reality and that should be realized before disappointments follow after the great enthusiasm and expectations.

The above question should be distinguished from the question as to whether or not a body (such as, say, an automobile) has length before measuring it. Such a question has nothing to do with Schroedingr's cat example because even enclosed in a box quantum mechanics gives with 100% certainty the answer that said body has length. The same way the cat in a box can indeed be either alive or dead under the circumstances of the Schroedinger's experiment. These are true, physical states of the cat. As is the length of the car in the box. There is no either/or there. There is no other possibility to be revealed after the experiment but one -- the car to have length. Measurement does not create the length. In the case of the cat, measurement, reveals which one of the two possible states of the cat, unbeknownst to the observer before opening the box (before doing the experiment), is the cat in.

Therefore, when addressing the problems in quantum mechanics one should be careful to pinpoint its real problems and not point to problems where there are none.

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_wh_, first welcome to the forum. I am not sure what you mean by your statement that the eigenvectors are at times unphysical. I've never seen such a case in my classes. That isn't to say they can't exist, but I have never seen or heard of them. The only "non-physical" things I've ever seen are the types of paradoxes that occur with, say, Bell's inequalities, or Dr. Schroedinger's cat. Can you give me an example of what you are talking about?

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@nanite1018,

Take, for instance, a singlet-state, write the observable representing the spin of the first and the second particle (the spin operators S1 and S2) and carry out the measurement, for simplicity, along, say, the z-direction. First, convince yourself that S1 and S2 are commuting, that is, S1 and S2 can have simultaneous eigenvectors. Then apply simultaneously S1 to the first particle and S2 to the second. You will find out that there is a non zero probability to have the system prepared after such simultaneous application of S1 and S2 (to have the psi-function collapsed) in a state whereby the particles will have both up and down spin. Such state of particles (say, electrons) has never been found experimentally. Thus, a result in full concordance with the QM formalism has no physical meaning. You may also want to take a look at the full psi-function analyzed by Einstein-Podolsky-Rosen and not at its above-mentioned simplified variant of a singlet-state, proposed by Bohm and then used by Bell in his theorem. You may find the situation to be even worse than what EPR have shown, namely, one gets a result whereby two particles though moving in opposite directions get closer and closer to each other -- a clearly non-physical outcome. There are many other problems with QM such as the lack of rest, for instance, leading to non-physical notions such as zero-point energy etc. but the above example based on the formalism of QM is enough to convince us that efforts should be made to curb the unbridled perception that all of the Hilbert space is physical. Certain restrictions should be imposed on the otherwise beautiful math of QM to have its solutions always have physical meaning and not get into the dead-end of non-physical notions such as non-locality, as another example.

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... the dead-end of non-physical notions such as non-locality, as another example.

The Bell Inequality is premised purely on local causation but the follow on experiments upon entangled photons particles of several types have always found the inequality to be violated. Non-locality has been promoted by experiment from the realm of a dead-end notion to a fact of nature with which physics must not contradict. The causation involved must be at least superluminal, a contradiction to relativity.

Wikipedia has a list of the experiments providing evidence for the non-local character of Nature.

Edited by Grames
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@Grames,

These are well-known experiments but their use for proving non-locality of QM can immediately be questioned by demonstrating experimentally that Bell's inequalities can be violated also purely classically, that is, in the realm where there's certainly no non-locality.

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Here's one example: Aerts D., Helv.Phys.Acta, 64, 1-23 (1991). There's more but I don't think this thread is the place to discuss it.

Bell's inequality is a completely general test for the statistical independence of two variables. The general derivation of Bell's inequality (correlation <= 2) is from the statistical independence of two variables, the measurements A and B. When a measured correlation is greater than 2 then the conclusion must be made that the measurements A and B are not independent. There is nothing peculiar or unique to QM in Bell's derivation. So of course you can use Bell's inequality for testing variables in classical physics, and the interpretation of violations of the inequality is that the two variables are not independent. For example Classical Bell’s Inequalities, Vesselin C. Noninski uses two water buckets constrained that the total volume of water contained equal to 20L. (I could not find the Aert's paper in a short search.)

What is unique to the Aspect type experiments is the specifically QM predictions for continuously varied polarizer angles. The water bucket example with a total volume constraint is of the local hidden variable type of correlation, but the correlation in QM is "locally inexplicable" because it is a function of the polarizer angles, and the polarizers were not local when the particle pair was created. See Bertlmann's Socks and the Nature of Reality.

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@ _wh_

I'll have to think about your spin example. It seems to run counter to everything I've encountered (every state I've ever seen for such systems collapses to where the system has a single well-defined classical-type state), but I'll look into it. As for the "particles moving in opposite directions but getting closer together, I haven't seen/heard that. Do you have a reference of some kind, a textbook say (my university's library is quite extensive).

As for "zero-point energy" and "non-locality": Non-locality, as Grames has said, is simply a fact. It won't be overturned any time soon. The world is far stranger than it seems to us way up here at the meter-scale level, but that does not mean that non-locality is nonphysical or a dead end. Indeed, the whole idea that effects can only propagate at the speed of light is relatively new- only since the turn of the 20th century. As for your contention that "zero-point energy" is unphysical, I don't see why. There will always be some minimum amount of energy left over, perfect rest is the non-physical view (there will always be some forces on a particle, and given non-locality this is more true then ever).

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@Grames,

Like I said before, the psi-function describing the system prior to the experiment contains all the eigenvalues that can be potentially revealed through the experiment (with their own probabilities, of course). The experiment will not produce eigenvalues that weren't "contained" within the psi-function describing the system prior to experiment. Schroedinger's cat illustration gives a very good idea about that (too bad QM isn't based on only physical outcomes as in that illustration) -- the cat is in one of two possible, physically viable, states prior to opening the lid. There's no third state in which the cat can be in. Similarly, there are no other possible outcomes from Aspect's experiment than the outcomes contained in the psi-function describing the system, no matter how it appears so someone observing the polarizing angles (noticing that they are continuous, for instance). In that sense all is tied up ahead of time within the state function describing the system just as in the classical case. There will be nothing unexpected created by the experiment, no eigenvalue that wasn't there to begin with will pop up due to experiment. The only unexpected would be what exact eigenvalue will be pulled out due to experiment out of the given, predetermined set (continuous or not).

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@nanite1018,

How about a parked car? It isn't changing its spatial coordinates with respect to the lamppost or with respect to the nearby building. Wouldn't you say, then, the said car is at perfect rest with respect to at least one system? Quantum mechanics unjustifiably denies that, only adding that the car is too big an object for its (QM's) conclusions to be noticeable.

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I do not know that a parked car is in total rest in comparison with the lamppost and a nearby building. I only know that it is very very nearly at rest. It is constantly being bombarded with energy (light for example, air molecules hitting it, etc.), so I in fact do not expect it to be in absolute rest, but rather only in average rest. That is, I expect its average velocity, even over short times, to be zero.

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@nanite1018,

So, all the objects that are at rest around you are in some kind of motion, although on the average in going to and fro they maintain their positions with respect to the walls, the floor or the ceiling. But then even the immovable objects will be producing kinetic energy which will inevitably turn into heat. Think about how many immovable objects there are on Earth. Do we not notice the kinetic energy constantly produced by them according to the above mechanism?

Edited by _wh_
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