# What is the wave function about?

by bohm2
Tags: function, wave
P: 4,612
 Quote by skippy1729 I have a question for Demystifier or anyone else who knows: I know that there are theorems stating dBB will produce the same statistical results as QM. Of course, results of individual events cannot be obtained since they are determined by unknown initial conditions. The question is: Is it possible to solve the dBB equations for some simple physical system for all possible initial conditions then use the ensemble of results to actually construct the statistics?
Yes, it's possible.

 Quote by skippy1729 Any references appreciated.
http://xxx.lanl.gov/abs/1103.1589
http://xxx.lanl.gov/abs/quant-ph/0403034
P: 4,612
 Quote by apeiron I was thinking of the fact that BM ontology treats particles as real (existing at some definite place and time) and so assumes that there is indeed a single preferred reference frame.
Existence at definite place and time has nothing to do with preferred reference frame. After all, classical relativistic particles also exist at definite place and time, and yet it does not involve a preferred reference frame.

To see why BM involves a preferred reference frame, and how that problem can be avoided, see
http://xxx.lanl.gov/abs/1002.3226 [Int. J. Quantum Inf. 9 (2011) 367-377]
PF Gold
P: 691
 Quote by ThomasT Standard 'uninterpreted' QM doesn't posit a physical 'collapse' of a wave shell in real space and time.
This is what I find so difficult to understand about the epistemic view. If one treats the wave function as a mathematical probability wave (an epistemic device to calculate the probability of finding a particle in a particular spatial location) it seems like a very strange sort of probability wave, since it can have "physical" effects like the interference pattern in double-slit experiments. Even the probability density doesn't appear like the classical notion of probability. I'll never understand this and I tried to understand Fuch's arguments but as hard as I tried, I just couldn't follow them.
P: 1,414
 Quote by ThomasT Standard 'uninterpreted' QM doesn't posit a physical 'collapse' of a wave shell in real space and time.
 Quote by bohm2 This is what I find so difficult to understand about the epistemic view. If one treats the wave function as a mathematical probability wave (an epistemic device to calculate the probability of finding a particle in a particular spatial location) it seems like a very strange sort of probability wave, since it can have "physical" effects like the interference pattern in double-slit experiments.
Well, interacting waves produce interference patterns. That shouldn't seem so strange. And it's good to keep in mind that wave-mechanical QM is based largely on classical wave mechanics.

I don't know exactly how Shroedinger came up with his wave equation, but maybe somebody here does.

You can treat the wave function as a mathematical probability wave because that's all that can be known for sure that it is. However, the fact that it actually works as well as it does seems to suggest that there's some more or less familiar wave mechanics happening in the underlying reality. But that might be misleading. I don't know. Anyway, probability distributions are waves, and the wave functions of QM are probability distributions.

 Quote by bohm2 Even the probability density doesn't appear like the classical notion of probability.
From Wiki:
Probability amplitude
Probability density function

 Quote by bohm2 I'll never understand this and I tried to understand Fuch's arguments but as hard as I tried, I just couldn't follow them.
I think you'll eventually understand it. And then you can explain it to me.

I don't think I've read the Fuchs article that I think you're referring to. Maybe I'll get to it this afternoon.
PF Gold
P: 691
 Quote by ThomasT I don't know exactly how Shroedinger came up with his wave equation, but maybe somebody here does.
I thought these were some interesting quotes by Schrodinger and others concerning wave function ontology;

Schrodinger started out trying to interpret the wave function realistically. For example, in an early paper on wave mechanics, he writes:

The true mechanical process is realised or represented in a fitting way by the wave processes in q-space, and not by the motion of image points in this space.

Schrodinger considers a two-particle system late in the paper but has only one sentence about the physical representation of the sixdimensional wave function:

The direct interpretation of this wave function of six variables in three-dimensional space meets, at any rate initially, with difficulties of an abstract nature.

Schrodinger wants to interpret the mechanical processes realized or represented by the wave function as taking place in three-dimensional space, but he does not see how this can be done. Lorentz picks up on this problem with multiparticle systems. In 1926, Lorentz wrote a letter to Schrodinger, in which he says:

If I had to choose now between your wave mechanics and the matrix mechanics, I would give the preference to the former, because of its greater intuitive clarity, so long as one only has to deal with the three coordinates x, y, z. If, however, there are more degrees of freedom, then I cannot interpret the waves and vibrations physically, and I must therefore decide in favor of matrix mechanics.

I'm not sure but it seems this wave is somewhere between a mathematical probability wave and some sort of weird "physical-like" wave existing in 3-N dimentional space? What's interesting, is if you assume a realistic interpretation and try to map the 3-N configuration space into 3-dimensional space, so that the 3-dimensional world is something that emerges from this 3-N configuration space you get more than one set of emergent 3-spaces. That's one reason why Monton argues against treating the 3 N-dimensional space in QM as "fundamental".
PF Gold
P: 2,432
 Quote by Demystifier Existence at definite place and time has nothing to do with preferred reference frame. After all, classical relativistic particles also exist at definite place and time, and yet it does not involve a preferred reference frame. To see why BM involves a preferred reference frame, and how that problem can be avoided, see http://xxx.lanl.gov/abs/1002.3226 [Int. J. Quantum Inf. 9 (2011) 367-377]
Can you briefly explain what is meant by the many-time wave function?

And does this approach really hinge on allowing particles to have velocities greater than c?

I found the paper's insistence on super-determinism and no room for freewill rather too implausible as a motivation. The arguments against experiments to test the ontology - such as systems set up to destroy themselves with retrocausal signals - seem arbitrary.

 R: A microscopic object cannot send a message that would contradict its own existence. O: Why not? R: First, because I assume that the microscopic object does not have free will, or even an illusion of free will, to send any message it “wishes”. Second, even if I discard this assumption, I certainly must assume that the microscopic laws are self-consistent, i.e., that such inconsistent systems do not appear as solutions of the mathematical equations describing the microscopic laws.
But 1) a human with the capacity to choose could choose to set up such an apparatus. Then 2) you only "must" assume this from the particular route to modelling general covariance suggested in the paper.

Then the argument to justify accepting superluminal action....

 R: This is like using the following argument on subluminal communication. If communication is subluminal, then there is a Lorentz frame in which the carrier of the message is at rest. If it is at rest in one Lorentz frame, then it is not at rest in any other Lorentz frame. Therefore, there is a preferred Lorentz frame with respect to which the carrier is at rest. Consequently, the principle of relativity is violated.
Wouldn't the real complementary story here have to be the possibility of things "moving slower than rest"?

Relativistic effects arise for matter because they effectively lag behind the natural speed of action/equilibration which is c. They can fall all the way down to the limit which is "rest" in some inertial frame which minimises their "massiveness".

So if it is nonsensical to think a massive particle can go "slower than rest", then by the same argument, it is nosensical to suggest it can go faster than c.
P: 1,414
 Quote by bohm2 ( ... ) I'm not sure but it seems this wave is somewhere between a mathematical probability wave and some sort of weird "physical-like" wave existing in 3-N dimentional space? What's interesting, is if you assume a realistic interpretation and try to map the 3-N configuration space into 3-dimensional space, so that the 3-dimensional world is something that emerges from this 3-N configuration space you get more than one set of emergent 3-spaces. That's one reason why Monton argues against treating the 3 N-dimensional space in QM as "fundamental".
Thanks. I've got some reading to do. Could take a while. It looks like I'm going to learn more about interpreting wave functions than I ever really wanted to.

Seems like you're making progress, insofar as broadening and deepening your knowledge, in your quest to understand this.
P: 4,612
 Quote by apeiron Can you briefly explain what is meant by the many-time wave function?
Yes, provided that you first tell me why the explanation in the paper is not clear to you.
PF Gold
P: 2,432
 Quote by Demystifier Yes, provided that you first tell me why the explanation in the paper is not clear to you.
How do you assign a time to individual particles unless you have already defined a reference frame to make those measurements?
P: 4,612
 Quote by apeiron How do you assign a time to individual particles unless you have already defined a reference frame to make those measurements?
Basically, in the same way one does that in classical relativistic mechanics:
First one takes some specific reference frame with coordinates x^\mu, \mu=0,1,2,3.
Then one assigns both time position x^0 and space position x^1, x^2, x^3 of an individual particle.
Finally one writes all equations involving x^\mu in a manifestly covariant form, which provides that physical results will not depend on the choice of reference frame.

For more details see
http://xxx.lanl.gov/abs/1006.1986
P: 4,612
 Quote by apeiron I found the paper's insistence on super-determinism and no room for freewill rather too implausible as a motivation.
Do you know ANY FUNDAMENTAL theory in physics which is compatible with free will? (I don't.)
PF Gold
P: 2,432
 Quote by Demystifier Do you know ANY FUNDAMENTAL theory in physics which is compatible with free will? (I don't.)
What, not even an "effective freewill"?
PF Gold
P: 2,432
 Quote by Demystifier First one takes some specific reference frame with coordinates x^\mu, \mu=0,1,2,3.
OK, this can be done for some subset of the universe, but can it be done for the universe as a whole?

Or is this where the further requirement for FTL particle velocities comes in?
P: 1,414
@ Demystifier,

You haven't replied to my post #27 which was in response to your post #19. Do you agree/disagree with it?

Also:
 Quote by apeiron I found the paper's insistence on super-determinism and no room for freewill rather too implausible as a motivation.
 Quote by Demystifier Do you know ANY FUNDAMENTAL theory in physics which is compatible with free will? (I don't.)
 Quote by apeiron What, not even an "effective freewill"?
I find the references to 'superdeterminism' and 'free will' to be somewhat off the mark, whether those terms are used in discussions about the compatibility of nonlocality and relativity or the compatibility of LRHV models of quantum entanglement and experimental results.

In Aspect et al. 1982 the analyzer settings are varied randomly and so, apparently, have nothing to do with 'free will'. The term 'superdeterminism' is simply a superfluous extension of the term 'determinism'. Considerations like 'going back in time' make no sense at all to me.

Am I actually missing something here? Or is it possible that none of this is relevant to anything?
P: 4,612
 Quote by apeiron What, not even an "effective freewill"?
Effective free will is the same as illusion of free will, which is consistent with physical laws as discussed in the paper.
P: 4,612
 Quote by ThomasT I find the references to 'superdeterminism' and 'free will' to be somewhat off the mark, ... Am I actually missing something here?
Perhaps you are missing the context, which is the paper mentioned in post #38.
P: 4,612
 Quote by ThomasT You haven't replied to my post #27 which was in response to your post #19. Do you agree/disagree with it?
At some points I don't really understand your reasoning, so it's hard to tell wheather I agree or not.
P: 1,414
 Quote by Demystifier Perhaps you are missing the context, which is the paper mentioned in post #38.
There's at least two ways to view determinism. Either the universe is evolving and we're part of that evolution, or we're travelling through a static universe. In the case of the former, going back or sending messages back in time is nonsensical because the past refers to spatial configurations that no longer exist. The latter case, on the other hand, suggests that we're somehow distinct from the universe, ie., travelling/evolving in some way separate from it, which seems to be prima facie nonsensical and anyway leads to all sorts of nonsensical stuff.

So, we choose the former view, the view that we're part of an evolving universe, and in that view it's impossible to send messages back in time or to revisit the past, even if we could send messages or transport ourselves instantaneously to any part of the universe.

Properly interpreted, in an evolving universe which we're a part of, there's no frame of reference wrt which even a FTL signal is actually travelling backward in time.

Thus, 'free will' has nothing to do with it. 'Superdeterminism' is a superfluous extension of determinism, because if the universe is evolving deterministically, then free will (in the sense of choices being independent of prior conditions/configurations) is ruled out anyway.

In your paper you say that "By assumption, superluminal signals are inherently quantum phenomena responsible for nonlocal correlations between entangled particles ..." . But this assumption isn't necessary for a certain understanding of the correlations between the angular difference of polarizer settings and coincidental photon flux, and in fact posits the existence of an entirely new class of physical (or nonphysical in the case of instantaneous action-at-a-distance) phenomena for which there's absolutely no physical evidence.

You say that, "The Bell theorem [1] shows that quantum mechanics (QM) is not compatible with local reality.", which isn't precisely correct. Bell's theorem shows that QM is not compatible with LRHV models of quantum entanglement (ie., coincidental photon flux). QM is quite compatible with LRHV models of photon flux at the individual detectors. In general, standard QM is essentially nonrealistic and so is not incompatible with an understanding of quantum entanglement via purely local transmissions and interactions.

You further say that, "This suggests that reality might be nonlocal." . But this isn't at all what's suggested if one looks at the correlations wrt established optics principles, and if one evaluates the meaning of Bell's theorem wrt the formal constraints on LRHV models of entanglement. In this view, LRHV models of entanglement are ruled out even if the universe is evolving strictly in accordance with local determinism.

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