Exploring the Relationship Between Schroedinger and Bohm's Quantum Mechanics

[ZapperZ]

Fair enough. I'd be very skeptical too if I didn't know this field very well for myself.

But I'm curious what you think of the Bell quote I gave earlier, the one where he says quite explicitly that, in his opinion, there is a fundamental conflict between relativity and quantum theory. Surely Bell understood Bell at least as well as all the folks writing papers on EPR. Are you also "very skeptical" that Bell himself could fundamentally misunderstand his own result?

I know both possibilities are difficult to believe. But either Bell himself didn't understand the significance of Bell's theorem, or a bunch of the subsequent commentators didn't understand it. (Of course, many others *do* understand it: David Albert, Tim Maudlin, Sheldon Goldstein, etc.) It's one or the other (or, I suppose, both) since Bell believed his theorem proved a deep inconsistency between QM (in any formulation) and relativity.

I have no response against what Bell has mentioned, the very same way that I have no response against Einstein when he claim that QM is incomplete. This is because these were not based on any physical findings. I have not seen, nor has Bell indicated, of any observables that has superluminal transmission. This comes back again to the very argument of information transfer - is there anything being transferred from one location to another? The very same way that the phase velocity of light can be of ANY speed but carries no information, a measurement made in an EPR type experiment transfers no info about a measurement in one location to the other EPR pair. If there is, then this will be a clear violation of SR. In ALL of the EPR experiments, there has been no insistance that this is the case.

I don't understand this. Could you clarify what you take SR to require or prohibit... and what you take "non-locality" to mean?

How to you account for Bell's belief to the contrary?

A matter of taste? No way. Absolutely not. It's a matter of replacing the "unprofessionally vague and ambiguous" interpretation that is currently dominant with something that is clear and consistent. I mean, I guess you can call that a matter of taste. But I would say anyone who prefers the taste of subjectivity and vagueness and inconsistency, doesn't deserve to be called a scientist.

But if it is subjective, vague, and inconsistent, it should not work. And it should not work this spectacularly. However, I'm a bit confused. You appear to have completely accepted Bohmian mechanics, even when faced with the problem of non-lorentz invariant. I know you have argued that, hey, it is only the beginning, they'll work this out, but aren't you a bit too certain about it? The Dirac/Klein-Gordon equation has successfully dealt with the relativistic aspect of the Schrodinger equation, so to argue that this is still a problem with the conventional QM that is being ignored is highly inaccurate. And yet, you think it is perfectly OK to abandon what HAS worked, and jump onto a bandwagon that is still untested and struggling to plug a lot of unsolved problems. And we're not just talking about conceptual problems either such as the "measurement" problem.

I like the way Bohm's idea has evolved, and continue to evolve. But is it actually read for Prime Time? I hardly think so. I have one test I use to see if a certain formulation is ready to be used - deriving the BCS theory of superconductivity. As a punishment to myself, I have derived this via variational method, field-theoretic method, and even "fudged" perturbation method. I have presented this as a challenge to a couple of people who are big advocates of Bohmian mechanics. Until this can be shown to work, I have no confidence in using it as a tool to solve real research problems.

Zz.

 

[ttn]

I have no response against what Bell has mentioned, the very same way that I have no response against Einstein when he claim that QM is incomplete. This is because these were not based on any physical findings.

What do you mean by "physical findings"? Direct experimental results? Well, OK, but then aren't you essentially saying that all of theoretical physics is hot air, and all that matters or is meaningful is the "raw" uninterpreted data of experiment? I think this attitude is mistaken; for example it would leave one unable to prefer the Copernican model of the solar system to the old Greek Ptolemaic theory. Moreover, I find it a bit offensive to essentially accuse two of the greatest physicists of the last century as basically being full of hot air.

This comes back again to the very argument of information transfer - is there anything being transferred from one location to another? The very same way that the phase velocity of light can be of ANY speed but carries no information, a measurement made in an EPR type experiment transfers no info about a measurement in one location to the other EPR pair. If there is, then this will be a clear violation of SR. In ALL of the EPR experiments, there has been no insistance that this is the case.

You're certainly right that none of the experiments literally saw a physical thing flying faster than c. No doubt. Yet despite this, Bell still firmly believed that there was a fundamental conflict between QM and relativity. Why do you think he believed this? And why do you think all the other smart people I mentioned earlier agree with Bell on this point?

But if it is subjective, vague, and inconsistent, it should not work. And it should not work this spectacularly.

What's subjective, vague, and inconsistent is the orthodox interpretation of the quantum formalism. It's the formalism itself which has demonstrated spectacular success. But nobody thinks the equations are wrong. I just think Bohr was dead wrong in virtually everything he said about what those equations *meant* about the way the world works.

However, I'm a bit confused. You appear to have completely accepted Bohmian mechanics, even when faced with the problem of non-lorentz invariant. I know you have argued that, hey, it is only the beginning, they'll work this out, but aren't you a bit too certain about it?

That wasn't my argument at all. I agree with Bell that *any* -- that is, *every* -- sharp formulation of quantum theory suffers from non-locality. So the non-locality of Bohm's theory isn't a problem to be worked out. It is a feature that must be present in any theory which accurately describes nature -- i.e., non-locality is a fact of nature. And (again like Bell) I believe non-locality and relativity are at odds. If nature is non-local, then relativity is wrong or broken or needs to be re-interpreted or something like that. So the fact that, e.g., attepts to formulate Bohmian versions of QFT require a preferred frame, does not appear to me to be a problem. It is just one of the possible ways of fixing up whatever it is that's broken with relativity. (Incidentally, at the risk of sounding like a broken record, this is the "fix" that Bell himself preferred, at least at times: see his wonderful article on "How to Teach Special Relativity" for example.)

The Dirac/Klein-Gordon equation has successfully dealt with the relativistic aspect of the Schrodinger equation, so to argue that this is still a problem with the conventional QM that is being ignored is highly inaccurate.

Wait, now you're the one failing to distinguish equations from interpretation. (If I recall, you stressed the importance of that distinction at the beginning of this thread.) The Dirac or KG equations are fine, and the usual recipes for using them are obviously correct. But the standard "story" that goes along with the use of these equations contains all the same vagueness about measurement and wave function collapse as is present in regular old non-relativistic QM. The equations are lorentz covariant, but the conceptual problems remain. Turning it around, the mere fact that the equations work doesn't prove that the currently dominant interpretation is correct (any more or any less than it proves any other interpretation is correct).

And yet, you think it is perfectly OK to abandon what HAS worked, and jump onto a bandwagon that is still untested and struggling to plug a lot of unsolved problems.

That's not true. The equations work great, and I'm all for keeping them. It's mostly Bohr's verbiage about completeness and measurement and collapse that I want to abandon -- precisely because those things haven't "worked" at all!

And we're not just talking about conceptual problems either such as the "measurement" problem.

Did you intend these as scare quotes? I don't follow you. Are you denying that the measurement problem is a real problem? You think it's just semantics or metaphysics or something?

I like the way Bohm's idea has evolved, and continue to evolve. But is it actually ready for Prime Time? I hardly think so.

I do. I have all sorts of questions about it -- there's lots of work left to be done, lots of interesting paths to pursue. But in my opinion it's the best thing available at present. So it's ready for prime time, baby. =)

I have one test I use to see if a certain formulation is ready to be used - deriving the BCS theory of superconductivity. As a punishment to myself, I have derived this via variational method, field-theoretic method, and even "fudged" perturbation method. I have presented this as a challenge to a couple of people who are big advocates of Bohmian mechanics. Until this can be shown to work, I have no confidence in using it as a tool to solve real research problems.

The various formulations you mention here aren't different interpretations of the quantum formalism, they're just different mathematical tools or perspectives on that formalism. So I don't see the point of your challenge. Any valid quantum mechanical derivation of the BCS theory could be understood from a Bohmian point of view, or a Copenhagen point of view (to the extent that's possible), or a MWI point of view, or whatever. They all share the same core formalism.

 

[ZapperZ]

Then I'm COMPLETELY confused. I could have sworn that I read a while back of your criticism of the "conventional" QM by pointing out the fact that the Schrodinger eqn. is also not covariant under lorentz transformation. When you said that (unless I imagined it), then I took it that you were disagreeing with the formalism of QM as presented in the conventional manner, NOT the interpretation.

Honestly, and I've said this a long time ago on here so someone else can verify this, I have little patience for "interpretation" philosophy. I view it as part of a necessary evil (inconvenience?). And the fact that people often confuse the interpretation with the formalism makes this even more annoying.

If you are unhappy with CI, then be my guest. I have absolutely ZERO problem with that unhappiness. However, the Schrodinger wavefunction approach is a different formulation of QM with compared to the Bohmian pilot wave formulation, which is then different then Feynman path integral approach, which is then different than the Heisenberg Matrix formulation, etc...etc. (Ref. to Dan Styer's paper). I thought that these difference in formulations are what we're debating on, not interpretation. It is why I used the BCS theory as the test case of any of these formulations to be shown as workable.

Zz.

 

[Rothiemurchus]

A slight diversion:

Could the Pauli exclusion principle be due to superconductivity -
assuming space around electrons in atoms is occupied by some highly ordered arrangement of charged particles?

The hyperphysics website repeats the assertion that Schrodinger equation cannot be
derived.It says:

"Though the Schrodinger equation cannot be derived, it can be shown to be consistent with experiment. The most valid test of a model is whether it faithfully describes the real world. "

 

[humanino]

The hyperphysics website's statement is not very precise : it cannot be derived outside the axioms of QM.

The Pauli principle is more fundamental. Besides, why would other states outside the the atom explain statistics ?

 

[ZapperZ]

A slight diversion:

Could the Pauli exclusion principle be due to superconductivity -
assuming space around electrons in atoms is occupied by some highly ordered arrangement of charged particles?

Not that I know of, and I've studied superconductivity for almost all of my college student years. Note that if it is due to superconductivity, then it shouldn't occur in atoms, in light, in the deBoer effect of Nobel gasses, etc., where there are no superconductivity.

The hyperphysics website repeats the assertion that Schrodinger equation cannot be
derived.It says:

"Though the Schrodinger equation cannot be derived, it can be shown to be consistent with experiment. The most valid test of a model is whether it faithfully describes the real world. "

I love the hyperphysics site and cite it regularly. However, they have made several inaccurate statements before and this would be one of them. [The other being that the energy gap in a superconducting density of states leads to the zero resistivity property. This is not correct - these two are correlated, but the gap is not the cause of zero resistance].

Zz.

 

[ttn]

Then I'm COMPLETELY confused. I could have sworn that I read a while back of your criticism of the "conventional" QM by pointing out the fact that the Schrodinger eqn. is also not covariant under lorentz transformation. When you said that (unless I imagined it), then I took it that you were disagreeing with the formalism of QM as presented in the conventional manner, NOT the interpretation.

No, I'm sorry, maybe I wasn't very clear before. The non-locality in the orthodox formulation of QM is not to be found in the Schroedinger equation. That has just the right sort of relativity (namely, Galilean invariance) to be a good non-relativistic dynamical equation (just as the Dirac and KG equations have the correct sort of invariance to be good relativistic dynamical equations). The non-locality is to be found, rather, in the collapse postulate. It's the collapse of the wave function which I believe violates the prohibitions of relativity (if we regard QM as complete).

Of course, one could get rid of the non-locality (and lots of the vague talk about "measurement") by simply jettisoning the collapse postulate. But then one's theory simply predicts the wrong thing, e.g., that the pointers on (what we call) measuring instruments end up pointing in definite directions at the ends of experiments.

So... just to clarify, I'm not at all against the formalism of QM. Of course that is correct -- it's been verified to an amazing degree by decades of experiments, many of which were specifically designed to test what people thought might be its weak points. My main goal in this discussion was simply to object to using the non-locality in Bohmian mechanics as an argument against Bohmian mechanics. I don't think this is a valid objection, since all other interpretations of QM (leaving aside many worlds, which has plenty of other problems to contend with) are non-local too.

(That was the point of the Bush/Kerry analogy. It's not that I think anyone who hates Bush must love Kerry. I just don't think it's appropriate to criticize Bush for a characteristic he shares with the other contenders in the ring -- at least, not without making it clear that one is aware of that fact.)

Honestly, and I've said this a long time ago on here so someone else can verify this, I have little patience for "interpretation" philosophy. I view it as part of a necessary evil (inconvenience?). And the fact that people often confuse the interpretation with the formalism makes this even more annoying.

I agree with the last part, but I guess, unlike you, I see interpretation as an absolutely central and essential part of the progression of science. Where would astronomy be without Copernicus' interpretation of the data about the solar system (or, if you like, the proto-equations that summarized all this data)? Where would physics be without Boltzmann's interpretation of the physical basis for the laws of macroscopic thermodynamics?

If you are unhappy with CI, then be my guest. I have absolutely ZERO problem with that unhappiness. However, the Schrodinger wavefunction approach is a different formulation of QM with compared to the Bohmian pilot wave formulation, which is then different then Feynman path integral approach, which is then different than the Heisenberg Matrix formulation, etc...etc.

Probably this is mostly just a dispute over terminology. But I don't think the difference between Standard QM and (say) Feynman Path Integrals, is the same as the difference between Standard QM and Bohmian mechanics. Path Integrals are just another mathematical tool for evolving wave functions forward in time (or, if you like, calculating matrix elements). They are mathematically equivalent to the Sch equation (or whatever the basic dynamical equation is of whatever type of quantum theory one is talking about) but they are sometimes computationally more elegant or more practical. Bohm's theory, on the other hand, provides a physical interpretation of the meaning of the equations -- one very different from the "standard" interpretation due to some superposition of Bohr, Heisenberg, and von Neumann.

(Ref. to Dan Styer's paper).

I know the paper you mean. I wouldn't recommend Styer as an expert on these issues, however. In his paper on "common misconceptions regarding quantum mechanics" (AmJPhys 64, 31-34) he basically dismissed Bohm's theory (and all other hidden variable type theories) by saying that the whole idea that the wave function represents an incomplete description of reality "was rendered untenable by tests of Bell's theorem which show that no deterministic model, no matter how complicated, can give rise to all the results of quantum mechanics."

This is really a terrible and false statement about what Bell's theorem shows. It's just not right at all. Indeed, Bohm's theory is an explicit counterexample to his claim, for it is a deterministic model (not even all that complicated) which gives rise to all the results of QM.

 

[humanino]

I am not saying the discussion is useless.

I see interpretation as an absolutely central and essential part of the progression of science.

I agree very much with that statement for instance.
But when it comes to

I think anyone who hates Bush must love Kerry

that kind of analogy, I must say I feel the discussion is not very scientific.

The EPR "paradox" has been discussed many times. QM is not intuitive, but it is rigorous.

Path Integrals are just another mathematical tool for evolving wave functions forward in time (or, if you like, calculating matrix elements). They are mathematically equivalent to the Sch equation (or whatever the basic dynamical equation is of whatever type of quantum theory one is talking about) but they are sometimes computationally more elegant or more practical.

The all mystery of the quantum world is in the path integral. Is it not ?

 

[wm]

Bell's theorem refuted; Bohmian possibilities

Here's what I know: Every version of Bell's theorem (BT) known to me is flawed. The probabilistic versions are based on BE (Bell's error); non-prob versions are based on ME (Mermin's error). These errors may be associated with the EPRCM (EPR's category mistake) but are (imo) best named as above for clarity.

Here's what follows: A local realistic QM is valid, in full accord with Einstein's ideas re relativity, locality & separability, and a commonsense view of reality; a reality that justifies the term "hidden variables" because the sub-stratum reality is (often) "hidden" or "veiled" from us due to perturbative measurement effects.

Here's what I suspect: That the quantum potential in Bohm's work might be re-interpretable as a logical consequence of the initial conditions. This suspicion arises from (so-called) "non-local effects" in other theories being replaced by logical consequences in a fully local-realistic theory. PS: I have little interest in this direction (wanting to focus elsewhere), but am sure that my refutation of BT (with little more than high school maths and logic) will encourage others to dig a little deeper with Bohm.

If anyone's interested, I suggest we start four new threads (to provide focus): EPRCM: EPR's category mistake? BE: Bell's error? ME: Mermin's error? BTR: Bell's theorem refuted? Could be fun.

 

[ttn]

Here's what I know: Every version of Bell's theorem (BT) known to me is flawed.

I would be interested to hear what you think the flaw is. But let's just say I'm not holding my breath.

Here's what follows: A local realistic QM is valid, in full accord with Einstein's ideas re relativity, locality & separability, and a commonsense view of reality; a reality that justifies the term "hidden variables" because the sub-stratum reality is (often) "hidden" or "veiled" from us due to perturbative measurement effects.

A local hidden variable theory that agrees with QM's predictions?! Let's see it!

 

[vanesch]

When do complex numbers arise?
Is there a well established theory already for what type of equations produce complex numbers as solutions?

One should study things in order
You talk about quantum gravity and then you ask the above question ; I don't want to sound offending, but it is a bit as if you subscribed to Formula 1 contests, and ask the technician on the starting line, what do people mean by "changing gears" ?
But I can understand that this comes from reading lots of popular science books. There is a not to be underestimated pleasure to be gained in doing things in the right order. Do you know real calculus ? (integrals, differentials etc...) We can take that maybe as a starting point.

cheers,
Patrick.

 

[Rothiemurchus]

vanesch:
But I can understand that this comes from reading lots of popular science books. There is a not to be underestimated pleasure to be gained in doing things in the right order. Do you know real calculus ? (integrals, differentials etc...) We can take that maybe as a starting point.

Rothie M:
It might surprise you to know that I know calculus of variations, Hamilton's principle,
how to solve differential equations and just about any useful mathematical procedure you can think of that relates to classical mechanics.I also know much of the maths of relativity - general and special relativity.I have studied complex numbers in detail - years ago - but I do not think they provide a reasonable or satisfactory description of reality.Physics is about ideas - not mathematics.Einstein said the maths will always follow from a good idea.
A mastery of mathematics does not guarantee an understanding of anything.
The trouble with quantum mechanics is this -
It has taken causality away from the world.It is de a defeatist point of view:it says " there are some things that just can't be understood in terms of the commonsense world."
Where is the proof of this? The most important question to ask about qm - in my opinion - is this:why is Max Born's guess ( that the wavefunction x complex conjugate of wavefunction is proportional to the probability of finding a particle at a certain position in space) so useful - what is a wavefunction? It must be something physical like Bohm's pilot wave.
There is a way to resolve the problem's associated with Bell's Theorem
and to restore causality to the world and that is to assume a signal exists that travels faster than light.But because such an idea shakes the foundations of relativity people will not get their heads around it.
But there was a time when nobody would have believed that the speed of a light wave catching up with the Earth equals the speed of a light wave approaching the Earth.

 

[vanesch]

Rothie M:
It might surprise you to know that I know calculus of variations, Hamilton's principle,
how to solve differential equations and just about any useful mathematical procedure you can think of that relates to classical mechanics.I also know much of the maths of relativity - general and special relativity.I have studied complex numbers in detail - years ago - but I do not think they provide a reasonable or satisfactory description of reality.

Well I then offer my apologies, but you have to understand that it is somehow contradictory to read the above, and:

When do complex numbers arise?
Is there a well established theory already for what type of equations produce complex numbers as solutions?

Do you see what I mean ?

cheers,
Patrick.

 

[ZapperZ]

The trouble with quantum mechanics is this -
It has taken causality away from the world.It is de a defeatist point of view:it says " there are some things that just can't be understood in terms of the commonsense world."

But you see nothing wrong in demanding that the world behaves only in ways that you approve DESPITE of all the experimental observations?

Where is the proof of this? The most important question to ask about qm - in my opinion - is this:why is Max Born's guess ( that the wavefunction x complex conjugate of wavefunction is proportional to the probability of finding a particle at a certain position in space) so useful - what is a wavefunction? It must be something physical like Bohm's pilot wave.
There is a way to resolve the problem's associated with Bell's Theorem
and to restore causality to the world and that is to assume a signal exists that travels faster than light.

I can play the same game as you do and ask you "Where is the proof of this"?

We didn't just make things up just so we can feel good about it and sleep comfortably at night. If you insist that there ARE signals traveling faster than light, then describe the nature of the signal so that it can be measured and proven to exist, and then be proven that it DOES travel faster than c. Till then, you're just making things up as you go along.

But because such an idea shakes the foundations of relativity people will not get their heads around it.
But there was a time when nobody would have believed that the speed of a light wave catching up with the Earth equals the speed of a light wave approaching the Earth.

The difference being that there were existing TANGIBLE, experimental observations that simply did not fit the old notion of how light speed behave. These were not based on simply a matter of tastes, which is all you have stated. There have been NOTHING, no clear experimental observation, to indicate violation of any of SR's postulates so far. You should not equate what have been done to advance our knowledge of light with what you are trying to do here, because they are not even close to being the same.

Zz.

 

[Rothiemurchus]

Zapper Z:
But you see nothing wrong in demanding that the world behaves only in ways that you approve DESPITE of all the experimental observations?


Rothie M:

I do not doubt that the mathematical predictions of qm match experiment and
that any theory challenging qm must explain why.
As for my piece on superluminal signals:are we left with any alternative to them to
explain what Einstein called " ghostly action at a distance."
Everything else seems to have been tried.
I would say that your attitude is "I think that unfortunately the world is just
incomprehensible at some level."
That could be true but there is no harm in challenging it.
And as you have said previously people test qm all the time - just in case.
And people were very surprised by the results of Michelson and Morley
on the speed of light relative to the Earth.

Vanesch:
No need to apologise, I do have a habit of asking what people call
"naive" questions.

 

[selfAdjoint]

There are no signals, according to QM. The particle is not "told" what attribute to assume from afar; the projection of its state to an eigenvalue tells it just as with any particle. The fact that the state was complicated and the projection contingent doesn't change this.

 

[ZapperZ]

I do not doubt that the mathematical predictions of qm match experiment and
that any theory challenging qm must explain why.
As for my piece on superluminal signals:are we left with any alternative to them to
explain what Einstein called " ghostly action at a distance."
Everything else seems to have been tried.
I would say that your attitude is "I think that unfortunately the world is just
incomprehensible at some level."
That could be true but there is no harm in challenging it.
And as you have said previously people test qm all the time - just in case.
And people were very surprised by the results of Michelson and Morley
on the speed of light relative to the Earth.

And you're forgetting that for the MM expt. to be designed, we must first know WHAT it is that we're trying to measure. The old ether theory CLEARLY stated the kinds of influences it exert on light and how it should change. In other words, it had something CONCRETE that we can measure. It didn't just say "oh, there must be an ether", and left it at that, the way YOU did. You can't just say "oh, there must be something moving faster than c" without describing WHAT it is that is moving, and what property does it have for us to be able to measure AND detect its speed.

As an experimentalist, I am SELDOM satisfied with being told "oh, that's just the way it is". However, I have no qualm in settling for the POSSIBILITY that the quantum world is NOTHING like what we are familiar with. I make NO DEMANDS that it should. Unfortunately, from your complaints, you WANT and insisit that it must conform to your classical perception of the world. I find that highly irrational.

Zz.

Vanesch:
No need to apologise, I do have a habit of asking what people call
"naive" questions.[/QUOTE]

 

[Rothiemurchus]

Zapper Z:
You can't just say "oh, there must be something moving faster than c" without describing WHAT it is that is moving, and what property does it have for us to be able to measure AND detect its speed.

Rothie M:
I will set up a website sometime for you to look at the details of what I had in mind.
They are the kind of details you want!

 

[humanino]

I know (...) any useful mathematical procedure you can think of that relates to classical mechanics

You need humility Rothie. I seriously doubt. You just demonstrated that you are not aware of the gigantic field of mathematics. I know some, and I am aware that is so few.

The last person considered to know all mathematics at his time is Poincare. That is what we say in France. Today, it simply impossible, even in a narrow field.

If I am wrong about you needing humility, you are a authentic genius in math. Above any in history.

 

[ZapperZ]

Zapper Z:
You can't just say "oh, there must be something moving faster than c" without describing WHAT it is that is moving, and what property does it have for us to be able to measure AND detect its speed.

Rothie M:
I will set up a website sometime for you to look at the details of what I had in mind.
They are the kind of details you want!

Oh no! Not one of those!

If you think you have anything authentic and valid, then please send it for publication in a peer-reviewed journal. If you don't, then you are no better than the tons of quackery we find on Crank Dot Net.

I don't read, nor do I pay any degree of emphasis on stuff that can only see the light of day on someone's website.

Zz.

 

[nrqed]

There are no signals, according to QM. The particle is not "told" what attribute to assume from afar; the projection of its state to an eigenvalue tells it just as with any particle...

But the particle *is* "told" in what state to collapse even though the measurement might have been made on the other side of the universe.

I am not saying that QM is wrong or that Nature should obey rules that are intuitive.

What I *am* saying is that it seems to me that the standard presentations of QM and SR can't be the whole story. For example, the measurement problem. We say "take the measurement of that particle here and *then* the wavefunction collapses. There is , imho, something obviously flawed here. In the case of two entangled photons separated by timelike intervals, the order of the measurements is frame dependent. So in one frame it's observer A which makes the wavefunction collapse, in another frame it's observer B. So it does not make sense to talk about a measurement making the wavefunction collapse. That means that, imho, the standard picture can't be right. The usual way used to describe QM measurements would have to be changed.


Just one example to be more specific: You have two entangled photons separated by timelike intervals. Their polarizations are measured by two observers.

Question 1: you are in a frame where measurement A is taken first. Compute the probabibilities of each measurement of A and then the proabilities of each measurement obtained by B. In the standard presentations, the results of A would be 50/50 and then the result of B would be determined at 100%.

Question 2: Now you are in another frame where B is measured first. Then the standard answer would be quite different than the first, it would be 50/50 for B, then entirely determined for A.

Obviously, there is no way to distinguish one interpretation from the other experimentally. But still, I think it would be important to rephrase the standard interpretation. It sounds to me that the correct phrasing would be to abandon completely the collapse part and to phrase things in a way that is from the start symmetric between the two cases. One should consider the measurements grouped together, with no notion of time delay between the two or of collapse of the wavefunction for that matter. One should then say:

A and B make measurements. There are two possible outcomes: A measures this type of polarization and B measures this other type of polarization, with a probability of 50%. OR the other way around with prob 50%.

That's it, no mention of spacetime interval, no collapse, no time delay, no space separation.

I guess that most people already think that way and see no big deal to it. But if we take his seriously, we should apply the same point of view to all QM measurements. For example, you measure the position of a particle, and then 10 hours later you measure its momentum. In the standard approach, the first measurement caused a collapse of the wavefunction. Then we time evolve the state to find the prob of different momentum measurements 10 h later. But maybe we whould never think of it that way and use the above, symmetric prescription. Then we should say that it's also equivalent to see the second measurement (the momentum one) as causing the collapse and specifying, back in time, the possible results of the x measurement.

My point is : if we adopt a point of view for some measurements, we should adopt the same point of view for all. It feels to me that people treat implicitly treat differently EPR type measurements then other types of measurements. That's what bothers me.

Pat

 

[vanesch]

So it does not make sense to talk about a measurement making the wavefunction collapse. That means that, imho, the standard picture can't be right. The usual way used to describe QM measurements would have to be changed.

Hi Pat,

What you write here bothered me also quite a while, until I realized that collapse of the wavefunction does make sense as long as it is an observer-bounded concept. This is a viewpoint which is somewhat intermediate in between the standard interpretation and MWI. Indeed, thanks to decoherence, you cannot distinguish between a measurement that gives rise to a true collapse, and one that just "decoheres".
So if you have two entangled particles, A and B, and you have two observers, P and Q, P which observes A and Q which observes B (and we assume these observation interactions to be spacelike separated - you write everywhere timelike but I suppose you mean spacelike), let us then take the point of view of P.
When P observes A, this is a true observation for P. But at that point, he doesn't know anything about B or Q, so it doesn't make sense for P to talk about a collapse of the state at Q. When Q travels to P to tell him the result of his measurement, P just considers this message from Q as another measurement (P makes a measurement on Q). All this is completely local at P, and his successive measurements (with collapse) make completely sense.
Q can do exactly the same, but then of course we have different quantum discriptions according to the observers.
I didn't work this out, maybe one can think of a propagating collapse wavefront going out from each observer ; or one considers that there is only one true observer in the universe, namely me :-)

cheers,
Patrick.

 

[selfAdjoint]

Patrick, it seems you have the esssence of a sound view here, if you will just lose the "propagating wavefront". Necessarily such a wavefront would be unphysical, since experiment has proved that the time between observations P and Q can be less than the distance between them in light units, i.e. the events showing the correlation can be spaclike. What I think is correct is that the correlation was born, though not yet physical, when the particles were produced entangled, and has spread with the particles; so the cause of the correlation lies in the past light cones of both particles. The only thing that happens at the later time is that the correlation becomes physically manifest at the first measurement; and if the measurements are spacelike related it is impossible to say meaningfully which one came first, since no one can view both of them, except historically.

 

[cepheid]

Again, this is an example on why, if one did not learn from the ground up, things will seem to appear out of nowhere.

We have gone over this in other threads of the importance of calculus of variation, and in particular the principle of least action. This is the only means of understanding the origin of the Lagrangian/Hamiltonian approach to classical mechanics. I strongly suggest you look this up.

Zz.

Cool, I'm learning this stuff just now, in a course called PHYS 350...Applied Classical Mechanics. My prof said the formulation is far more fundamental than the Newtonian formulation of mechanics in that it applies more universally and draws together many branches of physics. We've already seen things like Fermat's Principle of Least Time in optics. But both that course and this one are very difficult to understand.

Another funny anecdote. When the same prof (the 350 one) tried to show how the Hamiltonian/Lagrangian approach applied more broadly, he asked our class, "Have you studied quantum mechanics?" When he eventually got the sense that our sole exposure to QM in a previous course (Intro to Modern Phys.) consisted of being dumped with the Schrodinger Equation, and shown how to solve certain problems with it, his exact words were:

"You mean to say they never even went over the history of how the theory arose?" That's pathetic!"

I couldn't have agreed more. It was pathetic. I'm starting to realize that some of the treatment of physics for us in Engineering Physics might be lacking compared to the treatment in the pure physics programme. Still...*hopes fervently that QM makes more sense the second time 'round*

EDIT: Thanks for that link you gave us back on the 1st page Zz! That should help...

 

[ttn]

What I think is correct is that the correlation was born, though not yet physical, when the particles were produced entangled, and has spread with the particles; so the cause of the correlation lies in the past light cones of both particles. The only thing that happens at the later time is that the correlation becomes physically manifest at the first measurement; and if the measurements are spacelike related it is impossible to say meaningfully which one came first, since no one can view both of them, except historically.

Actually, if I understand you correctly, your view here is precisely what is shown by Bell's theorem to be impossible. If you assume that "the correlation lies in the past light cones of both particles" (i.e., that the particles get their properties correlated at birth) and if you assume that the outcomes of the two measurements depend only on that total, joint two-particle state (and not on the setting or outcome of the distant experiment) then you get Bell's inequality, which is violated by experiment. So the quantum correlations cannot be explained by any (local) model like the kind (I think) you have in mind.

But then, I'm not entirely sure what you meant by saying that "the correlation becomes physically manifest at the first measurement." If this allows for the first measurement to causally affect the state of the distant particle (or, more generally, the probability distribution for possible outcomes of the distant measurement) then this would be consistent with experiment. But it would of course be non-local.

 

[selfAdjoint]

I didn't mean to suggest classical movement of the correlation, or the quantum state. They evolve outside of spacetime. But the state _mmmm_, "pro-exists" where the two particles are, in the sense that it is available to provide probabilities to the experimenters. All of this - the essence of QM - is outside classical physics, and it is classical physics that yields the Bell inequality. It is nevertheless true that the extended state carries the information "If one of the particles is found to be in the "DOWN" state, the other will be in the "UP" state, and vice versa". And that state subsists in spite of separation, until a measurement is made. The collapse of the state, or its projection onto its spacetime eigenvalues, conveys the values appropriate value to both particles and doesn't need to travel from one to the other because it is available at both and its link is outside of spacetime, as all states are in QM.

 

[ttn]

I didn't mean to suggest classical movement of the correlation, or the quantum state. They evolve outside of spacetime. But the state _mmmm_, "pro-exists" where the two particles are, in the sense that it is available to provide probabilities to the experimenters. All of this - the essence of QM - is outside classical physics, and it is classical physics that yields the Bell inequality. It is nevertheless true that the extended state carries the information "If one of the particles is found to be in the "DOWN" state, the other will be in the "UP" state, and vice versa". And that state subsists in spite of separation, until a measurement is made. The collapse of the state, or its projection onto its spacetime eigenvalues, conveys the values appropriate value to both particles and doesn't need to travel from one to the other because it is available at both and its link is outside of spacetime, as all states are in QM.

So... when Alice makes a measurement on one side, Bob's particle is affected -- but the "information" that let's Bob's particle "know" to do this doesn't propagate through regular space, instead taking a detour outside of space and time on its way there?

Is this supposed to be consistent with relativity?! Or maybe you didn't intend it to be. But surely if it's really true that, according to QM, all states are "outside of spacetime", then QM is simply not consistent with relativity. This is a nice illustration of the point I made earlier in this thread: it's wrong to criticize Bohmian mechanics on the basis of its violating relativity's prohibition on superluminal causation, if one's favored alternative is to reject altogether the idea of micro-physical events unfolding on a space-time stage. The fact is, *no* sharp formulation of quantum mechanics is consistent with relativity. It's not just true because Bell said it, but he did say it, and it is true... and it seems like it's time people started recognizing this.

Also, what you said about the inputs to Bell's theorem isn't correct. The inequality is in no way based on "classical physics." I challenge you to point out any place in any of Bell's papers where he brings in something from classical physics. In fact, the inequality isn't based on *any* kind of physics. It's just pure statistics (plus some assumptions about what's allowed to depend on what, i.e., a locality assumption).

 

[vanesch]

Patrick, it seems you have the esssence of a sound view here, if you will just lose the "propagating wavefront". Necessarily such a wavefront would be unphysical, since experiment has proved that the time between observations P and Q can be less than the distance between them in light units, i.e. the events showing the correlation can be spaclike.

Yes I understood that of course. What I'm saying is that from P's point of view, Q doesn't make a measurement. It is only P who makes two measurements: first on particle A and second on "pseudoobserver Q" which remains itself in a decohered superposition until P (the only true observer in the universe) observes Q. P can only start to observe Q's results (Q's entanglement with B) when Q is in the past lightcone of P after the entanglement took place at Q.

So my point is that there is not necessarily a collapse at Q when P makes his first measurement. It is only when Q is in the past lightcone of P after the entanglement with B that potentially P can observe Q's results and hence that there must be a projection.

You can ask: and what about Q ? Well, Q is a different observer, and hence lives in a different quantum observer world. So he can observe completely different things, P can never find out. P can only make measurements on Q, and then P's measurements will be coherent with other measurements P made in his history record. This is the same issue as how different people perceive the color blue. When presented with something blue, both say that it is blue because told so since they were a child. But you'll never find out if what you perceive as "blue" isn't perceived as "orange" by the other person.

As I said before, this is very strange to me too! But it is the only way I found to have peace of mind with SR and QM, the way they are formulated.

cheers,
Patrick.

 

[Rothiemurchus]

Humanino:
You need humility Rothie. I seriously doubt. You just demonstrated that you are not aware of the gigantic field of mathematics. I know some, and I am aware that is so few.

Rothie M:
I was just emphasising that I am not completely ignorant of mathematics used in physics! You are right to say it is hard for anyone to know
all mathematics .In fact Feynamn went out of his way to learn only maths he thought would be useful.

Zapper Z:
Oh no! Not one of those!

If you think you have anything authentic and valid, then please send it for publication in a peer-reviewed journal.

Rothie M:
There is no real opportunity for alternative theories on this website
that is why I suggested setting up my own.A journal is the right place though.

 

[Rothiemurchus]

Photon correlations have been determined over a distance of 10 km.
If a particle or wave of some sort traveled from one photon to another,
then perhaps at a greater distance the second photon would be absorbed by the detecting apparatus before the correlating signal reached it.I think that it is important
to keep testing these correlations over greater distances.No doubt people will.