Is entanglement based on first principles?

[nortonian]

Consider the original paper, ON THE EINSTEIN PODOLSKY ROSEN PARADOX by J. S. Bell from which the following quotes are taken:

“Since the initial quantum mechanical wave function does not determine the result of an individual measurement, this predetermination implies the possibility of a more complete specification of the state.”

In this quote we see that Bell refers to a wave function that is not the result of an individual measurement. However, the wave function was introduced specifically to describe individual measurements by Schroedinger. I have never seen a proof that allows this more loosely defined interpretation. Please correct me if I am wrong by supplying specific references. Bell continues,

"Some might prefer a formulation in which the hidden variables fall into two sets, with A dependent on one and B on the other; this possibility is contained in the above, since λ stands for any number of variables and the dependences thereon of A and B are unrestricted. In a complete physical theory of the type envisaged by Einstein, the hidden variables would have dynamical significance and laws of motion; our λ can then be thought of as initial values of these variables at some suitable instant."

This is wrong. Einstein never envisaged “a complete physical theory in which hidden variables would have dynamical significance”. He actually referred to quantum mechanics as a touchstone which would have to be derived if a more complete theory is proposed. In fact Bell correctly quotes Einstein as saying the following:

"But on one supposition we should, in my opinion, absolutely hold fast: the real factual situation of the system S2 is independent of what is done with the system S1, which is spatially separated from the former."
A. Einstein

If we hold fast to the Schroedinger interpretation of a wave function then Einstein's quote merely refers to the actual measurements performed by Bob and Alice, not the questionable use of a wave function as referring to unobserved/unobservable systems, systems which come into existence in free space independently of the possibility of measurement. This is clearly a case of erecting a dummy Einstein and then defeating him. The actual mathematics of the EPR paper were given by Podolsky, not Einstein as stated in an earlier post on this forum by a philosophy major.

 

[Truecrimson]

Consider the original paper, ON THE EINSTEIN PODOLSKY ROSEN PARADOX by J. S. Bell from which the following quotes are taken:

“Since the initial quantum mechanical wave function does not determine the result of an individual measurement, this predetermination implies the possibility of a more complete specification of the state.”

In this quote we see that Bell refers to a wave function that is not the result of an individual measurement. However, the wave function was introduced specifically to describe individual measurements by Schroedinger. I have never seen a proof that allows this more loosely defined interpretation. Please correct me if I am wrong by supplying specific references.

The wave function (or more generally the quantum state) only predicts the probabilities of getting measurement outcomes, it does not predict individual measurement outcome. This is given by the Born rule and can be found in any textbook. Can you clarify what you mean by "the wave function was introduced specifically to describe individual measurements by Schroedinger"?

I'm not sure what you mean by "a wave function that is not the result of an individual measurement." We can talk about a wave function after a measurement but a measurement result is a value, not a wave function.

 

[Paul Colby]

If QM is taken as first principles isn't the trivial answer to the question yes?

 

[bhobba]

However, the wave function was introduced specifically to describe individual measurements by Schroedinger. .

Well things moved very quickly from when Schrodinger introduced the wave-function and what he envisioned it to be was quickly superseded by Diracs Transformation theory:
http://www.lajpe.org/may08/09_Carlos_Madrid.pdf

In fact Schrodinger goofed when he developed his equation - even though he got the right answer:
https://arxiv.org/pdf/1204.0653.pdf

Its the representation in the position basis of the quantum state. States, from the Born rule, most definitely do NOT determine the results of individual measurement. Einstein knew this championing the ensemble interpretation which is basically the Born rule taken to its logical conclusion.

But to answer your question as detailed in the title entanglement most definitely comes from first principles - its the superposition principle applied to compound systems. That is if 2 systems can be in state |a> and |b> then system 1 in state |a> and system 2 in state |b> is written as |a>|b>. Similarly system 1 in state |b> and system 2 in state |a> is written as |b>|a>. But the principle of superposition says any linear combination such as 1/root(2) |a>|b> + 1/root(2) |b>|a> is also a possible state. Such states are peculiar to QM and are called entangled.

Thanks
Bill

 

[bhobba]

If QM is taken as first principles isn't the trivial answer to the question yes?

Of course.

However I suspect the OP has something else in mind that perhaps needs further fleshing out.

Thanks
Bill

 

[nortonian]

I'm not sure what you mean by "a wave function that is not the result of an individual measurement." We can talk about a wave function after a measurement but a measurement result is a value, not a wave function.

States, from the Born rule, most definitely do NOT determine the results of individual measurement.

Please strike the word individual except in the quote from Bell.
I have to reflect a bit more before rephrasing my question.

 

[gnnmartin]

I'm not really sure what your question asks, but I assume from your earlier interest in the meaning of 'instantaneous' that you are looking for arguments that explain the effects of entangled states without the need to assume instantaneous communication, or alternatively to know exactly what instantaneous means in that context.

The problem was addressed by Bell, and (in effect) he shows that if our rules for the resolution of entangled states are correct, then when resolution is forced on two widely separated particles, the outcome at each particle is dependent on the outcome at the other. In particular, he shows how one can design an experiment to confirm that dependence. That is not quite what Bell says, but it follows from what he said.

The experiment has been done a number of times, but the outcome is in effect a sampling exercise, so the sample, the number of entangled pairs studied, must be large enough to make the probability of a false result small. In brief, the experiment sends entangled particles to two widely separated locations, and varies the state (meaning the orientation of the detectors) at one or both locations. The aim is to show that changing the state at one location A affects the outcome at the second location B, even when the change at A takes place outside the past light cone of the outcome at B. In other words, if information about the change of state travels from A to B and arrives at B in time to affect the outcome, it travels faster than light.

The experiment has been done a number of times in a number of ways, I believe, but can't quote the papers. There do seem to be a few people who claim that the experiments are not conclusive. The experimental result relies on (in effect) performing a series of similar experiments, each of which gives a result which quantum theory predicts (say) to have a 60% chance of one outcome (0, say) and 40% chance of the other (1, say). The total experiment relies on running so long a series that we can be sure that the probability of outcome is indeed 60/40, and the chance of a misleading result is vanishingly small. However, it is the nature of the experiment that not all of the individual results are recorded. Those who claim the experiments are not conclusive point out that if the failure of an individual result is somehow correlated with the outcome, then the logic underlying use of a long series of individual results is flawed. If a 1 outcome is more likely to be missed than a 0 outcome, then we will see more 0's but not because that outcome is more probable. I don't find the argument appealing, but I am just an amateur.

There is another more interesting experiment that as far as I know has not been attempted: perhaps it is still impractical. It relates to your earlier question about what 'instantaneous' means. If information about the change at A reaches B at faster than the speed of light, how much faster? If there is an answer to that, say at twice the speed of light, then we should still be able to find how fast by making the change of state later and the separation greater until we eventually manage to generate outcomes that do not obey the expected quantum law.

This is an experiment that we expect to fail, rather like the Michelson Morley experiment to find a variation in the speed of light. If against all our expectations we did find there was a window in which the quantum law did not apply, we would have narrowed down what we mean by 'instantaneous'.

 

[Paul Colby]

I'm not really sure what your question asks, but I assume from your earlier interest in the meaning of 'instantaneous' that you are looking for arguments that explain the effects of entangled states without the need to assume instantaneous communication, or alternatively to know exactly what instantaneous means in that context.

In the classical example of two gyroscopes the correlation is instantaneous and no one is shocked and surprised because there is no interaction involved. Both gyroscopes have a preexisting classical value prior to measurement. In the quantum case there is no contribution to the system hamiltonian or interaction term connecting the measurements, so no interaction occurs. However, like all quantum measurements, classical values are replaced by quantum operators, state vectors and an elaborate song and dance. Like all measurements in QM there is a strong dependence on the choice of the measurement device so there are no preexisting QM ones ever. So, the correlation is instantaneous and there is no interaction term. This is very likely a fundamental aspect of nature just like the speed of light being a universal constant.

 

[bhobba]

So, the correlation is instantaneous and there is no interaction term.

Exactly.

Its just a correlation with different statistical properties than classical correlations.

People make too big a deal out of it IMHO.

Its caused by the fact in QM things do not necessarily have values independent of measurement - if it does or doesn't is very interpretation dependent. The twist is if you insist it has values even when not measured then non local influences are required. but only if you insist.

Thanks
Bill

 

[Quantum of Solace]

There is another more interesting experiment that as far as I know has not been attempted: perhaps it is still impractical. It relates to your earlier question about what 'instantaneous' means. If information about the change at A reaches B at faster than the speed of light, how much faster? If there is an answer to that, say at twice the speed of light, then we should still be able to find how fast by making the change of state later and the separation greater until we eventually manage to generate outcomes that do not obey the expected quantum law.

That's partly why I started the other thread on delayed choice (apart from some misunderstanding on the nature of light, which was kindly corrected). Quantum effects collapse the whole system regardless of spacelike separation, but not at a 'speed', since the effect happens even regardless of event order. bhobba has made his thoughts on this very clear, and Dr Chinese was kind enough to (re)link a couple of papers and quote which are quite relevant. I will take the liberty of requoting here:

http://arxiv.org/abs/quant-ph/0201134
You can entangle particles AFTER they are detected, see page 5 for a discussion.

http://arxiv.org/abs/1209.4191
You can entangle photons that never co-existed, and therefore never interacted.
"The role of the timing and order of quantum measurements is not just a fundamental question of quantum mechanics, but also a puzzling one. Any part of a quantum system that has finished evolving, can be measured immediately or saved for later, without affecting the final results, regardless of the continued evolution of the rest of the system. In addition, the non-locality of quantum mechanics, as manifested by entanglement, does not apply only to particles with spatial separation, but also with temporal separation. Here we demonstrate these principles by generating and fully characterizing an entangled pair of photons that never coexisted. Using entanglement swapping between two temporally separated photon pairs we entangle one photon from the first pair with another photon from the second pair. The first photon was detected even before the other was created. The observed quantum correlations manifest the non-locality of quantum mechanics in spacetime."

 

[Nugatory]

There is another more interesting experiment that as far as I know has not been attempted: perhaps it is still impractical. It relates to your earlier question about what 'instantaneous' means. If information about the change at A reaches B at faster than the speed of light, how much faster? If there is an answer to that, say at twice the speed of light, then we should still be able to find how fast by making the change of state later and the separation greater until we eventually manage to generate outcomes that do not obey the expected quantum law.

The lower bound is at least 10,000 times the speed of light: http://arxiv.org/abs/1303.0614

 

[bhobba]

The lower bound is at least 10,000 times the speed of light: http://arxiv.org/abs/1303.0614

Of course one can try to measure any actual speed and if it is finite that would be very very interesting.

That said its the exact quantum analogue of putting red and green slips in envelopes. Open one and you immediately know the other but there is nothing involving any kind of communication going on - all you have done is correlate the slips.

As Einstein said 'God is subtle, but He is not malicious'. Don't try and over complicate it. As I said previously IMHO far too mush 'guff' is written about something that really isn't all that hard.

Thanks
Bill

 

[Quantum of Solace]

The lower bound is at least 10,000 times the speed of light: http://arxiv.org/abs/1303.0614

Don't delayed-choice experiments render this moot? Or do they still potentially suffer from the freedom-of-choice loophole?

 

[harrylin]

[..] People make too big a deal out of it IMHO.

Its caused by the fact in QM things do not necessarily have values independent of measurement - if it does or doesn't is very interpretation dependent. The twist is if you insist it has values even when not measured then non local influences are required. but only if you insist.
[..]

Of course one can try to measure any actual speed and if it is finite that would be very very interesting.

That said its the exact quantum analogue of putting red and green slips in envelopes. Open one and you immediately know the other but there is nothing involving any kind of communication going on - all you have done is correlate the slips.

As Einstein said 'God is subtle, but He is not malicious'. Don't try and over complicate it. As I said previously IMHO far too mush 'guff' is written about something that really isn't all that hard.
[..]

Those statements here seem to be inconsistent (are the red and green slips inside the envelopes not red and green??) and in striking disagreement with Bell!
As a reminder, he argued in his "Bertlmann's socks" article (and essentially that argument is called "Bell's theorem"):

"Dr. Bertlmann likes to wear two socks of different colours. Which colour he will have on a given foot on a given day is quite unpredictable. But when you see [..] that the first sock is pink you can be already sure that the second sock will not be pink. Observation of the first, and experience of Bertlmann, gives immediate information about the second. There is no accounting for tastes, but apart from that there is no mystery here. And is not the EPR business just the same ?"

[after arguing that it's quite different:] "Phenomena of this kind made physicists despair of finding any consistent space-time picture of what goes on the atomic and subatomic scale."
"It is as if we had come to deny the reality of Bertlmann's socks, or at least of their colours, when not looked at."

"Could it be that the first observation somehow fixes what was unfixed [..], not only for the near particle but also for the remote one? For EPR that would be an unthinkable "spooky action at a distance". To avoid such action at a distance they have to attribute, to the space-time regions in question, real properties in advance of observation, correlated properties, which predetermine the outcomes of these particular observations."
"It is important to note that to the limited degree to which determinism plays a role in the EPR argument, it is not assumed but inferred. What is held sacred is the principle of "local causality" - or "no action at a distance."

"If we do not accept the intervention on one side as a causal influence on the other, we seem obliged to admit that the results on both sides are determined in advance anyway, independently of the intervention on the other side, by signals from the source and by the local magnet setting. But this has implications for non-parallel settings which conflict with those of quantum mechanics. So we cannot dismiss intervention on one side as a causal influence on the other."

In other words: according to Bell, "denying the reality of the sock's colours when not looked at", can not explain the correlations as long as we adhere to Einstein-local causality. Which makes me wonder, how can either having no values when not measured, or having predetermined values before measurement, explain the correlations according to you?

 

[nortonian]

Sorry for the long delay, but writing about physics is a very difficult process. I have posted on this forum prematurely in the past and paid for it.

I'm not really sure what your question asks, but I assume from your earlier interest in the meaning of 'instantaneous' that you are looking for arguments that explain the effects of entangled states without the need to assume instantaneous communication, or alternatively to know exactly what instantaneous means in that context.

I joined the thread after it had changed from instantaneous to Bell's theorem. I am not interested in arguments about whether Bell's theorem is correct in its mathematical content. I had never completely understood it in physical terms until Dr. Chinese explained it very simply in terms of Bob and Alice detecting the polarization of the photons. That's when I could finally interpret it my own way.

But to answer your question as detailed in the title entanglement most definitely comes from first principles - its the superposition principle applied to compound systems. That is if 2 systems can be in state |a> and |b> then system 1 in state |a> and system 2 in state |b> is written as |a>|b>. Similarly system 1 in state |b> and system 2 in state |a> is written as |b>|a>. But the principle of superposition says any linear combination such as 1/root(2) |a>|b> + 1/root(2) |b>|a> is also a possible state. Such states are peculiar to QM and are called entangled.

My purpose in participating in this forum is not to convince anyone that I am right. Quantum mechanics is not going to change. I would like to be able to express my ideas rationally without trivial errors, and my participation here helps me to do that. My initial assumption is that qm is not wrong, but incomplete. I know that I am wrong within the context of accepted theory. If that offends to the point you can't respond in a reasonable way then don't.

To analyze entanglement from first principles we have to go back to the beginnings of qm. Dirac's transformation theory treats emission and absorption as symmetric processes. This evolved from an earlier paper by Dirac, The emission and absorption of radiation which stated the same idea. It is accurate for all formulations of qm because non-relativistic theory is about changes in energy. If we look at characteristics of field we see evidence that these processes are not symmetric. Wave mechanics is based on energy absorption and can be shown to be equivalent to matrix mechanics, derived from emission processes, because it can be used to calculate the diagonal matrix elements. However, the reverse is not true. Matrix elements are derived using Fourier analysis and include transition probabilities giving the intensity of the spectral lines which cannot be derived using the Schroedinger equations. So quantum mechanical properties of field are not symmetric if we look at the emission and absorption of radiation.

In my mind the question of whether entanglement is based on first principles boils down to whether the use of a wave function to describe the photons is legitimate. Ignoring for now the legitimacy of describing two spatially separate physical entities with a single function, which I also question, look at the symmetries involved. The photons are created by an emission process and detected by absorption. They are symmetric processes so long as we look at the energies involved, but Bell is basing his arguments on properties of the photon fields, their polarization, whose symmetry with respect to emission and absorption has not been demonstrated by anyone as far as I know. If they are not symmetric then Dirac did not take them into consideration in his transformation theory and I question whether they can be legitimately described within the context of transformation theory.

 

[bhobba]

Those statements here seem to be inconsistent (are the red and green slips inside the envelopes not red and green??) and in striking disagreement with Bell!

There is no inconsistency or disagreement with bell.

I will state it again.

Both the red and green slips and bell type correlations are simply that - correlations. The difference is the red and green slips remain red and green at all times, for bell type correlations that may or may not be the case depending on QM interpretation. They have different statistical properties - that's all - but does not change the fact they are still just correlations. If you want it to be like red and green slips then you must have non local interactions. That's all there is to it.

But people for some reason make more out of it.

Thanks
Bill

 

[bhobba]

Wave mechanics is based on energy absorption and can be shown to be equivalent to matrix mechanics, derived from emission processes, because it can be used to calculate the diagonal matrix elements. However, the reverse is not true. Matrix elements are derived using Fourier analysis and include transition probabilities giving the intensity of the spectral lines which cannot be derived using the Schroedinger equations.

That's false. Each can be derived from the other. It simply in the Schrodinger picture operators remain fixed but the state changes, whereas in the Heisenberg picture the state is fixed but the operators changes.

I gave a reference where Schrodinger got his equation from - its was basically a crock and had errors - it was from the Hamilton-Jacobi equation and nothing to do with energy absorption - to the best of my knowledge anyway.

In modern times it comes from symmetry considerations but that is a whole new thread.

Can I ask where you are getting this from?

Thanks
Bill

 

[bhobba]

In my mind the question of whether entanglement is based on first principles boils down to whether the use of a wave function to describe the photons is legitimate.

Well photons do not have a wave-function but that is itself a whole new thread and can be avoided by considering electrons in bell type experiments.

I gave the general definition/explanation of entanglement. Its simply applying the principle of superposition to compound systems.

Its very intuitive, but strictly speaking it is in fact an axiom of QM ie the tensor product of individual systems vector spaces is the space of the combined systems:
http://www-bcf.usc.edu/~tbrun/Course/lecture04.pdf

Thanks
Bill

 

[Zafa Pi]

There is no inconsistency or disagreement with bell.

I will state it again.

Both the red and green slips and bell type correlations are simply that - correlations. The difference is the red and green slips remain red and green at all times, for bell type correlations that may or may not be the case depending on QM interpretation. They have different statistical properties - that's all - but does not change the fact they are still just correlations. If you want it to be like red and green slips then you must have non local interactions. That's all there is to it.

But people for some reason make more out of it.

Thanks
Bill

Indeed you have stated it again and again. We will never know how Einstein would have reacted to Bell's observations, but given the degree to which Einstein was wedded to determinism it is reasonable to assume that he may have accepted Bell's Inequality and not the QM predicted correlations. Einstein was no slouch and that alone makes it a big deal. (it would be fantastic to know how he would have reacted to the confirming tests of QM) Everybody prior to 1900 would have accepted Bell's Inequality if told Alice and Bob couldn't communicate (locality). There are those that think Bell should have received a Nobel prize. I personally find it weird and beautiful. It is a big deal, and perhaps you understand it so well that you're jaded.

 

[bohm2]

The lower bound is at least 10,000 times the speed of light: http://arxiv.org/abs/1303.0614

It's also been argued that if the effects observed in Bell-type experiments propagate at any finite speed, then non-locality could be exploited for superluminal communication (e.g. 'can't stay hidden'):

The new hidden influence inequality shows that the get-out won't work when it comes to quantum predictions. To derive their inequality, which sets up a measurement of entanglement between four particles, the researchers considered what behaviours are possible for four particles that are connected by influences that stay hidden and that travel at some arbitrary finite speed. Mathematically (and mind-bogglingly), these constraints define an 80-dimensional object. The testable hidden influence inequality is the boundary of the shadow this 80-dimensional shape casts in 44 dimensions. The researchers showed that quantum predictions can lie outside this boundary, which means they are going against one of the assumptions. Outside the boundary, either the influences can't stay hidden, or they must have infinite speed.

We investigate possible explanations of quantum correlations that satisfy the principle of continuity, which states that everything propagates gradually and continuously through space and time. In particular, following [J.D. Bancal et al, Nature Physics 2012], we show that any combination of local common causes and direct causes satisfying this principle, i.e. propagating at any finite speed, leads to signalling. This is true even if the common and direct causes are allowed to propagate at a supraluminal-but-finite speed defined in a Newtonian-like privileged universal reference frame. Consequently, either there is supraluminal communication or the conclusion that Nature is nonlocal (i.e. discontinuous) is unavoidable.

Quantum non-locality based on finite-speed causal influences leads to superluminal signalling
http://www.nature.com/nphys/journal/vaop/ncurrent/full/nphys2460.html

Quantum correlations in Newtonian space and time: arbitrarily fast communication or nonlocality
http://lanl.arxiv.org/pdf/1210.7308.pdf

 

[bhobba]

Indeed you have stated it again and again. We will never know how Einstein would have reacted to Bell's observations, but given the degree to which Einstein was wedded to determinism

That was not Einsteins final objection to QM. He had no issue with its probabilistic nature. His objection was as per EPR - he believed in an objective reality independent of observation - ie he did not like an observation created reality.

Here is THE book to understand Einstein:
https://www.amazon.com/dp/0192806726/?tag=pfamazon01-20

Einsteins writings can be slightly misleading as his views changed somewhat over time. At first he thought QM incorrect and openly tried to disprove it. All his attacks were met and he eventually came to understand it was correct, but believed it incomplete because of the observer created reality.

Thanks
Bill

 

[Zafa Pi]

That was not Einsteins final objection to QM. He had no issue with its probabilistic nature. His objection was as per EPR - he believed in an objective reality independent of observation - ie he did not like an observation created reality.

Here is THE book to understand Einstein:
https://www.amazon.com/dp/0192806726/?tag=pfamazon01-20

Einsteins writings can be slightly misleading as his views changed somewhat over time. At first he thought QM incorrect and openly tried to disprove it. All his attacks were met and he eventually came to understand it was correct, but believed it incomplete because of the observer created reality.

Thanks
Bill

The question is whether Einstein would have accepted Bell's Inequality and thus reject the QM predicted violation. Probabilities are not the issue.
He believed QM incomplete because it didn't take hidden variables into account, and the hidden variables are the result of his attachment to determinism = realism which is what is needed to prove Bell's Inequality.
I did read about half of THE book, much was beyond me because I knew little physics.

 

[bhobba]

He believed QM incomplete because it didn't take hidden variables into account, and the hidden variables are the result of his attachment to determinism = realism which is what is needed to prove Bell's Inequality. I did read about half of THE book, much was beyond me because I knew little physics.

Determinism is not the same as realism - although it a bit of a subtle point. His view was a bit more nuanced than that - determinism was not the main issue - realism was.

He would have accepted Bell and accommodated it like he did throughout his life when his views on QM were proven false by slightly modifying them - but not his fundamental belief in realism.

There are a number of ways of bypassing Bell eg by assuming a theory that is not the same as QM, but reduces to it in some kind of limit - eg primary state diffusion:
http://arxiv.org/pdf/quant-ph/9508021.pdf

Its really unknown exactly in what way Einstein would have changed. Another view he would have had to modify is his Ensemble interpretation in light of Kochen-Specker. Ballentine had to change it as well - he chose one way - the other is the ignorance ensemble interpretation using decoherence. Unfortunately Ballentine for some strange reason does not believe decoherence has anything to do with interpretative issues. Would Einstein have sided with Ballentine or have taken decoherence on board? Who knows - although I suspect he would have taken it on board and changed to ignorance ensemble interpretation. This makes clear the fundamental issue with QM - why do we get outcomes at all. Einstein would have likely answered that with because reality exists independent of us and championed some way for QM to accommodate it like Bohmian Mechanics - although he thought BM too simplistic. It is getting off topic however; if you would like to discuss that start a new thread.

Thanks
Bill

 

[bhobba]

The question is whether Einstein would have accepted Bell's Inequality and thus reject the QM predicted violation. Probabilities are not the issue.

Forgot to mention - you are correct - its just like I said above Einsteins views were rather nuanced and determinism wasn't his main issue - but it is a bit of a subtle point.

Thanks
Bill

 

[bhobba]

There are those that think Bell should have received a Nobel prize. I personally find it weird and beautiful. It is a big deal, and perhaps you understand it so well that you're jaded.

It indeed is a big deal. And 100% for sure he would have got a Nobel if he lived.

My concern is the guff people read into it - not its importance - its very important.

And yes you are probably right - having read a lot about it and answered innumerable questions and misconceptions about it I am likely jaded.

Thanks
Bill

 

[Zafa Pi]

Determinism is not the same as realism - although it a bit of a subtle point. His view was a bit more nuanced than that - determinism was not the main issue - realism was.

He would have accepted Bell and accommodated it like he did throughout his life when his views on QM were proven false by slightly modifying them - but not his fundamental belief in realism.

You're right about the nuanced difference, a little too nuanced for me. However, DrChinese agrees that are far as proving Bell's Inequality, determinism realism, hidden variable, counterfactual definiteness are all equally effective. I was asking what he would do if he only saw Bell's Ineq and the predicted QM correlations that claim to refute it, not the later tests confirming QM. Since you feel he would keep realism, then that (along within no faster than light) is sufficient to prove Bell's Ineq. He would have to deny the validity of the QM predictions. If he later saw Aspect's work, that's a whole nother ballgame. Where do you think I'm off base?

I have this vision that circa 1981 Bohr would confront Einstein in heaven and say: "Well Albert my friend, what do you have to say now?" After a while Einstein would respond: "Lord, why have you forsaken me?" And instead of reaching out to touch Adam, Michelangelo" God would be casting dice into the void.

 

[nortonian]

That's false. Each can be derived from the other. It simply in the Schrodinger picture operators remain fixed but the state changes, whereas in the Heisenberg picture the state is fixed but the operators changes.

If its false then why did you refer me to http://www.lajpe.org/may08/09_Carlos_Madrid.pdf where the following is written:

"However Schrödinger was not able to establish the
mathematical equivalence between WM and MM due to
conceptual and technical difficulties [8, 9, 10, 11]. He did
prove indeed that WM is contained in MM, but not the reciprocal, and this is a serious flaw."

They can be derived from each other only in the case of diagonal elements, the energy eigenstates. This is not at all surprising because in that case they describe the same thing, the emission and absorption of radiation. So the symmetry you describe is 99% true in experimental physics, but it is nevertheless incomplete because it does not take field properties into consideration. If the derivations were completely symmetrical, true for all experiments without exception, then it would be possible to use wave mechanics to calculate the intensity of the spectral lines given by the off-diagonal matrix elements. Before you dismiss the asymmetry in quantum formulations which is fundamental to my arguments I think you need to look more closely at the references cited in the above article to see if they are justified and to understand it better. The fundamentals are more important than the formalism so I intend to do so as well.

Can I ask where you are getting this from?

From quotes and analysis taken from the original papers. The best description of the historical development of matrix mechanics and wave mechanics that I have found is in J. Mehra & H. Rechenberg, The Historical Development of Quantum Theory, Vol. II (NY: Springer, 1982-1988), which is highly detailed. However, there are other texts that discuss it as well. I've found that going back to the original papers is the only way to ensure that the physical interpretation of experiments has not been altered unintentionally over the years by the many authors who have discussed them. If you look at the original papers you will see that a lot of physics was not a true derivation, but an educated guess.

 

[Truecrimson]

If its false then why did you refer me to http://www.lajpe.org/may08/09_Carlos_Madrid.pdf where the following is written:

"However Schrödinger was not able to establish the
mathematical equivalence between WM and MM due to
conceptual and technical difficulties [8, 9, 10, 11]. He did
prove indeed that WM is contained in MM, but not the reciprocal, and this is a serious flaw."

That Schrödinger couldn't prove it doesn't mean that it's not true, as the paper acknowledges that John von Neumann eventually proved it. It's an isomorphism between square-integrable functions and square-summable sequences.

Sorry, I don't have access to the Mehra and Rechenberg's book, so you would have to explain in math why John von Neumann was wrong. Otherwise, we will just talk past each other.

I also second bhobba's suggestion to switch to massive particles like electrons instead to understand Bell and entanglement, that is, unless your real question is the equivalence between matrix and wave mechanics. But both emission and absorption will be explained in any quantum optics textbook using a single unified formalism that Bell used.

 

[bhobba]

That Schrödinger couldn't prove it doesn't mean that it's not true, as the paper acknowledges that John von Neumann eventually proved it. It's an isomorphism between square-integrable functions and square-summable sequences.

Exactly.

As the paper also explained Von Neumann proved it rigorously, as did Dirac, but he used math that at the time didn't have a proper basis. That has now been corrected and Diracs methods are just as rigorous as Von Neumann's.

This was clearly explained in the paper. Its very important to read all of any references given before jumping to conclusions.

Thanks
Bill

 

[bhobba]

So the symmetry you describe is 99% true

Its a theorem and is 100% true. If you think otherwise please detail the error in the proof that has escaped notice by the countless number of people that have studied it. Not some vague references to this or that but the actual error.

Wave mechanics can be used to calculate anything matrix mechanics can, and conversely.

And that standard QM is an approximation to field theory has nothing to do with the equivalence of wave and matrix mechanics which has been established rigorously.

My suspicion is, like the paper I linked to, is you are not fully understanding your references.

A good way to test that is to explain, in you own words, not pointing to references, but in your own words what's going on.

Thanks
Bill

 

[bhobba]

They can be derived from each other only in the case of diagonal elements, the energy eigenstates.

The proof makes no use of a particular basis an operators matrix representation is diagonal in. Its simply got to do with operators have matrix representation ie given ANY basis |bi>, O = ∑∑ |bi><bi|O|bj><bj| = ∑∑ <bi|O|bj>|bi><bj|. <bi|O|bj> is the matrix representation of O. In matrix mechanics the state doesn't change - only the operator so the state isn't explicitly part of it. Thus there is a one to one correspondence between matrix and wave mechanics. To be explicit given any matrix in matrix mechanics we can find the corresponding operator in wave mechanics and conversely. That's all there is to it really.

Now to support your claim detail the exact error in what I wrote above. Not a reference, but the exact error.

Thanks
Bill

 

[harrylin]

[..]they are still just correlations. If you want it to be like red and green slips then you must have non local interactions. That's all there is to it.

But people for some reason make more out of it.
..

Thanks for the clarification; I did not see people make more out of it.

 

[nortonian]

Wave mechanics can be used to calculate anything matrix mechanics can, and conversely.

So show how transition probabilities can be obtained from wave mechanics.

Its a theorem and is 100% true. If you think otherwise please detail the error in the proof that has escaped notice by the countless number of people that have studied it. Not some vague references to this or that but the actual error.

By first principles I meant duplicating the results of the original experiments. Of course MM and WM are equivalent they are talking about the same thing, atomic structure, but no I am not capable of determining where the mathematics is incomplete.

Now to support your claim detail the exact error in what I wrote above. Not a reference, but the exact error.

There is an obvious difference in what we interpret as "first principles".
.

 

[bhobba]

So show how transition probabilities can be obtained from wave mechanics.

That's Fermies Golden Rule and it is standard textbook stuff:
https://en.wikipedia.org/wiki/Fermi's_golden_rule

By first principles I meant duplicating the results of the original experiments.

What original experiments relating to entanglement are you taking about?

Of course MM and WM are equivalent they are talking about the same thing, atomic structure, but no I am not capable of determining where the mathematics is incomplete. There is an obvious difference in what we interpret as "first principles".
.

Now you lost me. First you say they are not equivalent, then you say of course they are. And yes different equivalent formulations of a theory have different interpretations but that in no way changes their equivalence.

You say you are not capable of determining where the math is incomplete, yet want to overturn current orthodoxy. The first requirement for overturning accepted science is to understand it.

I suggest you learn some QM. Virtually any good book on QM will explain the equivalence between WM and MM.

Thanks
Bill

 

[Dale]

Closed pending moderation

Edit: we will leave the thread closed, it seemed to be heading in a bad direction