Why is the Wave Function Central to Quantum Theory's Physical Interpretation?

[aaaa202]

As I understand it the wave function itself does not carry any physical interpration. Rather it is the square of it's absolute value. But that forces the question: Why construct a theory with the basic equation being about the time evolution of the wave function, when you could (I guess just as well) set up an equation for the time evolution of the absolute value of it squared. It just seems weird to me that we make this middle step, where we calculate something which actually carries no importance for the physical system.

 

[cattlecattle]

As I understand it the wave function itself does not carry any physical interpration. Rather it is the square of it's absolute value. But that forces the question: Why construct a theory with the basic equation being about the time evolution of the wave function, when you could (I guess just as well) set up an equation for the time evolution of the absolute value of it squared. It just seems weird to me that we make this middle step, where we calculate something which actually carries no importance for the physical system.

For one example, were it not for the wave function, you can't explain the double slit interference pattern which is caused by the addition of wave function of different phase as opposed to the addition of the probabilities. It's true that probability carries physical meaning, but it's false to claim wave functions don't. They carry physical meaning in an implicit way. It's like nobody can ever isolate individual quarks, but so far only by using the quarks model can we explain the results of scattering experiments.

 

[nanosiborg]

Why construct a theory with the basic equation being about the time evolution of the wave function, when you could (I guess just as well) set up an equation for the time evolution of the absolute value of it squared.

Try it. Does it work?

 

[DiracPool]

Why construct a theory with the basic equation being about the time evolution of the wave function, when you could (I guess just as well) set up an equation for the time evolution of the absolute value of it squared.

Strictly speaking, the wave function isn't squared, it is multiplied by its complex conjugate. Doing this produces two benefits, 1) it gets rid of the imaginary form of the wave function, which can't be plotted, i.e., the two Euler exponential parts of the wave function reduce to unity when multiplied. 2) it get's rid of any negative values of the wave function so that there is a clean, easy to understand graphical presentation of the probablility distribution.

Squaring that real part of the wave function doesn't change the probability distribution, as the normalized squared result still retains the relative amplitude relations across the distribution. I think you could even raise the modulus to the 4th power and it wouldn't change anything.

 

[akhmeteli]

As I understand it the wave function itself does not carry any physical interpration. Rather it is the square of it's absolute value. But that forces the question: Why construct a theory with the basic equation being about the time evolution of the wave function, when you could (I guess just as well) set up an equation for the time evolution of the absolute value of it squared. It just seems weird to me that we make this middle step, where we calculate something which actually carries no importance for the physical system.

Try it. Does it work?

I don't know about aaaa202, but someone Schrödinger tried:-). And it does work. Please see references and details in the following thread: https://www.physicsforums.com/showthread.php?p=3008318#post3008318 (for example, my posts 11 and 73 there). Briefly: a scalar wave function can be made real by a gauge transform (the relevant unitary gauge may seem inconvenient though). After that you may rewrite its time evolution in terms of its square, but it won't be linear.

 

[remnax]

I don't think it is possible to construct a useful theory with the absolut square of psi (or its
square) as variable: psi as a variable allows for gauge freedom - and the gauge mechanism describes the way external fields act on the objects described by psi. But it is a good
question

 

[nanosiborg]

I don't know about aaaa202, but someone Schrödinger tried:-). And it does work. Please see references and details in the following thread: https://www.physicsforums.com/showthread.php?p=3008318#post3008318 (for example, my posts 11 and 73 there). Briefly: a scalar wave function can be made real by a gauge transform (the relevant unitary gauge may seem inconvenient though). After that you may rewrite its time evolution in terms of its square, but it won't be linear.

Thanks for the links to that thread and your papers.

 

[TheBlackNinja]

how can probability waves interfere destructively?

 

[RUTA]

how can probability waves interfere destructively?

Exactly. In the Euclidean path integral approach to lattice gauge theory for example, the transition amplitude works like a partition function for computing expectation values of observables and one can obtain information (e.g., particle masses) without Wick rotating back to real time. But, when used to compute correlation functions, you have an amplitude and must Wick rotate back to real time, add amplitudes and square to produce a probability. The reason is precisely what BlackNinja points out -- different configurations can interfere, unlike classical stat mech. So, I'm also interested in the answer to this question.

 

[akhmeteli]

how can probability waves interfere destructively?

Exactly. In the Euclidean path integral approach to lattice gauge theory for example, the transition amplitude works like a partition function for computing expectation values of observables and one can obtain information (e.g., particle masses) without Wick rotating back to real time. But, when used to compute correlation functions, you have an amplitude and must Wick rotate back to real time, add amplitudes and square to produce a probability. The reason is precisely what BlackNinja points out -- different configurations can interfere, unlike classical stat mech. So, I'm also interested in the answer to this question.

Dear RUTA,

I intended to avoid replying to TheBlackNinja's (TBN) post, partially because his question may contain several different questions, so it may require a long answer, but your post was "the last straw", so I'll try to answer.

1) So one question that may be implicit in TBN's question is: irrespective of quantum theory, can a real, rather than a complex function, describe destructive interference?

I guess we can answer this question affirmatively, as, in general, wave equations can be written for real functions.

2) Another possible implicit question in TBN's question: can quantum theory be reformulated in terms of a real, rather than complex, wavefunction (not pairs of real functions)?

I gave an affirmative answer in post 5 in this thread. Let me explain in a slightly more explicit form here. As Schrödinger noted (Nature, v.169, p.538(1952)), if we have a solution of the Klein-Gordon equation in electromagnetic field, the solution is generally complex, but it can always be made real by a gauge transform (at least locally). The four-potential of electromagnetic field changes in the process as well, but electromagnetic field does not. Schrödinger intended to extend his results to the Dirac equation, but it seems there was no sequel to his 1952 work. However, such extension is indeed possible (J. Math. Phys., v. 52, p. 082303 (2011), http://akhmeteli.org/wp-content/uploads/2011/08/JMAPAQ528082303_1.pdf ). It turns out that, in a general case, three out of four complex components of any Dirac spinor solution of the Dirac equation in arbitrary electromagnetic field can be algebraically eliminated, yielding a fourth-order partial differential equation (PDE) for just one complex component. This equation is generally equivalent to the Dirac equation. As there is just one complex component left, Schrödinger’s trick can be used to make this component real by a gauge transform. Again, the four-potential of electromagnetic field changes in the process as well, but electromagnetic field does not. So the Dirac equation is generally equivalent to an equation for one real wave function.

3) Yet another possible implicit question in TBN's question: can quantum theory be reformulated in terms of the squared absolute value of wave function?

At least sometimes (meaning: for some equations of quantum theory), it is possible. For example, as the Klein-Gordon equation in arbitrary electromagnetic field can be rewritten as an equation for a real, rather than complex, wave function, obviously, it can be rewritten in terms of the square of the wave function (see, e.g., equations 29, 30 in http://arxiv.org/abs/1111.4630). However, the resulting equations are not linear. Probably, the same can be done with the non-relativistic Schrödinger equation, but I did not try that. As for the Dirac equation, it can be rewritten in terms of just one real component, so it can be rewritten in terms of the square of this component. However, the resulting equation will not be linear. It is not clear if the Dirac equation can be rewritten in terms of the sum of squares of absolute values of four components of the wave function.

4) Yet another possible implicit question in TBN's question: can quantum theory be reformulated in terms of probability?

Probably, yes, - for the non-relativistic Schrödinger equation. It can be rewritten in terms of the squared real wave function, which square equals probability. But the equation for probability will not be linear. As for the Klein-Gordon equation and the Dirac equation, the answer is not clear: we should remember that, for example, for the Klein-Gordon equation in electromagnetic field, probability does not equal \psi*\psi.

5) Finally, the explicit TBN's question: how can probability waves interfere destructively?

Based on the above, it looks like they can interfere for the non-relativistic Schrödinger equation. However, the relevant wave equation for probability is not linear, so there is no linear superposition (however, it is my understanding that interference is possible in some sense for nonlinear equations). Furthermore, there is another complication. When we consider \psi_3, which is a linear superposition of two other solutions of the Schrödinger equation, \psi_1 and \psi_2, then the relevant real wave functions \phi_1, \phi_2, and \phi_3 may correspond to different four-potentials of electromagnetic fields (but to the same electromagnetic field).

As for your arguments based on the path integral approach… I guess they can be circumvented in this case due to either nonlinearity or ambiguity of four-potentials of electromagnetic fields, or both, but I have not considered this issue in any detail.

 

[HomogenousCow]

The whole deal of adding the amplitudes and not the probabilities creates the weirdness in QM, take the double slit experiment as an example, once you add the amplitudes for both slits and square the modulus you get an "inteference term" and the usual classical probabilities, this inteference term is what caused that whole "the electron is going through both slits" thing

 

[TheBlackNinja]

I do not have a lot of knowledge in this, but OP's question seems pretty direct.

What I was thinking the initial question was like "could exist an equivalent of schroedingers equation with the born rule 'already applied'?" he mentioned "absolute of it squared", and that's a probability density function.

And what I though was that things which can cancel are things that are allowed to have different signals. They may be vectors in opposite directions, scalars with opposite signals etc. But what you get form the born rule are probability density functions, which maps to positive scalars. So I don't see how these can interfere. Not real scalars, positive real scalars

Sure that 'to do the math' you can invent anything, like negative probability(if you are famous enough), or maybe if the underlying phenomenon already accounts for destructive interference in some way. But that's not his quesiton.
,
As homogenousCow said, its like the 'news' quantum physics brought are something like "existence itself is 'vectorial'", it can sum up and cancel. If you get rid of it in Schroedingers equation you will end putting it somewhere else.

So akhmeteli, this is my question and my answer. would you give a word on it?

 

[RUTA]

The Klein-Gordon eqn reduces to the Schrodinger eqn in the non-relativistic limit and its solutions are related to SE amplitudes by a simple phase:

http://users.etown.edu/s/stuckeym/SchrodingerEqn.pdf

Therefore, one would expect to obtain probabilities from the Klein-Gordon solutions by squaring.

 

[RUTA]

The whole deal of adding the amplitudes and not the probabilities creates the weirdness in QM, take the double slit experiment as an example, once you add the amplitudes for both slits and square the modulus you get an "inteference term" and the usual classical probabilities, this inteference term is what caused that whole "the electron is going through both slits" thing

Exactly, the twin-slit experiment “has in it the heart of quantum mechanics. In reality, it contains the only mystery.” R.P. Feynman, R.B. Leighton and M. Sands, The Feynman Lectures on Physics III, Quantum Mechanics (Addison-Wesley, Reading,1965), p. 1-1.

I've attended many foundations conferences in the past 18 years and I've seen many researchers attempting to do QM with classical probability theory in the manner alluded to by akhmeteli. I have not seen anyone succeed for this very reason, i.e., they can't explain quantum interference without introducing negative probabilities, which doesn't make sense in physics (experimentally at least).

Like I said supra, it's very tempting to interpret QFT a la stat mech since the Wick-rotated or Euclidean path integral works like a partition function for expectation values of observables. However, its correlation functions must be rendered amplitudes to produce probabilities, so every QFT text contains a caveat warning against taking the stat mech analogy too far. QFT is still a quantum formalism in that configurations can cancel in the computation of probability and it is this "destructive interference" that, as Feynman says, makes quantum physics "mysterious," i.e., it contradicts intuition per classical physics.

 

[akhmeteli]

The Klein-Gordon eqn reduces to the Schrodinger eqn in the non-relativistic limit and its solutions are related to SE amplitudes by a simple phase:

http://users.etown.edu/s/stuckeym/SchrodingerEqn.pdf

Therefore, one would expect to obtain probabilities from the Klein-Gordon solutions by squaring.

Approximately - maybe, but still the expression for the relevant component of the conserved current is quite different for the Klein-Gordon: see, e.g., http://wiki.physics.fsu.edu/wiki/index.php/Klein-Gordon_equation , equation 9.2.10, - it is not even positive definite in a one-particle theory.

 

[RUTA]

Approximately - maybe, but still the expression for the relevant component of the conserved current is quite different for the Klein-Gordon: see, e.g., http://wiki.physics.fsu.edu/wiki/index.php/Klein-Gordon_equation , equation 9.2.10, - it is not even positive definite in a one-particle theory.

But the current is still obtained using the square of an amplitude.

 

[akhmeteli]

But the current is still obtained using the square of an amplitude.

I'm not sure I understand that - I gave the reference to the expression for the conserved current for the Klein-Gordon equation - its zeroth (temporal) component (which is supposed to correspond to probability density) cannot be a squared absolute value of \phi (other than approximately), again, this component is not even positive definite. Or, maybe you have something else in mind when you mention amplitude?

 

[RUTA]

I'm not sure I understand that - I gave the reference to the expression for the conserved current for the Klein-Gordon equation - its zeroth (temporal) component (which is supposed to correspond to probability density) cannot be a squared absolute value of \phi (other than approximately), again, this component is not even positive definite. Or, maybe you have something else in mind when you mention amplitude?

You solve the KG eqn for psi, use psi*(operator)psi to obtain the current, and psi is the amplitude whose non-relativistic limit is found via the SE. So, this doesn't strike me as a promising method for producing a theory of probabilities a la classical physics.

 

[akhmeteli]

You solve the KG eqn for psi, use psi*(operator)psi to obtain the current, and psi is the amplitude whose non-relativistic limit is found via the SE. So, this doesn't strike me as a promising method for producing a theory of probabilities a la classical physics.

I did not say anything about "promising" or "not-promising" methods. TBN asked: "how can probability waves interfere destructively?", so I only discussed possibility or impossibility. Specifically, I said about the non-relativistic Schrödinger equation in electromagnetic field that it can be rewritten in terms of probabilities only as follows: for each solution \psi of the Schrödinger equation in electromagnetic four-potential A^\mu you can build (using a gauge transform) a real solution \phi of the Schrödinger equation in electromagnetic potential B^\mu, where A^\mu and B^\mu produce the same electromagnetic field. Therefore, the non-relativistic Schrödinger equation in electromagnetic field is generally equivalent to the non-relativistic Schrödinger equation in electromagnetic field for a real wave function (to prove it, you just need to use the unitary gauge where the wave function is real). In the resulting equation, you can express the real wave function via its square, which is probability density (I emphasized that the equation for probability density is nonlinear). That will work, at least locally. Whether this is "promising" or not, I don't know and I don't care for now :-) Let me note that this approach does not use the Klein-Gordon equation in any way. Again, I just offered some information about little-known mathematical results. If you think the mathematics is flawed, please advise. As for interpretation of these results... That is a different story.

 

[akhmeteli]

The whole deal of adding the amplitudes and not the probabilities creates the weirdness in QM, take the double slit experiment as an example, once you add the amplitudes for both slits and square the modulus you get an "inteference term" and the usual classical probabilities, this inteference term is what caused that whole "the electron is going through both slits" thing

Exactly, the twin-slit experiment “has in it the heart of quantum mechanics. In reality, it contains the only mystery.” R.P. Feynman, R.B. Leighton and M. Sands, The Feynman Lectures on Physics III, Quantum Mechanics (Addison-Wesley, Reading,1965), p. 1-1.

I'm not sure the double slit experiment creates the weirdness in QM; however, if it does, this weirdness can be reproduced in classical mechanics. You may wish to look at this article: Yves Couder, Emmanuel Fort, Single-Particle Diffraction and Interference at a Macroscopic Scale, Phys. Rev. Lett. 97, 154101 (2006), where, in particular, two-slit diffraction is successfully modeled by classical objects. I guess the following recent article of the same authors is publicly available: http://iopscience.iop.org/1742-6596/361/1/012001/pdf/1742-6596_361_1_012001.pdf (I don't want to copy their abstract here or rephrase what they did - it would be better if you look at the original articles, if you're not aware of them yet). Nobody doubts that Feynman was a greatest physicist, but your quote is 50 years old. My understanding is nowadays people tend to see quantum weirdness in experiments with more than one particle, such as experiments on the Bell inequalities, rather than in experiments with one particle, such as double-slit experiments.

 

[akhmeteli]

I do not have a lot of knowledge in this, but OP's question seems pretty direct.

What I was thinking the initial question was like "could exist an equivalent of schroedingers equation with the born rule 'already applied'?" he mentioned "absolute of it squared", and that's a probability density function.

And what I though was that things which can cancel are things that are allowed to have different signals. They may be vectors in opposite directions, scalars with opposite signals etc. But what you get form the born rule are probability density functions, which maps to positive scalars. So I don't see how these can interfere. Not real scalars, positive real scalars

Sure that 'to do the math' you can invent anything, like negative probability(if you are famous enough), or maybe if the underlying phenomenon already accounts for destructive interference in some way. But that's not his quesiton.
,
As homogenousCow said, its like the 'news' quantum physics brought are something like "existence itself is 'vectorial'", it can sum up and cancel. If you get rid of it in Schroedingers equation you will end putting it somewhere else.

So akhmeteli, this is my question and my answer. would you give a word on it?

I told RUTA how the non-relativistic Schrödinger could be rewritten in terms of probability density only (my posts 10 and 19). Does that contradict what you're saying? I don't know. First, the resulting equation would be nonlinear, so there are no superpositions, second, there may be some difficulties with the square root, third, there may be some subtleties with the gauge choice. But it seems the equation can be written. Again, I just mentioned some mathematical results. You choose how to interpret them (I tend to think they allow different interpretations).

 

[RUTA]

I did not say anything about "promising" or "not-promising" methods. TBN asked: "how can probability waves interfere destructively?", so I only discussed possibility or impossibility.

My response was to your reference to the KG equation and the possibility of it providing probability interference per TBN's question. My statement stands.

 

[akhmeteli]

My response was to your reference to the KG equation and the possibility of it providing probability interference per TBN's question. My statement stands.

I may be somewhat confused about which statement you have in mind, but if it is "one would expect to obtain probabilities from the Klein-Gordon solutions by squaring", then again, this statement does stand, but only as an approximation.

 

[RUTA]

I'm not sure the double slit experiment creates the weirdness in QM; however, if it does, this weirdness can be reproduced in classical mechanics. You may wish to look at this article: Yves Couder, Emmanuel Fort, Single-Particle Diffraction and Interference at a Macroscopic Scale, Phys. Rev. Lett. 97, 154101 (2006), where, in particular, two-slit diffraction is successfully modeled by classical objects. I guess the following recent article of the same authors is publicly available: http://iopscience.iop.org/1742-6596/361/1/012001/pdf/1742-6596_361_1_012001.pdf (I don't want to copy their abstract here or rephrase what they did - it would be better if you look at the original articles, if you're not aware of them yet). Nobody doubts that Feynman was a greatest physicist, but your quote is 50 years old.

The twin-slit experiment does not "create the weirdness of QM," it serves as an example of it, i.e., the interference of probability amplitudes. This is what distinguishes QM probability from CM probability, a fact many in the foundations community would like explained 50 years after Feynman's quote.

The experiment you allude to will not explain the interference of amplitudes in QM or QFT, nor does it map onto the SE, since the particle can only receive updates for changing boundary conditions at the finite wave speed of the vibrating liquid. In that sense it has less explanatory power than DBB (admittedly a relatively popular interpretation of QM).

My understanding is nowadays people tend to see quantum weirdness in experiments with more than one particle, such as experiments on the Bell inequalities, rather than in experiments with one particle, such as double-slit experiments.

You are correct, there are other things that foundationalists want explained, e.g., entanglement.

 

[akhmeteli]

The twin-slit experiment does not "create the weirdness of QM," it serves as an example of it, i.e., the interference of probability amplitudes. This is what distinguishes QM probability from CM probability, a fact many in the foundations community would like explained 50 years after Feynman's quote.

The experiment you allude to will not explain the interference of amplitudes in QM or QFT, nor does it map onto the SE, since the particle can only receive updates for changing boundary conditions at the finite wave speed of the vibrating liquid. In that sense it has less explanatory power than DBB (admittedly a relatively popular interpretation of QM).

I am not trying to draw more profound conclusions from this experiment than warranted. I am just saying that it emulates some unusual features of the quantum double-slit experiment. It is not an explanation of everything under the sun. However, the Feynman's quote is about the double slit experiment, as far as I understand, not about "interference of probability amplitudes" in general, and Couder's experiment does tell us something new about the double slit experiment. Furthermore, as far as I understand, there is no positive experimental evidence of particles receiving updates for changing boundary conditions at infinite speed so far, whereas theoretical proof of the violations of the Bell inequalities has its share of problems as well, as we discussed elsewhere.

 

[bohm2]

The experiment you allude to will not explain the interference of amplitudes in QM or QFT, nor does it map onto the SE, since the particle can only receive updates for changing boundary conditions at the finite wave speed of the vibrating liquid. In that sense it has less explanatory power than DBB (admittedly a relatively popular interpretation of QM).

I know this might be slightly off-topic but there have been some attempts to use Couder's experiments to model QM including an understanding of non-locality and entanglement:

Although it is clear that the mentioned experiments can only provide analogies, at best, one has here, nevertheless, a scenario providing essential stimuli for model building also in the context of quantum theory...there are further insights to be gained from the experiments of Couder's group, which could analogously be transferred into the modeling of quantum behavior. Concretely, we do believe that also an understanding of nonlocality and entanglement can profitt from the study of said experiments.

And they offer some ideas in this direction:

One can only speculate at present, but it seems that a good candidate for an explanation would come from cosmological considerations. Note, for example, that for the universe in its initial phases, according to present-day models, one can admit, in addition to the particles existing in the very early universe, a set of phase-locked wave-like oscillations that would thus "resonate" throughout the whole small-scale universe. Then, it is conceivable that cosmic inflation, for example, would not destroy these oscillations, but rather "inflate" these fields as well, thus ending up with a much larger universe where the particles still oscillate in phase with the zero-point background, albeit with the latter now having turned a nonlocal one.

A Classical Framework for Nonlocality and Entanglement
http://lanl.arxiv.org/pdf/1210.4406.pdf

 

[rewtnode]

Could you explain with a few words or in a nutshell what the "gauge mechanism" is?

 

[RUTA]

I am not trying to draw more profound conclusions from this experiment than warranted. I am just saying that it emulates some unusual features of the quantum double-slit experiment. It is not an explanation of everything under the sun. However, the Feynman's quote is about the double slit experiment, as far as I understand, not about "interference of probability amplitudes" in general, and Couder's experiment does tell us something new about the double slit experiment.

Feynman is using the twin-slit experiment as a model of the point he wants to make, not as something to be explained in and of itself. See (1) - (3) of the Summary:

(1) The probability of an event in an ideal experiment is given by the square of the absolute value of a complex number phi which is called the probability amplitude.

(2) When an event can occur in several alternative ways, the probability amplitude for the event is the sum of the probability amplitudes for each way considered separately.

(3) If an experiment is performed so that it's possible to determine which alternative is actually taken, the probability of the event is the sum of the probabilities for each alternative. The interference is lost.

Furthermore, as far as I understand, there is no positive experimental evidence of particles receiving updates for changing boundary conditions at infinite speed so far, whereas theoretical proof of the violations of the Bell inequalities has its share of problems as well, as we discussed elsewhere.

I'm sticking to mainstream physics. Although PF permits me to answer the original question per my own published interpretation (Foundations of Physics, Classical and Quantum Gravity and Studies in the History and Philosophy of Modern Physics), I think it best to answer this OP per QM texts. I'm very interested in alternatives such as you have presented, that's why I attend conferences in foundations of physics. But, I don't want to lead the OP to believe such interpretations are mainstream. We're in a very tiny minority.

 

[RUTA]

I know this might be slightly off-topic but there have been some attempts to use Couder's experiments to model QM including an understanding of non-locality and entanglement:

And they offer some ideas in this direction:

A Classical Framework for Nonlocality and Entanglement
http://lanl.arxiv.org/pdf/1210.4406.pdf

Their statements are speculative. I'm trying to answer the post concerning probability amplitudes in textbook fashion. See my post immediately supra.

 

[akhmeteli]

However, the Feynman's quote is about the double slit experiment, as far as I understand, not about "interference of probability amplitudes" in general, and Couder's experiment does tell us something new about the double slit experiment.

Feynman is using the twin-slit experiment as a model of the point he wants to make, not as something to be explained in and of itself. See (1) - (3) of the Summary:

Your words do not contradict mine. The quote is still about the double slit experiment, and the Summary is several pages apart from the quote.

I'm sticking to mainstream physics. Although PF permits me to answer the original question per my own published interpretation (Foundations of Physics, Classical and Quantum Gravity and Studies in the History and Philosophy of Modern Physics), I think it best to answer this OP per QM texts.

I guess my approach is much less noble:-) I am not too shy to plug in articles that I admire or my own published articles, if some of them seem relevant. On the one hand, as you said, PF rules do allow that, on the other hand, why should I hide Schrödinger’s work, which is highly relevant, from OP? For example, hypothetically, OP could take up nanosiborg’s challenge (post 3 in this thread) and waste a lot of time, trying to invent a bicycle:-) Unfortunately, Schrödinger’s beautiful work is not mentioned in quantum texts, although it fully deserves it.

I'm very interested in alternatives such as you have presented

Thank you very much. I did not think you might be interested, as your approach is so different. I should note though that I did not present any interpretation in this thread, I just discussed some little-known mathematical and experimental facts.

But, I don't want to lead the OP to believe such interpretations are mainstream. We're in a very tiny minority.

I respect your point of view – it is certainly reasonable, but other considerations can also be important in specific situations.

 

[RUTA]

Your words do not contradict mine. The quote is still about the double slit experiment, and the Summary is several pages apart from the quote.

The Summary contains no mention of twin-slit. He used twin-slit to illustrate, as he states explicitly therein, the manner by which one produces probability in QM (which holds in QFT as well). The reason I introduced the quote was in response to the question, "how can probability waves interfere destructively?" In other words, I'm pointing out that per quantum physics, they don't. If your answer is the Couder experiment, then I infer that you're claiming quantum physics is severly flawed. In my dealings therein, the foundations community does not believe quantum physics is flawed. If anything, the community is moving towards an "all in" position as evidenced by widespread interest in quantum information theory and Many Worlds. [15 years ago there was some interest in using classical methods to replace quantum physics, but it's rare these days.]

I could be wrong. Perhaps there is a large or growing subset of foundationalists who want to see quantum physics replaced by classical methods. Do you believe this to be the case?

 

[akhmeteli]

The Summary contains no mention of twin-slit. He used twin-slit to illustrate, as he states explicitly therein, the manner by which one produces probability in QM (which holds in QFT as well).

This is just your interpretation of the quote. The Summary does not equal the quote. The quote stands (or at least can stand) on its own. Anyway, whatever Feynman meant, your specific use of his quote ("Exactly, the twin-slit experiment “has in it the heart of quantum mechanics. In reality, it contains the only mystery.” ") left no doubt that you were talking about "the twin-slit experiment." It turns out you had in mind something else. Well, I am no neurosurgeon, I could not read your thoughts:-)

The reason I introduced the quote was in response to the question, "how can probability waves interfere destructively?" In other words, I'm pointing out that per quantum physics, they don't.

I gave my opinion in post 10 in this thread (question 5).

If your answer is the Couder experiment,

As I said, I am not trying to deduce too much from the Couder experiment, but I think it is an instructive classical analogy of the quantum experiment. As a result, people who believe that features of the quantum two-slit experiment cannot be reproduced in classical mechanics (and there are a lot of such people) have to offer more sophisticated arguments. I should say that my approach to interpretation of quantum theory is quite different: I only consider systems of interacting matter and electromagnetic fields. On the other hand, this approach gave a surprising interpretation-independent spin-off: it turned out that the Dirac equation in an arbitrary electromagnetic field is generally equivalent to a fourth-order PDE for just one (complex or real) component.

then I infer that you're claiming quantum physics is severly flawed.

I don’t know about “severely”, but yes, I think, strictly speaking, standard quantum theory is indeed flawed, and, judging by your posts elsewhere, you know that it is so: there is the measurement problem, in particular, the contradiction between unitary evolution and the theory of quantum measurements, e.g., the projection postulate. You know very well that I did not discover or invent this problem:-).

In my dealings therein, the foundations community does not believe quantum physics is flawed. If anything, the community is moving towards an "all in" position as evidenced by widespread interest in quantum information theory and Many Worlds. [15 years ago there was some interest in using classical methods to replace quantum physics, but it's rare these days.] .

Well, I also go to conferences on quantum foundations (I have been at four this year:-) , but this was a fluctuation:-) ), but it is difficult for me to say what the community believes or does not believe. Your assessment is probably correct, but that does not necessarily mean that standard quantum theory is immaculate:-) Thanks god, I don’t need to explain to you that the measurement problem does exist:-) You said that we're in a very tiny minority, but it looks to me that everybody is in minority in quantum foundations: I’d say there are at least three mainstream interpretations (Copenhagen, Many Worlds, and “shut up and calculate”) and a lot of non-mainstream ones. This situation suggests that there is no satisfactory interpretation so far.

I could be wrong. Perhaps there is a large or growing subset of foundationalists who want to see quantum physics replaced by classical methods. Do you believe this to be the case?

Probably not, although there were and there are quite a few outstanding physicists who are not happy about mainstream interpretations. Again, the issue of interpretation cannot be decided by a popular vote. There is some steady incremental progress in foundations, both in theory and experiment, and I don’t think the final destination is a sure bet. We all will have to live with future progress, whether we’ll like what we’ll see in the future or not.

 

[bhobba]

I could be wrong. Perhaps there is a large or growing subset of foundationalists who want to see quantum physics replaced by classical methods. Do you believe this to be the case?

I think the emerging modern view is its the simplest probabilistic theory that allows continuous transformations between pure states which when you think about it is what is really needed to model physical systems:
http://arxiv.org/pdf/quant-ph/0101012v4.pdf

Still doesn't really make it less weird and its not my personal approach which is based on invariance but does seem to capture quite a bit of its essence.

Thanks
Bill

 

[DiracPool]

Wow, I can't believe this thread is still going. Here's the original question in case anyone forgot...

As I understand it the wave function itself does not carry any physical interpration. Rather it is the square of it's absolute value. But that forces the question: Why construct a theory with the basic equation being about the time evolution of the wave function, when you could (I guess just as well) set up an equation for the time evolution of the absolute value of it squared. It just seems weird to me that we make this middle step, where we calculate something which actually carries no importance for the physical system.

Shrodinger attempted to describe how an electron interacts with a proton within an atom. He did this by applying the Hamiltonian operator to the wave equation and came up with the SE, which described the behavior (e.g., position, momentum, energy) of that electron or, in fact, any particle, by a wave "function." The particluar function depended upon the particulars of the system being analyzed.

Upon reviewing the solutions to the SE that manifested these wave functions, everyone was puzzled as to what they meant. It was only when Max Born came along and said, hey, if we multiply this wave function by its complex conjugate, it looks like we can use this to determine the probability of the particle or "system" being at some small interval of space d-tau.

This method has worked for 80 years so why do we want to change it now? It's kind of like asking the Swanson company why they cook their frozen dinners before they package them. We could try to make the argument to them that they could save time by simply packaging them while they cook them at the same time. That might not come out so well, though. Squaring the result is one more step in equations that can run many pages long. Why not play it safe and cook the meal before you package it?

 

[RUTA]

As I said, I am not trying to deduce too much from the Couder experiment, but I think it is an instructive classical analogy of the quantum experiment. As a result, people who believe that features of the quantum two-slit experiment cannot be reproduced in classical mechanics (and there are a lot of such people) have to offer more sophisticated arguments.

Are you aware of this one: http://arxiv.org/abs/quant-ph/0111119? Anyway, since QM and QFT work, I think it's rather incumbent upon those who believe QM and QFT can be replaced by some classical formalism to make that happen, not for the quantum community to show it can't. And as of now, the people who believe classical formalism can account for all quantum phenomena have a looooooooooooong way to go.

I don’t know about “severely”, but yes, I think, strictly speaking, standard quantum theory is indeed flawed, and, judging by your posts elsewhere, you know that it is so: there is the measurement problem, in particular, the contradiction between unitary evolution and the theory of quantum measurements, e.g., the projection postulate. You know very well that I did not discover or invent this problem:-).

I don't believe QM and QFT (quantum physics) are flawed as physics, since we use them successfully in many varied applications. Quantum physics does strike me as flawed mathematically and conceptually. When I started working in foundations (18 years ago) I had the impression that most foundationalists shared this opinion. Now I'm starting to get the impression that the community is "buying in," as I see Many Worlds and quantum information theory dominating discussion and these interpretations don't suggest modifications to the formalism like, say, DeBroglie-Bohm.

Well, I also go to conferences on quantum foundations (I have been at four this year:-) , but this was a fluctuation:-) ), but it is difficult for me to say what the community believes or does not believe. Your assessment is probably correct, but that does not necessarily mean that standard quantum theory is immaculate:-) Thanks god, I don’t need to explain to you that the measurement problem does exist:-) You said that we're in a very tiny minority, but it looks to me that everybody is in minority in quantum foundations: I’d say there are at least three mainstream interpretations (Copenhagen, Many Worlds, and “shut up and calculate”) and a lot of non-mainstream ones. This situation suggests that there is no satisfactory interpretation so far.

Copenhagen = shut up and calculate. http://fisica.ciencias.uchile.cl/~emenendez/uploads/Cursos/callate-y-calcula.pdf . In the physics community Copenhagen dominates. In the foundations community ... I'd say Many Worlds has a plurality ... I could be wrong, quantum information may have it. DeBroglie-Bohm is popular. Cramer's Transactional interpretation and Aharonov's two-vector formalism have advocates -- time-symmetric approaches as a whole have an active following. Fuch's quantum Bayesianism has attracted Mermin's attention: http://users.etown.edu/s/stuckeym/MerminBayesian.pdf and generated some discussion. I've been to only two conferences this year, so I may not have a good pulse. What have you seen along these lines?

Probably not, although there were and there are quite a few outstanding physicists who are not happy about mainstream interpretations. Again, the issue of interpretation cannot be decided by a popular vote. There is some steady incremental progress in foundations, both in theory and experiment, and I don’t think the final destination is a sure bet. We all will have to live with future progress, whether we’ll like what we’ll see in the future or not.

Agreed, but I feel obligated to readers on PF who are not active in the community to give an accurate representation of what receives the most attention in the community. At the end of the day, physics is de facto a "popularity contest" in that all theories are underdetermined, yet there is a clear convention.

 

[RUTA]

I think the emerging modern view is its the simplest probabilistic theory that allows continuous transformations between pure states which when you think about it is what is really needed to model physical systems:
http://arxiv.org/pdf/quant-ph/0101012v4.pdf

Thanks for posting this, Bill. I meant to do so earlier and ... . Anyway, it's work like this that makes me skeptical about the possibility of replacing quantum physics with classical approaches.

 

[bhobba]

I don’t know about “severely”, but yes, I think, strictly speaking, standard quantum theory is indeed flawed, and, judging by your posts elsewhere, you know that it is so: there is the measurement problem, in particular, the contradiction between unitary evolution and the theory of quantum measurements, e.g., the projection postulate. You know very well that I did not discover or invent this problem:-).

If you are expressing a personal opinion it is flawed that's OK. But if you think in any kind of objective way that would be accepted by all mathematicians/physicists, or even most, it is flawed then you are sadly mistaken. All interpretations suck in their own special way it is true but it is purely a matter of opinion if any/all are flawed.

I believe decoherence solves the measurement problem for all practical purposes, meaning no experiment can ever show that you can't assume the pure state has been transformed into a mixed state and that the combined system and measurement apparatus is in the state it is observed to be prior to observation. You may not like that particular view because it doesn't explain how the state is selected or exactly where the collapse occurred, or even why there is any measurement outcome at all, but logically it is unassailable. It is purely a matter of philosophical debate rather than any kind of objective 'truth' if it has a flaw. Most certainly it whispers in your ear something more is going on and we like would a way of explaining the 'gaps' but whispering in your ear and actually being a flaw are not the same thing.

Thanks
Bill

 

[George Jones]

Steven Weinberg has written graduate-level quantum mechanics book that has just been published,

https://www.amazon.com/dp/1107028728/?tag=pfamazon01-20

and in it, Weinberg says

""My own conclusion (not universally shared) is that today there is no interpretation of quantum mechanics that does not have serious flaws, and that we ought to take seriously the possibility of finding some more satisfactory other theory, to which quantum mechanics is merely a good approximation.""

 

[bhobba]

"My own conclusion (not universally shared) is that today there is no interpretation of quantum mechanics that does not have serious flaws, and that we ought to take seriously the possibility of finding some more satisfactory other theory, to which quantum mechanics is merely a good approximation.""

Note the 'not universally shared'

Of course Weinberg is worthy of respect - but he does not speak for all physicists.

If QM is flawed is purely a matter of opinion - not actual fact.

My view is QM whispers in your ear there is something more going on - but that is far from it being a fact.

Thanks
Bill

 

[chill_factor]

what I find interesting is that the Schrodinger Equation does not look like a wave equation; it has a 1st order derivative to time, but 2nd order to position. That to me looks like a diffusion equation. Does that have any significance?

 

[bohm2]

what I find interesting is that the Schrodinger Equation does not look like a wave equation; it has a 1st order derivative to time, but 2nd order to position. That to me looks like a diffusion equation. Does that have any significance?

I think this is the model/perspective that the Grossing et al. group endorse:

The Quantum as an Emergent System
http://www.nonlinearstudies.at/files/ggEmerQuM.pdf

Historically, it had already been Schrödinger himself who pointed out the close resemblance of his time-dependent equation with the classical diffusion equation...

Emergence and Collapse of Quantum Mechanical Superposition:Orthogonality of Reversible Dynamics and Irreversible Diffusion
http://arxiv.org/ftp/arxiv/papers/1004/1004.4596.pdf

A lot of this group's work and most of their publications can be found here:

http://www.nonlinearstudies.at/

 

[akhmeteli]

Are you aware of this one: http://arxiv.org/abs/quant-ph/0111119?

Never heard of it. Looks like it has never been published. I looked at it briefly, and so far I am unimpressed. First, it is not obvious for me that entanglement necessarily implies violation of Einstein-Bell locality. Second, it looks like they start with plane electromagnetic waves and prove that the Bell inequalities are violated for some states constructed on the basis of such waves. However, violations of the Bell inequalities do not necessarily imply violation of Einstein-Bell locality - you need an extra condition: some events must be outside of each other’s light cones. I cannot imagine how this can happen for plane waves. So it looks like their proof may have a “locality loophole”:-) But again, I did not look into details of the article.

Anyway, since QM and QFT work, I think it's rather incumbent upon those who believe QM and QFT can be replaced by some classical formalism to make that happen, not for the quantum community to show it can't. And as of now, the people who believe classical formalism can account for all quantum phenomena have a looooooooooooong way to go.

I agree. But these are two different things: 1) proving that QM and QFT can be replaced by some classical formalism, and 2) proving that some features of a specific phenomenon believed to be an epitome of quantum can be reproduced in classical mechanics. I think 2) was done in Couder experiment for the two-slit experiment, but, as I emphasized earlier, maybe not much more. Nevertheless, the experiment seems very interesting and useful.

I don't believe QM and QFT (quantum physics) are flawed as physics, since we use them successfully in many varied applications. Quantum physics does strike me as flawed mathematically and conceptually.

I think we should make a distinction between a precise physical law and an approximation (and maybe this is exactly what you’re doing). Is the Coulomb law flawed as physics? No, as “we use [it] successfully in many varied applications.” But it is just an approximation and fails for fast processes. We cannot imagine physics without approximations, but typically we know they are just approximations, although they can be good, or very good, or excellent approximations. So we have a crucial question: is standard quantum theory a precise law or an approximation? One may ask: does it matter, if it works so well? I think it does matter, as physics is important even beyond any applications, as it is a basis of philosophy (certainly, not the only basis). For example, we make philosophical conclusions about fundamental locality or nonlocality of Nature based on physics. But I cannot understand how nonlocality can be approximate. Nature is either local or nonlocal. So is standard quantum theory a precise law? I don’t think it can be a precise law, as it contains mutually contradicting postulates (unitary evolution and the theory of measurements). Furthermore, it is shown in http://arxiv.org/abs/1107.2138 (accepted for publication in Physics Reports) how the Born rule can be derived from unitary evolution in some cases, but as an approximation (maybe an excellent approximation). If (standard) quantum physics is indeed flawed mathematically, as you think (and I agree), it cannot be a precise law. That does not mean that I don’t admire quantum physics as one of the best achievements of humanity.

When I started working in foundations (18 years ago) I had the impression that most foundationalists shared this opinion. Now I'm starting to get the impression that the community is "buying in," as I see Many Worlds and quantum information theory dominating discussion and these interpretations don't suggest modifications to the formalism like, say, DeBroglie-Bohm.

Again, you are talking about (prevailing) opinions, not about facts. I agree that “sociology” of physics is important, but it cannot change the facts. As we seem to agree that standard quantum physics is indeed flawed (“strictly speaking”, in my wording, or “mathematically and conceptually”, in yours), maybe we should not delve on this issue any further? It is not our task to convince everybody.

As for Many Worlds … (I know about quantum information theory even less than about Many Worlds:-) ) On the one hand, I am no fan of this interpretation, on the other hand, it is my understanding that it puts more emphasis on unitary evolution, whereas the status of the theory of measurements is somewhat lower there than in Copenhagen. And that may be a strong point of Many Worlds, in my book, as I think the contradiction between unitary evolution and the theory of measurements should be resolved in favor of unitary evolution.

Copenhagen = shut up and calculate. http://fisica.ciencias.uchile.cl/~emenendez/uploads/Cursos/callate-y-calcula.pdf .

I am not sure I agree. Mermin’s article is not a proof. Furthermore, even in that article, after the phrase "If I were forced to sum up in one sentence what the Copenhagen interpretation says to me, it would be "Shut up and calculate!", we find the following words: “In the intervening years, I've come to hold a milder and more nuanced opinion of the Copenhagen view”. John Bell wrote somewhere (cannot find the reference) that we owe deep respect to the Copenhagen interpretation. A primitive interpretation could not dominate physics for decades.

In the physics community Copenhagen dominates. In the foundations community ... I'd say Many Worlds has a plurality ... I could be wrong, quantum information may have it. DeBroglie-Bohm is popular. Cramer's Transactional interpretation and Aharonov's two-vector formalism have advocates -- time-symmetric approaches as a whole have an active following. Fuch's quantum Bayesianism has attracted Mermin's attention: http://users.etown.edu/s/stuckeym/MerminBayesian.pdf and generated some discussion. I've been to only two conferences this year, so I may not have a good pulse. What have you seen along these lines?

I am not sure. I am afraid my contacts were not representative, but your assessment seems fair.

 

[akhmeteli]

I think the emerging modern view is its the simplest probabilistic theory that allows continuous transformations between pure states which when you think about it is what is really needed to model physical systems:
http://arxiv.org/pdf/quant-ph/0101012v4.pdf

Anyway, it's work like this that makes me skeptical about the possibility of replacing quantum physics with classical approaches.

I guess I am less impressed by “work like this” than you are. The reason is such work looks too successful:-) for my taste: it reproduces the theory of quantum measurements, among other things, and, therefore, the contradiction of standard quantum theory (or at least something that contradicts unitary evolution). That’s not very good, in my book. Where is the source of such “success”? I did not study the article in detail, but the source may be the assumption of definite outcomes of quantum measurements in the reasonably looking axioms. Such definite outcomes, strictly speaking, contradict unitary evolution. How do we get the appearance of definite outcomes? I think the following work gives an idea (I mentioned it earlier): http://arxiv.org/abs/1107.2138 (accepted for publication in Physics Reports). Or you may wish to look at their earlier work http://arxiv.org/abs/quant-ph/0702135 (there are references to their journal articles there), which is much, much shorter.

 

[akhmeteli]

I don’t know about “severely”, but yes, I think, strictly speaking, standard quantum theory is indeed flawed, and, judging by your posts elsewhere, you know that it is so: there is the measurement problem, in particular, the contradiction between unitary evolution and the theory of quantum measurements, e.g., the projection postulate. You know very well that I did not discover or invent this problem:-).

If you are expressing a personal opinion it is flawed that's OK. But if you think in any kind of objective way that would be accepted by all mathematicians/physicists, or even most, it is flawed then you are sadly mistaken. All interpretations suck in their own special way it is true but it is purely a matter of opinion if any/all are flawed. :-).

Yes, this is my personal opinion. But this is not just my personal opinion: the measurement problem in quantum theory is recognized as a serious problem ( http://plato.stanford.edu/entries/qt-measurement/ - you may wish to search for “insolubility theorem” there ). The problem will not disappear even if I am eaten by alligators tomorrow:-). While it is important in physics who accepts what, what I am saying has some solid and “objective” basis. Let me note that I am not talking about “all interpretations”, just about standard quantum theory. By the way, I don’t quite understand how “flawless” interpretations can “suck”, but maybe that’s just because English is not my native language:-)

I believe decoherence solves the measurement problem for all practical purposes, meaning no experiment can ever show that you can't assume the pure state has been transformed into a mixed state and that the combined system and measurement apparatus is in the state it is observed to be prior to observation. You may not like that particular view because it doesn't explain how the state is selected or exactly where the collapse occurred, or even why there is any measurement outcome at all, but logically it is unassailable. It is purely a matter of philosophical debate rather than any kind of objective 'truth' if it has a flaw. Most certainly it whispers in your ear something more is going on and we like would a way of explaining the 'gaps' but whispering in your ear and actually being a flaw are not the same thing.

I am afraid your belief that “decoherence solves the measurement problem for all practical purposes” is far from being universally accepted (http://plato.stanford.edu/entries/qm-decoherence/ , especially “2.1 Solving the measurement problem?“) If you disagree, could you somehow substantiate your point of view?

 

[RUTA]

I agree. But these are two different things: 1) proving that QM and QFT can be replaced by some classical formalism, and 2) proving that some features of a specific phenomenon believed to be an epitome of quantum can be reproduced in classical mechanics. I think 2) was done in Couder experiment for the two-slit experiment, but, as I emphasized earlier, maybe not much more. Nevertheless, the experiment seems very interesting and useful.

Definitely interesting. Not sure if it will prove useful.

I think we should make a distinction between a precise physical law and an approximation (and maybe this is exactly what you’re doing). Is the Coulomb law flawed as physics? No, as “we use [it] successfully in many varied applications.” But it is just an approximation and fails for fast processes. We cannot imagine physics without approximations, but typically we know they are just approximations, although they can be good, or very good, or excellent approximations. So we have a crucial question: is standard quantum theory a precise law or an approximation? One may ask: does it matter, if it works so well? I think it does matter, as physics is important even beyond any applications, as it is a basis of philosophy (certainly, not the only basis). For example, we make philosophical conclusions about fundamental locality or nonlocality of Nature based on physics. But I cannot understand how nonlocality can be approximate. Nature is either local or nonlocal. So is standard quantum theory a precise law? I don’t think it can be a precise law, as it contains mutually contradicting postulates (unitary evolution and the theory of measurements). Furthermore, it is shown in http://arxiv.org/abs/1107.2138 (accepted for publication in Physics Reports) how the Born rule can be derived from unitary evolution in some cases, but as an approximation (maybe an excellent approximation). If (standard) quantum physics is indeed flawed mathematically, as you think (and I agree), it cannot be a precise law. That does not mean that I don’t admire quantum physics as one of the best achievements of humanity.

I believe there is a theory fundamental to quantum physics (whence quantum gravity, for example). One could divide interpretations along that line -- those that do and those that don't rely on concepts from a yet undetermined theory fundamental to quantum physics.

I am not sure I agree. Mermin’s article is not a proof. Furthermore, even in that article, after the phrase "If I were forced to sum up in one sentence what the Copenhagen interpretation says to me, it would be "Shut up and calculate!", we find the following words: “In the intervening years, I've come to hold a milder and more nuanced opinion of the Copenhagen view”. John Bell wrote somewhere (cannot find the reference) that we owe deep respect to the Copenhagen interpretation. A primitive interpretation could not dominate physics for decades.

Yes, you're right. Mermin says he was wrong to have characterized Copenhagen as "shut up and calculate," yet "shut up and calculate" certainly exists as an "interpretation." Therefore, Copenhagen is distinct. I've always (erroneously) conflated them, so now I will have to find a proper characterization of Copenhagen and add it to my list

 

[RUTA]

I guess I am less impressed by “work like this” than you are. The reason is such work looks too successful:-) for my taste: it reproduces the theory of quantum measurements, among other things, and, therefore, the contradiction of standard quantum theory (or at least something that contradicts unitary evolution). That’s not very good, in my book. Where is the source of such “success”? I did not study the article in detail, but the source may be the assumption of definite outcomes of quantum measurements in the reasonably looking axioms. Such definite outcomes, strictly speaking, contradict unitary evolution. How do we get the appearance of definite outcomes? I think the following work gives an idea (I mentioned it earlier): http://arxiv.org/abs/1107.2138 (accepted for publication in Physics Reports). Or you may wish to look at their earlier work http://arxiv.org/abs/quant-ph/0702135 (there are references to their journal articles there), which is much, much shorter.

For those with a psi-epistemic view, the measurement problem is not an issue.

 

[akhmeteli]

For those with a psi-epistemic view, the measurement problem is not an issue.

Again, maybe we don't need to delve on this further, as we both seem to regard the measurement problem as an issue.

 

[RUTA]

Again, maybe we don't need to delve on this further, as we both seem to regard the measurement problem as an issue.

Actually, my interpretation is a blockworld approach so there is no MP. We use a path integral where the future boundary conditions are input, so there is no wave function collapse, i.e., one computes the amplitude for an entire process to include outcomes. Accordingly, MP is a faux problem associated with incorrectly trying to understand a spatiotemporal phenomenon in terms of time-evolved entities.

 

[akhmeteli]

Actually, my interpretation is a blockworld approach so there is no MP. We use a path integral where the future boundary conditions are input, so there is no wave function collapse, i.e., one computes the amplitude for an entire process to include outcomes. Accordingly, MP is a faux problem associated with incorrectly trying to understand a spatiotemporal phenomenon in terms of time-evolved entities.

So, if I understand you correctly, you do not accept wave function collapse of standard quantum theory. Then we do agree on this point.

 

[RUTA]

So, if I understand you correctly, you do not accept wave function collapse of standard quantum theory. Then we do agree on this point.

You don't have wave function collapse in the path integral approach because the experimental outcome is a boundary condition, i.e., there is nothing being "time evolved," so there is nothing to "collapse." One is thinking spatiotemporally (4D) rather than dynamically ((3+1)D). By assuming 4Dism is the correct fundamental description and that not all 4D situations permit a (3+1)D story, MP and violation of the Bell inequality are no longer "mysterious," i.e., those are just situations where a 4D quantum result doesn't permit a (3+1)D time-evolved story.

By the way, I've seen several threads on PF about the mystery of the big bang, e.g., how do we have conservation of energy!? But, again, one has to understand GR is a 4D solution, so not all points on the spacetime manifold need possesses a "history," and the big bang is just such a point -- there is no (3+1)D time-evolved story to tell about the "cause" of the big bang. Thus, this "mystery" results from an inappropriate desire to tell dynamical stories where they're just not applicable.