why the wave function


by aaaa202
Tags: function, wave
akhmeteli
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#19
Dec2-12, 03:50 PM
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Quote Quote by RUTA View Post
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
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#20
Dec2-12, 09:02 PM
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Quote Quote by HomogenousCow View Post
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
Quote Quote by RUTA View Post
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/...1_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
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#21
Dec2-12, 10:26 PM
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Quote Quote by TheBlackNinja View Post
I do not have a lot of knowledge in this, but OP's question seems pretty direct.

What I was thinking the initial quesiton was like "could exist an equivalent of schroedingers equation with the born rule 'already applied'?" he mentioned "absolute of it squared", and thats 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 thats 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 quesiton 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
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#22
Dec3-12, 06:44 AM
P: 640
Quote Quote by akhmeteli View Post
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
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#23
Dec3-12, 08:39 PM
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Quote Quote by RUTA View Post
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
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#24
Dec4-12, 08:37 AM
P: 640
Quote Quote by akhmeteli View Post
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/...1_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).

Quote Quote by akhmeteli View Post
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
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#25
Dec4-12, 09:40 PM
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Quote Quote by RUTA View Post
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
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#26
Dec4-12, 10:13 PM
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Quote Quote by RUTA View Post
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
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#27
Dec5-12, 10:50 AM
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Could you explain with a few words or in a nutshell what the "gauge mechanism" is?
RUTA
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#28
Dec5-12, 11:28 AM
P: 640
Quote Quote by akhmeteli View Post
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.

Quote Quote by akhmeteli View Post
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
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#29
Dec5-12, 11:30 AM
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Quote Quote by bohm2 View Post
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
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#30
Dec5-12, 10:17 PM
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Quote Quote by akhmeteli View Post
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.
Quote Quote by RUTA View Post
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.

Quote Quote by RUTA
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.

Quote Quote by RUTA
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.

Quote Quote by RUTA
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
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#31
Dec6-12, 10:15 AM
P: 640
Quote Quote by akhmeteli View Post
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
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#32
Dec6-12, 09:57 PM
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Quote Quote by RUTA View Post
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:-)

Quote Quote by RUTA
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).

Quote Quote by RUTA
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.
Quote Quote by RUTA
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:-).

Quote Quote by RUTA
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.

Quote Quote by RUTA
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
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#33
Dec7-12, 02:25 AM
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Quote Quote by RUTA View Post
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
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#34
Dec7-12, 04:04 AM
P: 492
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
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#35
Dec7-12, 01:36 PM
P: 640
Quote Quote by akhmeteli View Post
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.

Quote Quote by akhmeteli View Post
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.


Quote Quote by akhmeteli View Post
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/~em...-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?


Quote Quote by akhmeteli View Post
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
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#36
Dec7-12, 01:43 PM
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Quote Quote by bhobba View Post
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.


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