The Refutation of Bohmian Mechanics

Demystifier

In practice, a very small number of people cares about BM, a larger but still relatively small number cares about standard QM, and a much much bigger number of people cares about certain non-scientific religious books. Can we conclude anything relevant from that?

A. Neumaier

Because the interpretation of the probabilisitic meaning of psi(x,t) is completely different in the two forms.
In the Schroedinger picture and in standard BM, the density of x at fixed t is given by |psi(x,t_0)|^2, while in Horwitz/Piron and in your relativistic BM, it is given by |psi(x,t)|^2delta(t-t_0). You cannot assert both simultaneously.

A. Neumaier

Yes: Religion is for everyone, quantum mechanics for the general scientist, and BM for the determinsitic scientist only. I am trying to address the first two groups only, though I know about the practices of the third one.

Demystifier

First, this is a difference in the probabilistic interpretation, not in the ontology. Second, in
http://xxx.lanl.gov/abs/0811.1905
I explain how both probabilistic interpretations may be right (but not simultaneously). One (Horwitz/Piron) is a fundamental a priori probability, while the other is a conditional probability. Which one is to be applied is context dependent.

A. Neumaier

But psi(x,t) can have only _one_ meaning consistent with the Schroedinger equation, which is _not_ context dependent. And it must be the one consistent with standard QM.

Swapping meanings as convenient for a particular argument is another of the trickeries of BM.

A fundamental theory must have a unique interpretation.

Demystifier

But there is only one FUNDAMENTAL probabilistic interpretation in my approach - the Horwitz/Piron one. The other interpretation is DERIVED from the fundamental one - by using the standard theory of probability, which includes the concept of conditional probability. You should know that, irrespective of physics, probability is strongly context dependent, depending on what one already knows about the system. Changing knowledge changes the probability, even if physics is the same.

Besides, even though such a fundamental Horwitz/Piron probability is not identical with the standard probabilistic interpretation, I show that the former is compatible with the latter. The former is a generalization of the latter, not merely a replacement of it.

akhmeteli

Dear A. Neumaier,

thank you for your reply.

Why would I do that? I clearly don't want you to be banned. Even if sometimes I use harsh words, I am not your enemy. I just respectfully asked you to voluntarily follow the rules, because otherwise you create very awkward situations: while what you say is just your personal theory, those members of the forum who are not very familiar with the issue tend to rely on your word, as you have their well-deserved respect, and they think that what you said is a well-established fact. As a result, they are misled at least with respect to the status of your statement. On the other hand, those of us who for some reason happen to know more about the specific problem, sometimes just don't want to silently swallow your statement and are forced to confront you and discuss your personal theory. I think what you do is not quite right, but I am not sure I will be able to explain that to you for a reason outlined at the end of this post.

With all due respect, not that I don't believe you, but I don't, for a reason outlined at the end of this post.

Yes, we disagree, and no, I cannot be sure I am right, but my main point is your statement just does not belong here, no matter how correct or wrong your statement is.
You said: “For example, you cannot do quantum computing in Bohmian mechanics” in post 18 in this thread. I looked for word “probably” in that post. That was a long search… You did use the word in your post 24, but there it related to a somewhat different statement: “Bohmians are not aware of many things; they probably never tried to bring quantum computing into their focus.”; furthermore, the damage was already done earlier, when you told us about quantum computing and the Bohm interpretation without qualifying or “caveating” your statement in any way. The same problem arises: it is not easy to tell a personal theory from the ultimate truth.

I truly respect you for taking your opponent’s argument seriously. But I had no intention to criticize you for not having read something “latest and greatest”. My problem was that, even when asked directly about the status of your statement about quantum computing in the Bohm interpretation, you chose to avoid a direct answer. You could say: “This was proven in such and such article”, or “Well, this is my personal opinion/theory”. You did not. This is unfortunate.
This phrase of yours makes me think that the chance to convince you is very slim and makes it difficult to believe that you fully respect the rules as you understand them. I tend to make the following two conclusions based on this phrase:
1. You read and understand the rules exactly as they are written, and
2. Then you do exactly what you want.

akhmeteli

Dear camboy,

Thank you for your response.

With all due respect, I am not sure the reference you supplied is indeed appropriate. I admit that I don't know much about quantum computing and don't have time to study your lengthy reference, so I can only judge it by formal criteria. It may well be that this is a paper of the century (at least it seems A. Neumaier wrote about it with some respect), but, as far as I am concerned, this is just an unpublished Master's thesis, so, under the forum's rules, it is not appropriate for discussion here. I am aware that the author's supervisor is well-known for his publications on the Bohm interpretation, but let us wait until Mr. Roser and Dr. Valentini publish this work properly.

As for my personal opinion on A. Neumaier's claim, I don't want to start a flame here, so maybe I'll PM you in a couple of days.

A. Neumaier

It is a myth believed (only) by the Bayesian school that probability is dependent on knowledge.

You cannot change the objective probabiltiies of a mechanism by forgetting about the knowledge you have.

Lack of knowledge results in lack of predictivity, not in different probabilities.
Then please tell me how the probability theory of the ground state of the 1-dimensional quantum harmonic oscillator with H= p^2/2 + q^2/2 - 1/2, where hbar=1 and p,q acting on psi(x,t) (x in R) in the standard way, which in standard QM is modelled by psi(x,t)=e^{-x^2/2} independent of t, is generalized to your fundamental view.

And how the standard view is obtained by taking conditional probabilites.

Demystifier

I strongly disagree, but elaboration would be an off topic.

If you disagree that probability may depend on knowledge, then there is no point in explaining it (which, by the way, I have already explained in a paper I mentioned several times on this thread).

A. Neumaier

It is not off-topic here:
http://www.physicsforums.com/showthr...89#post3278689This is strange, since the concept of conditional probability exists also in the frequentist school of objective probability and also in the interpretation-less Kolmogorov probability theory.
Did you really discuss there, as requested, the ground state of the harmonic oscillator?

A. Neumaier

I do follow the rules, of which I quote here the relevant part:
_Everything_ I say is my personal opinion (though it often agrees with established scientific fact), and when appropriate I give references to what I believe is a valid source. It is neither against the rules to voice a personal opinion (most contributors do that regularly) nor to refer to unpublished articles if they are ''part of current professional mainstream scientific discussion'' (Streater's book shows that my remarks on wrong signs in time correlations in BM is part of that).
The remainder of the discussion has shown in which sense my statement was a fact.
That a fact has no convenient reference doesn't make it a personal theory in the sense that it would belong only to the IR section of PF. It just takes more space to provide the evidence, and the discussion with Demystifier has provided it.
Our understanding of the rules is different, and your arguments did not convince me that your interpretation is better than mine. Only superior arguments than my own are suitable to convince me of something different from what I am already convinced of.

A. Neumaier

I assume you meant your paper http://xxx.lanl.gov/abs/0811.1905 . It explains the connection to conditional probability in (6) to (9). But this doesn't apply to the ground state of the harmonic oscillator since there psi(x,t)=e^{-x^2/2} (independent of t) considered as a function of (x,t) in R^4 is not normalizable.

Thus the allegedly more fundamental 4D description has serious normalization problems already in the simple example of the harmonic oscillator.

Demystifier

Yes.

See page 5, the paragraph that begins with "Before discussing ...".

A. Neumaier

I find it strange that you refer to the divergence of the integral over time as ''they cannot be localized in time'', since what you are trying to do is globalizing the state rather than localizing it.

But let me follow your recipe by taking finite time integration, and taking the limit at the end of the calculation. Assuming the already normalized 3D eigenstate psi_0, I normalize the state psi(x,t)=psi_0(x) over the interval [0,T]. This gives me the normalized state phi=psi/sqrt{T}. Now the probability of finding the particle anywhere in a time interval of length Delta is
[tex]\int dx \int_0^\Delta dt |\phi(x,t)|^2 =\Delta/T.[/tex]
Taking T to infinity tells me that there is a zero probability for finding the particle in any given time interval of length Delta.

What did i do wrong to get this very strange result?

Demystifier

You applied the limit too early, not at what I meant by the "end of calculation". A valid example of an appropriate use of the limit is discussed briefly in the last paragraph of Sec. 2.

Besides, the result is not strange at all. Indeed, it is easy to construct a classical analog of that result, provided that you accept (which you don't) Bayesian view of probability. For example, if the universe will last forever, what is the probability that you live now?

A. Neumaier

According to (6), it is a legitimate goal in your calculus to ask for the probability of finding a particle somewhere in spacetime is a legitimate goal. But now you seem to say that the interpretation in (6) is bogus and that your calculus doesn't give _any_ information about the probability of finding a particle somewhere in spacetime.