Understanding Bohmian Mechanics of Instrumentalists

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  • #76
PeterDonis
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I thought Copenhagen was an example of a non-realist interpretation
Copenhagen as usually understood does not take the quantum state to be the actual real state of the system, yes.

However, Copenhagen as usually understood also does not take any position on whether the indeterminacy in the math of QM regarding measurement results (i.e., that the math only predicts probabilities) reflects a "true" indeterminacy in reality. So I don't think Copenhagen as usually understood qualifies as "truly indeterminate/stochastic".

I thought QFT could be interpreted as non-realist
AFAIK QFT admits the same interpretations as QM in general, which would include both realist and non-realist ones.
 
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  • #77
Lynch101
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Copenhagen as usually understood does not take the quantum state to be the actual real state of the system, yes.

However, Copenhagen as usually understood also does not take any position on whether the indeterminacy in the math of QM regarding measurement results (i.e., that the math only predicts probabilities) reflects a "true" indeterminacy in reality. So I don't think Copenhagen as usually understood qualifies as "truly indeterminate/stochastic".
Ah I see, thank you for the explanation. I have read a few things which have gone from Copenhagen to a non-realist interpretation but I guess that should be viewed as appending an interpretation to Copenhagen. Is Copenhagen then synonymous with "Shut up and calcualte"?

AFAIK QFT admits the same interpretations as QM in general, which would include both realist and non-realist ones.
Are there other non-realist interpretations, outside of a non-realist interpretation of QFT?
 
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PeterDonis
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Is Copenhagen then synonymous with "Shut up and calcualte"?
Not quite. As far as I can tell, Copenhagen as it is usually understood adds to "shut up and calculate" the belief that there is in fact (not just as a matter of doing calculations to make predictions) nothing more there: there is no deeper "underlying reality" beneath the QM model.
 
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PeterDonis
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Are there other non-realist interpretations, outside of a non-realist interpretation of QFT?
I'm not sure what you mean. QFT is a quantum theory and, as I said, has the same interpretations as QM in general.
 
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Is Brownian motion not attributable to a fundamentally deterministic process though? With the apparent randomness being due to a lack of information on our part, but the underlying particle collisions being, themselves, deterministic?
That's true for the physical Brownian motion, but not for the mathematical Brownian motion. The latter, as a model for the former, is fundamentally non-deterministic.
 
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Even if you might only be able to offer an explanation that would be over my head, it might give me a starting point to look into it further.
As a first step, look at Ref. [49] in the paper.
 
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That's true for the physical Brownian motion, but not for the mathematical Brownian motion. The latter, as a model for the former, is fundamentally non-deterministic.
Is the same true for the Nelson interpretation, you mentioned before, where it is the mathematical model that is non-deterministic while the physical system itself is deterministic?

Going on what @PeterDonis has said about the GRW interpretation, would it be fair to say that the GRW interpretation suggests both physical and mathematical non-determinism?
 
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As a first step, look at Ref. [49] in the paper.
Thanks, I've downloaded a copy of that and will check it out now.
 
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Is the same true for the Nelson interpretation, you mentioned before, where it is the mathematical model that is non-deterministic while the physical system itself is deterministic?
No. The Nelson interpretation assumes that stochasticity is fundamental.

Going on what @PeterDonis has said about the GRW interpretation, would it be fair to say that the GRW interpretation suggests both physical and mathematical non-determinism?
Yes.
 
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So how does the probabilistic math of Markov Chain differ from the probabilistic math of partial differential equations in Quantum Mechanics?

The descriptions look very similar yet all partial differential equations are deterministic. What is the fundamental difference between the two?

https://en.m.wikipedia.org/wiki/Markov_chain
 
  • #89
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Some posts that added no value to the discussion have been deleted. Thread reopened.
 
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  • #90
Lynch101
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As a first step, look at Ref. [49] in the paper.
Thanks for the direction on this Demystifier. Firstly, apologies if the questions that follow are of the sort that you don't even know where to begin to try and explain. I have been in discussions before where someone poses a question that just doesn't seem to make sense and you can be left scratching your head as to how to even begin addressing it. So, no offence taken if this post falls into that category.

I read the paper but didn't understand most of it. I've started studying some maths again, so far refreshing what I've learned in high-school, so it'll be a long time before I can understand the maths in the paper. Is it possible to get a very rough, general idea of what the paper says, do you think, without the mathematics? In my mind I'm trying to get a rough understanding of the consequences of what the paper says, as opposed to being able to determine the accuracy of what is being said, if that makes sense?

In truth, I probably didn't understand too much after the introduction even (or possibly even in the introduction).
To allow for gravitational Lorentz violation without abandoning the framework of general relativity (GR), the background tensor field(s) breaking the symmetry must be dynamical. Einsteinæther theory is of this type. In addition to the spacetime metric tensor field gab it involves a dynamical, unit timelike vector field u a .
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I have a very limited understanding of fields, but I tend to think of them as analogous to a sheet of some sort stretched out through space, with a vector field having some sort of directionality to it at a given location - perhaps another analogy here might be like a putting green, the kind you see in golf video games, where arrows show the direction the ball is likely to break.

My understanding of the above would be that there some form of fundamental, deeper lying field - the background tensor field - which might break Lorentz invariance, which appears to be a necessity for Bohmian mechanics.

To say that the Earth and everything else is made of Ether, I am picturing some sort of fundamental field which gives rise to all matter. My intuitive thinking would be that this would be a single universal field, but I think you suggested that this might not be the case.

A separate, but related question: under the Bohmian interpretation, is the Universe continuous?
 
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Is the same true for the Nelson interpretation, you mentioned before, where it is the mathematical model that is non-deterministic while the physical system itself is deterministic?
In general, every deterministic theory can be obtained from a more fundamental stochastic theory, and every stochastic theory from a more fundamental deterministic one.
 
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  • #92
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@Demystifier
Another question just occurred to me: is there a "measurement problem" with Bohmian Mechanics?
 
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