I Understanding Bohmian Mechanics of Instrumentalists

[user30]

E

As far as I know, mathematically they do it the same way standard QM does; their predictions don't differ from standard QM in that respect. But I have not spent a lot of time digging into the details. You would have to do that to figure out in detail how they arrive at predictions for things like correlations in Bell-type experiments.

As a matter of interpretation, I don't know that these models resolve the open issues. But deterministic models don't either.

The math isn't the question, it's the conceptual inconsistency.

It should also be noted

"The GRW theory differs from standard quantum mechanics for the dynamical principles according to which the wave function evolves[10][11]."

So perhaps not appropriate to discuss in this forum since it is not a main stream view.

 

[PeterDonis]

The math isn't the question, it's the conceptual inconsistency.

What conceptual inconsistency?

it is not a main stream view

There isn't really a "mainstream view" as far as QM interpretation is concerned. That's why we have this forum separate from the plain QM one, to allow for the fact that discussions of QM interpretations are different in that respect.

That said, the GRW model is not really a QM interpretation, it's an alternative theory, since it does make different predictions from standard QM in some respects (for example, it predicts that there should be limits on how long, even in principle, quantum coherence can be maintained in a system, whereas standard QM says there is no limit to that in principle, the only limits are practical). But AFAIK it does not make different predictions about things like EPR correlations and violations of the Bell inequalities.

 

[user30]

What conceptual inconsistency?
There isn't really a "mainstream view" as far as QM interpretation is concerned.

According to the quote there is. Quantum jumps are exclusively in stochastic models, and not part of the standard view, and is thus an obscure model of quantum mechanics that is yet to gain traction.

 

[PeterDonis]

Quantum jumps are exclusively in stochastic models, and not part of the standard view

I get that, but I don't get how it's a conceptual inconsistency. The "standard view" is just the basic math of QM, which takes no position at all on whether the quantum state is "real" or whether the collapse that happens in the math when you make a measurement corresponds to a "real" process or not. So the "standard" view is consistent conceptually with a model like the GRW model.

It is true that the GRW model is not consistent with interpretations that do not treat the quantum state as "real", but that is a property of those particular interpretations of QM, not of QM itself.

 

[user30]

I get that, but I don't get how it's a conceptual inconsistency.

I was referring to quantum correlations only, since these indicate the very opposite of a stochastic world, and instead complete reliability and repeatability.

 

[PeterDonis]

I was referring to quantum correlations only, since these indicate the very opposite of a stochastic world

No, they don't. They just indicate that whatever stochastic processes might be involved have to be able to produce such correlations.

and instead complete reliability and repeatability.

Quantum correlations indicate no such thing, since the results of the experiments involved are not completely reliable and repeatable. The correlations can be repeatably observed, within experimental error, but the individual results of the individual measurements are not repeatable. If Alice and Bob are each measuring one of a pair of entangled photons, and their measurement angles differ by, say, 30 degrees, the individual measurement results, and whether they are the same or opposite, are not repeatable. Only the correlations shown in the statistics of a large number of repetitions are.

 

[Lynch101]

In the GRW model, yes, the "spontaneous localization process" is the model's version of collapse of the wave function. So in this model, the collapse is a real physical process.

Is it in anyway accurate to think that the wave function, in this case, represents a real physical thing, as in a field or a particle? I'm thinking of a particle or field spread out over some area but then spontaneously localising to a single location before it interacts with the measurement device.

 

[PeterDonis]

Is it in anyway accurate to think that the wave function, in this case, represents a real physical thing, as in a field or a particle?

In the GRW model, yes.

 

[Lynch101]

In the GRW model, yes.

Thanks Peter.

Would it then be fair to amend the previous statement and say: interpretations that are truly indeterminate/ stochastic AND not based in realism, would seem to require that the current state of the system be causally disconnected from its antecedent state. This would seem to necessitate the total absence of causality with events occurring without reference to a prior cause?

 

[PeterDonis]

interpretations that are truly indeterminate/ stochastic AND not based in realism

Are there any?

 

[Lynch101]

Are there any?

Not all interpretations are realist are they?

 

[user30]

Thanks Peter.

Would it then be fair to amend the previous statement and say: interpretations that are truly indeterminate/ stochastic AND not based in realism, would seem to require that the current state of the system be causally disconnected from its antecedent state. This would seem to necessitate the total absence of causality with events occurring without reference to a prior cause?

The Copenhagen interpretation does not think it's meaningful to speak of the antecedent stage since it does not have well defined properties. It simply bows out of the discussion. I suppose a good analogy would be your train of thought prior to wakening up. It's simply not relevant to define and speak of from the Copenhagen interpretations point of view.

 

[PeterDonis]

Not all interpretations are realist are they?

You said not realist and "truly indeterminate/stochastic". Are there any?

My point is that you should not be asking questions about hypothetical interpretations or general categories of interpretations that might or might not exist. You should be asking questions about specific interpretations that actually exist, and your questions should be based on what those actually existing interpretations actually say.

 

[Lynch101]

You said not realist and "truly indeterminate/stochastic". Are there any?

My point is that you should not be asking questions about hypothetical interpretations or general categories of interpretations that might or might not exist. You should be asking questions about specific interpretations that actually exist, and your questions should be based on what those actually existing interpretations actually say.

Ah, I see, my apologies.

It might have been better to ask if there are such non-realist interpretations and which one they are. Are you familiar with any such non-realist interpretations? I thought Copenhagen was an example of a non-realist interpretation, or at least a variation of it and I thought QFT could be interpreted as non-realist.

I know discussing the details of them would be off-topic in this thread. The general question about realist vs non-realist theories is, I would say, relevant to the discussion of Demystifier's paper, but probably at the boundaries. The details of non-realist interpretations might be too far in that direction though.

 

[Lynch101]

@Demystifier

Another idea that caught my attention in your paper was this statement:

What we propose here is that the Earth (and everything else) is made of ether. No experiment so far ruled out that possibility, so such a neo-Lorentzian ether theory is a viable possibility.

It certainly sounds like a very interesting suggestion. I'm not even sure what the right questions to ask are to delve into this further. In a very crude manner I would interpret this as there being a Universal field, of some sort, or that the Universe is a single [to use an even more crude term] "thing" or substance. Would you be able to offer any clarifications on how to think about this.

Apologies, this is a very brute force attempt to delve into this idea. I'm not even sure how to phrase the questions, I'm just hopeful that simply starting a discussion on it will lead somewhere. 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.

 

[PeterDonis]

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.

 

[Lynch101]

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?

 

[PeterDonis]

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.

 

[PeterDonis]

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.

 

[Demystifier]

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.

 

[Demystifier]

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.

 

[Lynch101]

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?

 

[Lynch101]

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.

 

[Demystifier]

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.

 

[user30]

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

 

[user30]

Here's someone asking the same question

https://physics.stackexchange.com/questions/74885/can-i-treat-a-quantum-process-as-a-markov-process

"The Schrodinger equation is deterministic, so the time evolution of its solutions would be a Markov process only in some trivial sense."

 

[PeterDonis]

The Schrodinger equation is deterministic

The math of QM is more than just the Schrodinger Equation.

https://www.physicsforums.com/insights/the-7-basic-rules-of-quantum-mechanics/

 

[Lynch101]

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 .

.
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?

 

[Elias1960]

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.

 

[Lynch101]

@Demystifier
Another question just occurred to me: is there a "measurement problem" with Bohmian Mechanics?