It's the ambiguity of the interpretation which realism can't stand - something has to be either real (1) or not (0). It can't cope with the idea that there are 'degrees of reality'. — Wayfarer

The ambiguity is expressed by the premises of special relativity as the relativity of simultaneity. If we consider that "reality" refers to what "is" the case, then the relativity of simultaneity defines the ambiguity of reality. In QM time and energy are canonically conjugated variables. However, due to the ambiguity of time expressed by special relativity, the positioning of time, within QM is not so straightforward. Apparently, von Neumann sought to place time as a quantum operator, with point particles existing in three dimensional space. At this time it had been impossible to establish consistency between relativistic principles and QM. But canonical positioning of particles (positioning within a given system) is conceptually different from spatial co-ordinates, due to that ambiguous nature of time, so this was problematic. Physicists now use 4d space-time fields, so that rather than attempting to resolve the ambiguity it is incorporated into the fields.

I don't understand them. I only know (from what's been said of them) that they add to the de Broglie–Bohm theory the one thing that it doesn't normally explain; particle creation and annihilation. If that is indeed what they do then they are non-local hidden variable theories that agree with the results of quantum mechanics up to at least quantum field theory. — Michael

I see. You don't have an argument, but you like playing buzzword bingo for points.

Here are some buzzwords:

Bell - local hidden variable theories do not agree with QM
Leggett - non-local hidden variable ...
Kochen-Specker - non-contextual hidden variable ...
Free Will Theorem - any hidden variable theory whatsoever ...
PBR - probabilistic distributions of any type of hidden variable theory ...

There is also a an experiment that had slipped my mind - the famous Before-Before experiment which refutes any Bohmian theory including relativistic versions.

Right. And how are you seeing any mathematics as amounting to any sort of ontological commitment whatsoever? — Terrapin Station

That's what it means to regard QM as an explanatory scientific theory. The alternatives are to either change the theory (e.g., dynamical collapse or Bohmian mechanics) or to abandon realism (Copenhagen, instrumentalism).

I see. You don't have an argument — tom

You didn't ask for an argument, and nor did I claim to have one. You asked for a hidden variable theory that agrees with the results of quantum mechanics. I provided what seems to be just that.

There is also a an experiment that had slipped my mind - the famous Before-Before experiment which refutes any Bohmian theory including relativistic versions.

The only mention of that I can find is by Antoine Suarez. I can't find any other sources that corroborate his findings, but I can find several that say that no experiment refutes Bohmian mechanics.

That's what it means to regard QM as an explanatory scientific theory. — Andrew M

I don't at all agree, and it wouldn't at all be agreed upon in the consensus of physicists, or scientists in general, that what it means to regard something an an explanatory scientific theory is to assign ontological commitments to mathematical models. Mathematical models on their own, sans ontological commitments, are taken to be sufficient for explanatory scientific theories.

This is essentially taking an instrumentalist approach to mathematical models, but it's neither an alternative nor a rejection of realism--it's rather noncommittal on the question because it's avoiding any ontological commitments.

Reading the Schrodinger equation as implying real, parallel worlds, rather than simply being a mathematical model that allows accurate predictions, is making ad hoc assumptions that are not implied by the mathematical model.

Mathematical models on their own, sans ontological commitments, are taken to be sufficient for explanatory scientific theories. — Terrapin Station

Every mathematical model is a diagrammatic representation of an ideal state of things. As such, any ontological commitments are manifested in the mapping of the model - as well as the accompanying rules for its analytical transformation - to something in experience. The model itself embodies only the relations that the one doing the modeling has judged to be significant, and ignores everything else. The analysis of it is intended to simulate contingent events with necessary reasoning, so its "accuracy" is limited by that of the underlying assumptions.

Every mathematical model is a diagrammatic representation of an ideal state of things. — aletheist

First I want to make sure that I'm clear on what you're claiming in this sentence and why you're claiming it. What is the source for that being what mathematical models are?

What is the source for that being what mathematical models are? — Terrapin Station

As you might have guessed, it is something that I picked up from Peirce. He favorably cited his father Benjamin's definition of mathematics as "the science that reasons necessarily," and added that necessary reasoning only strictly applies to ideal states of things. A diagram is an icon that embodies the significant relations among the parts of its object; both geometrical figures and algebraic equations qualify.

As you might have guessed, it is something that I picked up from Peirce. — aletheist

Haha--okay.

Saying that all mathematical models would be examples of necessary reasoning seems dubious to me.

Saying that all mathematical models would be examples of necessary reasoning seems dubious to me. — Terrapin Station

To clarify--constructing the model requires creativity and imagination (retroduction), but processing the model is entirely a matter of necessary reasoning (deduction). Once the model is created, the results are inevitable, given the transformation rules that govern the analysis.

Wait, why are we saying that models involve transformation rules and analysis?

For example, let's pick something simple. Say F=ma as a mathematical model of force.

F=ma is a diagrammatic representation that embodies the relations among force, mass, and acceleration--all of which are concepts that we have defined in order to facilitate this mapping of an idealized state of things to something in experience. The transformation rules are such that we can rewrite the equation as a=F/m or m=F/a. Analysis in this case is merely a matter of finding the third value when we only know two of them initially.

F=ma is a diagrammatic representation that embodies the relations among force, mass, and acceleration--all of which are concepts that we have defined in order to facilitate this mapping of an idealized state of things to something in experience. — aletheist

any ontological commitments are manifested in the mapping of the model — aletheist

The problem I see with this is that we're not mapping F=ma to F equaling m times a in experience, because there is no mathematical equality or multiplication in experience--mathematics isn't an empirical science.

The problem I see with this is that we're not mapping F=ma to F equaling m times a in experience ... — Terrapin Station

We are mapping F=ma to the real relations that we observe in experience among force, mass, and acceleration.

... mathematics isn't an empirical science. — Terrapin Station

This is true, in the sense that mathematics only pertains to ideal states of things. It is false, in the sense that mathematics is an observational science; we manipulate diagrams in accordance with transformation rules and observe what other relations become apparent that were not part of the diagram's original construction.

I don't buy that we can observe a multiplicative relation or that mathematics is observational.

You deny that we can observe (through experimentation) that force is directly proportional to both mass and acceleration? How else have we ascertained that the equation is an accurate representation of reality?

As for mathematics being observational, I suggest looking into what Peirce called theorematic (as opposed to corollarial) reasoning.

Mathematical models on their own, sans ontological commitments, are taken to be sufficient for explanatory scientific theories. — Terrapin Station

If a scientific theory, per instrumentalism, makes no ontological commitments (i.e., is neither true nor false), then neither can it be offering an explanation. In Duhem's words, "A physical theory is not an explanation; it is a system of mathematical propositions whose aim is to represent as simply, as completely, and as exactly as possible a whole group of experimental laws."

This is essentially taking an instrumentalist approach to mathematical models, but it's neither an alternative nor a rejection of realism--it's rather noncommittal on the question because it's avoiding any ontological commitments. — Terrapin Station

OK, but...

Reading the Schrodinger equation as implying real, parallel worlds, rather than simply being a mathematical model that allows accurate predictions, is making ad hoc assumptions that are not implied by the mathematical model. — Terrapin Station

This is akin to saying that the heliocentric model makes accurate predictions but it's an ad hoc assumption to suppose the model implies that the earth orbits the sun.

What you're calling an ad hoc assumption just is the implication of the model, whether or not you choose to be agnostic or instrumentalist about it.

I don't buy that we can observe a multiplicative relation or that mathematics is observational. — Terrapin Station

Multiplication is a scaling transformation. An example of observing this is when we see a car moving towards us from 200 meters to 100 meters away and consequently appears twice the size.

I'm an anti-realist on mathematics. I don't believe that any mathematics is an accurate representation of reality, because I don't believe there is anything like mathematics in reality. ("Real" here is referring to the extramental or objective world.) Mathematics is rather just a way that we conceptualize relations on an abstract level.

If a scientific theory, per instrumentalism, makes no ontological commitments (i.e., is neither true nor false), then neither can it be offering an explanation. — Andrew M

It's just a matter of what people consider an explanation or not. And a large percentage of relevant academics consider mathematical equations read instrumentally to be explanations.

You didn't ask for an argument, and nor did I claim to have one. You asked for a hidden variable theory that agrees with the results of quantum mechanics. I provided what seems to be just that. — Michael

All is not what it seems!

The only mention of that I can find is by Antoine Suarez. I can't find any other sources that corroborate his findings, but I can find several that say that no experiment refutes Bohmian mechanics. — Michael

Nicolas Gisin performed the remarkable experiment, and yes Bohmians are full of claims, but none has ever made any progress in quantum mechanics - unlike the Everettians who can claim several remarkable discoveries. The lack of progress by Bohmians is discussed in this otherwise positive paper by Gisin:

https://arxiv.org/abs/1509.00767

But science (unlike philosophy it seems) does in fact progress, and a recent experiment involving entangled histories falsifies Bohm and supports Everett. It was the idea of Nobel prize winning physicist Frank Wilczek. This is a very easy to follow article with some explanation:

https://www.quantamagazine.org/20160428-entanglement-made-simple/

This is akin to saying that the heliocentric model makes accurate predictions but it's an ad hoc assumption to suppose the model implies that the earth orbits the sun. — Andrew M

This is a good example, the model follows from the success of prediction. So let's say that the successful predictions lead to a Many Worlds model. Now, it's when the model which is necessitated by the successful math, does not make sense, as is the case with MW, that we have to turn back to the principles whereby the mathematics is applied, to see where the mistakes are.

The geocentric model followed from very successful mathematics and predictions. Yes the mathematics was more primitive at that time, but the predictions were very successful. However, the model did not make sense. There were too many issues which could not be worked out to complete the model. The model was missing many aspects necessary to be complete and coherent, as is the case with MW. So we have to go back to the principles which underlie the application of the mathematics to determine why the very successful mathematics produces an unacceptable model.

I'm an anti-realist on mathematics. — Terrapin Station

Yes, that is what I would have guessed. Just curious, then - how do you explain the element of surprise, the fact that there are genuine discoveries in mathematics?

So we have to go back to the principles which underlie the application of the mathematics to determine why the very successful mathematics produces an unacceptable model. — Metaphysician Undercover

Right, it is a matter of how we are mapping the (ideal) diagram to the (actual) universe - both in formulating the model, along with its accompanying transformation rules, and in interpreting the results. In other words, like so much of philosophy, it comes down to our assumptions.

Tom especially, and even Andrew M to a somewhat lessor degree just don't seem to get this.

Yes, that is what I would have guessed. Just curious, then - how do you explain the element of surprise, the fact that there are genuine discoveries in mathematics? — aletheist

That's simply playing a game of sorts per rules that one has set up beforehand. The rules are complex enough (and vary enough per different sorts of starting assumptions--for example, Euclidean vs Riemannian geometry)) that future constructions can be unpredictable, one can come to realizations about present constructions that weren't apparent at first, etc.

... future constructions can be unpredictable, one can come to realizations about present constructions that weren't apparent at first, etc." — Terrapin Station

Right, and my point was that this happens because mathematics is observational - manipulating and then reexamining a diagram can reveal new information. The difference, of course, is that we are observing our own (ideal) constructions, rather than something "out there" in the (actual) universe.

Ah--well, I wouldn't use "observational" in that way, since it's rather a construction, but if you use "observational" so that it would fit that, then okay.

It's just a matter of what people consider an explanation or not. And a large percentage of relevant academics consider mathematical equations read instrumentally to be explanations. — Terrapin Station

It's like the scientific method never happened!

No instrumentalists regard equations as explanations. That is the entire point of their philosophy; the purpose of a theory is to predict the outcome of experiments. Instrumentalists build the LHC for no other reason than they want to predict what the LHC does. The experiments, and more importantly the theories, tell us nothing about the Reality.

The scientific method is fundamentally based on the conception of theories as explanation - statements about what exists in reality, how it behaves, and why. This conception is necessary for a coherent epistemology.

As every instrumentalist knows, there are an infinite number of "theories" i.e. non-explanatory mathematical equations that agree with observations. This is a feature of the underdetermination of the laws of physics.

By contrast, good explanations are extremely difficult to come by!

Right, and my point was that this happens because mathematics is observational - manipulating and then reexamining a diagram can reveal new information. The difference, of course, is that we are observing our own (ideal) constructions, rather than something "out there" in the (actual) universe. — aletheist

Based on your ideas, how do you explain the discovery of quantum entanglement?