Thanks for the quote Agustino. Perhaps you should provide a reference just to make the context a little clearer.

You can go a little deeper and ask if the wavefunction is real and if so does that commit us to platonism.

Perhaps you should provide a reference just to make the context a little clearer. — Metaphysician Undercover

Reference to what do you mean?

You can go a little deeper and ask if the wavefunction is real and if so does that commit us to platonism. — Question

http://www.iep.utm.edu/wittmath/

Platonism (N)

Thus, are we fooled about reality when we take our models to be more real than reality itself by ascribing ontological/physical significance to their results? To what extent is Heisenberg's uncertainty principle anything more than simply the limitation of our capacity to model reality? — Agustino

It was Einstein's view that reality is more determinate than the knowledge limitation imposed by Heisenberg's uncertainty principle suggest it to be. It was the point of the famous Einstein, Podolsky, Rosen paper ("EPR") to argue for this. But experimental tests of the hypothesis of a more determinate underlying reality have put Einstein's hope for the vindication of "local realism", and the merely epistemic intepretation of Heisenberg's inequalities, under severe stress. It now rather seems like the uncertainty principle really is a true indetermination principle, as proponents of the Copenhagen interpretation had always argued. My favorite discussion of the EPR entanglement, and of non-locality and quantum measurement in general, figures in Michel Bitbol's paper Reflective Metaphysics: Understanding Quantum Mechanics from a Kantian Standpoint (Scroll down just a few pages or search on the linked page for "bitbol").

It was Einstein's view that reality is more determinate than the knowledge limitation imposed by Heisenberg's uncertainty principle suggest it to be — Pierre-Normand

HUP is not an epistemological artifact, it is a feature of reality. The relativistic version is the Bekenstein Bound.

But experimental tests of the hypothesis of a more determinate underlying reality have put Einstein's hope for the vindication of "local realism", and the merely epistemic intepretation of Heisenberg's inequalities, under severe stress. — Pierre-Normand

The only existing explanatory interpretation of QM is local realist. Einstein was correct. Epistemic interpretations such as Copenhagen are unfalsifiable, so will have a (diminishing) number of apologists for the foreseeable future.

It now rather seems like the uncertainty principle really is a true indetermination principle, as proponents of the Copenhagen interpretation had always argued. — Pierre-Normand

But according to Copenhagen, the indetermination is purely epistemic. According to Unitary theories, the HUP is a consequence of the ontology they invoke.

In my opinion this is a more widespread problem with the sciences in general, not just qm. It's rampant throughout physics, including fields like astrophysics.

But according to Copenhagen, the indetermination is purely epistemic. — tom

Is there any determination at all anywhere outside the epistemic realm?

In my opinion this is a more widespread problem with the sciences in general, not just qm. It's rampant throughout physics, including fields like astrophysics. — Terrapin Station

It's a TOY problem, which is completely UNPHYSICAL concocted for PEDAGOGICAL reasons.

There is no such thing as a 1-D particle on an infinite flat potential.

The problem is so UNPHYSICAL that the solution to Schrödinger's equation under these imaginary conditions is not NORMILIZABLE. It is an axiom of QM that the wavefunction is NORMALIZABLE!

By the way, what is the SPECTRUM of the values of k?

I tend to unfortunately agree. I really feel like all this science and mathematics is mumbo jumbo to be entirely honest. Useful mumbo jumbo, don't get me wrong, but definitely mumbo jumbo in that it pretends to be a lot more than it really is...

Is there any determination at all anywhere outside the epistemic realm? — John

All known physical laws, interpreted realistically are fully deterministic. Don't panic, there are subtleties.

Your reply has nothing at all to do with the question.The question has nothing to do with anything anyone might find panic-worthy, either, as far as I can see. Perhaps try saying something more relevant next time; that's the best way, if you genuinely want to engage in an actual conversation.

Your reply has nothing at all to do with the question.The question has nothing to do with anything anyone might find panic-worthy, either, as far as I can see. Perhaps try saying something more relevant next time; that's the best way, if you genuinely want to engage in an actual conversation. — John

The laws of physics are fully deterministic. Given the state at any time, the future can be retrodicted and the past can be predicted.

For my own personal interest, could you elaborate on the part about astrophysics? I ask because I ultimately agree (regarding other areas of science and mathematics), but astrophysics is a subject I've never looked into so I've not seen any occurrences of this myself. I'd just be interested to know.

Reference to what do you mean? — Agustino

You started your thread with a quote from me. Don't you think you should provide a reference as to where the quote was taken from? Otherwise it is a quote taken out of context.

Given the state at any time, the future can be retrodicted and the past can be predicted. — tom

I think you got that backwards. Laplace's demon? Not so, whichever way you want to read it. In any case, how has that anything to do with whether determination extends beyond the epistemic realm?

I think you got that backwards. Laplace's demon? Not so, whichever way you want to read it. In any case, how has that anything to do with whether determination extends beyond the epistemic realm? — John

The laws of physics are completely deterministic.

Do the laws of physics extend beyond the epistemic realm; beyond, that is, what is known? I made no assertion about whether the laws of physics are deterministic in any ontological sense, anyway. You seem to be projecting your own hobby horse onto what others are saying. The question is whether what we can determined extends beyond the epistemic; can we determine anything beyond what is known, that is? Are you saying that what we can determine, or the fact that we can determine it carries certain ontological entailments? If so, what are they and on the basis of what would you say that?

The apparent equivocatiion occurs because, at some level, the maths say something about physics we observe. I mean potential energy equations aren't a state of the world either. But can we say an engineer measurements really have nothing to do with the world because it's only a mathematical model? Are we only pretending the house won't fall down when we follow the engineers plans?

I don't think so. Mathematical models do have a significant beyond a play of numbers in our head
That's why the maths of physics aren't just counting. A limitation on what we can model in physics specifies a limitation of the world-- the world cannot express a model outside of it.

In the case of HUP, that we cannot use just a model in our head to tell what happens. We always need track the world too. Our ontology is such that it cannot be just a model, in any instance.

Epistemic interpretations such as Copenhagen are unfalsifiable, — tom

'The Copenhagen Interpretation' is not a scientific hypothesis, and accordingly was never conceived as something to which the criterion of 'falsifiability' applies. So to criticize it on the grounds of it being something that it never set out to be, surely indicates a misunderstanding of it.

The criterion of 'falsifiability' was advocated by Karl Popper as the basis of distinguishing scientific theories from philosophical ideas. 'The Copenhagen Interpretation' is not a scientific theory, it simply refers to the kinds of things that Bohr, Heisenberg, Pauli, and others, said could be inferred on the basis of quantum mechanics.

Among which was that such statements as these:

The laws of physics are fully deterministic — tom

could not be supported on the basis of the observations.

But I know from experience that Tom will say that this statement is validated by Everett's 'Relative State Formulation', so to save time, let's just get that out in the open.

To what extent is Heisenberg's uncertainty principle anything more than simply the limitation of our capacity to model reality? — Agustino

I wouldn't put it that way, because the inaccuracy predicted by the HUP is much smaller than our ability to perceive. So HUP does not impinge on our reality.

The problem which I think Agustino is alluding to in the op is the intrinsic uncertainty in the way that we measure time. There appears to be an uncertainty inherent within the measurement of any time period. This is related to, and perhaps analogous to Einstein's principle call the relativity of simultaneity. Because simultaneity is reference dependent, we can say that there is a degree of uncertainty with respect to any determinations of simultaneity. Likewise there is a degree of uncertainty with respect to any determinations of a length of time.

Let's assume an arbitrary duration of time, and assign to it the mathematical value of 1. It is 1 unit of time duration. Due to the uncertainty which is inherent within our ability to determine a measurement of time, we should assign a margin of error to 1. We can assign the arbitrary margin of error of + or - 1%. Now our period of time which is assigned the mathematical value of 1, is really somewhere between .99 and 1.01, or we could assume that it is all the values in between. When we're talking about time then, 1 does not actually equal 1. The mathematics is inherently uncertain.

I believe that what the Fourier transform indicates, is that as we move toward a larger and larger duration of time, this uncertainty, when expressed as a margin of error like this, becomes a smaller and smaller percentage of the overall length of the time period, moving toward a smaller and smaller margin of error. Conversely, as we move toward a smaller and smaller period of time, the margin of error, becomes larger and larger.

You started your thread with a quote from me. Don't you think you should provide a reference as to where the quote was taken from? Otherwise it is a quote taken out of context. — Metaphysician Undercover

:s I did provide a reference, what are you talking about? If someone clicks your name in my quote, they'll be taken to the post where the quote is from - to the context...

I wouldn't put it that way, because the inaccuracy predicted by the HUP is much smaller than our ability to perceive. So HUP does not impinge on our reality. — andrewk

So, you mean, all of the huge debates about the philosophical implications of the uncertainty principle have been misconstrued?

Mathematics constrains our conceptualisation of physics, and hence constrains even our capacity of measurement - we cannot measure that which we cannot conceive. But it is somewhat foolish I think to, without argument, ascribe the constraints established by mathematics to be the constraints of reality. That would need additional argument. To assume mathematical Platonism begs the question.

I wouldn't put it that way, because the inaccuracy predicted by the HUP is much smaller than our ability to perceive. So HUP does not impinge on our reality. — andrewk

Well, the HUP has been experimentally confirmed, so that means we can perceive its predictions, albeit indirectly - but isn't that the case with any model prediction? You could further argue that, the HUP being an integral part of quantum physics, and quantum physics being a very accurate theory, then if the HUP was quite wrong, the world would probably have been very different. So different indeed that we wouldn't be around to make that observation.

Which brings me to the OP question. What do people mean when they say things like "the math is not the world," "the map is not the territory," etc.? In one trivial sense this is, of course, true and undisputed: a theory, a model, is just a concept that we hold in our minds, it is not that which the concept is supposed to describe.

Is the statement merely impugning the accuracy of the model or its justification? That would stake out a scientific position. Needless to say, whoever makes this statement had better know the subject really well and be prepared to marshal scientific arguments and data in support of their position - otherwise there is no reason to take them seriously.

Is the statement saying that the whole of world probably isn't perfectly accountable by any of the existing models? That would be a defensible philosophical and even scientific position, but it is a very general statement, while the original sounds like a much more specific indictment.

If not any of the above, then what?

Well, the HUP has been experimentally confirmed — SophistiCat

We need to be careful here. I think it's safer to say that experimental evidence is consistent with what we would expect if the HUP holds. Maybe I'm getting too Popperian about this, but I wouldn't call that confirmation.

However, the 'reality' to which I refer, because I think that's what the OP had in mind, is the 'reality' of chairs and tables, dogs and cats - ie that which can be perceived without the aid of scientific instruments. I would class a reading from an instrument, of the kind that occurs in tests of the HUP, as part of the whole scientific edifice that the OP is considering. If we think of 'theory' as being on one side of the fence and 'reality' on the other, then it seems to me that a reading from the instrument is on the same side of the fence as the HUP - and distinct from 'reality'.

Certainly QM does affect reality - as the fact that we are using computers attests. But that is about macro impacts of QM. I'll go out on a limb and guess that any measurements that are fine enough to test the HUP will not be about macro impacts.

I haven't expressed this very well but it's late and I'm tired so sorry that's the best I have right now.

So, you mean, all of the huge debates about the philosophical implications of the uncertainty principle have been misconstrued? — Wayfarer

I would say those debates are about ontology and ontology is not about reality.

My apologies Agustino, I didn't realize that.

The problem is that physical theories, as they are mathematical in nature, are underdetermined. For any finite set of facts - where a fact takes a mathematical form of correspondence between two or more variables - a fact is simply a coordinate point in a space with as many dimensions as there are variables - there can be an infinite number of mathematical models (ie formulas) which describe the set of facts. For example, if I have the following set of facts in a two dimensional space, corresponding to two variables:

{ (0;3),
(2;4),
(3;1),
(1.5; 3),
(23; 20) }

I will have an infinite number of relationships that can account for the underlying structure of the two variables which have generated these facts. How does modelling them - creating one formula to account for them - even if I model them such that even the next observation seems to corroborate (for even then, I will reduce a larger infinity of possible models, to a smaller infinity of possible models) - how does this modelling tell me anything about how the world really is like - ie about ontology? At any point in time there are an infinity of models that will account for all the observations I currently have made, and all the observations that I will ever make in a given finite time.

Therefore at no point am I justified to prioritise one of those models from the infinity of possible models - and therefore at no point am I justified to attribute ontological significance to my model. For example the curvature of space-time - the curvature of space-time is NOTHING - it is an abstract mathematical object, not an ontological object. We chose to conceptualise it, and visualise it as the curvature of spacetime, but we could have chosen a million other ways. Atoms themselves are nothing - merely mathematical objects, because all their properties are mathematical. Therefore physics IS mathematics, and physics will never be able to tell us something that mathematics cannot tell us. The objects of physics aren't the tables and the chairs we see and interact with everyday - they are abstract mathematical objects - they are illusions, from an ontological point of view.