QM: confusing mathematics with ontology?
Quoting Metaphysician Undercover
http://www.ams.org/samplings/feature-column/fcarc-uncertainty
A lot of what physicists take to be true - including Heisenberg's uncertainty principle - emerge out of the mathematics that are used to model physical phenomena. We notice from the above that the uncertainty principle is nothing but a mere mathematical property because we see that it inheres within the mathematics, devoid of any physics at all. 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?
This problem manifests in the Fourier transform, and is well known as the uncertainty principle.
http://www.ams.org/samplings/feature-column/fcarc-uncertainty
A lot of what physicists take to be true - including Heisenberg's uncertainty principle - emerge out of the mathematics that are used to model physical phenomena. We notice from the above that the uncertainty principle is nothing but a mere mathematical property because we see that it inheres within the mathematics, devoid of any physics at all. 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?
Comments (35)
Reference to what do you mean?
http://www.iep.utm.edu/wittmath/
Platonism (N)
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").
HUP is not an epistemological artifact, it is a feature of reality. The relativistic version is the Bekenstein Bound.
Quoting 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.
Quoting 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.
Is there any determination at all anywhere outside the epistemic realm?
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?
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.
The laws of physics are fully deterministic. Given the state at any time, the future can be retrodicted and the past can be predicted.
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.
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?
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.
'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:
Quoting 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.
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.
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.
: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...
So, you mean, all of the huge debates about the philosophical implications of the uncertainty principle have been misconstrued?
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?
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.
I would say those debates are about ontology and ontology is not about reality.
{ (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.
Ok, no problem :)
The issue here I think, is that mathematics must be applied, in order that it may tell us anything about the world. This means that things in the world must be evaluated, assigned a mathematical value. If there is a margin of error, when we assign the mathematical value, such as that indicated in my earlier post, then the precision of understanding which we normally associate with mathematics is lost.
So for example, if we have a unit of time, a period of temporal duration, which we assign "1" to, such that it is one length of time, and there is a margin of error, then "1" in this situation is not really equal to "1". In this situation "1" is equal to every value within the range of that margin of error.
The stability of atoms has rather significant "macro-impacts". And you can demonstrate HUP at home with a laser pointer and some aluminium foil.
And despite this, we aren't exactly overwhelmed by competing scientific theories are we? It is trivial to write down endless ad-hoc modifications to our best theories, which will be empirically indistinguishable from the original. Why does no one do that?
Well, there are several reasons no one ad-hoc modifies theories, the most significant being that scientific theories are not models and they are not equations.
Then what are they if they are neither models nor equations? :s