Living Opponents of the Copenhagen Interpretation

[Fredrik]

we have multiple interpretations of Ballentine! I have never read Ballentine as opposing the wave function as "physically real" until this thread where that interpretation of Ballentine is mentioned by bhobba, kith and you. I have always read Ballentine as opposing a Copenhagen-style interpretation which one can also call instrumental/operational/orthodox/textbook/shut-up-and-calculate,

Then my interpretation of Ballentine is exactly the opposite of yours. He's supporting a Copenhagen-style interpretation which one can also call instrumental/operational/orthodox/textbook/shut-up-and-calculate. (I'm not sure that "orthodox" is right. I'd have to look up how that's defined). He's rejecting the view that a pure state "provides a complete and exhaustive description of an individual system". That's an exact quote from the description of the class of interpretations that he rejects. It's at the start of section 9.3 if you want to check.

I would define an "interpretation of QM" as a speculative statement about what really going on at all times, including at times between state preparation and measurement. Ballentine offers no interpretation of QM in this sense. He just describes a way to think about pure states that's appropriate if you don't subscribe to any particular interpretation of QM. This gives us an interpretation of pure states that's guaranteed to be appropriate, regardless of what else a pure state may represent.

The comment that assuming proper and improper mixtures to be equivalent is as good as assuming state reduction is found in section 2.5.4 "Decoherence Models versus the Copenhagen Interpretation" in Haroche and Raimond's https://www.amazon.com/dp/0198509146/?tag=pfamazon01-20.

Thanks. I haven't decided if I will check it out yet. The suggestion that there could be a difference between "proper" and "improper" is utterly bizarre to me. Hm, maybe saying that there's a difference is the same as saying that a pure state "provides a complete and exhaustive description of an individual system". A person who says that may want to resort to using he magical kind of collapse to not have to deal with many worlds. I should probably at least skim it to see what it's about, but I have to go to bed now. Maybe tomorrow.

 

[atyy]

You were talking specifically about a physical state reduction process and not about the general interaction between the measurement apparatus and the system. The problem with this view is that if you shift the boundary, you won't find the state reduction in the quantum dynamics. So you have to postulate that the boundary cannot be shifted and that the quantum regime ends somewhere. This is very strange because the statistical predictions of QM remain valid beyond this barrier.

Actually, I was asking two different questions, one about the interpretation of quantum mechanics and the concept of "really physical", and the other about the interpretation of Ballentine and language like "FAPP physical". Anyway, yes, let's stick for the moment to "really physical" in the context of state reduction. The idea I'm interested in understanding is whether one can say that state reduction is only updating our knowledge and does not correspond to anything physical. I do like the approach that state reduction is only updating our knowledge, that it is like throwing a die, and having the probability distribution collapse when you get a definite outcome. However, can this be justified beyond an analogy? To my knowledge, no one has done it yet. Some attempts to draw a close analogy to Bayesian updating indicate that the analogy is not complete (eg. http://arxiv.org/abs/quant-ph/0106133, http://arxiv.org/abs/1107.5849, and the Wiseman and Milburn book). For this reason, I don't rule out that state reduction may also be partly physical, in contrast to only updating our knowledge). So I am interested if you have an argument that makes the Bayesian analogy closer.

In the argument you give, it seems that you are more willing to consider unitary evolution as more physical than state reduction, so by "quantum dynamics" so mean unitary evolution. However, within Copenhagen, I don't know if unitary evolution is privileged, and in principle both unitary evolution and state reduction are quantum dynamics. Both are equally not necessarily real, and just tools to calculate probabilities of measurement outcomes.

 

[atyy]

Then my interpretation of Ballentine is exactly the opposite of yours. He's supporting a Copenhagen-style interpretation which one can also call instrumental/operational/orthodox/textbook/shut-up-and-calculate. (I'm not sure that "orthodox" is right. I'd have to look up how that's defined). He's rejecting the view that a pure state "provides a complete and exhaustive description of an individual system". That's an exact quote from the description of the class of interpretations that he rejects. It's at the start of section 9.3 if you want to check.

Well, our interpretations of Ballentine are not exactly opposite. I do think the view Ballentine is proposing is a Copenhagen-style view. Our difference lies in what we think he is opposing. Possibly because I did also know the 1970 review, and treated the book as an updated version of the review, I understood the view he is opposing to be Copenhagen. Even if the book does not mention Copenhagen, it seemed to be the same view he opposed in the review, and he still makes it seem like the view is a mainstream view with state reduction. So I read the book entirely within Copenhagen, as a debate between two flavours of Copenhagen, and the claim the Ballentine's flavour (Copenhagen B) was better than the flavour he opposed (Copenhagen A). Within Copenhagen A, I understood "a pure state provides a complete and exhaustive description of an individual system" to mean that one can think of a pure state as the state of an individual system, and it is complete and exhaustive within the theory (a choice of measurement apparatus and quantum system, operators and commutation relations, and Hilbert space) because a pure state is an extreme point of the space of density operators. On my initial reading, my puzzlement was that his Copenhagen B alternative "A pure state describes the statistical properties of an ensemble of similarly prepared systems." was not at all different from Copenhagen A, since in Copenhagen A one adds that the theory only predicts expectation values. I had always used both Copenhagen A and Copenhagen B interchangeably before reading Ballentine. To make sense of his claim, since he does attack state reduction in what I understood to be Copenhagen A, I thought he was claiming that state reduction was not required in Copenhagen B, and that if one used Copenhagen B, state reduction can be derived from unitary evolution without the introduction of any additional postulate.

However, I don't think what I understood to be his claim is true. I do think that Copenhagen A in which a pure state is thought to label an individual system, and in which there is state reduction, is a valid version of quantum mechanics. I do not think that Copenhagen B manages to derive state reduction from unitary evolution without any additional postulate. So I believe his claim of the superiority of Copenhagen B over Copenhagen A to be untrue. I also think that since his derivation of state reduction from unitary evolution fails, that his Copenhagen B is in fact lacking a postulate of Copenhagen-style quantum mechanics, and is therefore incomplete, and therefore wrong. I do believe there are valid approaches to QM without state reduction (reviewed in Wiseman and Millburn's book), but these do not easily accommodate a common-sense reality (whereas Copenhagen does accommodate it on one side of the cut, which can be shifted). I do of course acknowledge that there can be theories that reproduce QM without state reduction such as Bohmian mechanics, and interesting approaches to QM interpretation such as MWI that don't have state reduction, but introduce many worlds. If he is rejecting common-sense reality, introducing hidden variables or many-worlds, I believe these are unusual enough that he has to explicitly state them in order for us to understand that that is what he is doing.

Of course, if the alternative he opposes is not Copenhagen A but some non-mainstream view like physical collapse of the wave function (whatever that means - I have never heard it within QM - to me that refers to GRW or CSL), then I could hardly object to it. But I think I have a good case for my reading! Maybe in the future, when hidden variables have been experimentally discovered, and the interpretation of QM settled, there will be vigourous debates over the various Schools of Ballentine Interpretation:)

 

[Fredrik]

Our difference lies in what we think he is opposing. Possibly because I did also know the 1970 review, and treated the book as an updated version of the review, I understood the view he is opposing to be Copenhagen. Even if the book does not mention Copenhagen, it seemed to be the same view he opposed in the review, and he still makes it seem like the view is a mainstream view with state reduction.

I've read the review too, but it was years ago, so I don't remember details like how he used the term "Copenhagen". I don't doubt that he would call the A view in the book "Copenhagen", when "collapse" is also included. This seems to be very common. I think it's how Copenhagen was explained to me in my first QM course. Ballentine doesn't say it explicitly, but the A view without collapse is a many-worlds interpretation. So I would say that he's rejecting a larger class of interpretations, not just a flavor of Copenhagen.

To me, the most remarkable detail in the review is that in the interpretation presented there, particles have well-defined positions at all times, even when their wavefunctions are spread out. At first I thought that this was completely insane and impossible. I eventually realized that one of the reasons I thought so was that I had not been able to completely let go of the idea that the wavefunction is the system.

Within Copenhagen A, I understood "a pure state provides a complete and exhaustive description of an individual system" to mean that one can think of a pure state as the state of an individual system, and it is complete and exhaustive within the theory (a choice of measurement apparatus and quantum system, operators and commutation relations, and Hilbert space) because a pure state is an extreme point of the space of density operators.

I think the intended meaning of "provides a complete and exhaustive description of an individual system" is completely impossible to define within the theory. The claim that a pure state "provides a complete and exhaustive description of an individual system" is supposed to tell us something new about pure states, something that the theory isn't telling us, but if we use the theory to define the statement so that it's implied by the theory, then the statement is not telling us anything. It's supposed to be an interpretation of QM, not something that QM says is true by definition.

My interpretation of the claim that a pure state "provides a complete and exhaustive description of an individual system" is that it says that the pure state (and time evolution) is telling us what is "actually happening" to the system at all times, including at times between state preparation and measurement. It's telling us that the pure state "describes" all the "properties" of the system.

In statements like these, terms like "actually happening", "describes" and "properties" are primitives, i.e. terms left undefined. I know that the suggestion that it's OK to leave something undefined sounds like complete nonsense to a lot of people, so I will elaborate a bit. Every definition of a term has the problem that it can only be understood by a person who understands the terms used in the definition. So every definition seems to just lead to another definition. To avoid an infinite chain of definitions, we have to leave some terms undefined. These undefined terms are called "primitives". The fact that we're leaving them undefined doesn't prevent us from explaining how to think about them. These explanations are called "elucidations".

his Copenhagen B alternative "A pure state describes the statistical properties of an ensemble of similarly prepared systems." was not at all different from Copenhagen A,
[...]
I had always used both Copenhagen A and Copenhagen B interchangeably before reading Ballentine.

This is understandable, since you seem to have interpreted "provides a complete and exhaustive description of an individual system" in a way that makes the statement (the defining assumption of the A class of interpretations) vacuously true. If we do this, then there's no difference between A and B. (The defining assumption of B is also true in A).

To make sense of his claim, since he does attack state reduction in what I understood to be Copenhagen A, I thought he was claiming that state reduction was not required in Copenhagen B, and that if one used Copenhagen B, state reduction can be derived from unitary evolution without the introduction of any additional postulate.

I think that state reduction has a very different meaning in A and B. In A, it's some kind of magical nonsense that eliminates the need to conclude that there are many worlds. In B, it's the idea that an interaction that leaves a macroscopic (and therefore FAPP classical) object in one of several easily distinguishable positions, will either destroy the system or leave it in a state that's FAPP indistinguishable from an eigenstate. (Or something like that...I haven't thought about this enough to find a favorite explanation of what state reduction is. Isham describes it as something even more mundane, as a selection of a sub-ensemble on which to make measurements).

I do think that Copenhagen A in which a pure state is thought to label an individual system, and in which there is state reduction, is a valid version of quantum mechanics.

I think it's probably not. If I find out that I'm wrong, I may feel a little silly about having used language like "magical nonsense" to describe aspects of this intepretation, but for now, I'll take my chances. :)

 

[kith]

In the argument you give, it seems that you are more willing to consider unitary evolution as more physical than state reduction, so by "quantum dynamics" so mean unitary evolution.

Yes, I think that the term quantum dynamics should be reserved for what the system does as long as we use a quantum description. State reduction refers to a situation where we let the system interact with something which is not included in the quantum description. So quantum dynamics and state reduction are not on equal footing.

If we shift the boundary, the quantum dynamics of the combined system gives predictions which can be checked experimentally. This quantum dynamics doesn't involve state reduction within the combined quantum system. So calling only the former "physical" seems pretty straightforward. Terms like "FAPP physical" and "really physical" make my head spin and I don't see how they help to clarify anything.

But this is starting to go in circles and be mostly about terminology. I already had a number of discussions about state reduction with you and although I learned quite a bit from them, I never had the impression that we got past terminology issues and to the core of the disagreement. I'm not sure if there is real disagreement (maybe this is an argument for Copenhagen ;)) but I don't see a way to simply jump past these terminology issues. And right now, I'm not interested in dissecting lots of terminology for a few grains of real issues.

 

[naima]

There are are physicists who defines QM physical processes as unitary processes
Read http://arxiv.org/pdf/1004.5073.pdf
"We know that any physical process can be thought of as a unitary process in an enlarged Hilbert space"

 

[atyy]

I think it's probably not. If I find out that I'm wrong, I may feel a little silly about having used language like "magical nonsense" to describe aspects of this intepretation, but for now, I'll take my chances. :)

I'm pretty sure that Copenhagen A as I understood it is valid quantum mechanics, because it is identical to Copenhagen B with state reduction. However, I do agree that state reduction in Copenhagen A is magical nonsense - but it doesn't matter, because Copenhagen A, being a variety of Copenhagen, does not believe the wave function is necessarily real, and it is just a tool to calculate the probabilities of measurement outcomes. So in Copenhagen A, the wave function, unitary evolution and state reduction are all magical nonsense. In short, Copenhagen A makes successful predictions that have not been falsified at present, but it does admit that it has a measurement problem.

 

[atyy]

But this is starting to go in circles and be mostly about terminology. I already had a number of discussions about state reduction with you and although I learned quite a bit from them, I never had the impression that we got past terminology issues and to the core of the disagreement. I'm not sure if there is real disagreement (maybe this is an argument for Copenhagen ;)) but I don't see a way to simply jump past these terminology issues.

Yes, the issue I'd like to discuss is tangential to most of what is in this thread (living opponents of Copenhagen!). I think there isn't a refined enough standard terminology within Copenhagen to discuss reality/physicality, so I will start another thread about it. Regarding our old discussions, I always thought they were about whether state reduction is needed or not. My answer is that it is needed within Copenhagen, and I always thought you were agreeing with Ballentine that it is not needed if one uses his Ensemble interpretation. But now that I realize your interpretation (#64) and my interpretation (#73) of Ballentine are quite different, I do wonder! My default approach to quantum mechanics is indeed to assume Copenhagen. ;)

 

[carllooper]

This is Bohr summarising his semi-classical position:

"The new progress in atomic physics was commented upon from various sides at the International Physical Congress held in September 1927, at Como in commemoration of Volta. In a lecture on that occasion, I advocated a point of view conveniently termed "complementarity," suited to embrace the characteristic features of individuality of quantum phenomena, and at the same time to clarify the peculiar aspects of the observational problem in this field of experience. For this purpose, it is decisive to recognise that, however far the phenomena transcend the scope of classical physical explanation, the account of all evidence must be expressed in classical terms. The argument is simply that by the word "experiment" we refer to a situation where we can tell others what we have done and what we have learned and that, therefore, the account of the experimental arrangement and of the results of the observations must be expressed in unambiguous language with suitable application of the terminology of classical physics."

I interpret this as Bohr looking for a way to ensure QM is, before anything else, understood as a valid contribution to the history of physics, as opposed to some other discipline. One can imagine a lot of classically trained physicists walking around the conference in a huff saying things like "what is all this rubbish". And Bohr is trying to win them over to QM. Not in any dishonest way of course - just in a way that can be understood (to the extent it can) within a given climate and a certain history.

I'd have used different words from "phenomena transcending the scope of classical physical explanation". I'd have put it the other way - that classical physical explanation transcends the phenomena. The phenomena inspires or requires the introduction of certain limitations on classical concepts, rather than suggesting anything that transcends such concepts.

The vexed question of "reality" is something quite difficult to elaborate in physics. Its a lot easier to address this in philosophy than it is physics. But as a result it can then become very difficult to map such back into physics. Only a very small subset of philosophy maps back into physics. And typically it will be (understandably) the most conservative aspects of philosophy that do so. I'd suggest physics ends up doing it's own philosophy. It knows what philosophy it needs to construct. It creates that which belongs to physics.

C

 

[bhobba]

One can imagine a lot of classically trained physicists walking around the conference in a huff saying things like "what is all this rubbish". And Bohr is trying to win them over to QM.

QM was a mishmash of ideas until Dirac came up with his transformation theory in December 1926 (although some mathematical issues with that damnable Dirac Delta function remained - later fixed by Von-Neumann - but fully resolved with the development of Rigged Hilbert Spaces):
http://www.lajpe.org/may08/09_Carlos_Madrid.pdf

And indeed Copenhagen was only just completed in 1927 with a number of separate theories each calling itself QM prior to that. It was only after Diracs great breakthrough Copenhagen could have been finalised. So it's highly doubtful Bohr would have been trying to win anyone over in 1927 since it had such a long gestation and most physicists would have been aware of the situation. They knew classical physics was wrong by that stage - no convincing was required. The convincing would have been for the final form of QM that was then just developed.

But once Dirac's final form of QM was published, and especially after his book, Principles Of Quantum Mechanics, was available in 1930, opposition to QM as a theory disappeared. Even Einstein always carried around a copy of Dirac, and he spoke admiringly of Dirac of whom he said 'in my opinion we owe the most logically perfect presentation of quantum mechanics.' As a theory it was then mainstream - with little or no opposition, even by Einstein. Einstein's view at that stage had morphed - the 1930 Solvay conference was his last attempt to find fault with it - he failed - and it was reported he tipped his hat to Bohr when Bohr used Einsteins own principle of equivalence to show Einstein's latest objection was flawed. His debates with Bohr and others now convinced him the theory was correct - but incomplete. It was that conviction that reached its full flower in EPR.

Also by that stage most physicists were not concerned with its foundations - indeed Dirac's book and Von-Neumann's equally influential text - Mathematical Foundations of Quantum Mechanics - published in 1932, were pretty much agnostic towards philosophical issues (caveat - there is the issue of the Von-Neumann regress and conciousness - but that is another story):
http://www.physicsandmore.net/resources/Shutupandcalculate.pdf
'Both the two books were completely indifferent toward philosophical issues raised by Bohr, Schrödinger, Einstein and others, and were brilliant trend-setters in a precise formulation of quantum theory in mathematical terms because the authors felt that there was no point in half measures where quantum theory was concerned, and the need for the day was a set of concrete rules for mathematical calculations. Between them, the two books set forth the basic principles that were so brilliantly being made use of by the likes of Pauli, Schrödinger and Dirac in waves after waves of remarkable papers that were setting the entire world of physics on fire. Ever since, quantum theory has time and again demonstrated the power of the decree: shut up and calculate. Of course, there were people who asked questions.For instance, Feynman asked questions, but mostly he asked those in silence and never rested till he himself provided the answers. John S. bell asked questions, and was not satisfied a bit with the received wisdom but he, too, calculated and gave the world the famous inequality bearing his name that, more than anything else, brought in the information theoretic revolution in quantum theory dating from the nineteen eighties.'

The prevailing mood, as alluded to by the quote above, was shut up and calculate - which is often attributed to Dirac, or maybe Feynman, but, as the article correctly points out, is by David Mermin.

That has been pretty much the case since then. Most physicists couldn't really care a hoot - a few do - but for most - blah.

Of course to philosophy types, and students starting out, it's often the most important thing. But students soon get used to it and what they thought were problems melt away as they apply it or think about it more carefully - that happened to me - but took a while. Still some physicists and mathematicians are fascinated with its foundations - but it's not really a big concern generally - amongst scientists that is.

Thanks
Bill

 

[carllooper]

So it's highly doubtful Bohr would have been trying to win anyone over since the situation was a bit of a mess.

To suggest it is doubtful that Bohr can't be doing this because QM does not yet include that which Dirac will later contribute makes no sense at all. QM is what it is in Sept 1927. A work in progress, with promising developments, and a reason for being.

And while Einstein might be tipping his hat to Bohr in 1930, that doesn't stop him thinking through the problem further and coming back in 1935 with a new line of attack in the form of EPR, and temporarily throwing Bohr off balance. Bohr recovers his wits when he realizes that since you can't communicate information over the FTL channel, such a channel isn't physical, ie. it's 'philosophical' (or science fiction as I like to call it).

C

 

[bhobba]

To suggest it is doubtful that Bohr can't be doing this because QM does not yet include that which Dirac will later contribute makes no sense at all. QM is what it is in Sept 1927. A work in progress, with promising developments, and a reason for being.

It was completed in December 1926 - your quote was from 1927 - it was completed then, but maybe it hadn't percolated through the physics community yet. My suspicion is that was more the concern than than Bohr's views on complementarity.

What I am suggesting is that once that was done, because everyone knew that classical physics was kaput, Bohr didn't need to convince anyone about QM. What he was on about was his philosophical view of it which by that stage people didn't care that much about since shut up and calculate was taking hold.

And while Einstein might be tipping his hat to Bohr in 1930, that doesn't stop him thinking through the problem further and coming back in 1935 with a new line of attack in the form of EPR, and temporarily throwing Bohr off balance. Bohr recovers his wits when he realizes that since you can't communicate information over the FTL channel, such a channel isn't physical, ie. it's 'philosophical' (or science fiction as I like to call it).

I thought that's what I said. He no longer thought it incorrect, which is a big turn around, he thought it incomplete, which was what EPR was about.

That wasn't how Bohr refuted Einstein:
http://philosophyfaculty.ucsd.edu/faculty/wuthrich/teaching/2013_146/146QLect04_BohrEinsteinEPR.pdf
“Indeed the finite interaction between object and measuring agencies conditioned by the very existence of the quantum of action entails—because of the impossibility of controlling the reaction of the object on the measuring instruments, if these are to serve their purpose—the necessity of a final
renunciation of the classical ideal of causality and a radical revision of our attitude towards the problem of physical reality. In fact, as we shall see, a criterion of reality like that proposed by the named authors contains—however cautious its formulation may appear—an essential ambiguity when it is applied to the actual problems with which we are here concerned.'

Its highly likely Einstein knew what Bohr would say. However, as he wryly noted, everyone's response seemed to be different.

That said, my post wasn't primarily about Einstein, it was about the shut up and calculate view that took hold after QM was completed by Dirac - most people weren't that worried about Bohr's philosophical musings. Although it must be said when pushed on the matter physicists would retreat to Bohr's orthodoxy.

Thanks
Bill

 

[jbmolineux]

Any philosophical principles that Einstein may have used may very well have played an important, if not key role in his contribution to physics. Indeed, personally, I'm sure of it. But how can we conclude that if we "get those principles wrong" science will go astray? Bohr was equally inspired by philosophical principles, but a somewhat different set of principles, yet was perfectly able to make a contribution to physics.

The way in which physics generally works is that ideas are put to a physical test. If there's agreement between the physical test and the ideas that conceive it, then the idea is considered provisionally correct. Or useful. In other words, the idea could be philosophically right or wrong, but in terms of the physics it points out, (to the extent that it does) it wouldn't actually matter. What matters is whether it's physically so, (ie. physically wrong or provisionally correct). Not whether it's philosophically so.

Of course, in practice, it can get a lot more complicated than this.

C

Carllooper, I believe it is self-evident that if we get the philosophical principles underlying science wrong, that science will go astray. Unfortunately my sense is that not only is this not believed these days, but that the opposite idea has practically become orthodoxy--namely, the idea that the only meaning of a scientific theory is in its ability to make accurate predictions.

You say "what matters is if a theory is 'physically right or wrong' not whether it is 'philosophically so'." By a theory being "physically right or wrong" here, you could mean two things: (1) you could mean "physically" in the sense of having to do with the real physical matter of the world, and thus be saying something like "a physically true theory correctly describes what is actually out there in the world," or (2) which is practically the opposite of that, you could mean "physically" in the sense of "as in physics"--which, these days, often explicitly repudiates the idea that theories are describing a "world out there," but rather insists on the above point about just being about accurate experimental predictions.

In my view, a theory will only be able to make accurate predictions consistently by truly describing the actual world.

I know you will say, "what does it matter?"--let physics talk about experiments and philosophers talk about the meaning of scientific claims. But I think it does matter, and I think that the infiltration of physics by wrong philosophical assumption has affected it significantly.

I will try to say why I think this, but let me first give the disclaimer that I know very well that I am not an expert, and I am confident that there are many detailed replies to this that I will not be able to follow. What I have to say is more of a sense than it is grounded in something I fully understand. I am aware of this, and that's why I am interested in studying physics, and why I started this thread!

To me it appears that what has happened is that physicists started with choice #2 above (that physics does not describe a "world out there" but just makes predictions that either can, or can't be experimentally verified) and were led by that conclusion to disbelief in the out-there reality of the very particles they are supposed to be studying. You can clearly trace the lineage in the latter "scientific conclusion" to the former philosophical error. You can see how this would affect physical research. If you don't believe that the thing you are studying really exists (at least in any way you can make sense of) that is OBVIOUSLY going to affect the paths that you choose to study it!

Currently physics is moving forward largely under that understanding, and it seems to me that it is greatly affecting the path. What I see is a whole bunch of theories which all have to do with the ways that complex equations can match experiments--with fairly little progress on achieving consensus on theoretical advancement. That would be consistent with a mis-step of the type that I describe above, where a philosophical error would retard scientific progress.

And I feel like that explanation makes sense with what we know. Whereas classical physicists had the considerable advantage of being able to use their mental intuitions to form theories, today's physicists are trained in the art of NOT doing that. You have to accept that your intuitions (including the very fundamental intuition that physical theories are about the "real world" or the intuition that "everything has an explanation for being as it is," which was so important for Einstein) are of no use, and they are actually a hindrance to advancement. Well, if those intuitions are as essential to scientific advancement as I think they are (and as Einstein found them to be), then transforming the entire physics community into an institution that trains everyone who goes through it to mutilate those intuitions will obviously have a very negative effect.

Personally I simply can't conceive of why, if you don't actually believe the theory is about an independent objective world, you would expect experiments to match theories, or why you would care. In my view, you simply can't, and everyone carries that assumption around with them no matter how well they've trained themselves to mutilate it. So progress in physics may go on in spite of the error, but the error (and its having become orthodox) could be a significant hindrance.

Of course, I know that there are ways that we really do have to overcome our intuitions. I know we don't have the capacity to intuit general relativity, and to think in terms of it you have to in a sense twist your mind into a shape it just won't go. And furthermore, I know there really are things going on "down there" that are pretty much mind-blowing.

But whereas scientific advancement has often occurred by trying so solve paradox, it seems to me that part of the philosophy behind QM is very much the opposite. Rather than trying to solve the paradox, there is a sense in which they are deliberately embracing it. Rather than saying, "there is something that is going on here that we don't understand and we need to study it further," they are saying, "we understand exactly what is going on here, and it is that the particles cease to exist"--at just the point where they reach the limit of their ability to understand them! Thus it is with the alleged "completeness" of quantum theory. It amounted to transforming their inability to understand into a "scientific conclusion" (that was really a philosophical error, in my view) that (a) is taught to all students of science nowadays, and (b) actually puts a stop to the process of scientific inquiry.

So...if the philosophical error lead to physicists believing that there was no further need to study something because they had already understood everything there was to know about it, you can see why philosophy affects physical research, and so matters a good deal.

 

[bhobba]

Carllooper, I believe it is self-evident that if we get the philosophical principles underlying science wrong, that science will go astray.

I STRONLY disagree with that:
https://www.google.com.au/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&cad=rja&uact=8&ved=0CCAQFjAA&url=http://www.phys.washington.edu/users/vladi/phys216/Weinberg_Against_philosophy.doc&ei=fVJoVIXUNeL2mQWH_oCwCA&usg=AFQjCNHg_elaIirwh-1Q7Al_kVaI8Fz8YA&sig2=h2vnb14frw18jhYKClXrLw

But this forum is not the place to discuss it. The philosophy forums is the place.

Unfortunately my sense is that not only is this not believed these days, but that the opposite idea has practically become orthodoxy--namely, the idea that the only meaning of a scientific theory is in its ability to make accurate predictions.

It's not. Wienbergs view, which is the same as mine, is pretty common.

My post concerned the statement - 'One can imagine a lot of classically trained physicists walking around the conference in a huff saying things like "what is all this rubbish". And Bohr is trying to win them over to QM.'

I think by that time no one wasn't won over to QM. What Bohr was on about is his particular Copenhagen view - in this case complementarity. But shut up and calculate would soon predominate, if it hadn't already.

In my view, a theory will only be able to make accurate predictions consistently by truly describing the actual world.

Does Euclidean geometry describe the actual world? And if it does precisely how does QM differ from it.

Thanks
Bill

 

[Fredrik]

"Fredrik said:"

I didn't. The quote in bhobba's post #80 is from carllooper's post #79.

 

[Fredrik]

I STRONLY disagree with that:

Weinberg is dismissing the idea that philosophers can tell physicists which theories are plausible and which ones are not. I think everyone in physics agrees with him. But the idea that you can't find the right theory just by thinking about it is a philosophical principle that it's important to get right. So it would be more accurate to say that Weinberg is supporting the quoted sentence than to say that he's disagreeing with it.

In my view, a theory will only be able to make accurate predictions consistently by truly describing the actual world.

Now this is something I strongly disagree with. bhobba's example of Euclidean geometry shows that a theory can make good predictions even if's only an approximate description of the world. Here's an example of a theory that makes good predictions without even approximately describing the world:

Define $\Omega=\{1,2,3,4,5,6\}$. Let $\Sigma$ be the set of all subsets of $\Omega$. For each $E\in\Sigma$, let $|E|$ denote the cardinality of $E$, i.e. the number of distinct elements of $E$. Define $P:\Sigma\to[0,1]$ by
$$P(E)=\frac{|E|}{|\Omega|}$$ for all $E\in\Sigma$. Now let's turn this piece of mathematics into a theory about the real world by specifying that for each $E\in\Sigma$, $P(E)$ is the fraction of times we'll get a result in the set $E$ if we repeatedly throw a standard six-sided die a large number of times.

This theory isn't even approximate description of the world. In particular, it says nothing about what's actually happening to the die between state preparation (the throw) and measurement (the moment when it has landed with some side up).

 

[carllooper]

What I am suggesting is that once that was done, because everyone knew that classical physics was kaput, Bohr didn't need to convince anyone about QM. What he was on about was his philosophical view of it which by that stage people didn't care that much about since shut up and calculate was taking hold.

Ah ok. I see what you are saying.

 

[bhobba]

Weinberg is dismissing the idea that philosophers can tell physicists which theories are plausible and which ones are not. I think everyone in physics agrees with him. But the idea that you can't find the right theory just by thinking about it is a philosophical principle that it's important to get right. So it would be more accurate to say that Weinberg is supporting the quoted sentence than to say that he's disagreeing with it.

Its the old issue of being 'anti' philosophy. That is itself a philosophical position. But I think most understand what's meant without being ultra analytical about it.

Still - you are correct.

Thanks
Bill

 

[carllooper]

That wasn't how Bohr refuted Einstein:

It was one of Bohr's insights that emerged during his analysis of EPR. There is an agreement to be found between relativity and QM rather than a disagreement. The concept of information becomes clearer.

 

[bhobba]

bhobba's example of Euclidean geometry shows that a theory can make good predictions even if's only an approximate description of the world. Here's an example of a theory that makes good predictions without even approximately describing the world:

That's true, but the idea I was trying to get across is that QM is a mathematical model - specifically its a model about this primitive, loosely defined, thing called an observation. The archetype of all mathematical models is Euclidean geometry. Its primitives are these things called points and lines - again loosely defined - a point has position but no size, a line length but no width. The same with probability theory - its primitives are called events - and again loosely defined - in this case VERY loosely defined, so much so you get the gist by seeing examples.

I believe mathematical models describe the world in a certain domain of applicability. But that's just my view. My point though is whatever view you have of Euclidean geometry - its exactly the same for QM.

Thanks
Bill

 

[bhobba]

It was one of Bohr's insights that emerged during his analysis of EPR. There is an agreement to be found between relativity and QM rather than a disagreement. The concept of information becomes clearer.

I would agree with that.

Thanks
Bill

 

[carllooper]

You say "what matters is if a theory is 'physically right or wrong' not whether it is 'philosophically so'." By a theory being "physically right or wrong" here, you could mean two things: (1) you could mean "physically" in the sense of having to do with the real physical matter of the world, and thus be saying something like "a physically true theory correctly describes what is actually out there in the world," or (2) which is practically the opposite of that, you could mean "physically" in the sense of "as in physics"--which, these days, often explicitly repudiates the idea that theories are describing a "world out there," but rather insists on the above point about just being about accurate experimental predictions.

I don't why they would be opposed.

Physics (2) is, by definition, the study of the physical world (1).

I don't know what kind of physics would repudiate the concept of a "world out there". Physics certainly poses some challenges to classical philosophy, but it's not within physics scope to solve that for philosophy. Philosophy has to solve that.

Experiment plays an important role in physics. Without an experiment, it can be difficult to decide if something has some physical meaning or remains science fiction. Physics is very particular about that - far more than science fiction.

Prediction is only required if one needs to test out any potential conflicts or otherwise between a theory and it's experimental side. If the theory didn't include any predictions then there's no way to map the theory to the experiment. But many theorisations don't need to involve prediction. They can be working within a context in which the physical or experimental aspect has already been tested, and are elaborating the theoretical side, ie. in a mathematically consistent way that wouldn't violate the theory already tested.

C

 

[atyy]

But whereas scientific advancement has often occurred by trying so solve paradox, it seems to me that part of the philosophy behind QM is very much the opposite. Rather than trying to solve the paradox, there is a sense in which they are deliberately embracing it. Rather than saying, "there is something that is going on here that we don't understand and we need to study it further," they are saying, "we understand exactly what is going on here, and it is that the particles cease to exist"--at just the point where they reach the limit of their ability to understand them! Thus it is with the alleged "completeness" of quantum theory. It amounted to transforming their inability to understand into a "scientific conclusion" (that was really a philosophical error, in my view) that (a) is taught to all students of science nowadays, and (b) actually puts a stop to the process of scientific inquiry.

But here you are simply wrong. Quantum mechanics is widely acknowledged to have a problem called the "measurement problem". It is the most important problem in the foundations of quantum mechanics. Von Neumann's proof of the alleged "completeness" (to use your term) of quantum mechanics is widely known to be wrong, particularly after Bell's 1966 explanation of the error.

 

[jbmolineux]

I STRONLY disagree with that:
https://www.google.com.au/url?sa=t&rct=j&q=&esrc=s&source=web&cd=1&cad=rja&uact=8&ved=0CCAQFjAA&url=http://www.phys.washington.edu/users/vladi/phys216/Weinberg_Against_philosophy.doc&ei=fVJoVIXUNeL2mQWH_oCwCA&usg=AFQjCNHg_elaIirwh-1Q7Al_kVaI8Fz8YA&sig2=h2vnb14frw18jhYKClXrLw

But this forum is not the place to discuss it. The philosophy forums is the place.
It's not. Wienbergs view, which is the same as mine, is pretty common.

My post concerned the statement - 'One can imagine a lot of classically trained physicists walking around the conference in a huff saying things like "what is all this rubbish". And Bohr is trying to win them over to QM.'

I think by that time no one wasn't won over to QM. What Bohr was on about is his particular Copenhagen view - in this case complementarity. But shut up and calculate would soon predominate, if it hadn't already.
Does Euclidean geometry describe the actual world? And if it does precisely how does QM differ from it.

Thanks
Bill

Carl, I couldn't agree more with Weinberg's article. He literally demonstrates exactly what I am arguing--how bad philosophy has repeatedly led physics astray.

But the remedy for bad philosophy is not no philosophy. As Weinberg himself says, everyone has underlying philosophical assumptions. It's getting them right that matters, not simply not having them. The philosophy that says "physics should have no philosophy" is just one more bad philosophy. Thus "shut up and calculate" has allowed "the particle that cannot be measured does not exist" to dominate. And since you stop searching for what you don't believe exists, it has literally put a stop to scientific inquiry. Or so it seems to me.

The remedy for bad philosophy is good philosophy, and Weinberg seems to demonstrate a good deal of it in rejecting much of the bad philosophy that has come to dominate the academy. Since the bad philosophy has (according to Weinberg's article) done so much damage to physics--isn't that all the more reason for the importance of the conversation not being won by those who are in error? Doesn't that show precisely that good philosophy is important? As I think CS Lewis says, "good philosophy needs to exist, if for no other reason than that bad philosophy must be answered."

As to your question about Euclidean geometry, I'm not sure I would say that it "describes the world." I believe mathematical theories are different than scientific theories in that they aren't about the physical world. That's why you don't test them with measurements or experiments. But theories in physics ARE about the world, which is why you do test them with measurements and experiments.

Where I believe QM goes wrong (and apparently where Wienberg also believes it goes wrong) is in the claim that what cannot be measured cannot be the content of a theory.

 

[carllooper]

To me it appears that what has happened is that physicists started with choice #2 above (that physics does not describe a "world out there" but just makes predictions that either can, or can't be experimentally verified) and were led by that conclusion to disbelief in the out-there reality of the very particles they are supposed to be studying. You can clearly trace the lineage in the latter "scientific conclusion" to the former philosophical error. You can see how this would affect physical research. If you don't believe that the thing you are studying really exists (at least in any way you can make sense of) that is OBVIOUSLY going to affect the paths that you choose to study it!

No this is not the case at all. Physics does describe the world out there, but it's just not in a way that classical philosophy might describe it. For example Kant assumes a world in which time and space are separate. And this might be something one might like to use in physics. But if you are trying to use it with Relativity Theory it won't work, because Relativity employs the concept of time and space as not separate. It's not for any philosophical reason. And it's not due to the infiltration of any wrong philosophy. It's that an aspect of the world out there makes sense in terms of Relativity Theory. Or to put it another way: the world out there doesn't make nonsense of it.

Regarding particles.

The reality or otherwise of particles depends on what you mean by reality. A particle itself is defined by the mathematics. In many philosophies mathematics and reality are the same thing. So in those philosophies you could say the particle is real. In other philosophies its the particle detection which is real and the particle which isn't. But who's to say which philosophy is correct? And does it matter? As long as one understands what is being meant, in a particular context, by terms such as "particle", or "reality", or "non-existent" or "actual" etc. that's what matters.

C

 

[jbmolineux]

But here you are simply wrong. Quantum mechanics is widely acknowledged to have a problem called the "measurement problem". It is the most important problem in the foundations of quantum mechanics. Von Neumann's proof of the alleged "completeness" (to use your term) of quantum mechanics is widely known to be wrong, particularly after Bell's 1966 explanation of the error.

Yes, I am aware that QM has a measurement problem. But historically the measurement problem combined with the positivist idea that "only the measurable is meaningful" to the actual belief that the unmeasurable is nonexistent, which a stop to inquiry, as the Weinberg article above spells out. I have heard that later the repudiation of "completeness" by Bell came to be accepted, but obviously decades of research-that-could've-been were lost by what were ultimately philosophical mistakes.

Honestly, I am unable, even, to sort out where the conversation went from there. Perhaps you guys can help me to understand. Here is how I understand what happened (and please tell me where I am wrong here).

1. Logical positivists, in their zeal to "get metaphysics out of philosophy" put forth the empirical criterion of meaning, which says that the only meaningful propositions were those that could be empirically verified.

1. Once this was accepted, as soon as one considers some fact which "exists" (in the ordinary sense) but cannot be perceived for any reason--cannot be spoken about meaningfully at all. This was problematic and counter-intuitive, and led to many absurdities. But it was the clear implication of the empirical criterion of meaning.

1. Heisenberg brought to bear the empiricist criterion of meaning onto the position / velocity of particles at the quantum level, where the mere act of observing them by shinning light on them would affect them (the measurement problem). He pointed out that under the empirical criterion, such particles actually do not have a velocity or a position.
2. This was embraced by some (Copenhagen), and flatly rejected by others, including Einstein, who believed that this result contradicted the fundamental scientific intuition.
3. Eventually, the positivists won over most of the physics community. I believe Von Neuman's later-to-be-repudiated "completeness" proof was part of it. On this basis, the idea became orthodox in physics that particles do not "exist in the classical sense" but exist in a in a state of quantum uncertainty, and literally do not have both a position and velocity.
4. In the next few decades logical positivism would die out in philosophy (as it came to be accepted that is was directly self-defeating), and apparently Von Neuman's completeness was eventually repudiated by Bell.
5. As far as I understand it, Bell's theorem was tested experimentally a number of times in a way that is supposed to have vindicated the positivist QM interpretation.

This last step, unfortunately, is where I get lost. I haven't really been able to understand the Bell Test experiments, which is why I want to learn physics. But it seems to me that as soon as positivism is repudiated in philosophy and "completeness" in physics, that there would be a metaphysical revolution in physics to get things back on track. As the Weinberg article pointed out, bad philosophy had been leading physics astray for decades. If you could get it back on track, it seems that the astray-leading should stop. But it seems to me that physics is still so-heavily influenced by bad philosophy that it still hasn't really got back on track. (And, in my view, "shut up and calculate" amounts to "there is no objective physical world to be measured," or certainly allows it to flourish….) Or maybe I just don't understand the Bell Test experiments, and how they somehow vindicate some philosophical ideas that I have been considering errors.

Answers to a few questions might help me here:

• Why is it impossible to know both the position and the velocity of a particle by the rebound of a photon hitting it?

• On Entanglement experiments - why can't the cause be explained by the same properties in each at the source? (I know I am out of my league with this question, and I believe the answer might be Bell's theorem itself...is that true?)
• Why couldn't there be an entanglement-type experiment where both particles were sent out "in the same way" so that you learn the information from one to know about the other? In other words, can you do something at the beginning to ensure that the position and velocity are the same, and then measure the position of one and the velocity of the other?

 

[bhobba]

I believe mathematical theories are different than scientific theories in that they aren't about the physical world. That's why you don't test them with measurements or experiments. But theories in physics ARE about the world, which is why you do test them with measurements and experiments.

That's a misconception.

Both Euclidean Geometry and QM are mathematical models and make predictions that can be tested. Pure mathematics is something different again .

Where I believe QM goes wrong (and apparently where Wienberg also believes it goes wrong) is in the claim that what cannot be measured cannot be the content of a theory.

QM doesn't say that. Its simply a theory whose primitive is observations. It silent on the issue of what's going on aside from that - but we have conjectures (called interpretations) that have their own take.

Thanks
Bill

 

[Fredrik]

Quantum mechanics is widely acknowledged to have a problem called the "measurement problem".

The only reason for this is that what most people think of as QM is a great theory of physics plus the unnecessary and unscientific assumption that a pure state "provides a complete and exhaustive description of an individual system". Quantum mechanics as I would define it, doesn't have a measurement problem. There are things that this theory is unable to tell us, but that's not a problem. It's either something that only a better theory can answer, or something that's forever beyond the reach of science. If it's the latter, that's certainly a problem, but it's a problem with the real world, not a problem with the theory.

This is how Wikipedia describes the measurement problem:

If observers and their measuring apparatus are themselves described by a deterministic wave function, why can we not predict precise results for measurements, but only probabilities?​

This sounds like a very good question, until you realize that the claim that matter is described by pure states is either a tautology (if you define "describes" in a way that makes this idea true) or an unnecessary and unscientific assumption added on top of a perfectly fine theory (if you leave "describes" undefined). It's the same assumption that Ballentine worded "a pure state provides a complete and exhaustive description of an individual system".

To a person who hasn't made this assumption, the question above looks very naive. Consider my theory of a six-sided die defined in post #86. No reasonable reasonable person would ask "If dice are described by this theory, why can we not predict precise results for measurements, but only probabilities?" The reason why people ask such silly questions about QM is that the standard presentation of the theory makes it very tempting to literally identify pure states with systems. The temptation is so strong that a lot of people are simply unable to see that when they do, they have left science behind and made an unnecessary assumption

 

[bhobba]

Physics does describe the world out there, but it's just not in a way that classical philosophy might describe it.

Modern physical theories are mathematical models, exactly the same as the archetypical mathematical model - Euclidean Geometry.

Since antiquity it has been recognised as THE pristine intellectual achievement:
http://poetry.about.com/od/poems/l/blmillayeuclid.htm
Euclid alone has looked on Beauty bare.
Let all who prate of Beauty hold their peace,
And lay them prone upon the Earth and cease
To ponder on themselves, the while they stare
At nothing, intricately drawn nowhere
In shapes of shifting lineage; let geese
Gabble and hiss, but heroes seek release
From dusty bondage into luminous air.
O blinding hour, O holy, terrible day,
When first the shaft into his vision shone
Of light anatomized! Euclid alone
Has looked on Beauty bare. Fortunate they
Who, though once only and then but far away,
Have heard her massive sandal set on stone.

All modern physics does is carry on that exemplary tradition.

Thanks
Bill

 

[jbmolineux]

No this is not the case at all. Physics does describe the world out there, but it's just not in a way that classical philosophy might describe it. For example Kant assumes a world in which time and space are separate. And this might be something one might like to use in physics. But if you are trying to use it with Relativity Theory it won't work, because Relativity employs the concept of time and space as not separate. It's not for any philosophical reason. And it's not due to the infiltration of any wrong philosophy. It's that an aspect of the world out there makes sense in terms of Relativity Theory. Or to put it another way: the world out there doesn't make nonsense of it.

Regarding particles.

The reality or otherwise of particles depends on what you mean by reality. A particle itself is defined by the mathematics. In many philosophies mathematics and reality are the same thing. So in those philosophies you could say the particle is real. In other philosophies its the particle detection which is real and the particle which isn't. But who's to say which philosophy is correct? And does it matter? As long as one understands what is being meant, in a particular context, by terms such as "particle", or "reality", or "non-existent" or "actual" etc. that's what matters.

C

Carl, I certainly don't believe that any philosophical error on Einstein's part caused any problems in physics! Kant's idea that time and space are mind-dependent seems to me to be a philosophical precursor to relativity.

Yes, different people have different ideas of what constitutes "reality," "non-existent," "particle," etc.--as you point out. But then you go on to say that "as long as one understands what is being meant"--that’s what matters. But since there is no agreement about what is meant by those terms, how can it be understood what is being meant?

Further, the question of whether something even exists if it can't be measured by the technology of a certain time is certainly relevant! If scientists are taught something doesn't exist, it puts a stop to the inquiry that drives scientific progress!

 

[bhobba]

Yes, I am aware that QM has a measurement problem. But historically the measurement problem combined with the positivist idea that "only the measurable is meaningful" to the actual belief that the unmeasurable is nonexistent, which a stop to inquiry, as the Weinberg article above spells out

You are getting a bit confused between a theory that is silent about things other than observations, and philosophical guff that says that's all there is.

Thanks
Bill

 

[Fredrik]

That's a misconception.

Again the statement you're disagreeing with is something that I would say is definitely true. There is no piece of mathematics that says anything about the real world all on its own. Hilbert space theory doesn't say anything about the result of experiments. To turn it into a theory of physics, we have to add correspondence rules that tell us how to interpret the mathematics as predictions about possible results of experiments. The same goes for every piece of mathematics and the corresponding application to the real world. In the theory I defined in post #86, everything was pure mathematics that said nothing about the real world until I made that final assumption, the correspondence rule.

In some cases, it's so obvious what the correspondence rules are supposed to be that we may not even realize that we are using correspondence rules. Euclidean geometry is probably the best example. It's a piece of pure mathematics that was intended to be applied to the real world. We have known since we were kids how mathematical things in Euclidean geometry correspond to real-world things. Those correspondences are what turn this piece of pure mathematics into a theory of applied mathematics.

In general, I would say that the difference between pure mathematics and applied mathematics is correspondence rules. Applied mathematics is a subject that includes applied geometry, applied probability theory and physics.

 

[bhobba]

Kant's idea that time and space are mind-dependent seems to me to be a philosophical precursor to relativity.

Its the other way around.

Kant's carry on about the a priori nature of Euclidean geometry negatively affected the equally great mathematician Gauss from publishing his discoveries about non Euclidean geometry. This was required for Riemann to develop Riemannian geometry, the extension of that to pseudo Riemannian geometry being the basis of General Relativity.

Thanks
Bill

 

[jbmolineux]

Weinberg is dismissing the idea that philosophers can tell physicists which theories are plausible and which ones are not. I think everyone in physics agrees with him. But the idea that you can't find the right theory just by thinking about it is a philosophical principle that it's important to get right. So it would be more accurate to say that Weinberg is supporting the quoted sentence than to say that he's disagreeing with it.Now this is something I strongly disagree with. bhobba's example of Euclidean geometry shows that a theory can make good predictions even if's only an approximate description of the world. Here's an example of a theory that makes good predictions without even approximately describing the world:

Define $\Omega=\{1,2,3,4,5,6\}$. Let $\Sigma$ be the set of all subsets of $\Omega$. For each $E\in\Sigma$, let $|E|$ denote the cardinality of $E$, i.e. the number of distinct elements of $E$. Define $P:\Sigma\to[0,1]$ by
$$P(E)=\frac{|E|}{|\Omega|}$$ for all $E\in\Sigma$. Now let's turn this piece of mathematics into a theory about the real world by specifying that for each $E\in\Sigma$, $P(E)$ is the fraction of times we'll get a result in the set $E$ if we repeatedly throw a standard six-sided die a large number of times.

This theory isn't even approximate description of the world. In particular, it says nothing about what's actually happening to the die between state preparation (the throw) and measurement (the moment when it has landed with some side up).

Weinberg is dismissing the idea that philosophers can tell physicists which theories are plausible and which ones are not. I think everyone in physics agrees with him. But the idea that you can't find the right theory just by thinking about it is a philosophical principle that it's important to get right. So it would be more accurate to say that Weinberg is supporting the quoted sentence than to say that he's disagreeing with it.Now this is something I strongly disagree with. bhobba's example of Euclidean geometry shows that a theory can make good predictions even if's only an approximate description of the world. Here's an example of a theory that makes good predictions without even approximately describing the world:

Define $\Omega=\{1,2,3,4,5,6\}$. Let $\Sigma$ be the set of all subsets of $\Omega$. For each $E\in\Sigma$, let $|E|$ denote the cardinality of $E$, i.e. the number of distinct elements of $E$. Define $P:\Sigma\to[0,1]$ by
$$P(E)=\frac{|E|}{|\Omega|}$$ for all $E\in\Sigma$. Now let's turn this piece of mathematics into a theory about the real world by specifying that for each $E\in\Sigma$, $P(E)$ is the fraction of times we'll get a result in the set $E$ if we repeatedly throw a standard six-sided die a large number of times.

This theory isn't even approximate description of the world. In particular, it says nothing about what's actually happening to the die between state preparation (the throw) and measurement (the moment when it has landed with some side up).

Fredrik, I believe that theory IS describing the world. It's describing the fact that a six-side die is a cube which--if it is spun into the air and allowed to hit a hard surface from an undetermined height, at an undetermined angle and rate of rotation--are each equally-likely to end up facing upwards when it stops bouncing.

Obviously if you take out the "undetermined height, angle, and rate of rotation" aspects, the theory would not hold. I think Carl Popper describes it as a "propensity" that exists in the die which, by the very nature of its shape, leads to these results when it is repeatedly dropped in the way described above.

Or does anyone have another explanation of why the theory actually holds? Does it really have nothing to do with the shape of the die? If it doesn't have to do with the shape of the die (as described above), why does it work with a normal six sided die, and not a weighted die?--or an 8-side die?

Heck, I've never even tested that theory in a laboratory and I know it holds just by knowing the shape of the die! Has anyone here tested it in a laboratory? Since physics is just about the results of experiments about what can be repeatedly testable, wouldn't we have to test it in a lab to even be able to say that it holds?--and yet, having neither tested it in a laboratory nor bothered to read about what-we-already-know-would-happen if someone DID test it, we all know that the theory is true!

 

[bhobba]

Again the statement you're disagreeing with is something that I would say is definitely true.

I usually agree with your views.

However here I must dissent.

Euclidean Geometry as usually presented is a mathematical model whose statements can be tested eg do the angles of a triangle add up to 180%.

Hilbert's treatment however is another matter:
http://en.wikipedia.org/wiki/Hilbert's_axioms

Hilbert space theory doesn't say anything about the result of experiments.

No it doesn't. Its the mapping of resolutions of the identity to the primitive of observations that does that. That's what QM does - and that's what makes it a mathematical model.

The usual presentation of Euclidean geometry speaks of points of no size and lines of no width that are idealisations of stuff out there.

Thanks
Bill