Insights The Fundamental Difference in Interpretations of Quantum Mechanics - Comments

[bhobba]

You somehow manage to twist and misunderstand everything I say. Nowhere did I imply that we still use the same first principles that Newton used, I said that physicists still use derivation from first principles as invented by Newton,

And I could also say the same thing.

Didn't you get what was being inferred - we do not use the same methods as Newton because they do not work. We can't elucidate those 'first principles' you talk about, even for such a simple thing as what time is.

The modern definition of time is - its what a clock measures.

Wow what a great revelation - but as a first principle - well its not sating much is it beyond common sense - basically things called clocks exist and they measure this thing called time. It does however have some value - it stops people trying to do what Newton tried - and failed.

Want to know what the 'first principles' of modern classical mechanics is:

1. The principle of least action.
2. The principle of relativity.

Now, if what you say is true then you should be able to state those in your 'first principles' form. I would be very interested in seeing them. BTW 1. follows from QM - but that is just by the by - I even gave a non rigorous proof - see post 3:
https://www.physicsforums.com/threa...fication-of-principle-of-least-action.881155/

You will find it doesn't matter what you do, you at the end of the day end up with very vague, or even when looked at deeply enough, nonsensical statements. That's why it's expressed in mathematical form with some terms left to just common sense in how you apply it. In fact that's what Feynman was alluding to at the end of the second video you posted. Physics is not mathematics but is written in the language of math. How do you go from one to the other? Usually common-sense. But if you want to go deeper then you end up in a philosophical morass that we do not discuss here.

Thanks
Bill

 

[Auto-Didact]

And I could also say the same thing.

Didn't you get what was being inferred - we do not use the same methods as Newton because they do not work. We can't elucidate those 'first principles' you talk about, even for such a simple thing as what time is.

The modern definition of time is - its what a clock measures.

Wow what a great revelation - but as a first principle - well its not sating much is it beyond common sense - basically things called clocks exist and they measure this thing called time. It does however have some value - it stops people trying to do what Newton tried - and failed.

Want to know what the 'first principles' of modern classical mechanics is:

1. The principle of least action.
2. The principle of relativity.

Now, if what you say is true then you should be able to state those in your 'first principles' form. I would be very interested in seeing them. BTW 1. follows from QM - but that is just by the by - I even gave a non rigorous proof - see post 3:
https://www.physicsforums.com/threa...fication-of-principle-of-least-action.881155/

You will find it doesn't matter what you do, you at the end of the day end up with very vague, or even when looked at deeply enough, nonsensical statements. That's why it's expressed in mathematical form with some terms left to just common sense in how you apply it. In fact that's what Feynman was alluding to at the end of the second video you posted. Physics is not mathematics but is written in the language of math. How do you go from one to the other? Usually common-sense. But if you want to go deeper then you end up in a philosophical morass that we do not discuss here.

Thanks
Bill

I'm not sure that you understand that I am saying that our first principles are all literally mathematical statements - all our first principles are observational facts in the form of mathematical statements, the best example is the principle of general covariance.

This changes nothing of the fact that the physicist's method of doing mathematics and of deriving new laws looks almost nothing like the modern mathematician's axiomatic style of doing formal mathematics as is customary since Bourbaki; the gist of mathematics used in physics was maybe 'modern' in the 18th/19th century.

Derivation from first principles of physics is the de facto physicist technique of discovering physical laws and theories from principles based on observation in the form of mathematical statements. Derivation from first principles is however not rigorous mathematical proof based on axioms, nor will it ever be: these are two different methods of using mathematics, that is my point.

tl;dr mathematicians and physicists tend to use mathematics in completely different ways due to different purposes, this is a good thing.

 

[bhobba]

the best example is the principle of general covariance.

You know the principle of general covarience is wrong don't you (or rather is totally vacuous as first pointed out by Kretchmann to Einstein - and Einstein agreed - but thought it still had heuristic value)? But that is best suited to the relativity forum.

Its modern version is the principle of general invariance: All laws of physics must be invariant under general coordinate transformations.

Is that what you mean?

Then yes I agree. My two examples of the modern version of classical mechanics would fit that as well.

But I am scratching my head about why the principles I gave from Ballentine would not fit that criteria?

Thanks
Bill

 

[PeterDonis]

Its modern version is the principle of general invariance: All laws of physics must be invariant under general coordinate transformations.

Isn't that what "the principle of general covariance" means?

 

[bhobba]

Isn't that what "the principle of general covariance" means?

Not according to Ohanian:
https://www.amazon.com/dp/0393965015/?tag=pfamazon01-20

There has been long debate about it:
http://www.pitt.edu/~jdnorton/papers/decades.pdf
Ohanian (1976, pp252-4) uses Anderson’s principle of general invariance to
respond to Kretschmann’s objection that general covariance is physically vacuous. He
does insist, however, that the principle is not a relativity principle and that the general
theory of relativity is no more relativistic than the special theory (~257). Anderson’s
ideas seem also to inform Buchdahl’s (1981, Lecture 6) notion of ‘absolute form
invariance’.

Its Anderson's principle of invarience which technically is - The requirement that the Einstein group is also an invariance group of all physical systems constitutes the principle of general invariance.

I will need to dig up my copy Ohanian to give his exact definition of the two - ie invarience and covarience. What I posted is his definition of invarience which I will need to contrast to his definition of covarience. That will take me a couple of minutes - but need to go to lunch now. I will see if I can do it now, otherwise it will need to wait until I get back.

Added Later:
Found it - from page 373 of Ohanain - the Principle of General covarience is:
All laws of physics shall be stated as equations covarient with respect to general coordinate transformations.

The difference is, as Kretchmann showed (and others if I recall), any equation can be bought into covarient form, but invarience is stronger - the content of the law itself must be invariant under coordinate transformations - not just its form.

I think if anyone wants to pursue it further the relativity forum is the best place.

Thanks
Bill

 

[Auto-Didact]

You know the principle of general covarience is wrong don't you (or rather is totally vacuous as first pointed out by Kretchmann to Einstein - and Einstein agreed - but thought it still had heuristic value)? But that is best suited to the relativity forum.

Its modern version is the principle of general invariance: All laws of physics must be invariant under general coordinate transformations.

Is that what you mean?

Then yes I agree. My two examples of the modern version of classical mechanics would fit that as well.

But I am scratching my head about why the principles I gave from Ballentine would not fit that criteria?

Thanks
Bill

I learned GR from MTW, since they use the term general covariance it was what stuck with me.

Ballentines "derivation" is very much an axiomatic formalisation/deduction similar to using the Kolmogorov axioms to formalise probability theory. His "derivation" feels nothing at all like say deriving Maxwell's equations from experimental observations, like deriving Einstein's field equations from Gaussian gravity, or even like deriving the covariant formulation of electrodynamics from respecting the Minkowski metric. The key takeaway here is that Ballentine's 'principles' contain no actual observational content whatsoever, making them (mathematical) axioms not (physical) principles.

This of course is not to say that there aren't any first principles in QM, there definitely are, for example most famously Heisenberg's uncertainty principle, which is an experimental observation; a proper physics derivation of QM from first principles should contain a first principle like this, not some semantically (NB: I forgot the correct term) closed statement like the Born rule.

 

[fresh_42]

Before Newton there simply was no such approach to physics and therefore no true inkling of physical law; in this sense it can be said that Newton invented (mathematical) physics.

Why doesn't Kepler (1619) count? Because his laws certainly satisfy:

Derivation from first principles of physics is the de facto physicist technique of discovering physical laws and theories from principles based on observation in the form of mathematical statements.

In my opinion it has been simply a matter of the time he lived in. Several parallel developments in mathematics and physics took place and developed in a mathematical handling of physical laws. To reduce this complex process to a single person or even book is which I find disrespectful towards all others who have been involved in it. It is an oversimplification and irregular reduction of history.

 

[PeterDonis]

Not according to Ohanian

Looks like a variance in terminology, then. As @Auto-Didact mentions, MTW uses the term "general covariance" to mean what you are using the term "general invariance" to mean. (And since I also learned GR from MTW, I would use "general covariance" to mean that as well.) So you and he actually agree on the physics; you're just using different words.

 

[Auto-Didact]

Why doesn't Kepler (1619) count? Because his laws certainly satisfy:

In my opinion it has been simply a matter of the time he lived in. Several parallel developments in mathematics and physics took place and developed in a mathematical handling of physical laws. To reduce this complex process to a single person or even book is which I find disrespectful towards all others who have been involved in it. It is an oversimplification and irregular reduction of history.

Many modern mathematicians/scientists tend to mistake what is heritage for what is history. Coincidentally, Feynman also explained this difference: "What I have just outlined is what I call a ‘physicist’s history of physics’, which is never correct… a sort of conventionalized myth-story that the physicist tell to their students, and those students tell to their students, and it is not necessarily related to actual historical development, which I do not really know!". I quote Unguru “to read ancient mathematical texts with modern mathematics in mind is the safest method for misunderstanding the character of ancient mathematics".

From actual history, we know that Kepler did not yet have the full tools of Vieta's (elementary) algebra nor Descartes' analytic geometry, i.e. our conception of a formula was literally a foreign concept to his mind, while it is widely known that Newton directly self-studied Descartes which enabled him to invent calculus, i.e. those prerequisites were central to inventing mathematical physics and it was Newton and only Newton who did so; all other physical theories were subsequently modeled after Newton's paradigmatic way of doing mathematical physics using differential equations.

Addendum: In fact, it is known that Kepler even fudged his statistical analysis of the orbits to end up with his laws. His laws of course are not general enough to be called fundamental laws of physics, while Newton's clearly were; we still to this day say Newton's laws are limiting cases to GR. Still, you have a point that Keplers laws were stated using mathematics, just not in the mathematical physics way we state fundamental laws today. This is mostly because Kepler's laws are just a mathematical encoding of experimental phenomenology, i.e. they are principles, perhaps even fundamental ones. Much of the same can be said for Galileo's work.

 

[fresh_42]

From actual history, we know that Kepler did not yet have the full tools of Vieta's (elementary) algebra nor Descartes' analytic geometry ...

... and Newton didn't have differential geometry. This underlines my point of view as a matter of historical developments and doesn't contradict it. Newton wasn't the one and only, but rather one in a long row before and after him, many of them mathematicians by the way, who contributed to physics. It is as if you say before Euclid there wasn't geometry, or before Zermelo there wasn't sets. It is still a rough oversimplification. To distinguish heritage and history at this point is hair splitting. This might make sense in philosophy as you called Wittgenstein as your witness, but not here. Still, why shouldn't Kepler count? And this is only the easiest example I've found without digging too deep into years of date.

Anyway, this is a discussion which a) belongs in a separate thread and b) in a different sub-forum. I'll therefore end my participation in it now, the more as I have the feeling you try to convince by repetition instead of argumentation.

 

[Auto-Didact]

... and Newton didn't have differential geometry. This underlines my point of view as a matter of historical developments and doesn't contradict it. Newton wasn't the one and only, but rather one in a long row before and after him, many of them mathematicians by the way, who contributed to physics. It is as if you say before Euclid there wasn't geometry, or before Zermelo there wasn't sets. It is still a rough oversimplification. To distinguish heritage and history at this point is hair splitting. This might make sense in philosophy as you called Wittgenstein as your witness, but not here. Still, why shouldn't Kepler count? And this is only the easiest example I've found without digging too deep into years of date.

Anyway, this is a discussion which a) belongs in a separate thread and b) in a different sub-forum. I'll therefore end my participation in it now, the more as I have the feeling you try to convince by repetition instead of argumentation.

I agree, this discussion is somewhat fruitless. Both Kepler and Galileo used mathematics, and in that descriptive sense could be said to be doing 'mathematical physics'. The problem is that mathematical physics has historically always referred to calculus/analysis/differential equation type physics namely classical physics without modern physics i.e. what you and I learned in undergraduate physics along with most physicists post-Newton in history. The curriculum of course over the years has become supplemented with more and more subjects from mathematics, probably most strikingly linear algebra which almost no physicist knew before almost halfway past the 20th century. In any case, we are literally arguing semantics, so I'll stop as well.

 

[atyy]

I agree with all of this except specifically that collapse is de facto not actually an interpretation of QM because orthodox QM has no collapse, orthodox QM being purely the Schrodinger equation and its mathematical properties. As I said above however QM as a whole is a mathematically inconsistent conjoining of the Schrodinger equation and the stochastic selection of the state from the ensemble which occurs empirically.

Collapse is therefore a prediction of a phenomenologic theory which directly competes with QM, but which has yet to be mathematically formulated. This theory should then contain QM as some particular low order limit, analogous to how Newtonian mechanics is a low order limit of SR.

Orthodox QM does have collapse.

 

[Auto-Didact]

Orthodox QM does have collapse.

After having written that I was going to edit and make the post more complete since I actually think so as well, I agree that state vector reduction is directly part of standard QM.

It however isn't part of what many physicists deem to be 'orthodox QM', namely a pure mathematical treatment of the Schrodinger equation.

Collapse theories with dynamics such as GRW or DP OR are theories competing with QM/beyond QM.

 

[atyy]

After having written that I was going to edit and make the post more complete since I actually think so as well, I agree that state vector reduction is directly part of standard QM.

It however isn't part of what many physicists deem to be 'orthodox QM', namely a pure mathematical treatment of the Schrodinger equation.

Collapse theories with dynamics such as GRW or DP OR are theories competing with QM/beyond QM.

And actually that's why I am not sure Ballentine's axiomatization is correct. Ballentine has a huge rant against collapse. I consider Ballentine among the worst books on QM fundamentals, and not even worth discussing. In contrast, Hardy's "5 reasonable axioms" derivation and others following his footsteps like the "informational" derivation by Chiribella and colleagues does also derive collapse.

 

[Auto-Didact]

And actually that's why I am not sure Ballentine's axiomatization is correct. Ballentine has a huge rant against collapse. I consider Ballentine among the worst books on QM fundamentals, and not even worth discussing. In contrast, Hardy's "5 reasonable axioms" derivation and others following his footsteps like the "informational" derivation by Chiribella and colleagues does also derive collapse.

I'd put it much stronger, I'm sure Ballentine's derivation is incorrect, because it isn't a real physical derivation because it makes no direct statement whatsoever about observations or experimental facts in the world.

Ballentine's axioms are both semantically closed mathematical statements/propositions, which implies any deductions made from them can have no empirical content but only mathematical content, meaning whatever can be deduced solely on the basis of them can never legitimately be called a physical theory. To paraphrase Poincaré, those axioms are definitions in disguise.

 

[atyy]

I'd put it much stronger, I'm sure Ballentine's derivation is incorrect, because it isn't a real physical derivation because it makes no direct statement whatsoever about observations or experimental facts in the world.

Ballentine's axioms are both semantically closed mathematical statements/propositions, which implies any deductions made from them can have no empirical content but only mathematical content, meaning whatever can be deduced solely on the basis of them can never legitimately be called a physical theory. To paraphrase Poincaré, those axioms are definitions in disguise.

I understand what you mean, but maybe that is too strong. After all, the standard axioms are also mathematical. The standard axioms of classical mechanics are also mathematical (the are all definitions in disguise).

Aren't all axioms definitions in disguise? I guess this goes into the tricky issue of the relationship between axioms and models (eg. standard and non-standard models of arithemetic). But I guess scientists use second order logic, so the model is unique.

 

[Fra]

Here is where my viewpoint not just diverges away from standard philosophy of science, but also from standard philosophy of mathematics: in my view not only is Pierce's abduction necessary to choose scientific hypotheses, abduction seems more or less at the basis of human reasoning itself. For example, if we observe a dark yellowish transparant liquid in a glass in a kitchen, one is easily tempted to conclude it is apple juice, while it actually may be any of a million other things, i.e. it is possibly any of a multitude of things. Yet our intuition based on our everyday experience will tell us that it probably is apple juice; if we for some reason doubt that, we would check it by smelling or tasting or some other means of checking and then updating our idea what it is accordingly. (NB: contrast probability theory and possibility theory).

I was away yesterday, but in short. I agree with you on abduction. Indeed the human brain seems to be designed so that It encodes not a record to events, but it abduces the "best rule" and store that. This is what our memories are not always accurate, but are tweaked. Best rule, means the rule to best predict the future give the constraints of our limited capacity of storage and processing power. I don't dig up references now but this is supported by some neuroscientis working on understanding human brain.

After all this is perfectly natural and intuitive for anyone that understands evolution. The motivation for the brain to develop this behaviour is simply survival.

As inferences are general abstractions, there are analogies between inferences executed by the human brain, and the physical inferences executed by subatomic sys tems. But with that said, i am usually careful to mix the discussions as anyone who is not on the same page so to speak, are with highest possible certainly going to misunderstand things grossly, and think we are suggesting that the human brain of consciousness have a role to play in fundamental physics and measurement. This is not so.

/Fredrik

 

[Auto-Didact]

I understand what you mean, but maybe that is too strong. After all, the standard axioms are also mathematical. The standard axioms of classical mechanics are also mathematical (the are all definitions in disguise).

Aren't all axioms definitions in disguise? I guess this goes into the tricky issue of the relationship between axioms and models (eg. standard and non-standard models of arithemetic). But I guess scientists use second order logic, so the model is unique.

The difference is that in the case of the axioms for classical mechanics the content of every mathematical statement can be at least in principle connected to an observational statement, either through the principles involved, through the laws derived or through the postulates stated. On the other hand, Ballentine's mathematical statements upon closer inspection have only mathematical content, just look:

Ballentine has two axioms

1. Outcomes of observations are the eigenvalues of some operator.
2. The Born Rule.

As for your other question, probably, but I'm no logician/mathematician, so in my doing of mathematics I tend to avoid anything axiomatic or Bourbaki-esque like the plague. Then again I do like the word bijective :p

 

[atyy]

The difference is that in the case of the axioms for classical mechanics the content of every mathematical statement can be at least in principle connected to an observational statement, either through the principles involved, through the laws derived or through the postulates stated. On the other hand, Ballentine's mathematical statements upon closer inspection have only mathematical content.

As for your question, probably, but I'm no logician/mathematician, so in my doing of mathematics I tend to avoid anything axiomatic or Bourbaki-esque like the plague. Then again I do like the word bijective :p

So you are really talking about the informal motivation for Ballentine's axioms? I think by your ideas, even the orthodox axioms would be "wrong", but it would be better to say they are not well motivated. On the other hand, Hardy's axioms (equivalent to the orthodox axioms) are presumably better motivated.

 

[Fra]

but it's not a good way to learn quantum theory since their writings tend to clutter the physics with superfluous philosophical balast which confuses the subject more than it helps to understand it.

While i absolutely get your point, that to learn quantum theory, what the mature says, how to apply it etc, can probably be easiest done studying the cleaned up writings, where the historical context and the logic used to construct the theory is left out, as it unavoidable contains detoures and wrong turns.

But wether its wise to decouple the state of science from its historical inference is a question of wether you seek knowledge or understanding, just like Feynman said in the video in post#82 or Auto-Didact.

I seek understanding in order to progress knowledge, this is for me the fun part. Applications tend to bore me. I want to do new things. Once i understand them i loose interest. But this is just me.

I have read both kind of books, i also love the rigour of pure mathematics books. It is a different world though, thinking always in terms of what can be deduced from the given axioms, or the more fuzzy problems of understanding our world. And one does not exclude the other. because solving fuzzy problems with deductive tools simply does not work, because you can not even define the problem, and are then led to the fallacious conclusion that they are not worthy thinking about.

/Fredrik

 

[Auto-Didact]

So you are really talking about the informal motivation for Ballentine's axioms? I think by your ideas, even the orthodox axioms would be "wrong", but it would be better to say they are not well motivated. On the other hand, Hardy's axioms (equivalent to the orthodox axioms) are presumably better motivated.

Yes. I believe that a mathematical axiomatization of physics can and should only be done once physics is actually complete (Gödel says hi).

Before that, all mathematical simplification of physical theory should have as motivation the discovery of more physics or other sciences; any prematurely undertaken axiomatization which inhibits reaching this goal by pretentiously giving some completed deductive viewpoint which then also actually ends up hampering further progress in physics is nothing but an inadequate nuisance, at risk of becoming dogma. Using your less vitriolic words might be a better way of communicating this though.

 

[bhobba]

Looks like a variance in terminology, then. As @Auto-Didact mentions, MTW uses the term "general covariance" to mean what you are using the term "general invariance" to mean. (And since I also learned GR from MTW, I would use "general covariance" to mean that as well.) So you and he actually agree on the physics; you're just using different words.

When he mentioned he learned it from MTW I figured that. Ohanian makes a big deal out of it - MTW doesn't. Interestingly my personal favorite book - Wald - bypasses it by using the concept of diffeomorphism, although I have always thought its just a more rigorous version of the same thing. Maybe someone actually knows the difference. I will start a thread on the relativity forum about it.

Thanks
Bill

 

[bhobba]

I learned GR from MTW, since they use the term general covariance it was what stuck with me.

Now you mention MTW then I understand - only some texts make the distinction. Its not important and I will post my thoughts now you have clarified (at least to me) what you mean we can get to the heart of the issue. Wald is sneaky - he uses the concept of diffeomorphism - but I think its really the same thing - however that is definitely something for the relativity forum.

Thanks
Bill

 

[bhobba]

Orthodox QM does have collapse.

That depends on what you mean by orthodox. If you mean the formalism then you have to explain MW. The answer of course is its principles, axioms, whatever you want to call it doesn't have it.

Thanks
Bill

 

[A. Neumaier]

This is all solid scientific work and not wild "philosophical" speculation.

Philosophy need not be speculation. Neither Bohr's nor Einstein's nor Heisenberg's nor Feynman's philosophy was wild speculation.

 

[A. Neumaier]

So whatever is keeping us from making deterministic predictions about the results of quantum experiments, it isn't chaos due to nonlinear dynamics of the quantum state.

However, it is chaos in the (classical) part of the quantum state that is accessible to measurement devices.

 

[bhobba]

Phisolsophy need not be speculation. Neither Bohr's nor Einstein's nor Heisenberg's nor Feyman's philosophy was wild speculation.

Einstein and Feynman IMHO are good - they are clear - that is the key - for Bohr that wasn't always the case such as his explanation of EPR. Modern scholars, as I have posted elsewhere think his explanation, supposedly definitive, wasn't quite that. BTW Einstein, while clear was far from always right, not by a long shot. His math was particularly bad - his early papers required a lot of comments explaining the errors when collected and published - how they got through referees reports beats me - he wasn't famous then so it simply wasn't - well it's Einstein so who are we to criticize.

Thanks
Bill

 

[bhobba]

I will post my thoughts now you have clarified (at least to me) what you mean we can get to the heart of the issue.

OK we have the principle of general invariance - the laws of physics should be expressed in coordinate free form.

This is an actual physical statement because it makes a statement about physical things - laws of physics.

We have the Principle of Least Action about the paths of actual particles - same as the above.

What I don't understand is why you don't think the same of the statement observations are the eigenvalues of an operator. That seems to be exactly the same as the above - it talks about something physical - an observation.

Thanks
Bill

 

[A. Neumaier]

Einstein and Feynman IMHO are good - they are clear - that is the key - for Bohr that wasn't always the case

There is a big difference between not being clear (which is in philosophy never completely the case) and being wild speculation. Speculation has nothing to do with philosophy but is just unfounded reasoning.

 

[bhobba]

There is a big difference between not being clear (which is in philosophy never completely the case) and being wild speculation. Speculation has nothing to do with philosophy but is just unfounded reasoning.

Good point - they are different. But I have to say there is a tendency to call something philosophical BS if it not quite clear - I think I fall for that one often. You shouldn't - but I find it hard not to.

Tanks
Bill

 

[A. Neumaier]

there is a tendency to call something philosophical if it not quite clear

Philosophy = discussing the possible meanings, definitions, delineations, etc. of concepts, the arguments for or against the various uses, and associated fallacies.

This can be done (like anything else) with different degrees of clarity.

 

[microsansfil]

Philosophy = discussing the possible meanings, definitions, delineations, etc. of concepts, and the arguments for the various uses.

May be the misunderstanding about philosophy is that "The value of philosophy is, in fact, to be sought largely in its very uncertainty"

http://skepdic.com/russell.html

The value of philosophy is, in fact, to be sought largely in its very uncertainty. The man who has no tincture of philosophy goes through life imprisoned in the prejudices derived from common sense, from the habitual beliefs of his age or his nation, and from convictions which have grown up in his mind without the co-operation or consent of his deliberate reason. To such a man the world tends to become definite, finite, obvious; common objects rouse no questions, and unfamiliar possibilities are contemptuously rejected. As soon as we begin to philosophize, on the contrary, we find, as we saw in our opening chapters, that even the most everyday things lead to problems to which only very incomplete answers can be given. Philosophy, though unable to tell us with certainty what is the true answer to the doubts which it raises, is able to suggest many possibilities which enlarge our thoughts and free them from the tyranny of custom. Thus, while diminishing our feeling of certainty as to what things are, it greatly increases our knowledge as to what they may be; it removes the somewhat arrogant dogmatism of those who have never traveled into the region of liberating doubt, and it keeps alive our sense of wonder by showing familiar things in an unfamiliar aspect.

Best regards
Patrick

 

[atyy]

That depends on what you mean by orthodox. If you mean the formalism then you have to explain MW. The answer of course is its principles, axioms, whatever you want to call it doesn't have it.

Them you would say that Bell's theorem does not show that quantum mechanics is inconsistent with local realism.

 

[bhobba]

Them you would say that Bell's theorem does not show that quantum mechanics is inconsistent with local realism.

Your reasoning for that statement beats me - how about spelling it out.

I have given Ballentine's axioms - collapse appears nowhere in there. Continuity allows you to show after an observation the state has changed, if it has not destroyed what was being observed. That is undeniably true - and if that is your idea of collapse beyond doubt. But collapse is usually thought as more than that - the state discontinuously changes on observation - its that discontinuity that is the issue:
https://en.wikipedia.org/wiki/Copenhagen_interpretation
There have been many objections to the Copenhagen interpretation over the years. These include: discontinuous jumps when there is an observation, the probabilistic element introduced upon observation, the subjectiveness of requiring an observer, the difficulty of defining a measuring device, and to the necessity of invoking classical physics to describe the "laboratory" in which the results are measured.

In MW its explained by decoherence not happening discontinuously - very fast - but not immediately. In Ensemble it's simply another preparation procedure so by the definition of a preparation procedure of course the state changes - but again not discontinuously.

Thanks
Bill

 

[stevendaryl]

Just for reference the more convetional terminology for the various kinds of inferences here are, deductive vs inductive inference.

"hard contradictions" are typically what you get in deductive logic, as this deals with propositions that are true or false.
"soft contradictions" are more of the probabilistic kind, where you have various degrees of beliefs or support in certain propositions.

The issue I was talking about when I coined "soft contradiction" wasn't really inductive versus deductive. It was really about how we reason with huge numbers (or very tiny numbers). Let me give a toy example: Suppose I say that

1. A cat is completely described by Newton's laws.
2. A cat always lands on its feet

These two together might very well be contradictory. For some initial condition of a cat, maybe Newton's laws imply that the cat wouldn't land on its feet. But it might be completely infeasible to actually derive a contradiction. It certainly is not feasible to check every possible initial condition of a cat and apply Newton's laws to all the atoms making up the cat's body to find out if it would land on its back. Maybe there is some advanced mathematics that can be used to get the contradiction, using topology or whatever, but in the naive way that people might apply Newton's laws, chances are that a contradiction will never be derived.

Or imagine a mathematical statement S such that the shortest proof (using standard mathematical axioms, anyway) takes 10^{100} steps. Then if I add \neg S to my axioms, then the resulting system is inconsistent. However, it's unlikely that any contradiction will ever be discovered.

I feel that the rules of thumb for using QM may be a similar type contradiction. That recipe consists of

1. A rule for how microscopic systems evolve (Schrodinger's equation)
2. A rule for how measurements produce outcomes (Born's rule)

They work very well. However, since measurement devices are themselves quantum systems (even if very complex) and measurements are just ordinary interactions between measurement devices and the systems being measured, these two rules may very well be contradictory. But a detailed analysis of the measuring process as a quantum interaction may infeasible, so actually deriving a contradiction (that everyone would agree was a contradiction) may never happen.

There is actually an approach to making systems of reasoning with soft contradictions of the type I'm worried about into consistent systems. That is, instead of thinking of the rules as axioms in a mathematical sense, you organize them this way:

1. Split the possible situations that you might be in where you need to reason about something into "domains".
2. Within each domain, you have rules for reasoning within that domain.
3. If something is in the overlap of two domains, you come up with a "resolution domain" to reason about the overlap.

I think that's ugly, but I think it's doable. I think it's something like the way that we deal with the world in our everyday life. If you're trying to figure out how to get your girlfriend to stop being mad at you, you don't try to deduce anything using quantum field theory, you stick to the "relationship domain". Of course, there could be some overlap with other domains, because maybe the problem is that she suffers from headaches that make her irritable, and they might be due to a medical condition. So maybe you need to bring in the "medical domain". And maybe that condition could be treated by some kind of nanotechnology, which might involve physics, after all.

 

[atyy]

Your reasoning for that statement beats me - how about spelling it out.

MWI does not meet the conditions for Bell's theorem. Bell's theorem cannot be used to say that MWI is incompatible with local realism.

 

[bhobba]

MWI does not meet the conditions for Bell's theorem. Bell's theorem cannot be used to say that MWI is incompatible with local realism.

Come again - you better give the detail of that one.

All interpretations, every single one, has the formalism of QM so Bells follows.

Thanks
Bill

 

[atyy]

Come again - you better give the detail of that one.

All interpretations, every single one, has the formalism of QM so Bells follows.

No, because all outcomes occur in MWI.

 

[stevendaryl]

Good point - they are different. But I have to say there is a tendency to call something philosophical BS if it not quite clear - I think I fall for that one often. You shouldn't - but I find it hard not to.

As someone who has dabbled in philosophy and has friends who are professional philosophers, I feel like that is the opposite of the truth. To me, philosophy is about careful reasoning--spelling out what it is that you are assuming, what are the principles of reasoning you are using, what sorts of categories of things you are talking about (material objects versus subjective knowledge versus laws of physics versus mathematical objects, etc.). So when people reject philosophy as useless, it seems to me that they are really saying: I don't need to be careful about my reasoning.

Sometimes, they're right. Physicists, especially the good ones, have an intuitive notion of what constitutes good physics and what constitutes rigorous reasoning, and maybe they think that it's a waste of time and energy to second-guess those intuitions. They could be right.

I guess there is a connection between the careful reasoning aspect of philosophy and the wild speculation caricature that so many people attach to it, and it's this: Most people have common-sensical beliefs about the world, and intuitions about what is likely to be true and what's likely nonsensical fantasy. So hypotheses that are too wild are rejected out of hand without even putting any thought into it. That's probably a good way to be, because why waste time on fantasy when there are real-world things to work on? However, a philosopher who wants to be careful about his reasoning won't be satisfied with the fact that his gut feeling tells him that something is nonsense. He wants to understand that gut feeling, and understand how reliable it is. So a philosopher might very well explore a possibility that your average man on the street would immediately reject as nonsense.

 

[PeterDonis]

it is chaos in the (classical) part of the quantum state that is accessible to measurement devices.

Can you elaborate?

 

[Fra]

The issue I was talking about when I coined "soft contradiction" wasn't really inductive versus deductive. It was really about how we reason with huge numbers (or very tiny numbers). Let me give a toy example: Suppose I say that
...
I feel that the rules of thumb for using QM may be a similar type contradiction. That recipe consists of

1. A rule for how microscopic systems evolve (Schrodinger's equation)
2. A rule for how measurements produce outcomes (Born's rule)

They work very well. However, since measurement devices are themselves quantum systems (even if very complex) and measurements are just ordinary interactions between measurement devices and the systems being measured, these two rules may very well be contradictory. But a detailed analysis of the measuring process as a quantum interaction may infeasible, so actually deriving a contradiction (that everyone would agree was a contradiction) may never happen.

So by "soft contradiction" you mean a contradiction that occur only during certain - possible, but improbable - conditions.
Thus the softly flawed inference is justified?

If so, i would still think that relates to the discussion of general inference. I see your case as a possible kind of rational inference of a deductive rule but in an subjectively probabilistic inductive way, and it´s also something that can be generalized.

A possible driving force for a rational agent to abduct an approximative deductive rule, to base expectations and thus action on, is that of limited resources.

A deductive rule that are right "most of the time", can increase the evolutionary advantage of the agent in competition. As the agent can not store all information, it has not choice but to choose, what to store and how, and what to discard.

This is perfectly rational, but it also brings deep doubts on the timeless and observer invariant character of physical law.

I have also considered that this might even be modeled as an evolving system of axioms, where evolution selects for the consistent systems. An agent is associated with its axioms or assumptions. And different systems of axioms can thus be selected among, in terms of effiency of keeping their host agent in business. Meaning, efficient coding structurs for producing expectations of their environment.

This is also a way to see how deductive systems are emergent, and there is then always an evolutionary argument for WHY these axioms etc. Ie. while axioms in principle are CHOICES, the choices are not coincidental. This would then assume a one-2-one mapping between the axioms in the abstraction, and the physical postualtes which are unavoidably part in the mud of reality. In this view, the axioms are thus simply things that "seem to be true so far" but arent be proved, and they serve the purposes of a efficient betting system, but they can be destroyed/deleted whenever inconsistent evidence arrives.

These ideas gives a new perspecive into the "effectiveness of mathematics". Like Smolin also stated in this papers and talks, the deductive systems are effective precisely because they are limited. But to really appreciate this, you must also understand how and why deductive systems are emergent.

/Fredrik

 

[rubi]

There is nothing contradictory about having two types of time evolution (unitary evolution, collapse). In fact, this happens in classical Newtonian physics as well and we fully understand it. Whenever we have a stochastic description of some perfectly classical system, we have a probability distribution at $t=0$, which is then evolved by a probability conserving time evolution, then collapsed upon measurement, then evolved again, etc. The standard example is Brownian motion, which arises from completely classical equations like $F=ma$. In fact, this scheme applies to all classical probabilistic theories with time evolution, so it would actually be more mysterious if time evolution didn't work analogously in quantum mechanics, which too is probabilistic after all. In classical probability theory, the collapse too isn't an emergent phenomenon that just needs to be derived from a better theory. Instead, it's an elementary ingredient in the theory of stochastic processes, which can't be removed from the theory. And since classical probability theory is a special case of quantum theory (when all observables commute), there must be something within quantum theory that reduces to classical collapse if only commuting observables are considered.

Moreover, the notion of measurement in quantum theory is no less well-defined than in classical probability theory. A measurement in classical probability theory has occured, when the experimenter somehow has learned the measurement result. It's up to the experimenter to decide when this happened. However, the mathematical formulation is perfectly rigorous and if the experimenter knows the time of measurement and the measurement precision very well, then the theory will produce numbers that match the measured data very well.

Also, collapse is not in conflict with relativity. One can also have classical probabilitic theories of classical relativistic systems and of course they too will include collapse.

The only misconception about collapse is that it is often considered to be a type of time evolution. In fact, it's not a type of time evolution. It's just a necessary mathematical ingredient if you want to compute the probability distribution on the space of paths of a stochastic process. So by analogy, it's unlikely a type of time evolution in quantum theory either, because again, in the case of commuting observables, quantum theory reduces to classical probabilty theory.

The real quation about quantum theory is: Why does it make sense to have non-commuting observables in the first place?

 

[Stephen Tashi]

In classical probability theory, the collapse too isn't an emergent phenomenon that just needs to be derived from a better theory. Instead, it's an elementary ingredient in the theory of stochastic processes, which can't be removed from the theory.

A measurement in classical probability theory has occured, when the experimenter somehow has learned the measurement result.

I make the mild objection that "collapse" in the sense of a "realization" of some event in a probability space is not a topic treated by probability theory. It is a topic arising in interpretations of probability theory when it is applied to specific situations. What you are calling "classical probablity theory" is, more precisely, "the classical interpretations used when applying probability theory".

I agree that applications of probability theory to model macroscopic events like coin tosses involves the somewhat mysterious assumption that an event can have a probability of 1/2 of being "possible" and then not happen. (If it didn't happen, why can we assert it was possible?).

It would be interesting to hear opinions about whether there are problems in interpreting the "collapse" of the wave function that are distinct from the elementary metaphysical dilemma of applying probability theory to coin tosses.

One can also have classical probabilistic theories of classical relativistic systems and of course they too will include collapse.

What's an example of that?

 

[rubi]

I make the mild objection that "collapse" in the sense of a "realization" of some event in a probability space is not a topic treated by probability theory. It is a topic arising in interpretations of probability theory when it is applied to specific situations. What you are calling "classical probablity theory" is, more precisely, "the classical interpretations used when applying probability theory".

No, I really mean the rigorous measure theoretical formulation of probability theory and collapse is just the projection of the probability distribution. Of course, nobody in probability theory calls it "collapse". I don't like the word either, because it suggests that it is a physical process, but I just used it in order to stick with the terminology of the thread. Mathematically, it refers to the insertion of the projectors in the construction of probability measures on the space of paths of a stochastic process, i.e. the fact that these probability distributions have the form $UPUPUP \rho_0$, when evaluated on cylindrical sets. ($U$ denotes time evolution, $P$ denotes projection.)

I agree that applications of probability theory to model macroscopic events like coin tosses involves the somewhat mysterious assumption that an event can have a probability of 1/2 of being "possible" and then not happen. (If it didn't happen, why can we assert it was possible?).

I don't really understand how that relates to my post.

What's an example of that?

For example, you could study the Brownian motion of relativistic particles instead of Newtonian particles.

 

[RUTA]

These two options are generally called “psi-epistemic” and “psi-ontic,” respectively, in the foundations community. Psi-epistemic interpretations do not necessarily entail that QM is incomplete, see http://www.ijqf.org/wps/wp-content/uploads/2015/06/IJQF2015v1n3p2.pdf for example. I didn’t have time to read all 8 pp of this thread, so my apologies if something along these lines was already posted.

 

[Stephen Tashi]

No, I really mean the rigorous measure theoretical formulation of probability theory and collapse is just the projection of the probability distribution.

Projection of which probability distribution upon what?

For example, you could study the Brownian motion of relativistic particles instead of Newtonian particles.

I can imagine that as a topic in special relativity.

 

[rubi]

Projection of which probability distribution upon what?

When you have a distribution $\rho(x)$ at time $t$, then if you have gotten to know that $x\in A$, you multiply $\rho(x)$ by the characteristic function $\chi_A(x)$. The projection is $\rho(x)\rightarrow \chi_A(x)\rho(x)$. It's the same thing that happens to the quantum state $\psi(x)$ if you have learned the result of a measurement of the position operator $\hat x$. In quantum theory you have the additional complication that observables might not commute. If you have an observable in a different basis, you have to perform this multiplication in that basis, so for instance a measurement of the momentum $\hat p$ results in a multiplication of the Fourier transformed state $\tilde \psi(p)$ by the characteristic function $\chi_A(p)$. Every projector $\hat P$ in quantum theory is a multiplication operator by some characteristic function in the eigenbasis of the corresponding observable, so for the special case of commuting observables, the mathematics of projections is exactly the same as in classical probability theory.

I can imagine that as a topic in special relativity.

I probabily don't have time for a long discussion about this, but this seems to be a good overview article: https://arxiv.org/abs/0812.1996

 

[vanhees71]

Philosophy need not be speculation. Neither Bohr's nor Einstein's nor Heisenberg's nor Feynman's philosophy was wild speculation.

Well, Einstein was at least understandable in his very clear criticism against QT. As is clear since Bell's work and the confirmation of the violation of the Bell inequality he was wrong, and QT came out right. Bohr has his merits in clearly stating the idea of complementarity and that QT is about what can be prepared and measured in a atomistic world. Unfortunately he was not very clear in his own writings but had to be translated by others into understandable statements. I'm not too keen about Heisenberg. E.g., he didn't get his own finding of the uncertainty principle right and was corrected by Bohr. Also his version of QT, matrix mechanics, had to be clarified in the "Dreimännerarbeit" by him, Bohr, and Jordan.

 

[A. Neumaier]

So whatever is keeping us from making deterministic predictions about the results of quantum experiments, it isn't chaos due to nonlinear dynamics of the quantum state.

However, it is chaos in the (classical) part of the quantum state that is accessible to measurement devices.

Can you elaborate?

What we directly observe in a measurement device are only macroscopic (what I called ''classical'') observables, namely the expectation values of certain smeared field operators. These form a vast minority of all conceivable observables in the conventional QM sense. For example, hydromechanics is derived in this way from quantum field theory. It is well-known that hydromechanics is highly chaotic in spite of the underlying linearity of the Schroedinger equation defining (nonrelativistic) quantum field theory from which hydromechanics is derived. Thus linearity in a very vast Hilbert space is not incompatible with chaos in a much smaller accessible manifold of measurable observables.

 

[A. Neumaier]

I'm not too keen about Heisenberg.

His philosophy (what you called ''wild speculations'') lead him in 1925 to the discovery of the canonical commutation relations.