Quantum mechanics is not weird, unless presented as such

[A. Neumaier]

Does quantum mechanics have to be weird?

It sells much better to the general public if it is presented that way, and there is a long history of proceeding that way.

But in fact it is an obstacle for everyone who wants to truly understand quantum mechanics, and to physics students who have to unlearn what they were told as laypersons.

 

[A. Neumaier]

the following gives the modern view based on reasonable assumptions showing QM is not quite as weird as some make out:
http://arxiv.org/pdf/quant-ph/0101012.pdf

The first time I had seen QM derived from reasonable assumptions.

It is only the author's view, not ''the modern view''. It cannot be the truth because quantum mechanics was in operation on Earth (or the universe) long before the existence of preparation and measuring devices (which is assumed by Hardy at the end of p.1) - a true derivation must explain why certain multi-particle systems called measurement devices work as postulated! Also the number N of degrees of freedom, which he takes to be finite throughout, is infinite already for the harmonic oscillator, which makes his ''derivation'' invalid for any real system except those considered in quantum information theory.

Those who want to see that quantum mechanics is not at all weird (when presented in the right way) but very close to classical mechanics should read instead my online book Classical and Quantum Mechanics via Lie algebras. (At least I tried to ensure that nothing weird entered the book.)

 

[bhobba]

Does quantum mechanics have to be weird?

Well that's the question isn't it. I don't think so - but likely for different reasons than you.

My view of the fundamental basis of QM is as per Chapter 2 of Ballentine.

There the same diagram as in Hardy's paper is used to define a quantum state. That's its definition. Hardy shows that and a few other reasonable assumptions leads to the two axioms as found in Ballentine.

Your position is since states must exist independent of such an arrangement it can't be the basis of QM? Have I got that correct? If so then the ensemble interpretation is kaput and I think many would argue that one.

Thanks
Bill

 

[A. Neumaier]

then the ensemble interpretation is kaputt

Why? There is a difference between an interpretation and a derivation.

An interpretation of quantum mechanics relates the formalism to the actual informal practice of using quantum mechanics in our scientific culture.
Thus it may use objects familiar from our culture without having to explain their working. It must only show that there is a consistent relation between theory and practice.
** The minimal statistical interpretation (which you call the ensemble interpretation) does this for predicting the outcome of experiments. It is silent about the interpretation of quantum mechanics in the absence of measurements, and in particular about the interpretation of quantum physics applied to the far past before experiments were possible.
I think that this is a is a serious gap, but since the interpretation is silent here it is not wrong or broken (kaputt), just very incomplete (as it should be for a ''minimal'' interpretation).
** The Copenhagen interpretation that claims that nothing can be asserted in the absence of a measurement is also consistent, but it is part of the reason why quantum mechanics is considered to be weird - a tree fallen in the wood has fallen only after someone has seen it.
** In a many-world interpretation anything goes, and at not even specifiable times the world splits and splits, completely unnoticed by us. This is already weird by conception.
Thus neither interpretation is satisfactory.

A derivation of quantum mechanics must derive quantum mechanics from general assumptions, and hence must be applicable to all of quantum mechanics.
If it cannot derive how QM treats a harmonic oscillator it is worthless.
If it needs measurement devices as inputs it is worthless, too, since it cannot explain why QM worked before the first human measured something.
Hardy claims in his abstract that ''it is shown that quantum theory can be derived from five very reasonable axioms''. But his derivation fails on both accounts. He derives quantum information theory, not quantum mechanics.

 

[bhobba]

A derivation of quantum mechanics must derive quantum mechanics from general assumptions, and hence must be applicable to all of quantum mechanics.

Why can't a derivation that starts from the basis of the ensemble interpretation (ie the statistical theory of observation as per the diagrams in Hardy an Ballentine) be valid?

If it needs measurement devices as inputs it is worthless, too, since it cannot explain why QM worked before the first human measured something.

That I can't follow. A green leaf was green regardless of it is observed to be green - that's more or less the objective view of the world. Its really only philosophers that argue about such. If a state is the equivalence class of preparation procedures it does not mean that preparation devices and intelligent beings have to exist for it to be in such a class. It simply means, conceptually, if it was then that's what you would get.

Thanks
Bill

 

[A. Neumaier]

Why can't a derivation that starts from the basis of the ensemble interpretation (ie the statistical theory of observation as per the diagrams in Hardy an Ballentine) be valid?

Everywhere in logic, if an assumption is invalid, the derivation carries no weight.

The ensemble interpretation derives its assertions using, among others, the assumption that there have been observations.
But there were surely no observations when the Sun formed - which is analyzed in astrophysics as a quantum process.
Moreover, the ensemble had size 1 only, which makes any statistical interpretation meaningless.

Similarly, Hardy specifies as one of his assumption (still before the first axiom) that ''The number of degrees of freedom, K, is defined as the minimum number of probability measurements needed to determine the state''. There is no such minimum number for a harmonic oscillator, since its Hilbert space is infinite-dimensional. How can his derivation account for the building block of all QM (beyond a manipulation of qubits) if it doesn't satisfy his assumptions? It cannot. So it says very little about quantum mechanics. it is only a consistency check on toy problems.

That I can't follow.

[That = ''it cannot explain why QM worked before the first human measured something'']
The derivation of Hardy begins with ''The state associated with a particular preparation is defined to be (that thing represented by) any mathematical object that can be used to determine the probability associated with the outcomes of any measurement that may be performed on a system prepared by the given preparation.''.
If the system was not prepared and no measurement was performed, there was no outcome, hence the state is undefined. You may argue that Hardy gives a counterfactual definition, but this makes a very poor derivation.

 

[bhobba]

Everywhere in logic, if an assumption is invalid, the derivation carries no weight.

There I disagree. Its a conceptualisation that if you did it then that is the equivalence class it belongs to. But on this we will likely not reach agreement.

Thanks
Bill

 

[A. Neumaier]

There I disagree. Its a conceptualisation that if you did it

Oh, so there is no logic involved - where deducing something from a false statement never implies that the conclusion is correct.
It is then just a plausibility argument that the reader has to fill with his own details to make it logically sound.
Calling such an argument a ''derivation'' is inappropriate. At best it is a blueprint for a potential derivation.

 

[Martin0001]

QM weird or not?
Well, the more you think about QM, the more weird it is.
It fills our world with half dead cats and partially pregnant women (until pregnancy test is made).

I was also thinking about American/Russian drone killing Syrian peasant far away, in the desert, with no one there to observe it or finding his body.
The question is: "Did this poor peasant even exist?"

Now more seriously:
How to describe results of famous double slit experiment with better word than "weird"?

I suspect that many peoples work with QM and are getting good results but very few of those are understanding it even partially.

 

[phinds]

Does quantum mechanics have to be weird?

Possibly not to STEM types who are comfortable with math and complicated topics. To the layman, of course it is weird. Both QM (the very small) and cosmology (the very large) are such a great many orders of magnitude outside of the realm of human experience during the millions of years of our evolution that it would be a bit surprising were it otherwise.

 

[fresh_42]

Possibly not to STEM types who are comfortable with math and complicated topics. To the layman, of course it is weird.

This must not be the benchmark. Have you ever seen a quiz show in which the pure remembering of Pythagoras has been called math?
People like Hawking or Kaku do their best to explain physics in a common manner. And in contrast to many they don't insist on their ivory tower. It must be the goal to explain complicated issues such that most people can follow, which IMO requires an education to people so they can follow the explanations without being an expert. The current gap is by far to wide. On the other hand it requires a lot more honesty on the experts' side. Many things are simply unknown. Admit it and don't hide behind mathematical constructions or their failure. I've followed the discussion here about virtual particles and their non-existence. Pair production was one of the first things at all I've read about elementary particles long, long ago. I find they are still a good vehicle for explanations. In mathematics theorems are widely regarded as beautiful if they are simple (to state and to prove). I like to think of physics in a similar way. Let us assume for a second a SUSY will be a feasible way to model a GUT. That wouldn't mean there is an even better way to do so. We just might not haven't found the right tools.

 

[phinds]

This must not be the benchmark ...

I think you totally missed the point of my comment. I am not commenting on helpful teaching styles, just on the fact that QM and cosmology are so WAY far outside of normal human experience that many of the concepts involved will almost of necessity seem weird at first.

 

[fresh_42]

I think you totally missed the point of my comment. I am not commenting on helpful teaching styles, just on the fact that QM and cosmology are so WAY far outside of normal human experience that many of the concepts involved will almost of necessity seem weird at first.

Agreed. Yesterday I've read about our home address in Lanikea. It's so huge and yet a small part. Lifetime of a pion is so short. I bet although we all can handle the number it's not really imaginable. Not to speak about the Planck scale. But these are true for all of us.

 

[phinds]

Agreed. Yesterday I've read about our home address in Lanikea. It's so huge and yet a small part. Lifetime of a pion is so short. I bet although we all can handle the number it's not really imaginable. Not to speak about the Planck scale. But these are true for all of us.

Well, true for all of us, yes, but I think the normal STEM type person, rather that being weirded out by the unfamiliar simply says to him/herself, well this is stuff that other people understand and yeah there's going to be some math involved but that's fine. I can learn this stuff.

 

[fresh_42]

Well, true for all of us, yes, but I think the normal STEM type person, rather that being weirded out by the unfamiliar simply says to him/herself, well this is stuff that other people understand and yeah there's going to be some math involved but that's fine. I can learn this stuff.

I still try to figure out what STEM means. I know what it's about by reading your comments but what exactly?

 

[Greg Bernhardt]

I still try to figure out what STEM means. I know what it's about by reading your comments but what exactly?

STEM is an acronym for the fields of Science, Technology, Engineering and Mathematics

 

[bhobba]

Similarly, Hardy specifies as one of his assumption (still before the first axiom) that ''The number of degrees of freedom, K, is defined as the minimum number of probability measurements needed to determine the state''. There is no such minimum number for a harmonic oscillator, since its Hilbert space is infinite-dimensional. How can his derivation account for the building block of all QM (beyond a manipulation of qubits) if it doesn't satisfy his assumptions? It cannot. So it says very little about quantum mechanics. it is only a consistency check on toy problems.

The issue of state determination for states from infinite dimensional spaces is a problem. Personally I preclude them from discussions of QM foundations and only have finite dimensional states - infinite dimensions are introduced for mathematical convenience. This is the Rigged Hilbert Space approach where the physically realisable states are the space of all vectors of finite dimension but its dual is introduced for convenience.

That's the other insights paper I am thinking of writing - but its cricket and tennis season here in Australia and I am too bleary eyed from staying up late recording and watching it.

Thanks
Bill

 

[fresh_42]

That's the other insights paper I am thinking of writing - but its cricket and tennis season here in Australia and I am too bleary eyed from staying up late recording and watching it.

Tennis, ok, but cricket? Are you that disappointed from losing the final last year that you decided to watch cricket?

However, the roles of finite and infinite vector spaces and their meaning in physics would be interesting to read. Especially if it's about the difference between necessity and convenience and the problem of convergence.

 

[bhobba]

Tennis, ok, but cricket? Are you that disappointed from losing the final last year that you decided to watch cricket?

I am a cricket tragic from way back ever since I saw Jeff Thomson bowl so fast it made the colour drain from batsman's faces:
http://www.dailytelegraph.com.au/sport/cricket/ian-chappell-compares-pace-bowling-enforcers-jeff-thomson-and-mitchell-johnson/story-fni2fnmo-1226834729518
'He unleashed a delivery that didn’t hit a batsman, nor slam into the wicketkeeper’s gloves but it did more psychological damage than any other in a series where many English batsmen were traumatised. The delivery landed mid-pitch and it’s next bounce half-volleyed the sightboard. The batsman saw where the ball landed and the colour immediately drained from his face; that delivery, from takeoff to landing must have traveled at least sixty metres.'

There is nothing like watching the battle between fast bowler and the courage of batsman willing to face up to a cricket ball hurling at you at 100mph.

However, the roles of finite and infinite vector spaces and their meaning in physics would be interesting to read. Especially if it's about the difference between necessity and convenience and the problem of convergence.

Its nothing Earth shattering. All you do is take the space of all vectors of finite dimension. Then you consider its dual as approximations to the vectors of large dimension that are easier to handle mathematically. Its like in solving problems of hammer strikes and such you model it as a Dirac Delta function. It isn't really - but to get a mathematical grip on the problem you model it that way. Convergence is also interesting - you use so called weak convergence that is a whole lot easier - but you need to wait for the paper if you haven't come across it before.

Thanks
Bill

 

[A. Neumaier]

Well, the more you think about QM, the more weird it is.

No, the more I think about quantum mechanics, the less weird it is. I have written a whole book about it, without any weirdness; see post #2.

Quantum mechanics is weird only in the eyes of those who take the talk about it too serious and neglect the formal grounding which contains the real meaning.

 

[A. Neumaier]

How to describe results of famous double slit experiment with better word than "weird"?

There is nothing weird if you interpret it in terms of fields rather than particles. This was already known to Huygens in the 17th century.

Much of the weirdness comes from forcing quantum mechanics into the straightjacket of a particle picture. The particle picture breaks down completely in the microscopic domain, as witnessed by the many weird things it causes.

On the other hand, the field picture remains valid at all length and time scales.

 

[A. Neumaier]

virtual particles and their non-existence. Pair production was

Pair production has nothing to do with virtual particles, except that the pictures look identical.

The right way to understand pair production is via the S-matrix, which gives everything including the associated production rates between real particles. Whereas trying to understand it via virtual particles gives nothing but a picture.

 

[A. Neumaier]

only have finite dimensional states - infinite dimensions are introduced for mathematical convenience

So you say that the harmonic oscillator, multiparticle quantum chemistry, the quantum mechanics of lasers and transistors, and quantum field theory - all of which need an infinite-dimensional Hilbert space - are introduced for mathematical convenience.

Remarkable - I guess this holds for all of science then. At least for all of textbook quantum mechanics before 1990 when quantum information theory started to make some impact.

Finite-dimensional quantum mechanics is extremely limited; for example it accounts for only a tiny fraction of the uses of quantum mechanics in engineering!

the Rigged Hilbert Space approach where the physically realisable states are the space of all vectors of finite dimension but its dual is introduced for convenience.

The dual of a finite-dimensional vector space is again finite-dimensional, and the rigged Hilbert space collapses to the ordinary Hilbert space in this case. The rigged Hilbert space is of use only when the associated Hilbert space is already infinite-dimensional. In this case, the nuclear space at the bottom is also infinite-dimensional. You cannot escape infinite dimensions in quantum mechanics - except in quantum information theory, where nobody needs or uses the rigged Hilbert space.

 

[bhobba]

So you say that the harmonic oscillator, multiparticle quantum chemistry, the quantum mechnaics of lasers and transistors, and quantum field theory - all of which need an infinite-dimensional Hilbert space - are introduced for mathematical convenience.

Sure. Its simply not possible to tell the difference between a state from an infinite dimensional vector space and one of very large but finite dimension. Do you really think actually infinite dimensional spaces are physically realizable?

The dual of a finite-dimensional vector space is again finite-dimensional,

Of course. But the space of all, say for definiteness, row vectors of finite dimension, is infinite dimensional, and so is its dual. The reason its introduced is you assume the physically resizeable states are finite dimensional but perhaps of large dimension. You don't know exactly how large is required so you approximate it by an element from the dual.

Thanks
Bill

 

[martinbn]

Of course. But the space of all, say for definiteness, row vectors of finite dimension, is infinite dimensional, and so is its dual.

Thanks
Bill

I don't understand this. How can the space of row vectors of finite dimension be infinite dimensional?

 

[bhobba]

I don't understand this. How can the space of row vectors of finite dimension be infinite dimensional?

Its the space of ALL row vectors of finite dimension. Pick a finite basis - you will always be able to find a vector in the space of greater dimension.

And to reiterate the idea is simple. If you assume the physically realizable states are finite dimensional but perhaps of a very large but unknown dimension then they can be approximated by elements of the dual. For example can you tell the difference between a state of googleplex dimension and one of infinite dimension?

Thanks
Bill

 

[martinbn]

I see, of all possible dimension.

 

[bhobba]

I see, of all possible dimension.

Exactly.

And it isn't even my idea. I got it from a book I read over 30 years ago now. They called the dual a Dirac space - but it is the only book I have ever seen using that terminology. Its sort of the maximal Rigged Hilbert space.

You usually want to enlarge the test space so they have nice properties eg to open support test functions so its Fourier transform is also in the test space. That means its dual isn't as large. The space in the middle is of course a Hilbert space that is isomorphic to its dual which leads to the well known Gelfland triple.

Thanks
Bill

 

[zonde]

There is nothing weird if you interpret it in terms of fields rather than particles.

Buckyball field is rather weird thing IMO.

 

[A. Neumaier]

Do you really think actually infinite dimensional spaces are physically realizable?

You cannot have canonical commutation rules without infinite dimensions. But these are basic to even elementay quantum mechanics, and were at the very basis of the discovery of the formal core of QM. Any derivation of QM that doesn't account for it has failed to derive the most important ingredient.

By the same token, you'd have to argue that space has to be discrete, velocities no longer make sense, and that the differential calculus and the notion of a continuous symmetry are just mathematical convenience. All physics is gone with a single stoke.

Science depends in a very essential way on these mathematical conveniences. By looking at the history of science one can easily check that any gain in mathematical convenience leads to a gain in insight and predictability.

 

[A. Neumaier]

But the space of all, say for definiteness, row vectors of finite dimension, is infinite dimensional,

But then it is already outside the scope of Hardy's ''derivation'' of QM.

By the way, one of the most important rigged Hilbert spaces is the Gelfand triple consisting of Schwartz space on $R$, the Hilbert space $L^2(R)$, and the space of tempered distributions. It is the rigged Hilbert spaces relevant for the discussion of the Fourier transform. Everything is intrinsically infinite-dimensional, Hardy's theory says nothing at all about it, and your feeble attempt to reduce rigged Hilbert spaces to finite dimensions doesn't apply in a natural way.

 

[bhobba]

But then it is already outside the scope of Hardy's ''derivation'' of QM..

How so? The test space is all finite dimensional

By the way, one of the most important rigged Hilbert spaces is the Gelfand triple consisting of Schwartz space on $R$, the Hilbert space $L^2(R)$, and the space of tempered distributions. It is the rigged Hilbert spaces relevant for the discussion of the Fourier transform. Everything is intrinsically infinite-dimensional, Hardy's theory says nothing at all about it, and your feeble attempt to reduce rigged Hilbert spaces to finite dimensions doesn't apply in a natural way.

Indeed. That's the dual of the space of open support test functions. As I said you enlarge the test space for mathematical convenience - but they can be viewed as approximations to the space of vectors with finite dimension.

Thanks
Bill

 

[A. Neumaier]

Buckyball field is rather weird thing IMO.

Only because you have a too limited concept of a field.

A field is anything that has values at every point in a region of space. Thus the density of water is a field featuring in hydromechanics, and the density of polyethylen fibers is a field featuring in rheology.
They are different fields, as one can see by trying to mix the two.

Polyethylen consists of much larger molecules than a buckyball. Double slit experiments show that buckyball fields are indeed very natural objects.

 

[A. Neumaier]

The test space is all finite dimensional

No. You need to test with all vectors of all dimensions, which form an infinite-dimensional space. (Well, you also need to give a rule for adding vectors of different lenghts, but this was implied throughout your arguments.)

 

[bhobba]

No. You need to test with all vectors of all dimensions, which form an infinite-dimensional space. (Well, you also need to give a rule for adding vectors of differwnt lenghts, but this was implied throughout your aguemnts.)

Yes - but each element of the space is finite dimensional so covered by Hardy's derivation.

Thanks
Bill