I Quantum mechanics is not weird, unless presented as such

[Hornbein]

IMO quantum mechanics is not particularly weird. It is however contradictory to preconceptions brought over from the macro world. What is more, the popular expositions are clogged with the detritus of obsolete interpretations. To me, the big step was realizing that QM was something entirely new and stop trying to make analogies with familiar concepts. It doesn't help that physicists redefine common English words to mean technical terms that are different.

I like Feynman's QED. I'm also tempted to buy Rodney Brooks' "Fields of Color," which is an informal text about the field interpretation. Brooks was one of Schwinger's students and prefers Schwinger's view to that of Feynman. I'll take a look at Hardy's paper. It is (very) helpful to accept that QM is non-local.

 

[TonyS]

Landau points out in vol 3 of the course of theoretical physics, that it is impossible to formulate the basic concepts of quantum mechanics without using classical mechanics (paragraph 1). That, surely, qualifies as weird ?

 

[bhobba]

Landau points out in vol 3 of the course of theoretical physics, that it is impossible to formulate the basic concepts of quantum mechanics without using classical mechanics (paragraph 1). That, surely, qualifies as weird ?

Without wishing to challenge the great Landau have a read of Chapter 3 of Ballentine and see if you agree with what he says.

My view is both QM and Classical Mechanics are based on symmetry - but that is a whole thread in itself. That may be what Landau meant because his beautiful book on Mechanics develops that view ie classical mechanics is based on symmetry:
https://www.amazon.com/dp/0750628960/?tag=pfamazon01-20

Thanks
Bill

 

[stevendaryl]

Without wishing to challenge the great Landau have a read of Chapter 3 of Ballentine and see if you agree with what he says.

My view is both QM and Classical Mechanics are based on symmetry - but that is a whole thread in itself. That may be what Landau meant because his beautiful book on Mechanics develops that view ie classical mechanics is based on symmetry:
https://www.amazon.com/dp/0750628960/?tag=pfamazon01-20

Thanks
Bill

Well, I don't know what Landau meant, but I think you might be talking about something slightly different. You can come up with the Schrodinger equation or (Klein Gordon, or Dirac) based on symmetry, but that's only half of quantum mechanics. The other half is the interpretation of quantum amplitudes as giving (when squared) the probabilities for measurement outcomes. It seems that the notion of a "measurement outcome" depends on a classical notion of a measuring device.

 

[bhobba]

but that's only half of quantum mechanics.

Indeed. But the dynamics is determined by symmetry.

Thanks
Bill

 

[strangerep]

[...] But the dynamics is determined by symmetry.

I would have said the dynamics determines the symmetry. I.e., from the dynamical equations of motion, one can (in principle) find the group which maps solutions among themselves.

E.g., Galilean symmetry is (a subgroup of) what you get from considering the motion of a free particle.

 

[kmm]

I remember how weird it was to me when I learned that, in a vacuum, a feather and hammer would fall at the same rate. It doesn't feel weird anymore. But isn't anything that we haven't experienced and violates our intuition going to feel weird? As you learn more about it, your intuition will change and it will then become less weird.

 

[A. Neumaier]

So doing the same thing twice to totally inanimate objects doesn't always produce the same result. TOTALLY WEIRD.

Casting the same die twice usually gives different results. TOTALLY WEIRD?
No. Every childs understands that.

there is an intermediate violation of conservation of matter-energy

This is a misunderstanding. In general, finding TOTALLY WEIRD facts is a 100% sure sign of having misunderstood something.

The Heisenberg's Uncertainty principle. TOTALLY WEIRD.

One cannot resolve both time and frequency of a (classical) signal with arbitrary precision. TOTALLY WEIRD?
No, every engineer knows. It just shows that when going to extreme scales one has to train one's intuition to understand what is ''natural''.

It is only your understanding, not quantum mechanics, that is TOTALLY WEIRD.

 

[A. Neumaier]

It seems that the notion of a "measurement outcome" depends on a classical notion of a measuring device.

No. A measurement device is simply a large quantum object, and the measurement process can - like anything involving macroscopic quantum objects - be described by quantum statistical mechanics. It is only when starting quantum mechanics that one needs classical props to get an initial understanding. Later, quantum mechanics is completely self-contained.

 

[A. Neumaier]

both QM and Classical Mechanics are based on symmetry

Indeed. This is the topic of my book mentioned in post #2 of this thread.

The infinitesimal generators of a symmetry group form a Lie algebra, and Lie algebras figure everywhere in classical and quantum mechanics - once one learns how to spot them (which takes some practice). The conventional treatments hide this basic structure as long as possible, which I think is a mistake. So one only sees the formulas without the symmetry context.

For example, the cross product is important in physics because it defines the Lie algebra so(3) of infinitesimal rotations in 3-dimensional space. And the canonical commutation relations between position and momentum in quantum mechanics come from the Heisenberg algebra, part of the Lie algebra of infinitesimal generators of the symmetry group of a harmonic oscillator, which is central to a deeper understanding of quantum mechanics.

 

[bhobba]

E.g., Galilean symmetry is (a subgroup of) what you get from considering the motion of a free particle.

Hmmmm. Good point. But treatments I have seen (eg Landau) take the symmetry as given and develop the dynamics.

Thanks
Bill

 

[ShayanJ]

Later, quantum mechanics is completely self-contained.

Do you mean von Neumann's measurement scheme?

 

[samalkhaiat]

Indeed. But the dynamics is determined by symmetry.

Thanks
Bill

The dynamics, i.e., the force field, is determined by local symmetry. Global symmetries such as translation, rotation, etc, have no connection with any particular force law. They do, however, constrain the form of the allowed dynamical laws to a considerable extent, but by no means determine them. This line of thought leads one to think whether it might be possible to impose further stronger type of symmetry constraints so that the forms of the laws are determined. This is, indeed, what Yang and Mills did. Of course, the force (gauge) fields and their interaction must exist in order for certain local symmetries to be true.

 

[A. Neumaier]

Do you mean von Neumann's measurement scheme?

No; this is a caricature of most actual measurements only; it not even covers photodetection - upon detection of a photon, the photon doesn't go into an eigenstate of the nonexistent position operator, but becomes itself nonexistent.

The right key words are POVMs and Lindblad equations on the level of applications, and the projection operator formalism on the level of statistical mechanics.

 

[TonyS]

It seems that the notion of a "measurement outcome" depends on a classical notion of a measuring device.

Yes, this was the aspect of quantum mechanics that Landau was discussing.

 

[stevendaryl]

No. A measurement device is simply a large quantum object, and the measurement process can - like anything involving macroscopic quantum objects - be described by quantum statistical mechanics. It is only when starting quantum mechanics that one needs classical props to get an initial understanding. Later, quantum mechanics is completely self-contained.

I think that there is still a problem. The physical content of QM (and this includes QFT, as well) is that you calculate amplitudes, and these amplitudes give probabilities for observables having particular values. You can abstract away from the measuring devices, and just talk about observables. But I don't see how it changes anything to do that. The problem is that it is inconsistent to assume that all possible observables have values at all times. So for QM to be consistent, there has to be a way to make some observables more equal than others. Bohmian mechanics just picks position as the privileged observable, but other interpretations of quantum mechanics that have definite outcomes allow measurement to single out a preferred observable.

I know that some people believe that decoherence can replace measurement as the basis for choosing a preferred basis. But I don't see how it completely solves the problem.

 

[vanhees71]

Well, I don't know what Landau meant, but I think you might be talking about something slightly different. You can come up with the Schrodinger equation or (Klein Gordon, or Dirac) based on symmetry, but that's only half of quantum mechanics. The other half is the interpretation of quantum amplitudes as giving (when squared) the probabilities for measurement outcomes. It seems that the notion of a "measurement outcome" depends on a classical notion of a measuring device.

Exactly, but what makes it occur weird is just not accepting that this is it. We are so trained in thinking in terms of classical (deterministic) physics that it is hard to accept that nature is inherently probabilistic that we try to find some "metapicture" of the world answering the (in my opinion unscientific) question, what's behind this inherent randomness.

Natural science tells us how nature behaves (or what we can objectively know about its behavior) and needs not agree with the prejudices we have about it.

 

[zonde]

We are so trained in thinking in terms of classical (deterministic) physics that it is hard to accept that nature is inherently probabilistic that we try to find some "metapicture" of the world answering the (in my opinion unscientific) question, what's behind this inherent randomness.

That's not true. It's not hard to accept randomness. Randomness is present everywhere around us in classical world.
What is hard to accept is that certainty can emerge from randomness without some deterministic physical phenomena behind it.

 

[A. Neumaier]

The problem is that it is inconsistent to assume that all possible observables have values at all times.

Well, it is inconsistent to assert that all possible variables have infinitely precise values at all times. But this is an unnecessary, unduly strong assertion!

It is already violated in many situations of daily life, hence constitutes no real problem:

• The position of a soccer player on a football pitch is not defined to a precision better than perhaps 10cm.
• The area of a city is not better defined than to a few significant digits.
• Neither is the position of a piece of scientific equipment.
• Even integers such as the number of people in a room are not always determined to infinite precision (e.g., when a person is standing in the door).
• Neither is the number of clicks of a Geiger counter, during the short times when this number changes.

Thus infinitely precise values at all times for measurable quantities are convenient abstractions of classical physics that have no place in real life.

More importantly, outside classical physics, this assertion is nowhere used in theory or practice! Hence there is no need to assume it, and all problems that are artificially created by ghost stories about Schroedinger cats or Wigner's friend are gone.

One only needs to assume that quantum mechanics predicts expectation values, according to the standard rules. This assumption implies that it also predicts standard deviations, since these can be computed from expectations. A definite prediction is one in which the standard deviation is negligibly small. Just as in any classical stochastic model. Probabilities (of being in a region of space, say) can be defined as expectation values of characteristic functions.

Everything is fully consistent without any reference to classical objects.

To see in more detail that this works perfectly without assuming any quantum-classical correspondence, look at Chapter 10 of my book.

 

[stevendaryl]

Exactly, but what makes it occur weird is just not accepting that this is it. We are so trained in thinking in terms of classical (deterministic) physics that it is hard to accept that nature is inherently probabilistic that we try to find some "metapicture" of the world answering the (in my opinion unscientific) question, what's behind this inherent randomness.
Natural science tells us how nature behaves (or what we can objectively know about its behavior) and needs not agree with the prejudices we have about it.

I don't actually think that it's the randomness that causes so much conceptual difficulties. I think people can get an intuitive grasp on a certain kind of classical randomness by thinking in terms of coin flips: You're driving down a road, and you reach an intersection where you can either turn left or right. So you flip a coin to decide. Even though Newtonian physics would lead us to believe that result of a coin flip is predictable, I don't think that it's too big of a stretch for most people to accept that there can be genuine randomness, and that some processes such as radioactive decay are completely unpredictable.

The part that's mysterious is that QM seems to have a kind of nonlocal randomness. In an EPR-type experiment, it's as if Alice and Bob each flip different coins, and the results are random, but they always get the opposite result. It's the combination of randomness and certainty that is hard to grasp.

 

[vanhees71]

According to classical physics everything is deterministic, and randomness is only due to our inability to precisely know the initial conditions and to write down the exact equations of motion. There's no principle randomness, while quantum randomness is inherent in nature as a fundamental principle. A particle has neither a precisely determined position nor a precisely determined momentum (Heisenberg uncertainty relation), and this is not because we are not able to determine its location in phase space accurate enough but it just isn't possible according to the fundamental postulates for quantum theory. So if QT is a precise description of nature (and all our observations of the real world agrees with this view) then nature is just not deterministic.

 

[stevendaryl]

Well, it is inconsistent to assert that all possible variables have infinitely precise values at all times. But this is an unnecessary, unduly strong assertion!

It is already violated in many situations of daily life, hence constitutes no real problem:

• The position of a soccer player on a football pitch is not defined to a precision better than perhaps 10cm.
• The area of a city is not better defined than to a few significant digits.
• Neither is the position of a piece of scientific equipment.
• Even integers such as the number of people in a room are not always determined to infinite precision (e.g., when a person is standing in the door).
• Neither is the number of clicks of a Geiger counter, during the short times when this number changes.

I don't think that those examples are at all analogous to the incompatibility of observables in QM. In an EPR-type experiment, the startling fact isn't that Alice and Bob's measurements of spin are fuzzy--it's that they are very precise. If Alice measures spin-up along an axis, then Bob will definitely measure spin-down along that axis (in the spin-1/2 case). So appealing to fuzziness or infinite precision doesn't seem to help.

 

[vanhees71]

The part that's mysterious is that QM seems to have a kind of nonlocal randomness. In an EPR-type experiment, it's as if Alice and Bob each flip different coins, and the results are random, but they always get the opposite result. It's the combination of randomness and certainty that is hard to grasp.

The nonlocal EPR-type correlations are only weird, if you do not accept that they are inherent as the result of the preparation of the system and its (unitary) dynamical evolution afterwards. If you accept this, there's nothing weird about it, although the measured local observables at the far distant places of A and B are not determined by this preparation. It's just something very far from our classical notion of the world and not describable by classical deterministic models of the world.

 

[stevendaryl]

I don't think that those examples are at all analogous to the incompatibility of observables in QM. In an EPR-type experiment, the startling fact isn't that Alice and Bob's measurements of spin are fuzzy--it's that they are very precise. If Alice measures spin-up along an axis, then Bob will definitely measure spin-down along that axis (in the spin-1/2 case). So appealing to fuzziness or infinite precision doesn't seem to help.

There certainly can be fuzziness in a spin measurement--if you use a Stern Gerlach device and see if the electron goes left or right, there will be cases where it's not clear which way the electron is deflected. Or there will be times when you just fail to detect the electron. Or there will be times when you detect a stray electron that isn't actually from the source you thought it was from. So there is fuzziness. But that fuzziness doesn't seem to have any role in the violation of Bell's inequality.

 

[stevendaryl]

The nonlocal EPR-type correlations are only weird, if you do not accept that they are inherent as the result of the preparation of the system and its (unitary) dynamical evolution afterwards. If you accept this, there's nothing weird about it...

You seem to be saying that it's not weird, because it's a prediction of QM. That seems to be just defining away the weirdness. (Which is what the "shut up and calculate" interpretation does).

I find it weird for QM to split things into the three parts: (1) Preparation procedures, (2) Unitary evolution, (3) Measurements. At some level, (1) and (3) are just complicated physical processes, so that should be included in (2).

 

[A. Neumaier]

So if QT is a precise description of nature (and all our observations of the real world agrees with this view) then nature is just not deterministic.

''So'' doesn't follow, since there might be an underlying deterministic theory from which quantum mechanics is derived.

Even though I don't believe that Bohmian mechanics is the right mechanism, I do believe that God doesn't play dice.

The main reason is that the notion of inherent randomness is conceptually problematic, and I believe even ill-defined, especially since quantum mechanics obviously applies to unique objects such as the Earth or the Sun.

Whereas the appearance of randomness through chaos and limited knowledge is well-founded and mathematically well-understood, without any of the philosophical problems associated with classical probability.

For a thorough discussion of these problems, see the very informative books by
T.L. Fine,
Theory of probability; an examination of foundations.
Acad. Press, New York 1973.
and
L. Sklar,
Physics and Chance,
Cambridge Univ. Press, Cambridge 1993.

 

[Weddgyr]

I defy anyone to present an explanation of quantum entanglement which is not "weird".

I would actually go further than weird. Quantum entanglement correlations require nothing short of supernatural behaviour, as by Bell's theorem no natural model can explain them. Even non-locality provides no escape if relativity is included.

Supernatural is probably a better word than weird in general. When you have either events which arise from no cause, or objects which have no reality until they are measured, etc, etc, then are you not better off in the long term admitting that such things defy natural explanation instead of endless trying to reinterpret or reframe things. It's an ugly word of course, but the facts around entanglement are harsh.

 

[vanhees71]

Yeah, the shut-up-and-calculate interpretation is the best working one for the introductory QT lecture. Of course, it's worth while to think a bit deeper about the fundamental issues of interpretation, but after a lot of thinking I came back to the shut-up-and-calculate interpretation, now knowing that you can call it a bitbit nicer "minimal statistical interpretation".

 

[A. Neumaier]

So appealing to fuzziness or infinite precision doesn't seem to help.

You are changing the context. I was only discussing your statement

The problem is that it is inconsistent to assume that all possible observables have values at all times.

that you made to justify your conclusion

So for QM to be consistent, there has to be a way to make some observables more equal than others.

I was simply pointing out that you assumed an inconsistency that one does not need to assume in order to give meaning to observables. (And, by silent implication, that therefore your conclusion is not justified.)

 

[stevendaryl]

I find it weird for QM to split things into the three parts: (1) Preparation procedures, (2) Unitary evolution, (3) Measurements. At some level, (1) and (3) are just complicated physical processes, so that should be included in (2).

When people say that the problem in understanding QM is because it is too far removed from human experience and human intuition, I don't agree. To me, what's weird is the parts (1) and (3) above, and what's weird about them is that they seem much too tightly tied to human actions (or to humanly comprehensible actions). Nature does not have preparation procedures and measurements, so it's weird for those to appear in a fundamental theory.