Einstein's View of Quantum Mechanics

[MathematicalPhysicist]

Of course Zee may write as many things in his confusing book as he likes...

:-D LOL

 

[Zafa Pi]

I wrote, "Wave-particle duality to me is that some measurements of a photon make it seem wave like and other measurements make it seem particle (bullet) like. For instance, the double slit experiments. What's wrong with that? Admittedly, I don't know what it means to say a photon is simultaneously both a wave and a particle."
And you responded:

Did you read the section about it in the myths paper - its in there.

Myths paper? Is there something wrong with what I wrote?

So where do the probabilistic rules of the Copenhagen interpretation come from?'

In QM they come from the definition of a measurement as a random variable (probability of getting an eigenvalue), and in the lab measuring a polarized photon with a polarization analyzer.
Nothing in Copenhagen need be said about what transpires to obtain those values or what evolution the state of the photon goes through to its post measurement state (collapse).
Bohr should have remained silent about an observer and the status of the device, as did Newton when asked how masses pull off their mutual attraction.
It is not testable whether decoherence provides the answer. That the combined system of photon and device satisfy the deterministic unitary evolution of QM is all well and good, yet like a classical coin flip no one can predict the outcome so it is modeled stochastically.

 

[Zafa Pi]

Science is guess, experiment, guess, over and over. If experiment does not say what your guess says - then its wrong. It's that simple. You can have all sorts of opinions such as 'there are still yet unanswered mechanics involved in QM.' - but unless you can put them to the test then its so much hot air.

Even for me this is a bit simplistic. There has been an infinity of bad experiments, if you include the social sciences then the cardinality is c. Recently the Italians showed the relativity guess was wrong, since neutrinos go faster than light. And speaking of infinity,

I saw a proof of it in my undergrad years - but it was hard. Terry Tao has I think a better proof:
https://terrytao.wordpress.com/2008/06/18/the-strong-law-of-large-numbers/

His proof involves infinite sequences of r.v.s, which is what I thought you want to avoid.

 

[bhobba]

A good book on Epstein-Glaser renormalization is G. Scharf, Finite Quantum Electrodynamics, Springer-Verlag, 1989.

That's the book. Thank's for clarifying that - you read in places things like: Scharf presents a textbook for a course on quantum field theory that uses the causal method developed by Stückelberg and Bogoliubov during the 1950s, to make sure that no infinity appears. On refection you realize that's not quite the same thing as no re-normalization - but without thinking you can be fooled.

I also read in Dirac page 311 that he managed to do it without re-normalization in - Lectures On Quantum Field Theory. But he used the Heisenberg picture - and said - I quote - The calculation of the Lamb shift and anomalous magnetic moment are rather complicated. I hate to think of a calculation Dirac would call 'rather complicated' - the mind boggles. Any idea how he avoided it? I suspect he didn't - just had some sleight of hand so speak to circumvent it explicitly - but of course only conjecturing.

I personally prefer the more pragmatic BPHZ renormalization, which also doesn't need a regularization procedure, but reads the Feynman diagrams simply as the integrands of the loop integrals, does the subtractions (at a chosen renormalization scale or in a chosen renormalization scheme) on the level of the integrands and only then performs the integration. Also in this approach only well-defined finite integrals occur, and the idea of the renormalization-scale dependence is built in in a very intuitive way from the beginning. Of course the use of the "smeared operators" in the EG approach also inevitable introduces a scale which has directly the Wilsonian physical meaning.

I have read of others such as what one book called standard re-normalization and it consisted of shuffling infinities around. Didn't understand it, thought it total bunkum, and still think it's bunkum. Then it said there is another, totally equivalent method called BPHZ re-normalization - instantly everything was clear. It's the only method I understand. Others simply leave me cold. Have zero idea how they show its equivalent to the usual re-normalization since to me its totally bogus - but that's the claim.

Thanks
Bill

 

[bhobba]

Myths paper? Is there something wrong with what I wrote?

I think I posted what Copenhagen was about the time of Bohr - but for completeness will do it again:

1. A system is completely described by a wave function ψ, representing an observer's subjective knowledge of the system. (Heisenberg)
2. The description of nature is essentially probabilistic, with the probability of an event related to the square of the amplitude of the wave function related to it. (The Born rule, after Max Born)
3. It is not possible to know the value of all the properties of the system at the same time; those properties that are not known with precision must be described by probabilities. (Heisenberg's uncertainty principle)
4. Matter exhibits a wave–particle duality. An experiment can show the particle-like properties of matter, or the wave-like properties; in some experiments both of these complementary viewpoints must be invoked to explain the results, according to the complementarity principle of Niels Bohr.
5. Measuring devices are essentially classical devices, and measure only classical properties such as position and momentum.
6. The quantum mechanical description of large systems will closely approximate the classical description. (The correspondence principle of Bohr and Heisenberg)

Now let's look specifically at principle 4 - wave-particle duality:
Matter exhibits a wave–particle duality. An experiment can show the particle-like properties of matter, or the wave-like properties; in some experiments both of these complementary viewpoints must be invoked to explain the results, according to the complementarity principle of Niels Bohr.

To examine it more carefully let's see what that paper says:

In introductory textbooks on QM, as well as in popular texts on QM, a conceptually strange character of QM is often verbalized in terms of wave-particle duality. According to this duality, fundamental microscopic objects such as electrons and photons are neither pure particles nor pure waves, but both waves and particles. Or more precisely, in some conditions they behave as waves, while in other conditions they behave as particles. However, in more advanced and technical textbooks on QM, the wave-particle duality is rarely mentioned. Instead, such serious textbooks talk only about waves, i.e., wave functions ψ(x, t). The waves do not need to be plane waves of the form ψ(x, t) = e^i(kx−ωt) but, in general, may have an arbitrary dependence on x and t. At time t, the wave can be said to behave as a particle if, at that time, the wave is localized around a single value of x. In the ideal case (see the equation in the paper - it involves that dreaded Dirac Delta Function) then the position x of the particle has a definite value x The state is the eigenstate of the position operator, with the eigenvalue x. Typically, the wave attains such a localized-particle shape through a wave-function collapse associated with a measurement of a particle position. Moreover, the wave may appear as a point like particle for a long time if the particle position is measured many times in sequence with a small time interval between two measurements. This makes the wave to appear as a classical particle with a trajectory, which occurs, e.g., in cloud chambers. However, the position operator is just one of many (actually, infinitely many) hermitian operators in QM. Each hermitian operator corresponds to an observable, and it is widely accepted (which, as we shall see later, is also one of the myths) that the position operator does not enjoy any privileged role. From that, widely accepted, point of view, there is nothing dual about QM; electrons and photons always behave as waves, while a particle like behavior corresponds only to a special case. In this sense, the wave-particle duality is nothing but a myth. But why then the wave-particle duality is so often mentioned? One reason is philosophical; the word “duality” sounds very “deep” and “mysterious” from a philosophical point of view, and some physicists obviously like it, despite the fact that a dual picture is not supported by the usual technical formulation of QM. Another reason is historical; in early days of QM, it was an experimental fact that electrons and photons sometimes behave as particles and sometimes as waves, so a dual interpretation was perhaps natural at that time when quantum theory was not yet well understood. From above, one may conclude that the notion of “wave-particle duality” should be completely removed from a modern talk on QM. However, this is not necessarily so. Such a concept may still make sense if interpreted in a significantly different way. One way is purely linguistic; it is actually common to say that electrons and photons are “particles”, having in mind that the word “particle” has a very different meaning than the same word in classical physics. In this sense, electrons and photons are both “particles” (because we call them so) and “waves” (because that is what, according to the usual interpretation,they really are). Another meaningful way of retaining the notion of “wave-particle duality” is to understand it as a quantum-classical duality, because each classical theory has the corresponding quantum theory, and vice versa. However, the word “duality” is not the best word for this correspondence, because the corresponding quantum and classical theories do not enjoy the same rights. Instead, the classical theories are merely approximations of the quantum ones.

BTW in the above wave does not mean an actual wave - it is short for wave-function.

Now look again at the wording:
Matter exhibits a wave–particle duality. An experiment can show the particle-like properties of matter, or the wave-like properties; in some experiments both of these complementary viewpoints must be invoked to explain the results, according to the complementarity principle of Niels Bohr.

You are correct in saying sometimes it seems like a particle, and sometimes it seems like a wave. To be even plainer - there is nothing wrong with it at all. But that isn't what the above says - especially the bit: in some experiments both of these complementary viewpoints must be invoked to explain the results. It never needs to be invoked - period. A wave-function is simply the representation of a state in terms of position eigenvectors. That's all that needs to be invoked - nothing at all to do with wave-particle duality - its simply how some results 'seem' that way, as you say but only in very special circumstances. In virtually all circumstances it acts neither like a particle or a wave. Its OK to talk about this stuff in popularization's and/or beginner texts (although I wouldn't) but once one becomes more advanced it confuses more than illuminates because you now deal with all sorts if things - like a particle in a well, the hydrogen atom., the harmonic oscillator - none of which it acts like a particle or a wave. Yet student have been told it does. If you go back and correct that to something like you say - OK - but why bother - simply don't use it in the first place. Its a concept that is simply not needed.

Its not a founding principle of QM (merely what QM says in some special circumstances), its simply a left over form the early days of QM before it was understood as well as it is now, I would argue ever since Dirac published his textbook it should have been banished - but has hung on, and on, and on.

Yes - I agree Bohr should have remained silent about the status of the measuring device - but IMHO Bohr should have remained silent about a lot of things since I think much of what he says confuses rather than illuminates. That's just my view - he obviously was one of the greatest physicists that ever lived and grappled with QM as well as anyone could at the time - except maybe Dirac. But then again for Dirac it was - the math ma'am, just the math. Many do not have that attitude.

Thanks
Bill

 

[bhobba]

Even for me this is a bit simplistic. There has been an infinity of bad experiments, if you include the social sciences then the cardinality is c. Recently the Italians showed the relativity guess was wrong, since neutrinos go faster than light. And speaking of infinity,

Infinity - but I get your drift - and yes you are correct.

His proof involves infinite sequences of r.v.s, which is what I thought you want to avoid.

Yes - of course. Sorry I wasn't clearer - it's just an example of the only one I know - I do not know how to avoid infinite sequences. I will need to study your link to find out how its done.

Thanks
Bill

 

[bhobba]

It is not testable whether decoherence provides the answer. That the combined system of photon and device satisfy the deterministic unitary evolution of QM is all well and good, yet like a classical coin flip no one can predict the outcome so it is modeled stochastically.

Of course it isn't - like all interpretations.

It is testable, and has been tested, that decoherence exists.

Thanks
Bill

 

[Zafa Pi]

You are correct in saying sometimes it seems like a particle, and sometimes it seems like a wave. To be even plainer - there is nothing wrong with it at all. But that isn't what the above says - especially the bit: in some experiments both of these complementary viewpoints must be invoked to explain the results. It never needs to be invoked - period.

And I said, "Wave-particle duality to me is that some measurements of a photon make it seem wave like and other measurements make it seem particle (bullet) like. For instance, the double slit experiments. Admittedly, I don't know what it means to say a photon is simultaneously both a wave and a particle." So we are in agreement, and I agree with the rest of what you said.

When I tell an acquaintance I am interested in QM and they respond with, " Oh yeah, an electron can be a wave and particle at the same time." I come back with: The 1st amendment of the US constitution permits you to say that, and you can also say an electron can be in two places at the same time, and that QM justifies ESP, and the world is flat. But you will not find any of those statements in any QM text that I know of.

I do not know how to avoid infinite sequences. I will need to study your link to find out how its done.

I think Nelson wrote a beautiful book. When some asks me what is probability theory I tell the to read the 1st 8 pages of Nelson. He accomplishes finiteness via an elegant treatment of non-standard analysis.

 

[zonde]

Of course it isn't - like all interpretations.

It is testable, and has been tested, that decoherence exists.

Decoherence as a loss of visibility of interference effect is of course observable effect (usually undesirable).
But when you argue for emergence of classical reality from fundamental wavefuncion using decoherence, it is part of the interpretation.

 

[vanhees71]

Of course it isn't - like all interpretations.

It is testable, and has been tested, that decoherence exists.

Thanks
Bill

I'd put it the other way: To the dismay of quantum-computing afficionados it's quite difficult to avoid decoherence! That's the reason, why almost everything around us at a superficial glance looks as if it were behaving perfectly according to classical physics. Of course, if one knows about the compositeness of matter out of charged quanta, it becomes very clear that already the stability of matter, which only makes our own existence possible in the first place, is only understandable by QT (most importantly the fact that the constituents of matter, quarks and leptons, are fermions and thus behave according to the Pauli exclusion principle and Fermi-Dirac statistsics). The apparent classicality of macroscopic bodies is apparent and due to the fact that the relevant observables for such classical macroscopic systems are very much coarse-grained quantities, averaged over quite "large" (from a microscopic point of view) regions of space and also quite "large" time intervals. That's thanks to a separation of scales, separating the typical length scales and relaxation times of these macroscopic coarse-grained observables on the one hand and their quantum (and thermal) fluctuations on the other hand.

 

[vanhees71]

I wrote, "Wave-particle duality to me is that some measurements of a photon make it seem wave like and other measurements make it seem particle (bullet) like. For instance, the double slit experiments. What's wrong with that? Admittedly, I don't know what it means to say a photon is simultaneously both a wave and a particle."

There's nothing wrong with that, but it is overcomplicating things. Wave-particle duality is a notion of the socalled "old quantum theory" which AFAIK none of the "founding fathers" of QT ever took as "the final word". Einstein always emphasized after his photoelectric paper of 1905 that he cannot stop thinking about the problem (!) of understanding radiation. He even thought it's the far more challenging problem than his General Theory of Relativity.

IMHO these difficulties are overcome with the discovery of modern QT with Born's achievement of the probability interpretation of the quantum state as the key to the resolution of all mindboggling contradictions and inconsistencies of the old wave-particle-duality handwaving. According to moder QT neither a classical particle nor a classical field (or wave) description is a complete picture (in relativistic QT even a wave-mechanics picture a la Schrödinger's non-relativistic QT representation is impossible!). A quantum is a quantum. You cannot explain it by simpler ideas than QT itself. QT is today the fundamental theory of how matter and fundamental interactions are described. It cannot be reduced to something even more fundamental. Maybe that's possible in the future with even better and more fundamental theories, which might be discovered by some genius.

In you photon example, it's clear that the photon is the one freely moving quantum that has the least particle-like properties ever. It doesn't even let's you define a position observable in the strict sense, i.e., said in an operational way, you cannot localize it. All you can do is to calculate the detection probability of the photon at the localization of you detector. That's all that QED provides you, and so far there's no necessity to seek for something else than QED!

 

[bhobba]

I tell the to read the 1st 8 pages of Nelson. He accomplishes finiteness via an elegant treatment of non-standard analysis.

Non Standard Analysis ie ultrafilters and all that, that takes me back. I understood it - with difficulty - the math was HEAVY. The results without the proofs etc inst too bad.

Thanks
Bill

 

[Dale]

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[Evo]

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