Graduate Stephen Weinberg on Understanding Quantum Mechanics

[rubi]

Having this realization in one of these algebras is not enough for constructive QFT. One needs to have it in all, in a compatible way, which is equivalent to have it on unbounded domains.

Nevertheless, you can't specify a QFT by telling me the von Neumann classification of its observable algebra. (And one can even argue that one can measure observables only in bounded regions anyway, so the algebras of interest form a type $III_1$ factor.) A QFT consists of a concrete observable algebra, a concret state on it and a concrete representation of the symmetries as *-automorphisms. Specifying concretel examples is what is difficult.

And having a construction of the vacuum sector of QED in Wightman's sense would not yet be a construction of QED unless one also has constructed the charged sectors that are not described by the Wightman axioms. While they are probably determined by the vacuum sector they are not given by it. One needs a description of the 1-electron states (renormalized, dressed by their electromagnetic field), and these don't exist in the vacuum sector!

Well, Fell's theorem tells us that you cannot physically distinguish any algebraic state from a density matrix in the folium of a/the vacuum state. Hence, it is enough to construct a Wightman QFT and specify states in terms of density matrices. Of course, however, nobody stops you from working in the algebraic framework if you want to.

 

[A. Neumaier]

A QFT consists of a concrete observable algebra, a concrete state on it and a concrete representation of the symmetries as *-automorphisms. Specifying concrete examples is what is difficult.

Sure, but it must be specified on all bounded subsets, and hence everywhere, including the unbounded sets. And the approximations to the charged states guaranteed by Fell's theorem are awkward to work with; they are not needed for mathematical existence but for physical useability.

 

[Bird on a wire]

I am fascinated by this discussion and a somewhat out my depth. Nevertheless, a question: Can emergence as defined by Anderson help ? The quantum states collapse. A single world is what we have, even allowing multiple sensory pictures or for multiple human perceptions of reality.

 

[Demystifier]

Can emergence as defined by Anderson help ? The quantum states collapse.

Anderson-like emergence may help, provided that you know what you are talking about.

 

[Bird on a wire]

Thanks for the reply -I was hoping for something less condescending. There is a lot of critique by better physicists than us that emergence is developing from being the preserve of biologists and philosophers to something that is necessary to explain basic physical phenomena. If, as I do, you need to explain quantum effects to high school students, then the Copenhagen agreement is pretty weak and the standard model of matter sounds like black magic science. Anderson may not be an easy read for someone with a biochemical background, but McGlaughlin explains it well; by always looking for answers by going smaller and smaller, physics is losing the plot.

 

[gmalcolm77]

Since the universe has no outside source of universe (by definition), creating universe is a tall order.

Thats what I thought until I read Alan Guth's 'The Inflationary Universe' and learned about 'false vacuum'.

 

[cosmik debris]

Anderson may not be an easy read for someone with a biochemical background, but McGlaughlin explains it well; by always looking for answers by going smaller and smaller, physics is losing the plot.

I think that many scientists are abandoning the reductionist philosophy. Concepts like duality are replacing it with a more perspective oriented view.

 

[PeterDonis]

I think that many scientists are abandoning the reductionist philosophy.

Can you give some references on which you are basing this opinion?

 

[cosmik debris]

Can you give some references on which you are basing this opinion?

I was expecting this post :-) It is only an opinion gleaned from online lectures, especially by Leonard Susskind who mentions this several times, and by talking to physicists in my own organisation. Of course there is much discussion and there are proponents on both sides but I do sense some dissent in the purely reductionist point of view. The dualists (not the religious kind) seem to be in the String camp, so this may discredit them immediately in some people's eyes. :-)

Cheers

 

[PeterDonis]

The dualists (not the religious kind) seem to be in the String camp,

Then maybe we are using the word "reductionism" to mean different things, because to me string theory is the ultimate in reductionism, since it reduces the number of things in our ontology to one: the string.

 

[cosmik debris]

Then maybe we are using the word "reductionism" to mean different things, because to me string theory is the ultimate in reductionism, since it reduces the number of things in our ontology to one: the string.

Yes, I see your point, I think our terms probably need more definition. I think the String people are referring to the way a simple string can morph to a brane depending on coupling. We're probably off topic and heading for philosophy.

Cheers

 

[Demystifier]

Then maybe we are using the word "reductionism" to mean different things, because to me string theory is the ultimate in reductionism, since it reduces the number of things in our ontology to one: the string.

This is the 20th century string theory, where string really means string. But philosophy of 21th century string theory is different. For instance, according to AdS/CFT duality, string theory (on a certain background) is supposed to be equivalent to a field theory (on the boundary of that background).

 

[PeterDonis]

For instance, according to AdS/CFT duality, string theory (on a certain background) is supposed to be equivalent to a field theory (on the boundary of that background)

So the idea of being able to construct the background (spacetime manifold) from strings (so string theory could be a theory of everything) has gone away? Isn't that a step backwards?

 

[Demystifier]

So the idea of being able to construct the background (spacetime manifold) from strings (so string theory could be a theory of everything) has gone away? Isn't that a step backwards?

Yes, to both questions. But a step backwards is not necessarily bad. Sometimes you need to make a step backwards to continue the walk in the right direction.

 

[PeterDonis]

Yes, to both questions. But a step backwards is not necessarily bad. Sometimes you need to make a step backwards to continue the walk in the right direction.

Understood. I just wanted to make sure I was understanding correctly.

 

[martinbn]

Yes, to both questions. But a step backwards is not necessarily bad. Sometimes you need to make a step backwards to continue the walk in the right direction.

Шаг вперёд, два шага назад.

 

[houlahound]

Шаг вперёд, два шага назад.

Is this unreadable on you guys screens??

 

[martinbn]

It looks fine on my screen. Are you sure its the screen and not the alphabet that's unreadable to you?

 

[houlahound]

Yep alphabet. What does it mean?

 

[Demystifier]

Шаг вперёд, два шага назад.

Are you a Russian? I thought no Russian likes Bourbaki style.
And why do you think that I understand Russian? (Which I do, I've learned it in elementary school in former Yugoslavia.)

 

[Demystifier]

Yep alphabet. What does it mean?

A step forward, two steps back.
In Croatian: Korak napred, dva koraka nazad.

 

[martinbn]

Are you a Russian? I thought no Russian likes Bourbaki style.

No, I am not Russian.

And why do you think that I understand Russian? (Which I do, I've learned it in elementary school in former Yugoslavia.)

Well, you've said before that you are Croatian, and I was guessing that you are old enough to have studied Russian in school.

 

[Demystifier]

No, I am not Russian.

Well, you've said before that you are Croatian, and I was guessing that you are old enough to have studied Russian in school.

Did you also study Russian in school? If so, where are you from?

 

[martinbn]

Did you also study Russian in school? If so, where are you from?

Just enough so I can read maths and physics in Russian, but not enough to communicate or read anything else. I stopped when it was no longer compulsory. I probably can read maths and physics in Croatian. I was born in Bulgaria, but for the most part of my life I have lived in US/UK.

 

[gmalcolm77]

The Copenhagen rules clearly work, so they have to be accepted. But this leaves the task of explaining them by applying the deterministic equation for the evolution of the wavefunction, the Schrödinger equation, to observers and their apparatus.

What do you think of Feynman and his vector analysis of light and matter? Does this explain the wave/particle duality?

 

[bhobba]

What do you think of Feynman and his vector analysis of light and matter? Does this explain the wave/particle duality?

I assume you mean Feynman's sum over histories approach.

OK a few points:

1. There is no such thing as wave/particle duality - it was done away with when Feynman's hero, Dirac, came up with his transformation theory in 1926 - likely sooner. It just hangs about because of the semi-historical approach most beginner and even a few intermediate textbooks take. In advanced textbooks like Ballentine it, correctly, doesn't even get a mention. We all must start somewhere and popularizations and beginner texts often start with this wrong now outdated idea.

2. The sum over history approach is logically equivalent to Diracs transformation theory and both are in many modern textbooks (eg Ballentine) but strictly speaking its a hidden variable interpretation of the QM formalism of Dirac - but of a very novel type.

So the answer to your query is - yes Feynman's approach explains quantum behavior equally as well, or not as well, as ordinary QM depending on your viewpoint.

It's much more modern variant, decoherent histories, of which the sum over histories approach is just one example of a history, is a very well respected modern interpretation that is worthwhile studying - some say its Copenhagen done right - but I won't enter into that argument. Some also say its many worlds without this weird , unnecessary, and silly, many worlds stuff. I happen to agree with that - but here is not the place to discuss it, and its not really science - just a personal opinion. As a counter argument MW is mathematically very beguiling and beautiful - on that score even more so than decoherent histories. Like all interpretations its what you are attracted to. Feynman towards the end of his life was converted to it after attending some lectures by one of its originators, Murray Gell-Mann (they were both at Cal-Tech together). In fact that was why Murray went to Cal-Tech to be with Feynman and they collaborated a lot - to start with. But after a while he became a bit disenchanted with Feynman - not for any scientific reason, just simply his personality grated Murray. Feynman had this habit of promulgating all these anecdotes about himself you can read in Surely Your Joking Mr Feynman:


I love that sort of thing myself, and love the book as well - if you haven't read it please do. But it grated Murray and they drifted apart. Still they had the greatest respect for each other scientifically and would often attend each others lectures.

If you want to find more about Decoherent Histories (also called Consistent Histories), another of its originators, Griffiths, has kindly made his textbook on it available online:
http://quantum.phys.cmu.edu/CQT/index.html

Added Later
Just refreshing my mind about Gell-Mann and his views. My god - he is good:


And so did Feynman:
https://www.math.rutgers.edu/~oldstein/papers/qtwoe/qtwoe.html
The photograph shows Richard Feynman and one of us (Gell-Mann), and the caption describes Gell-Mann as ``one of the most sensible critics of orthodox quantum theory'' and Feynman as ``one of its most sensible defenders.'' In fact, both physicists held very similar views of quantum mechanics. Some months before Feynman's death in 1988, Gell-Mann described to a class at Caltech the status of our work on decoherent histories at that time. Feynman was in attendance, and at the end of the class, he stood up, and some of the students expected an exciting argument. But his comment was, ``I agree with everything you said.''

BTW even though I like Dechoerent Histories its not my favored interpretation but that is a whole new thread. It must be emphasized however, and it is of crucial importance, no interpretation is better than any other. The reason you study interpretations is they all shed some light on what the formalism is saying. For example, and even some textbooks fall into this trap, a superficial reading of QM can easily lead one to think that collapse is part of QM. It isn't - only of some interpretations - but it only becomes clear once you study interpretations with and without it.

Thanks
Bill

 

[vanhees71]

The Copenhagen rules clearly work, so they have to be accepted. But this leaves the task of explaining them by applying the deterministic equation for the evolution of the wavefunction, the Schrödinger equation, to observers and their apparatus.

What do you think of Feynman and his vector analysis of light and matter? Does this explain the wave/particle duality?

Wave-particle duality is very simple to explain: It doesn't exist anymore for nearly 92 years anymore. Since modern QT has been discovered by Heisenberg, Born, Jordan, Schrödinger, and Dirac there's no need for this idea from "old QT" anymore.

How to understand the emergence of a classical world for macroscopic systems is a longer issue. The key concept is "coarse graining".

 

[gmalcolm77]

I assume you mean Feynman's sum over histories approach.

Thanks for the information and references. All good. Malcolm.

 

[vanhees71]

I've no clue what "Feynman's sum over histories approach" might be. So it's for sure not, what I meant in #147.

 

[bhobba]

I've no clue what "Feynman's sum over histories approach" might be. So it's for sure not, what I meant in #147.

Its just another name for the path integral approach eg:
https://en.wikiquote.org/wiki/Path_integral_formulation
Feynman’s so-called path-integral, or sum-over-histories approach to quantum mechanics, set this remarkable concept out as a mathematical procedure. It remained more or less a curiosity for many years, but as physicists pushed quantum mechanics to its limits— applying it to gravitation and even cosmology—so the Feynman approach turned out to offer the best calculational tool for describing a quantum universe. History may well judge that, among his many outstanding contributions to physics, the path-integral formulation of quantum mechanics is the most significant.

Thanks
Bill