Classical and Quantum Mechanics via Lie algebras

Ken G

OK, then that's a detected buckeyball, just like if it hits the detecting screen. You can view it as the end of one experiment. Now what do you do?
That's just an assumption. How do you know you sent it to the emitter? Maybe you just sent a bunch of fields there that you are interpreting as a buckeyball. And when did it actually leave on its way? Maybe there is no specific moment when it left, being a field, there is only a moment when it was detected, being a detection. One must always watch very carefully where you make assumptions that are not in fact in evidence in the experimental setup. So you say, OK, I'll watch that darn buckeyball the whole time, so I'll know everything there is to know about it all the time, but then you are detecting it all the time-- it's not the same single experiment, it's a long string of new experiments, and its ultimate outcome could be a qualitatively different than that one single diffraction experiment we are trying to analyze.

Yes, that's correct, we cannot test that out because the intermediate states are not tested in the experiment you specify, and if you do test those states, it's a different experiment and may come out quite differently in the end. The way I like to put it is, any version of realism must contend with this apparent truth: a question that is not asked in a definitive way can also not be answered in a definitive way (where by "definitive" I mean "empirically demonstrated").
I'm sure that's true, he's a good scientist. But the first goal of any quantum interpretation is to make sure it arrives at all the same predictions as more standard approaches, because the standard approaches have been tested well. If he had a theory that made any testably different predictions, the nature of his rhetoric would be very different. Instead of "look what this way of thinking gives you in terms of descriptive power", it would sound like "do this particular experiment, find this particular result, and give me my Nobel prize."
I don't actually think the United States Academic circle would have any problem with his approach, it's just another interpretation. They might say "oh no, not another interpretation, that's all we need," but the truth is, every interpretation does have its lessons and insights, and I think this one does too. An amazing thing about scientific ontology is that it can be completely different for different scientists, but if the epistemology is agreed on, the science proceeds without much of a hitch. Even quantum mechanics!

rodsika

Why are you making it so difficult and confusing. I'll explain again. if we can
really see the buckyball using electron microscope. Then it's a particle. I
guess the field argument is that an aggregrate of field can be a particle. For
example. If my body atomic component is a field, but my biochemical body is a
whole object. Now. We can treat the buckyball as whole object because we can see
it directly just like we see a blood cell. Say after you view the buckyball
using electron microscope and pick it up with the finger and throw it at the
double slit, it should still appear at the detector. But Dr. Neumaier was
claiming that a double slit just slice up matter. Now you can't say that we
don't know what we are sending, because we have seen the buckyball directly. Or
let's take a more concrete example. Let say you pick up a rat and throw it at
the double slit, the rat should still appear at the detector whole. What Dr.
Neumaier was claiming was that the rat becomes mutilated in a number of pieces
in the detector. Hope you understand what I'm saying or I'll have to rephrase it
again in my reply in case you don't get it.

rodsika

I think I know now what you missed, Ken. Dr. Neumaier claim was that he has solved
the measurement problem. Let's first go to QFT and the measurement problem.

Let me illustrate: According to Mr. Butoxy in a thread in the QM forum:

"In quantum field theory the field does not replace the wave-function.
Wave-functions are still there, and they still collapse.
In elementary quantum mechanics, the dynamical quantity is position. Here, the
quantum mechanical uncertainties are captured by the wave-functions which are
functions of position. Its square magnitude has the interpretation of the
probability of finding the particle at a certain position.

Similarly, in quantum field theory, the dynamical quantity is the value of the
field at every spatial point, called the field configuration. The field
configuration may be a plane-wave, or something static like the electric field
in a capacitor. Here, the quantum mechanical uncertainties are captured by
wave-functions which are functions of field configurations. Its square magnitude
has the interpretation of the probability of finding the field with a certain
field configuration. Note that here, we are potentially talking about waves of
waves.

Wave-functions are still there in quantum field theory. And they collapse when
you make a measurement. The measurement problem is not solved."


Now How does Dr. Neumaier claim differs from the above.
His claim was that the wave function never collapse. His field is like the
classical field. So a molecule treated as field just travel classically and upon
reaching detector, there was no concept of collapse like in QFT.

Well. I guess you like his approach because you also want to make classical even
weak measurements as seen in the other thread. Is this why you are biased
supporting Dr. Neumaier when his conjecture is not even standard QFT as
discussed above?? Please think it clearly. If he was wrong, it doesn't mean you
were wrong too so don't put resistance in falsifying him.

Ken G

I have not seen much of what Dr. Neumaier has claimed, so can't speak to anything but my sense of the general usefulness of his interpretation. I would indeed be skeptical that he has solved the measurement problem, but there may be issues of language here. There are several different aspects to the measurement problem, the "hard" problem is how you get a single outcome from something that the theory treats as a probability amplitude/distribution/expectation, it doesn't really matter which. This is a toughy, even classical physics has not solved it in the context of chaotic systems, because whether or not we can characterize a state as "definite" depends on whether or not we can use the concept for predictions. States that can never be used for prediction, no matter how accurately known they are, can't really be considered "definite", so I think "definite" turns out to be a fuzzy concept. In other words, how nature decides the weather is still a question we have not mastered, so I don't see how interpretations of quantum mechanics could have "solved" that one either. But he may be referring to some particular aspect, some troubling question that he made go away. That wouldn't surprise me at all, if his approach can do that. Maybe he reduced the quantum measurement problem to a classical measurement problem.

The quote by Mr. Butoxy sounded reasonable to me, but he knows more about QFT than I do. The conclusion seems to be that focusing on fields does not eliminate the uncertainty issue and the strangeness of how nature achieves a quasi-definite state from a theory that is enmeshed in uncertainty. But Neumaier does seem to have reduced the nature of the uncertainty to something much more classical, or so it seems to me.
I'm not sure what that means, even the language above of one electron in the detector getting the energy from the field sure sounds like a collapse to me. Any time you have a perceived outcome that is more definite than the ontological status of the agents you used to predict that outcome, you have what might be called a collapse. But I don't know what claims are being made by Mr. Neumaier. Before your issue seemed to be with the ontology of his interpretation itself, not his claims about what one can do with that ontology. Those are two different things.
I don't want to make weak measurements classical, I want to make averages of weak measurements classical, because averages of quantum results are just what classical results are. That doesn't mean there isn't anything that isn't classical, it just means that we can use classical analogs to understand much of what is going on. Dr. Neumaier does seem to be adept at taking that to the max.

It's not at all clear that the thermal interpretation is not standard QFT. Claims about what one can do with it are something different. I don't consider myself to be biased, all I can do is take what limited expertise I have and bring it to bear on my opinions of what is going on in these various interpretations. I think the very first thing to establish is whether the thermal interpretation makes all the same predictions, because if it does, it is by definition an acceptable ontology. Then what claims can be made on that ontology are a very different issue, and would arise next.

rodsika

Ken. Your reply made me realized one thing. When I read this thread previously. I
thought Dr. Neumaier was talking about the direct current (D.C.) source in the
detector where a single electron trigger would use up the energy of the current.
But your reply made me realised it was the energy of the inpinging field itself
where it got the energy. So let me now ask this question directly to him.

Dear Dr. Neumaier.
First question. If a Buckyball composed of 430 atoms hit the detector. You claim
that its field hit all the regions of the detector at once. Now when an electron
is triggered, it gets all the energy of the inpinging field. Now question, the
energy of an inpinging Buckyball is more than the energy of an inpinging
electron. So why is only one electron triggered? Multiple electrons like 4 of
them should be triggered in this manner because the field has enough ionization
energy even for 5 electrons. What is your answer?

Second question. After the Buckyball field energy was absorbed by the electron.
What happens to the Buckyball which lost the energy. What does it mean to have a
field that no longer has energy. Are you saying the Buckyball 430 atoms simply
vanish into thin air after its energy is absorbed by the electron? If not. How
does an energyless 430 atoms field behave versus if it has energy?

Third question. What produced definite outcome which Ken was mentioning above.
Pls. address his comment about it. Apparently quantum and even classical
equations should only be stochastic. There should be no definite outcome unless
human consciousness perceive it (see more details in his message). What is your
solution to it?

Fourth question, I forgot to add this. If all is field and there is no particle. How can the electrons even exist in the detector if there is no particle in the first place?!
Thanks.

rodsika

　
Ken. Let's just focus on the more substantial Photoelectric Effect. Dr. Neumaier
was claiming that Einstein was wrong that a photon was particle. Here he
explains how pure photon field can trigger the detector. I think you are expert
in waves as seen in your weak measurement trajectory defence in the qm forum. So
please comment on the following in his original presentation. Please take time
on it as it is crucial in establishing the decision whether or not to get back
Einstein Nobel Prize for deceiving the world photons are particles. Remember de
Broglie got the idea matter are wave from Einstein conjecture. And wave/particle
duality has confused the world for over a century. Which part of the following
do you agree and not?
http://www.mat.univie.ac.at/~neum/ph...photodetection
------------------------ The photoelectric effect ------------------------
The photoelectric effect http://en.wikipedia.org/wiki/Photoelectric_effect is
usually explained (following Einstein, who received the Nobel price for this
explanation) by saying that a sufficiently energetic photon falling on a
photosensitive substance causes the latter to eject a single electron, which is
then magnified by a photomultiplier to produce a macroscopic and hence
observable effect - the ''click'' of the detector. This is commonly used in
discussions of experiments on entangled photons carried out by Alice and Bob,
who make statistics on clicks to prove or disprove things, or to communicate
secret information.

In the semiclassical picture known to Einstein 1905, currents are produced by
discrete electrons. In 1905, when Einstein proposed his explanation, the
photoelectric effect was a clear indication of the particle nature of light,
since no other model was available that could have explained the process.
Einstein's explanation was so important for the development of the subject that
he got 1921 the Nobel prize for it, a few years before modern quantum mechanics
was born. The modern concept of a photon was created only later (Lewis 1926,
Dirac 1927).

According to today's knowledge, just like Bohr's atomic model, Einstein's
explanation of the photoeffect is too simplistic, and is not conclusive. Now,
100 years later, his picture is known to be approximate only, and that currents
in metals are in fact produced by the continuous electron fields of QED.
Discrete semiclassical particles are just very rough approximations.

Indeed, the argument of Einstein put forward for the discrete nature of
radiation is spurious, since it ignores the quantum nature of the detector
(which was of course completely unknown at the time). As one can read in the
standard reference for quantum optics, L. Mandel and E. Wolf, Optical Coherence
and Quantum Optics, Cambridge University Press, 1995. the clicks in a photon
detector are an artifact of photodetection caused by the quantum nature of
matter, rather than proof of single photons arriving.

Mandel and Wolf write (on p.629, in the context of localizing photons), about
the temptation to associate with the clicks of a photodetector a concept of
photon particles: ''Nevertheless, the temptation to interpret the electronic
signal registered by a photodetector as due to a photon that is localized in
some sense is quite strong.'' The wording suggests that one should resist the
temptation, although this advice is usually not heeded. However, the advice is
sound since a photodetector clicks even when it detects only classical light!
This follows from the standard analysis of a photodetector, which treats the
light classically and only quantizes the detector.

Sections 9.1-9.5 show that the electron field responds to a classical external
electromagnetic radiation field by emitting electrons according to Poisson-law
probabilities, very much like that interpreted by Einstein in terms of light
particles. Thus the quantum detector produces discrete Poisson-distributed
clicks, although the source is completely continuous, and there are no photons
at all in the quantum mechanical model. The state space of this quantum system
consists of multi-electron states only. So here the multi-electron system
(followed by a macroscopic decoherence process that leads to the multiple dot
localization of the emitted electron field) is responsible for the creation of
the dot pattern. This proves that the clicks cannot be taken to be a proof of
the existence of photons.

Note that initially, only single photoelectrons are emitted, which would leave
no experimental trace without being magnified. A macroscopic magnification is
needed to make the photoelectrons observable. In a photodetector, a
photomultiplier is used to produce an observable current. In the case of
detection by a photographic plate, the detector is a photoemulsion, and the
photoelectrons are magnified via a chemical reaction that produces tiny dots
whose density is proportional to the incident intensity of the electromagnetic
radiation.

(The table of contents of the book by Mandel & Wolf is at
http://www.cambridge.org:80/servlet/...TEM_ENT_ID=233 If you are new to quantum
optics and want to have a shortcut through this book of over 1100 pages: At
first, you need enough classical background. To update your math, read or review
Sections 2.1-2.3 and 3.1 and go back to the pieces from Chapter 1 that you need
to make sense of these sections. Classical physics in a simplified setting
without polarization starts in Chapter 4 and 5, where you need at first only
4.1-4.3 and 5.6-5.7 -- again, reading omitted stuff you need for understanding
that as you go along. Full classical electromagnetism is covered in Chapters
6-8. You need 6.1-6.5. The quantum part starts in Chapter 9. You'd read 9.1-9.5,
10.1-10.5, 10.9, 10.10, 11.1-8, 11.13, 12.1-12.4, 12.10, 13.1-13.3, 14.1-14.6.,
15.1-3, 18.1-4, 20.1-6, 22.4. Then you have an overview over the central part of
quantum optics, and are well prepared to start a second, thorough reading of the
whole book.)

Section 12.11 is about the problems with photon position, and that there is no
associated operator, but only a POVM. It is in this section that they made the
remark referred to above. Sections 14.1-14.5 show that the semiclassical picture
of Chapter 9 holds with small corrections also in the quantum case, and is
virtually unaltered in case of coherent light.

We conclude that the discreteness of the clicks must be caused by the quantum
nature of matter, since there is nothing discrete in an incident classical
external radiation field.

I discussed the situation in some more detail in a public lecture given in 2008,
http://www.mat.univie.ac.at/~neum/ms/lightslides.pdf See Section 3 (pp.35-44);
names in smallcaps are accompanied by references, given at the end of the
slides.

Note that this holds even for very faint light. In deep-field astronomy,
'photographs' of perhaps several billion light years distant astronomical
objects using CCD detectors is routine. The time interval between individual
events on a CCD array of a few cm^2 can be several minutes or more in some
cases.

To explain the image, it is enough that the detector elements on the plate
respond locally according to a Poisson process with probability rate determined
by the incident energy density. This means it fires randomly at the rate
determined at each moment from the incident faint field. No memory is needed,
and energy loss is irrelevant (except for the efficiency of the process). The
local detector elements will respond independently and rarely but occasionally,
and waiting long enough will precisely reproduce the averaged intensity profile
- the goal of the imaging.

It doesn't make sense to somehow count photons classically and pretend that each
of the myriads of photons created in a distant star is a spherical wave
spreading out through space to be ''collapsed'' when entering the CCD detector.
The detector doesn't see the myriads of these extremely faint spherical waves
and decides to collapse just one of them. Instead, it ''sees'' the energy
density; according to its value, it feels more or less ''motivated'' to respond,
resulting in a Poisson statistics. The reason is that in QED, the local mean
energy density is an observable field, whereas the concept of a photon number
density cannot even be meaningfully defined.

　
　　

Ken G

That is certainly a pretty radical stance. Here is my take on it-- I don't have time to study the situation exhaustively, but my initial impression is that Dr. Neumaier is doing two different things that should be analyzed separately:
1) he is offering an alternative way to think about photons and radiation
2) he is critiquing the standard way (Einstein's) of thinking about photons.
As for point #1, I can see nothing overtly wrong in what he is saying. This gets back to my earlier point about the non-uniqueness of the equivalent ways we can translate the action of a theory into descriptive expressions (like photon) to help us successfully execute that theory. All too often, when we find a successful language for executing a theory, we think we have "found the truth the theory implies", but this is poor logic. To conclude that, we need to show that our language is unique, and that is often not true in the least. I suspect this is yet another example of that phenomenon.

If I'm right, then Dr. Neumaier's language is fully equivalent in terms of the execution of a theory into making testable predictions, though it sounds ontologically vastly different. This is actually not surprising, I see it all the time. As a particularly stark example, you may have been told that forces produce acceleration, like that was an ontologically true description. Imagine I said no, there's no such thing as forces, instead particles move so as to minimize a mathematical quantity, dependent on energy considerations, called the "action", you might say "get out, how can you say there is no such thing as forces, was Newton an idiot?" But you see, my statement is exactly equivalent to Newton's, even though the ontology sounds totally different. This really happens all the time, we should neither be bothered by it, nor take it too seriously. We shouldn't conclude that the previous ontology was wrong or its proponents were deluded fools. Instead, we just ask: if this new ontology is indeed equivalent, what new insights does it offer? No fuss, no muss.

About the only claim he makes that raises a red flag for me is: "The reason is that in QED, the local mean energy density is an observable field, whereas the concept of a photon number density cannot even be meaningfully defined. " I'm not sure what he means here, the mathematics of creation and annihilation operators is often regarded ontologically as being about discrete photons, and is very useful for executing the theory. He may mean something else by not being meaningfully defined though, I just don't know enough about it. Anyway, field theorists are quite comfortable with the photon concept and will be in no rush to toss it overboard, but that doesn't make Dr. Neumaier wrong when he claims certain advantages for his way of thinking. The key point is, it's just not an either/or situation, better is to be conversant in all the perspectives-- you never know where the next insight will come from. I'm just very suspicious of using science to arrive at some objectively true ontology, in my view all scientific theories are effective theories, and nonunique ontologies are just toys we play with.

my_wan

Perhaps Neumaier can comment on this to clear up some possible issues and correct anything I might get wrong.

It appears to me part of the issue with getting the interpretive content of the description is in how Gibbs ensembles are embedded in the QM wavefunction in such a way that it makes it look as if the wave structure and the wavefunction is the same thing. On one hand the thermal interpretation is taking the wave structure seriously, where particles are localized waves, though a wave does not have to be localized in all cases. On the other hand the wavefunction does not just define the state of the wave, it defines an ensemble of all possible states the wave can potentially be in given the constraints. I will again go to a very rough classical analog to describe the significance of ensembles in the QM wavefunction.

A Gibbs ensemble when used to describe a classical event such as a dice roll conceptually involves making many mental copies of that dice and treating the dice as if it was all of those copies at once. Then the state with the highest probability is the state that occurs most often when you role the dice. Fair dice presumably being equal probabilities for each state.

Now imagine a wave (water) tank where you are creating solitons on one side and seeing where they hit on the other. Each soliton will have a 'fairly' definite position and trajectory for each one created. To define a theory of where it is likely going to hit, on the far side of the tank, what that one soliton does is not very useful. So you create a wavefunction that includes not just what a particular wave does, but a probability density that defines the relative probabilities for countless many solitons. The wavefunction defining this probability density has the same basic structure as the wavefunction defining a particular wave. Because even a particular wave has similar density distribution on the surface as the probability density describes for the ensemble. So it gives the false impression that if the wavefunction is not real then the wave must not be real, leading back to the particle picture of matter. It is also this ensemble of "probable" waves that appears to collapse when in this picture the wave is still there, it just showed which of the Gibbs ensembles the actual wave state possessed. It was and remains a wave the whole time, without collapse. You now just have to throw away all those wave ensembles, like the dice rolls that did not happen, and calling it a wavefunction collapse.

In this way all the wave mechanics of standard QM is ontologically maintained while the wavefunction is no more real than a dice that lands on countless many sides at once. Does this make sense or need any corrections?

A. Neumaier

Yes. That's why I am stressing that quantum mechanics is nearly classical if viewed in the right way.

A. Neumaier

It damages the slit, and the experiment is over.

A. Neumaier

I never said this. The field behaves like a water wave when it goes through a slit - it changes it shape and gradually expands. Nowhere any fragments.

A. Neumaier

The field remains a field even when some collapse of the wave function happens. For the field is about expectation values, and these don't chnge their natture when the wave function collapses, or rather when the density matrix decoheres under the influence of the environment.

Thus the question of a collapse simply becomes irrelevant to the interpretation.

A. Neumaier

I was saying the stuff about a single electron for the case when an electron was sent through the slit.
For a buckyball, it is less clear what precisely happens. One would have to do a quantum statistical mechnaics calculation to find out what really happens. (This is like with other experiments. in simple cases, one can analyze the situation without calculation based on known principles, in more complex cases one needs to go through the calculations.) I might do some such calculations at some time but they are time-consuming, and currently I don't have the time for that.
The buckyball is not only energy. it also carries a carbon field. This is initially distributed along the detector, and presumably concentrates after a short time at a random position.
Even classical stochastic equations can be used to predict phenomena with good acuracy, if the noise is small, although there are no definite (i.e., inifinitely precise) results.

Ken G

A crystal clear examination of what are essential differences between the two, and what can be viewed as similarities, would be a very worthwhile program indeed.

A. Neumaier

　
You exaggerate. Einstein's picture has some validity, else it wouldn't have be that useful.
But that picture is not _needed_ to explain the photo effect. Thus ifr one wants to dispense with the particle picture in order to have a more sensible ontological picture of the world, one can do so without harm.

A. Neumaier

Your statement does not contradict mine. Photons have welldefined momentum states, to which the creation-annihilation picture applies, but this is not enough to guarantee a photon density.
This does not exist because of the lack of a position operator.

A. Neumaier

[QUOTE=my_wan;3369645]
It appears to me part of the issue with getting the interpretive content of the description is in how Gibbs ensembles are embedded in the QM wavefunction in such a way that it makes it look as if the wave structure and the wavefunction is the same thing. On one hand the thermal interpretation is taking the wave structure seriously, where particles are localized waves, though a wave does not have to be localized in all cases. On the other hand the wavefunction does not just define the state of the wave, it defines an ensemble of all possible states the wave can potentially be in given the constraints. I will again go to a very rough classical analog to describe the significance of ensembles in the QM wavefunction.[-QUOTE]
There are two kinds of wavesß

1. Those in configuation space, the wave functions. These are just computational tools to work out the predictions of QM. These may collapse under the influence of the environment, but in the thermal interpretation this is nearly irrelevant, just contributing a little to dissipation

2. Those in real, 3D space. Here quantum fields are located, and these are ontologically relevant fields in the thermal interpretation.