Classical and Quantum Mechanics via Lie algebras

[Ken G]

I think I know now what you missed, Ken. Dr. Neumaier claim was that he has solved
the measurement problem.

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.

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.

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.

Well. I guess you like his approach because you also want to make classical even
weak measurements as seen in the other thread.

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.

Is this why you are biased
supporting Dr. Neumaier when his conjecture is not even standard QFT as
discussed above??

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]

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.

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 realized 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://arnold-neumaier.at/physfaq/topics/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://arnold-neumaier.at/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]

　
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.

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]

I've been trying hard to draw the parallels between the quantum and classical pictures. I'm finding many people are unwilling to consider those kinds of parallels-- I even had one person tell me I was embarrassing myself by trying to point them out! There's a kind of myth that "quantum is quantum and classical is classical and never the twain shall meet." I'm not sure where that thinking comes from, it seems to completely ignore the correspondence principle, but maybe it's because educators have had to stress "quantum weirdness" in order to get students interested in that nether world. If so, they may have succeeded too well!

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

 

[A. Neumaier]

if you sent a cow to the
double slit. It slits the cow into dozens of pieces.

It damages the slit, and the experiment is over.

 

[A. Neumaier]

Dr. Neumaier said that after the buckyball was emitted. The
slits slit the field to various fragments and these hit the detector in all
regions.

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]

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. .

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]

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?

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.

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.

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.

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.

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]

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

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]

　
Ken. Let's just focus on the more substantial Photoelectric Effect. Dr. Neumaier
was claiming that Einstein was wrong that a photon was particle.

　
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]

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.

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]

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.

 

[A. Neumaier]

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.

On the level of wave functions, there are huge differences, since these have no classical equivalent. On the level of density matrices, or in the Heisenberg picture, the differences are marginal (more precisely of the order of the Planck constant. My book

Arnold Neumaier and Dennis Westra,
Classical and Quantum Mechanics via Lie algebras,
2008, 2011. http://lanl.arxiv.org/abs/0810.1019

shows how similar the classical and the quantum worlds are when consistently and from the start treated without significant reference to wave functions.

 

[Ken G]

Then the program has already been carried out, and in considerable formal rigor. That's impressive, I hope I get the opportunity to learn what's in there.

 

[rodsika]

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.

Ken and Dr. Neumaier (herein called Arnold for short with no disrespect...
to put Ken and Arnold in equal footing without biased). Let's focus on this
collapse issue as it is the heart and soul of the measurement problem.

In decoherence. Born rule is not applied. The system coupling with environment
just puts it in mixed state. So we shouldn't technically call it collapse.
Collapse only occur when one eigenvalue is chosen.

Now in pure particle ontology as in vintage QM, where particle positions are the
primary issues. It is difficult how to imagine a single particle can interfere
by itself in the double slit. So we use the concept of superpositon and
collapse. But in QFT, there is no position, in QFT wave function amplitudes.
Its square magnitude has the interpretation of the
probability of finding the field with a certain field configuration. Now what
did Arnold do. He removes the idea of pure collapse. That is. In his view.

collapse = restricting to a subensemble
= replacing a probability by a conditional probability.

Is this valid at all? The following is Arnold complete statement about Collapse
and Quantum Measurement. It is just brief so please give it a thought Ken. How
do you think Arnold deal with definite outcome? You argued very strong in the
other thread that definite outcome can only be perceived by conscious being who
can make a record of the definite outcome because it is not in the equations.
What is the equivalent of definite outcome in the following. Or did it just go
away since the quantum field is the ontology and wave function collapse doesn't
even exist (hence nothing to worry about definite outcomes)? 　　

http://arnold-neumaier.at/physfaq/topics/collapse

Collapse and quantum measurement
--------------------------------
Experiments involving measurements are oftern interpreted in terms of
a collapse of the state of the system. However, they can be interpreted
without any collapse.

In particular, in photon experiments, the collapse interpretation is
never applicable since a measured photon stops existing rather than
collapsing into an eigenstate of the measured operator.

Instead, a collapse is just a change of the description level.
The moment one changes the description level, everything changes
everywhere instantaeously, without making the slightest change to
the underlying reality.

One has the same instantaneous change already on the classical level.
We can calculate the probability that a star is of a certain kind.
This probability depends, however, on what we consider to be the
relevant ensemble. If we change the ensemble by restricting to a
subensemble, the probability may change. And it does so throughout
the universe, instantaneously, just by making our subjective decision
to consider only the subensemble instead of the whole ensemble.
This is nothing special to physics, it is an experience of everyday
life. It is as simple as this:

(*) collapse = restricting to a subensemble
= replacing a probability by a conditional probability.

The mathematical justification of the equality (*) is easy to see
by considering only commuting observables, in which case quantum
mechanics reduces to classical probability theory. Now measure
just one of a complete set of commuting observables, and interpret
the resulting formula classically.

It is up to the subject making a study when she will switch
to the conditional probability, and has nothing to do with her
knowledge. But once the ensemble is replaced by a subensemble
(by conditioning with respect to a partial observation on Ann's
side of the system), the view changes instantly, since it happens
only in the subjects head -- Ann decided to remodel the situation,
and so it changes accordingly.

But as long as one keeps fixed what is the system considered, we
have objective physics to tell us what happens with the system,
as far as it can be told at all.
　
The objective state of a physical system is a state of the total
system considered, and not one of its many partial traces,
which only give the perspectives of local observers.
Of course, the partial trace is observer-dependent. The dependence
comes from the freedom of a subject to choose what it will consider
as the system.

This is the _only_ subjectivist element in physics. It is already
present in classical physics, where changing the (subjective)
coordinate system changes everything. There we are trained to know
that these subjective elements are to be ignored, and that what
counts is just the coordinate-independent part of physics.

We know that ordinary optical perspective is something subjective,
and we correct for that by developing a more general objective
framework of space in which each perspective has its place.
In this objective framework, perspective is seen to reduce space by
one dimension, hence hiding information that objectively exists and
can be modeled but is ignored by the view.

This reduction of a scene by viewing it in a particular perspective
is in complete analogy to the reduction in quantum mechanics, where
the choice of which subsystem to consider affects the resulting view.
　　
　

 

[Ken G]

In decoherence. Born rule is not applied. The system coupling with environment
just puts it in mixed state. So we shouldn't technically call it collapse.
Collapse only occur when one eigenvalue is chosen.

Yes, to me "collapse" is not a physical thing happening to the system, it is a change in our description of the reality there, so I agree with much of Arnold's language there (I've even used the "collapse is a change in someone's head, not a change in a physical system" idea myself), but there is still a key question: which outcome? The "problem of collapse", then, is to me not "what physically happened to the system and how did it physically happen", but rather, "whatever caused our information about the system to change to outcome X instead of outcome Y." I'm not sure that question goes away when we view each observer as holding only a piece of the full objective reality, as we would in relativity, because we have no access to any observers who get outcome Y. In other words, the problem is somewhat the opposite as in relativity-- it relativity, our illusion is that we know more about reality than we can actually know, we think our time coordinate between two events separated from us is physically meaningful, but something less than that is actually physically meaningful. The problem with collapse is that something more than what we perceive appears to be the objective reality, or at least it would help our formal theories if that were true.

But Arnold raises the interesting example of perspective, where each observer sees a 2D window of a 3d objective reality. That's much more like the situation in quantum mechanics-- if we trust our perceptions, we only get part of the objective reality, we have to add something to it, using other observers, to get the full picture. But the disconnect I see is that in the perspective analogy, we have access to those other observers. We can ask them what they see. What is the analog to that in the collapse case? On the surface, it sounds like Arnold is saying that collapse is like the many-worlds interpretation, with the added element that the outcome we perceive is due to some choice we've made about what we regard as the system, or some choice that was thrust upon us if we did not make it consciously. But again, the real sticky part is that we have no access to the other observers who get outcome Y. This makes sense in many-worlds, since they are incoherent, but it's a stretch.

Let's imagine a many-worlds situation where somehow we can communicate with those other worlds. We ask those other observers what they see, and use their testimony to "flesh out" the full unitary state, the non-unitary "collapse" being just our own perspective on the situation. Now that would resolve everything, the interpretation of measurement would then be perfectly obvious. But why is that kind of communication impossible? What is that fact telling us that isn't there in the "perspective" analogy? That's what I see as the "collapse problem", and it doesn't seem to have gone away, though I'm not sure I'm understanding everything Arnold is saying here.

(ETA: cut out accidental inclusion.)

 

[rodsika]

　

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.

Arnold Thermal Interpretation has prediction that differs from the Standard
Interpretation. For example. Since the electrons existing already in the
detector are triggered by the impinging field and get its energy from the field.
One can design the source to send field with energy magnitude enough to trigger
more than than one electron in the detector. Can anyone propose this? First can
we create a buckyball (or using other molecules or objects) experiment such that
we know exactly how many are sent out and detected? Because if it is not equal
and let's say 5 sources sent out equals to 20 hits in the detector. Then Arnold
is right. But if 5 source equal 5 hits even though the energy of one source
field is enough to trigger a number of electrons, then Arnold is wrong. Let's
call this test Neumaier's Inequality (counterpart of Bell's Inequality.. lol).
If Neumaier's Inequality was violated. Then Neumaier is right and he gets a
ticket to Stockholm. The person who proposed the right experiment also gets
another ticket! Anyone want to try?

 

[A. Neumaier]

　
Arnold Thermal Interpretation has prediction that differs from the Standard
Interpretation.

No. It is only a new and more rational way to talk about the formal content of quantum mechanics. That's why it is called an interpretation and not a theory. Since all predictions come from the formal machinery, different ways of talking about the latter cannot change the predictive content.

 

[A. Neumaier]

In decoherence. Born rule is not applied. The system coupling with environment
just puts it in mixed state. So we shouldn't technically call it collapse.
Collapse only occur when one eigenvalue is chosen.

Collapse occurs if and only if one chooses to ignore the environment in favor of a simpler description of the problem. Thus it is determined by the simpler, but more approximate framework chosen.
If the observer chooses the no collapse version, he must add the whole environment to the quantum system - exactly (else the neglected part constitutes a new environment). Thus the observer decides upon what to regard as the system to work with, and this choice triggers a (usually partial) collapse, due to everything neglected.

But in QFT, there is no position,

In QFT, there is a concept of position, but as a argument of the field operators, on the same footing as time. But the field has no p[osition - it has values at each position. Particle-like objects are portions of the field in which these field values are nonzero only in a small neighborhood of a particular position.

in QFT wave function amplitudes.
Its square magnitude has the interpretation of the
probability of finding the field with a certain field configuration.

Yes. And the observation of this is always partial only. Hence the wave function never collapses fully. Thus collapse becomes a marginal phenomenon in QFT.

In his view.

collapse = restricting to a subensemble
= replacing a probability by a conditional probability.

Yes. By focussing on a subsystem of the full system (which included the environment), the system is conditioned on the state of the environement (which contains the information about measurement).

Thus the probabilites are now conditioned by the observations. This is the same mechanism in classical and in quantum mechanics.

 

[A. Neumaier]

But Arnold raises the interesting example of perspective, where each observer sees a 2D window of a 3d objective reality. That's much more like the situation in quantum mechanics-- if we trust our perceptions, we only get part of the objective reality, we have to add something to it, using other observers, to get the full picture. But the disconnect I see is that in the perspective analogy, we have access to those other observers. We can ask them what they see. What is the analog to that in the collapse case? On the surface, it sounds like Arnold is saying that collapse is like the many-worlds interpretation,

No. In the thermal interpretation, there is only one world. This one world is enough to explain everything that happens.

Collapse is the effect of ignoring the details of the interaction with the environment, keeping only an approximate summary in the form of a history of measurements and a POVM for the average influence of the environment upon measuring.

Even in the analogy with the 2D perspecticve, one doesn't necessarily need other observers, since one notices soon that the different views the single observer gets at different times can be coherently realted only by assuming a third dimension. Once this is realized, moving around is enough to gather rthe information needed to complete the 3D picture.

Therefore, in the thermal interpretation, there is no place anymore for mystery.

 

[rodsika]

No. It is only a new and more rational way to talk about the formal content of quantum mechanics. That's why it is called an interpretation and not a theory. Since all predictions come from the formal machinery, different ways of talking about the latter cannot change the predictive content.

But your Interpretation differs from the Standard in its prediction.
In your Interpretation. There is no Collapse. And the behavior in the double
slits can vary. For example. In Standard QM. When a Buckyball is emitted, always
one hit would be detected. But in your case, since it doesn't collapse and it is
alway a field, the energy of the buckyball is enough to trigger 5 or even 10
electrons at the detector. So your one Buckyball emission would result in 10 or
more hits due to the energy of the Buckyball field much more than an electron.
Here your interpretion obviously didn't have the same prediction as QM.

 

[my_wan]

But your Interpretation differs from the Standard in its prediction.
In your Interpretation. There is no Collapse. And the behavior in the double
slits can vary. For example. In Standard QM. When a Buckyball is emitted, always
one hit would be detected. But in your case, since it doesn't collapse and it is
alway a field, the energy of the buckyball is enough to trigger 5 or even 10
electrons at the detector. So your one Buckyball emission would result in 10 or
more hits due to the energy of the Buckyball field much more than an electron.
Here your interpretion obviously didn't have the same prediction as QM.

Collapse is NOT a prediction of QM. It is an interpretation of QM. In requires you to assume the wavefunction is physically real. Is the configuration space of a dice roll real. Does the fact that it is not real make the dice not real?

 

[Ken G]

No. In the thermal interpretation, there is only one world. This one world is enough to explain everything that happens.

In a restricted way only. Because there is no deterministic explanation that leads to the actual outcome, that's my point-- you have given a way to understand why we get a single outcome, because of how we choose to regard the system (I've called that a role of conscious perception in that other thread), but not how. You have not explained why we get the outcome we get, since asserting that it is random, in an ontologically true sense, runs afoul of Einstein's celebrated complaint about god and dice. As this is the real "measurement problem", a key aspect of it remains, even as a part of it is resolved by noticing the role of the physicist. One can always say, a la Bohr, that we just don't get to know that part, and indeed that's my own feeling, but I wouldn't exactly call that a resolution, merely an acceptance of certain inherent limitations.

Even in the analogy with the 2D perspecticve, one doesn't necessarily need other observers, since one notices soon that the different views the single observer gets at different times can be coherently realted only by assuming a third dimension. Once this is realized, moving around is enough to gather rthe information needed to complete the 3D picture.

That is true, and is just what we'd have to do if there were no other observers, or if we could not trust their testimony. But there are other observers, and we have found we can (usually) trust them, so we need to build a physical ontology that respects these facts. This is related to the "why that outcome" question-- why does everyone we get to talk to agree on that outcome? It's the crucial symmetry principle of relativity, we either need an ontology for that, or we need to recognize we are going to view it as unknowable.

Therefore, in the thermal interpretation, there is no place anymore for mystery.

There's always a place for mystery-- I like to say that science is not about removing mystery, it is about replacing superficial mysteries with much more interesting and profound ones.

 

[A. Neumaier]

But your Interpretation differs from the Standard in its prediction.
In your Interpretation. There is no Collapse. And the behavior in the double
slits can vary. For example. In Standard QM. When a Buckyball is emitted, always
one hit would be detected. But in your case, since it doesn't collapse and it is
alway a field, the energy of the buckyball is enough to trigger 5 or even 10
electrons at the detector. So your one Buckyball emission would result in 10 or
more hits due to the energy of the Buckyball field much more than an electron.
Here your interpretion obviously didn't have the same prediction as QM.

I had already mentioned earlier that what precisely happens when the buckyball field meets the screen must be calculated using statistical mechanics. The general principles suffice to say what happens for a single electron arriving but not for a single buckyball arriving.

And there is just as much collapse in my interpretation as statistical mechanics predicts. The literature contains a number of derivations of POVM's from statistical mechanics, and this captures all the observable features of (partial) collapse.

 

[A. Neumaier]

In a restricted way only. Because there is no deterministic explanation that leads to the actual outcome, that's my point-- you have given a way to understand why we get a single outcome, because of how we choose to regard the system (I've called that a role of conscious perception in that other thread), but not how. You have not explained why we get the outcome we get, since asserting that it is random, in an ontologically true sense, runs afoul of Einstein's celebrated complaint about god and dice.

Which outcomes one gets is predictable by the standard machinery of nonequilibrium statistical mechanics. This discipline tells how to compute (at least in principle, and for QED also in practice) field expectations, i.e., the measurable outcomes according to the thermal interpretation, in an approximation sufficient for many purposes.

I
That is true, and is just what we'd have to do if there were no other observers, or if we could not trust their testimony. But there are other observers, and we have found we can (usually) trust them, so we need to build a physical ontology that respects these facts. This is related to the "why that outcome" question-- why does everyone we get to talk to agree on that outcome?

It is because we all observe the same world, hence (if properly trained) we draw the same conclusions about the stuff we observe. This classical explanation holds in the thermal interpretation also for the quantum domain.

 

[A. Neumaier]

why we get the outcome we get, since asserting that it is random, in an ontologically true sense, runs afoul of Einstein's celebrated complaint about god and dice.

Actually, in a scientifically defendable sense (though I haven't yet written it up), God does not play dice, but he acts on incredibly fast time scales, which to us appears as randomness.

 

[rodsika]

Which outcomes one gets is predictable by the standard machinery of nonequilibrium statistical mechanics. This discipline tells how to compute (at least in principle, and for QED also in practice) field expectations, i.e., the measurable outcomes according to the thermal interpretation, in an approximation sufficient for many purposes.

It is because we all observe the same world, hence (if properly trained) we draw the same conclusions about the stuff we observe. This classical explanation holds in the thermal interpretation also for the quantum domain.

Ken, do you think Arnold explanation above solves how we get definite outcomes when the equations of physics don't allow them?

 

[Ken G]

It still leaves questions for me. The big one is, if we start with a simple system of one quantum in a definite spin state along one axis, and we use a macro instrument to measure its spin along an orthogonal axis, is there enough information in that system (perhaps including the instrument that prepared the quantum in the initial state) to determine what outcome we'll get, even though it is not practical to imagine we could ever have access to that information, or is it fundamentally necessary that we cannot have access to that information to get that probability distribution? If the latter, then how can we give meaning to information present that if we had access to it would not be present?

 

[A. Neumaier]

It still leaves questions for me. The big one is, if we start with a simple system of one quantum in a definite spin state along one axis, and we use a macro instrument to measure its spin along an orthogonal axis, is there enough information in that system (perhaps including the instrument that prepared the quantum in the initial state) to determine what outcome we'll get,

Yes. you get no response because the axis is orthogonal. Things get difficult only if the axes have a nontrivial angle.

In that case, since all macro predictions are made by statistical mechanics, I doubt that one can predict more than a statistics for the resulting event.. Whether it is possible in principle is a different matter - but to be ablre to do this would mean one know every quantum detail of the macro instrument, and whether this is even knowable is questionable.

 

[Ken G]

Right, so my point is that if we say there is some unknowable detail that determines the outcome, then nothing science could ever do could distinguish that from something that is simply not determined. So determinism or indeterminism exits science and becomes a personal philosophical choice, and that is what I would call "the measurement problem." It just plain wouldn't qualify as a measurement if it didn't have that property, and that I think is the fundamental paradox/limitation/weirdness of physics. The thermal interpretation has not made it go away, but amazingly, it has relegated it to a completely classical problem. The measurement problem is no longer in some strange quantum/classical interface (a la Copenhagen) nor is it strictly in the quantum domain (a la deBroglie-Bohm), it is still perfectly classical, and applies just as well when we shuffle a deck and pick a card.