Classical and Quantum Mechanics via Lie algebras

I was really intrigued by Neumaier's approach until I read this discussion and what it predicts for this case. Why use buckyballs? Something much simpler: any atomic or molecular beam prepared to interfere in the double slit experiment with deposition on plate that contains none of that atom or molecule. Run it only long enough for sparse deposition, and check for individual atoms consistent with an interference pattern. Shouldn't be hard to do (e.g. silver on glass plate).

I would literally bet a million dollars that the outcome would be consistent with conventional interpretations and falsify Neumaier's.

Sorry, I can't stay silent. The never-ending torrent of such sensationalist ill-informed remarks is getting a bit tedious.

The whole point about interpretations is that every interpretation predicts the same things for any given experimental setup. If they didn't, then interpretations would be experimentally decidable, and those in contradiction with experiment would be discarded. Arnold's interpretation is just that -- an interpretation. It does not contradict experimental results, but rather offers a more rational way of thinking about QM.

And others did "figure it out" (in related forms). Arnold already said elsewhere that his initially naive views about particles in QM were improved considerably after discussions with experts in quantum optics years ago.

If you want to search for a "right" interpretation, first master the most essential and basic interpretation, i.e., "shut up and calculate". Everyone with an interpretation must master "shut up and calculate" first, since that's what decides whether QM is or isn't in contradiction with experiment.

Regarding buckeyballs, atom interferometry, etc, the generic features of the "shut up and calculate" interpretation for a field incident on a double-slit were explained in post #73 of this thread:

http://www.physicsforums.com/showthr...82#post3171882

with an additional bit in post #78.

The more accurate calculations with a relativistic quantum field instead of a classical field do not change the gross features significantly. (Mandel & Wolf give details.)



It's an incident field, and it's already been discussed in the thread I mentioned above. The calculations from Mandel & Wolf indicate the probalistic nature of the predictions.

How could this have been figured out before 1911, at a time where not even the Schroedinger equation was discovered? The reason why it hasn't been discovered is that those working on the foundations rarely also work on quantum fields, and those who work on the latter usually have more pressing things to do than to indulge in foundational issues. So the interface between foundations and quantum fields has been very little explored.


A quantum field transports the energy in the same way as a classical field, namely by evolution according to the field equations. The energy of a radially expanding field is distributed uniformly.
So an extremely tiny amount of energy arrives at any place of the hollow sphere, integrating over the sphere to the energy of one electron. Thus energy is conserved. The probability of response anywhere is extremely tiny, too, so that uncertainties in the sphere by far dominate the effect, and nothing can be concluded.

Mainstream Quantum Interpretations are only accepted as valid candidates if they are at least scrutinized by 500 physicists. Neumaier's interpretation just less than ten. That is why I'm inviting others to help scrutinize it. You, Strangerep, is on Neumaier's side. So those who are neutral or can see the logical flaw of Neumaier's such as Pallin pls. elaborate. If at the end of the day, you can't see any theoretical flaws and agree it's a valid interpretation candidate. Then state so in order to make Neumaier's Interpretation part of pop-sci books.

Note that doing the experiment is far from easy. You need to make sure that
(i) the absorbing surface is completely silver-free,
(ii) one and only one silver atom is emitted by the source,
(iii) The silver field at the absorber had no time to redistibute itself during the procedure it takes to search the absorber for a single silver atom.

Pop-sci!???? Why would you want such a thing in the first place???
I thought we were talking REAL science here.

Yup .. that is why I proposed cooling the detector plate to 4K (or below), so that the atoms would stay in their original impact locations.

I would also modify (ii) to say that exactly one silver atom impacts the surface between imaging steps.

Cooling the detector is easy .. I have multiple 4K cryostats in my own lab. A much bigger problem is making sure that you only have a single atom coming through at a time, I can imagine several approaches to achieving that, but they are all non-trivial, and I am not sure they would work. Even if you could achieve that, imaging a single atom is extremely hard, unless you can narrow down its position to a fairly small region.

I think these experiments are doable, but would require at least a million dollars worth of equipment to achieve. As interesting as I find Neumaier's proposal, I am sad to say that I don't think there are many experimentalists out there willing to commit those kinds of resources to this project.

I think you're talking about statistical analysis used in coming up with values of variables for the quantum system itself, but I was talking about the macroscopic "pointer state", like the number that appears on a computer monitor after it runs its statistical analysis program (or the numbers representing raw data before analysis, which may not directly correspond to any quantum observable). That's an element of the physical world too, one which we can directly observe, if Neumaier's interpretation only gives probability distributions for such macro-states rather than definite values, then I would say it isn't a full model of the "one world" we find ourselves in. Again, I'm not requiring that a full model allow such states to be predicted in a deterministic way, it'd be fine if it had a stochastic element which randomly picks one macrostate based on the probability distribution, but as I said this element would have to be a nonlocal one.

Think of it this way: suppose you want to build a simulated universe running on a computer (or collection of computers, see below), and the simulation is supposed to model all the types of macrostates we can directly observe (while it doesn't need to have any model of microstates which we only infer based on macrostates). The model need not predict the results of particular trials of any real-world experiment, but we should be able to create a model of the same type of experiment on our computer(s), with the simulation yielding a series of macroscopic pointer states whose overall statistics should match the results of analogous experiments performed in the real world. If we require that the simulation be a "local" one, then we could imagine a bunch of computers which were each responsible for simulating a small element of space, and on each time-increment the computer should give an output based only on inputs from other computer outputs that lie within its past light cone (this is assuming the laws of physics can be approximated arbitrarily well be a simulation with discrete "pixels" of space and time; if not, you could imagine replacing the finite array of computers with a perfectly continuous array of "functions" at each point in space, which continuously produce outputs at each instant of time based only on inputs from points in their past light cone). And the computers can have stochastic random number generators built in, so if part of their output consisted of a probability distribution, they could also use that probability distribution to randomly select one specific output based on that distribution.

If observable macrostates in a region of space at a particular time are just a function of all the computers' outputs in that region at that time (outputs which may be thought of as "microstates" for specific points in space), then the point here is that no "local" simulation of this type, where the computers have no access to inputs outside their past light cone when generating outputs, can ever give a pattern of macrostates consistent with QM. Even if computers at each point can generate probability distributions in a local way, a stochastic rule for generating specific outcomes based on these probability distributions would have to operate nonlocally, with computers representing points at a spacelike separation coordinate their random choices to make sure they created the correct entanglement correlations. This is just a natural consequence of Bell's theorem. So, I think it's misleading to call Neumaier's interpretion a "local" one, it either fails to model the fact that we see particular outcomes for macroscopic pointer states (which all other interpretations attempt to account for) rather than just probability distributions, or if the model is made to include a stochastic rule for generating a series of particular macrostates, then the rule must operate in a nonlocal fashion.

I was really intrigued by Neumaier's approach until I read this discussion and what it predicts for this case.

I guess I missed it - what exactly is Neumaier's prediction (measurement-wise) for one or many buckyballs (or other particles not present in the detector) sent through a double slit? What would happen if one went looking for individual buckyballs at the detector?

Neumaier said that since there is no particle, there is no need to explain where the particle (or Buckyball) goes. Here's Neumaier answer in message #35:

"Most electrons in a real material are there smeared out in a way that the particle picture is misleading. Chemists use electron densities, not electron positions to describe things. Thus a newly arriving delocalized electron is nothing very special to the detector.

In an interference experiment, neither the electron nor the buckyball is a particle, since the latter is a semiclassical concept without meaning in case of interference. Since there is no particle, there is no need to explain where the particle goes.

The density of the electron field or the buckyball field increases at the target - that's all that can be said, and this is enough for verifying what one can actually measure - e.g. the silver film in a Stern-Gerlach experiment after a macroscopic amount of silver accumulated."

What do you think?

Well, I read that, but it is still not clear to me what the prediction is. If we shine a beam of buckyballs (plane wave function for buckyballs) on the double slit, what happens at the detector?

I think that the "beam" will be diffracted, and its intensity at a point on the detector will give the probability of detecting a buckyball strike at that point. For many buckyballs, this will give the density of buckyball strikes in the neighborhood of that point. If a buckyball just embeds in the detector without being destroyed, then you should be able to use an electron microscope to find it.

[...] it is still not clear to me what the prediction is. If we shine a beam of buckyballs (plane wave function for buckyballs) on the double slit, what happens at the detector?

I think that the "beam" will be diffracted, and its intensity at a point on the detector will give the probability of detecting a buckyball strike at that point. For many buckyballs, this will give the density of buckyball strikes in the neighborhood of that point. [...]

Strangerep (lone known supporter of Neumaier Interpretation) [...]

Exactly. The math (as in Mandel & Wolf) just predicts probabilities for interactions occurring (between incident field and detector) in any given region of the detector, in any given time interval. Arnold's interpretation is just an interpretation -- it doesn't make an experimentally testable prediction by itself separate from the theory. The math that actually makes a prediction is the same as mainstream quantum theory.



... maybe because I've actually worked through large amounts of the detail in his book, and his other papers on quantum theory.

I'd like to remind readers of this thread that Arnold's original purpose in opening this thread was to seek feedback on the presentation in the book prior to publication. (See opening post.) There's a LOT more in the book than just an interpretation, and much of it could benefit from feedback indicating specific areas which are unclear, or mis-sequenced, etc, etc. I.e., the sort of feedback that helps turn a draft into a publication.

Edit: One important theme in the book is already implicit in the title:
"Classical and Quantum Mechanics via Lie algebras".
Arnold addresses both the classical and quantum cases, also thermodynamics, and relates them with considerable insight into their common features, interwoven with Lie-algebraic ideas. This commonality (once comprehended) was a real eye-opener for me when I first began to understand it.

There is a discrepancy in here somewhere. Arnold and spectracat agreed that Arnold's theory predicted that a single buckyball diffracted by a double slit would not lodge at any single location on detector screen (it would activate, e.g. electrons in the detector, but would not, itself, lodge at one point). Spectracat and I believe that standard QM predicts the buckyball will lodge at one place, with the location consistent with the propabilities of the interference pattern. Arnold agreed this experiment would distinguish his theory from convention QM.

Please clarify the situation.