Yes.ZapperZ said:It appears that there are MANY aspect of this discusson that are simply not getting through to one another...
Because you are mixing the time evolution with the statistics. In QM, you can formally define a state |qo> and any formal measurement of the observable Q will give the outcome qo with 100%.ZapperZ said:This, I think, is the crux of the matter. I can make an energy measurement of a particular transition, and ALWAYS get the same value. But I cannot, for example, make a position measurement and always get the same value.
Now when you analyse the dynamics of QM and the way how to build such observable, you discover that it requires an infinite amount of energy to “fix” an input state into the |qo> and that if you stop the interaction fixing this state, the time after the sytem may be anywhere in the space (non relativistic approximation). Thus, you encounter several difficulties to apply such measurement to a “real” experiment (it will at least require a small amount of time): only though experiments are allowed. This is the same for CM: some observable are easier to see than others, but formally you can always get a 100% measurement outcome.
I assume that when you say CM, you say “statistical CM”. It depends on the initial probability distribution and the observable you see. Recall: I am not saying that consecutive measurements on the same system with different observables will display the same behaviour in statistical CM and QM. Just, that for each measurement of an observable on QM, we may define formally a CM experiment that gives the same measurement outcomes.ZapperZ said:I can flip a coin using a contraption that I mentioned earlier, under ideal, identical condition, and ALWAYS get ALL the outcomes that I can get identically, each time. There is nothing in classical mechanics, in principle, to say that I will not always get head, having the coin land in the exact position, after 12 bounces, and with the head point North. You don't get this in the H atom.
In QM, for the H atom, I just need to take 12 atomes with one energy state. This is simply a statistical mixture.
I will try to get access to those papers in order to separate the logical view from the interpretation view (I hope they are on the arxiv). But I think I will give an answer analogue to the previous ones.ZapperZ said:The example of the superpostion of states with odd and even parity that I gave came right out of the SQUID paper of Stony Brook that I cited. The states that I generated were identical to the ones they used. In fact, it is identical to the one Tony Leggett used. The degeneracy between the odd and even parity states were removed using an external magnetic field, the identical way one removes the generacy of orbital/spin angular momentum quantum number. The "energy" measurement is the energy gap between the even-odd states. This number is well-defined and not a statistics.
Note: A well defined number outcome is always statistics: it depends on the modelling tool you are using. Thus, a well defined number outcome in an experiment may define a probability distribution for an other observable:
Statistical CM view: a numeric voltmeter giving a 5V results with a 100% statistics means only 100% for the voltmeter observable 5V: you must not forget that this observable includes the uncertainty of the voltmeter measure. You still have a probability distribution that may be very different if you take another observable that amplifies the error of the measurement.
Thus I can have a 100% result while a keep a probability law different from the delta(q-qo).
ZapperZ said:In all of this, the major (and original reason why I intruded into this thread) is the objection to the suggestion that, just because the outcome of QM measurement is "statistical" in nature, and the flipping of a coin is also "statistical" in nature, then these two are the same thing. Therefore, since coin-flipping is actually deterministic since classical mechanics can actually describe such a thing, it is only because we are ignorant of the fine details of the dynamics that we impose a statistical description to this event. Conclusion? QM must be that way too... that there must be some "underlying" description that we don't know of and thus, QM simply reflects out ignorance of the underlying dynamics.
My question is, do you subscribe to such a view?
 A.J. Leggett, J. Phys.: Condens. Matt v.14, p.415 (2002).
I accept such a description/view as it is: just one description/view with a lot of interpretation (in a non pejorative sense). See below.
There is a lot of interpretation in your sentences.
1) “because we are ignorant of the fine details”.
This means that you select the deterministic bias to describe physics. Well, I have no opinion concerning this topic: should we describe physics with mathematical “deterministic” tools or “probability tools”? I really think this is only philosophy if you develop a little.
2) “since coin-flipping is actually deterministic”.
If I take the statistical CM formalism, you are assuming that there exist a delta(q-qo) probability distribution source for any experiment. Well, Up to know, I have never seen any physical experiment where I have such initial probability distribution. Thus, my current statement is that I always have a statistical distribution different from the delta(q-qo). And that my CM measurements outcomes only give outcomes that correspond to a probability law different from delta(q-qo).
So, I can only consider the delta(q-qo) distribution as a physical hypothetical state allowed by the theory. I can even add a superselection rule (a marketing word ;) to say that such a state is impossible to get in any experiment.
3) “it is only because we are ignorant of the fine details of the dynamics that we impose a statistical description to this event.” And “that there must be some "underlying" description that we don't know of and thus, QM simply reflects out ignorance of the underlying dynamics”
This is the typical sentence of the deterministic interpretation school. I cannot subscribe to this restriction. I accept both deterministic as well as a probabilistic description: I formally can do that with mathematics tools. Why should I select a view rather another one? I use the adequate one.
The approach of considering “probability sources” as an ignorance is a matter of interpretation. The mathematical axioms do not require such assumption and this applies both to QM and CM measurement results. Thus one question concerning these two models is to know if there is a non circular way to produce (i.e. ~a deterministic process) these sources. Both QM and classical CM does not solve this issue (out of scope of the model).