Re: [Phys-L] foundations of QM : fluctuations

[David Bowman <David_Bowman@georgetowncollege.edu>]

Regarding:

> On 02/18/2014 07:19 AM, David Bowman wrote:
> > In short, my point is a point about words, not physics.  Physical 
> > arguments won't affect that.
>
> Then we have nothing to discuss.  I'm interested in the physics.
> I'm not interested in playing word games.

In hindsight maybe I ought to have said my point was philosophical related to issues of the interpretation of quantum mechanics (and which of these issues ought to have priority in deciding the issue of motion) rather than have said it was about words.  What I meant about my point not being about physics is that it is not about any disagreement with the results of any properly done physical experiment, or the results of any properly done theoretical calculation.

> > My point is that zero point 'motion' ought to be called that if 
> > something is actually moving,
>
> The physics says that the atomic electron is moving.  This
> is objectively measurable.  Moving has to do with velocity.
> If the velocity were zero, then ⟨v^2⟩ would be zero, and
> it's not.

Whoa. The physics only says the average over a large ensemble of squared momentum measurements for an ensemble of identically prepared atomic systems is positive.  Or, equivalently, the distribution of values in the outcome for a measurement of each component of the momentum has a positive variance.  This is because there is more than one possible outcome of a measurement of any momentum component.  But *nothing* about that distribution nor the distribution of the multiple possible values of outcomes of position (or any other observable property) measurements depends on time.  I can do any measurement on the system at any time, and no matter when I do the experiment the distribution of outcomes has exactly the same probability for each outcome regardless of when the measurement was made.  Nothing knowable about the system has changed or is changing while I'm deciding when to do the experiment.  Ergo nothing knowable is actually moving.  One could hypothesize about particles actually having unknown hidden and fluctuating variable values for each of these properties when they are in a pure quantum state that is an undisturbed superposition.  But such hypothesizing is in addition to the predictions of the physical theory.  We can either say the values for properties in a superposed state become actualized upon measurement, or we can say the properties always have a unique yet fluctuating unknown hidden values where the fluctuations occur in an (in principle) unobservably nonlocal way that violates causality.

> It may be that the long-time average ⟨v⟩ is zero, but that
> does not mean that v itself is zero.  Indeed, that's pretty
> close to being a definition of fluctuation, when the average
> ⟨v⟩ is zero but ⟨v^2⟩ is not.

The length of time is not relevant in this situation.  But neither v nor v^2 need have any unique value at all until they are needed to tell an apparatus how to respond upon a measurement-like interaction.  The distribution of potential v-value outcomes has a nonzero variance because the prepared state is a superposition of a multiplicity of eigenstates of v.  Claiming the actual v-value exists and is fluctuating is an unnecessary, but not necessarily invalid, addition to what the physics is actually telling us.

> > measuring the radiation supposedly going in or out would require
> > measuring at least one photon's worth of radiation in transit.
>
> Nonsense!
>
> You can choose to measure anything you like, but bear in 
> mind that other people are free to choose differently.

True.  But I don't see how you can measure inbound or outbound radiation without measuring at least one quantum of it.

> In particular, I'm pretty sure that voltmeters exist.  If
> you measure the voltage, it fluctuates.  Really it does.
> This is objectively measurable.  No word-games are going
> to change this.

Let's be careful here.  You can measure the voltage on a system at some time.  You can then measure the voltage on another identically prepared system in exactly the same state at the same time and yet get two different answers.  You can repeat the experiment and get even more answers.  The distribution of voltage values obtained agrees with the quantum predictions.  If you attempt to continuously monitor the voltage in real time you have then changed the system at hand to a different system which is in a state of perpetual interaction with its environment via the voltmeter apparatus and is not in any stationary pure quantum state.  You are then looking at a different system than the one you claimed to be looking at, which was an atomic oscillator system in its zero entropy ground state.

> If you /choose/ to use the photon-number basis, you won't
> see the fluctuations, but that's a choice, not a universal
> law.  This is the opposite of looking under the lamp-post.
> If you insist on looking in the one single place where the
> phenomenon can't be seen, you won't see anything.  Meanwhile
> everybody else is seeing the fluctuations.

But what is seen is not the supposed fluctuating value in the purported isolated zero entropy system.  It is the fluctuating continuously monitored value in a system in an ongoing continuous interaction with the positive entropy environment.

> Voltmeters exist.  Voltmeters can see the fluctuations.
> Been there, done that.

Me too, unfortunately.  In my case they were thermal fluctuations. Those dang fluctuations messed up the signal we were hoping to see.

> Zero-point motion is motion.

Only to the extent one hypothesizes nonlocal causality violating hidden variables.  Such a hypothesis is not necessary, and making it is a metaphysical leap that goes beyond what the knowable physics tells us.  Not only do voltmeters exist; Bell's theorem exists as well.  There is nothing knowable that is time dependent in a zero entropy quantum ground state, or any other stationary state.  Nothing knowable is moving in zero point motion.

David Bowman