Yesterday, Amara Graps wrote:
>
>
>
> "To what extent does this information reside in us, and to what
> extent is it a property of Nature? Any theory about reality can have
> no consequences testable by us unless it can also describe what
> humans can see and know." Jaynes says that the proper tool for
> incorporating human information into science is simply probability
> theory or "Bayesian inference". Probability theory is an extension
> of logic, in order to reason in situations where we have incomplete
> information.
>
> However, amplitude Psi, according to our usual quantum mechanics
> texts is not now to be interpreted in as expressions of human
> ignorance of the true physical state. Jaynes says that it is our way
> that we interpret the amplitudes that is causing the confusion. The
> probabilities that we seek, must be in terms of mutually exclusive
> possibilities and must be represented in a "deeper hypothesis space"
> that contains more parameters, for example, phases. He doesn't go into
> details of what all other parameters must be included, he mainly points
> that our perspective has to shift into a wider view, and he says
> that we cannot hope to get our probability connections right until we
> get some basic points of logic right.
Amara follows this with the amplitude-squared equation that would form
the basis for quantum particle probability distributions, plus related
comments by Ariel Caticha:
> The main motivation for this article has come from realizing that
> the derivations in Cox still apply if real numbers are replaced by
> complex numbers as the encoders of partial truth.
So, all the properties of quantum waves could be coming from a
mathematically neat, expanded definition of what it means for a
particle's position to be uncertain? Follow Jayne's suggestion, consider
a higher phase space perhaps, and our own uncertainty about location in
that space could produce interference effects, qubit computers, and
everything else predicted by the standard quantum math?
Thanks for the further detail. Up to a point I do find this persuasive,
at least in the sense that it might well be wrong to assume the reality
of Many Worlds alternate histories. The flow of the anti--Many Worlds
argument here is that if quantum predictive structures (i.e., state
vectors, wave functions) *were* objectively real, then Many Worlds
*would* be quite strongly indicated (despite there being some other,
alternative interpretations, in the case of state vectors being real).
So, if the state vectors, etc., are only non-local probability
treatments for some advanced way of positioning in real space, you've
then eliminated the argument in favor of Many Worlds.
One area where I continue to doubt this "non-local vector" idea is when
I consider that an entire, difficult-to-foresee chain of consequences
can sometimes block the "travel" of these quantum waves or vectors. I've
read this in some of the ideas relating to interaction-free
measurements, where it is said that quantum measurements could even very
often tell if a "bomb" is live, as opposed to possibly being a dud! I
presume that the "bomb" in this case would have to be a small thing,
like one of those "SQUID" devices, so that one could cool it, and keep
it thermally isolated, so as to maintain it in quantum coherence while
one is testing to see if it is a live bomb or not.
Apparently, the "liveness" of the trigger on such a bomb, can *itself*
be enough for the trigger to block the quantum wave of a passing photon.
This is in a situation where a "dud" bomb's trigger essentially would
never block the path of the photon's wave in that location. In this
experiment, it seems that if we were going to track a photon through a
higher state space, consistent with these predictions, then that space
would *necessarily* contain information about whether the bomb *could*
explode or not! At the same time, if Nature's state space actually codes
this information about the "could be" explosion of the bomb, this is
similar to saying that the "could be" explosions really exist in Nature,
in such a way that the explosion event blocks the wave even as the
resulting new timeline branches away from our own. Notice that the
essence of this *is* in some sense quite statistical, since one half of
such test situations, done on a set of live bombs, will actually explode
the little bomb in our own timeline. It's the other half of the trials
that are the mysterious part, the times when quantum theory tells you
that a bomb is almost surely live, but where it doesn't explode in *our*
world.
If the true logic of this is as been described, it becomes difficult to
see the quantum wave properties as being only statistical models in our
minds. For example, if we could test parachutes in a comparable manner,
we'd never have to examine the 'chutes to see if they are folded right!
Instead, we'd just hang "quantum crash dummies" from them and certify
the ones that test as "sure to open" without *really* opening (if you
see what I mean). In this case, if it were specified that we were not
going to examine or model the details of the parachute, but quantum
testing could point out a good 'chute anyway, we'd be getting our
knowledge more from the quantum world itself than from any probability
representation of it. So, I still don't know the right answer to this
question of quantum alternate worlds, given that "might have beens" can
apparently have a direct causal effect on real measurements.
Maybe I'm just being stubborn or something, I don't know :)
David Blenkinsop <blenl@sk.sympatico.ca>
This archive was generated by hypermail 2b30 : Mon May 28 2001 - 09:50:15 MDT