Seasons

I like the multiple solutions idea, though!

Prob123 3948:

I like the idea of bringing chocolate into it!!!

Chocolate covered quantum physics? I'd bite tthe ears off that bunny.

Schroedinger's bunny. Half of it melts in your mouth!

The interesting question is where was the chocolate before it melted? Not in your hands.

Psimagus:

Are we embarrassing you with all this girl talk? We may be talking about waves, but at least we're not discussing periods!

You wrote:

But how do you view the eigenvalues? Are they anything more than a mathematical device to explain what we observe, or do you see them as describing something that is causally "real"?

Well, technically, an eigenvalue is just a number. But an eigenvalue associated with an operator associated with a physical quantity in QM - that eigenvalue also has physical significance. For example, for a pointlike particle, the eigenvalues of the position operator are all the positions that the particle can have (actually, since space is three-dimensional, it takes three eigenvalues, one for each co-ordinate). A simpler example is spin, which in certain situations can have only one of only two values, "up" and "down." So Psi gives a probability that the spin is "up" and the probability that the spin is "down". Such claims can be empirically tested by repeating the experiment many times, measuring the spin each time. If the probability of spin "up" is 2/5, then in the long run the measurement should yield "up" about 2/5 of the time (and hence "down" about 3/5 of the time).

Now, in the case of the two-slit experiment, as discussed on the various sites mentioned above, the interference pattern gives the probability: where the interference pattern is "strong", the probability that an M&M will hit there is high. Similarly with my "spit bullet" example of several days ago.

"eigenvalue" is a very impresive word (people about to mug me have been known to bow down to me when I utter it), but all it really means is a possible value for a certain physical parameter of a system. For example, the momentum eigenvalues of a system are just the values of momentum that the system might have.

Bev 3958:
Well, there's more than on place where chocolate could melt!

I mean, how often do you see chocolate vibrators?

Irina, subtext...SUBTEXT! That's text, right there. Watch the text.

This is a quantum discussion. The chocolate is there when you see it melted (or taste it, since it is your mouth). No one knows where it was when you couldn't see it. Maybe you would know where the M & Ms were all the time if you weren't blindfolded.

There once was a lawyer named Rex
Whose subtext transformed into text
When facing exposure
he said with composure
"de minmus non curat lex"

Irina,

No you don't, because I never said that the wavefunction for light was the same as the classical electromagnetic wave. In fact, I said that they weren't.

But it is. My objection is that the electromagnetic light wave is not the probability wave. The light does have electromagnetic wave-like properties (as well as particle-like properties,) and it is precisely this electromagnetic aspect of the wavicle that propagates.

Dear Psimagus:
you write:
It is psi that gives the probability, and this is never a negative value, thus cannot act in true "wave" fashion to exhibit destructive interference.

Psi gives the probability, but it isn't itself the probability. One gets the probability of (e.g.) the particle's being in a given spatial region by integrating Psi*Psi, the square of the modulus of (normalized) Psi, over the region [Psi* being the complex conjugate of Psi

You can integrate, conjugate, square, triangulate, or dance it round a maypole naked with ribbons in its hair. It doesn't change the fact that the "probability wave" (be it Psi, its modulus, or any function thereof,) is not the same as the electro-magnetic wave nature of the quantum (whether we call that a "light wave", a "pilot wave", a "carrier wave", or any other Bohmian euphemism.) The electromagnetic wave is a different wave entirely, as my previous ref. makes clear ("The Schrodinger wave equation does not describe an ordinary electromagnetic wave but a probability wave" http://www.electrogravity.com/AVECWAVE/AVecWave.pdf)

(yes, Bev, I am a great fan of complex conjugation)]. This gives a positive real number betweeen zero and one, as desired for a probability. Psi itself, however, is not so restricted. In fact, Psi typically takes on complex values.
Therefore, there is no problem with Psi exhibiting characteristically wavish phenomena such as diffraction and interference.

I would say there would be every problem, but whether or not that is so isn't relevant - while you claim the "personality wave" to actually be the electromagnetic quantum wave, any modelled quantum behaviour will unavoidably seem bizarre.
I'll take the opportunity to requote my previous refs, if I may, since the originals are now a good few pages back, but remain unaddressed:

"In accordance with this probability interpretation, it is not uncommon for the wavefunction to be called a 'probability wave'. However, I think that this is a very unsatisfactory description. In the first place psi(x) itself is complex, and so it certainly cannot be a probability. Moreover, the phase of psi (up to an overall constant multiplying factor) is an essential ingredient for the Schroedinger evolution. Even regarding |psi|^2 (or |psi|^2/||psi||) as a 'probability wave' does not seem very sensible to me. Recall that for a momentum state, the modulus |psi| of psi is actually constant throughout the whole of spacetime. There is no information in |psi| telling us even the direction of motion of the wave - it is the phase alone, that gives this wave its 'wavelike' character.
Moreover, probabilities are never negative, let alone complex. If the wavefunction were just a wave of probabilities, then there would never be any of the cancellations of destructive interference. This cancellation is a characteristic feature of quantum mechanics, so vividly portrayed in the two-slit experiment!" [Penrose The Road to Reality chap.21.9 p.519]


"The carrier of the non-local instantaneous action is the wavefunction similar to the de Broglie pilot wave and the reaction is the net observable local space result. The Schrodinger wave equation does not describe an ordinary electromagnetic wave but a probability wave, and the probability wave determines all of the action and reaction of the total electrogravitational interaction."
http://www.electrogravity.com/AVECWAVE/AVecWave.pdf

Since you clearly disagree, could you provide any counter-reference to indicate

a) propagation of the probability wave, or
b) equivalence of the probability wave and electromagnetic wave?