[sjastro]

Originally Posted by CraigS

Hi Peter;
Thanks for your post .. interesting .. exploring wavefunctions for a bit might be an interesting exercise ..

Correct me (anyone) if I’ve got any of the following wrong .. I’m also learning about QM with every step here, so here goes ...

I haven’t found anywhere in any of the main QM interpretations where it actually states that quantum interactions are probability waves. I also think that the main famous ‘Interpretations’, like deBroglie-Bohm and Many-Worlds, contain A LOT of Classical determinism, actually.

Craig,

The mathematics is the same for each interpretation. Mathematically the solutions are spherical harmonics or "wave-like" for the various QM operators such as the Hamiltonian (energy) or angular momentum.
The term wavefunction and probability waves are a reflection on the mathematics.
The square of a wavefuction gives the probability of obtaining a certain measurement. If we knew the superimposed wavefunction, the square of this wavefunction has a probability of one, which is not surprising as all the possible outcomes are included in the superimposed wavefunction.

At best, ‘Many Worlds’ seems to explain non-observations of ‘pure states‘ evolving in a determinable way, purely because our observations can’t detect the full ‘wavefunction’ of many worlds. DeBroglie-Bohm seems to start out interpreting quantum interactions as ‘fundamentally probability waves’ .. and a lack of history info about the system of interest, is caused by something unknown, but external to it (suspiciously very Godel-like and Classical Chaos Theory-like). This hence, seems to be the ultimate expression of Classical determinism at work, to me.

The Copenhagan interpretation seems to have fallen somewhat out of favour in QM Physics circles thesedays (from snooping around a bit ... something disliked about the ‘Heisenberg Gap’ approach ?)

Anyway, if three of the main QM interpretations don’t strongly bestow purely probabilistic behaviours as the exclusive domain of ‘QM’, then even these traditionally QM behaviours, don’t necessarily distinguish QM over Classical (as is commonly inferred). Also, as mentioned above, these interpretations also seem to be coming from very Classical, hence deterministic principles.

The key here is the role of the observer. In all interpretations of QM the observer and outcome are part of the measurement process. In classical physics the observer is independent of the measurement.
This is what distinguishes classical physics from QM.

Another area usually used to distinguish QM, is Wavefunction Superposition. So, Classical Mechanics treats ‘particles’ as particles. It would seem illogical to superimpose one particle on another in Classical. But I still think it could be done (??) Superposition is kind of a ‘wave’ concept, so how does one get a wave out of a particle.
Perhaps the path of a particle could be seen to be described by using superposition ?... I know in electrical field theory, superposition is all over the place (eg: Maxwell’s equations, from Classical). Fourier analysis is a good ‘flow-on’ example of this, too.

The properties of a particle such as energy, position, momentum, angular momentum, intrinsic spin etc can exist in superimposed states.
The concept of a particle existing as a wave is a direct consequence of the Heisenberg uncertainty principle where we are unable to precisely measure the position and momentum of particle at the same time.

Regards

Steven