The wave packet description

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If the source is not known in detail you don't know the electron's original wave function.

If the wall is not known in detail you don't know the electron's wave function before the detector.

If the detector is not known in detail you cannot know where the spot is produced.

I'm not even sure that we can speak about the electron's wave function as it is probably entangled with both the source and the wall.
You can postulate what the reasonable electron w.f. is. And this is how it is done.

Notice, that if one has a problem with guessing the electron's w.f. then somewhat bigger
issue arises if it comes to the w.f.s of the detectors, walls, etc.. There, one
has to deal with 10^25 or more atoms. How do you propose to determine details of w.f.
for those objects?

The only realistic way is to guess their wave functions.

Why bother then? Since heavy guessing is inevitable, why not to guess just the electron w.f. and focus on its properties?

Otherwise you fall into a circular reasoning:
1. To determine w.f. of an object you have to measure it.
2. You don't know what you measure if you don't know the w.f. of the measuring
apparatus.
3. So, you have to measure the w.f. of the measuring apparatus, and so on ...

I propose to cut this circle in the most convenient point i.e. the one that requires
the least amount of guessing.

Would gladly hear about another way out, though.

Cheers!
 
479
10
You can postulate what the reasonable electron w.f. is. And this is how it is done.

Notice, that if one has a problem with guessing the electron's w.f. then somewhat bigger
issue arises if it comes to the w.f.s of the detectors, walls, etc.. There, one
has to deal with 10^25 or more atoms. How do you propose to determine details of w.f.
for those objects?

The only realistic way is to guess their wave functions.

Why bother then? Since heavy guessing is inevitable, why not to guess just the electron w.f. and focus on its properties?

Otherwise you fall into a circular reasoning:
1. To determine w.f. of an object you have to measure it.
2. You don't know what you measure if you don't know the w.f. of the measuring
apparatus.
3. So, you have to measure the w.f. of the measuring apparatus, and so on ...

I propose to cut this circle in the most convenient point i.e. the one that requires
the least amount of guessing.
If you want to test the statistical character of QM’s formalism you cannot use statistics in doing the calculations, that's fallacious. At least you should estimate the errors introduced at each step.

If, for practical reasons, you cannot calculate anything without statistics that only means that the problem remains open for debate, not that you are right.

I have an idea of how to do a full QM calculation:

1. Use an as small as possible system (a single anion as the source, a molecule as beam splitter, a few cations as the detector.

2. Use a computer simulation, not a real experiment; use the wave function of the whole system.

3. Visualize the experiment evolving in time for different initial parameters, using perhaps Bohm's approach.

4. See if some interesting correlations appear (for example between the detector's state before the electron's emission, and the detection event).

This way we could see QM's true predictive power as far as this experiment is concerned.

Cheers!
 
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If you want to test the statistical character of QM’s formalism you cannot use statistics in doing the calculations, that's fallacious.
You are right. If I wanted the test that would stupid.

ueit said:
I have an idea of how to do a full QM calculation:

1. Use an as small as possible system (a single anion as the source, a molecule as beam splitter, a few cations as the detector.

2. Use a computer simulation, not a real experiment; use the wave function of the whole system.

3. Visualize the experiment evolving in time for different initial parameters, using perhaps Bohm's approach.

4. See if some interesting correlations appear (for example between the detector's state before the electron's emission, and the detection event).

This way we could see QM's true predictive power as far as this experiment is concerned.
I do similar simulations on the daily basis. Without calculating Bohm's trajectories,
because they do not provide any additional information.
What I have is the full evolution of many-body wave functions for systems with interacting
particles and for different initial wave functions.

What I get at the end of the evolution is another many body wave function. And this
is it for quantum mechanics.

The next step is to take the wave function modulus squared and sample it to generate possible
outcomes of a single run of the experiment.

Sometimes the structure of the wave function is such that only very limited class of single
run outcomes is possible, and they are observed in real life experiments. Mainly with condensates.


Cheers!
 

reilly

Science Advisor
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Reilly:....”

You consider only one aspect of the problem. Your description of the measurements fit perfectly the mathematical framework used in the classical physics. It essential feature is the use of analysis (classical,vector and tensor consequently). In the foundation of the analysis lies lim operation which can’t be reduced to addition and multiplication. It means intrinsically that for every predefined epsilon > 0 you may find suitable delta > 0. And thus your notion of accuracy fit it perfectly too.
However, QM do not follow that scenario.
Consider properly calibrated and functioning set of the measurement instruments. You perform the observation and obtain a point. Now you repeat the procedure for the identical system (the standard QM treatment of that notion). Your new observation is legal exactly as the previous. However, it do not always satisfy your requirement. Sometimes one obtain points where delta is arbitrary large. This do not mean that now your measurement equipment is spoiled. This mean that you met new physics (and new mathematics consequently).
Quantum world is not a classical world.
After spending time moving lead bricks around for shielding for electron scattering experiments, and working extensively with data from such experiments, I'll claim that the measurements don't know from quantum or classical. It's all in the eye of the beholder. Perhaps it's not quite a mantra, but "experiments are experiments", and "propagation of errors is propagation of errors." There's nothing quite like computing or measuring the 5th decimal place; tends to make one practical.

Regards,
Reilly Atkinson
 

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