How Does Quantum Mechanics Combine Particle and Wave Descriptions?

[vanesch]

Can you point me, please, to an article containing a clear formulation of MWI in terms of its postulates?

http://plato.stanford.edu/entries/qm-manyworlds/

 

[ueit]

http://plato.stanford.edu/entries/qm-manyworlds/

Thanks.

Although all worlds are of the same physical size (this might not be true if we take quantum gravity into account), and in every world sentient beings feel as "real" as in any other world, in some sense some worlds are larger than others. I describe this property as the measure of existence of a world.[5] The measure of existence of a world quantifies its ability to interfere with other worlds in a gedanken experiment, see Vaidman 1998 (p. 256), and is the basis for introducing probability in the MWI. The measure of existence makes precise what is meant by the probability measure discussed in Everett 1957 and pictorially described in Lockwood 1989 (p. 230).

Is this "measure of existence" deduced somehow or postulated to be identical with Born's rule?

 

[vanesch]

Is this "measure of existence" deduced somehow or postulated to be identical with Born's rule?

That's the big question in MWI. Personally, I think you have to postulate it, and I even think I have the proof that it is logically independent. But some people try to deduce it. They are encouraged by that by things such as Gleason's theorem and similar results which indicate that (with some weak additional assumptions) the only consistent way of assigning probabilities to terms in a wavefunction is through the Born rule (the Hilbert norm in fact).

Personally, I don't think it is a problem that this is an extra postulate, because after all, it is part of the link between the "objective universe state" and the subjective "world experience" which is in any case, in this setting, a postulated relationship.

 

[ueit]

With all due respect, I find it hard to believe that you read my post. In fact, I provide an outline of how to compute the effects of of electron-screen interaction. (#1 and #1A) I will agree to laziness; I'm quite sure that this calculation has been done, but I will leave it at that.

I've certainly read your post. I may be a little lazy but the reasons for not doing the calculations you suggested are:

1. I have little time (full time job + 1 little kid) and I've forgot much of the math required.

2. There is no chance to explain interference in this way because the pattern changes when we cover a slit. The force the electron "feels" at the slit should depend on the macroscopic structure of the wall so we need a much complicated calculation (including for example the lattice oscillations, which are a function of the wall shape).

Even if you can demonstrate that screen-electron interactions cause electron diffraction, you'll still have to worry about electron & neutron diffraction from crystal lattices. Tough job indeed.

What other possible explanation could be for the particle's change in momentum if not an interaction with the wall (crystal lattice, whatever)?

Not to worry about momentum conservation: inspection of the system confirms that it's ok to treat the screen as if it has an infinite mass. That is it takes a huge hit to get the screen to move -- in comparison to an electron boucing from the screen.

Sure, momentum conservation is only important to prove that there is interaction between the particles and the wall.

As a matter of fact, there is, I think, another factor that should be taken into account, the influence of the wall on the source, prior to the particle's emission. It's the only way we could explain EPR experiments in a local manner and this probably applies to the double-slit as well.

Regards,
Andrei Bocan

 

[ueit]

ueit,
This reply is late because I didn't notice that you actually referred to my post.

As a side note: the treatment I proposed is not semiclassical. The word semiclassical
usually means that some aspects of a dynamics of a system are treated classically rather
than quantally.
I propose to ignore the screen with the slits and the detector completely not just their quantum
nature. In their stead I recommend focusing on the wave function of the system of interest,
i.e. of the wave function of an electron just before it hits the detectors.

As you said, QM is statistics, so the wave function is just enough to generate outcomes
of an ideal experiment by sampling the corresponding probability density.

This way you escape from the measurement problem and from internal complexity of
the screen and the detectors.

Cheers!

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.

 

[zbyszek]

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!

 

[ueit]

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!

 

[zbyszek]

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.

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]

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