Quantum Mechanics and Determinism

[IlyaZ]

If I remember correct, some quantum mechanic principle says that you can't know the position of a particle at the same time as its velocity. Why's that?

And what about the double-slit experiment where you send photons and they go through both slits at the same time and create an interference. The observer effect I believe it's called. Does the interference effect disappear if you measure where the photon goes?

But what's a measurement? Why do you still get interference when you look at the experiment (with your eyes)? Isn't that a measurement? Of course the brain won't register the results, but it happens in front of your eyes, and if you could rewind and "zoom" you should be able to see the photons? Won't this experiment be possible with any particle?

What does all this imply to determinism?

 

[chris_183]

If I remember correct, some quantum mechanic principle says that you can't know the position of a particle at the same time as its velocity. Why's that?

it's called Heisenberg's uncertainty principle and it's just a fundamental aspect of reality...there isn't really a physical reason for it as such.

 

[Demystifier]

Quantum uncertainty does not imply a fundamental lack of determinism.
See e.g. Sec. 4 of
http://arxiv.org/abs/quant-ph/0609163 [Found. Phys. 37 (2007) 1563]

 

[IlyaZ]

Thanks, I'll read section 4.

If it's a fundamental aspect of reality, how did they arrive at that conclusion?

 

[DrChinese]

Thanks, I'll read section 4.

If it's a fundamental aspect of reality, how did they arrive at that conclusion?

As with any good theory, there is agreement with experiment and it is useful in making predictions. It cannot be derived from some other theory, so it is considered fundamental. As to why the HUP is part of reality, no one can explain that any more than why there is gravity.

 

[IlyaZ]

So they just found out that they couldn't measure the position and the velocity at the same time and later came to the conclusion that it's impossible? (it's a strong word).

And what's the "same time", wouldn't it be possible to approximate the speed/position if they measure speed and position separately at a any e=dt for all e>0.

 

[quadraphonics]

So they just found out that they couldn't measure the position and the velocity at the same time and later came to the conclusion that it's impossible? (it's a strong word).

Well, if you want more context, it's a consequence of the Fourier transform relationship between position and momentum. And since this relationship turns out to be such a good theory for explaining observations, that's what we end up with.

Also, it's not that it's *impossible* to measure the velocity and position at the same time, but that there's a limit to how precisely you can know both quantities. The more precision you have in the position measurement, the less you can have in velocity, and vice-versa. In physical terms, measurements of position inevitably alter the velocity of the particle being measured, and vice-versa.

 

[IlyaZ]

In physical terms, measurements of position inevitably alter the velocity of the particle being measured, and vice-versa.

Alright, but has it been proven that all possible measurement techniques will result in that situation?

 

[quadraphonics]

Alright, but has it been proven that all possible measurement techniques will result in that situation?

Yes. Like I said, there's a Fourier transform relationship between position and momentum, so the more tightly you confine, say, the position, the more dispersed the momentum becomes.

 

[DrChinese]

So they just found out that they couldn't measure the position and the velocity at the same time and later came to the conclusion that it's impossible? (it's a strong word).

Well, agreement with experiment is important. But the theory pointed the way for later experiments, which support the theory. And it is not just position and momentum that are affecting, there are other non-commuting observables as well. In fact, the issue may be easier to picture if you consider perpendicular spin components x & y of a free electron (which don't commute).

You measure in the x direction, and get "up". If you measure again in x, you will get up again, and you can repeat this test as many times as you like on that electron and you will get the same answer. These measurements do not appear to change the particle in any way.

Now, measure in the y direction, and you get an answer for that. Go back and measure the x component, and there is only a 50-50 chance you will still get up. That is the HUP at work. The previous x "answer" was erased by the non-commuting y measurement.

Obviously, measuring the x spin alone did not change the x results. But apparently, measuring the y component does reset the x component. (On the other hand, a spin component measurement does NOT affect the previously measured momentum.) In a realistic world, that should not be possible. So the act of measurement itself does not "disturb" the particle in the physical sense (at least that is not a prerequisite).

The idea that scientists gave up because it was too hard or too confusing is ridiculous. It is a strange theory, to be sure, but it has been enormously successful. The HUP has been attacked and challenged at every turn, but it has not yielded an inch in 80 years. There is nothing wrong with questioning it, but the evidence is overwhelming.