Heisenberg Uncertainty Principle

[tom_the_cowboy]

The Heisenberg Uncertainty Principle states that both the exact (as near as we can get to thusfar) position AND momentum of a particle cannot be obtained because in learning its exact position we alter its momentum and vice versa. Does this mean we only have rough measurements of particles produced in particle accelerators? If so, why can't two particles be produced from a collision and the momentum of one measured and the position of the other measured thereby giving exact measurements of both position and momentum for each (albeit after the measurements were taken both variables would have changed, but at least exact measurements at the point of collision could be obtained). Can this be done? Has it? Is there some basic physics principle I've forgotten about?

Thanks for your replies in advance.

 

[selfAdjoint]

The Heisenberg Uncertainty Principle states that both the exact (as near as we can get to thusfar) position AND momentum of a particle cannot be obtained because in learning its exact position we alter its momentum and vice versa. Does this mean we only have rough measurements of particles produced in particle accelerators? If so, why can't two particles be produced from a collision and the momentum of one measured and the position of the other measured thereby giving exact measurements of both position and momentum for each (albeit after the measurements were taken both variables would have changed, but at least exact measurements at the point of collision could be obtained). Can this be done? Has it? Is there some basic physics principle I've forgotten about?

Thanks for your replies in advance.

The uncertainty principle states that for "non-commuting observables" like position and momentum, The product of the uncertainty in one times the uncertainty of the other has a constant lower bound.

Note that you can get position as accurate as you like (and your experimental techniques can support), or you can do momentum as accurately as you want. You just can't do them BOTH with arbitrary precision at the same time. Classical readouts from accelerators, like bubble chambers, tried for position accuracy and simply didn't look at momentum. You got photographs of trajectories.

On the other hand "calorimeters", essentially stacked sheets of armor plate that measure momentum by seeing how many sheets the particle can penetrate, look only at momentum. So you see they DO obey the Uncertainty Principle - they have to! But they do manage to collect the information they need by looking at different events with different particles.

 

[cartuz]

The Heisenberg Uncertainty Principle states that both the exact (as near as we can get to thusfar) position AND momentum of a particle cannot be obtained because in learning its exact position we alter its momentum and vice versa. Does this mean we only have rough measurements of particles produced in particle accelerators? If so, why can't two particles be produced from a collision and the momentum of one measured and the position of the other measured thereby giving exact measurements of both position and momentum for each (albeit after the measurements were taken both variables would have changed, but at least exact measurements at the point of collision could be obtained). Can this be done? Has it? Is there some basic physics principle I've forgotten about?

Thanks for your replies in advance.

Dear Cowboy,
You are right! Your idea is the same which you can read in A. Einstein, P. Podolsky, R Rosen "Can the Quantum-Mechanical Description be Complete?" in Phys. Rew., 1935, p.777, Number I do not remember.
This paper is very often citation. But the EPR idea is change and now employ to the spin-states. In this paper you cannot see particles with SPIN. In the same time Bell's experiments was found on the this paper but Bell employ EPR idea to spin-statistics.
Cartuz.

 

[marlon]

Note that you can get position as accurate as you like (and your experimental techniques can support), or you can do momentum as accurately as you want. You just can't do them BOTH with arbitrary precision at the same time.

TO THE OP : Though this is very correct, i never understood why people explained the HUP like this. I find it very misleading. As a matter of fact you can get both position and momentum completely accurate, or at least as accurate as your measuring device alows you to acquire these data. What i mean is that for a given fixed position, you can get a definite momentum value. It is just that if you were to measure the momentum value again at that same position, you will acquire another value. This way of looking at the HUP also gives a clear view as to how you need to look at the calorimeter thing.

regards
marlon

 

[dextercioby]

i mean is that for a given fixed position,

And how do u define that using physical & mathematical terms...?

Daniel.

 

[marlon]

And how do u define that using physical & mathematical terms...?

Daniel.

just assume that the uncertainty of position is zero and the uncertainty of p is infinite. That's the whole point

marlon

 

[dextercioby]

U can't assume the uncertainty in position is zero.It's a nonphysical state.

Daniel.

 

[cartuz]

I can to clear HUP by my way.

$$xp=\hbar/2$$

$$xm\overset{\cdot}{x}=x\overset{\cdot}{x}\frac{F}{\overset{\cdot\cdot}{x}}=\hbar/2$$

It is the equation which I can name the quantum oscillation equation

$$\overset{\cdot\cdot}{x}-(\frac{2F\overset{\cdot}{x}}{\hbar})x=0$$
$$\omega^{2}=\frac{2F\overset{\cdot}{x}}{\hbar}$$

Than HUP is equal to oscillation equation! Because x and p not independent.

 

[dextercioby]

It doesn't make any sense what u wrote there,i sincerely hope u realize that,too.

Daniel.

 

[marlon]

U can't assume the uncertainty in position is zero.It's a nonphysical state.

Daniel.

I think you are missing the point. If you don't want to take a zero uncertainty, then just take a small one...Even you can take it as big as you want, it really does not matter to what i am trying to say. There is nothing that says you cannot place a detector at one fixed position and check out if a particle passed through it.

marlon

 

[dextercioby]

I think you are missing the point.

Maybe...

If you don't want to take a zero uncertainty,

Oh,but I do,but it's IMPOSSIBLE.

Daniel.

 

[caribou]

Does this mean we only have rough measurements of particles produced in particle accelerators? If so, why can't two particles be produced from a collision and the momentum of one measured and the position of the other measured thereby giving exact measurements of both position and momentum for each (albeit after the measurements were taken both variables would have changed, but at least exact measurements at the point of collision could be obtained). Can this be done? Has it? Is there some basic physics principle I've forgotten about?

Actually it's not even about measurement, as no particle exists in the theory with the properties of both a precise position and a precise momentum, so if quantum mechanics is the correct way to describe nature, then both can't be assigned to any particle in the way we might like.

 

[wangyi]

The Heisenberg Uncertainty Principle states that both the exact (as near as we can get to thusfar) position AND momentum of a particle cannot be obtained because in learning its exact position we alter its momentum and vice versa. Does this mean we only have rough measurements of particles produced in particle accelerators? If so, why can't two particles be produced from a collision and the momentum of one measured and the position of the other measured thereby giving exact measurements of both position and momentum for each (albeit after the measurements were taken both variables would have changed, but at least exact measurements at the point of collision could be obtained). Can this be done? Has it? Is there some basic physics principle I've forgotten about?

Thanks for your replies in advance.

I think EPR is the key to your question, as posts has discussed before, but i still have one point to say. at colliders, this is not a problem in experiment (although it is still a problem in theory), because the momentum is very large, and a uncertainty delta p can be egnored for practical insterest. That is why
at colliders it *seemed* to be able to measure x and p together.