Quantum Particle Momentum Measurement: Theoretical and Practical Considerations

[BWV]

Is it possible, practically or theoretically to measure the momentum of a quantum particle without altering the momentum? (the only real world tests I have read about involve collisions with other particles)

If so, what would be result of a measurement of momentum have if interjected between two measurements of spin on the same axis (like the Stern Gerlach experiment)? would the spin test still be repeatable or would perhaps the location of the particle change?

 

[edpell]

"Is it possible to measure the momentum of a particle without altering the momentum?"

No.

To measure it you must interact with it. The interaction changes it. If you can think of a way to make a measurement without interacting with the particle let us know.

 

[dlgoff]

For an interesting read on measuring position and momentum, check out this thread: https://www.physicsforums.com/showthread.php?t=516224"

 

[Naty1]

The first post is ok...here is a bit more.

You can't even measure the momentum of a planet without altering it...say with a radar signal...electromagnetic radiation pressure; Of course the change is imperceptably small, likely smaller than anything we can hope to measure, so it's inconsequential...and of little interest in general.

But when measuring quantum systems, like a subatomic particle, such effects may well be significant. To measure a particle's momentum,or any other dynamic variable, we need to interact with it via a detector, which localizes the particle. Will this be significant or insignificant? Conceptually there is no limitation on how precisely we can measure some variable of a single particle. But the practical problem is that the shorter the wavelength of light of the measuring system, for better resolution, better "precision", the more energy is transferred to the particle under observation and the more it becomes disturbed (energized) by ANY apparatus...so you can't in practice get an arbitrarily "accurate" measurement without disturbing the particle.

In addition, the accuracy of certain pairs of repeated simultaneous measurements are further limited by Heisenberg uncertaintly. Spin and momentum are not so limited.,,but position and momentum,for example, are limited by HUP.

 

[Naty1]

effect on spin:

I think the effects depend on whether you mean subsequent tests on the same particle or a typical stream of prepared experimental particles. I think it's generally agreed that if the measurement is promptly repeated on the same particle, without re-preparing the state, one finds the same result as the first measurement. But if you are measuring a stream of different particles using the exact same measurement approach, you'll get a statistcial distribution of measurement results.

 

[BWV]

Thanks for the responses, let me put the OP more simply

- after testing for spin on one axis you can repeatedly test for it on the same axis and get the same result, but once you test for spin on another axis, you cannot "recover" the original spin - the test on the x-axis will give 50/50 results regardless of what direction the x-spin was in the first test

my question is what happens if you test for spin on the x-axis and then perform some other test that collapses the wavefunction but for compatible variable (I was thinking momentum in the OP, but it could be anything other than spin). Would a second test for spin then repeat the results of the first test?

 

[maverick_starstrider]

I think you could get the momentum indirectly, if you have a scattering event or pair of particles interacting through some momentum-conserving potential you could then look at the momentum of the other particle and figure out the original.

 

[haael]

my question is what happens if you test for spin on the x-axis and then perform some other test that collapses the wavefunction but for compatible variable

The measurement of spin is associated with some "direction" in the configuration space. The measurement of other variable - with some other. The spin associated with the second measurement doesn't need to be the same as the first, but their correlation is dictated by the relative angle between the 2 measurement vectors. Or, to be more precise - by their scalar product.

If the second measurement is orthogonal to the first, the results are unrelated. If parallel - they are the same. In the middle case they are correlated to some extent.