Can Different Wavelengths Measure Particle Momentum and Position Simultaneously?

[blip]

The Uncertainty Principle says, in so many words, that if you use a shorter wavelength of light you obtain a more accurate value for the position of the particle, and that if you use a longer wavelength you obtain a more accurate value for the momentum. Of course the more accurate you are with one value the less accurate the other is.

What happens if you try and measure the momentum and location simultaneously using two different wavelengths?

I think I'm just confused on why you can't create a situation in which you can trap the particle. Perhaps by looking at something with incredible density (if it was possible).

 

[HallsofIvy]

"Trap the particle"? What do you mean by that?

If you use "two different" wave lengths (I presume you are thinking of one long and one short) you don't get anything better. The short wavelength will give you an accurate position but will "kick" the particle so that you no longer are sure of its momentum. Adding a long wave length to that will only add to the "kick".

If you are thinking of using a long wave length to determine its momentum first, then a short wavelength to determine its position, yes, you will momentarily have an accurate momentum but the instant you use that short wavelength (with higher energy), you no longer know what the momentum is.

 

[marlon]

A short wavelength will give you an accurate position for a very short while. A long wavelength will give an inaccurate position. Using the two simultaneously will disturbe the two measurements. The accurate position-value will become more inaccurate because of the long wavelength that you used. Besides you are forgetting about one other very important parameter : the minimal angle between two different points that is necessary to see these points as two different dots at a certain distance r...

marlon

 

[seratend]

uncertainty principle is the simple constatation that we cannot have a signal (say s(t)) that is at the same time a dirac pulse (a single value in time) and a sine wave (a single value in frequency).

When you use it with the position and momentum observables, you simply note that you cannot have at the "same time" a fixed particle (single x value) and a uniformly moving particle (single p value) (attention it is an oversimplified view).


Seratend.

 

[caribou]

Standard quantum theory doesn't actually have a mathematical description in it of something with both a precise momentum and a precise position at the same time, so if standard quantum theory is correct then nothing exists with that description. The theory could be wrong of course but it seems okay.

I'm not sure what happens physically if you try to perform a precise position and a precise momentum measurement at exactly the same time, though. Perhaps the photon for position measures both the particle and the photon for momentum, and the photon for momentum measures both the particle and the photon for position, and you end up with a whole lot of uncertainty in both cases.

 

[blip]

Thanks for the replies, I think I understand it a bit better now.