Laser Light & HUP: Understanding How Position & Momentum Affect Each Other

[LarryS]

A beam of light from a laser projected on a screen with a very small hole in it will spread after it traverses the pin hole because of the HUP: Measuring position so accurately causes loss of information about the momentum. I believe that in the case of laser light, only information about the momentum vector’s direction is lost. The magnitude of the photon’s momentum vector is still precise because the photon’s energy is still precise.

If that is correct, then why is it correct? In general, there is nothing in the HUP that allows the momentum magnitude to remain precise.

 

[Bill_K]

The Heisenberg uncertainty principle would apply if you really confined a system in the x and y directions. Passing it through an aperture is not really the same thing as confining it.

 

[LarryS]

The Heisenberg uncertainty principle would apply if you really confined a system in the x and y directions. Passing it through an aperture is not really the same thing as confining it.

Maybe "measuring" is a better word than "confining".

It is my understanding that the HUP applies to each dimension, x, y and z, separately.

If passing it through a very small aperature is not confining or measuring it in the, say y dimension, then what accounts for the spreading of the beam after the aperature?

 

[RedX]

A beam of light from a laser projected on a screen with a very small hole in it will spread after it traverses the pin hole because of the HUP: Measuring position so accurately causes loss of information about the momentum. I believe that in the case of laser light, only information about the momentum vector’s direction is lost. The magnitude of the photon’s momentum vector is still precise because the photon’s energy is still precise.

If that is correct, then why is it correct? In general, there is nothing in the HUP that allows the momentum magnitude to remain precise.

I think that's correct. Energy is conserved. Momentum changes direction, both in the direction of the slit and perpendicular to the slit, but the magnitude of the momentum is the same. I'm not completely sure though.