Uncertainty principle in action

[steevey]

So I heard that when you shine light like a laser through a narrow vertical slit, it appears as a dot. But, when that slit becomes very narrow, the light passing through starts to spread horizontally, and the reason for that is because your more precisely confining the area or measuring the area and therefore the less precisely the direction of the light is determined.

 

But, for some reason, that doesn't seem to make sense. Why wouldn't the light then spread vertically AND horizontally if the direction is becoming less determined?

 

It just seems like there's some conventional or classical way to explain this. Is there?

Edited January 30, 2011 by steevey

[Schrödinger's hat]

You're only constraining it's horizontal position, and thus unconstraining it's horizontal momentum.

3 degrees of freedom, x, y, z are independant. That includes the uncertainty principle as it applies individually to each (and to time, just the same)

 

EM theory is almost identical to quantum theory for this situation (Spin-1 wave equation is just maxwell's equation with a mass term). Quantum versions of measurement, and interaction terms are left out in this regard, but the classical EM wave equations describe this effect perfectly adequately.

 

Look up Fourier transforms and how they relate to EM.

 

As to why the Fourier transform rocks up to the party whenever you try and do anything, this is a mystery. I didn't send invitations to e, pi, or i either, but they're off in the back room doing something unwholesome.

[steevey]

You're only constraining it's horizontal position, and thus unconstraining it's horizontal momentum.

3 degrees of freedom, x, y, z are independant. That includes the uncertainty principle as it applies individually to each (and to time, just the same)

 

How is the momentum being unconstrained though? The photons of the beam generally have the same wavelength and frequency, but it seems as though when I constrain one direction, how it moves in the other direction is less constrained, it doesn't seem like the momentum is changing, just where the particles of the beam end up.

[swansont]

The constraint is the slit. The HUP tells you as you limit the spatial extent, the uncertainty in momentum gets larger. You're only doing that in one dimension.

[steevey]

The constraint is the slit. The HUP tells you as you limit the spatial extent, the uncertainty in momentum gets larger. You're only doing that in one dimension.

 

So there's literally different amounts of momentum from photon to photon as I constrain the slit even more? Why not just an uncertainty in one direction as I constrain the other?

[swansont]

So there's literally different amounts of momentum from photon to photon as I constrain the slit even more? Why not just an uncertainty in one direction as I constrain the other?

 

The directions are orthogonal. The momentum and position operators don't couple.