Uncertain if This is Just Diffraction

via zapperz

One thing that would have been useful, I think, is a calculation in support of this, even if it’s just an order-of-magnitude one, to tell us if this is reasonable. The size of the spot (maybe a cm?) gives you a bound on the uncertainty of the transverse momentum. It’s green light (probably 532 nm) and the screen is of order a meter behind the slit. That tells us what the transverse component of the momentum should be — the momentum of the photon multiplied by the sine of the angle (or just the angle, in the small-angle approximation, which is around 0.01 radians)

So the uncertainty of the momentum is around 0.01 of the momentum, given by $$h/lambda$$, so Planck’s constant drops out when we pop this into the uncertainty relation. Rearranging the equation tells us that $latexDelta{x} > frac{lambda}{4pitheta}$ or that we shouldn’t see this effect until the slits are separated by less than about 10x the wavelength of the light — which is around what we expect just from experience in diffracting light, that it only becomes an important consideration as you approach the wavelength of the light.

1 Comment so far

1. tibbles the cat on January 17th, 2013

forget numbers!
what would you see when trying to put balls trough a hole of given size ?
as in playing pool.
the ideal shot would go straight into the pocket, some would bounce off the cushion but still reach the pocket, and the occasional rare one would ‘with seemingly improbability, just scrape through’.
this has nothing to do with an artificial an arogant contruct but gives the same end result

if a photon was acredited with the size of an electron, and the smallest slit we could make was an atom thick (it was many times that) then there is quite a large side ‘ of the pocket’ for it to bounce ‘off’.

same pattern but no need to make up rubbish. no numbers needed.
wot you cant see something and measure what it is doing with out affecting it ?
can i quote you next time i get a speeding ticket ?

I was shrodingers cat, stuck in that fucking box ! did he exist in some quasi-quantum state from my poiint of view ?
No I was wondering why im in this box, where is my next meal comining from and i need to pee !

no numberrs required