Location or Momentum

Space Guy

Bruster Rockit: Space Guy!                           by Tim Rickard

A key element of quantum mechanics is Heisenberg’s uncertainty principle, which forbids the simultaneous measurement of the position and momentum of a particle along the same direction, as so aptly illustrated by Tim Rickard above. 

E = c \, p \!  for a photon, where E is the energy, c is the speed of light and p is the momentum.    So the momentum of a photon is equivalent to the energy of the photon divided by the speed of light or p =  E/c  where E is also related to the frequency of the photon by Planck’s Constant E = hf.   h is Planck’s constant and f is the frequency assigned to the photon.   f is also related to the wavelength of the photon by f = c/λ.  

So E = hc/λ = cp       Therefore    p = h/λ

But we know the values for both h (6.26×10^-34 joules sec.) and for λ if we know the color of the photon.  Usually if we are dealing with coherent light (red laser for example) then we know the wavelength λ very accurately.   Thus we know the momentum very accurately.

There is another factor in this equation – spin angular momentum of the photon which is independent of its frequency.  Spin angular momentum is essentially circular polarization for a photon.  Angular momentum is ±h/2π.   It is the helical momentum of the photon along its flight path.   In order to pin down the momentum we also need to know its angular momentum, but it is a constant that is either spinning one way or the other, no half spins no quarter spins just +h/2π or -h/2π.   

The key for this discussion is that we know the momentum for any photon if we know its wavelength.   p = h/λ and the direction of its spin ±h/2π.   According to Heisenberg’s principle we cannot know the location of the photon if we know its momentum.  Since we do know its momentum we are at a loss to try to pin the location to a particular spot such as through a narrow slot or pinhole.  

Whenever we try to fit a photon through a slot, we are trying to pin down the location as it goes through the slot.  The narrower we make the slot the closer we are trying to pin it down.   Nature resists by causing havoc with our measurements – fuzzy behavior/weird effects.

Pair Production

Pair production is a possible way for nature to slip one by us – putting a photon through both slots simultaneously, thus confounding our measurements completely.   When a photon hits an obstacle such as the thin barrier between the two slots, it melds through the slots around the barrier as in my earlier posts or possibly down-converts to a lower frequency pair of photons (or up-converts to a higher frequency) through pair production (conserving energy by the frequency change).  These pairs recombine on the far side of the barrier through an up (or down) conversion process causing an effective interference due to jiggling in the conversion process. 

Our barrier strip knocks the photon silly, and it responds by splitting up, zipping through the two slits independently, then recombining in a way that looks like interference.

Virtual Photons 

Another type of pair production would be through creation of a virtual photon – a pair with one real and one virtual as also mentioned in an earlier post.   The scenario is the same – barrier knocks photon silly, virtual photon forms, passes through other side, then effectively recombines while interfering with the “real” one.   The original and virtual photons could actually be down converted or up converted photon pairs that recombine by up or down conversion causing interference-like behavior.

In either case, blocking one slit or the other would prevent melding and also prevent pair production as well as the formation of virtual photons.

Pair production through down/up conversion and/or virtual pairs would fit better with particles with mass acting like waves that cause interference when passed through slits.  Even bucky balls and cats could potentially form virtual pairs if moving close to the speed of light.   Well, again, maybe not cats.


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