How come we can create a parallel laser beam?

The speed of a photon is the speed of light. According to Heisenberg’s uncertainty principle, its location is completely undetermined. How come we can create a parallel laser beam?

Asker: Eric, 72 years old

Answer

Two adjustments are needed to your problem statement. Heisenberg says that the product of uncertainties on position and on momentum (also called momentum), in the same direction, is greater than a given constant. For “classic objects” momentum is the product of velocity and mass, so the system is often abbreviated as “position vs velocity”. But photons have no mass when stationary, and for them the following applies: momentum = energy divided by the speed of light.

So:

(a) You must consider position and velocity/impulse IN THE SAME DIRECTION. In your question, the speed of light should therefore not be related to the width of the beam, but rather to the distance of the photons from the laser. The question then is, even though the speed of light is a fundamental constant, how can you say that a photon is at a given distance from the sender?

(b) To answer this last question, the difference between IMPULSE and velocity is important: the velocity of each photon is a fundamental constant, but their momentum depends on their energy, and on the latter there is an uncertainty distribution. So Heisenberg becomes: uncertainty on the energy of the photon, times uncertainty on the distance from the photon to the laser, is greater than a given constant. This presents no problem to define a position with finite uncertainty, as long as the energy of the photon is also slightly uncertain. And indeed: light of exactly given energy (=frequency) necessarily forms a wave, whose position is distributed over the whole space; while by superimposing a “packet” of waves with neighboring frequencies you can build a light signal whose amplitude is maximum only around a given position, we call this a photon.

Answered by

prof.dr.ir. Alain Sarlette

control engineering, automation, robotics, dynamical systems, applied mathematics, quantum physics

How come we can create a parallel laser beam?

university of Ghent

http://www.ugent.be

.

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