Re: More on superluminal light

[John Denker <jsd@MONMOUTH.COM>]

At 08:54 AM 7/21/00 -0400, Ed Schweber wrote:

> my interpretation of the uncertainty principle applied to photons is
> that the narrower a pulse, the greater the range of frequencies that
> have to form it - that is, the greater the momentum.

OK, provided:

1) I assume that you mean "spread in momentum" not "momentum" per se.

It is possible for a wave to have very large momentum but very little
spread in momentum;  the uncertainty principle implies that such a wave
must have a large spread in position.

2) I assume that by "frequency" you mean "spatial frequency" (cycles per
unit distance) not "ordinary frequency" (cycles per unit time).

Spatial frequency is an awkward term;  perhaps _wriggliness_ would be
better.  It is measured in units of wavenumber (cycles per cm).

========

Note that the statement quoted above requires Planck's constant only to
convert from wriggliness to momentum per photon.  If we rephrase things in
terms of wriggliness itself (not momentum) then the result applies to
classical electromagnetic waves:  The spread in position is inversely
related to the spread in wriggliness.  When stated in this way, the
uncertainty principle
 -- is not a law of quantum mechanics;
 -- indeed is not a law of mechanics, or even a law of physics;
 -- is a law of mathematics, applicable to a wide range of wave-like
phenomena.

>    Therefore, if we think in terms of individual photons, is it fair to say
> that the existence of superluminal light is a consequence of the uncertainty
> principle?

No.



"Superluminal" is usually taken to mean "propagating faster than the speed
of light".  The question is predicated on the "existence of superluminal
light" which does not exist.  Non-existent phenomena do not require
explaining in terms of the uncertainty principle or anything else.

Physics would be in pretty sorry shape if we were forced to choose between
 -- quantum mechanics (including the uncertainty principle) and
 -- special relativity (including relativistic causality, which says that
no signals can travel faster than the speed of light).
... But we do not have to choose.  A simple example is the Dirac equation,
which is a relativistically-correct generalization of the Schrödinger equation.

For more on this, pick up any book on Relativistic Quantum Mechanics or
Quantum ElectroDynamics.