X-Message-Number: 22045
Date: Sat, 21 Jun 2003 22:11:01 -0700
Subject: No physical infinity.
From: Peter Merel <>

Michael C Price writes,

> No, the real[*] photon number is a representation independent quantity.

I'm not certain I understand how any quantity can be distinguished 
independent of a representation. Can you say more on this?

> This goes back to Planck and Einstein's work on
> the photoelectric effect of 1899-1905.  A photon's energy is
> simply frequency (f) x Planck's constant (h) so that the number
> of photons totalling energy (E) is just E/hf.

Sure. But here we have a theory founded on distinctions of the 
behaviour of various but specific experimental apparatus. Except for 
its reliability in predicting this behaviour, and the behavior of 
apparatus in related experiments, the theory determines nothing about 
what's actually going on.

If we reformulate our theory wholely in terms of the range and 
resolution of experimental measurement, rather than in the artifacts of 
its interpretation, then due to resolution limits it is impossible to 
measure a zero, and any mathematical manipulation of it - division, 
log, etc. - cannot produce an infinity.

The infinity is simply an artifact of a point. Since De Cartes we speak 
of points in space, but we know that no process of subdivision of a 
space can produce a point except by taking a limit to infinity. Since 
we're physically incapable of achieving this limit, we're never going 
to encounter any points in any space describing an experiment. So the 
theory concerns itself, in the limit, with a nonsense.

> Because our sensors always have some threshold of sensitivity,
> only a finite number of soft photons can be measured by a
> particular detector.  Nevertheless the theory is unambiguous
> about the existence of an infinite number of soft photons.  The
> more sensitive the detector is made the more photons it will
> detect.

Since we can have no infinitely sensitive detectors we may say the 
theory is poorly framed. But as I said the program of correcting it is 
an extremely ambitious one, and I'm not volunteering for it.

> Division by zero to produce infinity often occurs in physics.
> In this example the zero is the photon's rest mass.and the
> infinity is the photon number.  These infrared divergences
> occur everywhere in quantum electrodynamics.

Yes. It's a little sad that we haven't asked ourselves whether such 
things could be artifacts of our language of description rather than 
empirically relevant phenomena. If we were to reformulate the math so 
that no infinities appeared, we might find ourselves with a basis for 
some interesting new empiricism, don't you think?

Peter Merel.

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