X-Message-Number: 22039
From: 
Date: Sat, 21 Jun 2003 04:19:09 EDT
Subject: Re: Infrared divergence

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From Michael C. Price:

> According the quantum field theory the number of virtual *and* 
> real photons emitted during Bremsstrahlung are *both* infinite.  
> See, for instance, Appendix 6 (Infrared Divergences to All Orders) 
> of Quantum Field Theory by Michio Kaku, which is quite explicit 
> on this point.
> 
> Cheers,
> Michael C Price
> 
Sorry to disagree, I stand on what I have said: If you use the common 

definition of infinite as very large number beyond computing capacity, then in 
all 
real situation the number of real photon must be finite. I have not read the 

Michio Kaku book, so I don't know what he exactly said here, but if he said what
you have understood, then he is wrong.

There is another way to say what I have said before: Assume there is an 

infinite number of real photons, all with positive energy (this is always true 
with 
real photons). Assume more than the total energy is finite in the way that 

the infinite set: 1+1/2+1/4+1/8+... has a finite sum equal to 2. Adding more and
more photon will give you the total energy with more and more precision, so 
the uncertainty on energy goes to zero.

From Heisenberg's uncertainty principle, that implies an infinite time 

uncertainty. So we are back at what I said first: an infinite number of real 
photons 
needs an infinite time. Because the universe age is finite, there is no 
process with infinite duration and so no infinite infrared photon number. That 

problem comes from the fact that stating the problem forget for the basic 
quantum 
uncertainty effect. If you reject it, I would ask for very strong experimental 
facts, not a book quote.

Sorry for Michio.

Yvan Bozzonetti.


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