X-Message-Number: 22039 From: Date: Sat, 21 Jun 2003 04:19:09 EDT Subject: Re: Infrared divergence --part1_b7.332f67b6.2c256efd_boundary Content-Type: text/plain; charset="US-ASCII" Content-Transfer-Encoding: 7bit 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. --part1_b7.332f67b6.2c256efd_boundary Content-Type: text/html; charset="US-ASCII" [ AUTOMATICALLY SKIPPING HTML ENCODING! ] Rate This Message: http://www.cryonet.org/cgi-bin/rate.cgi?msg=22039