X-Message-Number: 22070 From: "michaelprice" <> References: <> Subject: Infrared divergence and infinity Date: Wed, 25 Jun 2003 06:23:41 +0100 Yvan Bozzonetti wrote: >> 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: Sorry Yvan, your heuristic counter-argument amounts to no more than a restatement of the well known fact that energy eigen states are stationary states. No heuristic argument based on the uncertainty principle can stand against the detailed calculations of quantum field theory, since the latter includes the former. Kaku's views are mainstream and detailed and derive from quantum field theory -- any QFT text book that discusses the infrared divergences will show that the real soft photon number is infinite. > If you use the common definition of infinite as very large number > beyond computing capacity, then in all real situations the number > of real photons must be finite. A non-sequitar. Why should the behaviour of nature be constrained by our ability to compute it? Peter Merel and myself seem to be in agreement about whether an infinite number of photons may exist and that they can't be directly measured, since only a finite number will exceed the sensitivity threshold of any detector. Our disagreement seems to be whether this means the (quantum field) theory is "ill-framed" or not. Attempts to reformulate theories with infinite quantities in terms of finite measurable observables is called "renormalisation" and is a well studied and active area of research. However the numerical infinities from the infrared divergences are very mild (they don't involve infinite energies, for instance) and the common view seems to be that they are acceptable in theories precisely because they don't lead to any measurable paradoxes. A final point. >> 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? I was using "representation independent" in a narrow technical sense. In quantum mechanics / quantum field theory a "representation" refers to the choice of basis or axes within the Hilbert space. Physical or measurable quantities are unaffected by such a choice and are thus said to be scalar or representation independent . Real photon number is such a scalar quantity, even though the actual number measured is also dependent on detector sensitivity. Cheers, Michael C Price ---------------------------------------- http://mcp.longevity-report.com http://www.hedweb.com/manworld.htm Rate This Message: http://www.cryonet.org/cgi-bin/rate.cgi?msg=22070