On Sun, Jul 6, 2014 at 3:41 PM, <mix...@bigpond.com> wrote: You can get an idea of this from the HUP where delta E x delta t >= h_bar/2. > If delta E is the energy of the reaction (about 4 MeV), then you get a > time of > at least 8E-23 sec. > (I think this is the way it is normally calculated.) > In any event it is obvious that a process that only takes order 1E-22 > seconds is > far more likely to occur than one which takes 1E-9 seconds (I think this is > actually more like 1E-17 BTW, but I'm not sure whether these times can be > measured or this is just calculated.) >
So that's how conjugate variables are used. Note that the difference between 1E-22 s and 1E-17 s is significant for what we're talking about. A photon can travel atomic distances in 1E-17 s, while it will not get very far in 1E-22 s. I think the shortest duration measured (according to Wikipedia) is 12 attoseconds = 1.2E-17 s, so the 1E-22 must be a calculation or a lower bound. A photon is only virtual if the separation distance is less than the > wavelength > of the photon (actually I suspect that this should be wavelength/2*Pi). > According to this page [1], "in the case of photons, power and information transfer by virtual particles is a relatively short-range phenomenon (existing only within a few wavelengths of the field-disturbance, which carries information or transferred power)". Unless the statement is in error, it seems, then, the virtual photon can exist within several wavelengths rather than less than a wavelength. Note that the wavelength of a 24 MeV photon is 51 fermis. Several wavelengths would be perhaps 100-200 fermis. It seems that such a photon would not travel very far before having to become a real photon. If the 24 MeV could take the form of thousands of virtual photons, by contrast, they would each have a much smaller energy (24 MeV / 1000 = 24,000 eV, say), and a corresponding wavelength of 51,666 fm. Multiplying this wavelength by three to get several times the wavelength, the virtual photons would extend out to around 155 pm, which is on the order of the lattice spacing in a metal. The reason I like virtual photons over real ones is that it's nicer to have "messages being passed between interacting particles" (e.g., Feynman diagrams) than to have to have "gammas being intercepted" (e.g., Widom-Larsen). Eric [1] http://en.wikipedia.org/wiki/Virtual_particle
