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And the strangest thing about it is that those photons don't interact when being 'cajoled' into a coherent laserbeam, "the incident photon does not collide with the excited atom, apparently proximity alone triggers the stimulated emission." creating an exact copy of that photon in the process building up to that beam.
If you try to make a single cycle of a sinusoid (in time), like you have drawn, it involves a huge range of frequencies (bandwidth). To send a pulse of energy with a well defined frequency, the pulse must build up very slowly and decay slowly, too. This gives the photon a length of many many wavelengths - if you want to think of it that way. I think we have to accept the standard ideas about time domain / frequency domain relationships.I, personally, think it's a non starter and that people who talk in terms of tiny tiny photons haven't really thought it through. Certainly, the model you have drawn says nothing about the effective 'width' of a photon.I blame School Science and the use of the word 'particle' which is interpreted in the spatial sense (as in 'corpuscular theory of light' in the 16th / 17th Century).Why should the the smallness of a photon refer to anything other than its small energy?
I have always thought of a photon as one wave length of electromagnetic radiation. It consists of two points of saturated electric and magnetic amplitude always moving at the speed of light. The electric and magnetic fields exist in a spacial area around the saturated points and extend outward in space diminishing in amplitude with distance.The points of saturation appear to be particles; the fields appear to be waves.
You can have a single photon in thousands of wave lengths of an EM wave packet. It can't be as you say.
Is there, in fact, a phenomenon which necessitates the photon to be a particle? Classical em wave theory accounts for photon (wave) momentum, for instance.
Quote from: lightarrowYou can have a single photon in thousands of wave lengths of an EM wave packet. It can't be as you say.So, do you see a single photon as composed of many wave lengths? Would this be a certain number of wave cycles?
Quote from: sophiecentaurIs there, in fact, a phenomenon which necessitates the photon to be a particle? Classical em wave theory accounts for photon (wave) momentum, for instance.I suspect it is the maxima of the pointy photon wave that reacts with matter. The reaction of a single photon would be at a point because of the wave packet shape. Its exact reaction spot can't be predicted because the phase relation between the photon and its reaction partner affects the reaction location.Edit: Here's a different model; the points should be sine functions but are a little distorted.
The time function and frequency function are related by the Fourier Transform and I don't think you can ignore that.
Quote from: sophiecentaurThe time function and frequency function are related by the Fourier Transform and I don't think you can ignore that.I don't think the Fourier Transform can be applied to single photons. It is a kind of statistical analysis requiring many photon cycles. The same problem exists with describing a monochromatic signal using statistical analysis. Maybe we have become so accustomed to statistical analysis and probability functions that we can't visualize nature's reality. 
The Fourier transform is not statistical. It simply transforms from time to frequency domain. You drew a function in time and I told you something about the frequency domain version.
"The time duration for that one cycle can be exact. But you can't know the frequency until you see some more cycles"Nonsense, if I tell you that the time between the peaks on the electricity mains here is 0.02 seconds you can tell that the frequency is 50Hz.
You can only quote the frequency as 50HZ after measuring the time between two peaks if you make the assumption that time interval repeats indefinitely.if you simply make a spot check the frequency could be varying wildly.I think I have only repeated what Vern said!
The stimulated emission concept is quite interesting.Now we know that inherently the energy "gap" in the excited-state atom is perfectly matched to the rest of the laser-radiation in the cavity.We also know that the excited state has to be relatively "long lived" (metastable or whatever) to as to "hang around" long enough to be taken to the ground state predominantly by stimulated emission rather than random emission (sorry I can't think of the proper word). The fact that it "hangs around" could be interpreted/considered as some kind of energy potential-barrier.So if the excited atom momentarily "borrows" some energy from a passing "photon" then it can return to the ground-state.Buuuut... I said before the energy gap is "perfectly matched", which might imply a concept a bit like a high-Q resonant system has some relevance? ... something that would couple to an EM wave of the precisely correct frequency...? And if this was the case you might expect the stimulated "photon" to be phase-matched and polarisation-aligned to the stimulating "photon"?A bit handwavy I'm afraid - tis late at night, plus a decade or more since I studies undergrad photonics. What do you think? sophiecentaur?
Quote from: syhprum on 25/03/2009 20:35:46You can only quote the frequency as 50HZ after measuring the time between two peaks if you make the assumption that time interval repeats indefinitely.if you simply make a spot check the frequency could be varying wildly.I think I have only repeated what Vern said! That's correct syhprum.
Quote from: lightarrow on 25/03/2009 20:45:03Quote from: syhprum on 25/03/2009 20:35:46You can only quote the frequency as 50HZ after measuring the time between two peaks if you make the assumption that time interval repeats indefinitely.if you simply make a spot check the frequency could be varying wildly.I think I have only repeated what Vern said! That's correct syhprum.No it's not.Th FT is a mathematical operation like reciprocal.You can apply it to a data set and get an answer. That answer is correct, no matter what happened at some other tme.If the peaks were 20 msec apart then the frequency at that time was 50Hz.
As far as I remember, the FT of your function (I assume that it has zero value above and below the x values given) will be that of a single, top hat function modulated sinewave. That will be, basically a sinx/x spectrum extending on either side of the 'carrier' frequency - the sinewave you have drawn. The sidebands cover an infinite range.
What does that look like when you plot it?How are your graphing skills?
Your second graph looks like a pretty good sinx/x curve which is what one (I) would expect.The difference between a long burst and a short burst is very significant, when you're talking about the form of spectra from a substance emitting light.
Techmind, how do you think when you write "So if the excited atom momentarily "borrows" some energy from a passing "photon" then it can return to the ground-state."? Can one see a photon as something you can 'borrow' energy from? And still be a 'photon'. Also what are we talking about here, how does it lend that energy, by what 'mechanism' do you see it. The only way I see that happen is by HUP, and then one still have the problem of defining what 'energy' has been 'loaned' as it then will have the same 'energy' after the 'loan' as it had before? Wouldn't this be a violation of the idea of 'conservation' laws?But this still seem to be a result of HUP?