Ok, QQ, for $100, here is how to both measure the length of a photon and demonstrate that it really is traveling between the lamp and the detector although instead of the detector illustrated below I uses either (1) a small (large postage stamp size is ok) photograph film (well shield form any light not nearly the same paths as shown) and very long time exposure* or (2) just a piece of white paper as a screen when the lamp is bright. You can imagine this Film or Screen (hereafter called FS but only one used at a time) is flat against the bottom edge of the drawing (below the detector shown , which has been removed to not cast any shadow on the FS.
if that image not here go to:
http://en.wikipedia.org/wiki/File:Interferometer.svg
I said “nearly” the same path as I do not want the infinitely thin rays shown in red, but relatively narrow “fans of light” replacing each of the two ray paths shown. I will call these two paths T (for the one using the Top mirror) and the other “R” as it is using the Right mirror. “Relatively narrow” means that if I block either path T or R, no interference pattern is formed on the FS. There will be just a nearly uniformly illuminated screen or cause a nearly uniform darking of the film instead of an interference pattern somewhat like:
| | | | | | | | | but of course the intensity is not this “all or nothing” contrast as I must represent it here due to limits of my “typed drawing.” The intensity pattern is sort of like {sin(x) + 1}/2 where I have “normalized” to make the peak intensity of the pattern unity and the least intensity in the pattern zero but we need not be much concerned with the exact shape of the intensity distribution along the “x-axis.” (which is horizontal in my typed picture of the interference pattern).
Now I need to name the nine lines of my illustration pattern. They are: -4,-3,-2,-1, 0,1,2,3,4. Line zero has exactly the same length for paths T and R. It is where there is constructive interference for all wave lengths of light and thus sometimes called the “white light fringe” or white light line of the pattern. I will be more concerned with it that the others. The pattern lines (-1) and 1 are where paths lengths T and R differ by one wavelength also but they will moves wrt the white light fringe, 0. I.e. if made with long wave red light they are farther from 0 than if made with blue light. This is one way you can tell which is the 0 line without trying to measure and make the paths T and R exactly equal (or differ by a multiple of half wavelengths – more on this in third paragraph below) – an essentially impossible task to the accuracy required.
Now if I were to slowly move only mirror R further away from the half silvered mirror keeping it always parallel to its self (zero rotation as it moves) the 0 peak will cease to be unity strong and the previous perfect nulls will start to get light. When I have moved it ¼ of a wavelength the intensity pattern will be like: {cos(x) + 1}/2. I.e. the peaks will be where the nulls were and conversely the new nulls are where the peaks were. Thus the location of the white light fringe, 0, is now a null due to perfect destructive interference. I.e. path R = path T + half a wavelength. (The ¼ wavelength is traveled to and from the mirror for a ½ wavelength extra.)
This alone should show that something with a wavelength is traveling between the lamp and the screen. but I will continue on to describe how I learn how long this energy thing (called a photon) is:
If I continue to move mirror R further away when the total distance moved is ½ wave length, 0 point on FS is again a bright peak. This alternation between null and peak repeats for several thousand multiples of ½ wavelengths without noticeable difference in the pattern but if carefully observed the nulls are no longer totally without light and more difficult to measure/ observe, the peaks no longer have the full unity strength. The total energy reaching FS is not changing – the “nulls” are filling in and the peaks are being reduced. Eventually in the case of I measured when the mirror R had moved about 15 cm (path difference of 30 cm) the screen was uniformly illuminated – no longer with even a hint of either constructive or destructive interference.
Now to explain this I need to switch to film and very long exposures (weeks?) with very weak light – much lower than one can reliably detect with even the “dark adapted eye” looking straight at the lamp. So weak a light that the quantized packets of energy (Einstein got his Noble prize related to this quantization of the photo-electic effect with similar very weak lights.) rarely ever existing two at the same time. Most (>90%) of the time, not even one exists. After a week or so of exposing the film (very cold for reasons I will not go into much except to note that the same crystal in the film must have a second photon hit it before the effect of the first is lost to diffusion to be partially stabilized) and developing it, we still find that the interference pattern is recorded in the film.
This confirms the quantum mechanical theory prediction (“nonsense” to us humans) that each photon actually travels via both paths. I.e. when the light was strong (millions of photon existing at the same time) and I was looking at the screen, each photon was actually interfering with its self that had traveled the other path. – not interfering with any of the other million of photons.
When you stop to think about it – you already knew that. A perfect interference null in waves is only possible if the peaks are exactly 180 out of phase with the nulls of the wave. For example in analogy, if you have hundreds of loud speakers each driven by separate amplifiers all producing exactly the same 1000 Hz sound wave, but not “phase locked” together, then nowhere in the room is there anything even resembling silence – perfect cancellation. If you turn off all but one sound source there are hundreds of locations in the room where perfect cancellation is occurring. Without any phase locking of the various individual radiators, the phase of each wave is random – we call this an “incoherent” source.
Most light waves (all except lasers or laser driven sources) are incoherent. All simple lamps radiate as incoherent sources. Each radiating atom is just doing its thing independently of all the others. Thus, when I see a perfect null on the screen with millions of photons falling on it elsewhere, I know that QM’s perdiction and the experiment with very weak light / long exposure is also the strange for humans to understand self interference of each photon with its self. I.e. each photon even when millions of other do exist is going to the screen via both paths and of course is coherent or in phase with its self.
Now I will “type draw” one photon interfering in condition to interfere with its self when it gets to the screen. I show the “part” that travels via the T & R paths one above the other now:
First when the path lengths T and R are equal:
T:/\/\/\/\/\/\/\/\/\/\/\/\
R:/\/\/\/\/\/\/\/\/\/\/\/\
At the screen 0, this photon helps make the peak of the light pattern (constructive interference with itself).
Now when the path lengths differ by half a wavelength: (mirror R moved ¼ wave length away):
T:/\/\/\/\/\/\/\/\/\/\/\/\
R:\/\/\/\/\/\/\/\/\/\/\/\/
At the screen 0, the white light location, they add to zero, to make a null instead of filling it in.
Now I draw what is the condition when the path difference between T & R paths is about half the length of the photon (Ignore the …… they are just there as Sciforum would compress multiple spaces down to one if I did not put something there to hold the space against the “compression happy” sciforum computer.)
Also imagine that the screen is to the right. I.e. the “right end” of the photon is its “head” and arrives at the screen first. Remember the R path is a little longer now so that “R part’s head” will arrive at the screen a little after the “T parts head” is already beginning to interact / die in the screen (This is all being stated in human terms, trying to describe a QM type of event and not to be taken too literally.)
T:……................/\/\/\/\/\/\/\/\/\/\/\/\
R:/\/\/\/\/\/\/\/\/\/\/\/\
With front half of the T part of the photon (foolish human terms) dead in screen the interference is only half as effective. I.e. the “tail of the T part” and the “head of the R” part are arriving at the screen together and can interfere. But the tail part of the R part arrives alone. This happens for all of the photons and so the stastical average effect makes something like this intensity pattern I(x) on the screen:
Intrensity function, I (x) = [{sin(x) + 1}/4]+ 1/4
Note:
When sin(x) = 1 the intensity peak is about [{1+1}/4] +1/4 = 0.75 (no longer the old peak = 1.0 of equal path lengths.)
When sin(x) = -1 the first term is zero so, Intensity, I = ¼ (no longer the old perfect null of 0.0)
With some more movement of the R mirror away the photon parts look like (if one could see them without killing them):
T:…….....…………........……..……./\/\/\/\/\/\/\/\/\/\/\/\
R:/\/\/\/\/\/\/\/\/\/\/\/\
And the I(x) function is just a constant. I.e. I = 0.5 or in words, there is no interference pattern left – just a uniformly lighting of the screen. Never in any of these conditions has any energy been lost. The interference is only changing how it is distributed over the screen. With the lamp I was using , the screen interference pattern faded out as R move away and was undetectable when R had moved about 15 cm. I hope you now understand why I say the photons I was working with from my lamp were about 30 cm long.
SUMMARY:
Not only have I shown that there is something moving between the lamp and the screen, (the $100 prize requirement) but I have told you how long this “something” was and that it has something of a “split personality” characteristic that defies human understanding, which allows this one thing to travel over two widely separated paths! Also defying human understanding, it is “wave like” in that it has a wave length (four times the tiny movement which changes the screen intensity at the 0 position from null to peak),yet when it gets to the photographic film all of its energy is absorbed in one very tiny crystal* of the film emulsion! (or as Einstein discussed for the Nobel prize, ejects an electron, which is even smaller with at times it full energy (less what is called the “surface work function” but I will not explain that now as this post is already too long.)
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*See:
http://en.wikipedia.org/wiki/Reciprocity_failure
Where you can read:
“At low light levels, i.e. few photons per unit time, photons impinge upon each grain relatively infrequently; if the four photons required arrive over a long enough interval, the partial change due to the first one or two are not stable enough to survive before enough photons arrive to make a permanent latent image center.”
The decay of the effect of the first photon produced is by thermal mechanism, so keeping the film very cold can “restore reciprocity” that would other wise never let the slowly arriving photos cause and lasting or “quasi stable” effect which the “developer” could spread to the entire crystal later.
The photographic “reciprocity law” state that if you double the exposure time you can take a still picture in half the light intensity (Or half the lens opening). The failure of this law occurs with very low light levels (unless you really cool down the film, but then you must have very dry air – typically not even air but a “dry nitrogen” atmosphere contacting the film.)
PS
Wiki's drawing near top of this post is OK with a coherent light source (a laser no doubt) but a laser will only make bright and dark "spot fringes" that modulate the electronic detector’s output. – It will not make a 2D interference pattern like my 9 lines if as shown in Wiki's drawing which I stole.**
Also note that the half silvered mirror in Wiki's drawing is not exactly at 45 degrees to the other mirrors. This is why the beams returning to it from mirrors T & R do not exactly re-trace the paths of the beams coming to these mirrors from the half silvered. That separation of beams faciliates understanding of the drawing and will work, but makes minor complications when I move mirror R ,so as I used it the half silvered mirror is exactly at 45 degrees to both T & R mirrors. Then the beam using R returns from on exactly the same path it came to R on and moving R by 1/4 wave length then exactly increases the path that beam travels "extra" by 1/2 wave length as stated in my prior discussion, with being as detailed as here.
To do this replace that light source with an extended in 2D one behind a frosted glass and in front of the frosted glass there is a lens, which images the plane of the frosted glass on to the FS. Then you can get the interference pattern (like the nine lines I drew instead of just the laser’s spot.) It does not make any difference as each photon interferes with itself whether or not the light source is coherent or not but to get the 2D interference pattern you must have a 2D source imaged on the screen. The frosted glass is effectively the source you are using. Wiki tries, but often does not get things quite right.
** Where do you live QQ? Perhaps you buy me drink and dinner and give the rest to Wiki in payment for things I steal from them like the drawing.