A big thank you to the British Broadcasting Corporation for that. The opening lines to the daily 'Listen with mother' in the days when radio was King, before TV and film corrupted us with THEIR images, THEIR representations! When, as children, we could dream our own dreams, see our own characters not just a superfluous by-product of corporate greed. The closest thing to reading that it was possible to get! When you couldn't read. Just use your ears, not your eyes!
Also a little apology for the tardiness of this post. (a) I got sidetracked by a little triangle :) (b) the muse has been dragging me kicking and screaming towards faerie again and (c) MG is tearing his hair out over work :(. So...........
So, where does the photon go when it leaves the emitter? Well, it's not in a straight line to where it is pointed! :) The photon travels by all available paths. However quantum mechanics predicts that it will invariably travel in a straight line to its 'target'. How come? Well, we're back to good ol' Dick's arrows :) Told you they were useful!
If we take a very simplified look at the possible path(s) of the photon through spacetime, we might see something like this
......................................(a)....................................(b)
_________________ 
(c)
As you can see, the probability (amplitudes) at the beginning and the end tend to cancel themselves out (they just wander around without going anywhere) and what counts are the arrows in the middle which reinforce each other when you 'add' them all together and actually go somewhere. When you draw the single arrow (as before) between the start of arrow one and the end of arrow 'n' ('n' being an indeterminate number, however many arrows you choose, in our earlier example it was just two) you get the 'straight line' path we observe.
Now, I hear you say, that's just an over complicated way of saying light travels in a straight line, the way of least resistance, or better, the way of least energy. Light never uses more energy to get from (a) to (b) than is absolutely necessary. In that way light is very similar to the girl (or guy) at the supermarket checkout and explains why it takes 10 minutes to fill up your cart but 30 minutes to check it out. Always the least energy to move the cereal from (a) to (b).
So why do we need this complicated arrangement of the photon going by all available paths when we could just assume that light travels in a straight line (the dotted line in the diagram above, in case you've forgotten). Diffraction gratings, that's why!
Imagine, if you will, that we leave the experiment exactly as it is but we chop 2/3rds of the glass on the right away so we are just left with a little bit of the left hand side of the glass, where the arrows all meander around, going nowhere. We etch some lines at a particular spacing, it's different for red light and blue light. Then what? Obviously, no reflection! There's no glass in the middle to reflect from! WRONG! It's greatly reduced but the receptor at (b) DOES get hit by the odd photon (and it's predictable from the probability amplitudes) that manages to get itself out of the tangle at the left end and is not then cancelled by the now non existent tangle at the other end. So a photon does travel by ALL available paths! Try explaining that with conventional wave optics!
It's the same with Dick. I'm following you both until you get to the part about the glass. Then, I'm all "What glass?"
ReplyDeleteSo, I'm going to ask you "What glass?" and you can go ahead and tell me I'm a hopeless case. But I will go ahead and tell YOU I don't beleive it.
One thing I am is persistent. :)
PS- do you make up the word verifications? Because I could swear it says "cramp" as in I'm giving your brain a cramp. :)
Hope all is well.
ReplyDeleteThe American
Which bit about the glass exactly? The bit where I take 2/3rds of it away and just leave the 'rump' on the left side? So there's nothing for the photon to supposedly 'bounce off'?
ReplyDeleteI'm exceedingly dense, but I do want to learn this. As soon as you start the paragraph
ReplyDelete"Imagine, if you will...2/3 glass..." I get a mental block. Not sure if it is visual or just there.
I'm sorry if I am a bad pupil.
There are no such things as bad pupils, just bad teachers :) The trick is always to find one to suit :)
ReplyDeleteOK. A diffraction grating, those lines etched into the glass, are a way of scattering light, throwing it all around according to its wavelength (energy of the photon).
(There is a fairly useful article on Wiki, although it deals with it in a conventional 'wave theory' of light way, although it does emphasis that each point on the wavefront is treated as a separate 'point', whatever that means:)
So we agreed in this post that all available paths were potentially available to the photon in its path to the glass and thence to the receptor but that those near the centre had a tendency to reinforce each other and sort of 'force' the photon into the path we intuitively feel it has taken. Whereas other paths tended to cancel themselves out and so the probability of the photon arriving that way were dropping alarmingly close to zero.
However the diffraction grating changes that. Because it scatters photons according to the spacing of the lines, we've just increased the probability that the photon could go by a straight down route and if it does it could still end up at detector (b) because its options can no longer be cancelled by the 'reverse' low probabilities at the other end of the glass nor can it be over-ridden by the reinforcement of arrows in the middle. We've kind of limited its options of where it could go, where it could be, if we detect it. A photon that went thataway has an increased chance of detection.
Think of a photograph of a football game. If we take a picture of the 'action' and remove the ball in photoshop, we can accurately reflect the position of the ball if the quarterback has his arm extended behind him and somewhere upfield is a running back looking backwards. The ball is almost certainly in the quarterback's hand. Everything is there to make the prediction, just as in the first example in today's post. What if the quarterback has both hands at his side and no one is running, can we find the ball? Unlikely. It could be anywhere including bouncing behind the quarterback. So it is with photons. The more reinforcing information you have, the more likely you are to hit the first example, the more fuzzy it all gets, the more it could be anywhere, including the extreme left of the glass.
Dick makes the point a couple of times in QED that however much this all seems to be puzzling when related to our perception of the world, do not ask why or how. This is the way the world is and nothing comes close to explaining it than does QED. It is deeply disturbing to our sense of cause and effect, the way we see that x follows from y, that this is merely a statistical effect of large numbers. But it is. At that level, only statistics count, only probabilities.
Oh by the way, it gets worse, because when we measure the photon at the detector it's not the same photon as left the emitter :)