Imagine if you will a clock, one whose hand rotates 30,000 times a second, or thereabouts. It should be fairly obvious why it rotates so fast; the speed of light is very fast. Release a pure 'red' photon from a source which is directed somewhere. Start the clock. Measure where the hand is on your clock at the precise instant it hits the target. You have a little arrow pointing in some direction. The length of the arrow is determined by the square of its length (Unfortunately, neither MG nor I 'know' why it's the square, it just is in the equations - the maths - of which the arrows are simply a graphical representation.)
Now imagine a pure red light source situated at (a) which can fire 1 photon at a time (they do exist!) and a detector located at (b) with a sheet of glass located under them with another detector located at (c). Start firing photons and see where they are detected. After a sizable number of photons have been fired, we discover that 4% of the photons go to (b) and 96% go all the way through the glass and end up at (c). OK, so the length of the arrows has to be 0.2 (0.2x0.2=0.04 or 4%!).
(a) __________________ 
(b)
(c)
OK. Let's increase the thickness of the glass, does that make a difference? You'd think it wouldn't, wouldn't you? The photons must be bouncing off the top surface of the glass, yes? Well they're not and the thickness makes a difference. With the thicker glass the result is that 8% reach the detector at (b) and only 92% make it all the way to (c). So it's not just the surface that's reflecting is it? So let's make an assumption. The underside reflects as well. So it has its own little arrow. Except it will be a different pointing arrow, the photon takes longer to hit the back edge than the front edge, further to go. So we now have two arrows to deal with, those that hit the front and those that hit the back. Crucially, in this model, the arrow for the 'back hitting' photon is reversed in direction.
Now you can 'add arrows' together. Just attach the pointy bit of one to the tail of another and then draw another arrow between the two. Just so! The square of the length of the third (bolder) arrow gives you the probablity (amplitude) 0f the photon being reflected. Neat, huh?
So let's increase the thickness of the glass again. Oooh, we get 16% reflection! The thicker the glass the more reflection! Let's try it. Increase the thickness of the glass again and what do you get? 0%, no photon reaches (b)! Oh dear! Latest postulate, in Tom Cruise's words, "crashed and burned! Not a pretty sight!" Now, experiment has this sinusoidal oscillation happening at least 32,000 times in succession - there's a limit to how thick you can make glass without spending the entire Federal budget- o-16% every time. Why? After all it seems a little crazy, no?
The answer lies in the 'direction' of the arrows. You see at certain thicknesses of glass the arrows (the time it takes for the photon to traverse the thickness of the glass), according to our little 'clock hand', can point in exactly opposite directions, 0%, (an arrow joining them as above of zero length) or widely differing directions, as in the example above, 16% when you join them together.
Now before anyone starts getting out of their pram, this is a staggering oversimplification of what is going on but, crucially, it captures the essence of what is going on and, more importantly, the numbers add up, so we must be on the right track, even if it is simplified.
In the next exciting instalment of 'where the bloody hell did I leave my photons and why can you never find an electron when you need one', we'll look a little more carefully at where the photon goes as it leaves the source and why it always goes in a straight line to where it has been aimed. It doesn't really, sort of, it just looks that way! :)
Well, my number one conundrum (can we actually have conundrums, or are they just- there?) anyway, with physics is how they have taken this very random part of science and figured out how it is not random.
ReplyDeleteNo matter how clearly it is explained, I keep feeling like I need to go back to kindergarten, where they gave you a stack of identical blocks to work with. In reality (I'm using this example because it is a recent one) it seems like we are looking into a giant box of legos, all varying sizes and shapes.
So how do we know, or why would we suppose that a photon is always shaped the same, always travels the same way, in the same general linear way, that it bounces or refracts off or behind or absorbs into an object the same way?
There are so many variables.
It's overwhelming.
So the only way I know to deal with the legos is to sort them by some general characteristic: Color is the easiest one for me. Then the general shape, then the general function.
So much of learning physics is about teaching mind to organize the information in a way that it can create patterns to make use of.
I have to say, your writing is easier for me to read than Dick's but I think that is because Dick is dead. You are not dead.
:)
PS- did you create your own graphics?
MG did the 'not brilliant' graphics. It was that or nick them from Dick's book which would have been a breach of copyright :)
ReplyDeletePhotons of the same energy are essentially completely 'identical'. There is no way to tell one photon from another unless you deliberately set out to make them different, as in 'entanglement' experiments.
In one respect, it's the only way QED works. If photons 'could be intrinsically different to each other' a statistical analysis like QM wouldn't be so accurately aligned with experiment, which currently is around 'to 12 decimal places'.
(Dick used to 'half' joke that it was perfectly possible that there was only one electron in the universe, it just moved around in time and space very quickly.)
The probability of a photon behaving in a certain way is always the same but it's only when you deal with large numbers of them (remember isotopic decay) that the maths actually pans out.
Each individual photon is as capricious as you are :)
I think it is worth pointing out that Feynman was probably the greatest physicist of the 20th century. This is not to demean others, Heisenberg, Shroedinger, Einstein etc but Dick bailed QM out of the biggest hole with his diagrams and path integrals and with QED mapped out the future development of the discipline. It is not mere chance that QCD (quantum chromodynamics, the theory that relates to the nucleus) is modelled so closely on QED.
You see, what Dick did was to banish all that nonsense, so beloved of writers of/in blogs (and books), of wave/particle duality, the uncertainty principle, the collapse of the wave function, they teach it to you but it's not relevant. Do the maths, you get the answer. Don't ask why, or sometimes, even how, you'll never know, can never know, so they're pointless questions aren't they?
Humans have a habit of philosophising, but QM is the quintescence of science/maths. Philosophy has no place there.
Dead? Not dead? Until God lifts the box lid we'll never know, ay?
ReplyDeleteWhich is almost exactly how this conversation, nearly six months ago, began.
ReplyDelete(in reference to your last comment)
Okay, I explained the reason why I was angry over the "school-boy" math comment.
ReplyDeleteYou don't have to read it. But it's on my blog.
As allegory, it has the syncopation of truth. As truth, it has the counterpoint of allegory. As allegory and truth it should teach that inflicting pain of whatever kind on the innocent and defenceless in the name of a silent and awful 'word' merely debases the perpetrator and exalts the victim.
ReplyDeleteNot only God will have judgement, the rest of humanity will, eventually, exact their own brand of retribution.
Do we not revile Pontius Pilate and the Sanhedron?
Sir,
ReplyDeleteyour vocabulary is a bit advanced. Please explain.
Simplicity has its virtue.
You never have to beleive what I write on my blog. Some day it will be in a book. I don't know what will happen to it. Maybe it will sit on storeroom shelves. Maybe it will be bought, glanced over and thrown away.
ReplyDeleteWhat I hope is that someone will read it. Someone who can't put into words what we saw, what we knew, what our daily reality became. And, I hope they forgive me for all I did not say. I hope they forgive me for telling it, to our embarrassment.
But more than that, I hope they will find it in themselves to forgive themselves for what they ARE NOT.
I have flogged myself enough for us all. It is time for us to live, to be happy, to find something before our time runs out that makes everything that happened worth something more wonderful that we find in our futures.
Do the musical allusions interfere with comprehension? Syncopation is accenting a normally unaccented beat, think Scott Joplin's ragtime music or Debussy's 'Golliwog's Cakewalk'. Counterpoint is the device used to weave two (or more) melodies into a piece of music at the same time, eg Bach. So, in unmusical terms, I was trying to say that it's both allegory and a true recounting of events. And, as importantly, you can hold both in your head at the same time. One hand plays allegory, the other plays truth! It's all in your final paragraph, which I assumed was deliberately intended to obfuscate what had gone before.
ReplyDeleteForgive me.
ReplyDeleteI come from a musical family, and my last class (the one I was finishing up when I referenced Bach) for my AA was a musical class.
No, friend, it was in the arrangment (ha! no pun intended) of your score that I had difficulty. That, and the fact that it is nearly impossible to read your emotions through your words.
Yes, a bit of sarcasm near the end. Just so I don't go put the lid down on the commode and cry. Pretending I made it up seems so much more bearable.
Self-pity and self-loathing are closely entwined in the psyche.
Oh, I forgot to add. That final paragraph is very, very good! Your writing teacher would be proud! Borges, too, I think. The 'Garden of forking paths'.
ReplyDeleteI shall, at some point, subscribe to the book, but only when you finish it! :)
Self pity about what happens TO us and self loathing about what we have or have not DONE is common to us all and are forever intertwined. We each must deal with their impact as best we may. But as the Penguin is apt to say: 'Tomorrow is a new dawn........and there is always hope!'
Strange comments to leave on a blog about QED, don't you think? Whatever will posterity think? Lunatics! Probably. Amplitudently?
So now, let's get on with the topic at hand.
ReplyDeleteIndeed. They will deem us lunatic, or they will have accepted (at last) that everything, every iota, every photon, every atom, every nucleus is intricately connected and somehow in a way (they, hopefully will begin to discover) affects the individual neurons that fire in our brains, which cause our minds to wander, or stay put.
I think what we have here is a perfect quantum superposition of states. Only when it decoheres when measured does its reality become manifest!
ReplyDeleteStrange, Penrose goes down the same track :)
ReplyDeletePenrose?
ReplyDeleteWhat does he have to do with QED?
OK, pay attention at the back, there! :)
ReplyDeleteSir Roger Penrose, mathematical physicist. I mentioned him a while back, when deciding between Feynman and Dawkins in response to one of your comments, as someone to consider for future reading. AND how he has some weird views on how quantum mechanics ties in with human conscienciousness.
Your earlier comment just reminded me of it.:)
Yes, I did look it up. Quite forgot what we were speaking of, but remembered him as a philosopher, not a mathmatician.
ReplyDeleteThat is probably where I got that last idea, though I can't remember when I read anything by him. Probably came from Public Television.
Let's get back to QED. :)
Will it be super annoying to re-ask the trig question if I explain why i needed a simple (hopefully, if possible, one that does not involve sins and cosins?) solution?
ReplyDeleteIt has to do with a class I mentor-an advanced CS class for Middle School Kids and we are trying to draw an oblique. The teacher wants to just draw the final angle as "got to xz" (that is not the exactl command, but something like that.)
I was hoping we could teach them some way to do it without taking a short cut. So far the only way I know to do that is with the SAS formula (which, to be frank, is above my abandoned mind- or is it landmine? - okay, that was bad.)
However, our units are divided up into ranks and we don't do trig until Rank #3 which will be sometime later in the year.
The program is Turtle Logs, BTW. Don't know if that helps. The object lesson is to teach children to draw geometric shapes.
If at first you don't succeed.......
ReplyDeleteOK, I surrender! It's fair cop,guv. Just slap them bracelets on me wrists an' I'll come quietly. Don' won' no bovver, like!
Trust you to be difficult, it's what cosines are for, measuring the third 'unknown' side! Anyways latest blog has a suggestion.
The length of the arrow being in the square of its length seems to be a fallacy- how can you prove something is true by stating it is?
ReplyDeleteWhat I hear you saying (quite likely, I'm reading you wrong) is that:
L=L squared. How is that possible?
I can see that L, if L is the hand on a clock is the radius of the clock and therefore, the distance around the clock would be the formula for a circle. The total length traveled would be the distance traveled by the arrow.