Go! Here we are. Now I am bit embarassed. The other day I was pretty excited with the idea to tell you something about quantum mechanics (QM). Now I realize that it ain't gonna be easy. At all. What the hell, let's try...
I guess it could help if I start with some funny anecdotes. Do you know Richard Feynman? He's a great hero of theoretical physics. He made wonderful achievements in physics, and got a Nobel Prize for it (in 1965 with Schwinger and Tomonaga, for the discovery of the quantum theory of electromagnetism). He was also extremely charismatic, and that's not a surprise if he's been one of the most popular physicists ever. A very eclectic guy, actually. One of his famous pictures shows him playing bongo, some said he was a genius (say, he was gifted) at beating rythms. He's also famous for a great series of textbooks on physics, pretty intuitive and yet not that easy to read, written as he was lecturing in the 60s-70s in Caltech, California. He starts his lecture on QM with the result of an experiment performed by Thomas Young in the XIX century. Actually he starts the discussion with a Gedanken experiment. This is a famous word among physicists, that we could translate as a "mind experiment" (Gedanken meaning thinking in german, well, I... think). It is a "theoretical experiment" in which you imagine a setup which aims at exploring the consequences of a given theory. Einstein used to love them, but probably the most famous one is "The Schrödinger's cat" named after Erwin Schrödinger, one of the fathers of quantum physics. So let's start with the Young Gedanken experiment.
Suppose you shoot bullets (that's Feynman's example) - or whatever - through a wall with TWO slits, say A and B, which can be either opened or closed, independently. There's another wall behind the first one (thank God!), so go ahead, start shooting randomly, this is totally harmless (on top of being a Gedanken experiment). You repeat it quite a large number of times, coz it's fun and statistics never harms. For the time being, only one slit is open (say, A) and the other (B, you still follow?) is closed. At the end of the day, there will be many impacts distributed along the second wall, most of these being right behind slit A, of course. Then you do the contrary, let A closed and B open, and shoot again. The second wall has now many impacts, especially behind slit A and behind slit B, and probably a bit less in between (in particular if both slits are well separated). Of course, you know for sure that, instead of having first opened A only and then B only, you could have equally started shooting twice more with both slits A and B opened at the same time, you would have gotten the
same final result. In other words, since each bullet goes either though slit A or through slit B, the probability to have an impact somewhere on the wall (call that point x) is precisely the probability that this damn bullet has gone there through A
plus the probability that it's been through B. To be cool, let me write this mathematically:
P(x) = P(x|A) + P(x|B), (equation #1)
where P(x) is the probability that the bullet reached the point x and |A or |B meaning "through slit A" and "through slit B". At this point, you should start getting bored. Perhaps coz your favourite blogger confuses you with those bullets, slits, probability etc. and you have no idea where he wanna go with that Gedanthing, or simply because it's so obvious after all, no need to write a long post about it. Except that it's not boring at all. The above guess is plain wrong, and this is precisely what makes you (and me) so different from the fathers of quantum mechanics! No offense.
Quantum mechanics does not work this way. How does it work then? Well, when you have 2 (or many in general) possibilities for "something-to-happen" (in this context the bullet gets to point x) AND if you don't know which possibility actually occurred (e.g. bullet through A or B), what you have to do is to take the square root of the probabilities of each possibility, √P(x|A) and √P(x|B), add or subtract them, and then square your result to get the probability P(x). We can write this:
P(x) = [√P(x|A) +/- √P(x|B) ]^2 (equation #2)
This is almost like before, but not quite. What is written just above is P(x) = P(x|A) + P(x|B), like our naive guess at the beginning, PLUS or MINUS another thing (2*√P(x|A)*√P(x|B) for the experts). It is that little something which you add or subtract which makes us different from Nobel prize winners (apologies if you're being one, in which case I would feel very much honoured and intimidated, yet it's pretty unlikely. Again, no offense to my non-Nobel fellow readers). Like Feynman used to say throughout his lectures, don't ask why Nature behaves this way! Doing physics is rather to know
how Nature works the way it does. Coming back to our experiment after this philosophical digression, the bullets will
not be distributed in the same way whether we first opened the two slits one after another or both at the same time. That's life. This is what the Young experiment showed explicitely, except that light was sent instead of bullets. As expected, Young observed a shiny spot behind the opened slit when the other one was closed. What happens when
both slits are opened, then? Two bright spots, one behind each slot? Surprisingly no, rather a funny alternation of bright and dark spots appeared all along the second wall when both slits were open at the same time. This alternation comes from the PLUS or MINUS something that we saw before. Suppose that for some location x on the wall the equation #2 should be written with a "plus" sign, the probability for having a "light-bullet" (also known as the photon) at this very point is high, in which case a
bright spot is observed (the larger the number of light-bullets at a given place, the brighter the spot). However, if we move a little bit away from that point, the formula #2 should now be written with a "minus" sign (trust me): the probability P becomes very small, even null if √P(x|A)=√P(x|B). Only a very small number of light-bullets has reached that point, and therefore the spot is pretty dark. And if we move even a little further, we get again a "plus" sign and a bright spot. And so on and so forth. Easy, isn't it? For those of you (are there still someone here? Léo?! Grandma??) who worry and feel uncomfortable about the fact that light is something really different than a bullet, let me tell you that the Young experiment has been done much later with electrons shot one after another (and an electron is
almost the same as a bullet), and the result is identical. To make an analogy, suppose you throw two stones in a pond. Wavelets will spread and even meet, if the stones did not fall too much apart. When the two waves cross (we say interfere), the crest of a wave can meet a crest of the other wave: this is a constructive interference and this will produce a higher crest. In the analogy, √P(x|A) and √P(x|B) add together, resulting in a brighter spot. On the contrary, the crest of one wave could equally meet the trough of the other wave, the resulting height of the crest being decreased. In that case, we call this a destructive interference, and this would correspond to a darker spot in the Young experiment. Remember this is only an analogy: the bullets are particles! But simply, the "square root" of the probabilities for a particle to go from one place to another within various paths interfere constructively or destructively, in a very same way as waves in a pond.
One more strange thing and then I let you go. You remember I said that we should add/subtract the square roots and so on
only if we don't know which path was taken by the bullet. Now suppose we open both slits and look carefully at a given slit whether each bullet has gone through it. From now on, we
know the path taken by the bullet, and we should NOT add/subtract the square roots, simply add P(x|A)+P(x|B) as we first suspected in the equation #1! Physically, we'll have then the same result whether each slit is opened one after another (for which we should always add the probability) or whether both slits are open altogether under the condition that we spy the path chosen by the bullet. Isn't that ackward? It means that, in quantum mechanics, the observer modifies somehow the result of the experiment. If you look at a flower, you will throw light at it, and doing so you modify a little bit what you're supposed to observe. Of course, the hope is that looking at a flower will almost not change anything to it, and in practice this is almost always the case. As long as we deal with BIG objects. So our very first guess - which we call Classical Mechanics - is a very very good approximation to (quantum) reality. It is because we live in such a macroscopic world (as compared to some microscopic scale) that classical mechanics appears so "obvious and logical" - hence our first naive guess - and quantum physics that mysterious and counterintuitive - hence why Planck, Schrödinger, Pauli, Heisenberg and others were such geniuses.
Grandma, I admit this post was probably much more difficult to follow than the previous lecture on quark-gluon plasma. Sorry for this. Next time I promise to talk about something easier. Anyway, if something remains obscure, don't hesitate to give me a call!
Nota bene: I oversimplified a little bit when I said PLUS or MINUS, it is slightly more complex than that, if I may say, but basically the idea is this one.
I used to listen a lot of blues, say 10-15 years ago (wow, makes me feel old!), slightly less since then. Yesterday not only I was in Chicago but also back to these "Blues years". I felt I was 15. Or 72. God I'd love to be in such a good shape when I'm Buddy's age. No wonder the music was perfect, what I did not expect was such a show!!! He's like a kid, joking and making funny faces, walking through the public, even let a 10 year-old boy strumming his guitar while Buddy was making great riffs with his left hand. As for the music, he gratified us with some great classics such as Muddy Water's Hoochie Coochie Man or a homemade version of Fever. Those artpieces were also balanced by more intimate songs, including a beautiful one to appear in his next CD: I just can't wait!
supposed to say in Scenery V of the first Act?") and genuine excitement. I guess that's what we call a positive pressure. And once on stage, well, it's even better! There are so many contradictory little things which you take into account: you must know your text, of course, live your character, react on how the other actors behave. And feel the public. As a physicist, I would call it fantastically and highly unstable, unsteady happening. I find it heady, thrilling. And above all, what is really impressive is that on the following day everything starts again from scratch, the pressure, the excitement and all that. This is actually the only regret I have: we performed only twice! All that work for only two performances. I hope we could still do it a few more times, perhaps next fall who knows. Coz' theater is really addictive. I'm gonna miss it this summer. And during all those Tuesday nights to come.
ot for me. Only destined to women, and whose main worry is of course to be as slim as possible for the coming summer. Or to men wearing bikinis and sharing the same concern, which is not my case either. Even those guys seem not allowed: on the back it is written Come on girls, let's start. I am really suprised that Kellog's deliberately deny itself of half its potential customers. What's wrong with you guys?! It must be some marketing strategy which goes well beyond my understanding. As we usually say in particle physics, parity is violated (future post!). And as long as parity between men and women is violated even on a cereal box, I don't really see how it could be applied to any other field.
