Is there only one electron in the Universe?

I started teaching Nuclear and Particle Physics to the 3rd year Physics students today. I decided to warm up with a few basics about elementary particles and their properties – all pretty standard stuff and no hairy mathematics. Cue pretty picture:

This doesn’t show the whole picture, of course, because for every particle there is an antiparticle, so there are antiquarks and antileptons. The existence of these was first suggested by Paul Dirac in 1928 based on his investigations into relativistic quantum theory, basically because invariance of special relativity is compatible with the existence of both positive and negative energy states, i.e.

has two sets of solutions, one with and the other with . Instead of simply assuming the latter set were physically unrealistic, Dirac postulated that they might be real, but completely filled in “empty” space; these filled negative-energy states are usually called the “Dirac Sea”. Injection of an appropriate amount of energy can promote something from a negative state into a positive one, leaving behind a kind of hole (very similar to what  happens in the case of semiconductor). This process creates a pair consisting of a (positive energy) particle and a (negative energy) antiparticle (i.e. a hole in the Dirac Sea). In the case of electrons, the hole is called a positron.

The alternative, and even wackier, explanation of antimatter I usually mention in these lectures derives, I think, from Feynam who noted that in quantum (wave) mechanics the time evolution of particles involves things like

which have the property that changing into has the same effect as changing into . This is, in essence, the reason why, in Feynman diagrams, antiparticles are usually represented as particles travelling backwards in time…

This is a useful convention from the point-of-view of using such diagrams in calculations, but it allows one also to raise the wacky bar to a higher level still, to a suggestion that, coincidentally, was  doing the rounds very recently – namely whether it is possible that there may really be only one electron in the entire Universe:

….I received a telephone call one day at the graduate college at Princeton from Professor Wheeler, in which he said, “Feynman, I know why all electrons have the same charge and the same mass” “Why?” “Because, they are all the same electron!” And, then he explained on the telephone, “suppose that the world lines which we were ordinarily considering before in time and space—instead of only going up in time were a tremendous knot, and then, when we cut through the knot, by the plane corresponding to a fixed time, we would see many, many world lines and that would represent many electrons, except for one thing. If in one section this is an ordinary electron world line, in the section in which it reversed itself and is coming back from the future we have the wrong sign to the proper time—to the proper four velocities—and that’s equivalent to changing the sign of the charge, and, therefore, that part of a path would act like a positron.”

—Feynman, Richard, Nobel Lecture December 11, 1965

In other words, a single electron can appear in many different places simultaneously if it is allowed to travel backwards and forwards in time…

I think this is a brilliant idea, especially if you like science fiction stories, but there’s a tiny problem with it in terms of science fact. In order for it to work there should be as many positrons in the Universe as there are electrons. Where are they?

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Hungry Philosophers

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Feynman on a Flower

I have a friend who’s an artist and has sometimes taken a view which I don’t agree with very well. He’ll hold up a flower and say “look how beautiful it is,” and I’ll agree. Then he says “I as an artist can see how beautiful this is but you as a scientist take this all apart and it becomes a dull thing,” and I think that he’s kind of nutty. First of all, the beauty that he sees is available to other people and to me too, I believe. Although I may not be quite as refined aesthetically as he is … I can appreciate the beauty of a flower. At the same time, I see much more about the flower than he sees. I could imagine the cells in there, the complicated actions inside, which also have a beauty. I mean it’s not just beauty at this dimension, at one centimeter; there’s also beauty at smaller dimensions, the inner structure, also the processes. The fact that the colors in the flower evolved in order to attract insects to pollinate it is interesting; it means that insects can see the color. It adds a question: does this aesthetic sense also exist in the lower forms? Why is it aesthetic? All kinds of interesting questions which the science knowledge only adds to the excitement, the mystery and the awe of a flower. It only adds. I don’t understand how it subtracts.

Richard Feynman (1918-1988)

And this time, as a bonus, here’s a clip of him saying the words..

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Feynman on Computers

This is a special one for all those people who prefer fiddling about with computers to actually doing science with them!

Well, Mr. Frankel, who started this program, began to suffer from the computer disease that anybody who works with computers now knows about. It’s a very serious disease and it interferes completely with the work. The trouble with computers is you *play* with them. They are so wonderful. You have these switches – if it’s an even number you do this, if it’s an odd number you do that – and pretty soon you can do more and more elaborate things if you are clever enough, on one machine.

After a while the whole system broke down. Frankel wasn’t paying any attention; he wasn’t supervising anybody. The system was going very, very slowly – while he was sitting in a room figuring out how to make one tabulator automatically print arc-tangent X, and then it would start and it would print columns and then bitsi, bitsi, bitsi, and calculate the arc-tangent automatically by integrating as it went along and make a whole table in one operation.

Absolutely useless. We *had* tables of arc-tangents. But if you’ve ever worked with computers, you understand the disease – the *delight* in being able to see how much you can do. But he got the disease for the first time, the poor fellow who invented the thing.

Richard Feynman (1918-1988)

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Feynman on Poetry

Poets say science takes away from the beauty of the stars – mere globs of gas atoms. I too can see the stars on a desert night, and feel them. But do I see less or more? The vastness of the heavens stretches my imagination – stuck on this carousel my little eye can catch one – million – year – old light. A vast pattern – of which I am a part… What is the pattern, or the meaning, or the why? It does not do harm to the mystery to know a little about it. For far more marvelous is the truth than any artists of the past imagined it. Why do the poets of the present not speak of it? What men are poets who can speak of Jupiter if he were a man, but if he is an immense spinning sphere of methane and ammonia must be silent?

Richard Feynman (1918-1988)

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Late Talking

In the course of linking my previous post to Richard Feynman’s wikipedia page, I happened upon an interesting fact:

Feynman (in common with the famous physicists Edward Teller and Albert Einstein) was a late talker; by his third birthday he had yet to utter a single word.

I therefore have something in common with these famous physicists. I didn’t learn to speak until I was well past my third birthday, as my mum never tires of reminding me.  In fact, as I have blogged about before,  I was a very slow developer in other ways and when I started school was immediately earmarked as an educational basket case.

I subsequently discovered that

Neuroscientist Steven Pinker postulates that a certain form of language delay may be associated with exceptional and innate analytical prowess in some individuals, such as Albert Einstein, Richard Feynman and Edward Teller.

Which is obviously where the similarity between me and these chaps ends, as I certainly don’t have “exceptional and innate analytical prowess”. I am however intrigued by the fact that I at least shared their  failure to develop language abilities on the same timescale as “normal” infants. I don’t know very much at all about this field, even to the extent of not knowing at what age most children learn to talk…

So here’s a couple of questions for my readers out there in blogoland. Were any of you late talkers? And how unusual is it for a child not to speak until they’re three years old?

Contributions welcomed through the comments box!

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Feynman on Wine

A poet once said, ‘The whole universe is in a glass of wine.’ We will probably never know in what sense he meant it, for poets do not write to be understood. But it is true that if we look at a glass of wine closely enough we see the entire universe. There are the things of physics: the twisting liquid which evaporates depending on the wind and weather, the reflection in the glass; and our imagination adds atoms. The glass is a distillation of the earth’s rocks, and in its composition we see the secrets of the universe’s age, and the evolution of stars. What strange array of chemicals are in the wine? How did they come to be? There are the ferments, the enzymes, the substrates, and the products. There in wine is found the great generalization; all life is fermentation. Nobody can discover the chemistry of wine without discovering, as did Louis Pasteur, the cause of much disease. How vivid is the claret, pressing its existence into the consciousness that watches it! If our small minds, for some convenience, divide this glass of wine, this universe, into parts — physics, biology, geology, astronomy, psychology, and so on — remember that nature does not know it! So let us put it all back together, not forgetting ultimately what it is for. Let it give us one more final pleasure; drink it and forget it all!

Richard Feynman (1918-1988)

 

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Ways of Thinking

I’m putting one more Richard Feynman clip up. This one struck me as particularly interesting, because it touches on a question I’ve often asked myself: what goes on in your head when do you mathematical calculations? I think I agree with Feynman’s suggestion that different people think in very different ways about the same kind of calculation or other activity.

There’s no doubt in my mind that I’ve become slower and slower at doing mathematics as I’ve got older, and probably less accurate too. I think that’s partly just age – and perhaps the cumulative effect of too much wine! – but it’s partly because I have so many other things to think about these days that it’s hard to spend long hours without interruption thinking about the same problem the way I could when I was a student or a postdoc.

In any case, although much of my research is mathematical, I’ve never really thought of myself as being in any sense a mathematical person. Many of my colleagues have much better technical skills in that regard than I’ve ever had. I was never particularly good at maths at school either. I was sufficiently competent at maths to do physics, of course, but I was much better at other things at that age. My best subject at O-level was Latin, for example, which possibly indicates that my brain prefers to work verbally (or perhaps symbolically) rather than, as no doubt many others’ do, geometrically or in some other abstract way.

Another strange thing is the role of vision in doing mathematics. I can’t do maths at all without writing things down on paper. I have to be able to see the equations to think about solving them. Amongst other things this makes it difficult when you’re working things out on a blackboard (or whiteboard); you have to write symbols so large that your field of view can’t take in a whole equation. I often have to step back up one of the aisles to get a good look at what I’m doing like that. Other physicists – notably Stephen Hawking – obviously manage without writing things down at all. I find it impossible to imagine having that ability.

But I endorse what Richard Feynman says at the beginning of the clip. It’s really all about being interested in the questions, which gives you the motivation to acquire the skills needed to find the answers. I think of it as being like music. If you’re drawn into the world of music, even if you’re talented you have to practice long for long hours before you can really play an instrument. Few can reach the level of Feynman (or a concert pianist) of course – I’m certainly not among either of those categories! – but I think physics is at least as much perspiration as inspiration.

In contrast to many of my colleagues I’m utterly hopeless at chess – and other games that require very sophisticated pattern-reading skills – but good at crosswords and word-puzzles. Maybe I’m in the wrong job?

The Inconceivable Nature of Nature

I had a couple of requests to post yet another Feynman clip. This one – about electromagnetic waves and swimming pools – is one that I vividly remember watching on BBC when it was first broadcast donkeys’ years ago. I think it’s totally wonderful.

Through the Looking Glass

I’m afraid I’m too busy again for a proper post, so I’ll resort once again to the supply of wonderful Richard Feynman clips on Youtube. Here’s a particularly nice one, about the mysterious matter of mirrors. I might use this later on this year when I talk about parity to my particle physics class!