## Is there only one electron in the Universe?

Posted in The Universe and Stuff with tags , , , , , , , , on February 1, 2012 by telescoper

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.

$E^2 = p^2c^2 +m^2 c^4$

has two sets of solutions, one with $E>0$ and the other with $E<0$. 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

$\exp(i\omega t)=\exp(i Et/\hbar),$

which have the property that changing $E$ into $-E$ has the same effect as changing $t$ into $-t$. 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?

## When Energy Becomes Form

Posted in Art, The Universe and Stuff with tags , , , , , , on February 28, 2010 by telescoper

I’m back in Cardiff, exhausted but, at the same time, rather exhilirated by the past few days in Geneva. Before I crash out I thought I’d update the post I filed a couple of days ago.

On Friday we visited CERN, the highlight of which visit was, for me, seeing the facility where they test the superconducting magnets used in the Large Hadron Collider. We also saw the surface buildings of the ATLAS experiment, but since the LHC was getting ready to rumble again after its winter break we weren’t allowed to see the thing itself, 100 metres below ground. Coincidentally, I learned today that the LHC is now back making collisions once more. Obviously, the practical tips I passed on while I was there did the trick. One likes to help where one can.

The rest of Friday, back in downtown Geneva, was bizarre to say the least. We had the obligatory Swiss dinner of fondue, which is basically a big bowl of melted cheese into which you dip bits of bread repeatedly while hoping that at some point they’re going to bring some proper food. They don’t. To make matters worse we were serenaded by Swiss folk music:  cowbells, alphorns, yodelling – the works. One of the musicians was the spitting image of Dr Evil from the Austin Powers movies but at least there was no sign of Mini-me. I was traumatised by the thought that the world might be brought to a premature end, not by the LHC creating black holes but by excessive yodelling.

After that, as midnight approached, all 24 of us – 8 scientists, 8 artists and 8 architects – gave very short presentations about our work to the others in the hotel lobby area.  I couldn’t do justice to the range of ideas and forms presented there in a short blog like this so I’ll just say it was totally fascinating to listen to these people, see examples of their work, and have the chance to ask questions.

Saturday was the most intense and also the most interesting day. We were housed in a beautiful 19th Century house in the old part of Geneva that used to be the French ambassador’s residence the whole day. Split into various groups we thought, discussed, sketched, scribbled and generally brainstormed our way towards ideas for something to exhibit on our allocated theme. We got together at the end so each group could exchange their ideas with the others. It seemed every group had great fun and there seemed to be some great concepts floating around.

The artist I’m collaborating with is Carlos Garaicoa, who was born in Cuba and who has exhibited his work all over the world. He now shares his time between Havana and Madrid. He showed us examples of his work encompassing a huge range of materials and technologies: video, photography, sculpture – you name it. One of the themes he has been interested in is the idea of documentary matter, meaning objects of various kinds that bear testimony to events or forces acting on them.  Eyal Weizman is the architect Carlos and I will be working with.  He’s a research architect who has, amongst other things, recently completed a long project looking at the construction of the wall that the Israeli government has built in the west bank

And then there was me, like a fish out of water. I had looked at the title of the programme, Beyond Entropy: How Energy Becomes Form and decided that it might be interesting to get across the central idea in general relativity, i.e. that gravitational forces can be described in terms of the curvature of space. In my presentation I took this to an extreme and tried to explain how the large-scale structure of the Universe is shaped by small ripples in space in the early Universe that evolve under the action of gravity to produce the structures we see on scales as large as 100 million light years. It seemed to be a good example of gravitational energy becoming form. I summed it up with a quote from John Archibald Wheeler:

Matter tells space how to curve. Space tells matter how to move

Taking cue from these perspectives we had a wide-ranging conversation that took the idea of gravity as an effect of space, and explored this in more general contexts and from different angles. Space is often understood through its boundaries or through the surfaces constraining it and these edges take on a form that represents a sort of diagram of the forces that have acted on it. On a human scale we thought about walls and how the path they follow is shaped not only by topographical constraints but also by socioeconomic considerations. Walls and buildings generally suffer decay or damage too, including catastrophics events like explosions or earthquakes.

We also talked about the relationship between surfaces and the spaces they enclose or divide. The path of a wall such as the west bank barrier is extremely complicated because of the interplay between such factors. It curves in and out seemingly at random, but its shape makes it a document that contains information about the forces that have shaped it. It is a document in itself, not just because it happens to have things written on it in some places!

This thread of discussion got us interested in the possibility of using material objects to reconstruct the history of the processes that formed them: the Moon’s surface offers an example wherein the sequence of impacts can be inferred from the pattern of overlying and underlying craters. This led on to discussions about the relationship between surfaces and volumes generally, taking in holography as a specific example where  two-dimensional object contains three-dimensional volumes.

This all took us quite a long way from the initial riff, but I’m glad of that. My main worry about getting involved in this was that we might end up producing something that was merely didactic, just a fancy metaphorical treatment of basic physics. I wanted to avoid that because I think it would be very boring. I think I shouldn’t have worried that we might head in such a dull direction.

Some of the other groups managed to work up concrete ideas for prototypes to be exhibited. We didn’t really get that far. We were much keener to explore as many concepts as possible before settling on one. For myself, I was just really enjoying the discussion! There are no real constraints on what we can make – within reason of course. Sculptures, plans, buildings, installations, videos, photographs, and even books are all possibilities. It’s quite scary having such a blank canvas. We discussed a number of ways we might develop our discussion into material that can be exhibited but they all need a lot of work to develop, so we’ll carry on our collaboration remotely. I’m quite keen to bring some sort of holographic element into it, and promised to investigate the possibility of making some prototypes.

For the meantime, however,  it’s back to reality for me. A lecture to prepare and give, problem sets to get ready and an exercise class to run, an examination paper to finish writing, and a whole afternoon at the School’s research committee. I wonder if what I’ve been doing over the weekend will count as having “impact”?