MadSci Network: Physics

Re: Do positron trails show up in cloud chamber photos?

Date: Wed Jun 3 12:32:20 1998
Posted By: Robert Macke, Grad student, Physics,
Area of science: Physics
ID: 896709051.Ph

The question you ask is not an easy one to answer without delving too deeply into the wonderful world of elementary particle physics and quantum field theory. As such, I will attempt to explain via analogy. Like most analogies, this one oversimplifies the problem and the analogy should not be carried too far without extreme caution, however I hope it will shed light on the subject.

The answer to your question is yes, positrons _do_ display tracks in cloud chambers. They are detected as particles of the same mass but exactly the opposite charge as the electron. However, this does not violate their backwards-in-time nature, as you suggest. I'll explain, but first let me explain the nature of physics with antiparticles.

The theoretical existence of antiparticles came about in 1927 as a solution to the Dirac equation, which is sort of a Lorentz invariant version of the Shroedinger equation from quantum mechanics. This solution of interest has negative energy and momentum. Dirac's original interpretation was that all negative energy states were filled by electrons. When a negative energy state was unoccupied it would appear as a particle of charge +e, which was called a positron. However, there were some problems with this interpretation which I will not get into right here. Nevertheless, the positron was discovered experimentally by C.D. Anderson in 1932. In fact, he used cloud chambers to make the discovery! Later on, scientists such as Feynman and Stuckelberg came up with the currently accepted interpretation of these negative energy states as particles travelling backwards in time. This solved the problems which plagued Dirac's interpretation.

Now for the question of why we can detect them. Here's where the analogy comes in. Take a ball and bounce it off the floor once. Plot the trajectory of the ball on an x-y plot, where y is the vertical axis. Now change the y-axis to a time axis, so increasing time means higher on the plot. When the ball is heading downward, it is like a positron since it is travelling in a negative timeward direction. When it is going up, it is like an electron. The floor imparts momentum to the ball to make it go up, and as such it is like the photon. Now draw horizontal lines across your graph. These are lines of constant time. Note that where time is negative (below the floor, before the pair production event), you see nothing (except a photon). After the event, you have two particles at each point in time, even though one of those is heading downward (backwards in time). So you see, what we see as a positron can be interpreted simply as the physical manifestation in "real time" of the electron operating in "reverse." And what we see as pair production is in a way just the electron deflected by the photon in a timelike way.

I hope this helps. It may help to draw it out on a piece of paper, so you can actually see what I am talking about. One place where the analogy breaks down is the matter of charge, since antiparticles have opposite charges to their normal counterparts. This is a consequence of the physics involved. One way to see that it must be so is by looking at current. The current of a negative energy electron should be the same as that of a positive energy positron. In order for this to be true, the charge must be reversed between the two. Another argument for this is that opposite charge is necessary to maintain charge conservation, which is one of the basic conservation laws of physics.

Of course, this explanation is an oversimplification of what is in reality a very complicated question. For a more "correct" answer, I suggest you read through a particle physics or quantum field theory textbook if you have the background to wade through the jargon and formalism. (There's enough jargon and formalism in some texts to confuse anybody.) It would take too many pages to fully answer it here.

I hope I satisfactorally answered your question. Have a good day.

---Bob Macke
MIT S.B. Physics '96
in St. Louis Ph.D. candidate, Physics

BCNU <*>

Possible References to look up:
A Cloud Chamber Photograph of the original discovery of the positron (Source: Lawrence Berkeley National Laboratory (LBNL) Image Library)
Kenyon, I.R., Elementary Particle Physics, RKP, London, 1987
LC catalog no. QC793.2.K46
Halzen, F. and Martin, A.D., Quarks and Leptons, Wiley&Sons, 1984
LC catalog no. QC793.5.Q2522H34
Anderson, C.D., Phys Rev, 43, 491 (1933)

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