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## Saturday, September 26, 2015

### Is There Only One Electron?

Update October 26, 2015: A very good Pop Physics/Mathematics lecture by Prof. Robbert Dijkgraf The Unreasonable Effectiveness of Quantum Physics in Modern Mathematics is youtubed here. From about minute 19 to minute 22, Dijkgraf explains and offers some history on the theory discussed in this post, albeit without offering an answer to the reason the theory is rejected here. The whole thing is highly recommended as both accessible to the interested layman and offering some amusing details to the professional.

Note: This post contains a strong hint regarding the author’s proposed answer to a puzzle he once posted.

There is an amusing, if probably ultimately flawed, theory that seeks to explain the remarkable fact that of all the $$10^{80}$$ or so electrons or so in the observable universe, every single one appears to have exactly the same mass and charge. Moreover, all the positrons (i.e., the electron’s anti-matter twin) also seem to have exactly the same mass and exactly opposite charge.

The theory posits that, contrary to what one might think, there is only a single electron/positron in the universe. This electron/positron just occasionally changes the time-wise direction in which it is traveling. When it is going forward in time, it looks like an electron. When it is going backward in time, it looks like a positron.

How would such a time-traveling electron/positron look to a time-bound observer? When it switches from going backward in time to going forwards, it absorbs a handy photon and it looks like the classical example of electron-positron pair-creation. That is exactly how we believe that almost all electrons and positrons arose. Conversely, when it switches from going forward in time to going backwards, it emits a photon and the event appears like the classical example of electron-positron pair-annihilation.The title image of this post is a Feynman diagram of both of these events.

This is rather ingenious! It explains how a single time-traveling particle could appear to us to be a vast number, while exhibiting interactions exactly like the ones we observe.

Sadly, this theory probably fails. Not all electrons and positrons enter or leave the laboratory from far away. Some measurable electron/positron pairs are created and annihilated in closed-loop Feynman diagrams. They never enter or leave the laboratory. So they cannot be the single time-traveling electron/positron. Yet, they still all exhibit exactly the same mass and charge. For this the theory can offer no explanation.