It's difficult to know for sure how many electrons are in the Universe. British physicist Arthur Eddington (1882-1944) came up with a number in 1938, now known as the 'Eddington number'.
Eddington’s calculation was actually for the number of protons in the Universe, but based on our knowledge of the physics of the early Universe, and the known strength of the electromagnetic force, we can assume this is the same as the number of electrons.
Eddington’s number was 1.57 x 1079.
Unfortunately, this estimate was based on rather dubious physics. More modern estimates put this number slightly higher, at almost 1080 (that’s 1 followed by 80 zeros).
However, according to American theoretical physicist John Wheeler (1911–2008) there could be only one electron in the Universe.
The story behind this idea was first recounted by physicist Richard Feynman (1918–1988) during a speech for his jointly awarded 1965 Nobel Prize in Physics.
Feynman said that Wheeler telephoned him in the spring of 1940, saying, “I know why all electrons have the same charge and the same mass”. When asked to explain, Wheeler said, “because they’re all the same electron!”
Wheeler had realised that, mathematically speaking, electrons and their antiparticles, positrons, could be thought of as the same particle, but moving in opposite directions through time.
Electrons have negative charge and move forwards through time, while positrons have positive charge and move backwards.
But, thought Wheeler, particles could move through ‘space-time’ in complex ways, so a single particle could trace out a tight ‘knot’ of countless trajectories in both space and time.
We could see this particle manifest itself at multiple locations simultaneously, giving the impression that it’s different particles. The electrons we see would correspond to the trajectories moving forward through time, and the positrons to trajectories moving backwards through time.
There are problems with Wheeler’s idea.
The most important is that the Universe contains many more electrons than positrons (and there’s more matter than antimatter), while the one-electron theory suggests these should be equal.
Wheeler originally suggested, unconvincingly, that the missing positrons could be ‘hiding’ somewhere, perhaps inside protons.
The one-electron theory may also violate the principle of causality.
This single-electron theory was never pursued by Wheeler, or anyone else. It’s now regarded as an interesting, but discounted, ‘thought experiment’.
However, the idea of the time-reversal of electrons and positrons was a major influence on some of Feynman’s later work.
This article is an answer to the question (asked by Alissa Schneider, London) 'How many electrons are there in the Universe?'
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