I have been working for the past two months within three degrees of the equator and re-watching The Ascent of Man (an excellent BBC series from the 1970s). Led thereby to consider:
1. the fact that a point on the surface of the earth at the equator spins faster than a point nearer the poles; thus
2. verified according to Einstein's theory of relativity – as speed increases, time must move slower to preserve the absolute limit of the speed of light – time must move a tiny bit slower for me than folks back home up north.
This led me to wonder what the speed of an electron around an atomic nucleus might be, whether it would approach the speed of light and what that might mean about the nature of reality. The nature of reality is already very strange. Consider that what appears to us as solid matter – from the atom on up – is mostly just empty space. There is so much space inside ordinary matter that you could squeeze our sun down to the size of Manhattan Island (or something like that) and make it one big and very heavy neutron. Things seem solid to us because of electro-static forces that hold together and repel assemblages of atoms and molecules. This strangeness doesn't even include the weirdness of quantum physics. Anyway, what might be going on as an electron spins around inside an atom?
Of course, electrons actually don't orbit the nucleus like little planets around a sun. Electrons exist in a kind of cloud of probabilities subject to certain allowed energy levels that can be thought of as shells. It is possible, mainly as a thought experiment, to estimate a kind of notional speed of an “orbiting” electron leading to a value of around five million MPH. That is fast but still only about 1% of the speed of light. So while time would certainly pass more slowly for an electron than for me, there would not be any profound relativistic effects.
This then led me to consider the strangeness of salt. Salt is made from the ionic combination of a poisonous gas (chlorine) and a soft metal that burns in air (sodium). It is also vital to life. Perhaps because life evolved in the sea, sodium and chlorine ions are essential elements for the functioning of core biological systems. What rules of the universe led to the sixth most abundant element in the earth's crust (sodium) marrying so happily and fortuitously with the 21st (chlorine)?
The sodium atom has a lone electron in its outer shell that it quite willingly donates to the chlorine making the sodium a negative ion and the chlorine a positive ion. That allows the two to remain together through that electro-static charge in a crystal lattice to make common salt. Electrons do not move at relativistic speeds because they are given mass through interaction with the Higgs Field. If they did move at the speed of light, as do massless photons, atoms would not exist and we would not be here.