If an electron were increased to the size of an apple, how big, proportionately, would a human being be?

Asked by: Lou Spadaccini

Answer

Well, the classical radius of an electron (this is the 'electo-magnetic field' type of radius - nobody has actually measured the exact radius of an electron.) is about 2.82 x 10^{-15} m. An average size of an apple is about 4 cm or 0.04 m in radius (at least the apples I just got today from the supermarket:-).

So the scalling factor is just: radius of the apple / radius of the electron which is: 4 x 10^{-2} m / 2.82 x 10^{-15} m = 1.42 x 10^{13}

This means that in the universe where the electron is as big as an apple in ours everything will be bigger by a factor of 1.42 x 10^{13} or 14,200,000,000,000 (fourteen trillion and two hundred billion times bigger.)

So now you can calculate how big would the human be: for example I am 6 ft (1.83 m) tall so in your apple-sized-electron universe I would be: 1.83 m x 1.42 x 10^{13} = 2.6 x 10^{13} m tall!
Just to give you an idea how tall I would be: it would take light a full day to travel from my toes to my nose! (and it only takes about 8 minutes for light to travel from the Sun to the Earth.) Also, I would be about 3.5 times taller than the diameter of our Solar System (farthest reaches of the Pluto orbit are at about 7.37 x 10^{12} m.)
Answered by: Anton Skorucak, M.S. Physics, PhysLink.com Creator

'The mathematician's patterns, like the painter's or the poets, must be beautiful; the ideas, like the colours or the words, must fit together in a harmonious way. Beauty is the first test: there is no permanent place in the world for ugly mathematics.'