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

'There is no inductive method which could lead to the fundamental concepts of physics. Failure to understand this fact constituted the basic philosophical error of so many investigators of the nineteenth century.'