Quantum Physics: How Small? How Fast? How Long?

by Max Andrews

Length

Atomic nuclei range from about 10-4 to 10-5 of the size of an atom.  If the atom were about the size of a medium-sized airport (say, 3 km) then the nucleus would be about 30 cm, about the size of a basketball.  Now imagine the airport, 3 km, having a sphere encompassing it.  If you change the basketball to a golf ball you have a rough scale of the hydrogen atom with its central proton.  Inside the golf ball are the quarks.  Change the scale from the proton being the size of a golf ball to the size of a marble, about 1 cm.  The sphere is now the size of the earth’s orbit.  The actual size of a proton is about 10-15m.  This is equivalent to one femtometer, or one Fermi (1 fm).  The smallest distance probed is 10-18m, which is one thousandth of a fermi.  The fundamental particles such as quarks are smaller than this.

The radius of the Hubble volume, or known universe, is about fourteen billion light years, which is about 1026m away.  The size of your desk is about 1026 times smaller than the universe and only 1018 times larger than the smallest probed distance.  The mean distance between the large distance of the universe and the smallest distance probed is 104m, or 10 km.  This means that the mean distance of the universe is about six miles.

The Planck length is about 10-35m.  This is 1020 times smaller than a proton.  This proton is a hundred billion billion times larger than the Planck length.  This is the scale at which strings perform their gymnastics and the quantum foam bubbles.

Speed

A snail’s speed is about 0.01m per second.  A person walks at about 1m/s and drives a car at about 30m/s.  The typical speed of an airplane reaching the speed of sound is about 740 miles per hour.  Light travels much faster, almost a million times faster at about 3×108m/s.  The hypothetical particle, or a massless photon, which is suspected to travel faster than the speed of light is called a tachyon.

Time

For humans, a year is a long time and a second is a short time.  For a particle, a hundredth of a second is an eternity.  For the universe a few hundred million years is simply dinner.  Particles that live long enough to leave tracks in a detector have lifetimes of 10-10 to 10-6 s.  A neutron is abnormally long with a lifetime of 15 minutes.  If the universe is 13.7 billion years old then it is roughly 1018 seconds old.  The Planck time is 10-44 seconds, smallest meaningful unit of time.

CERN

Material from Ken Ford’s The Quantum World (Cambridge, MA: Harvard University Press, 2004), 10-16.

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