The Foucault Pendulum
A short chapter from the book Beyond Space And Time
Often, at a science center or in a planetarium building,
you see some great pendulum swinging in the hall. What does it keep track of? Usually it is set up so that every few minutes
the pendulum knocks over a peg, because the building, on the merry-go-round of the Earth's spin, slowly turns beneath
Often the posted announcement will say that the pendulum keeps track of the Earth's spin. But alas, it pays
no attention to the Earth's spin and gaily knocks over the pegs as they come by. Then what does it pay attention to? What
does it care about?
Sometimes the books say that the pendulum keeps track of the "fixed stars," but you know
and the stars know that there are no "fixed stars." And anyhow, how could the pendulum keep track of them?
suppose we change our mode of attack. Suppose we consider a pistol, radio controlled, loaded and cocked, with a rifled barrel,
and out between the stars. And we ask it to shoot. Now because of the rifled barrel, the bullet comes out spinning. Does the
gun spin in the opposite direction? Yes, of course, and with the same amount of spin but in the opposite direction. The bullet
is lighter and spins faster, and the gun is heavier and spins slower. Because angular momentum is how heavy you are multiplied
by how fast you're spinning, the lighter one spins faster and the heavier one spins slower, but with equal angular momentum
in opposite directions. Also the bullet is lighter and goes faster, and the gun is heavier and goes slower. Because linear
momentum is how heavy you are multiplied by how fast you're going, and in what direction. So the lighter one goes faster
and the heavier one goes slower. And the moral to all this is: "Never shoot a pistol that weighs less than the bullet!"
Now, for a time, you might think that the gun keeps track of the momentum of the bullet. But we're going to let
the bullet fall into a supernova star which scatters the momentum all over the galaxy. So now what does the gun keep track
of? It still keeps track of the other half of its momentum which used to be packaged in the bullet but is now packaged in
the Universe at large. So it keeps track of the Universe at large.
Momentum is always half of something. And the Universe
is "all dressed up with no place to go." Because there is nothing with respect to which it could have some momentum.
Momentum, angular momentum and electric charge are always half of something, and the other half, the opposite half, is packaged
in the Universe at large. And if you can watch the great Foucault pendulum swinging in the hall at the science center or the
planetarium and not get goose bumps, it may just be that you're asleep.
Now in 1965, the mathematician John Bell
came up with an interesting theorem. And his theorem says that if matter behaves as quantum mechanics says it should behave,
then one of two things must fail. Either objectivity fails or local causation must fail. Either the Universe does not exist
outside and independent of the observer, or it must be possible to send messages faster than the speed of light.
in the 1970's and 1980's, it was conclusively shown that where Bell's theorem is concerned, matter does indeed
behave as our quantum mechanical understanding says it should behave. So either the Universe is not "out there"
as we thought it was, or material influences can be transmitted faster than the speed of light.
Since that time many
careful and interesting experiments have been performed to show that local causation fails, that material influences must
be transmitted faster than the speed of light.
But we already saw that material influences must be transmitted faster
than the speed of light or the Foucault pendulum could not keep track of the momentum of the rest of the Universe. It cannot
wait for the influence to come in from all the rest of the Universe at the speed of light.
And anyway, what is meant
by the speed of light? The speed of light is simply the ratio of space to time. One light year is equal to one year. In Einstein's
special theory of relativity, space and time come into the geometry as a pair of opposites. And that puts the total separation,
the space-time separation, the objective separation, between the emission of light and its absorption at zero. The emission
and absorption events of the photons are adjacent in space-time. And that puts the real separation between the emission events
of the light which we think we see outside and the absorption events of that light in our eyes at zero. And this seriously
calls in question the objectivity of the world which we seem to see outside.
Well, maybe the Foucault pendulum is telling