The Double-Slit Experiment
Published 2004-10-22 13:05:52
Richard Feynman has pointed out that every statement in quantum mechanics is a restatement of Heisenberg' uncertainty
principle. Now Heisenberg's uncertainty principle states that the product of our uncertainty in the position of a particle
and our uncertainty in its momentum can never be less than a certain small quantity, namely Planck's constant over two
pi. Also that our uncertainty in the energy of a particle and our uncertainty in when it has that energy can never be less
than that same small amount.
Feynman has also pointed out that the entire mystery of quantum mechanics is in the double-slit
experiment. And that is what makes it so very interesting. From the standpoint of common sense, as Feynman himself has pointed
out, the behavior of Nature is absurd. And this absurdity is nowhere more obvious than in the double-slit experiment. But
before we discuss the double-slit experiment, let us go back to Einstein's 1905 geometry.
is a theoretical geometry about a theoretical space that does not in fact exist. And Newton's physics is a theoretical
physics about a theoretical world that does not in fact exist. So we have had to change all that with relativity and quantum
mechanics. In 1905 Einstein succeeded in putting time into geometry where it belongs. He changed our geometry form 3-D to
4-D. and in Pythagoras' theorem for four dimensions, time comes in squared with a minus sign, so that if the space and
time separations between two events are equal, the total space-time separation between them is zero. Distances in space are
not objective, nor are lengths of time. Observers moving with respect to each other may disagree on how far it is from there
to here and on how long it took from then till now, but they will all agree on the total space-time separation between there-then
and here-now. Four-dimensional addresses (where and when) are objective, and the space-time intervals between them are also
objective, regardless of your position or your state of motion.
Now in discussing the double-slit experiment, it will
be important to remember what happened to our geometry in 1905. Space and time come into that geometry as a pair of opposites.
And since, between the emission and the absorption events of a single photon, the time separation as always equal to the space
separation (for all observers), the total separation between those two events must always be zero. When Einstein threw out
the luminiferous ether, he should have thrown out the photons that moved in it. They do not show up in his physics. When he
threw out the lake, he should have thrown out the fish that swam in it.
The mystery of the double-slit experiment is
this: that if the photons go one at a time through the slits, how do they know that both slits are open?
From a little
distance away we shoot a laser through two closely spaced slits and watch the absorption events on a scintillating screen
behind the slits. What we see is that when one slit is closed, most of the scintillation points fall behind the other slit,
as we would expect. But when both slits are open, most of the scintillation points fall not behind the two slits, as we would
expect, but between them. It is as though the photons had come through as waves and showed an interference pattern on the
screen. And the question is this: since photons come through one at a time, how do they know that both slits are open?
will be necessary here to remember that space and time are a pair of opposites and that the total separation between the emission
and absorption events are adjacent in space-time. Now the adjacency has two components, a space component and a time component,
and it is in the space component of the adjacency that both slits are open. It is not that the photons go through one or the
other slit, but only that the space components of the trajectories have both slits open.
But suppose we do the double-slit
experiment with electrons instead of photons. Then the emission and absorption events will not be adjacent in space-time,
because the electrons can't travel at the speed of light. And then the space and time components of the trajectories will
not be equal. What the? Still we get the same result. If both slits are open, we get interference on the screen behind the
slits. Why? Because even if the space and time components fo the trajectories are not equal, still both slits are open for
the space components.
As Amit Goswami says, "We never, never see the wave aspect of a single quantum object."
The wave aspect is in the space component of the trajectory.
Feynman's "sum-over-histories" approach
suggests that we must allow that the photon (or the electron) could have gone by any possible way from the laser (or the electron
gun) to the screen, and we sum-over-the-histories to calculate the probability of its arrival. Actually what we do is to sum-over-the-space-components-of-the-trajectories,
whether for a photon or an electron.
For a detailed description of the double-slit experiment please see Richard Feynman's
Six Easy Pieces. It's in the last chapter on Quantum Behavior.