Solvay 1927
Is Quantum Theory the Whole Story?
Odds, and Nothing More?
In October 1927 the people who had just built quantum theory met in Brussels to talk it over. The theory already worked. It explained the colors that atoms give off, and it would soon explain chemistry. What it gave, though, were odds. Send light through two slits one photon at a time, and the theory says where the photons will tend to land. It never says where the next one will.
Albert Einstein pointed to what that means. His own example sent electrons through one small hole toward a curved film, but photons at two slits show the same thing. Before a photon lands, its wave spreads over the whole screen. Then the photon is caught in one spot, and by the theory’s rule, at that instant the chance of finding it anywhere else drops to zero, all over the screen at once. Einstein saw two ways to read this. Perhaps the wave is only a list of odds, and the photon was headed for its spot all along, by some route the theory does not describe. Then the theory is leaving something out. Or the wave is the photon itself, and its landing acts across the whole screen at once, faster than any light could carry the news.
Niels Bohr took the other side. The theory is complete, he held. Physics says what instruments will record, and that is all it can say. In a setup that shows stripes, nothing records where the photon was before it landed. To ask anyway is to ask what those instruments cannot show, so in that setup the question has no answer to find.
Einstein is remembered for saying that God does not play dice, a line from a letter he wrote the year before. Chance was not his deepest worry, though. A colleague who knew his thinking well wrote later that Einstein’s starting point was not that every event must be fixed in advance. It was that a thing has a real state of its own, where it is, whether or not anyone looks. The theory gave the photon no such state, only a wave that answered for the whole screen at once.
Which Slit, and Stripes Too?
At the meeting, as those there told it years later, Einstein brought challenges to breakfast, and Bohr had answers by dinner. One went like this, in its simplest form. Stripes behind two slits appear only when nothing records which slit each photon took. So hang the plate with the slits on springs. A photon turned aside at a slit gives the plate the opposite kick. For a photon that lands at a given spot, the kick from one slit differs a little from the kick from the other, because the two slits sit at slightly different angles to that spot. Read the plate’s kick, and you know the slit. Do the stripes still appear?
Bohr answered with the uncertainty principle, applied to the plate itself. The two kicks differ by very little. To tell them apart, the plate’s own motion must be known more finely than that difference before the photon arrives. A thing whose motion is known that finely is spread out in place. Work it through, and the plate’s place is unsure by about the spacing of the stripes. The stripes from each place in that range are shifted against one another, and together they wash into an even spread. Read the kick, and the stripes are gone. Keep the stripes, and the kick cannot be read. Bohr called this complementarity: path and stripes are both needed for the full picture, but each shows only in a setup that rules out the other.
This is now an experiment, not just an argument. Physicists have made the movable slit a single atom, held in the focus of a laser beam and cooled to the lowest energy its motion can have. Photons scatter off it one at a time, along two paths that are then brought back together to interfere, and each path kicks the atom a different way. Hold the atom loosely, so that its motion is sharp, and the kick leaves a mark in it: the interference fades. Hold it tightly, and the kick is lost in the spread of its motion: the interference comes back. The fading matched the uncertainty principle’s reckoning, once a slight warming of the atom was allowed for.
Another team used more than ten thousand atoms held in a lattice of laser light, each atom a slit. They also switched the light off, taking the springs away altogether, and measured within a millionth of a second, before the atoms could drift. Nothing changed. What decides it is not the spring but how spread out each atom is. For an atom in its lowest state, as these were, the wider its spread in place, the sharper its motion, the more clearly it records each kick, and the fainter the interference.
Every device of this kind ended the same way. Each seemed to beat the uncertainty principle, and each turned out to obey it in some part that had not been looked at closely: here, the plate. The cleverest one made Bohr reach for Einstein’s own theory of gravity.
A Box of Light on a Spring
At the next meeting, three years later, Einstein brought a box. Fill a box with light and hang it from a spring. Inside, a clock opens a shutter for a moment and lets out one photon. Weigh the box before and after: the weight it lost is the photon’s energy, since energy has weight. The clock says when the photon left. A photon let out in a short moment should hold a spread of energies, as a short flash holds a spread of colors. Yet here both seem as sharp as you like.
Bohr found the answer in the weighing itself. The weight one photon carries off is tiny, and over the time you watch the pointer, it gives the box only a tiny push. To weigh finely, you must know the box’s motion more finely than that push. Then, by the same rule as before, its height is unsure. And a clock runs faster the higher it sits, as Einstein’s theory of gravity says. A clock whose height is unsure keeps time that is unsure. Bohr worked it out: the finer the weighing, the less sure the time, by just enough that energy and time are never sharper together than the uncertainty principle allows.
The effect Bohr used is measured today. Two atomic clocks have shown it across 33 centimeters of height, and a single clock has found it across a cloud of atoms a millimeter tall.
Einstein said later that he had not meant to break the uncertainty principle at all. Less than a year after the box, a friend reported him saying he had long stopped doubting it. His point was another. Once the photon has flown off, as far as you like, you can still choose. Weigh the box again, and you can predict the photon’s energy exactly. Or skip the weighing, open the box and compare its clock with yours, and you can predict exactly when the photon will arrive. Nothing done to the box can touch the photon now. So, he reasoned, the photon must carry both answers, and a theory that holds only one at a time is incomplete.
Choose Here, Know There
With the box, one of the two answers was a time read off a clock. In 1935 Einstein made the same argument with two particles and two things a particle itself has: its position, and its momentum, the quantity of motion that collisions never lose. The paper, written with Boris Podolsky and Nathan Rosen, gave the puzzle its name. Let two particles fly apart from one meeting, with their positions linked, and their momenta linked too. Measure where one is, and you can predict exactly where the other is. Measure the first one’s momentum instead, and you can predict the other’s. The far one is never touched.
Their rule was simple. If you can predict a quantity for sure without disturbing a thing, the thing has that quantity. So the far particle has a sharp position and a sharp momentum at once, which no state in the theory allows. Either the theory is incomplete, or measuring here changes what is real over there, at once, at any distance. Einstein called that second option spooky action at a distance, and would not accept it.
Today the argument is usually told with light. Photons made in pairs by a crystal pass or stop at two filters. Each side alone is a coin toss, but set both filters at the same angle, any angle, and the pair always agrees. Choose an angle here, and you can predict the far photon’s answer at that angle. By Einstein’s rule, it must carry a ready answer for every angle, like a glove that is left or right from the start.
Bohr replied within months. Nothing touches the far particle, he granted. But the choice made here decides which questions about the far particle have answers at all. The two particles and the instruments form one whole, and there is no sense in giving either particle properties of its own. Such a shared state of two particles is now called entanglement. Most physicists took the matter as settled, or as philosophy, and went back to work.
The puzzle in its first form, with two quantities that clash, has been shown with matter as well as light. Physicists split a cloud of atoms, cooled almost to absolute zero, into two clouds of about 700 atoms each, held apart. Measurements on one cloud predicted either of two clashing quantities of the other: how far its atoms’ spins, added up, pointed along one line, or along another. Summed over hundreds of atoms, those two behave like position and momentum: the sharper one is, the less sharp the other. Taken together, the two predictions were sharper than the uncertainty principle allows any single cloud to be.
A Question With a Number
For almost thirty years, no one saw an experiment in which ready answers and Bohr’s view would disagree, and choosing between them looked like a matter of taste. Then John Bell found where they part. Give each filter three angles, a sixth of a turn apart, and pick one at random for each pair, just before the photons arrive. Photons that carry ready answers, with nothing passing between them faster than light, must agree at least one time in three when the angles differ: of three ready answers, each pass or stop, at least two are alike. Quantum theory says one time in four.
Apart from one early run that a repeat did not bear out, the experiments came out for quantum theory. Later ones switched the angles while the photons were in flight, so no signal could carry one side’s choice to the other in time. The latest close both main gaps at once: no signal could cross between the sides in time, and too few particles went uncounted to fake the result. They did it with photons, with electrons in two diamonds more than a kilometer apart, and with two superconducting chips 30 meters apart, run more than a million times.
One assumption cannot be closed: that the angles are picked freely, and not fixed together with the photons by some cause in their shared past. It can only be pushed back. Light from two quasars, the blazing cores of distant galaxies, has picked the angles, light that set out billions of years ago. Any plan to arrange the result would have had to be laid before the Earth existed.
So Einstein’s way out is closed, as far as any test can close it. Photons do not carry ready answers for every angle, unless something passes between them faster than light, or the angles were never free to choose. Yet nothing that could carry a message passes faster than light. Each side alone still sees a coin toss, whatever is done on the other, and the pattern shows only when the two lists of results are brought together, by ordinary means. Relativity’s speed limit stands.
Who Was Right?
Bohr was right that the theory holds together. Every device built to beat the uncertainty principle, on paper and now in the lab, obeys it. Einstein was right that the question was real. Bohr’s side had treated what lies beneath the odds as a question without content, and it had content: a number that experiments could measure. The answer went against the picture Einstein hoped for, in which each particle simply carries its own answers, as a glove carries left or right.
What the theory describes is still argued. Some take the wave as real, with every result happening in a branch of its own. Some add particles with definite paths, steered by the wave, and accept an influence that acts at once at a distance. Some read the wave as what an observer knows, and some add a physical collapse that no test has yet seen. Each view still standing fits every experiment so far, and none has been confirmed over the others.
The box touches one more open question. Bohr’s answer drew on quantum theory and gravity at once. For gravity as weak as Earth’s, the two combine without trouble. A single theory that holds both where gravity is strong is not settled: proposals exist, and none has yet been confirmed.
For thirty years, very good physicists filed the question under philosophy, for reasons that seemed sound. It took someone looking for a measurable consequence, and the consequence had been there all along. Some questions about the world may have no answer that any experiment can reach. Others are waiting for their Bell, and it is hard to tell the two apart in advance.
