einstein
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einstein
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the electrons are recorded as they hit a photographic plate. Various other elements, such as a shutter to open and close the slit instantaneously,<br />
were posited by Einstein in his ingenious efforts to show that position and momentum could in theory be known with precision.<br />
“Einstein would bring along to breakfast a proposal of this kind,” Heisenberg recalled. He did not worry much about Einstein’s machinations, nor<br />
did Pauli. “It will be all right,” they kept saying, “it will be all right.” But Bohr would often get worked up into a muttering frenzy.<br />
The group would usually make their way to the Congress hall together, working on ways to refute Einstein’s problem. “By dinner-time we could<br />
usually prove that his thought experiments did not contradict uncertainty relations,” Heisenberg recalled, and Einstein would concede defeat. “But<br />
next morning he would bring along to breakfast a new thought experiment, generally more complicated than the previous one.” By dinnertime that<br />
would be disproved as well.<br />
Back and forth they went, each lob from Einstein volleyed back by Bohr, who was able to show how the uncertainty principle, in each instance, did<br />
indeed limit the amount of knowable information about a moving electron. “And so it went for several days,” said Heisenberg. “In the end, we—that<br />
is, Bohr, Pauli, and I—knew that we could now be sure of our ground.” 30<br />
“Einstein, I’m ashamed of you,” Ehrenfest scolded. He was upset that Einstein was displaying the same stubbornness toward quantum<br />
mechanics that conservative physicists had once shown toward relativity. “He now behaves toward Bohr exactly as the champions of absolute<br />
simultaneity had behaved toward him.” 31<br />
Einstein’s own remarks, given on the last day of the conference, show that the uncertainty principle was not the only aspect of quantum<br />
mechanics that concerned him. He was also bothered—and later would become even more so—by the way quantum mechanics seemed to permit<br />
action at a distance. In other words, something that happened to one object could, according to the Copenhagen interpretation, instantly determine<br />
how an object located somewhere else would be observed. Particles separated in space are, according to relativity theory, independent. If an<br />
action involving one can immediately affect another some distance away, Einstein noted, “in my opinion it contradicts the relativity postulate.” No<br />
force, including gravity, can propagate faster than the speed of light, he insisted. 32<br />
Einstein may have lost the debates, but he was still the star of the event. De Broglie had been looking forward to meeting him for the first time,<br />
and he was not disappointed. “I was particularly struck by his mild and thoughtful expression, by his general kindness, by his simplicity and by his<br />
friendliness,” he recalled.<br />
The two hit it off well, because de Broglie was trying, like Einstein, to see if there were ways that the causality and certainty of classical physics<br />
could be saved. He had been working on what he called “the theory of the double solution,” which he hoped would provide a classical basis for<br />
wave mechanics.<br />
“The indeterminist school, whose adherents were mainly young and intransigent, met my theory with cold disapproval,” de Broglie recalled.<br />
Einstein, on the other hand, appreciated de Broglie’s efforts, and he rode the train with him to Paris on his way back to Berlin.<br />
At the Gare du Nord they had a farewell talk on the platform. Einstein told de Broglie that all scientific theories, leaving aside their mathematical<br />
expressions, ought to lend themselves to so simple a description “that even a child could understand them.” And what could be less simple,<br />
Einstein continued, than the purely statistical interpretation of wave mechanics! “Carry on,” he told de Broglie as they parted at the station. “You are<br />
on the right track!”<br />
But he wasn’t. By 1928, a consensus had formed that quantum mechanics was correct, and de Broglie relented and adopted that view. “Einstein,<br />
however, stuck to his guns and continued to insist that the purely statistical interpretation of wave mechanics could not possibly be complete,” de<br />
Broglie recalled, with some reverence, years later. 33<br />
Indeed, Einstein remained the stubborn contrarian. “I admire to the highest degree the achievements of the younger generation of physicists that<br />
goes by the name quantum mechanics, and I believe in the deep level of truth of that theory,” he said in 1929 when accepting the Planck medal from<br />
Planck himself. “But”—and there was always a but in any statement of support Einstein gave to quantum theory—“I believe that the restriction to<br />
statistical laws will be a passing one.” 34<br />
The stage was thus set for an even more dramatic Solvay showdown between Einstein and Bohr, this one at the conference of October 1930.<br />
Theoretical physics has rarely seen such an interesting engagement.<br />
This time, in his effort to stump the Bohr-Heisenberg group and restore certainty to mechanics, Einstein devised a more clever thought<br />
experiment. One aspect of the uncertainty principle, previously mentioned, is that there is a trade-off between measuring precisely the momentum<br />
of a particle and its position. In addition, the principle says that a similar uncertainty is inherent in measuring the energy involved in a process and<br />
the time duration of that process.<br />
Einstein’s thought experiment involved a box with a shutter that could open and shut so rapidly that it would allow only one photon to escape at a<br />
time. The shutter is controlled by a precise clock. The box is weighed exactly. Then, at a certain specified moment, the shutter opens and a photon<br />
escapes. The box is now weighed again. The relationship between energy and mass (remember, E=mc 2 ) permitted a precise determination of the<br />
energy of the particle. And we know, from the clock, its exact time of departing the system. So there!<br />
Of course, physical limitations would make it impossible to actually do such an experiment. But in theory, did it refute the uncertainty principle?<br />
Bohr was shaken by the challenge. “He walked from one person to another, trying to persuade them all that this could not be true, that it would<br />
mean the end of physics if Einstein was right,” a participant recorded. “But he could think of no refutation. I will never forget the sight of the two<br />
opponents leaving the university club. Einstein, a majestic figure, walking calmly with a faint ironic smile, and Bohr trotting along by his side,<br />
extremely upset.” 35 (See picture, page 336.)<br />
It was one of the great ironies of scientific debate that, after a sleepless night, Bohr was able to hoist Einstein by his own petard. The thought<br />
experiment had not taken into account Einstein’s own beautiful discovery, the theory of relativity. According to that theory, clocks in stronger<br />
gravitational fields run more slowly than those in weaker gravity. Einstein forgot this, but Bohr remembered. During the release of the photon, the<br />
mass of the box decreases. Because the box is on a spring scale (in order to be weighed), the box will rise a small amount in the earth’s gravity.<br />
That small amount is precisely the amount needed to restore the energy-time uncertainty relation.<br />
“It was essential to take into account the relationship between the rate of a clock and its position in a gravitational field,” Bohr recalled. He gave<br />
Einstein credit for graciously helping to perform the calculations that, in the end, won the day for the uncertainty principle. But Einstein was never<br />
fully convinced. Even a year later, he was still churning out variations of such thought experiments. 36<br />
Quantum mechanics ended up proving to be a successful theory, and Einstein subsequently edged into what could be called his own version of<br />
uncertainty. He no longer denounced quantum mechanics as incorrect, only as incomplete. In 1931, he nominated Heisenberg and Schrödinger for<br />
the Nobel Prize. (They won in 1932 and 1933, along with Dirac.) “I am convinced that this theory undoubtedly contains a part of the ultimate truth,”<br />
Einstein wrote in his nominating letter.<br />
Part of the ultimate truth. There was still, Einstein felt, more to reality than was accounted for in the Copenhagen interpretation of quantum<br />
mechanics.