In the annus mirabilis of 1905, Albert Einstein made several seminal contributions to science. Among them were the special theory of relativity and the recognition of the wave-particle duality of light—the latter a characteristic of the quantum theory soon to emerge. Modern physics rests on quantum mechanics and relativity. Both revert to classical physics under everyday circumstances: quantum mechanics for things sufficiently large; special relativity for things sufficiently slow. Within their domains, both theories have consequences that seem crazy, counterintuitive, and contrary to experience. For decades I have striven to convey the delights of modern physics to science-averse undergraduates, but many of them persist in rejecting the concepts as either unacceptable or unbelievable.
Antoine Lavoisier and James Prescott Joule were wrong! Relativity revealed energy and mass to be interconvertible, satisfying a single, unified conservation law. Who could believe that simultaneity is relative, or that no missile nor missive can travel faster than light? A clock in motion, said Einstein, ticks more slowly than an identical clock at rest. Relativistic time dilation is ordinarily negligible, except to science fiction writers, philosophers, and physicists who study rapidly moving particles.
What Is Real? is a book focusing on the counterintuitive nature of quantum theory, the difficulties in its interpretation, and the various doomed attempts to introduce hidden variables into its structure. I found it distasteful to find a trained astrophysicist invoking a conspiracy by physicists and physics teachers to foist the Copenhagen interpretation upon naive students of quantum mechanics.
No one can doubt that quantum mechanics is strange. Who could believe that particles can briefly violate energy conservation so as to pass through otherwise impenetrable barriers?1 Who could believe that a body’s position and velocity could not both be known to an arbitrary degree of precision, yet this is Heisenberg’s uncertainty principle. Who could believe that not more than one electron can occupy the same quantum state, yet this is Pauli’s exclusion principle? How can it be that electrons and protons behave like waves, just as electromagnetic waves behave like particles? All attempts to skirt these quantum-mechanical principles have failed.
As Adam Becker concedes, “[Q]uantum physics certainly works.”2
Erwin Schrödinger’s cat is one of Becker’s pet preoccupations. The first of her several dozen appearances in his book is on page 2, the last seven on page 257. I shall examine a simplified version of the famous thought experiment, but first we must appreciate how it is that the earliest and clearest demonstration of the intrinsically probabilistic nature of quantum mechanics was established a quarter century before quantum theory was developed. Max Planck discovered the quanta of radiation in 1900. Ernest Rutherford and Frederick Soddy established the law of radioactive decay in 1902. Einstein was a junior patent clerk at the time, Niels Bohr, an avid high-school footballer, and Werner Heisenberg, an infant. A decade later, Rutherford discovered the atomic nucleus. The stage was set for Bohr to develop his incompletely justified quantum rules. They worked, but Bohr could not quite say why.
The Rutherford–Soddy law states that every radioactive nuclear species has a unique half-life t1/2. The half-life of a particular isotope is the interval over which half the atoms in a sample decay. Half-lives can be very small, that of Beryllium-8 being only a tenth of a femtosecond, or very large, that of Rhenium-186 being four hundred billion years. For a sample of N identical atoms, the mean number of survivors after an interval t is N exp –t/τ, where τ ln 2 ≡ t1/2. Suppose a certain isotope, X, has a half-life of four hours. If the initial sample contains a million X atoms, about half of them survive the first four hours, about 250,000 survive the second, and a bit fewer than 1,000 are likely to survive the tenth.
What’s so remarkable about radioactive half-lives? After all, people have them too. Life expectancy at a given age is the time interval for half of one’s age cohort to die off. The half-life of American men is seventy-six at birth, thirty-eight at age forty, and eight years at age eighty. People age, and as they do their half-lives shrink. But atoms, whether stable or radioactive, do not age. The probability for a given atom to decay within one second remains unchanged throughout its life. Unlike American men, all atoms of a given isotope are identical. Neither practice nor principle can determine which of an ensemble of identical radioactive atoms will decay now, and which will survive a hundred half-lives.
My thought experiment is like Schrödinger’s, but without the cat. A single X atom is placed in a sealed box. Four hours later, the box is opened. The atom survives in roughly half the times the experiment is repeated. Is the confined atom in a superposition of having decayed or not decayed until the box is opened? Does the act of opening the box collapse the wave function?
No, and no again.
To prove this, imagine a detector to be placed within the box to record and announce whether and when the atom decays. The outside observer need not open the box to tell if and when the atom has decayed. There is never a superposition or a wave function to collapse. The detector itself can remain imaginary. It suffices that the moment at which the atom in the box decays could in principle be communicated to the observer outside. The detector may be omitted and the cat added to the box, but nothing very untoward will ensue. The atom decays, or not; the cat is alive, or dead.
Why does Becker continue to beat that old dead cat?
In pursuing the nature of reality, Becker asks whether theories can be shown to be true, or proven to be false. This is a relevant question today in view of the popularity of string theory and the multiverse landscape, for which empirical tests are essentially absent.3 Referring to W. V. O. Quine, Becker writes that, “there was no way to verify single statements—all attempts to verify a statement inevitably involve the assumed truth of other statements.”4 This thesis is illustrated with an anecdote involving a malfunctioning TV remote control. Several pages later on, after a brief introduction to the thoughts of Thomas Kuhn, Becker comes to the realization that, “replacing the batteries is a reasonable thing to do, because your knowledge of remote controls, televisions, and batteries suggests that dead batteries are the most likely reason for the remote to stop working.”5
In a chapter entitled “Copenhagen Versus the Universe,” the damaged device is called upon yet again, this time to prove that theories cannot be falsified. “Say Karl Popper’s remote control isn’t turning his television on, and he theorizes” that the fault lies in its dead batteries.6 After an unconvincing argument, we are told that, “our beliefs about the world can only be tested against the world as a group, not individually, and this holds for falsification just as much as for verification. No theory, in isolation, is falsifiable.”7 The flaw in this statement is the phrase “in isolation.” Quine would never claim for a theory of physics what he says about a single statement. I would argue that a theory is true if and only if its envelope of applicability has been established. This is surely the case for Newtonian mechanics and Maxwellian electrodynamics, less so for quantum field theory, and not at all for string theory.
Can theories admitting no conceivable experimental test, like string theory or multiverse cosmology, be useful contributions to physics? “Claiming that no data,” Becker argues, “could ever force the rejection of a multiverse theory is merely stating that a multiverse theory is just like any other theory.”8 But the multiverse is not like any other theory. To accept it is to reject any possibility of understanding how neutrinos acquire mass, why weak interactions violate parity, or what determines the mathematical structure of the Standard Model. These mysteries and whatever secrets lie beyond the Standard Model are simply accidents of birth of our particular universe.
Becker admits that quantum mechanics may be useful, even if it does not always make sense to him. “[Q]uantum physics is certainly telling us something about what is real.”9 This is encouraging. A bit later he writes that, “[q]uantum physics works, but”;10 and later yet, that “it’s not immediately clear what the theory is saying about the world.”11 Elsewhere, Becker writes that, “quantum physics is at least approximately correct,”12 and we learn that, “[t]here is something real, out in the world, that somehow resembles the quantum.”13 It is a matter of regret that Becker does not yet know what that means. The quantum theory discussed in his book is indeed approximate. Heisenberg, Schrödinger, and their contemporaries knew well that the theory they devised could not be made compatible with Einstein’s special theory of relativity. First order in time, but second order in space, Schrödinger’s equation is nonrelativistic. Although quantum field theory is fully compatible with the special theory of relativity, a relativistic treatment of quantum measurement has yet to be formulated.
The weirdness of quantum theory is exemplified by the so-called Einstein–Podolsky–Rosen paradox. Two particles with an entangled wave function, even if spatially separated, appear to communicate with one another instantaneously. Einstein referred to this as spukhafte Fernwirkung, or spooky action at a distance. He could not accept it because such behavior violated his principle of local realism. Additional elements of reality, or hidden variables, must surely underlie and explain this paradox, or so he thought. Becker clearly describes several thought experiments by which quantum theory’s spooky action at a distance could be observed.
In 1959, John Stewart Bell deduced his eponymous theorem: that no system of hidden variables can reproduce all of the consequences of quantum theory. In particular, he deduced an inequality pertinent to observations of an entangled system consisting of two separated particles. If experimental results contradicted Bell’s inequality, hidden-variable models could be ruled out. Experiments of this kind seemed difficult or impossible to carry out. But, in 1972, Alain Aspect succeeded. His results contradicted Bell’s inequality. The predictions of quantum mechanics were confirmed and the principle of local realism challenged. Ever more precise tests of Bell’s inequality and its extension by John Clauser et al. continue to be performed,14 including an experiment involving pairs of photons coming from different distant quasars. Although a few tiny loopholes may remain, all such tests to date have confirmed that quantum theory is incompatible with the existence of local hidden variables. Most physicists have accepted the failure of Einstein’s principle of local realism.
While experimental physicists were repeatedly showing quantum mechanics to be both spooky and correct, Becker remains troubled that the Copenhagen interpretation has clouded the minds of physicists. They persist in ignoring the alleged inadequacies of quantum theory, meekly following the dictum, “Shut up and calculate,” which appears in quotes no fewer than seven times in What Is Real?
The phrase is offensive and inappropriate. It was coined by the physicist David Mermin, who wrote in 1989: “If I were forced to sum up in one sentence what the Copenhagen interpretation says to me, it would be ‘Shut up and calculate!’”15 Fifteen years later, Mermin recanted: “I’m not proud of having said it. It’s not a beautiful phrase. … It’s snide and mindlessly dismissive.”16 Rejecting the allegation that he had misappropriated the phrase from Richard Feynman, he wrote: “I have nothing to be ashamed of other than having characterized the Copenhagen interpretation in such foolish terms—a lesser offense than unconscious plagiarism.” Somewhat incoherently, Becker assigns the currency of the phrase “Shut up and calculate!” to events taking place eighteen years before it was first used.
The postwar boom in physics funding that had fueled the rise of “shut up and calculate!” was coming to a sudden and precipitous end. … No wonder, then, that the pragmatic allure of good work in other fields was no longer enough to keep the Fundamental Fysiks Group from puzzling over the foundations of quantum physics—and no wonder that John Clauser had trouble finding work when even “respectable” physicists were out of a job.17
I doubt that “Shut up and calculate” had much to do with Clauser’s employment problems. The 1970s may not have been generously funded, but they turned out to be the most exciting and productive period for fundamental physics since the 1920s. They saw the creation of the Standard Model of elementary particle physics by the Fundamental Fysiks Group, of which I was and remain a proud member.
Bell never completed his planned quantum mechanics textbook because he could not devise a suitably relativistic theory of measurement. Murray Gell-Mann and James Hartle pursued this issue in a long series of collaborative articles. The last concludes:
The problem with the “local realism” that Einstein would have liked is not the locality but the realism. Quantum mechanics describes alternative decohering histories and one cannot assign “reality” simultaneously to different alternatives … [R]esolution of the problems of interpretation presented by quantum mechanics is not to be accomplished by further intense scrutiny of the subject as it applies to reproducible laboratory situations, but rather through an examination of the origin of the universe and its subsequent history. Quantum mechanics is best and most fundamentally understood in the context of quantum cosmology. The founders of quantum mechanics were right in pointing out that something external to the framework of wave function and Schrödinger equation is needed to interpret the theory. But it is not a postulated classical world to which quantum mechanics does not apply. Rather it is the initial condition of the universe that, together with the action function of the elementary particles and the throws of quantum dice since the beginning, explains the origin of quasiclassical domain(s) within quantum theory itself.18
Becker is consumed with distaste for the Copenhagen interpretation of quantum mechanics. The phrase, or its abbreviation “Copenhagen” appears on fully a quarter of the book’s pages, with a climactic nine appearances on one page alone.19 The phrase may first have been employed by Heisenberg as the “Kopenhagener Geist” (Copenhagen Spirit) in his 1930 book The Physical Principles of Quantum Mechanics.20 Although much discussed by philosophers of science, the concept rarely appears in graduate textbooks.21 An excellent quantum mechanics textbook by Kurt Gottfried and Tung-Mow Yan, published in 2004, in its one mention of the Copenhagen interpretation merely points out that it led to Heisenberg’s indeterminacy relation and Bohr’s principle of complementarity.22 An equally fine textbook by Ernest Abers, also published in 2004, says only that, “in the early days of quantum mechanics some people speculated that … the wave function ‘collapsed’ when it was measured … This is not a widely held view today.”23
“Schroedinger’s cat,” Abers remarks, “was never in a state that is a linear combination of alive and dead.”24
Discussions of quantum measurement and the foundation of quantum mechanics are certainly important and interesting, but I have never felt the need for a deeper sense of quantum mechanical reality. I am satisfied by Paul Dirac’s view:
[T]he main object of physical science is not the provision of pictures, but is the formulation of laws governing phenomena and the application of these laws to the discovery of new phenomena. If a picture exists, so much the better; but whether a picture exists or not is a matter of only secondary importance. In the case of atomic phenomena no picture can be expected to exist in the usual sense of the word “picture,” by which is meant a model functioning essentially on classical lines. One may however extend the meaning of the word “picture” to include any way of looking at the fundamental laws which makes their self-consistency obvious [emphasis original]. With this extension, one may gradually acquire a picture of atomic phenomena by becoming familiar with the laws of quantum theory.25
It was quite all right all along to shut up and calculate.
