###### In response to:

*The Trouble with Quantum Mechanics* from the January 19, 2017 issue

*To the Editors*:

My article “The Trouble with Quantum Mechanics” [*NYR*, January 19] provoked a flood of comments. Some were from nonscientists charmed to learn that physicists can disagree with one another. Here there is only room to outline a few comments from physicists who offered arguments in favor of interpretations of quantum mechanics that would make it unnecessary to modify the theory. Alas, these interpretations differ from one another, and none seems to me to be entirely satisfactory. (Several letters on this matter received by *The New York Review* appear in full following this letter.)

N. David Mermin of Cornell argued with characteristic eloquence for what I (but not he) would call an instrumentalist approach. In his view, science is directly about the relation between each person’s total experience and the outside world that includes that experience. I replied that I hoped for a physical theory that would allow us to deduce what happens when people make measurements from impersonal laws that apply to everything, without giving any special status to people in these laws. I suggested that our difference is just that Mermin thinks I had been hoping for too much. He agreed, with the understanding that those hopes are mine, not his.

In contrast, Thomas Banks of Rutgers in our correspondence and the draft of a new book, *Quantum Mechanics: An Introduction*, described his elegant efforts to avoid bringing human measurement into the laws of nature. He describes measurement as an interaction of the system being measured with a macroscopic system, in which probabilities appear much as they do in classical physics. But it is still necessary to bring into the laws of nature assumptions about these probabilities that I can only understand as probabilities of the values found when humans decide what to measure.

I had an interesting correspondence with Robert Griffiths of Carnegie Mellon and James Hartle of the University of California–Santa Barbara regarding an approach to quantum mechanics variously known as “decoherent histories” or “consistent histories,” which was introduced in 1984 by Griffiths and further developed by Hartle and Murray Gell-Mann. The laws of nature are supposed to attribute probabilities to histories of the world, not just to the results of single measurements. I had described this approach in detail in my textbook *Lectures on Quantum Mechanics* but did not cover it in my article, because I thought it has the same drawbacks that I attributed to all instrumentalist approaches.

The wave functions for these histories involve averaging over most quantities, with a few held fixed, as if they were being measured, but histories with different things held fixed are incompatible, and it is humans who must choose the particular kind of history to which to attribute probabilities. Griffiths developed a sort of quantum logic consistent with his approach, but it leaves me uncomfortable. Hartle and Gell-Mann may share some of this discomfort, for they have moved toward identifying one “true” kind of history that does not have to be selected by people; but they have to attribute weird negative probabilities to histories of this kind. My discomfort remains.

Jeremy Bernstein, a contributor to these pages, thinks like Mermin that there is no trouble with quantum mechanics as it stands, but he supplied an anecdote that runs in the opposite direction. A visitor to Einstein’s office in Prague noted that the window overlooked the grounds of an insane asylum. Einstein explained that these were the madmen who did *not* think about quantum mechanics.

Steven Weinberg

Austin, Texas

###### Selected letters in response to Steven Weinberg’s article on Quantum Mechanics:

*To the Editors*:

I agree with Steven Weinberg that “it is a bad sign that those physicists today who are most comfortable with quantum mechanics do not agree with one another about what it all means” [“The Trouble with Quantum Mechanics,” *NYR*, January 19]. This ninety-year failure to reach anything like a common understanding of such a spectacularly successful theory indicates that physicists might share an unrecognized prejudice about the nature of scientific explanation that prevents each of them from seeing what quantum mechanics actually means.

In explaining why he finds untenable what he calls “the instrumentalist approach,” Weinberg gives voice to just such a widespread prejudice: “Humans are brought into the laws of nature at the most fundamental level.” Weinberg is not ready to give up the goal of understanding the relation of humans to nature by deducing it “from laws that make no explicit reference to humans.” And so he endorses, with a touch of pessimism, a long-term goal of seeking modifications of quantum mechanics that “are not only speculative but also vague.” He embraces this bleak prospect because he cannot accept incorporating the relation between people and nature into “what we suppose are nature’s fundamental laws.”

But why not? Science is a human activity. As empiricists most scientists believe that their understanding of the world is based entirely on their own personal experience (which, importantly, includes the words of others that they have heard and read). Why shouldn’t the science that I use to understand the world be directly about the relation between my total experience and the world outside of me that induces that experience?

Erwin Schrödinger (a David Levine cartoon of whom illustrates Weinberg’s essay!) traced this deep prejudice of scientists back to the ancient Greeks. He thought it was essential for the early development of science, but that it removed an important part of the story. He did not suggest that abandoning it dissolved the puzzles of quantum mechanics, but in the early twenty-first century Christopher Fuchs and Rüdiger Schack argued that it does.

For example Weinberg and many others complain that there is “no way to locate the boundary between the realms in which, according to Bohr, quantum mechanics does or does not apply.” Fuchs and Schack have a simple answer: the boundary is elusive because it depends on the scientist who is using quantum mechanics, but for each such user it is unambiguous: I apply quantum mechanics to the world I infer from my own experience; the role of my classical world is played for me by that experience.

Last year Hans Christian von Baeyer published a beautiful exposition of this new point of view, *QBism: The Future of Quantum Physics.* I recommend von Baeyer’s little book to readers of Weinberg’s essay. It addresses Weinberg’s concerns, is written at an entirely nontechnical level, and makes it clear that the resolution applies not only to quantum mechanics but also to even older, if less vexing, puzzles in classical physics.

N. David Mermin

Horace White Professor of Physics Emeritus

Cornell University

Ithaca, New York

*To the Editors*:

Steven Weinberg’s article on quantum mechanics is written with his usual clarity and brilliance. But I think that it is misguided. The probabilistic interpretation of the Schrödinger wave function was introduced by Max Born in a very brief note in 1926. He considered the collision of an electron with a target and studied the wave function that represented the electron after the collision. It is a function of position and he said that the wave function determined the probability that the electron would occupy that position. Later he modified it to say that it was the square of the wave function and still later he said the absolute value determined the probability. The notion that this is “derived” is absurd. It was a postulate. Now the present generation of quantum theorists—some of them—find this unsatisfactory and want to produce a derivation. Of course it can’t be derived from quantum mechanics as we understand it so they want to introduce “quantum” mechanics from which it can be derived, In the most recherché versions of this, “quantum” mechanics has slightly different predictions from quantum mechanics. If they are right it would be revolutionary but to me the whole enterprise is a solution looking for a problem.

Jeremy Bernstein

Aspen, Colorado

*To the Editors*:

Early on, students of quantum mechanics rhymed: “Erwin with his psi can do calculations quite a few, but one thing has not been seen: just what does psi really mean?” The answer was first given by Max Born, who received the Nobel Prize for giving meaning to psi, the wave function of a system, stating that the absolute square of this function is the probability of finding the system under observation in a given state. Steven Weinberg claims that the trouble with quantum mechanics is that the wave function “is governed by an equation, the [Erwin] Schroedinger equation, *that does not involve probabilities*.” Since this equation is perfectly deterministic, he asks, “how do probabilities get into quantum mechanics?”

But also in classical mechanics, given the inevitable uncertainties in the initial conditions, the situation is actually similar, because only probabilities of the outcome at a later time can be predicted. The main difference with quantum mechanics is that in this theory there is a limit on the relative size of the initial uncertainties, e.g., the position and velocity of an object. In his Nobel Prize speech, Born stated that “ordinary mechanics must also be statistically formulated…the determinism of classical physics turns out to be an illusion…and cannot be used as an objection to the essentially indeterministic statistical interpretation of quantum mechanics.” The nature of reality in the atomic world, however strange, is revealed by experiments, and not by requiring that it fit some prejudices from classical mechanics as Weinberg indicates.

Michael Nauenberg

Professor of Physics, Emeritus

University of California

Santa Cruz, California

*To the Editors*:

Steven Weinberg has stated clearly and unambiguously that there is something rotten in the kingdom of the “Copenhagen interpretation” of quantum mechanics. Though they often continue to pay lip service to that “interpretation” in their courses and papers, an increasing number of physicists realize this, and nobody is quite sure nowadays what that interpretation really means. As Weinberg says, “It is a bad sign that those physicists today who are most comfortable with quantum mechanics do not agree with one another about what it all means.”

Weinberg identifies the basic problem with quantum mechanics: that one applies a different rule of evolution to the wave function of a system when it does not contain an observer or measuring device (one then uses the deterministic Schrödinger evolution) from when it does (one then collapses the wave function in a random fashion, following a rule, due to Max Born, for the probabilities of the result). That not only puts the “observer,” whether it is a human subject or an instrument in a laboratory, outside the ordinary laws of physics, but also renders that “observer” indispensable to make sense of those laws. We agree with Professor Weinberg that this is deeply unsatisfactory.

Weinberg mentions two “ways out” of the problems of quantum mechanics: the “many-worlds interpretation” of Hugh Everett and the “spontaneous collapse” theories of Gian Carlo Ghirardi, Alberto Rimini, and Tullio Weber. For the first option, Weinberg observes that he doesn’t see how to justify the use of the usual quantum mechanical probabilities, given by Born’s rule, within that framework, though he is aware of a variety of attempts to do so. According to the second option, the predictions of quantum theory are not quite correct, but only a very good approximation to the more correct predictions of the spontaneous collapse theory. Many experiments are being carried out in order to decide between spontaneous collapse theories and quantum mechanics. So far, there is no indication that quantum mechanics is wrong and its spectacular successes show that, if its predictions are indeed violated in some situations, this will not be easy to demonstrate.

Weinberg presents the Copenhagen interpretation on the one hand, and many-worlds and spontaneous collapse theories on the other, as corresponding respectively to what he calls an instrumentalist and a realist approach to the wave function. In the instrumentalist approach the wave function is not regarded as something to be taken seriously as real or objective, but merely as a convenient tool for describing the behavior of measuring devices and the like. In the realist approach, according to Weinberg, the wave function is not only real and objective but also exhaustive, providing a complete description of the physical state of affairs. In other words, the alternatives for the wave function for Weinberg are either that it is nothing or it is everything.

However, Weinberg does not mention a third possibility, the de Broglie–Bohm theory or Bohmian mechanics, in which the wave function is something but not everything. This theory, which we consider to be, by far, the simplest version of quantum mechanics, does not require any modification of the predictions of ordinary quantum mechanics, nor a bizarre (to say the least) multiplication of parallel universes. It was proposed by Louis de Broglie in 1927 and rediscovered and developed by David Bohm in 1952. For several decades its main proponent was John Stewart Bell, the physicist who did more than any other to establish the existence of the quantum non-locality mentioned by Weinberg.

In Bohmian mechanics a system of particles is described by actual positions of actual particles in addition to its wave function: particles actually do have positions at all times, hence trajectories and also velocities. Their time evolution is guided in a natural way by the wave function, which functions as what is often called a pilot wave. This should be contrasted with the role of the wave function in the instrumentalist approach: to predict the behavior of (clearly nonfundamental) measuring devices. Thus the wave function in Bohmian mechanics is somewhat similar to the forces or the electromagnetic waves guiding the particles in classical physics.

The wave functions of closed systems in Bohmian mechanics, even systems containing observers and measuring devices, always follow Schrödinger’s equation and never collapse. Thus, observations are no longer a deus ex machina in that theory. When one analyzes in Bohmian mechanics what is called a “measurement” in ordinary quantum mechanics, one finds that the behavior of the particles yields a world in which measurement results conform precisely to the quantum mechanical predictions. Such an analysis of quantum measurements also explains why the fact that particles have both positions and velocities at all times does not contradict the Heisenberg uncertainty principle. In particular, although Bohmian mechanics is perfectly deterministic, one can recover the statistical predictions of ordinary quantum mechanics (the Born rule mentioned by Weinberg) by making natural assumptions on the initial conditions of physical systems (something which has become familiar among physicists with the development of modern “chaotic” dynamical systems theory).

While Bohmian mechanics is a version of nonrelativistic quantum mechanics and not of quantum field theory, the basic idea of Bohmian mechanics—that the wave function should be something but not everything—applies to any quantum theory. In fact there are a variety of Bohmian versions of quantum field theory, though it would be fair to say that there is no agreed-upon best or canonical version for relativistic physics.

Jean Bricmont

Professor of Theoretical Physics

University of Louvain

Louvain-la-Neuve, Belgium

Sheldon Goldstein

Distinguished Professor of Mathematics, Physics and Philosophy

Rutgers University

New Brunswick, New Jersey

Tim Maudlin

Professor of Philosophy

New York University

New York City