Einstein's Unfinished Revolution

by Lee Smolin

  This starts to make sense. Not everything that is possible is real. But a small part of the possible has definite properties that justify assigning it to a new category of the real and possible.

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  THERE ARE ALSO RECENT DEVELOPMENTS on the magical realism side. Back in the 1990s Julian Barbour proposed a quantum theory of cosmology that has many moments rather than many worlds.8 This has been revived in a recent proposal by Henrique Gomes. As we are not concerned with technical details, I’ll describe the original approach of Barbour, but most of what I’ll have to say applies to Gomes’s version9, as well as more recent work of Barbour and his collaborators.

  A moment, for them, is a configuration of the universe as a whole. These configurations, according to Barbour and Gomes, are relational configurations, which code all the relations that can be captured in a moment, such as relative distances and relative sizes.

  We seem to experience time passing as a smooth flow of moments. Barbour insists that the passage of time is an illusion and that reality consists of nothing but a vast pile of moments, each a configuration of the whole universe. You now are experiencing a moment. Now you are experiencing a different moment. According to Barbour, both moments exist eternally and timelessly, in the pile of moments. Reality is nothing but this frozen collection of moments outside time. Each experience of a moment also exists timelessly—as part of its moment. The fleeting aspect of a moment is in reality just an aspect of the moment, a feature it has eternally.

  The moments all coexist, and each is a configuration of the whole universe. But there is an important way they can differ. The pile can have more than one copy of a configuration, and the number of copies may vary from many copies to none at all.

  Barbour hypothesizes that we are equally likely to be experiencing any of the moments in the pile. But since some are more common than others, there is structure to our experience, as we are most likely to experience the more common moments.

  The collection of moments is structured so that the most common moments are those configurations that, to some degree of approximation, can be strung together as if they were a history of the universe generated by a law. This gives us the illusion that laws are acting, but there are no laws generating histories, and indeed no history. Reality is just the vast collection of moments.

  Barbour hypothesizes that the most common moments contain structures which speak to us of other moments. A book, even while frozen forever in a moment, may tell stories that are only comprehensible as a sequence of events that played out over time. A book has a publication date, which references a happy event (at least for its author) sometime in the past. And it was brought into existence by a printing company, a publishing company, and a paper mill, each of which has a history, which evokes more stories.

  Barbour calls objects like books, which contain eternally frozen, momentary structures that are pointers to other moments, time capsules. Anything that is, or contains, a record, such as a DVD or a video file, is a time capsule. So it can be any built structure or manufactured object. Indeed, it can be any living thing.

  For most of us, the fact that the natural world is chock-full of time capsules is evidence that time is real and fundamental. Events are ordered in time because past events cause present events. But according to Barbour, even the impression we have of living within a flow of moments is an illusion. All the memories, records, and relics we have that give the impression that there was a past are, in fact, aspects of a present moment. Each moment lives eternally in the pile of moments.

  An unordered pile of moments, which is all that makes up a Barbourian universe, might easily contain few moments with time capsules. Why then is almost every moment of our universe full of them?

  To elucidate our world, Barbour has to explain what determines which configurations are common, having many copies in the pile, and which are less common, or altogether absent. This is dictated by an equation, which is the only law that acts to structure the pile. It does so by choosing which configurations are represented in the pile, and by how many copies. This is a version of Schrödinger’s equation, but one with no explicit reference to time. It is called the Wheeler-DeWitt equation; we can call it Rule 0. This equation chooses as solutions piles of moments which are populated by those that can be strung together to permit the illusion of history to emerge.

  If this is right, then the passage of time is an illusion, which is due to a present moment containing the experience of memories of the past. Causality is also an illusion.

  These “many moments” theories are realist, in that they take a stand on what is real, which is the timeless collection of moments. But these theories are beyond naive realism in that they posit a real world enormously different from the time-bound world we experience, in which we perceive a succession of moments, one at a time.

  The lesson I draw from these theories is that to extend quantum mechanics to a theory of the whole universe, we have to choose between space and time. Only one can be fundamental. If we insist on being realists about space—as Barbour and Gomes do—then time and causation are illusions, emergent only at the level of a coarse approximation to the true timeless description. Or we can choose to be realists about time and causation. Then, like Rovelli, we have to believe that space is an illusion.

  There is much more that could be said about these recent non-realist and magical-realist perspectives. But the bottom line is that if your interest is pragmatic, and you want to use quantum theory to understand questions other than those arising from quantum foundations, any of these will serve to frame your calculations and the explanations you draw from them. But if you want to solve the measurement problem in a way that gives a detailed description of what goes on in an individual physical process, nothing but a realist description will do.

  THIRTEEN

  Lessons

  The main message of this book is that however weird the quantum world may be, it need not threaten anyone’s belief in commonsense realism. It is possible to be a realist while living in the quantum universe.

  However, simply affirming realism is not enough. A realist wants to know the true explanation for how the world works. There would be no sense in believing that the world has a detailed explanation, and not being interested in what that explanation is. Thus the next question to ask is whether any of the available realist versions of quantum physics are compelling as true explanations of the world. That is, are we done, or do we have more work ahead? Unfortunately, I believe the answer is that, so far, none of the well-developed options are convincing. All the realist approaches that have so far been studied have serious drawbacks. To explain why, let me review the available options, with a focus on the strengths and weaknesses of each.

  PILOT WAVE THEORY

  Pilot wave theory completes quantum mechanics by providing additional degrees of freedom which, together with the wave function, fully specify what is going on in an individual physical system. These are the particle trajectories. We called these hidden variables, but that is perhaps not the best way to talk, as the particles are, after all, what is observed. A better way to describe the options is to use the term “beables,” as suggested by John Bell. Realists want a theory to take a stand about what really exists; these are the beables. In pilot wave theory the waves and particles are both beables.

  Pilot wave theory solves the measurement problem, because the particle always exists and it is always somewhere. When an experimental device looks for the particle, it finds it where it is.

  The equations of pilot wave theory are deterministic and reversible, which argues for the completeness of the theory. Probability is explained by our ignorance of the initial positions of the particles, just like in other applications of probability to physics. The Born rule, the relationship between probability and the square of the wave function, is explained by the demonstration that this is the only stable probability distrib
ution, and all others evolve to it.

  In addition, pilot wave theory is complete and unambiguous. Some of the other modifications of quantum mechanics come with new free parameters, which may be adjusted to hide various embarrassments and protect the theory from experimental disproof. Pilot wave theory has no additional parameters and allows no choices to be made. This is a very important point in its favor.

  Because it gives a clean, unambiguous, and explicit description of the quantum beables, pilot wave theory continues to be a popular option within the small community of quantum realists. Partly this is because there remains a lot to do to develop the applications of the theory. It is one thing to demonstrate generally that the predictions of pilot wave theory and conventional quantum mechanics will often agree, but it is another to see how this works out in detail. Physicists like to have well-defined problems to work out, and pilot wave theory offers no shortage of these.

  There are challenges for pilot wave theory. If it is to replace quantum mechanics, it must do so in all the contexts in which the usual theory works. This includes relativistic quantum field theory, which is the basis of the standard model of particle physics. There has been good work done on this, but important questions remain unresolved. There have also been very interesting explorations of pilot wave theory applied to quantum gravity and cosmology, but these are far from definitive.

  But the most important aim of research in pilot wave theory must be to discover and open up domains where experiments will distinguish the new theory from the older one. Here there is exciting work being done on the cosmological scale by Antony Valentini and others.

  At the same time, there are several reasons pilot wave theory is not entirely convincing as a true theory of nature. One is the empty ghost branches, which are parts of the wave function which have flowed far (in the configuration space) from where the particle is and so likely will never again play a role in guiding the particle. These proliferate as a consequence of Rule 1, but play no role in explaining anything we’ve actually observed in nature. Because the wave function never collapses, we are stuck with a world full of ghost branches. There is one distinguished branch, which is the one guiding the particle, which we may call the occupied branch. Nonetheless, the unoccupied ghost branches are also real. The wave function of which they are branches is a beable.

  The ghost branches of pilot wave theory are the same as the branches in the Many Worlds Interpretation. In both cases they are a consequence of having only Rule 1. Unlike the Many Worlds Interpretation, pilot wave theory requires no exotic ontology in terms of many universes, or a splitting of observers, because there is always a single occupied branch where the particle resides. So there is no problem of principle, nor is there a problem of defining what we mean by probabilities. But if one finds it inelegant to have every possible history of the world represented as an actuality, that sin is common to Many Worlds and pilot wave theory.

  A perceptive reader might be troubled by this similarity to the Many Worlds Interpretation. Assuming that its proponents do succeed in giving Everettian quantum mechanics a sensible physical interpretation via decoherence, subjective probabilities, and the works, couldn’t we apply exactly the same interpretation to the branching wave function of pilot wave theory—and simply ignore the particles? The answer is yes, you can ignore the particles, and then you are squarely back in Everett’s multiverse. This brings up a hidden, perhaps unconscious assumption made by the adherents of pilot wave theory, which is that the reality that we observers perceive and measure is composed of matter constructed from the particles of pilot wave theory.

  Just because both the particles and the waves are beables in pilot wave theory does not make them equivalent. To make sense of pilot wave theory we must privilege the particles and postulate that the world we perceive consists of the particles. The waves are there in the background, but their role is to guide the particles—they are not perceived directly, and only affect our observations through their role as guides.

  From the point of view of either explaining or predicting the world, the ghost branches play little role in pilot wave theory. The probability that a ghost branch of a macroscopic system will interfere with the occupied branch, changing the future of that system, is truly tiny. It is tempting then to introduce some mechanism to prune back the ghost branches. This would be a combination of pilot wave theory and spontaneous collapse models. I am not aware of any work in this direction, but it seems an interesting avenue to explore.

  This brings up another issue with pilot wave theory, which is that there is an asymmetry of causes. The wave function guides the particle, but the particle has no influence back on the wave function. This is unlike the way causes work in ordinary physics. In nature, and so in most of physics, causes are usually reciprocal. Everything you push on pushes back. This is due to Newton’s third law, which states that every action is met by an equal and opposite reaction. It is then very strange that the particle cannot influence the wave function. The lack of a reciprocal effect strongly suggests something is missing.

  Even if the ghost branches can often be ignored, they can’t always be. Some clever experiments have been devised which show that the branch of the wave function which the particle doesn’t take can influence the future as much as the occupied branches.1 These tricky cases involve two quantum particles which interact with each other, such as an atom and a photon.

  According to pilot wave theory, the atom is both a particle and a wave. Let’s call them the atom’s particle and the atom’s wave. The photon is also a particle and a wave, and, likewise, we’ll call them the photon’s particle and the photon’s wave. In each case, the wave guides the respective particle. But suppose we set things up so that the photon is to collide with the atom. Which entity interacts with which?

  You might be tempted to suppose that the atom’s particle collides with the photon’s particle. But that turns out to be wrong. The two particles are each invisible to the other. They will easily pass right through each other. Instead, what happens is that the two waves interact and scatter off each other. Then, as the waves retreat from their collision, the atom’s wave pulls the atom’s particle with it, while the photon’s wave likewise pulls the photon’s particle away.

  But whether a wave function scatters another wave function doesn’t depend at all on whether it is an occupied branch or a ghost branch. This has some pretty weird consequences, but they are equally weird for conventional quantum mechanics and pilot wave theory. For example, it can appear that a particle bounces off the empty ghost branch of another particle’s wave function.

  The fact that wave functions bounce off wave functions doesn’t count against pilot wave theory. Indeed, it shows that the theory works even in such counterintuitive situations; this should strengthen our confidence in it. But it teaches us the cost, which is to give up comfortable pictures in which the particles are the main story and the ghost branches are discounted.

  The fact that the particles are guided by the wave functions has other weird consequences, one of which is that the motions the particles make in response to their guidance by the wave function fail to conserve momentum and energy. The particles behave like UFOs in bad science fiction movies—for example, they can sit still for hours, which is what they do in states of definite energy, and suddenly jump up and run away in response to changes in the guiding wave function.

  This did not shock de Broglie, and it doesn’t perturb his modern followers, such as Valentini. They understand it has to be that way, because part of the guidance equation’s job is to bend the paths of particles around obstacles and through slits, to reproduce the diffraction of light, and a particle that alters its direction without colliding with another particle is one that changes its momentum. But this was a deal breaker for Einstein and, I would guess, it has been for others.

  If one averages a system that is in quantum equilibrium over many possible trajectories of the part
icles, then on average momentum and energy are conserved. This is one reason I’ve come to favor formulations in which the probabilities refer to ensembles of particles that really exist. I will be discussing these in the next chapter.

  Pilot wave theory offers a beautiful picture in which particles move through space, gently guided by a wave, which also flows in space. The reality is a bit less intuitive. When applied to a system of several particles, the wave function doesn’t flow through space; it flows on the configuration space, which is multidimensional and thus hard to visualize. And, as I’ve emphasized, the particles are not your grandmother’s little round spheres—they react to things near and far, including sudden nonlocal influences transmitted through the guidance equation. Still, the particles can do nothing else if pilot wave theory is to reproduce the results of quantum mechanics.

  A third problem with pilot wave theory is that there is a strong tension with relativity theory. This is because of nonlocality. The experimental tests of Bell’s restriction tell us that any attempt to go beyond the quantum, to give a description of individual events and processes, must explicitly incorporate nonlocality.

  This nonlocality must somehow be coded into the pilot wave theory, because that theory is a completion of quantum mechanics and agrees with its predictions. And indeed, nonlocality is built in. How can that be? Let us consider a system of two entangled particles, which are very distant from each other. The secret is that the quantum force that one particle experiences depends on the position of the other particle. This dependence remains even if the two particles are very far from each other.