Einstein's Unfinished Revolution

by Lee Smolin

  A less precise definition of information was given by Gregory Bateson, an English anthropologist, who called it “a difference that makes a difference.” This idea is sometimes expressed instead as “a distinction which makes a difference.” This is directly applicable to physics, where we might translate it as “If different values of a physical observable lead to measurably different futures of a physical system, that observable can be considered to constitute information.” Put this way, almost every physical observable potentially conveys information. This definition would imply that “information” is present every time the values of two physical variables are correlated. But there is nothing profound about this, unless it is the appreciation of the interdependence of the different components of the physical world. And we already have measures of correlation. We can rename these “information,” but a change of names that weakens the specificity of an idea is more likely to result in confusion than it is to bring about revolution in our conception of the world.

  Computers process information in Shannon’s sense. They take an input signal from a sender and apply to it an algorithm, which transforms it into an output signal to be read by a receiver. Such contexts are very special. The choice of an algorithm to be embodied is a crucial part of the definition of a computation. Most physical systems are not computers, and the process by which the initial data at one time evolve to the data at a later time cannot always be explained in terms of the application of an algorithm or a sequence of logical operations.

  Some authors appear to confuse and conflate the two definitions of information, which tempts them into wanting to describe nature as a computer and the relation between states of the world at different times as a computation. I am not convinced that such a radical hypothesis is justified.

  This is not to say that some physical systems cannot be modeled to some degree of approximation by a computation, which is again trivially true. You can define approximations to the main equations of physics, such as those of general relativity or quantum mechanics, which can be coded as algorithms, which are then run on a digital computer. This is often a very useful way to get approximate solutions to the equations. But there is always an approximation involved.

  The sound a symphony orchestra makes can be captured by a digitization, to an approximate degree, but this always involves an approximation, which truncates the range of frequencies. The full experience of listening to the orchestra live is never fully conveyed, which is why there is still an audience for performance as well as a market for vinyl, purely analog recordings. It is the same for physics: a digitization of Einstein’s equations can be very useful, but it never captures all that the equations do.

  Even if physics is not in general comprehensible as information processing, it may be asserted that the quantum state represents not the physical system, but the information we have about the system. Rule 2 certainly makes it seem to be the case, because the wave function changes abruptly just when we gain new information about the system. But if the wave function represents the information we have about a system, then the probabilities quantum mechanics predicts must be seen as subjective, betting probabilities. This viewpoint can be developed by understanding Rule 2 as an update rule by which our subjective probabilities for future experiments change as a measurement is made. This is what is called quantum Bayesianism.5

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  A RATHER ELEGANT APPROACH, which also sees the quantum state as conveying information that one system has about another, is called relational quantum theory. According to this view, which sits between operationalism and a form of realism, quantum states are associated with splits of the universe into two parts, observer and observed, and represent what the former can know of the latter. This idea had its roots in quantum gravity, and arose out of conversations between Louis Crane, Carlo Rovelli, and me in the early 1990s.

  Our inspiration was a very elegant body of mathematical descriptions of very simplified cosmologies, which Crane and other mathematicians had developed, called topological field theories. In these theories there is no quantum description of a whole universe. There is no quantum state describing the universe as a whole. Instead, there is a quantum state for each way of dividing the universe into two subsystems. These can be thought of as carrying the information that an observer on one side of the divide could have about the quantum system on the other side.

  This reminded us of Bohr’s insistence that quantum mechanics requires a split of the world into two parts, one classical, the other quantum, and that any split will do. The models Crane and other mathematicians had studied took Bohr’s philosophy a step further, for there were two quantum states for every boundary—one for each side. This is because there are two ways to read each split. If Alice lives on one side and Bob lives on the other, then Alice will see herself as a classical observer, measuring a quantum Bob, but Bob will see things the other way around.

  The models were very simple, so that there was only one question that could be asked, which was: How similar were the two views? What is the probability that Alice’s quantum description of Bob will be the same as Bob’s quantum description of Alice? The mathematicians set up their theories so that the answer was the same however the universe was split. In that case, the probability of one side’s view resembling the other side’s view measures something universal, which would characterize how that universe is connected, i.e., what mathematicians call the universe’s topology. This is why they were called topological field theories.

  Crane brought these model universes to Rovelli’s and my attention because he saw that the mathematical structures involved could be extended to encompass loop quantum gravity. He turned out to be right about that, but that is another story. Crane also proposed that the new mathematics offered a way to extend quantum mechanics to the universe as a whole. He was right about that too, and the result was relational quantum theory.

  We were each inspired to apply this idea to quantum theory in general, and we each published a version of it.6 Rovelli’s formulation was the most general, and has become the best known, so I’ll describe his formulation of the idea.

  Bohr taught that quantum physicists must speak always of two worlds. We observers live in the classical world, but the atoms we study live in a quantum world. The two worlds satisfy different rules. In particular, objects in the quantum world can exist in superpositions, but observable properties of things in the classical world always take sharp values, and so cannot be superposed. Bohr’s point is that both worlds are necessary for science.

  The instruments we use to manipulate and measure the atoms live at, and in a sense define, a boundary between them and us. Bohr emphasized that the placement of this boundary is arbitrary, and could be drawn differently for different purposes, so long as it divides the world into two domains.

  Let us think of the Schrödinger’s cat experiment. One way to draw the boundary is to consider the atom and photon as the quantum system, keeping the Geiger counter and cat in the classical world. In this picture the atom may exist in a superposition, but the Geiger counter will always show a definite state—either YES, it saw a photon, or NO, it did not. But we can redraw the boundary, including the detector in the quantum world. In this picture, the cat is always either dead or alive, but the Geiger counter may be in an entangled superposition with the atom. Or, and this was Schrödinger’s point, you can instead draw the boundary to coincide with the walls of the box, so the cat is now also part of the quantum system and can exist in entangled superpositions with the atom and Geiger counter. The classical world then includes a friend of ours, Sarah, who opens the box and looks in. Sarah, we presume, is macroscopic and classical and so can be treated as always being in a definite state. From her viewpoint, Sarah experiences herself to be on the classical side of the boundary, so, according to her, she always sees the cat to be either alive or dead.

  Eugene Wigner suggested we take this fable one
step further and consider that the quantum system includes also our friend Sarah, together with the box, the cat, and the box’s other contents.* I remain outside the boundary, so I see Sarah become part of a superposition of entangled states. In one part of the superposition the cat is alive and Sarah sees it to be alive, while in another part of the superposition the cat is dead and she sees it to be dead.

  Thus we have five different ways to divide the world into quantum and classical, where by quantum we mean it could be in a superposition, while classical means that physical quantities always have definite values. These different descriptions appear to disagree with each other. We see Sarah to be in a superposition whereas she always sees herself to be in a definite state.

  Rovelli’s proposal is that these are all equally correct, partial descriptions of the world. All are part of the truth. Each gives a valid description of a part of the world, defined by a boundary. Is Sarah truly in a superposition, or does she definitely see and hear a live cat? Rovelli would like to not have to choose between these. He insists that a description of physical events and processes is always made with respect to some particular way of drawing the boundary between quantum and classical. He posits that all ways of drawing the boundary are equally valid and all are part of the total description.

  Simply put, Rovelli would say that it is true, from Sarah’s point of view, that the cat is alive, and it is also true, from my point of view, that Sarah is entangled in a superposition of “seeing dead cat” and “seeing live cat.”

  Is there any truth that is not qualified by a point of view? My understanding is that Rovelli would say no. In the story as I’ve told it, Sarah and I agree that she opened the box and inspected the cat, even if we don’t agree on the outcome. But it could have been the case that Sarah’s decision to open the box depended on the outcome of a quantum event such as the decay of an unstable atom, in which case I may describe Sarah as being in a superposition of having looked in the box and not. But Sarah will experience one or the other.

  Notice that there is a weak kind of consistency, in that my description of Sarah does not preclude hers. Notice also—and this is central—that every way of drawing a boundary splits the world into two incomplete parts. There is no view of the universe as a whole, as if from outside of it. There is no quantum state of the universe as a whole.

  If relational quantum theory had a slogan, it would be “Many partial viewpoints define a single universe.”

  This proposal can be seen through various lenses. A pragmatic operationalist sees each way to divide the world in two with a boundary as defining a system that can be treated with quantum mechanics. Each choice results in a description, which contains all the information that an observer on the classical part of the boundary can have about the quantum system on the other side of the boundary. For such an operationalist, the collection of quantum states contains the information that an observer can have at each level, defined by a boundary that sets her apart. Each observer uses a quantum state to code the information they have about the system on the other side of their boundary; these different states are different because they are descriptions of different subsystems.

  Seen through this operational lens, relational quantum mechanics has something in common with Everett’s original relative state interpretation. Each describes the world in terms of contingent statements that code correlations between different subsystems, which are established when they interact.

  But this is not the way that Rovelli sees relational quantum mechanics. Rovelli wants to call his view realism, but it means something different from naive realism, as I have used the term so far. For him, reality consists of the sequence of events by means of which a system on one side of a boundary may gain information about the part of the world on the other side. Thus, we can say that Rovelli is a realist about causation. This reality is dependent on a choice of boundary, because what is a definite event—something that definitely happened for one observer—could be part of a superposition for another. Thus, Rovelli’s realism is different from naive realism, according to which what is real consists of events that all observers will universally agree took place.

  Rovelli denies that that kind of naive realism is possible in our quantum world, so he proposes we adopt his radically different version of realism, according to which what is real is always defined relative to a split of the world that defines an observer. Rovelli uses very different words than Bohr, and achieves a formulation which is more precise, but the two employ a similar logic, which denies the possibility of naive realism about quantum systems.

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  ANOTHER APPROACH WHICH DENIES that naive realism is possible is based on elevating the category of the possible—things that might be true—to the world of the real. Naively, when we say that something is possible, such as that my son’s lizard might become pregnant in the next year, we mean it is among the things that might happen. When something possible happens it becomes part of the real; but till then it is not real.

  Language and logic reflect the very different status of the possible, and distinguish it from the real. The law of the excluded middle says that something real cannot simultaneously have a property and not have it. Our neighbor’s bunny rabbit cannot be both gray and not gray. But possible states of affairs have no such constraint. The rabbit our friend will buy at the pet store next week might possibly be black and it also might possibly be white.

  In real life the actual and the possible have an asymmetric relation. The real existence of our neighbor’s daughter makes a rabbit a possible future pet for their family. So what is possible is influenced by what is real. But knowledge of the possible, while helpful, is not strictly speaking necessary for working out what will be real; to the extent that the laws of Newtonian physics are deterministic, all you need to predict the actual future is a complete description of the actual present.

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  SEVERAL WRITERS, beginning with Heisenberg and including my teacher Abner Shimony, have proposed that the world of the possible has to be included as part of reality—because in quantum physics the possible influences the future of the actual. This view has been recently developed by my friend Stuart Kauffman, in collaboration with Ruth Kastner and Michael Epperson.7

  There is no way to describe this view that doesn’t cause some tension with ordinary language usage, but keep an open mind and I’ll aim to be clear. We start by stating that there are two ways for a circumstance to be real. It can be actual, which means that it is part of the world in the same way that a Newtonian particle has a definite position. But something real can also be “possible” or “potential”; this is the status we assign to properties that are superposed in the wave function, such as a leftist having equal cat and dog preference, or a particle which could go through the left slit or the right slit, or Schrödinger’s cat being both alive and dead.

  Things that are real but possible don’t obey the law of the excluded middle, but they are to be considered part of the real because they can influence the actual. This is, according to this perspective, what is different and new about quantum physics. According to Kauffman and his coauthors, experiments are processes that convert potentialities to actualities. Thus, Schrödinger’s cat is potentially alive and potentially dead, not in the sense of something that is one or the other, but about which we are ignorant, and not in the sense of some undetermined state of affairs, but because its actual reality consists of this potentiality for one or another to be realized by an experiment.

  The fact that experiment plays a distinct role in converting the possible to the actual, with probabilities given by the Born rule, is enough to tell us that this is not a naively realist perspective, i.e., a description of the world as it would be in our absence, in which experiment cannot play any role. But it is a direction, perhaps, to be developed, if realism fails.

  Here is a way we might develop
the view that the possible is part of the real. Bring in time, and let us take the view that the present moment and the flow or passage of moments are real and fundamental.* Part of what I mean by this is that there is an objective distinction between the past, present, and future. In such a view, the present is real. The present consists of events which have happened, but which have yet to give rise to the future events that will be their replacements.

  The past consists of those events which were once present and real. They no longer exist, although their properties can be captured and remembered in presently existing structures.

  The future is not real. Moreover, the future is slightly open, in the sense that rare novel events with novel properties may happen every once in a while. (See my principle of precedence below.) But if for a moment we ignore that possibility, then there does exist in the present a finite set of possible next steps, which are possible next events and their properties.

  Given the present state of the world, not everything can happen in the next time step. Those events that might be next Kauffman calls the adjacent possible. The possible near-future events that make up the adjacent possible are not yet real, but they define and constrain what might be real.

  The adjacent possible of Schrödinger’s cat includes a live cat and a dead cat. It does not include a brontosaurus or an alien dog. So the elements of the adjacent possible have properties, even if the law of the excluded middle does not apply to them. As objects with properties, there are facts of the matter about them. This is the sense in which we may say that a small part of the possible may be considered real.