The Universe Is a Big Layer Cake

Is the universe deterministic or indeterministic? A clockwork or a craps table? In this month's issue of Scientific American, I have an essay arguing that the answer is: both. The world can be deterministic on some levels and indeterministic on others; these two categories are not mutually exclusive. To me, this is the essence of Einstein's critique of the orthodox Copenhagen Interpretation of quantum mechanics. Einstein recognized that quantum indeterminism could perch atop a deeper deterministic layer and, given the theory’s loose ends, seemed to have to. I've already been getting some interesting responses by email, so I thought I'd open up a comments thread to get a discussion going.

Traditionally the supposed dichotomy between determinism and indeterminism has been as much about people as about particles. Determinism seems to deprive us of free will—a concern that weighed on the creators of quantum mechanics and made many of them receptive to indeterminism. Max Born wrote Einstein in 1944: "I cannot understand how you can combine an entirely mechanistic universe with the freedom of the ethical individual… To me a deterministic world is quite abhorrent—this is a primary feeling." To which you might reply that indeterminism is no less abhorrent. If God plays dice with the universe, he also plays it with human fate.

By dissolving the dichotomy, philosophers such as Daniel Dennett of Tufts University and Christian List of the London School of Economics have argued that we can be the authors of our own acts even if the particles in our bodies move in completely preordained ways. The unpredictability and openness of human decisions is a type of higher-level indeterminism. It is decoupled from whatever happens at the foundations of reality.

Another way to put it is that free will—and indeterministic behavior in general—is an emergent property, one that doesn't exist at the microscopic level but arises in the aggregate. Sometimes the word "emergence" is thrown around without elaboration. In this case, it's really quite simple. There's redundancy in how macroscopic objects are put together. A change at the macro level implies a change at the micro level: if you roll a die twice and it lands on different sides, the atoms in the die must have taken different paths. (This condition is known as "supervenience".) But the converse is not true. If the atoms take different paths, the visible outcome might still be the same. Consequently, the workings of microscopic and macroscopic laws need not mesh.

To illustrate, here's a pair of figures from List. They show the development of a system—a gas, say—at five moments in time, with time running upward. The first figure shows how the situation looks on the microlevel. The system begins in one of six possible microstates, each of which evolves in a purely unambiguous, deterministic way. The second figure shows the macrolevel (or "agential" level, meaning the human scale). The resolution of this level is lower, and the gridlines show how the microstates blur together into macrostates. In physics jargon, the macrolevel is "coarse-grained." In several places, the lines branch: the gas could evolve in two possible ways as seen from the macrolevel, and it looks as though the gas chooses one of them at random.

Roughly speaking, you might think of the dots as molecules and the boxes as the maximum resolution of a microscope. At the start, the molecules are bunched, so you see two lumps. At t=2, a third lump suddenly materializes on the left. It arises because the left group of molecules has spread apart, but you don't see the molecules. To you, it looks as though a new lump has popped out of thin air. The dynamics of the macrolevel is as much a product of the coarse-graining as of the microscopic dynamics.   In this scenario, the system evolves from a high-redundancy state to a low-redundancy one. In physics terms, that means it goes from high entropy to low entropy—which is opposite to what you'd expect for a closed system. But List assures me that entropy can also increase, so that the emergence of indeterminism from determinism doesn't presume unusual conditions; it's a general phenomenon. Another feature of the simple scenario is that the macro level is just a blurrier version of the micro, making the division into levels somewhat arbitrary. But the relationship among levels can be, and usually is, more opaque. Macrostates and microstates typically involve completely different variables, so that you can't resolve the microstate merely by turning up the magnification; you need a change of conceptual framework. The bulk properties of gases, such as temperature, do not exist at the molecular level; they are collective quantities. Quarks and gluons are not simpler littler versions of the protons and other particles they make up.

If you went to an even higher level of description, you might well find that the system behaves deterministically again, as the randomness gets averaged out. The microscopic motions are deterministic, and so are macroscopic phenomena such as diffusion, wave motion, and fluid flow, but in between is a "mesoscopic" realm governed by probabilistic laws. The mesoscopic equations are formulated in terms of macroscopic variables, but include random noise to capture the suppressed microscopic details. You see this in climate models, which use random variables to capture physics that occurs below the resolution of the computer simulation. Some theorists, following Einstein, think of quantum mechanics as a probabilistic mesoscopic theory. For instance, Steven Adler at the Institute for Advanced Study has derived quantum mechanics with random corrections from an underlying theory that is not only deterministic, but also nonspatial.

Many physicists and philosophers find this kind of analysis deeply unsatisfying. Sure, they say, higher-level laws may be indeterministic if formulated in terms of higher-level variables—but that's a big if. Those laws can still be deterministic in terms of lower-level variables. If you encounter any uncertainty over how the world will unfold, you can zoom into the microscopic level and everything will come into focus. Our decisions may seem open to us, but are preordained on the lower level. This issue is tied up with a broader debate over the concept of emergence. Strict reductionists think of emergent properties not as objective features of reality but as convenient approximations to the fundamental physics. In other words, the world really has only a single level, and if it is deterministic, any indeterminism we perceive merely reflects our imperfect knowledge about the real goings-on.

Thing is, we do observe multiple levels in nature. Each is self-contained: it follows laws that are most succinctly described by what happens at that level, without reference to below or above. (This is an important feature of quantum field theory.) List developed this point in an earlier paper with the late Australian philosopher Peter Menzies. Suppose the macrolevel can be in one of three states, A, B, and C, each of which—because of redundancy—corresponds to a large set of microstates, {a_i}, {b_i}, and {c_i}. Now, suppose that some of the a_i’s deterministically evolve to b_i’s and the rest to c_i’s. From the macroscopic perspective, A indeterministically splits to B or C. Nothing would be gained by spelling out all the microscopic outcomes; to the contrary, you'd fail to grasp the way the microstates are grouped. There's real structure here, not just a mirage caused by imperfect knowledge. "If we were to try to capture all scientific phenomena just at the lower level, we would actually miss out on some important higher-level regularities," List says.

Much the same reasoning about levels could dissolve other dichotomies of physics, such as locality vs. nonlocality, the subject of my forthcoming book. In fact, questions of determinism vs. indeterminism and locality vs. nonlocality often go hand-in-hand. Any large, complex system will undergo random statistical fluctuations (an effective indeterminism) and, when the system has not achieved internal equilibrium, the fluctuations at different locations will be correlated (an effective nonlocality). In quantum mechanics, particles can act in lockstep despite the distance between them, so they must either be deterministic (so that their coordinated behavior can be preprogrammed into them) or nonlocal (so that they can coordinate on the fly)—this is the dilemma that Einstein articulated in the famous EPR paper of 1935. For many physicists and philosophers, quantum nonlocality suggests that spacetime is derived, and in most approaches, the reality that underlies spacetime obeys some primitive notion of locality.

Yet again, physics demonstrates its power to demolish our neat pigeonholes, to show that the world need not conform to our human categories.