An Interpretation Too Many?

A Review of Something Deeply Hidden, by Sean Carroll

“One person’s absurdity is another person’s answer to all of life’s questions.”

S. Carroll (from Something Deeply Hidden)

Sean Carrol is a masterful writer with an enviable style. He has the ability to take a complicated idea and lull the reader into an easy sense of being in safe hands. He navigates complex subjects with impressive dexterity and explains them in a convincing way. All that is to be greatly admired. I wish I could tell stories so easily. But I’m more uneasy with the writing as an exercise in critical thinking.

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Carroll is a great writer, but I’ve been trying to understand why his writings don’t sit well with my gut. I’ve seen him on television and in public debates too, and he often advocates for a particular popular view of current orthodoxy, as if glued to a party-political line of reasoning, or keen to ingratiate himself with what seems like the most promising popular opinion of the day. He presents science as if it were a fait accompli, even as he tells us there is much to learn. The wiggle room for doubt is locked down tightly. This has become a disturbing trend in science writing about physics in particular.

Compare that to other popular educators, like Sabine Hossenfelder, who has built a brand as someone who bravely goes in where others fear to tread, who speaks plain reason — and is happy to find fault and expose flaws — and I know where I would place my money. Feynman once said that our first duty is not to fool ourselves. Be critical rather than advocate. For lay readers this may seem picky, but it is how science self-corrects.

Carroll’s new book is one of a number of recent books that tells of a resurgence of interest in the fundamental ideas about Quantum Mechanics (QM) — see also Lee Smolin’s book Einstein’s Unfinished Revolution, for a contrasting view. I’m happy to see this resurgence, because it’s a dangerous blindness when physicists trust equations with blue-eyed nonchalance. But aside from the skill with which the book has been written, I confess to a distaste for what it has set out to do — to convince readers about a rather silly interpretation of Quantum Mechanics know as the Many Worlds interpretation, by selective reasoning.

Carroll has placed himself in the spotlight to represent the views of a small number of quantum theorists who tout that “Many Worlds” (an idea that goes back to Kripke and others) is the best resolution to some of the confusions about fundamental physics, namely that the universe is constantly splitting like a cancerous tumour into a shadowy realm we cannot observe. His approach, as a writer, is to lead the reader through a confidence building exercise, establishing a safe space for trust. Then he sets up a series of mysteries and conundrums and proceeds to dismiss them as simple fodder. For instance, “spooky action at a distance” used to be feared. Now we just call it “a field”. So by naming it, we take away its power and the problem goes away. A different argument is used for entanglement, on the other hand, so we are not quite consistent. There is trickery here; it’s like saying — there was once a mysterious stranger in the village that no one could understand; now we call him John, so it’s all good now. He futher offers renditions of a few philosophical platitudes to dismiss other objections. First you take a position on a matter and then choose your six impossible things to believe in — hence the quote at the start of the review.

It’s a story of trusting blindly. Carroll is a practicing scientist — so we should believe him, right?. After all, science is objective and therefore when someone speaks forcefully, with authority, we should be impressed. But the truth is that most scientists are rather timid and need the moral backing of someone bolder than themselves in order to support a point of view. Bold views may can be misrepresented as more important than they really are, because they come from a source of boldness. Followers may fool themselves too. This is why a lot of science is political, and revolves around personalities. The number of people who support an opinion really has nothing to do with how right or wrong it is.

Trusting blindly is exactly what this book is about. The source of its argument lies in an unfounded trust in a single equation: the Schrodinger equation and the meaning of its solutions. The wavefunction solution is held up as “being” what particles are, without any real question. There are no tables or chairs, only wave functions, he tells us. The arguments in the book rely on particles, matter and energy. One could question why we should believe in them then — why particles, matter, and energy, separated by classical convention? — but he doesn’t (except in an oblique reference to P.C.W. Davies’ essay in Bryce DeWitt’s 60 year festschrift). One could further question the placement of the Schrodinger equation itself on a unique pedestal of ultimate significance. The truth is that the Schrodinger equation itself was written down as an effective explanation of phenomena on the scale of an atom. It’s intended meaning (by Schrodinger himself) is not even the interpretation that was later adopted as part of the pragmatic recipe we now know for its calculable answers. No one claimed it was or should be the final word on elementary physics, but that is the assumption that this book seems to make. One could question all that. But, again, he doesn’t.

This is not about Carroll, so I should not get personal, but it is about a kind of lazy mystical thinking that some authors like to popularize.

The Schrodinger equation is an eigenstate equation: it finds a menu of self-consistent possible outcomes, compatible with the distribution of the classical energy concept, in a system that’s constrained by a fixed boundary. What is interesting is that the number of solutions is often finite, like a choice of Happy Meal. The equation does not (and cannot) select any particular solution unless we later know more about its boundary conditions, such as when we make a specific measurement. Actually, this is true of the solution of any differential equation. In other words, an equation is just a constraint: it makes no prediction at all until actual information is injected into it (e.g. by fixing boundary data).

Without boundary data, the Schrodinger equation only expresses the conservation of classical energy. The Many Worlds interpretation takes a bizarre standpoint — claiming that all possibilities are physically realized all the time. But on what basis? If we apply that thinking to the Schrodinger equation, then we should apply it to all equations. The square root of 4 is both 2 and -2 at the same time, but when does the universe split? This is nothing to do with Quantum Theory per se. Does this apply only to temporal processes? What if we then eliminate time as a variable, say, as economists do?

I’ll skip a lot of points, and jump to a big one. There is a whole ream of criticisms one could level at the Many Worlds interpretation, but one of them stand outs as a key problem with the branching argument. It doesn’t scale. It seems to matter how we model the world. The equation is incomplete in its information, yet it is supposed to describe a fundamental process about the universe. It would seem to matter whether we represent a proton as a single particle or as three quarks. Does the branching of the universe really depend on how we choose to model it? Are there more branches if we think about quarks than if we think about a proton? If I choose left instead of right, it that two branches or one for each subatomic particle in my body? That’s surely silly. But Many Worlds view is that the wavefunction is a kind of surrogate for God, with such power to decide. Carroll neatly dances around this issue throughout the book. When convenient, the wavefunction just applies to an atom. Other times it’s the whole universe. But a truly fundamental theory needs to scale sensibly. That can only be done bottom up, and Schrodinger theory (the correspondence principle) is top down.

The Schrodinger equation was written down as a large scale (“long wavelength”) effective field theory of atomic systems. Arguably, its Hamiltonian generalization by Dirac (as a symplectic, canonical form) offers a reason to extend its possible meaning, but one doesn’t escape the concepts that are tied to a particular range of semi-classical scales where gradients of smooth functions are the generators. That happens to be the domain of the modern world of materials, and its successes are undeniable — but there is no reason at all to expect it to apply to Quantum Gravity, for instance, on a much smaller scale, where gradient is fundamentally non-local. Schrodinger abstracts backgrounds as smooth potentials, so it can’t be a fundamental description. Why would physicists waste time trying to dress it up as one? This is surely a question physics needs to confront.

The trust that the whole wave function “is” the electron is a hidden nonsense that some physicists mistakenly assume to be true. Bohm and De-Broglie’s pilot wave model take a different view, as Carroll discusses, but they are also unable to let go of the concept of a particle as a physical object, rather than just the outcome of a measurement. We can understand why they believe this from the history of philosophy of ideas, but not from theory itself.

Take a somewhat analogous situation— an Internet search. When you Google something, there are two processes involved: there is a “crawler”, a long timescale process that assembles a picture of what information lies where and makes it accessible, based on the boundary conditions out there in the real world. The result may or may not be cached in a database. More importantly the result does not propagate until it has stabilized. This corresponds roughly to the what the Schrodinger equation describes — a distribution of energy in space which is compatible with all boundary information. Then there is a browser lookup (a measurement) which selects specifically from that distribution as a separate process (on a much shorter timescale), like a filter. This picture matches yet another interpretation of QM, called the Transactional Interpretation.

In fact this sender-receiver, source-filter structure is represented in the quantum formalism too in the form of bra and ket (using Dirac’s notation), or as adjoints in the wavefunctions of inner products. Statistically, these are self-adjoint to conserve energy, but not individually. In other words, on average, there is a Hermitian property of a Hilbert space, which means that classical energy is conserved in the limit (whatever energy is). Nature is full of such processes that are decoupled, and which run by their own clocks, but which together form a sampling process that leads to observer relativity. This is why I’ve argued earlier (see Smart Spacetime), that we need to make Quantum Theory compatible with Information Theory before introducing too many mystical notions. If we forget about the ranking of results in a Google search, the order selected by the observation will be quite random. So we will observe a “hit” like a random variable. But if we apply ranking statistics, we can still find the relative probabilities.

The Internet does not collapse when you query it. There is no retroactive force that causes the Internet and its state of reality to be reset. These are independent things, weakly coupled by a communications channel. By the same token, the artificial notion of wavefunction collapse in QM has grown up from a doctrine that “the wavefunction is the electron” rather than being a more natural information channel, i.e. that it is an objective single source of deterministic truth. That’s just not the simplest or most natural explanation of things, and it’s incompatible even with the statistical interpretation of probability. The apparent non-locality of measurement is a result of the separation of timescales between processes, some of which are “deeply hidden”.

So there are other possibilities, potentially simpler answers, if we are still willing to think more deeply — -whether this example is right or wrong for the laws of QM is something we just don’t know, but it at least has simple precedents, and it’s a lot cheaper than branching universes. When you do a Google search for “Quantum Mechanics”, the Internet doe not collapse onto the result you found. Similarly, when you first observe an elephant after some evolutionary changes occur, there is a selection process to establish which ones are observed in the asymptotic limit — yet the observation of that animal does not wipe out all genetic deviants, or fork the universe into quantum foam. It’s just an outcome of an isolated observational process, filtered by selection, with straightforward causal independence from the process that generated it.

I could go on, but I don’t need to, because I already wrote a lot in my own book — and there are plenty of counter arguments to be read by other writers too.

Carroll is a very good writer, but I believe his bravery in standing up for this outlier interpretation about QM is misplaced. His arguments, borrowed from others, seem to be made in order to preserve a classical interpretation of the meaning of equations as the medium of truth in physics. To preserve that tradition, we should ignore the informational aspects of the problem that are different from classical modelling (the discrete sampling of information in particular), and replace it with an outrageous idea: the proposal that the entire universe splits like a malignant cancer.

By the end of the book, Carroll does present some alternative interpretations, and comes to the idea that I believe is key: an agent based model of spacetime is the far simpler way of partitioning outcomes from different perspectives. But it means spacetime has interior memory for the superposition. That’s a far less drastic notion than splitting the entire universe, and it has a wealth of precedence in phenomena all the way up the hierarchy of scales to our classical world. The implication is that spacetime is not the inert background that classical differential equations, based on coordinates (including the Schrodinger equation), assume.

The prison, from which discourse on QM seems unable to escape, is the notion that everything must come from a simple equation whose solution represents the primary entities of reality, all embedded within an inert spacetime. Neither the medium nor the receiver entity play a role in what is observed, even though downstream components of the information flow are the natural selection criteria for observed phenomenology. But that view violates a rather different theory: Information Theory, where the overlapping responsibilities of the sender and the receiver are involved. If a theory is truly local, then what happens at one location should not be able to completely determine what happens at another without some interaction that’s accepted by both ends.

To summarise, when you read Carroll’s book, don’t feign a collapse of common sense just to go along with a good story. Stay alert. Some ideas make for entertaining stories that suspend your disbelief, but the plot may still be flawed. Read the book, buy the book, but beware the book.

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