For me, a highlight of an otherwise ill-spent youth was reading mathematician John Casti’s fantastic book “Paradigms Lost“. The book came out in the late 1980s and was gifted to my father who was a professor of economics by an adoring student. Its sheer range and humor had me gripped from the first page. Its format is very unique – Casti presents six “big questions” of science in the form of a courtroom trial, advocating arguments for the prosecution and the defense. He then steps in as jury to come down on one side or another. The big questions Casti examines are multidisciplinary and range from the origin of life to the nature/nurture controversy to extraterrestrial intelligence to, finally, the meaning of reality as seen through the lens of the foundations of quantum theory. Surprisingly, Casti himself comes down on the side of the so-called many worlds interpretation (MWI) of quantum theory, and ever since I read “Paradigms Lost” I have been fascinated by this analysis.

So it was with pleasure and interest that I came across Sean Carroll’s book that also comes down on the side of the many worlds interpretation. The MWI goes back to the very invention of quantum theory by pioneering physicists like Niels Bohr, Werner Heisenberg and Erwin Schrödinger. As exemplified by Heisenberg’s famous uncertainty principle, quantum theory signaled a striking break with reality by demonstrating that one can only talk about the world only probabilistically. Contrary to common belief, this does not mean that there is no precision in the predictions of quantum mechanics – it’s in fact the most accurate scientific framework known to science, with theory and experiment agreeing to several decimal places – but rather that there is a natural limit and fuzziness in how accurately we can describe reality. As Bohr put it, “physics does not describe reality; it describes reality as subjected to our measuring instruments and observations.” This is actually a reasonable view – what we see through a microscope and telescope obviously depends on the features of that particular microscope or telescope – but quantum theory went further, showing that the uncertainty in the behavior of the subatomic world is an inherent feature of the natural world, one that doesn’t simply come about because of uncertainty in experimental observations or instrument error.

At the heart of the probabilistic framework of quantum theory is the wave function. The wave function is a mathematical function that describes the state of the system, and its square gives a measure of the probability of what state the system is in. The controversy starts right away with this most fundamental entity. Some people think that the wave function is “epistemic”, in the sense that it’s not a real object and is simply related to our knowledge – or our ignorance – of the system. Others including Carroll think it’s “ontological”, in the sense of being a real entity that describes features of the system. The fly in the ointment concerns the act of actually measuring this wave function and therefore the state of a quantum system, and this so-called “measurement problem” is as old as the theory itself and kept even the pioneers of quantum theory awake.

The problem is that once a quantum system interacts with an “observer”, say a scintillation screen or a particle accelerator, its wave function “collapses” because the system is no longer described probabilistically and we know for certain what it’s like. But this raises two problems: Firstly, how do you exactly describe the interaction of a microscopic system with a macroscopic object like a particle accelerator? When exactly does the wave function “collapse”, by what mechanism and in what time interval? And who can collapse the wave function? Does it need to be human observers for instance, or can an ant or a computer do it? What can we in fact say about the consciousness of the entity that brings about its collapse?

The second problem is that contrary to popular belief, quantum theory is not just a theory of the microscopic world – it’s a theory of everything except gravity (for now). This led Erwin Schrödinger to postulate his famous cat paradox which demonstrated the problems inherent in the interpretation of the theory. Before measurement, Schrödinger said, a system is deemed to exist in a superposition of states while after measurement it exists only in one; does this mean that macroscopic objects like cats also exist in a superposition of entangled states, in case of his experiment in a mixture of half dead-half alive states? The possibility bothered Schrödinger and his friend Einstein to no end. Einstein in particular refused to believe that quantum theory was the final word, and there must be “hidden variables” that would allow us to get rid of the probabilities if only we knew what they were; he called the seemingly instantaneous entanglement of quantum states “spooky action at a distance”. Physicist John Bell put that particular objection to rest in the 1960s, proving that at least local quantum theories could not be based on hidden variables.

Niels Bohr and his group of followers from Copenhagen were more successful in their publicity campaign. They simply declared the question of what is “real” before measurement irrelevant and essentially pushed the details of the measurement problem under the rug by saying that the act of observation makes something real. The cracks were evident even then – the physicist Robert Serber once pointedly pointed out problems with putting the observer on a pedestal by asking if we might regard the Big Bang unreal because there were no observers back then. But Bohr and his colleagues were widespread and rather zealous, and most attempts by physicists like Einstein and David Bohm met with either derision or indifference.

Enter Hugh Everett who was a student of John Wheeler at Princeton. Everett essentially applied Occam’s Razor to the problem of collapse and asked a provocative question: What are the implications if we simply assume that the wave function does not collapse? While this avoids asking about the aforementioned complications with measurement, it creates problems of its own since we know for a fact that we can observe only one reality (dead vs alive cat, an electron track here rather than there) while the wave function previously described a mixture of realities. This is where Everett made a bold and revolutionary proposal, one that was as courageous as Einstein’s proposal of the constancy of the speed of light: he surmised that when there is a measurement, the other realities encoded in the wavefunction split off from our own. They simply don’t collapse and are every bit as real as our own. Just like Einstein showed in his theory of relativity that there are no privileged observers, Everett conjectured that there are no privileged observer-created realities. This is the so-called many-worlds interpretation of quantum mechanics.

Everett proposed this audacious claim in his PhD thesis in 1957 and showed it to Wheeler. Wheeler was an enormously influential physicist, and while he was famous for outlandish ideas that influenced generations of physicists like Richard Feynman and Kip Thorne, he was also a devotee of Bohr’s Copenhagen school – he and Bohr had published a seminal paper explaining nuclear fission way back in 1939, and Wheeler regarded Bohr’s Delphic pronouncements akin to those of Confucius – that posited observer-generated reality. He was sympathetic to Everett but could not support him in the face of Bohr’s objections. Everett soon left theoretical physics and spent the rest of his career doing nuclear weapons research, a chain-smoking, secretive, absentee father who dropped dead of an unhealthy lifestyle in 1982. After a brief resurrection by Everett himself at a conference organized by Wheeler, many-worlds didn’t see much popular dissemination until writers like Casti and the physicist David Deutsch wrote about it.

As Carroll indicates, the MWI has a lot of things going for it. It avoids the prickly, convoluted details of what exactly constitutes a measurement and the exact mechanism behind it; it does away with especially thorny details of what kind of consciousness can collapse a wavefunction. It’s elegant and satisfies Occam’s Razor because it simply postulates two entities – a wave function and a Schrödinger equation through which the wave function evolves through time, and nothing else. One can calculate the likelihood of each of the “many worlds” by postulating a simple rule proposed by Max Born that assigns a weight to every probability. And it also avoids an inconvenient split between the quantum and the classical world, treating both systems quantum mechanically. According to the MWI, when an observer interacts with an electron, for instance, the observer’s wave function becomes entangled with the electron’s and continues to evolve. The reason why we still see only one Schrödinger’s cat (dead or alive) is because each one is triggered by distinct random events like the passage of photons, leading to separate outcomes. Carroll thus sees many-worlds as basically a logical extension of the standard machinery of quantum theory. In fact he doesn’t even see the many worlds as “emerging” (although he does see them as

*emergent*); he sees them as always present and intrinsically encoded in the wave function’s evolution through the Schrödinger equation.
A scientific theory is of course only as good as its experimental predictions and verification – as a quote ascribed to Ludwig Boltzmann puts it, matters of elegance should be left to the tailor and the cobbler. Does MWI postulate elements of reality that are different from those postulated by other interpretations? The framework is on shakier ground here since there are no clear observable predictions except those predicted by standard quantum theory that would truly privilege it over others. Currently it seems that the best we can say is that many worlds is consistent with many standard features of quantum mechanics. But so are many other interpretations. To be accepted as a preferred interpretation, a theory should not just be consistent with experiment, but uniquely so. For instance, consider one of the very foundations of quantum theory – wave-particle duality. Wave-particle duality is as counterintuitive and otherworldly as any other concept, but it’s only by postulating this idea that we can ever make sense of disparate experiments verifying quantum mechanics, experiments like the double-slit experiment and the photoelectric effect. If we get rid of wave-particle duality from our lexicon of quantum concepts, there is no way we can ever interpret the results of thousands of experiments from the subatomic world such as particle collisions in accelerators. There is thus a necessary, one-to-one correspondence between wave-particle duality and reality. If we get rid of many-worlds, however, it does not make any difference to any of the results of quantum theory, only to what we believe about them. Thus, at least as of now, many-worlds remains a philosophically pleasing framework than a preferred scientific one.

Many-worlds also raises some thorny questions about the multiple worlds that it postulates. Is it really reasonable to believe that there are literally an infinite copies of everything – not just an electron but the measuring instrument that observes it and the human being who records the result – splitting off every moment? Are there copies of me both writing this post and not writing it splitting off as I type these words? Is the universe really full of these multiple worlds, or does it make more sense to think of infinite universes? One reasonable answer to this question is to say that quantum theory is a textbook example of how language clashes with mathematics. This was well-recognized by the early pioneers like Bohr: Bohr was fond of an example where a child goes into a store and asks for some mixed sweets. The shopkeeper gives him two sweets and asks him to mix them himself. We might say that an electron is in “two places at the same time”, but any attempt to actually visualize this dooms us, because the only notion of objects existing in two places is one that is familiar to us from the classical world, and the analogy breaks down when we try to replace chairs or people with electrons. Visualizing an electron spinning on its axis the way the earth spins on its is also flawed.

Similarly, visualizing multiple copies of yourself actually splitting off every nanosecond sounds outlandish, but it’s only because that’s the only way for us to make sense of wave functions entangling and then splitting. Ultimately there’s only the math, and any attempts to cast it in the form of everyday language is a fundamentally misguided venture. Perhaps when it comes to talking about these things, we will have to resort to Wittgenstein’s famous quote – whereof we cannot speak, thereof we must be silent (or thereof we must simply speak in the form of pictures, as Wittgenstein did in his famous ‘Tractatus’). The other thing one can say about many-worlds is that while it does apply Occam’s Razor to elegantly postulating only the wave function and the Schrödinger equation, it raises questions about the splitting off process and the details of the multiple worlds that are similar to those about the details of measurement raised by the measurement problem. In that sense it only kicks the can of complex worms down the road, and in that case believing what particular can to open is a matter of taste. As an old saying goes, nature does not always shave with Occam’s Razor.

In the last part of the book, Carroll talks about some fascinating developments in quantum gravity, mainly the notion that gravity can emerge through microscopic degrees of freedom that are locally entangled with each other. One reason why this discussion is fascinating is because it connects many disparate ideas from physics into a potentially unifying picture – quantum entanglement, gravity, black holes and their thermodynamics. These developments don’t have much to do with many-worlds per se, but Carroll thinks they may limit the number of “worlds” that many worlds can postulate. But it’s frankly difficult to see how one can find definitive experimental evidence for any interpretation of quantum theory anytime soon, and in that sense Richard Feynman’s famous words, “I think it is safe to say that nobody understands quantum mechanics” may perpetually ring true.

Very reasonably, many-worlds is Carroll’s preferred take on quantum theory, but he’s not a zealot about it. He fully recognizes its limitations and discuss competing interpretations. But while Carroll deftly dissects many-worlds, I think that the real value of this book is to exhort physicists to take what are called the foundations of quantum mechanics more seriously. It is an attempt to make peace between different quantum factions and bring philosophers into the fold. There’s a huge number of “interpretations” of quantum theory, some more valid than others, being separated by each other as much by philosophical differences as by physical ones. There was a time when the spectacular results of quantum theory combined with the thorny philosophical problems it raised led to a tendency among physicists to “shut up and calculate” and not worry about philosophical matters. But philosophy and physics have been entwined since the ancient Greeks, and in one sense, one ends where the other begins. Carroll’s book is a hearty reminder for physicists and philosophers to eat at the same table, otherwise they may well remain spooky factions at a distance when it comes to interpreting quantum theory.

"whereof we cannot speak of, therefore we must be silent" Good God, what a butchering.

ReplyDeleteHa, butchering indeed! Corrected.

DeleteGreat post!! However, I think the back half of paragraph 10 is incorrect. Wave-particle duality (i.e. deBroglie's pilot wave) is not an absolutely necessary part of the explanation in light of MWI. For example, Deutsch argues that MWI is the more parsimonious explanation of the double-slit experiment: particles in other universes collide with the observable particles in ours resulting in the interference pattern. Or, in other words, there is no duality: the particles in our universe and their counterparts causing the interference *constitute* a wave, but it is a wave made up of particles in the multiverse.

ReplyDelete