A Nice Explanation of Quantum Mechanics, with Thoughts on What Makes Science Special

Michael Strevens teaches philosophy at New York University. In his book, The Knowledge Machine: How Irrationality Created Modern Science, he argues that what makes modern science so productive is the peculiar behavior of scientists. From the publisher’s site:

Like such classic works as Karl Popper’s The Logic of Scientific Discovery and Thomas Kuhn’s The Structure of Scientific Revolutions, The Knowledge Machine grapples with the meaning and origins of science, using a plethora of . . .  examples to demonstrate that scientists willfully ignore religion, theoretical beauty, and . . . philosophy to embrace a constricted code of argument whose very narrowness channels unprecedented energy into empirical observation and experimentation. Strevens calls this scientific code the iron rule of explanation, and reveals the way in which the rule, precisely because it is unreasonably close-minded, overcomes individual prejudices to lead humanity inexorably toward the secrets of nature.

Here Strevens presents a very helpful explanation of quantum mechanics, while explaining that physicists (most of them anyway) are following Newton’s example when they use the theory to make exceptionally accurate predictions, even though the theory’s fundamental meaning is mysterious (in the well-known phrase, they “shut up and calculate”):

To be scientific simply was to be Newtonian. The investigation of nature [had] changed forever. No longer were deep philosophical insights of the sort that founded Descartes’s system considered to be the keys to the kingdom of knowledge. Put foundational matters aside, Newton’s example seemed to urge, and devote your days instead to the construction of causal principles that, in their forecasts, follow precisely the contours of the observable world. . . .

[This is] Newton’s own interpretation of his method, laid out in a postscript to the Principia’s second edition of 1713. There Newton summarizes the fundamental properties of gravitational attraction—that it increases “in proportion to the quantity of solid matter” and decreases in proportion to distance squared—and then continues:

I have not as yet been able to deduce from phenomena the reason for these properties of gravity, and I do not feign hypotheses. For whatever is not deduced from the phenomena must be called a hypothesis; and hypotheses, whether metaphysical or physical, or based on occult qualities, or mechanical, have no place in experimental philosophy. . . . It is enough that gravity really exists and acts according to the laws that we have set forth and is sufficient to explain all the motions of the heavenly bodies and of our sea.

The thinkers around and after Newton got the message, one by one.

[Jumping ahead three centuries:]

According to Roger Penrose, one of the late twentieth century’s foremost mathematical physicists, quantum mechanics “makes absolutely no sense.” “I think I can safely say that nobody understands quantum mechanics,” remarked Richard Feynman. How can a theory be widely regarded both as incomprehensible and also as the best explanation we have of the physical world we live in?

. . . Quantum theory derives accurate predictions from a notion, superposition, that is quite beyond our human understanding. Matter, says quantum mechanics, occupies the state called superposition when it is not being observed [or measured]. An electron in superposition occupies no particular point in space. It is typically, rather, in a kind of “mix” of being in many places at once. The mix is not perfectly balanced: some places are far more heavily represented than others. So a particular electron’s superposition might be almost all made up from positions near a certain atomic nucleus and just a little bit from positions elsewhere. That is the closest that quantum mechanics comes to saying that the electron is orbiting the nucleus.

As to the nature of this “mix”—it is a mystery. We give it a name: superposition. But we can’t give it a philosophical explanation. What we can do is to represent any superposition with a mathematical formula, called a “wave function.” An electron’s wave function represents its physical state with the same exactitude that, in Newton’s physics, its state would be represented by numbers specifying its precise position and velocity. You may have heard of quantum mechanics’ “uncertainty principle,” but forget about uncertainty here: the wave function is a complete description that captures every matter of fact about an electron’s physical state without remainder.

So far, we have a mathematical representation of the state of any particular piece of matter, but we haven’t said how that state changes in time. This is the job of Schrödinger’s equation, which is the quantum equivalent of Newton’s famous second law of motion F = ma, in that it spells out how forces of any sort—gravitational, electrical, and so on—will affect a quantum particle. According to Schrödinger’s equation, the wave function will behave in what physicists immediately recognize as a “wavelike” way. That is why, according to quantum mechanics, even particles such as electrons conduct themselves as though they are waves.

In the early days of quantum mechanics, Erwin Schrödinger, the Austrian physicist who formulated the equation in 1926, and Louis de Broglie, a French physicist—both eventual Nobel Prize winners—wondered whether the waves described by quantum mechanics might be literal waves traveling through a sea of “quantum ether” that pervades our universe. They attempted to understand quantum mechanics, then, using the old model of the fluid.

This turned out to be impossible for a startling reason: it is often necessary to assign a wave function not to a single particle, like an electron, but to a whole system of particles. Such a wave function is defined in a space that has three dimensions for every particle in the system: for a 2-particle system, then, it has 6 dimensions; for a 10-particle system, 30 dimensions. Were the wave to be a real entity made of vibrations in the ether, it would therefore have to be flowing around a space of 6, or 30, or even more dimensions. But our universe rather stingily supplies only three dimensions for things to happen in. In quantum mechanics, as Schrödinger and de Broglie soon realized, the notion of substance as fluid fails completely.

There is a further component to quantum mechanics. It is called Born’s rule, and it says what happens when a particle’s position or other state is measured. Suppose that an electron is in a superposition, a mix of being “everywhere and nowhere.” You use the appropriate instruments to take a look at it; what do you see? Eerily, you see it occupying a definite position. Born’s rule says that the position is a matter of chance: the probability that a particle appears in a certain place is proportional to the degree to which that place is represented in the mix.

It is as though the superposition is an extremely complex cocktail, a combination of various amounts of infinitely many ingredients, each representing the electron’s being in a particular place. Taste the cocktail, and instead of an infinitely complex flavor you will—according to Born’s rule—taste only a single ingredient. The chance of tasting that ingredient is proportional to the amount of the ingredient contained in the mixture that makes up the superposition. If an electron’s state is mostly a blend of positions near a certain atomic nucleus, for example, then when you observe it, it will most likely pop up near the nucleus.

One more thing: an observed particle’s apparently definite position is not merely a fleeting glimpse of something more complex. Once you see the particle in a certain position, it goes on to act as though it really is in that position (until something happens to change its state). In mixological terms, once you have sampled your cocktail, every subsequent sip will taste the same, as though the entire cocktail has transformed into a simple simple solution of this single ingredient. It is this strange disposition for matter, when observed, to snap into a determinate place that accounts for its “particle-like” behavior.

To sum up, quantum mechanical matter—the matter from which we’re all made—spends almost all its time in a superposition. As long as it’s not observed, the superposition, and so the matter, behaves like an old-fashioned wave, an exemplar of liquidity (albeit in indefinitely many dimensions). If it is observed, the matter jumps randomly out of its superposition and into a definite position like an old-fashioned particle, the epitome of solidity.

Nobody can explain what kind of substance this quantum mechanical matter is, such that it behaves in so uncanny a way. It seems that it can be neither solid nor fluid—yet these exhaust the possibilities that our human minds can grasp. Quantum mechanics does not, then, provide the kind of deep understanding of the way the world works that was sought by philosophers from Aristotle to Descartes. What it does supply is a precise mathematical apparatus for deriving effects from their causes. Take the initial state of a physical system, represented by a wave function; apply Schrödinger’s equation and if appropriate Born’s rule, and the theory tells you how the system will behave (with, if Born’s rule is invoked, a probabilistic twist). In this way, quantum theory explains why electrons sometimes behave as waves, why photons (the stuff of light) sometimes behave as particles, and why atoms have the structure that they do and interact in the way they do.

Thus, quantum mechanics may not offer deep understanding, but it can still account for observable phenomena by way of . . . the kind of explanation favored by Newton . . . Had Newton [engaged with scientists like Bohr and Einstein at conferences on quantum mechanics] he would perhaps have proclaimed:

I have not as yet been able to deduce from phenomena the nature of quantum superposition, and I do not feign hypotheses. It is enough that superposition really exists and acts according to the laws that we have set forth and is sufficient to explain all the motions of the microscopic bodies of which matter is made.

Newton . . .  was the chief architect of modern science’s first great innovation. Rather than deep philosophical understanding, Newton pursued shallow explanatory power, that is, the ability to derive correct descriptions of phenomena from a theory’s causal principles, regardless of their ultimate nature and indeed regardless of their very intelligibility. In so doing, he was able to build a gravitational theory of immense capability, setting an example that his successors were eager to follow.

Predictive power thereby came to override metaphysical insight. Or as the historian of science John Heilbron, writing of the study of electricity after Newton, put it:

When confronted with a choice between a qualitative model deemed intelligible and an exact description lacking clear physical foundations, the leading physicists of the Enlightenment preferred exactness.

So it continued to be, as the development and acceptance of quantum mechanics, as unerring as it is incomprehensible, goes to show. The criterion for explanatory success inherent in Newton’s practice became fixed for all time, founding the procedural consensus that lies at the heart of modern science.

Could This Be a More Sensible Timeline? (Quantum Mechanics Edition)

This post has nothing to do with politics.

One of the big mysteries or surprises in quantum physics is “non-locality”. This is the apparent fact that two particles can be “entangled”, such that even though they’re a billion miles apart, when something happens to one, something automatically happens to the other. The particles are far away in spacetime, but it’s as if they’re somehow right next to each other, possibly in some “deeper” reality. If that’s true, it’s pretty damn cool. 

From Quanta Magazine:

In a series of breakthrough papers, theoretical physicists have come tantalizingly close to resolving the black hole information paradox that has entranced and bedeviled them for nearly 50 years. Information, they now say with confidence, does escape a black hole. If you jump into one, you will not be gone for good. Particle by particle, the information needed to reconstitute your body will reemerge. Most physicists have long assumed it would; that was the upshot of string theory, their leading candidate for a unified theory of nature. But the new calculations, though inspired by string theory, stand on their own, with nary a string in sight. Information gets out through the workings of gravity itself — just ordinary gravity with a single layer of quantum effects. . . .

What it all means is being intensely debated in Zoom calls and webinars. The work is highly mathematical and has a Rube Goldberg quality to it, stringing together one calculational trick after another in a way that is hard to interpret. Wormholes, the holographic principle, emergent space-time, quantum entanglement, quantum computers: Nearly every concept in fundamental physics these days makes an appearance, making the subject both captivating and confounding.

And not everyone is convinced. . . .

But almost everyone appears to agree on one thing. In some way or other, space-time itself seems to fall apart at a black hole, implying that space-time is not the root level of reality, but an emergent structure from something deeper. Although Einstein conceived of gravity as the geometry of space-time, his theory also entails the dissolution of space-time, which is ultimately why information can escape its gravitational prison. . . .

The researchers drew on a concept that Richard Feynman had developed in the 1940s. Known as the path integral, it is the mathematical expression of a core quantum mechanical principle: Anything that can happen does happen. In quantum physics, a particle going from point A to point B takes all possible paths, which are combined in a weighted sum. The highest-weighted path is generally the one you’d expect from ordinary classical physics, but not always. If the weights change, the particle can abruptly lurch from one path to another, undergoing a transition that would be impossible in old-fashioned physics.

The path integral works so well for particle motion that theorists in the ’50s proposed it as a quantum theory of gravity. That meant replacing a single space-time geometry with a mélange of possible shapes. To us, space-time appears to have a single well-defined shape — near Earth, it is curved just enough that objects tend to orbit the center of our planet, for example. But in quantum gravity, other shapes, including much curvier ones, are latent, and they can make an appearance under the right circumstances. . . .

For [Stephen Hawking], space-time might knot itself into doughnut- or pretzel-like shapes. The extra connectivity creates tunnels, or “wormholes,” between otherwise far-flung places and moments. These come in different types.

Spatial wormholes are like the portals beloved of science-fiction writers, linking one star system to another. So-called space-time wormholes are little universes that bud off our own and reunite with it sometime later. Astronomers have never seen either type, but general relativity permits these structures, and the theory has a good track record of making seemingly bizarre predictions, such as black holes and gravitational waves, that are later vindicated. Not everyone agreed with Hawking that these exotic shapes belong in the mix, but the researchers doing the new analyses of black holes adopted the idea provisionally. . . .

Theorists in the West Coast group imagined sending [radiation escaping from a black hole] into a quantum computer. After all, a computer simulation is itself a physical system; a quantum simulation, in particular, is not altogether different from what it is simulating. So the physicists imagined collecting all the radiation, feeding it into a massive quantum computer, and running a full simulation of the black hole.

And that led to a remarkable twist in the story. Because the radiation is highly entangled with the black hole it came from, the quantum computer, too, becomes highly entangled with the hole. Within the simulation, the entanglement translates into a geometric link between the simulated black hole and the original. Put simply, the two are connected by a wormhole. “There’s the physical black hole and then there’s the simulated one in the quantum computer, and there can be a replica wormhole connecting those,” said Douglas Stanford, . . . a member of the West Coast team. This idea is an example of a proposal by [Juan Martin] Maldacena and Leonard Susskind  . . . in 2013 that quantum entanglement can be thought of as a wormhole. The wormhole, in turn, provides a secret tunnel through which information can escape the interior [of the black hole] . . .

Theorists have been intensely debating how literally to take all these wormholes. The wormholes are so deeply buried in the equations that their connection to reality seems tenuous, yet they do have tangible consequences. . . .

But rather than think of the wormholes as actual portals sitting out there in the universe, [some physicists] speculate that they are a sign of new, nonlocal physics. By connecting two distant locations, wormholes allow occurrences at one place to affect a distant place directly, without a particle, force or other influence having to cross the intervening distance — making this an instance of what physicists call nonlocality. “They seem to suggest that you have nonlocal effects that come in” [one physicist] said. In the black hole calculations, the island and radiation are one system seen in two places, which amounts to a failure of the concept of “place.” “We’ve always known that some kind of nonlocal effects have to be involved in gravity, and this is one of them . . . Things you thought were independent are not really independent.”

At first glance, this is very surprising. Einstein constructed general relativity with the express purpose of eliminating nonlocality from physics. Gravity does not reach out across space instantly. It has to propagate from one place to another at finite speed, like any other interaction in nature. But over the decades it has dawned on physicists that the symmetries on which relativity is based create a new breed of nonlocal effects. . . 

All this reinforces many physicists’ hunch that space-time is not the root level of nature, but instead emerges from some underlying mechanism that is not spatial or temporal. . . 

Skepticism is warranted if for no other reason than because the recent work is complicated and raw. It will take time for physicists to digest it and either find a fatal flaw in the arguments or become convinced that they work. . . .

Unquote.

So it looks like the universe is making more sense. Maybe we’ve entered a more sensible timeline, in which physics is less paradoxical and the president behaves like an adult politician/human being!

Quantum Reality by Jim Baggott

The author is a former academic physicist with a leaning toward the experimental side of physics, as opposed to the theoretical side. From the preamble:

I know why you’re here.

You know that quantum mechanics is an extraordinarily successful scientific theory, on which much of out modern, tech-obsessed lifestyles depend. . . .You also know that it is completely mad. Its discovery forced open the window on all those comfortable notions we had gathered about physical reality . . . and shoved them out. Although quantum mechanics quite obviously works, it appears to leave us chasing ghosts and phantoms, particles that are waves and waves that are particles, cats that are at once both alive and dead, lots of seemingly spooky goings-on, and a desperate desire to lie down quietly in a darkened room.

But, hold on, if we’re prepared to be a little more specific about what we mean when we talk about “reality” and a little more circumspect about how we think a scientific theory might represent such a reality, then all the mystery goes away [Note: not really] . . . 

But . . . a book that says, “Honestly, there is no mystery” would . . . be completely untrue. For sure we can rid ourselves of all the mystery in quantum mechanics, but only by abandoning any hope of deepening our understanding of nature. We must become content to use the quantum representation simply as a way to perform calculations and make predictions, and we must resist the temptation to ask: But how does nature actually do that? And there lies the rub: for what is the purpose of a scientific theory if not to aid our understanding of the physical world.

. . . The choice we face is a philosophical one. There is absolutely nothing scientifically wrong with a depressingly sane interpretation of quantum mechanics in which there is no mystery. If we choose instead to pull on the loose thread, we are inevitably obliged to take the quantum representation at face value, and interpret its concepts rather more literally. Surprise, surprise, The fabric unravels to give us all those things about the quantum world that we find utterly baffling, and we’re right back where we started.

My purpose in this book is (hopefully) . . . to try to explain what it is about quantum mechanics that forces us to confront this kind of choice, and why this is entirely philosophical in nature. Making different choices leads to different interpretations or even modifications of the quantum representation and its concepts, in what I call . . . the game of theories.

Mr. Baggott follows the usual path that includes the work of Einstein and Niels Bohr and Erwin Schrödinger and ends with various theories of the multiverse. He lost me around page 160 in chapter 7. Up until then, I felt like I was understanding almost everything. Given the nature of quantum mechanics, that probably meant I was deeply confused. After that, my confusion was obvious.

He does make clear how anyone trying to understand the reality behind quantum mechanics, or to “interpret” it, ends up veering into philosophical speculation. His strong preference is for interpretations that can be tested empirically. That’s one reason he’s skeptical about multiverse theories, which don’t seem to be testable at all.

I’m glad I read the book, but I could have jumped from chapter 7 to the Epilogue, which is entitled “I’ve Got a Very Bad Feeling About This”:

I hope I’ve done enough in this book to explain the nature of our dilemma. We can adopt an anti-realist interpretation in which all our conceptual problems vanish, but which obliges us to accept that we’ve reached the limit or our ability to access deeper truths about a reality of things-in-themselves. The anti-realist interpretations tell us that there’s nothing to see here. Of necessity, they offer no hints as to where we might look to gain some new insights of understanding. They are passive; mute witnesses to the inscrutability of nature.

In contrast, the simpler and more palatable realist interpretations based on local or crypto-local hidden variables offered plenty of hints and continue to motivate ever more exquisitely subtle experiments. Alas, the evidence is now quite overwhelming and all but the most stubborn of physicists accept that nature denies us this easy way our. If we prefer a realist interpretation, taking the wavefunction and the conceptual problems this implies at face value, then we’re left with what I can only call a choice between unpalatable evils. We can choose de Broglie-Bohm theory and accept non-local spooky action at a distance. We can choose to add a rather ad hoc spontaneous collapse mechanism and hope for the best. We can choose to involve consciousness in the mix, conflating one seemingly intractable problem with another. Or we can choose Everett, many worlds and the multiverse. . . . 

There may be another way out. I’m pretty confident that quantum mechanics is not the end. Despite its unparalleled success, we know it doesn’t incorporate space and time in the right way [it seems to presume absolute space and absolute simultaneity, not Einstein’s relative spacetime]. . . . It may well be that any theory that transcends quantum mechanics will still be rife with conceptual problems and philosophical conundrums. But it would be nice to discover that, despite appearances to the contrary, there was indeed something more to see here.

That’s the end of the book. 

I got a copy of Quantum Reality after reading a very positive review by another physicist, Sabine Hossenfelder. She said it’s “engagingly written” and requires “no background knowledge in physics”. Maybe not, but a background would help, especially when you get to chapter 7.

I did acquire one idea, which fits with an idea I already had. It seems that the famous two-slit experiment, in which a single photon appears to take multiple paths, has a simple solution. When the photon is sent on its way, it’s a wave. It passes through both slits at the same time. Then, when it hits the screen on the other side of the two slits, it becomes a particle. Maybe this is the de Broglie-Bohm theory referred to above, which implies “spooky action at a distance”. But it sounds plausible to me.

The wave instantaneously becoming a particle seems (to me) to fit with the way entangled particles simultaneously adopt opposing characteristics. One is measured and found to be “up”, which means the other instantly becomes “down”, no matter how far away the two particles are. This suggests that spacetime isn’t fundamental. The distance we perceive as being far too great for two particles to immediately affect each other isn’t the fundamental reality. There’s something going on that’s deeper than spacetime. So the way in which a wave that’s spread out simultaneously disappears, resulting in a single particle hitting a screen, reveals the same thing.

So I feel like I’m making a bit of progress in understanding physics. This is most likely incorrect, but it makes me feel better. Now all I have to do is figure out why physicists claim we couldn’t find the location of the Big Bang. Sure, space is expanding in all directions from the Big Bang, they say, but they deny the universe has a center, where the Big Bang occurred (it would make a great location for a museum and a gift shop). I don’t understand their reasons for saying there is no center.

But one small, confused step at a time.

Maybe It’s All Jelly

From The New York Times:

It would be one thing to concede that science may never be able to explain, say, the subjective experiences of the human mind. But the standard take on quantum mechanics suggests something far more surprising: that a complete understanding of even the objective, physical world is beyond science’s reach, since it’s impossible to translate into words how the theory’s math relates to the world we live in.

[Angelo] Bassi, a 47-year-old theoretical physicist at the University of Trieste, in northeastern Italy, is prominent among a tiny minority of rebels in the discipline who reject this conclusion. “I strongly believe that physics is words, in a sense,” he said across the picnic table. [He makes] a case for what a vast majority of his colleagues consider a highly implausible idea: that the theory upon which nearly all of modern physics rests must have something wrong with it — precisely because it can’t be put into words.

Of course, much about quantum mechanics can be said with words. Like the fact that a particle’s future whereabouts can’t be specified by the theory, only predicted with probabilities. And that those probabilities derive from each particle’s “wave function,” a set of numbers that varies over time, as per an equation devised by Erwin Schrödinger in 1925. But because the wave function’s numbers have no obvious meaning, the theory only predicts what scientists may see at the instant of observation — when all the wave function’s latent possibilities appear to collapse to one definitive outcome — and provides no narrative at all for what particles actually do before or after that, or even how much the word “particle” is apropos to the unobserved world. The theory, in fact, suggests that particles, while they’re not being observed, behave more like waves — a fact called “wave-particle duality” that’s related to how all those latent possibilities seem to indicate that an unobserved particle can exist in several places at once….

Bassi’s research is focused on a possible alternative to quantum mechanics, a class of theories called “objective collapse models”…. And [he is] now leading the most ambitious experiment to date that could show that objective collapse actually happens….

The hard part [was making sure the new theory didn’t] contradict any of quantum mechanics’ many unerring predictions. The trick, it turned out, was to endow fundamental particles with some funky new properties.

“You should remove the word ‘particle’ from your vocabulary,” Bassi explains. “It’s all about gelatin. An electron can be here and there and that’s it.”

In this theory, particles are replaced by a sort of hybrid between particles and waves: gelatinous blobs that can spread out in space, split and recombine. And, crucially, the blobs have a kind of built-in bashfulness that explains wave-particle duality in a way that is independent of human observation: When one blob encounters a crowd of others, it reacts by quickly shrinking to a point.

“It’s like an octopus that when you touch them: Whoop!” Bassi says, collapsing his fingertips to a tight bunch to evoke tentacles doing the same.

If objective collapse were to be confirmed, … the way the world works will once again be expressible in words. “Jelly that reacts like an octopus” will be the new “particles subject to forces.” New, exotic phenomena will be identified that could spawn currently inconceivable technologies. Schrödinger’s cat will live or die regardless of who looks or who doesn’t. Even the unpredictability of the subatomic world could turn out to be illusory, a false impression given by our ignorance of octopoid innards.

Einstein’s Unfinished Revolution: The Search for What Lies Beyond the Quantum by Lee Smolin

Lee Smolin is a theoretical physicist who is dissatisfied with the state of theoretical physics. He is not alone in being dissatisfied. Physicists have two wonderful theories —  quantum mechanics (which deals with the very small) and general relativity (which deals with the very large) — that don’t fit together. Some of them have been trying for decades to reconcile the two theories. In addition, there is a lot about quantum mechanics that seems crazy or at least paradoxical. It’s been argued, therefore, that the theory is incomplete.

Smolin believes that there is a fundamental reality separate from our perceptions that underlies both quantum mechanics and general relativity. He would like to figure out what that reality is. He says this makes him a “realist”.

The first part of the book discusses what Smolin calls “anti-realist” views, primarily the so-called Copenhagen interpretation of quantum mechanics (sometimes referred to as the “shut up and calculate” view). He then outlines some competing views, such as Einstein’s, according to which quantum mechanics is incomplete.

In the final chapters, he offers the beginnings of his own theory. I won’t try to explain it, but he begins with an idea proposed by the brilliant German philosopher Gottfried Willhelm Leibniz (who died 300 years ago). Leibniz suggested that the universe is composed of an infinite number of simple substances called”monads”. The Wikipedia article on Leibniz says “each monad is like a little mirror of the universe”, i.e. a mirror reflecting all the other monads.

Near the end of the book, Smolin offers a one-sentence summary of his theory:

The universe consists of nothing but views of itself, each [view being from the perspective of] an event in [the universe’s] history, and the [universe’s] laws act to make these views as diverse as possible [271].

For Smolin, time is a fundamental feature of the universe. Space isn’t. Space emerges from events. Furthermore, the fact that space isn’t fundamental helps explain how two particles that are millions of miles away from each other can be “entangled”, so that an effect on one can immediately affect the other. That’s the idea of “non-locality” that Einstein called “spooky action at a distance”.

Smolin is sure that he doesn’t have all the answers, but he believes it’s worth trying to find them. If you’d like to know more, you’ll have to read the book or find someone else to explain it. There are diagrams and no math!