Maxwell’s Non-Local Hammer Came Down Upon Their Heads (Or Not)

The English have an inborn suspicion of theory, cialis and disparagingly characterize those who are prone to coming up with fancy, stuff impractical explanations for things as being “too clever by half.” This is a designation that could well have been applied to the ancient Greeks, ask who managed to convince themselves through deductive a priori reasoning of conclusions that are patently absurd. Apart from the clearly false idea that the divinity that created the world must be all-good, unchanging and immortal (an idea that was imported into Christianity by smart-ass Greek converts and caused no end of problems for the poor theologians), some argued that motion was impossible (this one goes to Zeno of Elea and his stupid story about how Achilles would supposedly never catch up with a tortoise with a head-start), while others held that stasis was impossible and everything was in motion. Now, part of this idea rested on the observation that the senses are fallible. Everyone’s seen the optical illusion whereby a solid ruler is half stuck into water, and it looks as if the edge of the bit under the water does not follow the line of the edge above the water. Well, voilà, your senses are obviously unreliable, so you brain can cook up whatever stupid arguments seems to follow logically, no matter how much they deviate from observable reality. After all, whatever Zeno might argue, who doesn’t know that a fast runner can always catch up with a tortoise?

Well, we’ve had occasion recently to take note of the dueling absurdities of the theory of relativity and quantum mechanics. Seems Wyatt ERP challenged Schrödinger and his cat to a shoot-out at the Academic Corral, but even though Sheriff ERP had the quantum-mechanical German in his sights, the bullet moved at the speed of light and so the cat was already dead by the time they opened the box. Or something like that. Anyway, turns out that the quantum krap is a whole lot more complicated and a whole lot more absurd than even Keyser had dared to imagine.

Our intuition, going back forever, is that to move, say, a rock, one has to touch that rock, or touch a stick that touches the rock, or give an order that travels via vibrations through the air to the ear of a man with a stick that can then push the rock—or some such sequence. This intuition, more generally, is that things can only directly affect other things that are right next to them. If A affects B without being right next to it, then the effect in question must be indirect—the effect in question must be something that gets transmitted by means of a chain of events in which each event brings about the next one directly, in a manner that smoothly spans the distance from A to B. Every time we think we can come up with an exception to this intuition—say, flipping a switch that turns on city street lights (but then we realize that this happens through wires) or listening to a BBC radio broadcast (but then we realize that radio waves propagate through the air)—it turns out that we have not, in fact, thought of an exception. Not, that is, in our everyday experience of the world.

We term this intuition “locality.”

Quantum mechanics has upended many an intuition, but none deeper than this one. And this particular upending carries with it a threat, as yet unresolved, to special relativity—a foundation stone of our 21st-century physics.

Horrors! Not only is your antiquated “intuition” that Human A has to apply force to Hammer B in order to brain Physicist C totally outdated, but “special relativity” is under threat too. (Parenthetically, Keyser is surprised that they’ve let the cat out of the box, as it were, by mentioning the unfortunate fact that poor little Jimmy Relativity had to take the “special ed” classes, but Keyser is impressed with their honesty. Keysers suspects that part of the problems in this story arise from Jimmy still harboring resentment at all those taunts of “retard!” that were hurled at him at a tender age, but we won’t talk further about this troubled period from his youth.)

Anyway, to get back to our story, seems that “locality” is the sort of thing that makes you think that Achilles could never catch up with a tortoise. So what is that Jimmy Relativity is so pissed off about?

Prior to the advent of quantum mechanics, and indeed back to the very beginnings of scientific investigations of nature, scholars believed that a complete description of the physical world could in principle be had by describing, one by one, each of the world’s smallest and most elementary physical constituents. The full story of the world could be expressed as the sum of the constituents’ stories.

Quantum mechanics violates this belief.

Real, measurable, physical features of collections of particles can, in a perfectly concrete way, exceed or elude or have nothing to do with the sum of the features of the individual particles. For example, according to quantum mechanics one can arrange a pair of particles so that they are precisely two feet apart and yet neither particle on its own has a definite position. Furthermore, the standard approach to understanding quantum physics, the so-called Copenhagen interpretation—proclaimed by the great Danish physicist Niels Bohr early last century and handed down from professor to student for generations—insists that it is not that we do not know the facts about the individual particles’ exact locations; it is that there simply aren’t any such facts. To ask after the position of a single particle would be as meaningless as, say, asking after the marital status of the number five. The problem is not epistemological (about what we know) but ontological (about what is).

Physicists say that particles related in this fashion are quantum mechanically entangled with one another. The entangled property need not be location: Two particles might spin in opposite ways, yet with neither one definitely spinning clockwise. Or exactly one of the particles might be excited, but neither is definitely the excited one. Entanglement may connect particles irrespective of where they are, what they are and what forces they may exert on one another—in principle, they could perfectly well be an electron and a neutron on opposite sides of the galaxy. Thus, entanglement makes for a kind of intimacy amid matter previously undreamt of.

But entanglement also appears to entail the deeply spooky and radically counterintuitive phenomenon called nonlocality—the possibility of physically affecting something without touching it or touching any series of entities reaching from here to there. Nonlocality implies that a fist in Des Moines can break a nose in Dallas without affecting any other physical thing (not a molecule of air, not an electron in a wire, not a twinkle of light) anywhere in the heartland.

Well, if Keyser understands this rightly, it turns out that he can in fact brain a physicist without having move the hammer himself, which opens up all sorts of interesting possibilities (from a legal standpoint at any rate). It would seem that the possibility of being brained at a distance by a disbeliever in his silly ideas was deeply disturbing to Albert Einstein (who was one of the three-headed Cerberus known as Wyatt ERP:

Albert Einstein had any number of worries about quantum mechanics. The overquoted concern about its chanciness (“God does not play dice”) was just one. But the only objection he formally articulated,
the only one he bothered to write a paper on, concerned the oddity of quantum-mechanical entanglement. This objection lies at the heart of what is now known as the EPR argument, named after its three authors, Einstein and his colleagues Boris Podolsky and Nathan Rosen. In their 1935 paper “Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?”, they answer their own question with a tightly reasoned “no.”

Their argument made pivotal use of one particular instruction in the quantum-mechanical recipe, or mathematical algorithm, for predicting the outcomes of experiments. Suppose that we measure the position of a particle that is quantum mechanically entangled with a second particle—so that neither individually has a precise position, as we mentioned above. Naturally, when we learn the outcome of the measurement, we change our description of the first particle because we now know where it was for a moment. But the algorithm also instructs us to alter our description of the second particle and to alter it instantaneously, no matter how far away it may be or what may lie between the two particles.

Entanglement was an uncontroversial fact of the picture of the world that quantum mechanics presented to physicists, but it was a fact whose implications no one prior to Einstein had thought much about. He saw in entanglement something not merely strange but dubious. It struck him as spooky. It seemed, in particular, nonlocal.

Nobody at that time was ready to entertain the possibility that there were genuine physical nonlocalities in the world—not Einstein, not Bohr, not anybody. Einstein, Podolsky and Rosen took it for granted in their paper that the apparent nonlocality of quantum mechanics must be apparent only, that it must be some kind of mathematical anomaly or notational infelicity or, at any rate, that it must be a disposable artifact of the algorithm—surely one could cook up quantum mechanics’s predictions for experiments without needing any nonlocal steps.

And in their paper they presented an argument to the effect that if (as everybody supposed) no genuine physical nonlocality exists in the world and if the experimental predictions of quantum mechanics are correct, then quantum mechanics must leave aspects of the world out of its account. There must be parts of the world’s story that it fails to mention.

Bohr responded to the EPR paper practically overnight. His feverishly composed letter of refutation engaged none of the paper’s concrete scientific arguments but instead took issue—in an opaque and sometimes downright oracular fashion—with its use of the word “reality” and its definition of “elements of physical reality.” He talked at length about the distinction between subject and object, about the conditions under which it makes sense to ask questions and about the nature of human language. What science needed, according to Bohr, was a “radical revision of our attitude as regards physical reality.”

Let’s begin by noting that this section appears to be using “uncontroversial” in a some sense previously unknown to Keyser. Must be the sort of thing on entangled particle says to another. Anyway, if Keyser understands this bit of sophistry rightly, Wyatt said that since the quantum types posited “nonlocal” places but there were no such things, then they must be retards. “Takes one to know one!” replied Niels Bore, but since that was a low blow against someone who had risen so far from his special ed classes, all the science books politely ignore that excited particle. Instead, they concentrate on his reply, “Yeah, and there are zillions of them out there but you’re too stupid to see them!”

Or to be more exactly, people ignored this cage fight of the retarded for thirty years, when somebody came up with some blather about it, and that was politely ignored for another thirty years, until someone else published a tiresome book on the subject in 1994. Which brings up to speed (as it were) with the latest excogitations on the topic (Keyser will spare you the details, but feel free to follow the link and find out the ensuing thrills, spills and chills, if you’re so inclined).

Apparently, once you wrap your head around the bent ruler in the bathtub, you can convince yourself of pretty much any shit you want. And this is what you get:

This work is still very much in its infancy. No one has yet been able to write down a satisfactory version of Tumulka’s theory that can be applied to particles that attract or repel one another. Moreover, his theory introduces a new variety of nonlocality into the laws of nature—a nonlocality not merely in space but in time! To use his theory to determine the probabilities of what happens next, one must plug in not only the world’s current complete physical state (as is customary in a physical theory) but also certain facts about the past. That feature and some others are worrying, but Tumulka has certainly taken away some of the grounds for Maudlin’s fear that quantum-mechanical nonlocality cannot be made to peacefully coexist with special relativity.

The other recent result, discovered by one of us (Albert), showed that combining quantum mechanics and special relativity requires that we give up another of our primordial convictions. We believe that everything there is to say about the world can in principle be put into the form of a narrative, or story. Or, in more precise and technical terms: everything there is to say can be packed into an infinite set of propositions of the form “at t1 this is the exact physical condition of the world” and “at t2 that is the exact physical condition of the world,” and so on. But the phenomenon of quantum-mechanical entanglement and the spacetime geometry of special relativity—taken together—imply that the physical history of the world is infinitely too rich for that.

The trouble is that special relativity tends to mix up space and time in a way that transforms quantum-mechanical entanglement among distinct physical systems into something along the lines of an entanglement among physical situations at different times—something that in a perfectly concrete way exceeds or eludes or has nothing to do with any sum of situations at distinct temporal instants.

That result, like most theoretical results in quantum mechanics, involves manipulating and analyzing a mathematical entity called a wave function, a concept Erwin Schrödinger introduced eight decades ago to define quantum states. It is from wave functions that physicists infer the possibility (indeed, the necessity) of entanglement, of particles having indefinite positions, and so forth. And it is the wave function that lies at the heart of puzzles about the nonlocal effects of quantum mechanics.

But what is it, exactly? Investigators of the foundations of physics are now vigorously debating that question. Is the wave function a concrete physical object, or is it something like a law of motion or an internal property of particles or a relation among spatial points? Or is it merely our current information about the particles? Or what?

Quantum-mechanical wave functions cannot be represented mathematically in anything smaller than a mind-bogglingly high-dimensional space called a configuration space. If, as some argue, wave functions need to be thought of as concrete physical objects, then we need to take seriously the idea that the world’s history plays itself out not in the three-dimensional space of our everyday experience or the four-dimensional spacetime of special relativity but rather this gigantic and unfamiliar configuration space, out of which the illusion of three-dimensionality somehow emerges. Our three-dimensional idea of locality would need to be understood as emergent as well. The nonlocality of quantum physics might be our window into this deeper level of reality.

“Or what?” indeed. Regular folk (deluded you and Keyser) believe that it’s possible to sa
y “the world was like this” at time X, and “the world was like this” at time Z, whereas in fact “the phenomenon of quantum-mechanical entanglement and the spacetime geometry of special relativity—taken together—imply that the physical history of the world is infinitely too rich for that.” What this means is that there’s not just a “fourth dimension” floating around out there but a “gigantic and unfamiliar configuration space.” Again, this must be a usage that Keyser is “unfamiliar” with. Keyser was of the view that “unfamiliar” referred to something that could be known and simply wasn’t rather than a crock of shit that makes no sense at all and is contrary to all observable reality.

We’re supposed to imagine that world of straight rulers and the use of hammers to kill hare-brained physicists is a snare and a delusion, and that we need to go beyond the “falsity” of the perceptible world around us and peer through some non-existent window into “this deeper level of reality.” Whether it’s God or quantum physics, Keyser is always deeply suspicious of schools of belief that demand faith in things that not only have no inherent plausibility but actually contradict what we see to be true.

Then again, maybe in this deeper reality, Achilles really can’t catch up with that tortoise. And maybe we can “non-locally” brain these physicists and get away with it (“Wasn’t me, your honor! Must have been some entangled particle or other.”). On second thought, this “deeper reality” could be pretty sweet after all.