The Unsettling Physics of Causality
A general relativity theorist, Bert (GR) and a quantum mechanist, Bomm (QM), find themselves in a bar that’s about to close down.
Bartender: I will allow you to talk aloud about physics, but it’s late, I’m tired, and if I have to listen to you both ramble on at 12 midnight, you have to leave out all the math.
Bert (GR) : Blasphemous! Understanding general relativity without Einstein’s equations is like smelling fine wine without tasting it. The beauty, the simplicity…
Bomm (QM) : And quantum mechanics doesn’t make sense outside of Schrödinger’s equations. The wavefunction is all that is real.
Bartender: Ok, say the world is large video game working on a computer. How do I get from point A to B inside the game?
Bert (GR) : That would depend on how far point A and B are. And how fast you’re travelling.
Bartender : It’s a video game. I should be able to get from point A to B at infinite speeds.
Bert (GR) : That is impossible, of course. Everything in the universe video game must have a speed upper limit. Otherwise, if things happened at infinite speeds, all observable events would happen simultaneously. There would be nothing separating cause and effect. No concept of time. All causes and and all effects would happen at once. The video game would start, and end, at the same time.
Bartender: Makes sense. So what’s our universe’s speed upper limit?
Bert (GR) : The speed of light. 300,000 km/s. That’s around a million times the speed of an airplane, which is why it might seem infinitely fast, but isn’t. Physics is all about causal interactions. A bullet leaves a gun and hits a person, the person then dies. The person can’t die BEFORE the bullet hits him. Cause and effect. The speed of light, hence, is the speed of causality – i.e. the upper limit to the speed at which things happen.
Bartender : Ah. If I’m driving on the highway and there is car on the other road travelling towards me, I see it travelling at twice my speed. If my car could travel at the speed of light, I would see the opposite car travel at twice the speed of light. Doesn’t that violate your upper limit?
Bert (GM) : Ah but you see, that’s where the universe is clever in how it works. There is no absolute time, or length, or velocity. i.e. there is no absolute, fixed order of causes and effects distributed in time. It’s all relative to the speed at which you’re travelling i.e. your frame of reference.
Bartender: I’ve heard of this one. The theory of relativity.
Bert (GM) : So if two cars were travelling towards each other at the speed of light, time would slow down for the person sitting in both those cars, so that the order of observable events would always be restricted to the speed of light. Time would grow, and distance travelled would shrink, so the velocity (which is distance divided by time) of the two cars would appear to contract. So that if the two velocities were added, it would always be less than the speed of light. Since the ordering of cause and effect is relative to the speed at which you’re travelling, all participants – the two drivers, and also an observer standing on the side of the road – can agree on the order of observable events, even though their individual clocks don’t match. In no case, or, in no frame of reference, can a person die, before a bullet hits him.
Bartender: So it’s a hack to prevent causal conflicts in the world. I could live with that.
Bert (GM): Well, crudely put, yes. We physicists call this locality – local causal relativity. Local cause and effects mean cause and effect separated by the maximum speed of causality. All of Einstein’s laws of how planets move, how black holes work, how gravity works, arise from this fundamental sacred truth. General relativity, too, simply describes the geometry of causality.
Bartender: I notice Bomm here has been quiet all along. Looks like he isn’t too happy with this explanation. What’s wrong?
Bomm (QM) : Quantum mechanics is at odds with this idea. Not only is it NOT local, it is, quite unsettlingly so, explicitly non-local.
Bartender: You mean to say that causality works faster than light? At infinite speeds?
Bomm (QM): Yes. Macroscopic objects we see around us seem to have one fixed property at a time. This tissue is white, this whisky is black . Objects at microscopic level behave differently. When isolated and until observed, they exist as a superposition of two or more possibilities – say State Black and State White, at the same time. They collapse into one when you observe them. When you bring two of them together – they entangle in an inseparable way. So inseparable, that if you took these two to opposite ends of the universe, separated them by lightyears, and then measured one of them, it would collapse into one of the possibilities. Say you observed Black. You would then see that the other atom would be White. Or if one was White, other would be in Black. Everytime. The atoms would seem to have conspired from across the universe to be exactly correlated, or anti-correlated. Spooky action-at-a-distance. Cause and effect separated by seemingly infinite speeds. Laboratory experiments have pinned this to 50,000 times the speed of light, but it could be much much higher. Infinite.
Bartender: Perhaps the atoms could have conspired beforehand about which state they would collapse into, and we just can’t see how they did so?
Bomm (QM) : Ok let’s run an experiment. Say I put you and Bert in a room, and told you I would ask you both three Yes-No questions, A, B, & C separately when you came out. There are two ways you could conspire to correlate answers for all 3 without me finding out – First way, you could decide before hand to always answer Yes, or No, or some combination. For 3 questions, that is 2^3, or 8 combinations. Or the Second way – when I ask you the question, you could call each other and decide on the answers you could give. Is there any other way you can think of in which to get exactly correlated answers to all three questions?
Bartender : No, I don’t think so.
Bomm (QM) : So as you notice here, both the ways are strictly local – whether you conspire beforehand, or call each other at the time of asking, cause and effect are always separated by the speed of causality. No instantaneous communication happens at the moment I ask the questions. One could similarly think that the atoms too could have such local communication via methods hidden from us, and Yes/No answers to be Black/White. Still with me?
Bartender : I think so.
Bomm takes out a napkin and writes down all the possibilities for the answers to the questions.
Bomm (QM) : Our implicit assumption here, is locality. If we indeed do assume the first way, here are all the 8 possible combinations you could have conspired to beforehand. The fact is then, that in each pre-determined conspiracy, there are at least two questions with the same answer. If we repeated this experiment a million times, would you not say then that if we added up the frequencies of the answers being same to any two questions, the sum would be greater to or equal to one? That you would at least be assured that any two questions have the same answer?
Bartender : Half of the possible combinations has at least two answers same, so I’d say half for any two questions chosen. And since there are three ways to choose any two questions, the maximum would be three times half, or 3/2, and the minimum would 1.
Bomm (QM): Correct! But experimental evidence seems to contradict this obvious result. If we repeated this experiment a million times with a pair of entangled atoms, and added up the frequencies of the answers being same to any two questions, the sum comes to hover around 3/4. Which is less than 1. Not greater than or equal to one, as our mathematical description of pre-determined strategies necessitates. A contradiction!
Bartender : Which means there is no way that the answers could have been pre-determined, no hidden conspiracy could have made them correlate their states exact with respect to the other?
Bomm (QM) : Precisely! And here lies the problem. The hidden pre-determined conspiracy in physics is called a theory of local hidden variables. General relativity may wear out, so might quantum theory, but there is no way to escape this statistical contradiction, this..this inequality, as John Bell put it. As long as 3/4 is not greater than or equal 1, there can be nolocal hidden variable theories. Since locality was our only assumption, and it has been disproved, we must assume non-locality.
Bartender: So at the moment the question is asked, the atom instantaneously communicates with it’s entangled pair, faster than the speed of light? Does that mean we can use this to boost internet speeds? Download things faster than the speed of light?
Bomm (QM) : No, I’m afraid not. While the two entangled atoms are indeed correlated across huge distances, which state one of them would collapse into is completely random. You can’t control which state one of them collapses into, and so you can’t control the other’s state. Information is about controlling the flow of 0s and 1s. Here, there is no way you can control the transfer of information at speeds faster than that of light – it would be like sending garbled random noise from one place to another. Useless.
Bartender : Ah so from what I understand, we have one theory of physics where everything happens at the speed of light, and another where everything happens at once. My car’s gear train is a local mechanism. Motion passes from one gear wheel to another in an unbroken chain. Break the chain by taking out a single gear and the movement cannot continue. Without something there to mediate it, a local interaction cannot cross a gap. On the other hand, the essence of non locality is unmediated action-at-a-distance. A non-local interaction jumps from body A to body B without touching anything in between. Like a voodoo doll injury.
Bomm (QM) : You’re picking things up really fast!
Bartender: However, it seems like both of you deal with difficult scales – Bert deals with large objects, and Bomm with really small ones. There’s just different laws for each. What’s to be in conflict about?
Bert (GR) : Because none of these theories put a theoretical scale at which the respective theory stops working. There is no defined line between the microscopic and the macroscopic. Theoretically, quantum mechanics works at ALL scales. So does general relativity. Yet, the universe doesn’t work that way. Which means both are incomplete. They cannot be reconciled. Yet.
Bartender : How can two models of physics of the world be so diametrically opposite to each other? One of you swears by locality and the other can’t do without non-locality.
Bert: Pfft, very rich for bartenders to complain about it.
Bomm: What do you think brings us here everyday?