“We are all agreed that your theory is crazy. The question which divides us is whether it is crazy enough to have a chance of being correct. My own feeling is that it is not crazy enough.” -

Niels Bohr

You know who Einstein is, I’m sure. The E=mc^{2} guy, the speed of light guy, and — perhaps most prestigiously — as the inventor of the best theory of gravity that we have: general relativity.

One of the notable things about gravity — which is also true of *all* of Einstein’s theories — is that it’s completely **deterministic**.

What does that word mean, **deterministic**, to a physicist?

It means that, if I tell you all the initial information about a system — like the positions, momenta, etc., of all its particles — you can tell me, *without any doubt or uncertainty*, everything I could possibly want to know about its final state at some later time.

And when quantum mechanics was first discovered, there were a series of hotly contested public debates on the topic. Between two titans of physics: Albert Einstein and Neils Bohr.

It was in these debates that Einstein declared his *real* greatest blunder:

“God does not play dice with the Universe.”

This was, of course, in reference to the fact that quantum mechanics is *not* a deterministic theory. Rather, if I give you all of that initial information — positions, momenta, quantum states, etc. — all you can give me, by the laws of quantum mechanics, are **probabilities** of what the final state will be. One of the greatest demonstrations of this is the double slit experiment.

If you take a **single particle**, like an electron, and shoot it at a double slit (two parallel slits spaced slightly apart from one another), a *deterministic picture* tells you that the electron will go through either the slit on the left or the slit on the right. But if you allow the electron to be an *indeterminate* object, it can, perhaps, pass partially through **both** slits, and interfere with itself!

Sounds like something out of science fiction, doesn’t it? Well, that’s why we do the experiments, isn’t it? And what happens if you actually send electrons through a double slit, one-at-a-time?

**You have no idea where any one particular electron is going to end up!** You can compute the probabilities that it will wind up at any location, but that’s hardly the *deterministic* result you were after. So you do what any self-respecting experimentalist would do. You say to yourself, “Alright, I’m *going to look*.”

And you design an experiment the same exact way, except this time you *measure* which of the two slits the electron goes through. Perhaps you shine a photon across both slits, and when one gets absorbed, that tells you which slit the electron goes through. And when you do that, what do you get?

You get **no interference pattern**. By measuring which slit the particle goes through, you *change the outcome*!

As bizarre as it seems, this is something that is predicted and well-understood about quantum mechanics. In principle, there are three possible explanations for why this happens:

- Properties of these quantum particles are
*not real*, as we understand “real” numbers. (See, for example, the “i” in the Schrodinger equation.) - All properties of quantum particles
*are*real, but there is**non-local**phenomena, sometimes colloquially called faster-than-light transmission of information. - Or, perhaps everything is real
*and*nothing gets transmitted faster than light. Called local realism, there must be some sort of “hidden variable” that — although we do not observe it — determines what the final states are.

Perhaps maddeningly, all of these are *possible* in principle. They are just different *interpretations* of quantum mechanics. (For example, my favorite is the Copenhagen Interpretation, which falls in the first category, although one can argue about its locality.) Others favor the second type, like the de Broglie-Bohm Interpretation, which is just as valid, but *no different* in its predictions from the Copenhagen Interpretation for any experiment we’ve devised. Currently, there are no ways to distinguish between most of the interpretations of types one and two.

But what about the *third* type, the types where everything is predetermined from the outset?, as was favored by Einstein, determined by some unobservable but *local* (with nothing being transmitted faster than light) and *real* variables?

Amazingly, there are some *very* clever tests of this that have been devised, and the experiments performed. The resultant theorem, known as Bell’s Theorem, demonstrates very definitively that the “Hidden Variables” approach fails when confronted with experiment.

So what do we learn from all this?

Sorry, Einstein, your steadfast belief that “God does not play dice” has been demonstrated to be wrong, no matter how much people try to resurrect it. Not only that, but you have to accept that these “dice” obey rules that may make you *very* uncomfortable, and there’s no way around it. Whether you give up realism or give up locality (or both), you simply can’t have it all in this Universe.

I first addressed this topic years ago on the old blog, and was pointed to this paper in the comments. I sort of flippantly replied something to the effect of, “Well, you can devise math to do whatever you want, but the math needs to make physical predictions. And in this case, the predictions do not agree with the experiments, and therefore this math doesn’t describe our reality.” I was so sure of myself because, well, I had read this excellent book on Quantum Mechanics, which I now believe is **the most underrated and underused graduate text** on the subject. If only that were the end of it. After all, “local realism” means that the following three things must be true (taken from this site):

- First, the assumption that real things exist regardless of whether or not we observe them.
- Second, the assumption that we can legitimately reach general conclusions from consistent observations and experiments.
- Third, the assumption that no form of matter or energy can propagate faster than the speed of light.

Three years later, I got an email from Sascha of alpha-meme, who asked me to weigh in on an exchange he had with the author of that same paper, who has written more papers reaching the same erroneous conclusions. Let it be known that **Sascha is correct**, and all known quantum mechanical interpretations that demand both locality and realism, as far as we know today, conflict with experiments that are sensitive to such predictions. If you want to agree with the experiments of quantum physics, at least one of the above three statements must be false. Since we really, *really* place importance on the second one — that, to put it bluntly, seein’ is believin’ — it means that the Universe really *does* play dice in some form or other.

As much as we all admire Einstein, don’t keep making his greatest blunder. I’ll leave the last word to Bohr, who allegedly said,

“Don’t tell God what to do with his dice.”

**Update 07/02/2011**: To clarify, it isn’t simply that there’s randomness; that at some level, “God plays dice.” Even local, real interpretations of quantum mechanics with hidden variables can do that. It’s that we know something about *the type of dice* that the Universe plays. And the dice cannot be both local and real; people claiming otherwise have experimental data to answer to.