Spooky action and quantum marbles

There’s a phenomenon in quantum mechanics popularly known as “spooky action at a distance”. One manifestation of it is known as the EPR paradox. It’s usually explained using a thought experiment similar to the following.

Spooky action at a distance “explained”

Start with a particle that has a total “spin” of zero. Allow it to decay into two entangled photons that will be emitted in opposite directions. Spin is a kind of angular momentum, so it must be conserved. When measured, a photon’s spin can only be one of two values: “UP”, or “DOWN”. So, if both entangled photons are measured in the same way, one of them will be UP, and the other will be DOWN.

Entangled photons (according to the theory of quantum mechanics) do not have a well-defined spin until they are observed. Only then do they decide if they are UP, or DOWN.

The photons arrive at distant observers A and B. Observer A measures the first photon. That photon flips a coin and chooses either UP or DOWN. Suppose the result is DOWN. Then the second photon will definitely be UP. But the second photon is far away, and its decision cannot be delayed. The only way it can know to be UP is for the photons to have somehow communicated with each other faster than light.

A few things to note:

  1. There’s nothing special about photons. Other kinds of particles would also work, including massive particles that travel slower than light.
  2. There’s nothing special about spin. There are other quantum properties that work in a similar fashion.
  3. Nobody is claiming that we could use entangled photons to send information faster than light.

The scientifically-minded non-physicist reader ponders this for a moment, then realizes the worlds greatest physicists are morons. What if, he thinks, the photons’ eventual spin is actually determined at the time of entanglement? The photons carry the information with them, in some sort of “hidden variables”, until they are measured. If need be, the hidden variables could be like little computer programs that select the spin in a manner dependent on how the measurement is done.

No faster-than-light communication is happening. If the theory of quantum mechanics says otherwise, then quantum mechanics is just being needlessly obtuse.

And the non-physicist is absolutely correct. Well, he’s correct that the described experiment is perfectly explicable without superluminal communication.

The problem is that the author of the thought experiment has simplified it the point where it no longer does the one thing it was intended to do. There are other experiments, similar but more complex, whose predicted results cannot be explained by hidden variables. The canonical one is Bell’s inequality.

But I find Bell’s inequality to be somewhat difficult to grasp. I can understand it, for a while, but I think there’s just nothing interesting enough about it to make it stick in my mind. It’s just numbers.

So I will attempt to present what I think is a better way to explain the phenomenon. It is a fanciful version of an experiment invented by Lucien Hardy in 1993. Caution: I’m not a quantum physicist, so I may not have gotten this right.

Quantum marbles

A quantum marble is part red, part yellow. If even one photon of light touches a quantum marble, it decays in a flash of red or yellow light, apparently depending on where it was touched. A pair of quantum marbles can be entangled.

It’s true that if both members of a pair of entangled marbles are measured in the same way, one will flash red, and the other will flash yellow. (Or, if they are measured in opposite ways, they will flash the same color.) But there’s more to entanglement than that.

Now the experiment. You turn off the lights, entangle two quantum marbles, and put them in boxes labeled 1A and 1B. You do a similar thing for 999,999 other pairs of marbles and boxes. You orient each pair of boxes in the same strategic way, and give the A boxes to your associate Alice, and the B boxes to your associate Bob. For good measure, they get in separate spaceships, and travel 0.5 light-years away in opposite directions.

Each box has two doors: a “top” door, and a “front” door. (Don’t worry about exactly where the doors are located on the boxes — that’s just what I’m calling them.) For each box, Alice and Bob randomly and independently select one door to open. They open all the boxes, recording which door they opened, and whether they saw a red or yellow flash of light. Then they fly back to your lab.

You analyze the results, and find that:

  1. When Alice and Bob opened different doors for a particular box number, they NEVER both got red. (AFR-BTR never happened, and ATR-BFR never happened.)
  2. SOMETIMES they both opened the top door and both got red. (ATR-BTR happened.)
  3. They NEVER both opened the front door and both got yellow. (AFY-BFY never happened.)

There were no extremely rare outcomes. If an outcome ever occurred, it occurred at least, say, 1% of the time (10000 times).

In case it’s not clear, my description of this experiment leaves out some details, such as how to orient the boxes. The point is that such details can be chosen so as to yield the stated results. I don’t mean that you will get these results no matter what.

These results seem to be impossible, unless entangled marbles can influence each other with a faster than light signal. Why are they impossible? By (2), assume box #100 was ATR-BTR. But what would Alice have seen if she’d opened the front door of box #100? By (1), she’d have seen yellow (AFY-BTR). What would Bob have seen, if it had instead been him that opened the front door of box #100? By (1), he’d have seen yellow (ATR-BFY). Putting it together, if they had both opened the front door of box #100, they would have both seen yellow (AFY-BFY). But that contradicts (3). One or more of our premises must be wrong.

But we hardly assumed anything at all, other than the limitation of the speed of light. There are ways to salvage the speed of light, but no matter what, something big has to give. For example, the universe could all be a figment of your imagination. Or we could be living in a multiverse of parallel universes that interact in a certain way.

The functional equivalent of this experiment has been carried out in real life, obviously not as described, but instead with particles and not-so-distant detectors. It works as predicted.

Note that the experiment does not assume that quantum mechanics is correct. It tests the principle of locality, not quantum mechanics. Quantum mechanics could be totally wrong, and it wouldn’t change the fact that locality (or some other basic principle of reality) has been experimentally disproved.

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