This post is part of the Quantum Physics Sequence.
Followup to: Where Philosophy Meets Science, Joint Configurations

Behold, I present you with two electrons. They have the same mass. They have the same charge. In every way that we've tested them so far, they seem to behave the same way.

But is there any way we can know that the two electrons are really, truly, entirely indistinguishable?

The one who is wise in philosophy but not in physics will snort dismissal, saying, "Of course not. You haven't found an experiment yet that distinguishes these two electrons. But who knows, you might find a new experiment tomorrow that does."

Just because your current model of reality files all observed electrons in the same mental bucket, doesn't mean that tomorrow's physics will do the same. That's mixing up the map with the territory. Right?

It took a while to discover atomic isotopes. Maybe someday we'll discover electron isotopes whose masses are different in the 20th decimal place. In fact, for all we know, the electron has a tiny little tag on it, too small for your current microscopes to see, reading 'This is electron #7,234,982,023,348...' So that you could in principle toss this one electron into a bathtub full of electrons, and then fish it out again later. Maybe there's some way to know in principle, maybe not—but for now, surely, this is one of those things that science just doesn't know.

That's what you would think, if you were wise in philosophy but not in physics.

But what kind of universe could you possibly live in, where a simple experiment can tell you whether it's possible in principle to tell two things apart?

Maybe aliens gave you a tiny little device with two tiny little boxes, and a tiny little light that goes on when you put two identical things into the boxes?

But how do you know that's what the device really does? Maybe the device was just built with measuring instruments that go to the 10th decimal place but not any further.

Imagine that we take this problem to an analytic philosopher named Bob, and Bob says:

"Well, for one thing, you can't even get absolute proof that the two particles actually exist, as opposed to being some kind of hallucination created in you by the Dark Lords of the Matrix. We call it 'the problem of induction'."

Yes, we've heard of the problem of in...

Hax

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