This is one of several shortened indices into the Quantum Physics Sequence.

Suppose that someone built an exact duplicate of you on Mars, quark by quark - to the maximum level of resolution that quantum physics permits, which is considerably higher resolution than ordinary thermal uncertainty.  Would the duplicate be really you, or just a copy?

It may seem unlikely a priori that physics, or any experimental science, could have something to say about this issue.

But it's amazing, the things that science can tell you.

In this case, it turns out, science can rule out a notion of personal identity that depends on your being composed of the same atoms - because modern physics has taken the concept of "same atom" and thrown it out the window.  There are no tiny billiard balls with individual identities.  It's experimentally ruled out.

"Huh?  What do you mean, physics has gotten rid of the concept of 'same atom'?"

No one can be told this, alas, because it involves replacing the concept of little billiard balls with a different kind of math.  If you read through the introduction that follows to basic quantum mechanics, you will be able to see that the naive concept of personal identity - the notion that you are made up of tiny pieces with individual identities that persist through time, and that your identity follows the "same" tiny pieces - is physical nonsense.  The universe just doesn't work in a way which would let that idea be meaningful.

There are more abstract and philosophical arguments that you could use to rule out atom-following theories of personal identity.  But in our case, it so happens that we live in a universe where the issue is flatly settled by standard physics.  It's like proposing that personal identity follows phlogiston.  You could argue against it on philosophical grounds - but we happen to live in a universe where "phlogiston" itself is just a mistaken theory to be discarded, which settles the issue much more abruptly.

And no, this does not rely on a woo-woo mysterian interpretation of quantum mechanics.  The other purpose of this series of posts, was to demystify quantum mechanics and reveal it as non-mysterious.  It just happens to be a fact that once you get to the non-mysterious version of quantum mechanics, you find that the reason why physics once looked mysterious, has to do with reality being made up of different stuff than little billiard balls.  Complex amplitudes in configuration spaces, to be exact, though here I jump ahead of myself.