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.

If you read all the way to the end, you will, I hope, gain an entirely new perspective on where your "identity" is located... once the little billiard balls are ruled out.

You will even be able to see, I hope, that if your brain were non-destructively frozen (e.g. by vitrification in liquid nitrogen); and a computer model of the synapses, neural states, and other brain behaviors were constructed a hundred years later; then it would preserve exactly everything about you that was preserved by going to sleep one night and waking up the next morning.

Mind you, my audacious claim is not that uploading preserves identity - this audacious claim has been made many times before.  I am claiming that once you grasp modern physics, you can actually see this as obvious, even if it would not be obvious to someone thinking in terms of Newtonian billiard balls in classical physics.  This is much more audacious, and I am well aware of how unlikely that sounds; but if you read all the way to the end, it is fully supported.

• Reductionism:  We build models of the universe that have many different levels of description.  But so far as anyone has been able to determine, the universe itself has only the single level of fundamental physics - reality doesn't explicitly compute protons, only quarks.
• Zombies! Zombies?:    Don't try to put your consciousness outside physics.  Whatever makes you say "I think therefore I am", causes your lips to move; it is within the chains of cause and effect that produce our observed universe.
• The Generalized Anti-Zombie Principle:  We can try to generalize the Anti-Zombie principle to show that anything which exerts only an infinitesimal influence on your brain, should not be able to make your consciousness go out like a light.
• Quantum Explanations: Quantum mechanics doesn't deserve its fearsome reputation.  If you tell people something is supposed to be mysterious, they won't understand it.  It's human intuitions that are "strange" or "weird"; physics itself is perfectly normal.  Talking about historical erroneous concepts like "particles" or "waves" is just asking to confuse people; present the real, unified quantum physics straight out.  The series will take a strictly realist perspective - quantum equations describe something that is real and out there.  Warning:  Although a large faction of physicists agrees with this, it is not universally accepted.  Stronger warning:  I am not even going to present non-realist viewpoints until later, because I think this is a major source of confusion.
• Configurations and Amplitude: A preliminary glimpse at the stuff reality is made of.  The classic split-photon experiment with half-silvered mirrors.  Alternative pathways the photon can take, can cancel each other out.  The mysterious measuring tool that tells us the relative squared moduli.
• Joint Configurations: The laws of physics are inherently over mathematical entities, configurations, that involve multiple particles.  A basic, ontologically existent entity, according to our current understanding of quantum mechanics, does not look like a photon - it looks like a configuration of the universe with "A photon here, a photon there." Amplitude flows between these configurations can cancel or add; this gives us a way to detect which configurations are distinct.  It is an experimentally testable fact that "Photon 1 here, photon 2 there" is the same configuration as "Photon 2 here, photon 1 there".
• Distinct Configurations: Since configurations are over the combined state of all the elements in a system, adding a sensor that detects whether a particle went one way or the other, becomes a new element of the system that can make configurations "distinct" instead of "identical".  This confused the living daylights out of early quantum experimenters, because it meant that things behaved differently when they tried to "measure" them.  But it's not only measuring instruments that do the trick - any sensitive physical element will do.
• Where Philosophy Meets Science: In retrospect, supposing that quantum physics had anything to do with consciousness was a big mistake.  Could philosophers have told the physicists so?  But we don't usually see philosophers sponsoring major advances in physics; why not?
• Can You Prove Two Particles Are Identical?:  You wouldn't think that it would be possible to do an experiment that told you that two particles are completely identical - not just to the limit of experimental precision, but perfectly.  You could even give a precise-sounding philosophical argument for why it was not possible - but the argument would have a deeply buried assumption.  Quantum physics violates this deep assumption, making the experiment easy.
• Classical Configuration Spaces: How to visualize the state of a system of two 1-dimensional particles, as a single point in 2-dimensional space.  A preliminary step before moving into...
• The Quantum Arena: Instead of a system state being associated with a single point in a classical configuration space, the instantaneous real state of a quantum system is a complex amplitude distribution over a quantum configuration space.  What creates the illusion of "individual particles", like an electron caught in a trap, is a plaid distribution - one that happens to factor into the product of two parts.  It is the whole distribution that evolves when a quantum system evolves. Individual configurations don't have physics; amplitude distributions have physics.  Quantum entanglement is the general case; quantum independence is the special case.
• Feynman Paths: Instead of thinking that a photon takes a single straight path through space, we can regard it as taking all possible paths through space, and adding the amplitudes for every possible path.  Nearly all the paths cancel out - unless we do clever quantum things, so that some paths add instead of canceling out.  Then we can make light do funny tricks for us, like reflecting off a mirror in such a way that the angle of incidence doesn't equal the angle of reflection.  But ordinarily, nearly all the paths except an extremely narrow band, cancel out - this is one of the keys to recovering the hallucination of classical physics.
• No Individual Particles: One of the chief ways to confuse yourself while thinking about quantum mechanics, is to think as if photons were little billiard balls bouncing around.  The appearance of little billiard balls is a special case of a deeper level on which there are only multiparticle configurations and amplitude flows.  It is easy to set up physical situations in which there exists no fact of the matter as to which electron was originally which.
• Identity Isn't In Specific Atoms, Three Dialogues on Identity: Given that there's no such thing as "the same atom", whether you are "the same person" from one time to another can't possibly depend on whether you're made out of the same atoms.
• Decoherence: A quantum system that factorizes can evolve into a system that doesn't factorize, destroying the illusion of independence.  But entangling a quantum system with its environment, can appear to destroy entanglements that are already present.  Entanglement with the environment can separate out the pieces of an amplitude distribution, preventing them from interacting with each other.  Decoherence is fundamentally symmetric in time, but appears asymmetric because of the second law of thermodynamics.
• The So-Called Heisenberg Uncertainty Principle: Unlike classical physics, in quantum physics it is not possible to separate out a particle's "position" from its "momentum".  The evolution of the amplitude distribution over time, involves things like taking the second derivative in space and multiplying by i to get the first derivative in time.  The end result of this time evolution rule is that blobs of particle-presence appear to race around in physical space.  The notion of "an exact particular momentum" or "an exact particular position" is not something that can physically happen, it is a tool for analyzing amplitude distributions by taking them apart into a sum of simpler waves.  This uses the assumption and fact of linearity: the evolution of the whole wavefunction seems to always be the additive sum of the evolution of its pieces.  Using this tool, we can see that if you take apart the same distribution into a sum of positions and a sum of momenta, they cannot both be sharply concentrated at the same time.  When you "observe" a particle's position, that is, decohere its positional distribution by making it interact with a sensor, you take its wave packet apart into two pieces; then the two pieces evolve differently.  The Heisenberg Principle definitely does not say that knowing about the particle, or consciously seeing it, will make the universe behave differently.
• Where Physics Meets Experience: Meet the Ebborians, who reproduce by fission.  The Ebborian brain is like a thick sheet of paper that splits down its thickness.  They frequently experience dividing into two minds, and can talk to their other selves.  It seems that their unified theory of physics is almost finished, and can answer every question, when one Ebborian asks:  When exactly does one Ebborian become two people?
• Where Experience Confuses Physicists: It then turns out that the entire planet of Ebbore is splitting along a fourth-dimensional thickness, duplicating all the people within it. But why does the apparent chance of "ending up" in one of those worlds, equal the square of the fourth-dimensional thickness?  Many mysterious answers are proposed to this question, and one non-mysterious one.
• On Being Decoherent: When a sensor measures a particle whose amplitude distribution stretches over space - perhaps seeing if the particle is to the left or right of some dividing line - then the standard laws of quantum mechanics call for the sensor+particle system to evolve into a state of (particle left, sensor measures LEFT) + (particle right, sensor measures RIGHT).  But when we humans look at the sensor, it only seems to say "LEFT" or "RIGHT", never a mixture like "LIGFT".  This, of course, is because we ourselves are made of particles, and subject to the standard quantum laws that imply decoherence.  Under standard quantum laws, the final state is (particle left, sensor measures LEFT, human sees "LEFT") + (particle right, sensor measures RIGHT, human sees "RIGHT").
• The Conscious Sorites Paradox: Decoherence is implicit in quantum physics, not an extra law on top of it.  Asking exactly when "one world" splits into "two worlds" may be like asking when, if you keep removing grains of sand from a pile, it stops being a "heap".  Even if you're inside the world, there may not be a definite answer.  This puzzle does not arise only in quantum physics; the Ebborians could face it in a classical universe, or we could build sentient flat computers that split down their thickness. Is this really a physicist's problem?
• Decoherent Essences: Decoherence is implicit within physics, not an extra law on top of it. You can choose representations that make decoherence harder to see, just like you can choose representations that make apples harder to see, but exactly the same physical process still goes on; the apple doesn't disappear and neither does decoherence.  If you could make decoherence magically go away by choosing the right representation, we wouldn't need to shield quantum computers from the environment.
• The Born Probabilities:  The last serious mysterious question left in quantum physics:  When a quantum world splits in two, why do we seem to have a greater probability of ending up in the larger blob, exactly proportional to the integral of the squared modulus? It's an open problem, but non-mysterious answers have been proposed. Try not to go funny in the head about it.
• Large number of posts skipped here, see the main sequence for them.
• Mach's Principle: Anti-Epiphenomenal Physics: Could you tell if the whole universe were shifted an inch to the left? Could you tell if the whole universe was traveling left at ten miles per hour?  Could you tell if the whole universe was accelerating left at ten miles per hour?  Could you tell if the whole universe was rotating?
• Relative Configuration Space: Maybe the reason why we can't observe absolute speeds, absolute positions, absolute accelerations, or absolute rotations, is that particles don't have absolute positions - only positions relative to each other.  That is, maybe quantum physics takes place in a relative configuration space.
• Timeless Physics: What time is it?  How do you know?  The question "What time is it right now?" may make around as much sense as asking "Where is the universe?" Not only that, our physics equations may not need a t in them!
• Timeless Beauty: To get rid of time you must reduce it to nontime.  In timeless physics, everything that exists is perfectly global or perfectly local.  The laws of physics are perfectly global; the configuration space is perfectly local.  Every fundamentally existent ontological entity has a unique identity and a unique value.  This beauty makes ugly theories much more visibly ugly; a collapse postulate becomes a visible scar on the perfection.
• Timeless Causality: Using the modern, Bayesian formulation of causality, we can define causality without talking about time - define it purely in terms of relations.  The river of time never flows, but it has a direction.
• Timeless Identity: How can you be the same person tomorrow as today, in the river that never flows, when not a drop of water is shared between one time and another?  Having used physics to completely trash all naive theories of identity, we reassemble a conception of persons and experiences from what is left.  This is the point at which you become able to see that uploading a person preserves everything of importance about them.
• Thou Art Physics:  If the laws of physics control everything we do, then how can our choices be meaningful?  Because you are physics.  You aren't competing with physics for control of the universe, you are within physics.  Anything you control is necessarily controlled by physics.
• Timeless Control: We throw away "time" but retain causality, and with it, the concepts "control" and "decide".  To talk of something as having been "always determined" is mixing up a timeless and a timeful conclusion, with paradoxical results.  When you take a perspective outside time, you have to be careful not to let your old, timeful intuitions run wild in the absence of their subject matter.
• Living in Many Worlds: The many worlds of quantum mechanics are not some strange, alien universe into which you have been thrust.  They are where you have always lived.  Egan's Law:  "It all adds up to normality."  Then why care about quantum physics at all?  Because there's still the question of what adds up to normality, and the answer to this question turns out to be, "Quantum physics."  If you're thinking of building any strange philosophies around many-worlds, you probably shouldn't - that's not what it's for.