After reading the above blog, I feel how much I don’t understand what I understand. Do you have any opinion professor?

It is not at all clear that you are free to conclude that the probability of survival is 1/N for N duplications. If you restore and play again, once a day, you are constantly increasing N, and so if you look at it from Lara’s point of view, should your probability of survival depend on the N on tuesday or on wednesday? What if you run on a processor that sometimes stores a backup copy in a cache, and so internally duplicates some data? Should you count that double? What if you run on 2-petahertz processor vs a 1-petahertz, should the internal probability measure include the duration of existence of the Lara copies?

The only way I know to stop being endlessly confused on this point is to formulate this positivistic way— to ask “what answers to questions that I ask will the Lara’s give” (just as Everett did for quantum mechanics). This is after all the only way to acquire data on the internal experience of the Lara’s. Then the probability measure that you observe when asking questions of Laras depends on the details of which copies of Lara you choose to ask question of, and with what probability.

For example, you could just erase all the Lara events where Lara does not survive, and only talk to survivors. In this coupling between the external and internal world, the chance of survival is certainty, since if you ask the Lara’s whether they always survive, they will answer “yes”. You could talk to all the injured Lara’s, and they would have a different opinion on the danger of the puzzle then if you talk to the uninjured ones. If you keep all the Lara’s, then the great majority would associate some risk to each puzzle, but this again depends on the selection measure for who you choose to end up communicate with. So it is not at all clear that the question of internal experience in this model world has a unique right answer.

But in quantum mechanics the probability measure does have a unique right answer: it’s psi-squared. It’s not determined by an outside agent looking in, or at least, it’s the same for all the outside agents looking in, if you take the Copenhagen interpretation and consider us to be the outside agents. The probabilities in QM are nothing like the reciprocal of an integer, and that effect, which I don’t think should be thought of as necessarily true in the Tomb Raider world, has nothing to do with what physicists call “quantization”.

There is no naive way to go from copy-counting to the probability measure of quantum mechanics, but there is a naive way of identifying classical probability with copy-counts (which is the ensemble interpretation of probabilities). The measure in quantum mechanics is determined by Hilbert space massiveness of states, by a psi-squared measure on the states, not by any naive copy-counting. It is an interesting exercise to construct a copy-counting measure which reproduces quantum mechanical psi-squared probability (that’s DeBroglie Bohm theory, since a classical probabilistic ensemble which can be given a copy-counting frequentist interpretation, and DeBroglie Bohm gives a classical probabilistic ensemble which matches quantum mechanics)

You always run into the same philosophical question when you treat a physical system as self-contained correct model of reality. you have to somehow identify the experience of observers with the mathematical objects inside the theory. When the theory is either probabilistic, quantum mechanical, or duplicates observers, the identification of the correct probability measure from copy-counting is impossible a-priori, you need additional (mild) assumptions. The assumptions for a classical probabilistic theory is that there is an ensemble “underneath it all” and the number of worlds is proportional to the classical probabilities. For QM it’s that worlds with small hilbert space norm are unlikely. For duplicative theories, it requires knowing the way in which duplicates are most likely to talk to an outside observer.

This is the sticky point for many-worlds type interpretations, and it is present in duplicating classical theories in the exact same way, or an even worse way, depending on your point of view. It’s a philosophical problem, not a physical or mathematical one, and the resolution I think works is to adopt a more Platonic philsophy regarding the relation of the computational structures in the mind to the physical objects described by wavefunctions in the world.

Unfortunately, the philosophers who discuss this field don’t often take a functionalist philosophy of mind, so they don’t really get the interesting confusions. Pauli and Einstein discussed similar things first, although Everett brought in the duplication of course.

One thing though: I don’t understand Jaques’ Distler’s comments. The noncommutativity of observables is a non-sequitor for this philosophical issue. Non-commuting observables are just what happens when you describe an orthogonal collection of states and observable-values by a matrix. I don’t see why this algebraic property should be singled out— it’s an opaque algebraic way to restate the principle of superposition and the notion of orthogonality, which are all you need for a philosophical discussion.

General Relativity says that mass deforms the shape of space-time. There are different shapes for the same mass that can produce this deformation.

Is there a way to construct a schrodinger type of equation whose solutions are the possible shapes for a given mass that can give rise to the same curvature in space-time?

Thanks,
Ganesh Raghavan