Another really weird thought experiment

Suppose we accept a memory theory of personal identity and accept that people can be moved from one set of hardware to another. Now suppose Alice is an internally determinstic person, currently without inputs from the outside world, whose mental state is constantly backed up to a hard drive. Suppose now that Alice is a person who in hardware AliceOne has experiences E₀, E₁, E₂, E₃ at times 0,1,2,3, respectively. Then the initial hardware is destroyed, and the backup from just before time 2 is restored into another piece of hardware, AliceTwo, who goes on to have experience E₂. Then AliceTwo is destroyed, and a backup from just before time 1 is restored into AliceThree, who goes on to have experience E₁, after which all the hardware and the backups are destroyed by a natural disaster.

What is the order of Alice’s experiences? The obvious answer is:

• E₀, E₁, E₂, E₃, E₂, E₁ at times 0−5, respectively.

In particular, when Alice is experiencing E₂ for the second time, if she were informed of what is going to happen, she would be rationally dreading E₁ if E₁ is unpleasant. For E₁ would be in her future.

What makes it be the case that the second E₁ is experienced after the second E₂? It is the order of external time, according to which the second E₁ comes after the second E₂. It is not the order of causal connections in Alice (since the second E₂ comes from first E₁ while the second E₁ comes from the first E₀, and since there need be no causal connection between the hardware AliceTwo and AliceThree).

I think this is all a bit odd. To make it odder, let’s imagine that AliceTwo and AliceThree are in a room that time-travels in such a way that it is first at time 5 and then at time 4. Now, perhaps, Alice experiences the final E₁ before she experiences the final E₂. That’s really unclear, though.

The more I think about various combinations of time-traveling backups and time-traveling hardware, the more indeterminate it looks to me whether the final E₂ comes before the final E₁.

This is not much of an argument. But the above lines of thought lead me to think that one or more of the following is true:

1. Time travel is impossible.

2. People cannot be moved from one piece of hardware to another.

3. One does not survive restoration from a backup.

4. The order of experience does not have tight connections to rationality of attitudes.

5. The order of experience can be quite indeterminate.