In problems where multiple different agents in the universe “could be you,” (i.e. share information), you really don’t have to do anything fancy. Just assign equal probability to all agents in the entire universe who, as far as you know, can match your current state of information.
If there are two copies of Earth, and, hypothetically, only these two copies of me in the universe, I assign 50% probability to being each. This stays the same whether these Earths are at different points in space, or at different times, or sped up or slowed down or played in reverse order due to strange entropic boundary conditions. All that matters is that on each Earth there is a copy of me that has the same information as me from their own internal perspective, and I just count these copies up.
In problems where multiple different agents in the universe “could be you,” (i.e. share information), you really don’t have to do anything fancy. Just assign equal probability to all agents in the entire universe who, as far as you know, can match your current state of information.
If there are two copies of Earth, and, hypothetically, only these two copies of me in the universe, I assign 50% probability to being each. This stays the same whether these Earths are at different points in space, or at different times, or sped up or slowed down or played in reverse order due to strange entropic boundary conditions. All that matters is that on each Earth there is a copy of me that has the same information as me from their own internal perspective, and I just count these copies up.