Thank you so much for this question! It’s silly of me that I haven’t seriously thought about quantum Poincare recurrences in this context, but now that I did, I finally see a path towards formally testing the “no BB in FCR” claim.
Explanation for readers who are following some of the formal details of FCR:
Consider the same setting of Gergely’s post that I linked, but instead of making time evolution stop after T steps, we can make it go on forever. The agent’s memory tape is still of size T, so it will end up cycling through it and (reversibly) overriding it infinitely many times. My conjecture is that, in this new setting, we still have a version of Theorem 4.19 with a non-trivial lower bound. This would imply no BB in the traditional sense: despite the Poincaré recurrences, the agent does not experience all possible histories.
Why would that be true? Because, if you measure the agent’s memory time at a time in which its memory tape is full of “garbage”, the results conveys only a little information about its policy, and its unlikely to make the agent “experience” too much in the formal sense defined by the bridge transform. Whereas if you measure the agent’s memory at time in which the Poincare recurrence recently reset the tape, the “minimal computations” principle would make it likely for it see the same observations it saw during previous such cycles.
Explanation for readers who are not following the formal details of FCR:
The thing is, whether we “must” compute something or not is not a binary. Rather, the probability we compute something increases with the total variation distance between the distributions we need to distinguish. So, as long as different agent policies produce similar distributions, we only have a low probability of computing the policy (which in this framework is equivalent to the agent “experiencing” something). I think this also addresses your remark about “NP”: it’s likely easy to approximate the thermal equilibrium distribution without simulating brains.
Other “observers” without subjective experiences:
I don’t know, but you can in principle use this theory to predict the experiences of an agent inside something like Wigner’s friend experiment or any other scenario that violates decoherence. Implementing such an agent would require a quantum computer.
Actually, I think things might be even better than this: in semiclassical quantum gravity in asymptotically de Sitter spacetime, your quantum state is necessarily mixed (due to tracing over things outside the cosmological horizon, which is how you get Unruh radiation). So, there are no quantum Poincare recurrences. If you plug a stationary mixed state into the FCR interpretation, all the observables become completely frozen in time. If you’re just converging towards a stationary mixed state, I expect the observables to converge towards becoming frozen.
Quantum Poincare recurrences:
Thank you so much for this question! It’s silly of me that I haven’t seriously thought about quantum Poincare recurrences in this context, but now that I did, I finally see a path towards formally testing the “no BB in FCR” claim.
Explanation for readers who are following some of the formal details of FCR:
Consider the same setting of Gergely’s post that I linked, but instead of making time evolution stop after T steps, we can make it go on forever. The agent’s memory tape is still of size T, so it will end up cycling through it and (reversibly) overriding it infinitely many times. My conjecture is that, in this new setting, we still have a version of Theorem 4.19 with a non-trivial lower bound. This would imply no BB in the traditional sense: despite the Poincaré recurrences, the agent does not experience all possible histories.
Why would that be true? Because, if you measure the agent’s memory time at a time in which its memory tape is full of “garbage”, the results conveys only a little information about its policy, and its unlikely to make the agent “experience” too much in the formal sense defined by the bridge transform. Whereas if you measure the agent’s memory at time in which the Poincare recurrence recently reset the tape, the “minimal computations” principle would make it likely for it see the same observations it saw during previous such cycles.
Explanation for readers who are not following the formal details of FCR:
The thing is, whether we “must” compute something or not is not a binary. Rather, the probability we compute something increases with the total variation distance between the distributions we need to distinguish. So, as long as different agent policies produce similar distributions, we only have a low probability of computing the policy (which in this framework is equivalent to the agent “experiencing” something). I think this also addresses your remark about “NP”: it’s likely easy to approximate the thermal equilibrium distribution without simulating brains.
Other “observers” without subjective experiences:
I don’t know, but you can in principle use this theory to predict the experiences of an agent inside something like Wigner’s friend experiment or any other scenario that violates decoherence. Implementing such an agent would require a quantum computer.
Actually, I think things might be even better than this: in semiclassical quantum gravity in asymptotically de Sitter spacetime, your quantum state is necessarily mixed (due to tracing over things outside the cosmological horizon, which is how you get Unruh radiation). So, there are no quantum Poincare recurrences. If you plug a stationary mixed state into the FCR interpretation, all the observables become completely frozen in time. If you’re just converging towards a stationary mixed state, I expect the observables to converge towards becoming frozen.