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P.S. Time reversibility by itself does not entail determinism, and the Norton dome is a counterexample. Time reversed solutions to the ones mentioned above, when a ball sits on top of the dome for arbitrary time, and then rolls off in arbitrary direction, are also solutions (the shape of the dome makes equations of motion non-Lipschitz, and uniqueness of solutions is lost). What it does entail is that if information can be destroyed it can also be created "out of nothing", like the ball's elapsed time and direction of movement. The peculiarity of the dome is that self-initiation of motion requires no energy input here, not even an infinitesimal push. This is close to what free will libertarians want, free will acts as causa sui, and hence injects new information into causal chains. I should mention that many physicists consider the Nortom dome "unphysical", and "free will creates information""free will creates information" is likely to be as controversial as "consciousness causes collapse".

P.S. Time reversibility by itself does not entail determinism, and the Norton dome is a counterexample. Time reversed solutions to the ones mentioned above, when a ball sits on top of the dome for arbitrary time, and then rolls off in arbitrary direction, are also solutions (the shape of the dome makes equations of motion non-Lipschitz, and uniqueness of solutions is lost). What it does entail is that if information can be destroyed it can also be created "out of nothing", like the ball's elapsed time and direction of movement. The peculiarity of the dome is that self-initiation of motion requires no energy input here, not even an infinitesimal push. This is close to what free will libertarians want, free will acts as causa sui, and hence injects new information into causal chains. I should mention that many physicists consider the Nortom dome "unphysical", and "free will creates information" is likely to be as controversial as "consciousness causes collapse".

P.S. Time reversibility by itself does not entail determinism, and the Norton dome is a counterexample. Time reversed solutions to the ones mentioned above, when a ball sits on top of the dome for arbitrary time, and then rolls off in arbitrary direction, are also solutions (the shape of the dome makes equations of motion non-Lipschitz, and uniqueness of solutions is lost). What it does entail is that if information can be destroyed it can also be created "out of nothing", like the ball's elapsed time and direction of movement. The peculiarity of the dome is that self-initiation of motion requires no energy input here, not even an infinitesimal push. This is close to what free will libertarians want, free will acts as causa sui, and hence injects new information into causal chains. I should mention that many physicists consider the Nortom dome "unphysical", and "free will creates information" is likely to be as controversial as "consciousness causes collapse".

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Determinism is a bigger problem. MostIt is a mathematical consequence of quantum mechanical formalism that unitary evolution by itself conserves information (more precisely, the von Neumann entropy). It is the non-unitary "collapse of the wave function" that creates problems, which is perhaps why most quantum information theorists, like Deutsch, subscribe to the Everett interpretations of quantum mechanics. There there is no collapse, and decohered states, which create an impression of it, can in principle recohere, unlikely though that is. Everett's is a strange "determinism" though, his branches realize every possible outcome rather than predetermine one, hence each branch "creates" itself through its past "choices". Only the global state is predetermined, but it is everything whatever anyway. Essentially, the unobservable branches are postulated so that there is somewhere for the "lost" information to go (or come from).

In statistical interpretations "collapse" amounts to observer specific reconditioning of probabilities, and so any information "loss" it entails will also be observer specific, it does not happen "objectively". Under objective collapse, and indeterministic interpretations of classical physics, one would indeed have to reject the conservation of information. If a ball rolls to the top of the Norton dome and then stops there, there is no recovering afterwards from whence it came and how long it stayed on top. This means of course that quantum mechanical formalism per se is neutral on the issue.

P.S. I came to realize that timeTime reversibility by itself does not entail determinism, and the Norton dome is a counterexample. Time reversed solutions to the ones mentioned above, when a ball sits on top of the dome for arbitrary time, and then rolls off in arbitrary direction, are also solutions (the shape of the dome makes equations of motion non-Lipschitz, and uniqueness of solutions is lost). What it does entail is that if information can be destroyed it can also be created "out of nothing", like the ball's elapsed time and direction of movement. The peculiarity of the dome is that self-initiation of motion requires no energy input here, not even an infinitesimal push. This is close to what free will libertarians want, free will acts as causa sui, and hence injects new information into causal chains. I should mention that many physicists consider the Nortom dome "unphysical", and "free will creates information" is likely to be as controversial as "consciousness causes collapse".

Determinism is a bigger problem. Most quantum information theorists, like Deutsch, subscribe to the Everett interpretations of quantum mechanics. There there is no collapse, and decohered states, which create an impression of it, can in principle recohere, unlikely though that is. Everett's is a strange "determinism" though, his branches realize every possible outcome rather than predetermine one, hence each branch "creates" itself through its past "choices". Only the global state is predetermined, but it is everything whatever anyway. In statistical interpretations "collapse" amounts to observer specific reconditioning of probabilities, and so any information "loss" it entails will also be observer specific, it does not happen "objectively". Under objective collapse, and indeterministic interpretations of classical physics, one would indeed have to reject the conservation of information. If a ball rolls to the top of the Norton dome and then stops there, there is no recovering afterwards from whence it came and how long it stayed on top. This means of course that quantum mechanical formalism per se is neutral on the issue.

P.S. I came to realize that time reversibility by itself does not entail determinism, and the Norton dome is a counterexample. Time reversed solutions to the ones mentioned above, when a ball sits on top of the dome for arbitrary time, and then rolls off in arbitrary direction, are also solutions (the shape of the dome makes equations of motion non-Lipschitz, and uniqueness of solutions is lost). What it does entail is that if information can be destroyed it can also be created "out of nothing", like the ball's elapsed time and direction of movement. The peculiarity of the dome is that self-initiation of motion requires no energy input here, not even an infinitesimal push. This is close to what free will libertarians want, free will acts as causa sui, and hence injects new information into causal chains. I should mention that many physicists consider the Nortom dome "unphysical", and "free will creates information" is likely to be as controversial as "consciousness causes collapse".

Determinism is a bigger problem. It is a mathematical consequence of quantum mechanical formalism that unitary evolution by itself conserves information (more precisely, the von Neumann entropy). It is the non-unitary "collapse of the wave function" that creates problems, which is perhaps why most quantum information theorists, like Deutsch, subscribe to the Everett interpretations of quantum mechanics. There there is no collapse, and decohered states, which create an impression of it, can in principle recohere, unlikely though that is. Everett's is a strange "determinism" though, his branches realize every possible outcome rather than predetermine one, hence each branch "creates" itself through its past "choices". Only the global state is predetermined, but it is everything whatever anyway. Essentially, the unobservable branches are postulated so that there is somewhere for the "lost" information to go (or come from).

In statistical interpretations "collapse" amounts to observer specific reconditioning of probabilities, and so any information "loss" it entails will also be observer specific, it does not happen "objectively". Under objective collapse, and indeterministic interpretations of classical physics, one would indeed have to reject the conservation of information. If a ball rolls to the top of the Norton dome and then stops there, there is no recovering afterwards from whence it came and how long it stayed on top. This means of course that quantum mechanical formalism per se is neutral on the issue.

P.S. Time reversibility by itself does not entail determinism, and the Norton dome is a counterexample. Time reversed solutions to the ones mentioned above, when a ball sits on top of the dome for arbitrary time, and then rolls off in arbitrary direction, are also solutions (the shape of the dome makes equations of motion non-Lipschitz, and uniqueness of solutions is lost). What it does entail is that if information can be destroyed it can also be created "out of nothing", like the ball's elapsed time and direction of movement. The peculiarity of the dome is that self-initiation of motion requires no energy input here, not even an infinitesimal push. This is close to what free will libertarians want, free will acts as causa sui, and hence injects new information into causal chains. I should mention that many physicists consider the Nortom dome "unphysical", and "free will creates information" is likely to be as controversial as "consciousness causes collapse".

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Determinism is a bigger problem. Strict microscopic reversibility would entail microscopic determinism, which is probably why mostMost quantum information theorists, like Deutsch, subscribe to the Everett interpretations of quantum mechanics. There there is no collapse, and decohered states, which create an impression of it, can in principle recohere, unlikely though that is. Everett's is a strange "determinism" though, his branches realize every possible outcome rather than predetermine one, hence each branch "creates" itself through its past "choices". Only the global state is predetermined, but it is everything whatever anyway. In statistical interpretations "collapse" amounts to observer specific reconditioning of probabilities, and so any information "loss" it entails will also be observer specific, it does not happen "objectively". Under objective collapse, and indeterministic interpretations of classical physics, one would indeed have to reject the conservation of information. If a ball rolls to the top of the Norton dome and then stops there, there is no recovering afterwards from whence it came and how long it stayed on top. This means of course that quantum mechanical formalism per se is neutral on the issue.

P.S. I came to realize that time reversibility by itself does not entail determinism, and the Norton dome is a counterexample. Time reversed solutions to the ones mentioned above, when a ball sits on top of the dome for arbitrary time, and then rolls off in arbitrary direction, are also solutions (the shape of the dome makes equations of motion non-Lipschitz, and uniqueness of solutions is lost). What it does entail is that if information can be destroyed it can also be created "out of nothing", like the ball's elapsed time and direction of movement. The peculiarity of the dome is that self-initiation of motion requires no energy input here, not even an infinitesimal push. This is close to what free will libertarians want, free will acts as causa sui, and hence injects new information into causal chains. I should mention that many physicists consider the Nortom dome "unphysical", and "free will creates information" is likely to be as controversial as "consciousness causes collapse".

Determinism is a bigger problem. Strict microscopic reversibility would entail microscopic determinism, which is probably why most quantum information theorists, like Deutsch, subscribe to the Everett interpretations of quantum mechanics. There there is no collapse, and decohered states, which create an impression of it, can in principle recohere, unlikely though that is. Everett's is a strange "determinism" though, his branches realize every possible outcome rather than predetermine one, hence each branch "creates" itself through its past "choices". Only the global state is predetermined, but it is everything whatever anyway. In statistical interpretations "collapse" amounts to observer specific reconditioning of probabilities, and so any information "loss" it entails will also be observer specific, it does not happen "objectively". Under objective collapse, and indeterministic interpretations of classical physics, one would indeed have to reject the conservation of information. If a ball rolls to the top of the Norton dome and then stops there, there is no recovering afterwards from whence it came and how long it stayed on top. This means of course that quantum mechanical formalism per se is neutral on the issue.

Determinism is a bigger problem. Most quantum information theorists, like Deutsch, subscribe to the Everett interpretations of quantum mechanics. There there is no collapse, and decohered states, which create an impression of it, can in principle recohere, unlikely though that is. Everett's is a strange "determinism" though, his branches realize every possible outcome rather than predetermine one, hence each branch "creates" itself through its past "choices". Only the global state is predetermined, but it is everything whatever anyway. In statistical interpretations "collapse" amounts to observer specific reconditioning of probabilities, and so any information "loss" it entails will also be observer specific, it does not happen "objectively". Under objective collapse, and indeterministic interpretations of classical physics, one would indeed have to reject the conservation of information. If a ball rolls to the top of the Norton dome and then stops there, there is no recovering afterwards from whence it came and how long it stayed on top. This means of course that quantum mechanical formalism per se is neutral on the issue.

P.S. I came to realize that time reversibility by itself does not entail determinism, and the Norton dome is a counterexample. Time reversed solutions to the ones mentioned above, when a ball sits on top of the dome for arbitrary time, and then rolls off in arbitrary direction, are also solutions (the shape of the dome makes equations of motion non-Lipschitz, and uniqueness of solutions is lost). What it does entail is that if information can be destroyed it can also be created "out of nothing", like the ball's elapsed time and direction of movement. The peculiarity of the dome is that self-initiation of motion requires no energy input here, not even an infinitesimal push. This is close to what free will libertarians want, free will acts as causa sui, and hence injects new information into causal chains. I should mention that many physicists consider the Nortom dome "unphysical", and "free will creates information" is likely to be as controversial as "consciousness causes collapse".

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