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Yes, it is possible in quantum mechanics. Such setups are known as closed timelike curves (CTCs). As you may know, time travel may lead to the Grandfather's paradox.

There are two mathematical ways to resolve the paradox in QM. The corresponding timelike curves are called D-CTCs (named after David Deutsch who proposed them) and P-CTCs (postselected CTCs).

The D-CTC resolves the paradox by postulating that any paradoxical event converges to a fixed point which is usually a mixed quantum state (like in Schroedinger's cat paradox). The disadvantage of such CTC is that the content of the loop cannot be measured in the future: any measurement collapses the wavefunction and destroys the CTC and does not depend on the input due to inevitable convergence to the fixed point. As such, the information cannot be read or written to/from the loop, the loop just exists by itself.

The P-CTC resolves the paradox by postulating that paradoxical outcomes are prohibited and contradicting histories are eliminated. This has been demonstrated in an experiment.

Such property of P-CTC allows time travel to be utilized for computation, that is, using the same time interval for multiple calculations. Unfortunately, only one result can be read in the future, so such quantum computer would require special algorithms.

Note that the observer himself never can travel to the past because any histories which lead to entropy decrease would be erased from his memory and as such, unobservable. Whatever the path of the observer, he always sees entropy to increase.

The field that studies closed timelike curves is called non-linear quantum mechanics.

The closed timelike curves in General Relativity, if exist, are thought to resolve paradoxes in a similar way, through non-linear quantum mechanics.

Yes, it is possible in quantum mechanics. Such setups are known as closed timelike curves (CTCs). As you may know, time travel may lead to the Grandfather's paradox.

There are two mathematical ways to resolve the paradox in QM. The corresponding timelike curves are called D-CTCs (named after David Deutsch who proposed them) and P-CTCs (postselected CTCs).

The D-CTC resolves the paradox by postulating that any paradoxical event converges to a fixed point which is usually a mixed quantum state (like in Schroedinger's cat paradox). The disadvantage of such CTC is that the content of the loop cannot be measured in the future: any measurement collapses the wavefunction and destroys the CTC. As such, the information cannot be read or written to/from the loop, the loop just exists by itself.

The P-CTC resolves the paradox by postulating that paradoxical outcomes are prohibited and contradicting histories are eliminated. This has been demonstrated in an experiment.

Such property of P-CTC allows time travel to be utilized for computation, that is, using the same time interval for multiple calculations. Unfortunately, only one result can be read in the future, so such quantum computer would require special algorithms.

Note that the observer himself never can travel to the past because any histories which lead to entropy decrease would be erased from his memory and as such, unobservable. Whatever the path of the observer, he always sees entropy to increase.

The field that studies closed timelike curves is called non-linear quantum mechanics.

The closed timelike curves in General Relativity, if exist, are thought to resolve paradoxes in a similar way, through non-linear quantum mechanics.

Yes, it is possible in quantum mechanics. Such setups are known as closed timelike curves (CTCs). As you may know, time travel may lead to the Grandfather's paradox.

There are two mathematical ways to resolve the paradox in QM. The corresponding timelike curves are called D-CTCs (named after David Deutsch who proposed them) and P-CTCs (postselected CTCs).

The D-CTC resolves the paradox by postulating that any paradoxical event converges to a fixed point which is usually a mixed quantum state (like in Schroedinger's cat paradox). The disadvantage of such CTC is that the content of the loop cannot be measured in the future: any measurement collapses the wavefunction and destroys the CTC and does not depend on the input due to inevitable convergence to the fixed point. As such, the information cannot be read or written to/from the loop, the loop just exists by itself.

The P-CTC resolves the paradox by postulating that paradoxical outcomes are prohibited and contradicting histories are eliminated. This has been demonstrated in an experiment.

Such property of P-CTC allows time travel to be utilized for computation, that is, using the same time interval for multiple calculations. Unfortunately, only one result can be read in the future, so such quantum computer would require special algorithms.

Note that the observer himself never can travel to the past because any histories which lead to entropy decrease would be erased from his memory and as such, unobservable. Whatever the path of the observer, he always sees entropy to increase.

The field that studies closed timelike curves is called non-linear quantum mechanics.

The closed timelike curves in General Relativity, if exist, are thought to resolve paradoxes in a similar way, through non-linear quantum mechanics.

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Yes, it is possible in quantum mechanics. Such setups are known as closed timelike curves (CTCs). As you may know, time travel may lead to the Grandfather's paradox.

There are two mathematical ways to resolve the paradox in QM. The corresponding timelike curves are called D-CTCs (named after David Deutsch who proposed them) and P-CTCs (postselected CTCs).

The D-CTC resolves the paradox by postulating that any paradoxical event converges to a fixed point which is usually a mixed quantum state (like in Schroedinger's cat paradox). The disadvantage of such CTC is that the content of the loop cannot be measured in the future: any measurement collapses the wavefunction and destroys the CTC. As such, the information cannot be read or written to/from the loop, the loop just exists by itself.

The P-CTC resolves the paradox by postulating that paradoxical outcomes are prohibited and contradicting histories are eliminated. This has been demonstrated in an experiment.

Such property of P-CTC allows time travel to be utilized for computation, that is, using the same time interval for multiple calculations. Unfortunately, only one result can be read in the future, so such quantum computer would require special algorithms.

Note that the observer himself never can travel to the past because any histories which lead to entropy decrease would be erased from his memory and as such, unobservable. Whatever the path of the observer, he always sees entropy to increase.

The field that studies closed timelike curves is called non-linear quantum mechanics.

The closed timelike curves in General Relativity, if exist, are thought to resolve paradoxes in a similar way, through non-linear quantum mechanics.