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Relativity consists of special relativity (SR) and its generalization general relativity (GR), which includes gravity.

In SR, the history of an object is described by its world-line through spacetime. Every event has future and past light cones, and a material object such as a person's body is limited to "traveling" from the past light cone to the future light cone. Therefore you can't have a world-line that forms a closed loop. A world-line such as a material object's that always stays inside the light cone is called timelike.

In GR the situation is considerably modified. GR allows the existence of closed timelike curves (CTCs), which, although timelike everywhere, nevertheless close back on themselves. To conceptualize this, you can imagine drawing an ordinary timelike world-line on a piece of paper, but then wrapping the paper up into a cylinder. As far as we know, our universe doesn't contain CTCs, and there is no natural or artificial process that could create them. If the universe doesn't already contain any CTCs, then it's believed (Hawking 1992) that creating a new CTC from scratch would require exotic forms of matter (essentially, matter with negative mass). Even if one did have access to exotic matter, creating a CTC would require manipulation of matter on a godlike scale.

Supposing that a CTC exists, there are all kinds of other issues that come up involving causality (time-travel paradoxes) and quantum mechanics. A good (but somewhat out of date) popular-level discussion is given in Thorne 1995.

Hawking, S.W., (1992) The chronology protection conjecture. Phys. Rev. D46, 603-611.

Thorne, Black Holes and Time Warps: Einstein's Outrageous Legacy

Relativity consists of special relativity (SR) and its generalization general relativity (GR), which includes gravity.

In SR, the history of an object is described by its world-line through spacetime. Every event has future and past light cones, and a material object such as a person's body is limited to "traveling" from the past light cone to the future light cone. Therefore you can't have a world-line that forms a closed loop. A world-line such as a material object's that always stays inside the light cone is called timelike.

In GR the situation is considerably modified. GR allows the existence of closed timelike curves (CTCs), which, although timelike everywhere, nevertheless close back on themselves. To conceptualize this, you can imagine drawing an ordinary timelike world-line on a piece of paper, but then wrapping the paper up into a cylinder. As far as we know, our universe doesn't contain CTCs, and there is no natural or artificial process that could create them. If the universe doesn't already contain any CTCs, then it's believed (Hawking 1992) that creating a new CTC from scratch would require exotic forms of matter (essentially, matter with negative mass). Even if one did have access to exotic matter, creating a CTC would require manipulation of matter on a godlike scale.

Hawking, S.W., (1992) The chronology protection conjecture. Phys. Rev. D46, 603-611.

Relativity consists of special relativity (SR) and its generalization general relativity (GR), which includes gravity.

In SR, the history of an object is described by its world-line through spacetime. Every event has future and past light cones, and a material object such as a person's body is limited to "traveling" from the past light cone to the future light cone. Therefore you can't have a world-line that forms a closed loop. A world-line such as a material object's that always stays inside the light cone is called timelike.

In GR the situation is considerably modified. GR allows the existence of closed timelike curves (CTCs), which, although timelike everywhere, nevertheless close back on themselves. To conceptualize this, you can imagine drawing an ordinary timelike world-line on a piece of paper, but then wrapping the paper up into a cylinder. As far as we know, our universe doesn't contain CTCs, and there is no natural or artificial process that could create them. If the universe doesn't already contain any CTCs, then it's believed (Hawking 1992) that creating a new CTC from scratch would require exotic forms of matter (essentially, matter with negative mass). Even if one did have access to exotic matter, creating a CTC would require manipulation of matter on a godlike scale.

Supposing that a CTC exists, there are all kinds of other issues that come up involving causality (time-travel paradoxes) and quantum mechanics. A good (but somewhat out of date) popular-level discussion is given in Thorne 1995.

Hawking, S.W., (1992) The chronology protection conjecture. Phys. Rev. D46, 603-611.

Thorne, Black Holes and Time Warps: Einstein's Outrageous Legacy

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Relativity consists of special relativity (SR) and its generalization general relativity (GR), which includes gravity.

In SR, the history of an object is described by its world-line through spacetime. Every event has future and past light cones, and a material object such as a person's body is limited to "traveling" from the past light cone to the future light cone. Therefore you can't have a world-line that forms a closed loop. A world-line such as a material object's that always stays inside the light cone is called timelike.

In GR the situation is considerably modified. GR allows the existence of closed timelike curves (CTCs), which, although timelike everywhere, nevertheless close back on themselves. To conceptualize this, you can imagine drawing an ordinary timelike world-line on a piece of paper, but then wrapping the paper up into a cylinder. As far as we know, our universe doesn't contain CTCs, and there is no natural or artificial process that could create them. If the universe doesn't already contain any CTCs, then it's believed (Hawking 1992) that creating a new CTC from scratch would require exotic forms of matter (essentially, matter with negative mass). Even if one did have access to exotic matter, creating a CTC would require manipulation of matter on a godlike scale.

Hawking, S.W., (1992) The chronology protection conjecture. Phys. Rev. D46, 603-611.