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**by Robert Nemiroff Michigan Tech**

Time Travel II by Robert Nemiroff Michigan Tech

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**Physics X: About This Course**

Officially "Extraordinary Concepts in Physics" Being taught for credit at Michigan Tech Light on math, heavy on concepts Anyone anywhere is welcome No textbook required Wikipedia, web links, and lectures only Find all the lectures with Google at: "Starship Asterisk" then "Physics X"

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**Time Travel: Machines Extending Conventional Physics**

Time travel might be allowed using: Faster than light (FTL) movement or information transfer Unusual cosmologies Black Holes Cosmic Strings Wormholes Alcubierre drive

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**Time Travel Mechanism: Faster than Light Travel (FTL)**

Alice flashes her light. When Bob sees that light, he flashes his light. All observers moving slower than the speed of light will agree that Alice flashed her light first.

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**Time Travel Mechanism: Faster than Light Travel (FTL)**

Alice flashes her light again. Before Bob sees that light, Bob flashes his light. Although no information was transferred, a flash signal went from Alice to Bob faster than light. Some observers will think that Bob flashed first. Some observers nearer Bob, for example. This "signal" would appear to them to move backward in time. Cause and effect cannot be universally established.

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**Time Travel Ideas: Faster than Light Travel (FTL)**

Alice flashes her light again. Before Bob sees that light, Bob flashes his light. Extending this scenario, it appears possible, somehow, that Alice sees Bob's light flash BEFORE Alice was going to flash her light. This shows that FTL communication allows backwards time travel.

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**Time Travel Ideas: Faster than Light Travel (FTL)**

Mass cannot be accelerated from slower than light to faster than light. That would take an infinite amount of energy. Perhaps, though, mass can be created moving FTL and always remain such.

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**Tachyons particles that move faster than light (FTL).**

violate causality can no longer know what causes what will strike you before you see them. will see two images of a tachyon that just passed you one moving away from you in the direction that the tachyon approached one moving away from you in the direction that the tachyon is moving away

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**General Relativity: Spacetime Intervals**

Two events happen in spacetime. They are separated in space by dr and in time by dt. Time-like interval One event can affect the other c dt > dr Space-like interval One event cannot affect the other (without backwards time travel) c dt < dr Light-like interval Light from one could affect the other c dt = dr

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**General Relativity: Spacetime Motion**

Two events happen in spacetime. They are separated in space by dr and in time by dt. Closed timelike curve (dr = 0; dt < 0) A curve that comes back to the same spatial point at an earlier time closed timelike curves allowed in GR allows (backwards) time travel need other physics to disallow?

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**Time Travel: Cosmologies with closed time-like curves**

Godel gave Einstein a "present" of a cosmological solution to General Relativity that admits simple time-like curves. Objects traveling on these curves would go back in time, and could arrive at their starting points before they left.

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**Time Travel: Wormholes**

Generic example: a black hole connected to a white hole through a "shortcut" in space. Generic simple wormholes would kill anyone who entered by compressing them to infinite density. Traversable wormholes might exist but are controversial. They would have two ends -- a traveler goes in one end and appears "instantly" on the other end. Some type of dark energy is thought needed. This also allows FTL communication.

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**Time Travel: Wormholes**

Moreover , were one end of the wormhole brought near a black hole (for example), then time would run more slowly for the black hole end than for the non-black-hole end. As time (as measured by an observer far away) progresses, the two ends could get years out of synch. The two ends could then be brought close together. Going in the non-black hole end of the wormhole and coming out the once black-hole end would take an observer only a brief time on the traveler's watch. But they would come out years in their own past -- time travel!

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Wormholes A "shortcut" through spacetime. Also known as an Einstein-Rosen Bridge.

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**Time Travel: Tipler Cylinder**

A solution to GR near an infinitely long massive cylinder. If spun fast enough, the cylinder will cause frame-dragging in such a way that accelerating through that region allows a closed time-like curve, and hence time travel. No singularlities or black holes are involved! Unfortunately, the cylinder must be infinitely long (in present understanding.

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**Time Travel: Alcubierre drive**

A GR attempt to create a real "warp drive." A GR metric is envisioned that describes a bubble of spacetime that moves with a ship. Time dilation acts around this bubble, which could make it move faster than light when compared to distant observers. Inside the bubble, motion is slow, and nothing moves FTL. Physics is controversial. One might need negative-energy like localized dark energy. At best, one might need a tremendous amount of mass to get this to work. At worst, one could not communicate with the front of the bubble, and the hot Hawking radiation would be deadly.

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RELATIVITY TOOLKIT Time Dilation: t(v) = [1/(1 – v 2 /c 2 ) 1/2 ] t(0) Length Contraction: d(v) = (1 – v 2 /c 2 ) 1/2 d(0) Change in Synchronization:

RELATIVITY TOOLKIT Time Dilation: t(v) = [1/(1 – v 2 /c 2 ) 1/2 ] t(0) Length Contraction: d(v) = (1 – v 2 /c 2 ) 1/2 d(0) Change in Synchronization:

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