Time Travel

If it ever becomes possible to travel at an infinite speed or to make a hyperspace jump instantaneously to some other point in space, then time travel can be accomplished. This conclusion follows immediately from the relativity of simultaneity.

If a person travels at an infinite speed or makes an instantaneous hyperspace jump to some other point in space, his time of departure and time of arrival are simultaneous in some frame of reference. But what is simultaneous in one frame is not simultaneous in another. Therefore, the same hyperspace jump that is simultaneous in one frame will be time shifted in another frame. This time shift can be backward in time just as easy as it can be forward in time. And by making two hyperspace jumps in two different frames of reference, a person can return to his place of origin prior to his departure.

Suppose, for example, that a person installs a hyperspace jump engine into a spaceship. Then he makes a hyperspace jump instantaneously to a point in space located 100 c y (light years = speed of light times one year) away. Then he accelerates the spaceship away from the earth to a speed of 0.6 c. In his new frame of reference the earth is moving away at a speed of 0.6 c y at a contracted distance of 80 c y, and time has shifted Dt = vDx/c² = 60 y into the past. By making a second hyperspace jump instantaneously back to the earth, he need only match speeds with the earth and land, physically arriving 60 y before he left. From that time forward, he can explore all kinds of time travel paradoxes. For example, he could imprison his younger self before he makes the trip, thereby preventing himself from ever doing what he has already done.

The only way to avoid such paradoxes in relativity is to prohibit infinite velocities, hyperspace jumps, and instantaneous teleportation.

Problems:

P1. Time Travel

A spaceship leaves the earth traveling at half the speed of light. It then makes a hyperspace jump instantaneously backward and beyond the other side of the earth a distance of 100 light years in its own frame of reference. When it comes out of hyperspace it decelerates to a stop relative to the earth and then makes a second hyperspace jump instantaneously back to the earth. (a) What will be the distance of his second hyperspace jump? (b) At what time will he arrive back on earth?

P2. In the year 3000 AD, after hyperspace travel has been perfected, a spaceship makes a hyperspace jump instantaneously from the earth to a planet 1000 light years away. Then the pilot quickly accelerates the spaceship to 0.8 c away from the earth and makes a second instantaneous hyperspace jump back to the earth. What does the earth calendar read when the spaceship gets back to earth? (A) 2200 AD (B) 2800 AD (C) 3000 AD (D) 3200 AD (E) 3800 AD.
A 5153211

ModPhy1/Unit1/SpecialRelativity/RelativeView/Time/Simultaneity/Causality/