How does a tachyonic antitelephone work?

Question

Based on my current knowledge on physics (which is not a lot), a tachyonic antitelephone is a hypothetical device that will allow information to travel back in time, created based on the theory of the tachyon which is a hypothetical faster-than-light particle. But then I was extremely confused by the concept of sending a signal to your own past. To send a signal to the past the speed of the particle must exceed infinity. A particle at infinite speed could send a message to anywhere in the universe which no delay at all, but to make the delay into a negative number, the speed of the particle will need to travel faster than infinite which as we know is impossible. So the part that I'm confused with is that since the speed of light is finite, then if the particle is faster than light but slower than infinite, how is it possible to send a signal to the past?

Sorry for the inconvenience, I'm just a random 4th grade kid trying to learn basic physics, sorry if this doesn't make any sense.

Answer 1

Welcome to physics.SE!

I think the key to clearing this up is the following. Suppose that infinite speed would be necessary to travel from event A to event B at infinite speed. This is just another way of saying that events A and B are simultaneous. But in relativity, simultaneity is relative. That is, observers in different states of motion don't agree on what is simultaneous.

I don't know if you're familiar with spacetime diagrams (=Minkowski diagrams). If not, then a good book to check out is Takeuchi, An Illustrated Guide to Relativity. On this type of diagram, the tachyonic antitelephone looks like this:

In this type of diagram, forward in time is toward the top of the page, while the directions to the left and right across the page represent space. If this was Newton and Galileo's version of the universe, then lines of simultaneity would all be parallel to each other, and we would then probably choose to orient the paper so that such lines were directly horizontal. But in Einstein's version, observers don't have to agree on simultaneity, so lines of simultaneity can be non-parallel, as in this diagram. Takeuchi does a nice job of presenting these diagrams, including important ideas like the light cone.

Observer 1 sends a signal from A to B, at a speed that seems instantaneous to her. Then observer 2 retransmits the signal from B to C, at a speed that seems instantaneous to him. The result is that 1 gets receives her own signal in the past, before it was sent.

Now according to observer 2, the signal from A to B does go backward in time. However, according to 1 it's not backward in time, it's propagating at infinite speed. Because of these disagreements, it's not really useful to talk about speeds for these faster-than-light signals. In special relativity, we talk about speeds only for things that go slower than light.