Can you direct me to a more simplistic explanation of how FTL allows Time Travel, and the Light Cone concept

Question

I keep seeing questions about FTL, and explanations about how in a Hard-Science setting FTL doesn't work, or if it did it would allow time travel.

Most of these go way over my head.

Even the Wikipedia article on "light cone" was hard for me to follow.

Can someone explain it in more simple terms, or point me to a good primer/explanation?

Also, the FTL-Timetravel argument; I'm basically reading this as, if I travel via some instantaneous method to the Sun (8 light minutes away), then turn around and immediately travel back to Earth the same way, I arrive 16 minutes before I left. Is this right? Is this the argument?

Answer 1

if I travel via some instantaneous method to the Sun (8 light minutes away), then turn around and immediately travel back to Earth the same way, I arrive 16 minutes before I left. Is this right? Is this the argument?

No. The return time can be anything. In the single-reference-frame concept or other non-causality-violating relaxation of that, you will arrive after you left, never before.

You can understand this from the most basic beginning of a tutorial on your main question. Draw a graph with one spacial dimension, x, horizontally, and time vertically so up is +t.

Draw two vertitical lines represending earth and sun at rest relative to each other (the actual motion is too small to see on this scale where the separation of your lines, say 8 inches, is 8 light minutes, and the vertical scale is 1 inch per minute).

Draw a light cone (as noted on some of my illustrations) as 45° angles. Normal motion would be a line moving upwards at a lean away from the vertical. Think about it: plot you position at each time. The speed of light is the diagonal cone. Light travels along the cone, upwards left or right. Normal motion stays inside that cone. You never move as fast as light, in either x or −x directions.

Draw a line outside the light cone. That is an FTL track. If you are at Earth at t=0, you can see that a light ray would connect that point to the sun's position at t=8 minutes. Matter movement is at a more vertical tack and thus intersects the sun's x position at a later time.

Now connect a line from the starting point (x=0=Earth, t=0) to (x=8=Sun, t=4). That line indicates your position at each point in time and is a ftl track.

Draw a line from (0,0) to (8,−3). That is also a ftl track (as it lies outside your light cone) and goes back in time.

Looking at just 1 reference frame, the x vs t plot is a perfectly understandable graph.

The hard part is plotting other reference frame’s axes on the same drawing. Then, the understanding that whether the ftl track is pitched up or pitched down depends on your reference frame and is not an absolute thing.

That's the rub: any chosen ftl transit can be measured as travelling into the future, simultanious, or into the past, depending on the observer’s relative motion.

Answer 2

Let's start with the standard scenario for the relativity of simultaneity:

The starting point of everything is the postulate that the speed of light does not depend on the frame of reference.

Now consider a train station. On one end of the platform, there are stairs, while on the other end there's just a wall. Exactly in the middle of the platform is a lamp. When the lamp is lit, the light moves away from the lamp with light speed. Since the lamp is in the middle of the platform, it reaches the stairs and the wall at the same time. Nothing unusual yet.

However, now consider a train going through the train station, entering from the side of the wall. It doesn't stop, but just goes through with constant speed. And it does so just as the lamp is lit. For an observer in the train, the light again travels at the speed of light. But the platform is also moving as well. Therefore the light has to play catch-up with the wall, while the stairs are approaching. Therefore obviously the light will arrive at the stairs before it will arrive at the wall.

Therefore the events "the light reaches the stairs" and "the light reaches the wall", which happen at the same time for the observer on the platform, happen at a different time for the observer in the train.

In particular, if the observer in the train has a device that can send FTL signals, he can use that to send a message from besides the stairs when the light arrives there, and have it received later besides the wall when the light reaches the wall.

Now let's add another train going in the opposite direction. Of course the same argumentation applies also for that other train, but since it is going in the other direction, it's now the stairs that the light has to play catch-up with, while the wall is approaching. An observer in that train will therefore find that the light reaches the wall before it reaches the stairs.

Now consider again the FTL signal above. That FTL signal was sent when the light reached the stairs, and was received when the light reached the wall. But for this observer, the light reached the stairs after it reached the wall. Therefore the FTL message was sent to the past.

And of course, if that observer has a FTL device, too, he can send a signal from the wall event to the stairs event. Indeed, if he sends a bit faster, he can even send after the light reached the wall, and have it arrive before the light reached the staircase. Which allows him to react to whatever was sent with the first FTL signal.

But if the signal arrives on the stairs before the light does, it especially means it arrives before the original signal was sent from there. So we have a manifest causal loop, as the observer in the first train could now react to the response to his message before he sends the message.

To make that into a full-blown time travel, you only have to have a person instead of a message do the two FTL travels, and have the person change trains (which needs only ordinary sub-light acceleration). Obviously the time is too short to do that with the trains, but with spaceships and interstellar distances, that would be completely doable.

Answer 3

I suggest trying this article "The Graphic Demise of FTL" by G David Nordley at his website and it is in PDF format. So you can download it to study at your leisure.

What is good about Gerry's article is that he lays the groundwork by explaining the basics of special relativity before tackling the relativistic paradoxes arising from faster-than-light events.

Don't expect the answers to be obvious. Take your time and try to understand one bit at a time.

The question you ask about travelling to the Sun with an instantaneous FTL drive should be straightforward and easily answered. I haven't seen anywhere where someone has calculated or shown how the calculations are made to work out the time for a FTL vessel to travel from one place to another and back again. If this puzzles you, take heart you are not alone.