Now do it twice.

Maybe I'm completely misunderstanding you or the problem - feel free to correct me, please. I'd really like to understand how causality is broken by FTL but could never grok it.

The phrase "at the same time" means different things in different inertial reference frames. So what is FTL to one observer, is traveling backwards in time to another. If you can warp from any reference frame, you can therefore travel backwards in time.

As for why "at the same time" changes meanings, let's adapt Einstein's example.

I'm in the middle of a moving train. You're on the train station. As we pass, lightning strikes right between us. Will the light from the lightning arrive at both ends of the train at the same time?

According to me, obviously. In my reference frame the train is not moving. Light has a constant speed. It will reach both ends at the same time.

According to you, obviously not. Light travels at constant speed, but the train is moving. Therefore the back of the train is moving towards the light, and the front is moving away. So the light gets to the back of the train before the front.

So when the person on the train says that an event in front and behind happened at the same time, the person not on the train says that the event behind happened before the event in front.

Now consider this. I'm on a spaceship with a warp drive. This is a great warp drive, travels instantly in whatever reference frame I'm in.. I warp forward a long distance - like a light year. I accelerate forward. I warp backwards and arrive back a bit behind where I started at. I decelerate, and I'm in my own past!

That's the causality problem.

You left out the "accelerate forward" bit. That changes your reference frame. Without changing your reference frame, you don't get FTL to turn into time travel.

If you have FTL but on a time scale determined by one reference frame, then as I pointed out in https://news.ycombinator.com/item?id=37012594, no causality issues exist. You need FTL in 2 reference frames to create a closed time-like loop.

So it becomes complicated. But as long as FTL goes forward in time by some unique global definition of time, there is no causality problem.

A warp drive that only works against the fixed reference frame of the distant stars introduces no causality issues.

Physics doesn't have privileged frames of reference.

As for not having privileged frames of reference, that doesn't stop interactions with your environment from mattering.

For a trivial example, "at rest" is a privileged frame of reference for you. If you start moving in a different frame of reference you'll encounter weird things like "wind".

For a non-trivial example, the Standard Model says that there is no privileged ratio of masses between the electron and the proton in the laws of physics. The actual ratio of masses is set by an interaction with the part of the environment known as the Higgs field.

Astronomy shows that the fixed reference frame of the distant stars is environmentally privileged. It is also somewhat privileged physically as well. For example Mach's principle (see https://en.wikipedia.org/wiki/Mach%27s_principle if you don't know it) says that we notice we are rotating when we are rotating relative to that reference frame.

We know of no way to react to this feature of our environment and get from here to there faster than the speed of light. But there is no fundamental principle of physics that we know of which says it is not possible - we just have no clue how it might happen.

And I have no idea why you don't notice that this is moving fast. That's the irony.

https://en.wikipedia.org/wiki/Alcubierre_drive shows that this is, in principle, not a violation of general relativity. But that drive depends on finding something with negative mass. Most physicists don't think that that can be done. (But the phenomena of extracting zero point energy with the Casimir effect holds out a slender ray of hope for cranks who think that they have done it.)

So it isn't that I didn't notice that something was moving fast. It is that I know that the idea is to get from here to there by doing something other than moving.

I think that this is a semantic distinction without any practical difference.

What you think doesn't matter.

General Relativity says that the Alcubierre drive would work if you could find a source of negative mass. It can get a vehicle from here to there, outside of its light cone. And yet that's not game over.

That's not a word game. That's mathematics applied to our best model of how space-time works.

If you want to imagine it, imagine ants crawling on a balloon. Motion is their crawling. But now start blowing up the balloon as it crawls. Distances are changing, and it isn't the ant doing it! Think this is unrealistic? The current model of the Big Bang says that things we see from 13.7 billion year old light are now 47 billion light years away from us. Our naive ideas of motion can't explain that. But general relativity does, and it is exactly parallel to the ants on a balloon image.

Now imagine coming along, pinching the balloon, having the ant walk over the fold, then unpinching the balloon. The ant got from here to there faster than it could possibly walk! That's the idea of a warp drive.

Is it possible? Probably not. But we know of nothing that forbids it other than the fact that we can't figure out how to do it.

> It can get a vehicle from here to there, outside of its light cone. And yet that's not game over.

It's time travel, so game over for causality. You're fixated on the details of how you get there, and it is irreverent.

> if you could find a source of negative mass. It

Word games with imaginary numbers.

No, it isn't necessarily time travel.

See https://news.ycombinator.com/item?id=37013305 for my presentation of the standard argument that FTL leads to causality violations. Note that you need it to be FTL in more than one reference frame to do it. That's why, as I pointed out in https://news.ycombinator.com/item?id=37012594, FTL only in the fixed reference frame of the distant stars does NOT lead to causality violations.

Again, we have no reason to believe that this is possible. But if it were possible, the standard objections would not apply.

Word games with imaginary numbers.

No, that's tachyons. This one was just negative numbers.

Of course there are other scenarios where you can get backwards signaling. But some recent papers showed that in these cases, were they possible, then events would arrange themselves to be consistent overall, even though some events have causes from their futures.