If you "instantly" teleported to alpha centauri, then there would be a frame of reference in which you arrive before you left. To another observer, you would travel back in time. It's not something you can disagree on. Instead, convince yourself by studying the spacetime diagram: http://www.physicsmatt.com/blog/2016/8/25/why-ftl-implies-ti...

Note that "instantly" is ill-defined in SR. Simultaneity of events is observer-dependent.

Edit: this is also known as the tachyonic antitelephone. It's described here: https://en.m.wikipedia.org/wiki/Tachyonic_antitelephone

Instead of warning about shrimp you could easily tell your past self to buy a certain stock.

> If I instantly teleported to Alpha Centauri, that wouldn’t put me in the future.

If the teleport is using a wormhole - a device which connect two points in space - we can consider this.

We have experimental confirmation of time dilation, if we have an accelerated motion. In other words, let's make the wormhole entry on Earth move for some time so that its time is behind, say, by 10 years from the Alpha Centauri.

Then, if you instantly teleport to Alpha Centauri by stepping from Earth into the wormhole, the time at Alpha Centauri is 10 years before. You may use, say, 7 years to fly back to Earth through "ordinary" space, with sub-light speed, and you'll arrive to Earth 3 years before you left.

True teleportation would not hit the same limits. The idea is, in conventional travel, your velocity has a time and space component that are hard linked, the faster you are traveling through space, the slower you are traveling through time. The speed of light is the maximum speed you can travel through space, because you've run out of the time component you must take away from to get a larger spatial component. An object that has a spatial speed greater than the speed of light must have a negative time component, aka traveling into the past, which under current understanding isn't possible.

It doesn't really make sense until you grok how relativity thinks of events and "observing" them, and then stare at the relevant spacetime diagram for a while.

Note that the time when the light arrives from (in your scenario) Earth is not the same as "observing" it; observing is a much stronger sort of hypothetical measurement, more like assembling all the evidence in retrospect and deducing a consistent physical story. That's the story where, if stuff is moving FTL, you start seeing cause and effect reversed.

Ed: the key difference between c and your hypothetical speed of sound is that light is the same speed no matter how fast the observer is moving. Two observers both have to see a laser moving at c, even if A also sees B moving in the same direction at c/2. With your example, B can actually see the relative speed of an object moving at s as s/2.

You could do something on Alpha Centauri, instantly teleport back, and then make a bet on what’s going to be observed in 4 years time.