Ultimately, Special Relativity is based on observation. The only means we have to observe anything comes down to EM, which propagates at c (in a vacuum). Note how every description of SR talks about “an observer” and “another observer, over here”. I can imagine that FTL could fail to violate causality but exceed our ability to observe it. If I got in the magic ship, flew to VY Canis Majoris, and got there next week, it would still be next week, not some time in the past. I would be observing things happening there next week, and when I got home next month, I could tell everyone about events that we would be able to observe here in about 156 generations from now, but I would not in any way have violated causality.
This reminds me of a question that popped into my head when New Horizons arrived at Pluto.
The press would report that the radio signals were arriving at Earth about half a day after being transmitted at Pluto. By this reckoning, the probe had already sailed past Pluto before we got the news.
I wonder if the more correct relativistic viewpoint is that (in our frame of reference) the Pluto flyby AND our receipt of signals of the flyby are simultaneous. (Please forget that the probe was too busy with the flyby to call home during that process for the purposes of this question- pretend it had lots of watts and antennae and whatnot and had stayed in touch without breaks.)
No, and in fact there is no way for two events that are separated by a time-like interval (one in which there is a measureable path length that can be traversed by an observer in an inertial frame of reference moving at less than c) to be said to occur simultaneously. Only from the frame of reference of a photon travelling from New Horizons to Earth, moving at c (and thus, travelling on the null or ‘light-like’ interval) do the events (and all other events it will ever ‘experience’) occur simultaneously with respect to time.
Stranger
But you’re only thinking about causality in your own frame of reference.
If you were able to travel to VY Canis Majoris in only a week, then there would be at least one inertial reference frame in which you arrived before you left. According to relativity, all IRFs are equally valid. But you described a situation in where you violated causality in some IRFs but not others. So, either it’s NOT true that all IRFs are equally valid, or we have to live with the fact that an effect can precede its own cause and there goes causality.
If Voyager is anything to go by going past warp 10 results in freaky salamander sex.
Thanks for the replies all, fascinating reading.
That is where the problem is. When you start talking about “what time is it right now on VY Canis Majoris?”, the answer is dependent on the frame of reference. When you say “next week, at VY Canis Majoris”, you mean that statement to mean “next week, at VY Canis Majoris, as reckoned in a reference frame that is stationary relative to Earth”. There are other reference frames in which that same moment in time is far in the future, or far in the past.
IIRC Special Relativity permits some exceptions and/or loopholes to the speed of light speed limit.
One of them is that the limit applies only to entities which possess mass, and tachyons are thought to be massless, so SR is not violated by tachyonic superluminal speed.
Another exception: space as a whole is exempt from the speed limit (I think that is the right way of putting it). That exception enables the theory of the Inflationary early universe, when space is considered to have expanded at a rate far in excess of c.
Presumably that’s how Alcubierre drive could achieve FTL speeds without violating modern physics.
How fast would a change in the past ripple to the future? For example, today I send a poisoned lollipop 40 years in the past to my room where the kid version of me eats it and dies. Would that change take 40 years to reach today, by which time I’ve aged another 40 years? Or would it instantly affect me?
Like if I’m traveling down the river in a boat and just as I approach some marker, I throw a bomb backwards which dams the river. It doesn’t yet affect me or the river at the marker. After some time there will be no water at the marker, but by that time I’m further down the river. If I don’t look back, I may never realize anything has changed about the river. I may only notice the change if I actually go upstream and see that there’s no water in the river.
Or would the change be more instant, where as soon as I threw the bomb all the water in the river downstream from the dam was instantly gone and my boat would fall through the air to the riverbed?
Masslessness isn’t really a loophole – massless particles travelling faster than light still violate causality.
Note that tachyonic fields, rather than creating actual tachyons, undergo tachyon condensation to become non-tachyonic fields.
There is no sensible answer to that question which is why physicists like to assume that a rigorous causalilty exists and is enforced (the chronology protection conjecture) even if there are theoretical means by which a closed time-like curve could exist it either could not be formed or an object on the path would not be able to exit without coming back to the starting point.
Some (at least in fiction) like to point to the Everett-DeWitt Relative State/Many Worlds interpretation of quantum mechanics as offering the possibility of “branching” into a different universal quantum state, but there is zero evidence or even credible conjecture that this is how an alteration in time resulting from a closed time-like curve would or could work, or indeed, that there is any way for an observer to change between states at all, as the observer has to be considered as part of the state he is embedded in.
Stranger
Only particles travelling at the speed of light can have zero mass, but non-zero energy. Technically though you’re not incorrect as there is nothing forbidding free zero-energy particles travelling at above c, but such particles by their own definition don’t exist as they don’t have any means to affect any other particle.
If a tachyon has real mass, then its energy is imaginary, if it has imaginary mass then its energy is real (and negative). When talking about tachyons the former possibility is often excluded.
The expansion of the Universe isn’t measured in units of speed, but recessional velocity (as a result of expansion) is, and indeed recessional velocities can exceed c (not just during inflation).
The Enterprises and all the other spacecraft didn’t travel faster than light. They squeezed space with giant clothes pins and hopped over the folds.
So no infinitely large ships and hewmans, no time paradoxes and no alternative universes.
Contracting space is still effectively travelling faster than light with the same attendant paradoxes and requiring negative energy density that (probably) cannot exist at the macroscopic scale without creating other novel violations of general relativity. Multiply connected spaces (wormholes or ‘folded space’ or whatnot) is not technically a violation of general relativity per se, but models that don’t assume a smooth, simply connected Lorentzian manifold give nonsensical answers, hence the assumption that naked singularities and other topological defects have to be hidden behind a space-like horizon. Being able to jump from one locale to another “instantaneously” (as measured in any single inertial frame) gives the same result as actual time travel.
Either the science fiction conceit of superluminal transit is purely fictional magic, or the universe is much, much stranger and horrifically unpredictable than we can concieve on a fundamental physical level. However, that is exactly the conclusion one comes to when considering behavior at the quantum level, so there is still much wierdness to explore before anyone starts prematurely declaring that we are at “the end of physics”.
Stranger
There isn’t even a sensible question to that question.
“Technically though”? I did not say anything incorrect or misleading, so leave out the disguised snark. The rest of the your comment above is a welcome elaboration, however. Congratulations on being useful.
Saying that recessional velocity is measured in units of speed is tautological.
Furthermore, the discinction you make is not made by this Cornell astrophysics site:
How fast is the Universe expanding?
and is not made by this Harvard astrophysics site:
It is therefore reasonable to doubt the need to make such a distinction at all.
Thank you for the information.
I thought “Alcubierre” must be one of those tiresome Star Trek references, but it is interesting real McCoy science.
McCoy science is one variety of Star Trek (TOS) science (often at odds with Spock science).
I meant that TFTL was what needed a loophole.
Aaaargh!!!