How is that not the same thing? You cant even get to lightspeed if you have mass.
Well, within spacetime it is, but there’s (perhaps) ways around that – like the aforementioned Alcubierre drive, where you take your bubble of spacetime with you, relative to which you move very slowly (if at all), any sort of traversable wormhole, or something known as a Krasnikov tube.
And in a sense, there are velocities that exceed the speed of light, even without invoking any exotic spacetime metrics – those of extremely far-away galaxies receding from us, thanks to the expansion of the universe.
In principle, I believe it’s also the case that general relativity allows for tachyonic solutions, which can’t travel slower than c, only approach it ‘from above’ the same way ordinary matter can approach it ‘from below’; however, quantum field theory pretty much just doesn’t work when you allow for such things.
That said, though, generally, you’re right about anything with (real) mass not being able to exceed (or even reach) c; even infinite energy wouldn’t help you out here.
While seriously considered time travel methods seem to be impossible as a practical matter (colossal amounts of energy, negative matter, etc.) I do not think science has completely tossed out time travel as an actual impossibility as far as the laws of physics are concerned.
FTR Kip Thorne is a very respectable physicist and not some crackpot.
BTW…
IF (note the big “if”) you can build a traversable wormhole then you have a time machine at the ready. Simply put one end of the wormhole on a spaceship and fly it around at relativistic speeds while the other end of the wormhole stays here on Earth. After flying around a bit the ends of the wormhole will be situated at different points in time. Jump through to go back and forth into the future/past.
Note this method would explain why we do not see time travelers now. They could only go back in time to the point where the WH was created. You also could not dial in intermediate stops. Only go between the two “fixed” points of the WH.
Yeah, the thing to remember is that we’re all traveling through time already. And relativity teaches that we can even travel through time relative to other objects and people as long as we’re moving the right way. The difficulty is in going backwards through time and in going to the future (faster than normal) without having to go warp speed. There is also the question of reversibility.
So I don’t think you can say time travel is an impossibility. At most, going backwards in time is an impossibility, but our physics isn’t really advanced enough to say. The rest is just an engineering problem.
I just remembered about Ronald Mallett, who’s proposing a time machine using a ring laser; however, there appear to be several problems with this proposal.
“Very respectable” is an understatement. I would argue that he’s the greatest theoretical physicist in the world right now, or at least pretty darned close. Of course, he doesn’t spend all of his time on time travel; mostly lately he’s working on gravitational waves.
To sum up the current state of knowledge concerning time travel (by which I mean closed timelike loops, not just mundane things like traveling into the future at varying rates):
According to Special Relativity, time travel is exactly equivalent to FTL. Any device that can get you from Point A to Point B before a massless particle could get there through vacuum could also be used for time travel, or vice-versa. This is true regardless of what the method is, be it warp drives, hyperspace, wormholes, or magic carpets.
Also according to Special Relativity, it’s impossible to accelerate a normal object with real mass up to speeds greater than c, since that would require an infinite amount of energy.
Special Relativity does not, however, rule out the possibility of particles with imaginary mass, called tachyons, which would normally travel at speeds greater than c, and which would require an infinite amount of energy to slow them down below c.
However, if tachyons exist, they can’t interact in any way with normal matter, and there isn’t even a sound theoretical reason to suspect they exist, so we might as well assume they don’t.
Special relativity also does not rule out the possibility of means of getting from Point A to Point B that do not involve actually accelerating up to a speed. So you might still have something that can “jump” faster than light, or into the past.
General relativity can describe a number of hypothetical situations which do in fact allow means of producing an FTL or time travel effect without violating anything in SR.
However, all such scenarios known, and it’s believed all such scenarios, either require the existence of matter with negative mass, or for the entire Universe to be constructed in a way which is manifestly different from the Universe we observe. Negative mass has never been observed, and there’s good reason to believe that if it were possible, it’s be easy to produce.
And finally, no matter how you contrive your time travel, time travel inevitably leads to the possibility of paradox, and nobody has yet found a way to rigorously deal with such paradoces.
How does that jibe with what Thorne said:
“Recent calculations by Thorne indicate that simple masses passing through traversable wormholes could never engender paradoxes — there are no initial conditions that lead to paradox once time travel is introduced. If his results can be generalised, they would suggest that none of the supposed paradoxes formulated in time travel stories can actually be formulated at a precise physical level: that is, that any situation in a time travel story turns out to permit many consistent solutions.”
Well ok…that is Wiki with all the caveats about relying on Wikipedia but assuming that is largely correct what is Thorne saying there?
It’s impossible, or at least, it takes infinite energy to accelerate mass past light speed, but there is nothing preventing something from already being past the speed of light. And there’s nothing preventing space itself from going FTL, it already does - the universe itself expanded FTL - so if you could form a ‘warp bubble’ within which the ship didn’t accelerate, the bubble itself could travel FTL.
There are a lot of theories that permit time travel but they all involve insanely large masses or energy, or require X factors that we have never observed like exotic mass.
Is that the billiard experiment? I think the gist of that was that if you created a stable time wormhole, and tried to send a ball through to knock itself in the past out of the way of ever entering the wormhole that there was no way to do it - it would always knock itself back into the wormhole. Not sure how that would translate into more complex paradoxes though.
Paradox: how alternate timelines start.
I confess that I skimmed over the quote before, since I though I knew what it said. I wasn’t aware that he had done those calculations-- I’ll need to read up on them.
(snip)
Thanks Mark. That’s good, sound logical thinking. If Calvin (and Watterson) says so, then it HAS to be true! 
Just remember: don’t kill Hitler.
That’s good.
Yet another argument for domestic oil exploration and drilling.
Just making sure I’m not missing a subtle point here. Chronos, did you mean “it’s impossible to accelerate a normal object with real mass up to a speed equal to c (or greater)”
Correct, accelerating a massive object up to c also takes an infinite amount of energy. But you’d have to accelerate to c before you could accelerate past c.
I am far from an expert here. I think Kip’s jist is that the paradoxes are resolved if you allow the ‘future’ to ‘influence’ the past. For example if you send an object through a wormhole and then immediately send it back from a nearby one so that it intercepts itself something will happen to make it not deflect itself completely. If you push it to say, make it a contact bomb then what would happen is that you would shoot this bomb to the first wormhole and then you would see a bomb fragment emerge from the second…hit the initial bomb so that it explodes and a bomb fragment will go through the first hole…which will return and blow up the bomb.
It is a consistent turn of events and creates no paradoxes. It seems more like the ‘time police’ but without actual entities.
That’s easy enough to say for billiard balls and bombs, which can have a continuum of different states, but it’s considerably trickier for quantum systems which genuinely have two and only two possible states. I’ve dabbled a bit in the question myself, but I’m sure that Kip has done more than dabbling on it, and has actually approached the question rigorously. That’s what I’d like to look up.
Yes, look it up…I probably butchered it and too simplified it.