The consensus interpretation is that FTL is not possible in normal space, since the speed of something is just another way of looking at how "fast" it travels through time - FTL becomes impossible by definition.
However, there is reason to assume a lot of things may be going on that are not strictly speaking taking place in normal flat space.
The article mentions the expansion of the universe as an example, and that's actually a good point to start. By virtue of the universe expanding, the distance between points grows faster than the speed of light as long as those points are sufficiently far apart. This becomes more interesting when you realize that new space in between these points is being created. Sure, the galaxies traveling on this expanding medium are not actually speeding apart powered by classical movement, but they are nevertheless changing position relative to one another in an interesting way.
In fact, what we're interested in when we talk about FTL is not classical movement at all - what we want is to change positions instead. There are places in nature where we know this is happening right now, for example we do know space can "flow" faster than the speed of light on the far side of event horizons.
So if we abandon the idea that we need to accelerate towards a destination, FTL becomes a broader idea of manipulating spacetime in order to be somewhere in less time than if we had actually flown there at the speed of light. There exist proposals for propulsion systems that go in this direction, for example the "warp drive" ideas that cheat by simply shortening the amount of space a vessel has to travel through. Some of these concepts seem to work in theory, for some definition of work.
The trouble with all these ideas is they need impractical amounts of energy. Which is wasteful, since we only need to bend spacetime for a short while and then return it to its original state behind us, something that works analogous to a catalyst would be much better.
At the most fundamental level though, what we are missing is a way of hacking spacetime. Huge masses and energies are how nature bends it, but ideally we would need some other way of manipulating the fabric of existence directly. This is the reason why drive systems in science fiction all have some kind of yet-unknown mystery substance critical to their function. Given how little we actually know about the basic fabric of the universe, ways of doing these manipulations may well exist. They might not. We most likely won't find out for centuries, if ever.
Until then, we must answer the question so that yes, FTL is most likely possible in theory, but it's not even remotely within our grasp right now. It might never work in practice.
Another observation worth considering: cosmic travel times seem utterly problematic right now because we individually live for extremely short periods of time. Spending a few thousand years in transit is much less worrisome if you're, say, an autonomous machine carrying an AI through the galaxy.
We in the west are a bit too obsessed with moving fast.
What do we call a common trick in fantasy and SF that allows someone or something to move large distances in a short time? Teleportation. Spacetime stays the same, you just move through it very fast, whether physically or electronically.
By contrast, fantasy tales in China, Japan, and Korea, both modern and traditional, often show the protagonists practicing shukuchi [1], a trick that literally means "reduced earth" or "compressed land". Space is shrunk, and then you move through the shrunk space at a normal speed. It's basically warp drive, but imagined at least a thousand years before Star Trek. The guru's eyelashes don't even blow in the wind because, after all, he's just walking at his usual pace.
A change of paradigm indeed opens the door to a lot more possibilities, at least in theory if not in practice.
Quite a lot of our Sci-Fi's "FTL drives" are actually "Jump Drives". Take, for instance, Battlestar Glactica. They don't move through space, they jump to a new place within it.
> The consensus interpretation is that FTL is not possible in normal space
I don't think this really makes sense, because "normal space" is not a well-defined term.
What our current relativistic theories say is that spacetime contains a causal structure marked out by light cones, and nothing can move outside the light cones. In certain spacetimes (like the one that describes our expanding universe), it is possible to assign coordinates to events so that it looks like objects are moving apart "faster than light", but when you look at the light cones in those same coordinates, you can confirm that the objects are still moving inside the light cones.
> new space in between these points is being created
This isn't really part of the physics of the expanding universe; it's an interpretation that some people put on it. There's nothing in the actual math that corresponds to "new space being created".
> space can "flow" faster than the speed of light on the far side of event horizons
This isn't really part of the physics either; it's an interpretation (part of what's often called the "river model" of black holes) that can help with visualization, but again there's nothing in the actual math that corresponds to "space flowing faster than light".
> ways of doing these manipulations may well exist
According to our current theories, any such manipulations would require what is called "exotic matter". There are good physical reasons to think that it is not possible to create exotic matter, especially in the quantities we would need to "hack spacetime" (nice phrase!) on the scales we would want to do it. Given that, I don't think it's fair to say that "FTL is most likely possible in theory"; I would say it's most likely not possible on our best current theories.
> I don't think this really makes sense, because "normal space" is not a well-defined term.
You are of course technically correct.
> There's nothing in the actual math that corresponds to "new space being created".
True, and this might end up being a horrible crutch, but right now it helps me to conceptualize what's (possibly) going on. I'm sorry for having exported this hypothesis into a context where it shouldn't have been said without additional qualifiers, but it's too late now to edit it out.
> This isn't really part of the physics either; it's an interpretation
That's actually one I stand by. In the end, this seems really more about how you choose to express ideas in a language that doesn't have any exact words for things going on in an object that lies far outside of our normal experience. You might (and I suspect you do) choose to not say anything at all and let equations speak for themselves, but that doesn't really work for most people. So you're stuck with choosing lenses that render this foreign reality on a canvas you can actually picture. I also think there is nothing wrong in principle about choosing this particular representation.
> I would say it's most likely not possible on our best current theories.
Well, we know spacetime is not rigid. We know that interesting dynamics exist at the extreme limits of physical values. We also know that there is a large chunk yet to be discovered about the nature of the substrate on which reality rests. You are completely within your rights to look at everything we know and have ruled out so far and proclaim a high likelihood of impossibility, but along the same line of thought I reserve the right to declare the glass half full ;)
The truth is that neither of us are likely to live to see a definite answer play out.
If you mean, you like using it as an interpretation, no problem; a lot of people do.
If you mean you think it's more than an interpretation, then you're going to have to show me explicitly where in the math the "flow of space" is represented.
Yes, I'm using it as a mental representation of a process which I can't picture directly. How do you deal with such things? I mean aren't you ever tempted to use a tool like that? I don't think there is anything wrong with the idea.
I'm having some trouble picturing how it could be more than an interpretation.
Whenever two objects are in relative motion to one another, they each perceive a time dilation taking place at the other object. The flow of time is directly linked to the relative speed of an object. On an object that moves at the speed of light, time stands still. For more information on the mathematics, I refer you to the Lorentz transformation (http://en.wikipedia.org/wiki/Lorentz_transformation), but it's actually enough if you imagine that increases in speed are causing a decrease in the flow of time, the limit of that process has to be the velocity at which the flow of time is zero.
Ok. When you say 'how fast an object moves through time', you mean 'how fast time passes for a moving object, as seen from the inertial reference frame of another object'.
I regard objects as moving at the same speed through time - 1 second per second.
It's of course a matter of taste what expression sounds more fitting to you, precisely because time is such a fluid concept.
Personally, when I think about a neutrino for example, I'd say that neutrinos go crazy fast, and they experience time unimaginably slowly, so it feels more natural for me to think that velocity and time are tradeoff values of each other.
> Whenever two objects are in relative motion to one another, they each perceive a time dilation taking place at the other object.
This is true.
>The flow of time is directly linked to the relative speed of an object.
I'm not sure this is even a coherent statement. "Flow of time" along what?
Consider for comparison: what would the "Flow of latitude" refer to on a planet's surface? Any coherent statement about the "Flow of time" should also make sense when applied to the "Flow of latitude", and I can't think of any way of conceptualizing the "flow of latitude" that makes sense.
Maybe I'm not understanding what you mean by "flow", but in relativity dimensions do not "flow" in any conventional sense, and the notion that "increases in speed are causing a decrease in the flow of time" makes no sense: to an observer on an object clocks continue to run at a constant rate, and the whole point of relativity is that observers on objects are just as good as observers anywhere else.
The laws of physics are the same for everyone (this is the principle of relativity) so since an observer on an object does not observe co-moving clocks slowing down, any talk of "a decrease in the flow of time" requires a violation of the principle of relativity.
> but in relativity dimensions do not "flow" in any conventional sense
That is not really the point. You are concentrating on the word flow, and maybe I chose that foolishly, so bear in mind that I'm of course not a native speaker.
If we discard for a moment things that move at the speed of light, that leaves us with objects for which time does not stand still. Whether or not you agree with the word "flow", is it really that objectionable to characterize the experience of time as a movement through a fourth dimension?
My entire point in this regard was really that relative velocity and time dilation are linked. Which they are. It's right there in the math. Maybe my mistake was to use "flow" conversationally, but if you could see past that it would probably a more productive discussion for both of us.
> "a decrease in the flow of time" requires a violation of the principle of relativity
You misunderstood what I was trying to say, in a colossal way. I apologize for not being clearer. At no point was I suggesting a global "flow of time". In fact, I made a special effort to talk about individual reference frames.
It is mentioned in the linked article. Since speed is always relative (to a frame of reference), Special relativity by definition proposes that, nothing can go faster than C. The article gives an example, if a spaceship is traveling at 0.6c, and another spaceship is traveling at 0.6c - away from first first ship. Their relative velocities are not 1.2c, but 0.8c (http://math.ucr.edu/home/baez/physics/Relativity/SR/velocity...)
Another observation worth considering: cosmic travel times seem utterly problematic right now because we individually live for extremely short periods of time. Spending a few thousand years in transit is much less worrisome if you're, say, an autonomous machine carrying an AI through the galaxy.
Interesting. Especially if the AI can learn and evolve along the way.
>Another observation worth considering: cosmic travel times seem utterly problematic right now because we individually live for extremely short periods of time.
Doesn't relativity "solve" this this problem if we can reach near lightspeed, and don't mind it being a one way trip?
Sort of. While being on the move at extreme speeds you would take advantage of the local slow-down you're experiencing. Of course, a lot of time will still pass in the meantime both at the origin and the destination locations. I'd argue for the traveler it's subjectively not much different from being in a state of stasis while going at sub-relativistic speeds for thousands of years.
No, there is still an lower limit of 4.37 years to get to alpha-centauri within any frame of reference no matter how much you accelerate within conventional space.
What relativity does, is that if you travel close to speed of light time taken for the trip as measured on ship versus on earth could be different by many orders of magnitude.
edit: Was wrong, as per [0] "This is something many readers don't understand well, so it bears repeating: The journey times as experienced by those on the ship are not limited by the speed of light. Instead what they experience is the planetary reference frame getting relativistic."
That's not true. From the perspective of the travelers space will appear to contract dramatically - though the speed of light remains constant, the distance traveled is reduced.
Your equation is correct in a Newtonian universe, but does not consider relativistic effects.
Generally when we talk about an object's acceleration, we are talking about its acceleration in its own reference frame. By definition, an object's velocity in its own reference frame is always 0, so acceleration does not become more difficult (ignoring the fact that the surrounding matter will be impacting you at higher speeds). From the perspective of an outside observer who is not accelerating, time would appear to slow down on the accelerating object, and the outside observer would record a decreasing acceleration.
2) Even though you don't observe yourself moving at increasing speeds, you do observe the rest of the universe moving at increasing speeds. This means that small particles impacting your ship will hit it with increasing energy.
However, there is reason to assume a lot of things may be going on that are not strictly speaking taking place in normal flat space.
The article mentions the expansion of the universe as an example, and that's actually a good point to start. By virtue of the universe expanding, the distance between points grows faster than the speed of light as long as those points are sufficiently far apart. This becomes more interesting when you realize that new space in between these points is being created. Sure, the galaxies traveling on this expanding medium are not actually speeding apart powered by classical movement, but they are nevertheless changing position relative to one another in an interesting way.
In fact, what we're interested in when we talk about FTL is not classical movement at all - what we want is to change positions instead. There are places in nature where we know this is happening right now, for example we do know space can "flow" faster than the speed of light on the far side of event horizons.
So if we abandon the idea that we need to accelerate towards a destination, FTL becomes a broader idea of manipulating spacetime in order to be somewhere in less time than if we had actually flown there at the speed of light. There exist proposals for propulsion systems that go in this direction, for example the "warp drive" ideas that cheat by simply shortening the amount of space a vessel has to travel through. Some of these concepts seem to work in theory, for some definition of work.
The trouble with all these ideas is they need impractical amounts of energy. Which is wasteful, since we only need to bend spacetime for a short while and then return it to its original state behind us, something that works analogous to a catalyst would be much better.
At the most fundamental level though, what we are missing is a way of hacking spacetime. Huge masses and energies are how nature bends it, but ideally we would need some other way of manipulating the fabric of existence directly. This is the reason why drive systems in science fiction all have some kind of yet-unknown mystery substance critical to their function. Given how little we actually know about the basic fabric of the universe, ways of doing these manipulations may well exist. They might not. We most likely won't find out for centuries, if ever.
Until then, we must answer the question so that yes, FTL is most likely possible in theory, but it's not even remotely within our grasp right now. It might never work in practice.
Another observation worth considering: cosmic travel times seem utterly problematic right now because we individually live for extremely short periods of time. Spending a few thousand years in transit is much less worrisome if you're, say, an autonomous machine carrying an AI through the galaxy.