# I Why would we need faster than light travel?

1. Mar 4, 2017

### marksyncm

This is something I often read in news on established websites, and countless times more in different forums. It goes something like this: someone says that in order for us to be able to do something, we would have to reach distant galaxies. To which someone replies "Yeah, but unfortunately faster than light travel is impossible, so we're never getting there."

I thought that the closer we got to the speed of light, the shorter the relative distances on the axis of travel would become? In other words, we never really need to exceed the speed of light to get to the most distant parts of the universe - all we have to do is get close enugh to C and we could travel pretty much any distance in the known universe in a matter of seconds (hypothetically of course).

Am I missing something? This was something I considered obvious since a long time, but I'm seeing the "Well, unfortunately we'll never be able to travel faster than light" argument so often lately that I'm starting to question my own understanding.

2. Mar 4, 2017

### Ibix

You are correct that you can travel any distance in a finite amount of your own personal time by travelling ffst enough. Seconds probably isn't achievable without splattering yourself over the back wall of your ship, but certainly years is manageable. I think we showed recently that 100 years at 1g will get you $10^{22}$ light years (with some caveats).

However, if you're planning on a return journey then everyone you know will be dead and gone $10^{22}$ years ago. It's an early-days-of-sail one-way-to-Australia type deal.

Also the energy requirements are prohibitive. Even if one postulates a 100% efficient matter/anti-matter rocket.

3. Mar 4, 2017

### marksyncm

Hi,

Thanks for the reply. Yes, I understand all of that. But I'm still not sure I see the meaning behind the statement I mentioned, ie. the sentiment "if only we could travel faster than light". We'd first need to reach the speed of light and then go "beyond it", so either way everyone I know would be dead when I arrive back. Right?

Or is there something I'm missing that would be completely different if we were "able to travel faster than light"? Is there a sort of assumption behind this that we would then be able to escape the implications of traveling at near the speed of light?

4. Mar 4, 2017

### Ibix

You can accelerate and accelerate for ever but you will never exceed the speed of light. It's impossible that way.

Any way to move faster than light must duck the whole "acceleration" issue somehow - wormholes allowing shortcuts between distant points for example. So people speculating about faster than light travel are simply hoping to duck your objections by some form of magi-tech. I think that's what you're missing.

There's no known way to do that. I gather that even the semi-plausible ideas like the Alcubierre warp drive permit causality violations such as returning before you left, which probably means they're impossible.

5. Mar 4, 2017

### marksyncm

Got it. Thanks!

6. Mar 4, 2017

### Mister T

Perhaps they just don't understand what you understand, which is that the distance does contract so the light speed limit doesn't prevent a traveler from getting there in any arbitrarily short amount of time.

But there may be more to it than that. When someone says that in order for us to do something we would need to reach distant stars or galaxies, what is that something? Suppose it were to share technologies. Well, we can send out a traveler, who can later return. But it will be centuries into the future before he does return, so in that sense we can't really share their technology. Our descendants can, but we can't.

7. Mar 5, 2017

### PAllen

Actually, it was 1044, per me and Dr. Greg.

8. Mar 5, 2017

### Ibix

Indeed. 1022 light years was the mistaken answer. Sorry.

It's a big number, either way.

9. Mar 6, 2017

### Khashishi

There are some points in the universe that you cannot reach by traveling at the speed of light, due to the expansion of the universe, assuming the universe continues to expand.

10. Mar 8, 2017

### MattRob

Also, afaik, they would be a sort of way to "cheat" the energy requirements. As you said, they're prohibitive, but if you can create a spacetime geometry that allows for coordinate acceleration, then since you're really not "accelerating" you don't have to expend energy at all, except for whatever's needed to make that spacetime geometry. So really it's a nifty way to get around those prohibitive energy requirements, even if FTL travel is impossible. Though the trade-off is that you don't get that time dilation/length contraction that allows you to go so far (since proper clocks inside an Alcubierre "bubble" tick at the same rate as distant coordinate clocks).

11. Mar 19, 2017

### nitsuj

imo this statement completely ignores physics at and over the boundary of the "bubble"...for a good reason im sure :D

12. Mar 19, 2017

### Chris Miller

I've gained a lot of better understanding here, but it still seems that if I accelerate at 1g, I'll reach (and maybe exceed) c, relative to earth's frame of ref, in under one of my years. And, in my frame of ref, I'll expend no unusual amount of e. Of course no one on earth will/can ever observe me doing this this, just as they could not see me fall into a black hole, even though, in my frame of ref, I will have.

13. Mar 19, 2017

### jbriggs444

You can never reach c by acceleration. You can never exceed c by acceleration. You will need to explain why either of these seems unavoidable to you.
Energy conservation is not required (and is not always even sensible) in an accelerated frame of reference. When you mention an "expenditure of e", you are invoking energy conservation.

14. Mar 19, 2017

### Chris Miller

By no unusual e, I meant just whatever Newtonian force was required to keep me accelerating at 1g. Right that I can't reach or exceed c relative to another frame, but only because the distances shrink to 0. There's nothing special about my frame as I approach c relative to yours. Of course my universe will be nothing like your universe.

15. Mar 19, 2017

### jbriggs444

If you mean to say something about force, you should mention "force". The variable name e typically denotes energy.
But the distances do not shrink to zero either.
There is one thing that is special. Your frame is not inertial.

16. Mar 19, 2017

### Mister T

That's the basis upon which everything you've learned in this thread is founded.

Only relative to another frame. And they approach zero, they never reach zero.

Note that the very phrase "approaching a speed of $c$" makes no sense without a reference to something else. So if you want to think you can travel at a speed of $c$ or faster, but not relative to any frame of reference, then your understanding of the very notion of speed is different from how it's defined in physics. If your understanding has you believing you can get from here to there before a light beam can, then your understanding has been refuted. On the other hand, if you think you can't then your belief that you can travel faster than light contradicts itself.

17. Mar 19, 2017

### Janus

Staff Emeritus
No, you can't reach c relative to the Earth, even as measured from your frame. The way velocities add prevents this. You can illustrate this by the following scenario:
You start off at rest with respect to the Earth. You then accelerate away at a constant 1g(as measured by you), until you reach some velocity wit respect to the Earth. At which time you release an object and then keep accelerating. You now wait until you are moving at that same speed relative to this object and measure your speed relative to the Earth.
So let's say you were moving at 0.1c relative to the Earth when you let go of the object, and then accelerate to 0.1c relative to the object.
The addition of velocities theorem says that you will now measure your velocity with respect to the Earth to be:
$$\frac{0.1c+.1c}{1+\frac{0.1c(0.1c)}{c^2}}= 0.198c$$
Note that this is less than what you get with Newtonian velocity addition.
If you now release a second object and accelerate to 0.1c relative to it, your velocity with respect to the Earth will be:
$$\frac{0.198c+.1c}{1+\frac{0.198c(0.1c)}{c^2}}= 0.2922c$$
Your increase in speed relative to the Earth has increased by less this time than even the last time.
You can keep on doing this and each time you will add less and less to your total velocity with respect to the Earth.
But for you, the time it takes to accelerate up to 0.1c relative to the last object you dropped is the same as it was for any of the previous objects.
The actual relationship between time as measured by you and your speed relative to the Earth works out to be:
$$v= c \tanh \left (\frac{at}{c} \right )$$

By the above, after 1 year of your own time, you will be moving at ~0.77c relative to the Earth.
After 2 years, 0.968c and after 3 years 0.996c. You can continue to accelerate for year after year and all you do is get closer and closer to c, but never reach it.

18. Mar 19, 2017

### Chris Miller

Yes, I understand velocity is always relative to another frame, that there's no universal frame of reference (save maybe the CMB?). And that energy <> force. And that a 1g accelerated frame is not inertial. And that the distance separating two frames as their convergence approaches c only approaches, but never reaches, zero. As in becomes infinitesimally small.

19. Mar 19, 2017

### jbriggs444

There is no such thing as "the distance separating two frames".

20. Mar 19, 2017

### Chris Miller

frames of reference (i.e., points within), I think you understand what I'm trying to say, thanks for again correcting my terminology.

21. Mar 19, 2017

### jbriggs444

Unfortunately, the difficulty at hand is not a problem of terminology. The problem is that nothing you are saying is sensible. There is no notion of "distance separating two frames of reference".

22. Mar 19, 2017

### Chris Miller

Actually, I believe it is my poor terminology. I'm basically learning a foreign language that uses familiar words. Maybe only math is literal enough. How about points? I know distance is a sensible concept?

23. Mar 19, 2017

### PAllen

Actually, in SR distance is only sensible if you specify who measures it. In GR, it is even less meaningful, in that different measurements that are the same in SR may come out different in GR.

24. Mar 19, 2017

### phinds

When you measure the distance between two points you are doing so in exactly one frame of reference. Bringing another FOR into it is nonsensical. I think you have not yet quite gotten that. You seem to think that if you are measuring one point in one frame of reference and the other point in another frame of reference, you are somehow measuring a "distance" between the two frames of reference. This is nonsensical and you need to think it through and make sure you understand that before going further.

25. Mar 19, 2017

### nitsuj

So with respect to what Chris and jbriggs44 were saying; Chris didn't mention which of the two frames were making the measurement so the statement "distance separating two frames of reference" is non sensible ?