LogFAQs > #914589187

teepan95 posted...

TarElessar posted...

DevsBro posted...

Nah, you can travel anywhere you want in any amount of time you want if you go fast enough. Once you get moving fast enough, you actually have less distance to go. It's an interesting consequence of special relativity. Like, if you could accelerate to relativistic speeds instantly, the trip to Andromeda could be a ten foot trip. Only thing is getting to that speed requires stupid amounts of energy.

Let me comment on that in slightly more detail.
As we are all well aware of, the second postulate of special relativity predicts that the speed of light is the same in all (inertial) frames of reference.
This has the interesting consequence that we cannot use length contraction and time dilation to just justify anything.
For those of you who don't know (I'll use a simplified version for easy understanding): Time dilation predicts that time as viewed from our moving spaceship moves differently than proper time as view from our planet. However, length contraction also predicts that a similar thing happens to space itself.
Now, length contraction behaves as our Lorentz factor (or the inverse of it, depending on which frame you view it from), which can take values from 1 to infinity. So yes, we could theoretically reach a speed in which the distance we are trying to travel becomes as small as we want it to be. This changes our time scale the other way around though, as such we still cannot violate the second postulate.
I'd be happy to discuss this in more detail, but doubt anyone will even read it lol.

My understanding was that as your speed approaches c, the distance of the moving object (ie its length) contracts, and not (as I understand DevsBro to have stated) the length of the path travelled

Ah, I think I see where the problem is.
Most people seem to think that an object moving means that magically lengths morph around or something, which is fundamentally wrong.
Imagine we're not in relativity: You're driving on the Autobahn and a car passes you on the other side. It obviously appears to be approaching faster since you have a speed v on your own, but its actual velocity doesn't change. But that's not really because your car is moving, it's actually because you're in a moving frame (let's call this moving frame S' as opposed to the "normal" frame S).
So you might now ask yourself, what actually is speed? Is the speed we perceive in S or S' its real speed?
Let's consider relativity with a simple example: A photon moves towards you as you drive your car. Now we can't simply add speeds (v + c) to the perceived speed as this would give a value greater than the speed of light. Without going into detailed derivation, the explanation is that it still appears to move with c and space itself is simply behaving differently.
Imagine now you draw a line of 1m on the ground. How long is it? Well, in the frame S of you drawing it obviously 1m. Now imagine you accidentally spotted Sunhawk in a local pub and are trying to run away to avoid being seen, with a high speed close to c. You're running past the masterpiece of a line you drew and it suddenly seems shorter, say, about 0.5m. This is because you're now in the moving frame S' in which lengths seem shorter. This is NOT because you're running, it's because your eyes (points of observation) are moving in a different frame. For all other people in S, the length still seems to be 1m.

That being said, you should see that the actual length does not change, it's just that lengths are different when you're moving (I'm repeating this because it's hard to wrap your head around at first). That obviously means that you need to travel less distance when you're in frame S' (i.e. moving). However, you still move the same distance in frame S. As such, you can't just magically move with FTL as the "proper" length will stay the same in S and you CANNOT be faster than light in /any/ frame.

Does this clarify things?