This isn’t quite right. As you approach the speed of light, space will indeed contract, but time outside the plane will slow down, not speed up. As you look out the window, the clocks you fly past will be ticking more slowly than your own.
As you zoom past a planet at .99c and look out the window at the clocks on the planet, who is moving–you or the planet? It’s just as reasonable to say that you are stationary and the planet is zooming past you at .99c. So a guy on the planet looking through your windshield will see the exact same effect as you see when you look at his clock as you zoom past.
The only reason the guy in the spaceship like to say that he is moving and the planet is stationary is that the planet has very close to the same velocity as a lot of other stars and planets in our galaxy. But you could say that Earth and the Sun are zooming off at .99c toward Cosmic Anomaly X, and so is Alpha Centauri, and so is the rest of the galaxy, and so is your spaceship, since it starts with the same velocity as Earth since you launched it from Earth. And you turn on your engines at full thrust, not to speed you up to .99c, but to slow you down relative to the breakneck speed Earth and the rest of the galaxy is traveling.
Oh wow. Twist up another one.
It’s worth noting (and I did not see them noted yet in this thread. If I missed them, sorry!) two things:
First, when people talk about the speed of light as some sort of speed limit, they mean the speed of light in a vaccuum. Which is almost irrelevant, because…
Second, “Speed of Light” is kind of an unfortunate name. Light is made up of photons and photons are (heavily presumed in most cases to be) massless. All massless particles travel at a certain constant speed regardless of your frame of reference.
As an aside, photons can apparently develop an effective rest mass in superconducting materials which I assume would cause light to no longer travel at the “Speed of Light”.
One way to answer the question is to realize that we are already travelling at the speed of light relative to something, and it all looks pretty normal to us.
I’m pretty sure this is incorrect. No frame of reference could see us traveling at the speed of light, or faster than the speed of light. No matter what reference frame you use, c is invariant, and you cannot observe particles traveling at c.
False, mostly because traveling very fast also messes with your perception of time, among other things.
First, traveling at or in excess of the speed of light is theoretically impossible.
The basic example used for thought experiment is a train car traveling very near the speed of light, with a light source near the middle, and a light activated switch to open the door at each end. To a person inside the car, it will appear that the light comes on and both doors open at the same time, which would be exactly as long at it would take light at the speed of light to travel from the light to the switch and activate the switch.
But to an observer who is outside the car and not traveling with it, it would appear that the rear door opened first and the front door opened later, because the rear door was rushing towards the light while the front door was rushing away from it.
Perhaps Einstein’s biggest contribution to science was the notion (so far supported by experiment) that the way things look to us depends on our own frame of reference. If you are moving, time passes differently for you. And no matter how fast you are moving, you will always perceive light as moving at the same speed relative to you.
If your head doesn’t hurt yet, this may push you over: I though that for years, but recently have learned that it is possible for something to appear to be moving faster than light, if it is moving very fast, and the space between you and it is expanding.
Yeah, I don’t really get it either.
I’m not sure what you are saying. By “speed of light” I meant “approaching the speed of light”, and in the frame of reference of a particle traveling near the speed of light in our frame reference, are we not traveling near the speed of light?
Then you meant something very different from what you said. It might not seem that way, but given relativistic considerations “approaching the speed of light” is very different to “at the speed of light”.
Damn it Jim, I’m a poster, not a scientist. 
ETA: But the point I was trying to make, was that when we think about what happens when we start to approach the speed of light people often forget that we are already moving at a variety of speeds relative to other objects.
It’s true that extrapolation of the Hubble constant implies that parts of the universe are moving away from us faster than the speed of light and so will forever be beyond our view. But this is spacetime expansion. That’s not subject to the restriction of light speed and means something different.
I think this is the wrong point. The fact that everything looks “normal” to us is true for everybody. The speed you are traveling shouldn’t make any difference at all to the way things look. Things moving away will be red-shifted in their appearance, just as we would be red-shifted if we could magically shift places to their viewpoint, but they seem “normal” to themselves.
What’s really weird, therefore, is that nothing happens to you as you move toward the speed of light. It’s just that other people look even odder than usual.
You are missing my point. A particle that passes us at C-x sees that *we *are passing *it *at C-x.
And that is my point. In the OP’s example, a person on a plane traveling near the speed of light relative to the earth sees no difference in how the forward facing lights behave. One way to understand that is to realize that a normal plane is actually moving at a variety of speeds depending on what frame of references it is in, and in some of those it is already traveling near the speed of light.