h2g2 The Hitchhiker's Guide to the Galaxy: Earth Edition

You forgot that n is either a constant or a function of x when you differentiated. If n is constant you get 0 = 0. Else you have to differentiate (n times) what ever that means.

Everything works exactly the same no matter what speed you go at. Including lamps. If you want to do imaginary things (like drive at the speed of light) you can also have imaginary lamps that work however you want them to work.

But that's evading the question. The whole point (as with any thought experiment) is to figure out how we could travel at light speed _and_ still obey the laws of physics.

And anyway, it's not at all true that everything works exactly the same no matter what speed you go at. Clocks, for example, run just a little bit slower in a moving airplane than on the ground.

Urlsula LeGuin. The starships in her books traveled faster than light, but through the loophole mentioned in my first post.

BTW: Lincoln Said You can fool all of the people some of the time, and some of the people all of the time, but not all of the people all of the time, about 70 years before Churchill

The closest analogue we have is supersonic flight. Sound travels at a constant speed (plus or minus) throughout a medium, in this case air.

Below the speed of sound, the sounds ahead of the plane get a head start, and the pitch increases. Behind the plane the get a late start and drop in pitch. (If you've ever been passed by a ambulance or fire truck, and heard the pitch change, same thing.)

When planes fly faster than the speed of sound, and sound coming from them is bounced off of the still air, and reflected backwards.

Subsonic Supersonic
_______ / /
/ ___ \ / /
/ / \ \ ()<
| |() | | \ \ \___/ / \ \_______/

Light, behaving like a wave, will do the same thing beyond the speed of light. The headlights would bend around the path of the Rover.

Dang, I had a pretty ASCII art illustration that got trashed. (That's what that mess is.)

Yes, but that would be when you travel _faster_ than light, not at light speed which is what we're contemplating.

But you probably won't want to travel _at_ the speed of light, what with all those difficulties of gaining infinite mass and infinite lack of length.

Supersonic aircraft do not travel at the speed of sound as you would end up travelling in a ever-increasing sound wave front which would end up destroying your vehicle.

If the Rover was able to accelerate up to the speed of light, it would be more sensible to break through the light barrier, rather than just staying at c and watching those clocks back on Earth not move at all.

But you can't break the light barrier. Nothing can travel faster than light.

Yeah, well a Rover would be hard pushed to reach 100 quicker than a Maclaren F1, but we're still talking about theoretics here.

Anyway, bad news travels faster than anything else in the known universe.

No! I meant differentiate with respect to n. BTW (n times) refers to the number of terms on the RHS.

Yes, but there are levels and levels. Even if the Rover could reach light speed, it still couldn't surpass it.

Can you imagine what kind of horrid names they'd think up to give the poor child?

Firstly, Travelling at the speed of light you'll have have an essential energy type of an existence.

But what do you think? Someone back there said that travelling faster than light would be travelling back in time. But then will you still arrive to you destination, or just keep getting further away from it?

Hmmm...maybe you'd get there, but before you started (although it wouldn't seem that way to you.)

Hmm.. "nothing can travel faster than light"... Why?

Just because we currently know nothing that -does- travel faster, that doesn't mean nothing -can-.. at least it proves nothing to me.

Not true, the laws of physics only preclude traveling precisely AT the speed of light, because we would end up dividing one quantity by zero. Beyond the speed of light we attain "imagionary" componentes to the mass, what Electrical Engineers deal with all the time in electricity.

Technically speaking, flipping a light switch is impossible because it creates an infinite spike if power for that split millesecond between the "off" state and the "on" state.

A "pub physicist" that I trust once assured me that if anything WAS travelling faster than light, the same equasions that stop us from speeding up to lightspeed would stop the hypothetical faster-than-light body from slowing down to the speed of light...

This is why travelling at the speed of light is and always will be impossible in a physical state within reality. It's the same as saying parallel lines join at infinity or that a number can be bigger than infinity - all true but not possible to occur physically in reality.

Ahhhh. I stand corrected.