# Why cant you go faster than the speed of light?

by rrutter81
Tags: faster, light, speed
 P: 5 Simple question. Supposedly if an observer A (lets call it a particle accelerator) is accelerating an electron near the speed of light infinite energy is needed to achieve it. However if we were to put a rocket on the electron so that it would push the electron relative to it's speed then it wouldn't require the infinite energy because time is not slowing. eg: An electron appears heavier as it is accelerated yet the electron relative to the electron weighs the same.
 Emeritus Sci Advisor PF Gold P: 9,520 This post calculates the energy required to accelerate a mass m to speed v. Note that the calculation doesn't depend on how the mass accelerates. DrGreg's posts in this thread explain why the world line of a rocket undergoing constant proper acceleration is a hyberbola $-t^2+x^2=-1/a^2$ in the inertial frame where the rocket started out at rest. The a on the right is the proper acceleration. Note that I'm using units such that c=1, and Greg isn't.
 P: 5 ok that is in relation to the observer though. To the observer "pushing" the object to that speed it would be infinite. However, lets say that the electron had a jet pack on it. It would need far less energy relative to the electron than say... you or me pushing it to such speeds.
Emeritus
PF Gold
P: 9,520
Why cant you go faster than the speed of light?

 Quote by rrutter81 ok that is in relation to the observer though. To the observer "pushing" the object to that speed it would be infinite.
What do you mean would be infinite?

Proper acceleration is the coordinate acceleration in the co-moving inertial frame. It's the acceleration measured by an accelerometer on the ship.

 Quote by rrutter81 However, lets say that the electron had a jet pack on it. It would need far less energy relative to the electron than say... you or me pushing it to such speeds.
So?
P: 5
 Quote by Fredrik So?
exactly

Why the velocity and not the speed?
 Emeritus Sci Advisor PF Gold P: 9,520 I don't understand what your argument is. You know that no amount of work is sufficient to reach v=c, and you know that constant proper acceleration is insufficient too (because the hyperbola approaches the straight line t=x, which represents speed 1 (=c)). How is that not enough?
P: 1,568
 Quote by rrutter81 exactly Why the velocity and not the speed?
$$v=\frac{at}{\sqrt{(1+(at/c)^2}}$$

What happens when $$t->oo$$?
Emeritus
PF Gold
P: 2,361
 Quote by rrutter81 ok that is in relation to the observer though. To the observer "pushing" the object to that speed it would be infinite. However, lets say that the electron had a jet pack on it. It would need far less energy relative to the electron than say... you or me pushing it to such speeds.
Rockets are still limited to below c, as discussed in this post:

http://www.physicsforums.com/showpos...7&postcount=23

Take particular note to the last part; where, due to the way velocities add in Relativity, your electron can continuously accelerate at the same rate from its own view point, but still never reach c with respect to any frame as measured by the electron.
 P: 6 Let's say that a person is sitting in a spaceship that is traveling at very close to the speed of light. Would a person who is [trying] to observe (see) that spaceship even see it? Because, wouldn't the photons that are reflecting off of it take that much longer to reach you, and thus you wouldn't see the true position of the spaceship? Also, if you were observing the Earth from the spaceship, wouldn't it appear to be a blur around the sun, because the photons from it take so much longer to reach you that the light from the Earth would just be bend around the sun, so that it would appear that the Earth exists everywhere in its path around the sun at the same time? And it seems to me that the reason that time slows down for anything that is traveling at near the speed of light is because the speed of light determines the rate at which time passes? So for example, a person's brain waves, traveling at the speed of light, had to catch up to a different part of the person's brain, which is traveling at very close to the speed of light, it would take an extremely long time for it to reach its destination, thus slowing down the cells' aging process, and thus slowing down time! So basically, an atomic clock traveling at the speed of light would register a very very slow passage of time because the radiation emitted by the atom would take that much longer to catch up to the clock, making it "tick" more slowly. Obviously, this is extremely simplified and in a layperson's terms. But am I on the right track? http://www.youtube.com/watch?v=hbFxN...eature=related In the video, it is stated that it is theoretically possible to travel faster than the speed of light, and when you do, time will go backwards. But what I don't understand is that if it's impossible to travel faster than the speed of light, then how on Earth (no pun intended) would you travel faster than light speed, and thus back in time, if you went around a black hole, as is shown in the video? From the outside, it just seems that an object (such as a spaceship) is traveling faster than the speed of light around the black hole, but if that's not possible, then how the heck does it happen? It just doesn't seem to make any sense.
 Mentor P: 17,526 Why can't you go faster than light? Because you have mass which means that your four-momentum is timelike. This is true in any coordinate system, inertial or non-inertial.
 Sci Advisor P: 2,950 I would just like to say, I found it really amusing to picture electrons strapped to tiny tiny jet packs. XD On topic: I think the poster is trying to say that in the rest-frame of the electron the electron see's no mass dilation and can therefore be accelerated.
 P: 300 E=mc2 pretty much explains it. Put simply, m increases with energy, and thus the energy needed to push it. But the more energy you give it, the more massive it is, and thus you'd need even MORE energy. This cycle repeats itself infinitely. This is why we say that nothing massive can travel at the speed of light.
P: 4,630
 Quote by DaleSpam Why can't you go faster than light? Because you have mass which means that your four-momentum is timelike. This is true in any coordinate system, inertial or non-inertial.
Yes, the mass is the ultimate reason why a relativistic particle cannot travel faster than light. Yet, the concept of mass can be generalized to the concept of scalar potential, which shows that motions faster than light can also be compatible with relativity:
http://xxx.lanl.gov/abs/1006.1986