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.
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 [itex]-t^2+x^2=-1/a^2[/itex] 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.
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.
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. So?
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?
Rockets are still limited to below c, as discussed in this post: https://www.physicsforums.com/showpost.php?p=2669917&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.
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.
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.
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.
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.
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
It may help to point out that velocities in relativity don't add the same way they do in relativity that they do in Newtonian physics. For example, suppose I use some means (like a a magnet, or a mini-jetpack) to accelerate an electron from being at rest relative to me to moving at 0.9c relative to me, using a finite amount of energy in the process. Then, an observer who happens to also be moving at 0.9c relative to me uses exactly the same process (and the same amount of energy in his frame) to accelerate the electron from being at rest relative to him to moving at 0.9c relative to him. Since the electron is now moving at 0.9c relative to this observer, and this observer is moving at 0.9c relative to me, does that mean the electron is now moving at 1.8c relative to me? No, because the relativistic velocity addition formula says that if object A (the electron) is moving at speed v in the frame of object B (the observer), and object v is moving at speed u in the same direction in the frame of object C (me), then A's velocity in C's frame is given by (u + v)/(1 + uv/c^2). So, in this case the electron would be moving at a speed of (0.9c + 0.9c)/(1 + 0.81) = 1.8c/1.81 = 0.994475c relative to me, still slower than light.
Relativity 15th ed, 1952 by Albert Einstein. The velocity addition formula is gone into by Dr. Einstein in a very detailed manner in section XIII which is on page 40 of my copy. This is what JesseM refers to in his post above (#14.) Once that concept is understood and accepted one sees that it is impossible to leap-frog to a speed >c.
If you can send information faster than the speed of light, you can make a telephone with which you can talk to yourself in the past.
It may be helpful to know something I recently learned reading one of Einstein's papers. It is not light that determines the speed limit of the universe, c. The speed limit of the universe can be calculated without involving light. The speed limit is represented by c, and since the speed of light is exactly or almost exactly c, it is also represented by c. (The paper I read said it might not actually be exactly c.) So the question you really want the answer to is why does the universe have a speed limit? Why is there a limit to the speed an object can be accelerated to? The answer I have read again and again it that the mass of an object increases exponentially as it approches c, and therefore requires exponentially more energy to accelerate. So the question really really is why does the mass of an object increase with speed?
That's not the cause, it's a symptom. The question still is why does the universe have a speed limit? I don't know.
Like you I have never encountered any other explanation but: Doesn't the statement "the mass of an object increases with speed" directly conflict with basic principles of SR. It is equivalent to saying the rate of a clock decreases with speed. If you start with the assumption that proper mass does not increase with speed and that the relativistic mass increase in inertial frames is simply that I.e. Relative ; without physical meaning, then you would seem to left adrift once again with no reasonable explanation for a limit.