Why cant you go faster than the speed of light?

[rrutter81]

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.

 

[Fredrik]

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.

 

[rrutter81]

ok that is in relation to the observer though.

To the observer "pushing" the object to that speed it would be infinite. However, let's 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.

 

[Fredrik]

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.

However, let's 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?

 

[rrutter81]

So?

exactly

Why the velocity and not the speed?

 

[Fredrik]

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?

 

[starthaus]

exactly

Why the velocity and not the speed?

v=\frac{at}{\sqrt{(1+(at/c)^2}}

What happens when t->oo?

 

[Janus]

ok that is in relation to the observer though.

To the observer "pushing" the object to that speed it would be infinite. However, let's 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:

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.

 

[dezso3]

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.

 

[Dale]

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.

 

[Matterwave]

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.

 

[moonman239]

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.

 

[Demystifier]

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

 

[JesseM]

ok that is in relation to the observer though.

To the observer "pushing" the object to that speed it would be infinite. However, let's 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.

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.

 

[stevmg]

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.

 

[Count Iblis]

If you can send information faster than the speed of light, you can make a telephone with which http://en.wikipedia.org/wiki/Tachyonic_antitelephone"

 

[stevmg]

If you can send information faster than the speed of light, you can make a telephone with which http://en.wikipedia.org/wiki/Tachyonic_antitelephone"

I talk to myself now (I don't have money in the bank) and don't need warp speed to do it.

 

[CosmicVoyager]

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?

 

[Ich]

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.

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.

 

[Austin0]

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?

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.

 

[my_wan]

If you consider that from your own point of view your mass doesn't increase, and everything appears normal, you can say you can't go faster than the speed of light because you can never get there before you left. You can never outrun yourself. Note that you see a star 1 light year away 1 light year in the past. That's in some sense what it means when it's said your four-momentum is timelike. You cannot have a spacelike separation from yourself. So even if you take relativistic mass increase and such as some kind of illusion (in some sense it's not), you can get there as fast as you want, nearly at the same time you left, but it take you much more time for everybody else back home. Hence your kids can grow older than you by the time you get back.

 

[HallsofIvy]

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.

In its rest frame, the electron is always at rest and so cannot be accelerated!

 

[ExecNight]

i will change his example to something different, a platform slowly accelerated to 0.999999c and OP is standing on top of it. So, can he walk forward? What happens when he wants to run how do the legs react =)

 

[redthinker]

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.

an easier way to explain it is that if you get close enough to the speed of light, time slows down relative to your surroundings to prevent you from reaching that high speed making it impossible

 

[jtbell]

i will change his example to something different, a platform slowly accelerated to 0.999999c and OP is standing on top of it. So, can he walk forward? What happens when he wants to run how do the legs react =)

He can walk forward the same way he can walk forward on a moving airliner. As far as he's concerned he's at rest, regardless of the fact that the platform had to accelerate to that final speed.

Suppose you produce the relative velocity of 0.999999c by having you yourself accelerate to that speed in the opposite direction, with nothing at all "happening" to the platform. Same result.

 

[stevmg]

Energy and mass are equivalent thus the increase in mass with velocity (kinetic energy.)

I don't know the exact equations any more.

The limit was shown or proven by H. Lorentz and Einstein and has been experimentally verified over and over again.

 

[ExecNight]

He can walk forward the same way he can walk forward on a moving airliner. As far as he's concerned he's at rest, regardless of the fact that the platform had to accelerate to that final speed.

Suppose you produce the relative velocity of 0.999999c by having you yourself accelerate to that speed in the opposite direction, with nothing at all "happening" to the platform. Same result.

So according to someone who is watching the platform, he don't need infinite energy for that acceleration. Just some muscle power =) I guess that answers OP's question, although i like the electron with jetpacks idea =D

 

[stevmg]

No way -

The velocity addition formula and concept quite clearly explained by Einstein himself in Relativity section XIII rules that out.:

W = (v + u)/(1 + uv/c²) where W = the composite velocity and u and v represent the component velocities.

Nice try, but no cigar...

Steve G
Melbourne, FL

 

[Aaron_Shaw]

If you moved at the speed of light the rest of the universe would shrink to a point in the direction you are moving. Therefore you can go anywhere in the universe in an instant. Therefore it makes perfect sense that you would never go faster than C because C is the speed at which all the coordinate values in the direction youre heading contract to a single point and time stops passing.

The real question is not why there is a speed limit, but why it is the value it is. If The universal speed limit was greater than C, then we could go greater than C in the space coordinates while still having spare speed left over for the time coordinate to chage too.

**edit**

Well... i guess we could ask why there is a limit too. But the important part is that it's not a speed limit in the x/y/z coordinates imposed by some physical thing like mass increasing. Assuming we could overcome that and reach the speed of light we still could not go faster because we'd then already be wherever we wanted to go. How can you arrive somewhere quicker when you're already there?

 

[stevmg]

Sports Fans...

Think of it this way...

Have you ever seen the musical "Fiddler On The Roof?" In it, the hero, Tevye, I believe, explains that if he were the Tsar, then he would be richer than the Tsar. "How so?" ask his friends. "If I were the Tsar, I would have all the power and wealth of the Tsar...
.
.
.
and I would do a little teaching on the side."

That's where this coversation is going.