# Faster than the speed of light

I just read today in Stephen's Hawkings book that the energy of an object is increased with its acceleration and that in turn increases the mass because enegry and mass are interchangeable because of E=mc2. Therefor it takes more energy to increase the acceleration of an object going fast because of that additional mass.

He writes that when an object comes closer to the speed of light it aquires infinite mass and therefor would take infininte energy to increase the acceleration to the speed of light.

This bothered me for three reasons.

1. I remember reading in a book called Relativity Visualized that why we nothing is able to go faster than the speed of light is not clear. The author of that book suggested his own "myth" as to why things cannot go faster than the speed of light. So who is right?

2. I might just be showing off by ignorance here, but intuitively I can't grasp why energy which is carrying an object in a certain direction should cause it to be harder to have the object accelerated in the same direction.

3. I also wonder why it is that it happens to be that at the speed of light the object acquires infinite mass?

I hope I made my questions clear.

Thanks

Jonathan

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1. Don't read pseudoscience, Einstein is right.

2-3. According to relativity, increased kinetic energy of an object is actually increased mass of an object. Here we talk about relative mass (which depends on the frame of reference), not the rest mass of an object. Anyway, since the object gains inertia when it speeds up, it is harder to accelerate. When the relative speed of two objects accelerates towards the speed of light, the relativistic mass of an object increases exponentially. This means that you need more and more energy to accelerate. This is why you can't go faster than the speed of light, or even as fast as the speed of light.

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Whether we say the relativistic mass goes to infinity or that the energy goes to infinity, it comes to the same thing; relativity says you can not accelerate up to the speed of light, and by accelerating you can't get to GREATER than the speed of light without crossing that speed. Also the speed of light is constant across intertial observation frames, so any relative motion you might have been observed to have to begin with won't affect the result either. So you can't get there from here.

pervect
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I just read today in Stephen's Hawkings book that the energy of an object is increased with its acceleration and that in turn increases the mass because enegry and mass are interchangeable because of E=mc2. Therefor it takes more energy to increase the acceleration of an object going fast because of that additional mass.
He writes that when an object comes closer to the speed of light it aquires infinite mass and therefor would take infininte energy to increase the acceleration to the speed of light.
This bothered me for three reasons.
1. I remember reading in a book called Relativity Visualized that why we nothing is able to go faster than the speed of light is not clear. The author of that book suggested his own "myth" as to why things cannot go faster than the speed of light. So who is right?
2. I might just be showing off by ignorance here, but intuitively I can't grasp why energy which is carrying an object in a certain direction should cause it to be harder to have the object accelerated in the same direction.
3. I also wonder why it is that it happens to be that at the speed of light the object acquires infinite mass?
I hope I made my questions clear.
Thanks
Jonathan
There are a couple of different ways of explaining why objects cannot exceed the speed of light by accelerating.

The key point to realize is that this is a true statement - you can't reach the speed of light with a massive object, no matter how long you accelerate.

Minor differences in terminology (such as the age-old argument of whether mass, unqualified, means _invariant mass_ or _relativistic mass_ should NOT confuse you on such a basic point.

See
http://math.ucr.edu/home/baez/physics/Relativity/SR/mass.html
for more on the definitions of different types of "mass" in relativity.

I tend to favor the explanation involving the velocity addition formula. If we have three obserers, A, B, and C

A stands still
B ----> goes .9c relative to A
C-----------> goes .9c relative to B

we can ask - how fast does C go relative to A?

The answer is that he goes at a speed of (.9+.9)*c / (1+.9*9) = 1.8 c / 1.81.
This result can be generalized, such that the addition of *any number* of velocities < c will always yield a resulting velocity < c.

There is more on how velocities add in SR at
http://math.ucr.edu/home/baez/physics/Relativity/SR/velocity.html

thanks

thanks for the replies. There is a lot here that I would need to spend a lot of time working on to understand. I hope I can spend that time.

Thanks

1. Don't read pseudoscience, Einstein is right.

2-3. According to relativity, increased kinetic energy of an object is actually increased mass of an object. Here we talk about relative mass (which depends on the frame of reference), not the rest mass of an object. Anyway, since the object gains inertia when it speeds up, it is harder to accelerate. When the relative speed of two objects accelerates towards the speed of light, the relativistic mass of an object increases exponentially. This means that you need more and more energy to accelerate. This is why you can't go faster than the speed of light, or even as fast as the speed of light.
Ok, but what causes the increase in mass? To say that energy increases therefore you need more energy to accelerate isn't a proper explanation for the increase in mass. There must be a cause for this effect.

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