# Is there any Limit to the kinetic energy

1. Oct 12, 2009

### raknath

Hi

Does SR predict any limit to the kinetic energy/momentum that the body can actually reach.

Given that the mass energy equivalence holds, how is it that there is no upper limit to the energy/mass that a body can gain

2. Oct 12, 2009

### Nabeshin

In SR, there is no upper limit. Kinetic energy is simply a function of rest mass and gamma, and since gamma is unbounded, so is kinetic energy.

However, I think at a certain point the energy density would become large enough to form a black hole. That might not be true though, but certainly the first statement is.

3. Oct 13, 2009

### Ich

No: velocity is relative, Black Holes are not.
But as you said, kinetic energy is unbounded, even if there is no rest mass.

4. Oct 13, 2009

### raknath

No i dont understand this.

If i assume that kinetic energy is essentially the energy gained on motion, then there needs to be an upper limit.

Essentially some velocity, assuming energy is gained through velocity cannot push infinite mass.

Also if we say that mass and energy are quite non divorcible then does mass contribute to the energy or velocity?

5. Oct 13, 2009

### Ich

Why not? Because E=m/2 v², or for what reason?

6. Oct 13, 2009

### raknath

Yes , also i am assuming that the actual push is the acceleration tied to the velocity, which becomes zero when velocity is constant

Am i wrong here someway?

7. Oct 13, 2009

### Ich

Yes, you missed the last 104 years.
Just a hint: $$E=m_0 c^2 \sqrt{\frac{1}{1-v^2/c^2}}$$ - that's what Nabeshin meant. Plot this function and have a look at it.
But you should read some basic introduction to SR, it's hard to answer specific questions if there is nothing one could start from.

8. Oct 13, 2009

### raknath

Thats just the mass change with increase in velocity. I get that my question is how is this mass limited and if it is not why is it not?

9. Oct 13, 2009

### Ich

That's total energy, sometimes called "relativistic mass". If you subtract the rest energy, you get kinetic energy. So yes, you're asking if this total energy is unbounded. And it is, as far as we know.

10. Oct 13, 2009

### Staff: Mentor

Let's assume that you are correct and there is some finite maximum energy. Now, suppose we have an object travelling with that energy. Since it is finite we know that v<c. If we then shine a single photon on that object we know that the photon will eventually reach the object (since the photon is going faster). When it reaches the object, by conservation of energy and momentum, the energy and momentum of the object must increase which would make it greater than the maximum, which is a logical contradiction. Therefore there cannot be any finite maximum energy.

11. Oct 13, 2009

### raknath

I was talking about bodies moving with the speed of light, i.e that is the maximum speed that the body can attain, so even something at the speed of light cant catch up with it

12. Oct 14, 2009

### Staff: Mentor

Use the equation Ich posted and tell me, what finite energy can you give to a 1kg mass so that it moves with the speed of light?