Is there any Limit to the kinetic energy

[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

 

[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.

 

[Ich]

However, I think at a certain point the energy density would become large enough to form a black hole.

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

 

[raknath]

No i don't 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?

 

[Ich]

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

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

 

[raknath]

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

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?

 

[Ich]

Am i wrong here someway?

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.

 

[raknath]

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.

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?

 

[Ich]

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?

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.

 

[Dale]

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

Let's assume that you are correct and there is some finite maximum energy. Now, suppose we have an object traveling 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.

 

[raknath]

Let's assume that you are correct and there is some finite maximum energy. Now, suppose we have an object traveling 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.

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 can't catch up with it

 

[Dale]

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 can't catch up with it

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?