Is there any Limit to the kinetic energy

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Discussion Overview

The discussion revolves around the limits of kinetic energy and momentum as predicted by Special Relativity (SR). Participants explore whether there is an upper limit to the kinetic energy that a body can achieve, considering concepts such as mass-energy equivalence and the implications of relativistic speeds.

Discussion Character

  • Debate/contested
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • Some participants propose that in SR, there is no upper limit to kinetic energy because kinetic energy depends on rest mass and the gamma factor, which is unbounded.
  • Others argue that at high energy densities, a body could theoretically form a black hole, although this claim is contested.
  • One participant expresses confusion, suggesting that if kinetic energy is gained through velocity, there should be an upper limit to the energy that can be imparted to a mass.
  • Another participant challenges this view, stating that the relationship between energy and velocity does not imply a finite maximum energy, citing conservation of energy and momentum in interactions with photons.
  • There is a discussion about the concept of relativistic mass and total energy, with some participants clarifying that total energy is unbounded as far as current understanding goes.
  • One participant questions how mass is limited if kinetic energy is unbounded, seeking clarification on the relationship between mass and energy in the context of relativistic speeds.
  • Another participant emphasizes that the speed of light is the maximum speed attainable, raising questions about the implications for energy transfer at that speed.

Areas of Agreement / Disagreement

Participants express multiple competing views regarding the existence of an upper limit to kinetic energy, with no consensus reached on the implications of relativistic effects and the nature of energy at high velocities.

Contextual Notes

Some statements rely on specific interpretations of relativistic physics, and there are unresolved assumptions regarding the definitions of energy and mass in the context of high-speed motion.

raknath
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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
 
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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.
 
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.
 
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?
 
Essentially some velocity, assuming energy is gained through velocity cannot push infinite mass.
Why not? Because E=m/2 v², or for what reason?
 
Ich said:
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?
 
Am i wrong here someway?
Yes, you missed the last 104 years.
Just a hint: [tex]E=m_0 c^2 \sqrt{\frac{1}{1-v^2/c^2}}[/tex] - 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.
 
Ich said:
Yes, you missed the last 104 years.
Just a hint: [tex]E=m_0 c^2 \sqrt{\frac{1}{1-v^2/c^2}}[/tex] - 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?
 
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.
 
  • #10
raknath said:
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.
 
  • #11
DaleSpam said:
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
 
  • #12
raknath said:
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?
 

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