Name: Anonymous 2009-02-19 19:06
What is the highest possible velocity a particle can be accelerated to?
Before anyone says "Speed of Light in a vacuum," "c," or anything related, let me point out why I ask this question:
1) Einstein's Theories of General and Special Relativity both say that no particle with a rest mass >0 can be accelerated to the speed of light in a vacuum.
2) As energy is added to a particle, it's velocity, as well as it's mass, increases. Up until roughly 70.7% of c, the velocity of the particle increases faster than the particle's mass. After 70.&% of c, the opposite occurs. This is seen in the Lorentz equation.
3) So, hypothetically, an infinite amount of energy can be added to a particle (this would increase the particle's mass to infinity, as a consequence).
4) The universe does not have an infinite energy supply, so there is a definite limit to how much energy a particle can carry.
Now if we take points 1, 2, and 3, we have a problem. When E = inf, then the particle's velocity would be c (the .999999...=1 proof that any decent algebra student knows). So, even in a universe that had an infinite energy supply, relativity would break down.
If we take all four points, then there is still a limit (a limit that is close to c, but is still less than c).
Now I know that there is the GZK limit that places a theoretical limit on how much energy a particle can carry (which direct observation has proven the calculations of the GZK limit to be wrong), but even when I look for values of the GZK limit, there are none to be found. All I get is information about pions and other useless shit like that.
So my question is: What is the highest velocity/energy a particle can achieve? or What is the highest lorentz factor a particle can have?
Let's face it, there has to be a limit. And if there's a limit, then why are we pussy-footing around with inferior particle colliders when we could build the ultimate biggest and baddest collider possible?
Before anyone says "Speed of Light in a vacuum," "c," or anything related, let me point out why I ask this question:
1) Einstein's Theories of General and Special Relativity both say that no particle with a rest mass >0 can be accelerated to the speed of light in a vacuum.
2) As energy is added to a particle, it's velocity, as well as it's mass, increases. Up until roughly 70.7% of c, the velocity of the particle increases faster than the particle's mass. After 70.&% of c, the opposite occurs. This is seen in the Lorentz equation.
3) So, hypothetically, an infinite amount of energy can be added to a particle (this would increase the particle's mass to infinity, as a consequence).
4) The universe does not have an infinite energy supply, so there is a definite limit to how much energy a particle can carry.
Now if we take points 1, 2, and 3, we have a problem. When E = inf, then the particle's velocity would be c (the .999999...=1 proof that any decent algebra student knows). So, even in a universe that had an infinite energy supply, relativity would break down.
If we take all four points, then there is still a limit (a limit that is close to c, but is still less than c).
Now I know that there is the GZK limit that places a theoretical limit on how much energy a particle can carry (which direct observation has proven the calculations of the GZK limit to be wrong), but even when I look for values of the GZK limit, there are none to be found. All I get is information about pions and other useless shit like that.
So my question is: What is the highest velocity/energy a particle can achieve? or What is the highest lorentz factor a particle can have?
Let's face it, there has to be a limit. And if there's a limit, then why are we pussy-footing around with inferior particle colliders when we could build the ultimate biggest and baddest collider possible?