Particle Physics Question

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?

>>1

silly question, at least according to my (very basic I might add) understanding of it.

GZK limit isn't a physical limit, it's to do with the fact that once the source of the cosmic ray is far enough away it should decay a certain amount before it reaches earth, however we actually see cosmic rays with higher energies then we expect from this model, so obviously something's wrong anyway.



I think your problem is in point 4. If you accept point 4 is true, then a limit should exist.

However quantum effects mean you can "borrow" energy, as long as it only affects the particle for a "small" amount of time (related to the amount of energy).

I'd have though, that whilst the probability of it happening tends to zero, for all energy levels there is still a possibility, however remote, that it might happen, therefore there can be no limit on the speed of a particle (well, below c).


Correct me if I'm wrong 4tran