Can we accelerate particles to arbitrarily high energies?

[arroy_0205]

Is it possible in principle to accelerate particles to arbitrarily high energies? Suppose technology is no bar and there is sufficient money to build accelerators. Can we accelerate particles beyond say Planck energy? or is there is some limit? For example from special relativity we know that to accelerate a particle to speed of light we need infinite amount of energy. It seems like that there is a natural upper energy limit.

 

[Vanadium 50]

There is the energy of the universe.

 

[ZapperZ]

Is it possible in principle to accelerate particles to arbitrarily high energies? Suppose technology is no bar and there is sufficient money to build accelerators. Can we accelerate particles beyond say Planck energy? or is there is some limit? For example from special relativity we know that to accelerate a particle to speed of light we need infinite amount of energy. It seems like that there is a natural upper energy limit.

Haven't you just answered your own question here?

Zz.

 

[malawi_glenn]

yes speed has limit, but the important thing is center of mass energy.

 

[Meir Achuz]

Is it possible in principle to accelerate particles to arbitrarily high energies?

Yes. The Planck energy is just a convenient (or inconvenient) unit. It is not an upper limit to anything.

 

[Haelfix]

Well there is one. If you accelerate a particle to close to the Planck regime, its center of mass energy density will exceed the Scharwschild radius and collapse into a black hole. The more energy you stick into the accelerator, you end up making larger and larger black holes.

 

[malawi_glenn]

can an elementary particle become a BH ?

 

[Haelfix]

A point particle doesn't really have spatial extent so its not really a well posed question. But, certainly an interaction like what you would use a particle accelerator to probe is expected too.

 

[Vanadium 50]

Well there is one. If you accelerate a particle to close to the Planck regime, its center of mass energy density will exceed the Scharwschild radius and collapse into a black hole.

I don't see this. In its center of mass frame, it has its mass. The fact that some other observer is whizzing by shouldn't make any difference.

 

[Haelfix]

All you really need in principle is for the compton wavelength to be on the order of the Scharwschild radius.

 

[Timo]

All you really need in principle is for the compton wavelength to be on the order of the Scharwschild radius.

- Mathematically, you can achieve this by boosting to a different frame. Having effects happen in one frame but not in the other seems to break Lorentz invariance.
- The original Schwarzschild solution is for the cms frame (more specifically for a spherically symmetric distribution).

 

[Haelfix]

Timo, that works classically as well. You can boost a stellar object to the point where it will look like its collapsed into a black hole, and indeed people have written down that solution.

You might argue that either an object is or is not a black hole, and that's a little subtle b/c you get into how you would actually measure such an object (eg via hawking radiation) and then you get into far field discussions and so forth.

Anyway, from the point of view of the center of mass frame in a collision at a particle accelerator at sufficiently high energies, this sort of collapse is sort of the upper limit to its utility and where the whole thing ceases to probe substructure and instead goes into a classical regime.

 

[kdv]

Well there is one. If you accelerate a particle to close to the Planck regime, its center of mass energy density will exceed the Scharwschild radius and collapse into a black hole. The more energy you stick into the accelerator, you end up making larger and larger black holes.

There is an entry at John Baez' site that has a different conclusion

http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/black_fast.html

 

[Vanadium 50]

Timo, that works classically as well. You can boost a stellar object to the point where it will look like its collapsed into a black hole, and indeed people have written down that solution.

I don't see this. I'm sitting on a star, when an arbitrarily fast observer comes whizzing by. (I can pick the frame where I'm at rest, not the frame where he's at rest) Why should I collapse to a BH?

 

[Haelfix]

This is a classic debate incidentally, not everyone agrees with the resolution.

Its almost entirely equivalent to the 'electron on a table' problem. Which goes something like this 'You have an electron sitting at rest on a table, and an observer whizzes by the electron' Relative to the observer in motion, he see's a moving electron, and thus should measure radiation. But the electron is motionless in the frame of the observer watching from earth. So naively two observers will disagree about the results of an experiment done on the electron (say on a glass of water that presumably the radiation will heat up). Now run it viceversa (you drop an electron on a table), relative to the observer on Earth it should radiate, but someone who is in freefall with the electron should not.
So what gives?

There are various different ways out of the problem, and they all hinge on exactly what you mean by 'radiation'. Ditto for black hole formation. Implicitly the definition relies on a reference point at infinity, and therein lies the subtlety. Anyway, i'll try to find a source when I have the time.

 

[Vanadium 50]

Its almost entirely equivalent to the 'electron on a table' problem. Which goes something like this 'You have an electron sitting at rest on a table, and an observer whizzes by the electron' Relative to the observer in motion, he see's a moving electron, and thus should measure radiation.

I don't think he does. Moving electrons don't radiate. Accelerating electrons radiate.

 

[Haelfix]

Err yes, I should say the observer accelerates by the electron. Just like the electron accelerates by gravity in freefall (when you drop it on the table).

 

[Vanadium 50]

Okay, but a) we're talking about large velocites, not accelerations, so I don't think your analogy is appropriate, and b) while one cannot tell which of two observers is moving, one can tell which of two observers is accelerating.

 

[Haelfix]

Granted, but what I had in mind for the classical black hole 'paradox' was indeed about uniformly accelerating observers (point observers incidentally). The problem's resolution is very close to the electron dropping on a table analogy, since it gets into exactly what you mean by a 'blackhole' and a 'horizon'. The definition requires very specific farfield asymptotics, and neither observer can agree on those things (one has Minkowski, the other has something like Rindler). In the case of field theory, it boils down in a related way to to observer dependent effects on the vacuum configurations.

With regards to mini black hole production, the details do hinge in part on something formally similar (eg what you mean by black hole production relative to simply boosting or accelerating frames); at least so it was explained to me when I asked this very same question.
See G. ’t Hooft, Phys. Lett. B 198 (1987) 61; who I believe was the first to postulate the dynamics of mini black hole production in transplanckian accelerators.