Question on the speed of collisions in the LHC

acurno

Hi All,
Was looking at some videos on the LHC and one of the physicists said that the speed of the particles travelling through the accelerator are only approx 10m/s slower than the speed of light.

http://www.sixtysymbols.com/videos/lhc.htm

I've always read though that if matter approached the speed of light, the energy required, and mass, would increase exponentially and the mass would increase infinitely big. e=mc squared and all that.

Have I got this pear-shaped somehow? Totally novice question I know.

Enkidu

Yes, everything you say is correct. However the particles aren't at the speed of light, they're simply very close to it.

Also I should say there is such a thing as the invariant mass of the particles, which does remain the same. Rather their Energy and Momentum grow enormously.

acurno

So are you saying individual particles don't increase in mass as they approach c? What kind of matter would grow exponentially as it approached this speed?

Back to the LHC, is 10m/s that the particles travel at way slower 'relatively' to the speed of light? Is this as fast as they could theoretically travel in a man-made collider?

Sorry for all the questions, this subject fascinates me.

AlmightyCushion

acurno wrote: »

So are you saying individual particles don't increase in mass as they approach c? What kind of matter would grow exponentially as it approached this speed?

Back to the LHC, is 10m/s that the particles travel at way slower 'relatively' to the speed of light? Is this as fast as they could theoretically travel in a man-made collider?

Sorry for all the questions, this subject fascinates me.

They could probably travel faster as long as the speed is less than the speed of light but the energy required to go faster than they currently are would be enormous. At least that is my understanding of things.

rccaulfield

Don't those particles have zero mass?

AlmightyCushion

rccaulfield wrote: »

Don't those particles have zero mass?

I thought photons were the only particles that don't have mass.

Improbable

http://journal.batard.info/post/2008/09/12/lhc-how-fast-do-these-protons-go

Enkidu

acurno wrote: »

So are you saying individual particles don't increase in mass as they approach c?

They do from our perspective, but in reality they do not.

Back to the LHC, is 10m/s that the particles travel at way slower 'relatively' to the speed of light? Is this as fast as they could theoretically travel in a man-made collider?

A larger collider could make them go faster. However due to relativity, from the point of view of the particles, light is still moving 300,000,000 m/s faster than them.

Morbert

AlmightyCushion wrote: »

I thought photons were the only particles that don't have mass.

The gluon is also massless, as well as the theoretical graviton. The particles the LHC will be dealing with are hadrons, and have mass.

Enkidu

AlmightyCushion wrote: »

I thought photons were the only particles that don't have mass.

They are! Although physicists use massless particles occasionally as a mathematical convience in calculations, the standard model doesn't predict the existence of any except photons.

Morbert

Enkidu wrote: »

They are! Although physicists use massless particles occasionally as a mathematical convience in calculations, the standard model doesn't predict the existence of any except photons.

Hmmm... What about the gluon?

Enkidu

Morbert wrote: »

Hmmm... What about the gluon?

The gluon only appears in perturbative calculations, but isn't part of the spectrum of the actual field theory. In quantum field theory there isn't usually a one to one correspondance between fields and particles, however since virtually all field theories (except certain two dimensional ones) are analytically intractable we commonly expand about a free theory in order to do calculations. This causes us to use particles of the free theory. In the case of Quantum Chromodynamics this free theory is one with particles carrying a color charge called gluons, so we use the gluons in calculations. However in nonperturbative formulations they never show up, neither does color charge, they are simply artefacts of perturbation theory.

Morbert

Enkidu wrote: »

The gluon only appears in perturbative calculations, but isn't part of the spectrum of the actual field theory. In quantum field theory there isn't usually a one to one correspondance between fields and particles, however since virtually all field theories (except certain two dimensional ones) are analytically intractable we commonly expand about a free theory in order to do calculations. This causes us to use particles of the free theory. In the case of Quantum Chromodynamics this free theory is one with particles carrying a color charge called gluons, so we use the gluons in calculations. However in nonperturbative formulations they never show up, neither does color charge, they are simply artefacts of perturbation theory.

This isn't really my area so I am unsure of a lot of things. I knew you had to include unphysical scalar Grass-mann fields to sort out gluon polarisation states, but did not know the gluons themselves are considered unphysical because they are part of a perturbative formulation. I thought it was accepted that three-jet events imply the existence of gluons.

Enkidu

Morbert wrote: »

This isn't really my area so I am unsure of a lot of things. I knew you had to include unphysical scalar Grass-mann fields to sort out gluon polarisation states, but did not know the gluons themselves are considered unphysical because they are part of a perturbative formulation. I thought it was accepted that three-jet events imply the existence of gluons.

I can understand the confusion. Often it is just much easier to talk in terms of the particles we use in calculations, since these can be visualised using feynman diagrams.

Let me say it this way. QCD is a quantum field theory whose perturbation theory is expressed through feynman diagrams composed of lines and verticies like all quantum field theories. Some of these lines in the diagrams behave as the lines produced by free massless particles with a charge, we call these gluons. They're not actual, physically real particles predicted by QCD, but it's "nicer" to think of them as particles than just diagram lines*. So saying

"three-jet events imply the existence of gluons"

is really just a short way of saying

"three-jet events are only predicted by quantum field theories with feynman diagrams containing lines which are like massless, charged particles hence seeing three jet events is evidence for these theories"

WalterMitty

are particles going in opposite directions that hit each other colliding with an effective speed greater than the speed light as both are travelling at near light speed ?

Morbert

WalterMitty wrote: »

are particles going in opposite directions that hit each other colliding with an effective speed greater than the speed light as both are travelling at near light speed ?

Velocities don't add linearly at high speeds. If you have two particles travelling at speeds v and u in opposite direction, the relative velocity is not v+u. It's

(v+u)/(1+v*u/c*c)

where c is the speed of light.

http://en.wikipedia.org/wiki/Velocity-addition_formula

mikhail

WalterMitty wrote: »

are particles going in opposite directions that hit each other colliding with an effective speed greater than the speed light as both are travelling at near light speed ?

This is one of the points where relativity confuses me a bit. I'm pretty confident that from the perspective of either of the particles, the other particle is only moving at the speed of light relative to them, but as for the perspective of your stationary observer, I'm not clear.

Morbert

mikhail wrote: »

This is one of the points where relativity confuses me a bit. I'm pretty confident that from the perspective of either of the particles, the other particle is only moving at the speed of light relative to them, but as for the perspective of your stationary observer, I'm not clear.

Let's take a specific example.

Imagine two particles travelling at .99 c (99% of the speed of light) with respect to a stationary observer. I.e. A stationary observer sees both particles travelling at a speed of .99c in opposite directions. If we shift to the perspective of one of the particles, they will see the other particle moving at a speed of

.99c+.99c/(1+.99c*.99c/c*c)

= 1.98c/(1+.9801c*c/c*c)

= 1.98c/(1.9801)

= 0.999949c (99.9949% of the speed of light)

So no observer witnesses any particle travelling faster than the speed of light.

mikhail

Yeah, cheers. I know that much (though I was a little lax in what I said above). I just have this niggling idea in the back of my head that the stationary observer can't use the figure of 1.98c for relative velocity. It's so nebulous that I'll have to chalk it up to not having formally looked at relativity since I was a teenager (and hardly even then).

Morbert

mikhail wrote: »

Yeah, cheers. I know that much (though I was a little lax in what I said above). I just have this niggling idea in the back of my head that the stationary observer can't use the figure of 1.98c for relative velocity. It's so nebulous that I'll have to chalk it up to not having formally looked at relativity since I was a teenager (and hardly even then).

1.98c could, in a sense, correspond to a 'speed' in which the distance between the particles is shrinking from the perspective of the stationary observer (from the perspective of the particle, it would be .999949c). This notion of 'speed' isn't forbidden by relativity. In a similar manner, you could sweep a shadow across the moon at any 'speed' you wanted. In both cases, there is nothing that is technically travelling faster than light. No information, for example, could be sent between the particles, or across the moon, at 1.98c

WalterMitty

is time slowing down at very high speeds relevant?

mikhail

WalterMitty wrote: »

is time slowing down at very high speeds relevant?

Yeah, that's pretty much how the two particles see each other moving at less than c.