# Approaching the speed of light

1. Nov 1, 2012

### ShayanJ

You know that in accelerators like LHC,particles are accelerated to speeds very near to that of light
I want to know what phenomenons are observed in such high speeds,because lorentz transformations don't seem very clear there
Thanks

2. Nov 1, 2012

### tiny-tim

uhh?

they're perfectly clear there … that's exactly where they're designed for!

were there any particular phenomena you were thinking of?​

3. Nov 2, 2012

### ShayanJ

The point is,the numbers are so near to c and I just didn't think they're so straight forward
Also,I heard in an animation explaining about LHC,that the particles when are at a speed very near to that of light,if accelerated,won't increase speed but mass
I know about the mass increase during the acceleration from the first but the explanation seemded to suggest sth new
well,sorry for the nonsense question

4. Nov 2, 2012

### Ibix

As I recall, $F=\gamma^3ma$. You get less acceleration for the same force the faster the particle goes - obviously, because otherwise you could accelerate past light speed. One interpretation of that is that "mass increases as you get closer to the speed of light", defining a relativistic mass, $m_r=\gamma^3m$ so that $F=m_ra$.

That explanation is quite popular because it plays well with the "modern physics is so weird!!!!!!!" narrative that has got built up. It doesn't get much love here; I suspect the reasons for that are twofold. One, $p=\gamma mv$ (note, no cube), so here we would define a different relativistic mass. That would get confusing fast. Second, Einsteinian Relativity isn't just Newtonian Relativity with a couple of extra terms. It is dubious that defining a relativistic mass so that some of the equations look the same is at all helpful.

So, what happens in the LHC is that the particles' energy is increased, but as they are already doing near-lightspeed, this does not translate to much of a velocity increase. Then they collide and high-velocity low-mass particles have a chance to become low-velocity high-mass particles.

Last edited: Nov 2, 2012
5. Nov 2, 2012

### tiny-tim

Hi Shyan!
The speed does increase slightly, but the mass increases more!

It's probably easiest to consider the rapidity

the rapidity increases steadily and towards infinity.

Rapidity is α, where tanhα = v/c, coshα = γ = 1/√(1 - v2/c2) (so tanh∞ = 1 = c/c, and infinite rapidity is speed c),

see http://en.wikipedia.org/wiki/Rapidity

6. Nov 3, 2012

### ShayanJ

Here's a,I guess, more complete treatment

7. Nov 3, 2012

### Staff: Mentor

Which is of course different from the "relativistic mass" that most people know about, namely $m_r = \gamma m$. The difference is in the direction of the force with respect to the particles's motion. The standard "relativistic mass" works if the force is perpendicular (transverse) to the motion. Your version works if the force is parallel (longitudinal) to the motion. Some early treatments of SR acknowledge both versions and call them "transverse mass" and "longitudinal mass."

If the force is neither longitudinal nor transverse, things get messy. The acceleration isn't even in the same direction as the force! :yuck:

8. Nov 3, 2012

### harrylin

Almost correct: m=γm0 is in SR only a function of speed, not of direction - in fact it replaced the unhandy "transverse mass" and "longitudinal mass" definitions. And of course, no definition can change the fact that for force under an angle, the acceleration is not in the same direction anymore. :tongue2:

Anyway, it is indeed a "special" effect from high speeds that an additional energy increase results into more momentum at very little speed increase. The happy thing about momentum is that there is only one definition that includes the γ.

Last edited: Nov 3, 2012