Particle accelerators reaching light speed

Question

I just have a question in mind that's stuck in my head, and it's why particle accelerators cannot accelerate any particle to the speed of light. I'm assuming it involves Einstien's theory of relativity.

Possible duplicate: http://physics.stackexchange.com/q/63555/8521, http://physics.stackexchange.com/q/1557/8521 — DilithiumMatrix, Jan 06 '16 at 20:52

Floris · Accepted Answer · 2016-01-06T20:41:49.153

2

They get awfully close. Rather than talk about the "velocity" of particles, the folks at CERN end up talking about the "energy" - because once you're at 0.99 c and above, your energy continues to increase (basically, mass increases) but the velocity doesn't - much. That is expressed by the factor $$\gamma = \frac{1}{\sqrt{1-\frac{v^2}{c^2}}}$$ yes, it is a consequence of the theory of relativity. The current record of energy is about 7 TeV for a lead nucleus which has a "rest mass" of ~0.2 TV, meaning $\gamma=14$ and v=0.997 c

In 2015, the LHC was running with 6.5 TeV protons (link); since their mass is much smaller than the mass of lead (938 MeV), this corresponds to a $\gamma$ of about 6900, and $$v = 0.9997 c$$

edited Jan 06 '16 at 20:41

answered Jan 06 '16 at 20:21

Floris

118,905

That's the record for nuclei at the LHC. Protons of course go faster, LEP II had electrons at still higher gamma, and neutrino beams get even higher gamma than that. – dmckee --- ex-moderator kitten Jan 06 '16 at 20:26
@dmckee - right. Protons go faster, but I don't think they have higher energy - do they? Please feel free to add more information. I originally just had this as a comment... – Floris Jan 06 '16 at 20:29
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The bending limit is actually given by momentum (which should therefore be the same between the beams), but I was mostly thinking in therms of $\gamma$. They have the same energy and lower mass so they have higher Lorentz factor. – dmckee --- ex-moderator kitten Jan 06 '16 at 20:32
The LEP collider accelerated electrons (and positrons) to 104 GeV. This was a $\gamma=\frac{104,000}{.511}=2\times 10^5$ which makes $\frac{v}{c}=.99999999999$. Pretty close to c! – Gary Godfrey Jan 06 '16 at 21:41
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The speeds are deduced from their energy. But since the accelerating mechanism of the CERN gives a push every time a bunch of particles comes by, and the frequency of pushing and the length of the trajectory are very well known, you can measure their speed with considerable accuracy. – Floris Jan 06 '16 at 22:17

score -11 · Answer 2 · answered Jan 06 '16 at 20:58

I just have a question in mind that's stuck in my head, and it's why particle accelerators cannot accelerate any particle to the speed of light.

It's because of the wave nature of matter. We can quite literally make matter out of light waves in pair production. Then we can diffract electrons. And in atomic orbitals electrons "exist as standing waves". Images like this de Broglie atom by Kenneth Snelson are a bit of an oversimplification, but they get the point across:

enter image description here

Floris referred to the Lorentz factor. Have a look at the simple inference of time dilation due to relative velocity in the Wikipedia time dilation article. The Lorentz factor can be derived from Pythagoras's theorem. The hypotenuse of a right-angled triangle represents the lightpath where c=1 in natural units. The base represents your speed as a fraction of c:

enter image description here _{Public domain image by Mdd4696, see Wikipedia}

The height gives the Lorentz factor $\gamma$, and we use a reciprocal when appropriate, for example to distinguish time dilation from length contraction.

I'm assuming it involves Einstein's theory of relativity.

It does. The mass of a body is a measure of its energy-content. A radiating body loses mass. In electron-positron annihilation to gamma photons, two radiating bodies lose mass. We have evidence of things like magnetic moment and electron spin where the Einstein de Haas effect demonstrates that "spin angular momentum is indeed of the same nature as the angular momentum of rotating bodies as conceived in classical mechanics". So look at the picture of the de Broglie atom again and think of the electron as a wave going round the n=1 circle: O. Then turn the circle on its side like so: | . Then move it, and it resembles the light beam above: /\. It can be likened to stretching out a helical spring. It gets harder and harder to stretch it out, and you can't stretch it straighter than straight. In similar vein you can add more and more energy but you can't get the electron moving faster than light.

Particle accelerators reaching light speed

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