*Iveta Bartošová, Two Years' Vacations (1988). Lyrics: "You [the beam] used to say: I will be back right away. It's just two years' vacation, nothing more." Well, OK, it was originally two years of military service but I found the pop song relevant, anyway.*

The collider is designed for the center-of-mass energy of \(14\TeV\). I guess that it's still the plan to get to that level – maybe sometime during 2015. However, March 2015 will begin the acceleration to a somewhat lower energy, \(13\TeV\) which means \(6.5\TeV\) per proton. Collisions used by physicists should be available from May 2015. See some Google News.

The near-doubling of the energy may open a completely new realm. Some hypothetical new particles may be practically inaccessible at \(8\TeV\) but they may be produced routinely at \(13\TeV\). I think it's totally plausible that deviations from the Standard Model will emerge after the first inverse femtobarns of the 2015 collisions. Just to be sure, I am not saying that it is "extremely likely". It is just plausible. The probability could be dozens of percent.

The doubling (of energy) is a rather big step on the logarithmic scale and you may look at the energy scales of the known physics to see that in many cases, it would have been enough for a qualitative step.

It may be fun to mention a couple of particular numbers linked to this energy of a proton, to emphasize that the LHC is working with quadrillions of protons that are ultrarelativistic and the special theory of relativity is the daily bread-and-butter for the LHC folks and their consumers. The rest mass of the proton is\[

m = \frac{1}{c^2} \cdot 0.938\GeV

\] It follows that the Lorentz gamma factor at the 2015 energies equals\[

\gamma = \frac{E_p}{mc^2} = \frac{6,500\GeV}{0.938\GeV} \approx 6,930.

\] The hadron is 6,930 times heavier than it is at rest. We are used to tiny speeds at which the increase of the total mass is a tiny, usually unmeasurable fraction of 1%. At the LHC, it's not only comparable to 1% or 100%. It is a 690,000% increase of the rest mass. ;-)

You should understand that this gamma is given by the usual formula that Lorentz has played with some years before Einstein realized what the proper laws of relativity were:\[

\eq{

\gamma &=\frac{1}{ \sqrt{1-v^2/c^2} }\\

\frac{1}{\gamma^2} &= 1- \frac{v^2}{c^2}\\

\frac{v}{c} &= \sqrt{1- \frac{1}{\gamma^2} }

}

\] Substitute our value of \(\gamma\) and you will see that the 2015 speed of the protons is\[

\frac{v}{c} = \sqrt{1-2.08\times 10^{-8}} \approx 1 - 1.04 \times 10^{-8}

\] The speed \(v\) is smaller than \(c\) but only by 10 parts per billion; the speed is 99.999999% of the speed of light (the digit "nine" is there eight times, no exaggeration here). One billionth of the speed of light is 30 centimeters per second or so. So the speed of the protons is smaller than the speed of light by 3 meters per second.

Imagine that the LHC protons and photons compete in a race – 7.5 laps around the equator which is almost exactly 300,000 kilometers. It takes a second to complete the race. After those 7.5 laps, the photon will win the race but it will only be ahead by 3 meters – or 10 nanoseconds, a few cycles of your microprocessors.

*Theme song of a TV serial, Two Years' Vacation.*

At this speed, the proton is shortened in the direction of the motion. It is 6,930 times longitudinally contracted. Its life processes are slowed down, too. So its average lifetime in the lab frame is 6,930 times longer than the (already extremely long if not infinite) life expectancy of a proton at rest.

If the proton were sending some radiation, the observed frequency would be increased or decreased by the longitudinal relativistic Doppler shift given by the coefficient\[

\frac{f_1}{f_2} = \sqrt{ \frac{1+v/c}{1-v/c} } = \gamma \zav{1+\frac vc} \approx 2 \gamma \approx 13,860.

\] The frequency would jump or drop fourteen thousand times! You may also talk about the rapidity \(\varphi\), the "hyperbolic angle" in the Minkowski \(t\)-\(x\) plane. It may be computed from\[

\frac{v}{c} = \tanh \varphi

\] or from \[

\gamma= \cosh \varphi.

\] The pseudorapidity ends up being \({\rm arccosh\,}6,930 \sim 9.54\); verify that you get the same result using the \({\rm arctanh}\) method, too. It's much less than those seven thousands but it's still a lot. If it were not rapidity but an ordinary angle – if the "h" ("hyperbolic") were absent in all the formulae – then it would make sense to write \(9.54\) as \(3.04\pi\). It would be about \(1.5\) periodicities. However, unlike the usual angle, rapidity (the hyperbolic angle) is not a periodic variable. It goes to infinity.

However, you can still see that the accelerator is boosting these protons and switches from the lab frame to the proton frame which is rather far away. It's so far that if there were some "natural" violations of the Lorentz symmetry implied by the assumption that the fundamental laws are not Lorentz-invariant at the basic level, we would have almost certainly seen such deviations.

So far, the results from the LHC seem to be compatible with the Standard Model – if we ignore a few inconclusive hints of a deviation and the so far unpublished papers. We don't know whether this agreement will continue. But I would still like to point out that the agreement of the LHC results with the special theory of relativity and other pillars of physics could also be interpreted as a nontrivial agreement. And this compatibility has been tested much more accurately and in a much broader range of applications.

Certain laws in physics are robust and verified very accurately and universally and there are reasons to think that special relativity will hold in similar experiments for centuries and probably forever; others, like the sufficiency of the Standard Model for experimental particle physics, are temporary working hypotheses whose life expectancy may be comparable to a few years or decades.

Typo in your title, 2013 instead of 2015

ReplyDeleteOops, thanks, I never proofread titles. They should be proofread several times! ;-) I subtracted the two years in some way, or got confused by March's being the 3rd month, or something like that. Alcoholic beverages from parties yesterday - I will avoid even one beer today. ;-)

ReplyDeleteI can imagine poor guys, stuck in some military shack for two years, watching Iveta on TV.

ReplyDeleteHopefully, LHC will bring pleasant surprises after two years of waiting. Personally I would like to see Suzy.

Dear Tony, I finally decided not to write these off-topic reminders. But the video is 25 years old, it is a love song of a girl to her BF who has to go to the army for 2 years, and Iveta committed suicide 8 months ago:

ReplyDeletehttp://motls.blogspot.com/2014/04/iveta-bartosova-1966-2014-murdered-by.html?m=1

She jumped under the train, after some problems with men, alcohol, and I would say "especially" with incredibly hostile tabloids.

Substitute a muon for an electron in an atom. Its ground state orbital radius contracts to 1/206.8. In a heavy atom it can orbit

ReplyDeleteinsidethe nucleus! [U(91+) is rather awesome all by itself re Lamb shift.] An atomic nucleus is rather dense. The muon only sees electric charge.The universe could be a wild and hairy place indeed - but only if you strike the interaction that sees it. LHC could be looking in the wrong place. Validating theory is nice, falsifying theory is useful. Look where theory assumes it is safe, and in a different way.

Dear Uncle Al, the muon decays for "internal reasons" - i.e. independently of its incorporation in the environment - after two microseconds in average which limits the usefulness of such bound states.

ReplyDeleteHowever, during those 2 microseconds, such objects may still be studied theoretically and experimentally and they're not so mysterious. Note that the rest mass of the muon is 106 MeV, comparable to the binding nuclear energies, which is why these things may really be of the same order when muon is found around some nuclei.

But the muon is color-neutral and even though the nucleus looks dense, you should still imagine that it's moving through an empty space inside the nucleus where just a few partons live, and they only interact with the muon electromagnetically (plus weak interactions which are very weak, and we neglect gravity). Those are objects we may be unfamiliar from the experience but it doesn't mean that there's something totally mysterious about them. They're pretty much the same conceptually as many things we know - at least I believe that you can't find any contradiction between their behavior and the state-of-the-art physics.

Electrons (and positrons) in the Tevatron had a gamma of nearly 2 million (US million=10^6). The energy was lower than at LHC, but electrons are a *lot* lighter than protons. Cosmic ray derived neutrinos must have a much higher gamma still. We don't know the rest masses, but they have to be pretty small.

ReplyDeleteIf I were looking for violations of Lorentz invariance (I am not), I'm not sure I would be looking at LHC.

Hi Lubos: Is it possible to get some idea of energies with which individual quarks and gluons will be colliding? I understand it must be a complicated distribution function of energy and direction in which the quarks and gluons are moving. But do they have plots of this kind?

ReplyDeleteLOL, Ralph. I assure you that the Tevatron would always accelerate the protons against antiprotons, so the mass is exactly the same as here, and never electrons or positrons. It was a hadron machine just like the LHC!

ReplyDeleteThey have not only plots but all the relevant distributions and their impact on all interactions so that they may emulate what's going on. If they didn't have it, they couldn't predict what is observed at the LHC at all.

ReplyDeleteThanks. They probably use these parton distribution functions to analyze each event. How about non valence, virtual quarks and gluons?

ReplyDeleteNot contradiction but rather unexpected non-interaction when simplistically viewed. There is only one working gravitation theory, GR. GR is a continuous geometry that does not empirically quantize. Gravitation

ReplyDeleteisquantized. There is a carefully invisible footnote existing theory violates.I call for bench top geometric tests of the Equivalence Principle. I'm told they cannot be fertile. That's the footnote - where nobody looks. There is only one purely discontinuous symmetry, chirality. It is removed by Green's theorem in classical physics (but never proven to be within GR). Chirality beats quantizations bloody, fixed by curve fittings. Look at the source.

It is sad and at the same time fascinating story. Her hairstyle reminded me of someone, long time ago, which prompted me to comment, but I almost can't believe the story.

ReplyDeleteHow did they double the energy of the LHC?

ReplyDelete