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Gravity is ignored in the SM. The proton rest mass is ~0.938 GeV/$c^2$. LHC protons will move with 7 TeV energy, presumably with a relativistic mass about 7,450 times rest mass. A cosmic ray with the highest energy was detected at about $6\times 10^{21}$ eV. If it was a proton, its relativistic mass would have been about $6.4\times 10^{12}$ times rest mass. My question is, at what energy levels would it be necessary to include gravity in the SM? I recognize this isn't an issue for forseeable particle accelerators, but astronomical events like supernova are capable of generating extremely high energy particles.

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Until I started hanging around physics.SE, I had no idea so many people still talked about "relativistic mass." As far as I know, practicing physicists pretty much never use this terminology anymore. (See among others for some rants against the idea of relativistic mass.) But terminological issues aside, if I'm not mistaken the only relevant energy scale here is the Planck energy, about $10^{19}$ GeV. A particle accelerator smashing things together on that energy scale would have to account for gravitational effects. – Ted Bunn Mar 24 '11 at 18:04
@Ted: that's my impression as well, that "relativistic mass" is an outdated term. People do use it occasionally, but in many cases I think it's used informally and could be read as "mass equivalent of the total energy." This seems like it could be one of those cases (although I don't know what Michael intended). – David Z Mar 24 '11 at 18:13
Sorry if it sounded like I was jumping on Michael Luciuk. I think the question is perfectly reasonable, and this is just a point of terminology. I mention it just because I have seen tons of mentions of relativistic mass on physics.SE, far more than, say, back when I used to participate in the Usenet physics groups back in the 90's. I'm genuinely curious about why that is, although obviously that question is off-topic here! – Ted Bunn Mar 24 '11 at 18:28
summing up: there is no extra gravitational contribution from particles moving inertially at any speed whatsoever. – lurscher Mar 24 '11 at 18:28
Hi gentlemen. My "relativistic mass" was intended to mean Ted's "mass equivalent of the total energy" or gamma x rest mass. Is there a another word for this? – Michael Luciuk Mar 24 '11 at 18:37

This question is a bit open ended. There are theories and maybe some experimental hints of extra large dimensions and black hole or AdS amplitudes with heavy ion collisions. The jury is of course still out, but there might be some gravity physics creeping into the standard model + QCD in the TeV energy range and above.

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At or near Planck energy gravity has to be taken seriously and directly. But even at much lower energy scale number of extra ordinary phenomena should take place which should be "beyond standard model". However no body knows for sure about the exact energy scale of this "beyond standard model" physics. It is likely that some "beyond S.M." physics should be observed at the LHC energy scale.

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