First collisions at the LHC with unprecedented Energy! (Ask a particle physisicist)

[Alex K]

contd.:

Removing the infinities: so, when you use quantum field theory to calculate anything, many quantities will naively come out infinite. Heisenberg already had sleepless nights over this problem, a generation before Feynman, Schwinger, Tomonaga,Dyson and friends. It was therefore thought that field theory is bunk.

The trick to remedy this is called renormalization. The important insight is that the free parameters of the theory are not themselves observable quantities. People always assumed they were finite numerical quantities and got infinite results for observable values such as particle masses and scattering cross sections. The insight now was that the input parameters are not finite numerical values. By sending them to infinity simultaneously in a controlled fashion, the observable results of the calculations become finite. How one can still specify the free parameters of the theory by specifying numbers one can write down on a piece of paper and do calculations with, is a technical trick - one fixes the scheme of what relatove values one adds to each of the parameters in sending them to the limit ->infinity, and can then specify actual numbers, which are however not meaningful in their own right, but only if one specifies in which manner one had to add "infinity" to each of them in the sense of a mathematical limit.

[Alex K]

QCD: indeed, QCD has the curious property that the interaction becomes stronger at large distances/low energies, which makes studying it much harder. Why QCD has this property is hard to explain visually. Possibly because I don't understand it well enough. Maybe this: the larger the distance and the longer one waits, the more time the virtual particles between say two quarks have to build up force. It indeed ends up looking like a sticky mass of glue between them.

I need to buy a better intuition plug-in.

If the interaction is stronger at larger distances, shouldn't the amount of work needed to remove the particles (quarks?) away from one another make the far apart particle condition one of higher (internal) energy?  Or isn't the interaction one of binding the particles together?  I'm confused about what high/low energy means in this context.

That is a very smart question. So yes, on the one hand, by investing higher energy one can probe shorter distances and finds that the internal energy of the binding one observes in the process becomes - less!, and therefore quickly so much less than the energy you put into the whole reaction as to become irrelevant ("asymptotic freedom of the quarks at high collision energies"). If you invest less energy into the collision, you will probe physics at larger distances and will see interactions with, oddly, larger binding energy, so the binding energy goes up if you put less energy in. At some point, this binding energy will grow beyond the energy you put into the system to make the observation in the first place. At that point, you will for this reason stop resolving the quarks, and will only see protobs, neutrons...

[JuliaL]

That is a very smart question. So yes, on the one hand, by investing higher energy one can probe shorter distances and finds that the internal energy of these binding becomes less, and therefore quickly so much less than the energy of the whole reaction as to be irrelevant. If you invest less energy into the collision, you will probe physics at larger distances and will see interactions with, oddly, larger binding energy. At some point, this binding energy will grow beyond the energy you put into the system to make the observation in the first place. At that point, you will for this reason stop resolving the quarks, and will only see protobs, neutrons...

I've been in this situation before. Some experienced instructor will explain a situation carefully and repeatedly yet in slightly different ways, initially with little effect. Eventually I experience a revelation and with great enthusiasm repeat back to them exactly what they have been telling me over and over. I feel something new and amazing. It's pretty dull for the teacher.

So you can hit the quark-gluon conglomeration with a high energy something and not see the (low) binding energy because it gets lost in the noise of the energetic interaction. Or you can hit it with something less energetic and still see nothing because the less energetic (collision?)(interaction?) is not able to resolve the individual components.

Hubble was able to watch Pluto for a long time but not very clearly. New Horizons could see Pluto with fine resolution, but couldn't watch very long. That's some catch, that catch 22.

[Alex K]

(I slightly edited above answer since your quote)

Kind of, yes. If you hit it with less energy, you don't see nothing though, you see bound states doing something. The objects of the theory are different particles at that level of coarse grainy observation than one has microscopically. The transition between the two worlds (called the matching of one theory -that of protons, neutrons etc- to the other - that of quarks and gluons-) is very challenging and only partly understood, precisely because the interactions become so strong at that point, and strong interactions means difficult to calculate.

[JuliaL]

Kind of, yes. If you hit it with less energy, you don't see nothing though, you see bound states doing something. The objects of the theory are different particles at that level of coarse grainy observation. The transition between the two worlds (called the matching of one theory -that of protons, neutrons etc- to the other - that of quarks and gluons-) is very challenging and only partly understood, precisely because the interactions become so strong at that point, and strong interactions means difficult to calculate.

I'm still at the billiard ball level of particle visualization.
Are wave packets a better metaphor? The waves I'm familiar with oscillate some medium.
Is there an equivalent in QCD?
Do gluon packets travel from baryon to baryon? If so, is this in what you've called gluon and quark fields?
Is there anything in the math that explains how they get started?
Somehow, this all hangs together in the best empirically verified theory in all of science.

[Alex K]

Nope, particle wave functions are not thought to be oscillations in a medium, mainly because Einstein's relativity killed the notion of the aether for light, and this paradigm shift is inherited by the other particles.

[Alex K]

Wave packets are a better metaphor - remember that narrow wave packet means large energies are involved - this is why one needs large energy to probe small distances.

The fields are... Also not a medium. They really are mathematical descriptions how particles are created.

[JuliaL]

Thanks, it's been informative and educational.
Still, I've always been confused by waves in nothing.
Seems to me there at least has to be a potential to have a wave there and that's something.

That's also why creation ex-nihilo never made any sense to me either Divine creation wasn't from nothing, it was from at least a causal potential to create in God itself.
But religion doesn't have to make sense. It works better that way.

[Alex K]

JuliaL,

Are you less irritated by matter moving through the void?

[Sappho]

No, it might suprise you but I did not read these 28 pages of physics.
But I am very interested in this kinda stuff, although I don't really know much about it yet.

What is energy? I mean this in a way as: how should I imagine it?
It is not always bound with matter (potentional, kinetic) so it can float trough space, but it has no shape nor seize nor volume.
Matter at least is, for what i've read, one-dimensional, or a wave-function presenting the possiblity of being somewhere.
But energy is the thing that always disturbs me.