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From what I heard, unless we have some kind of other influence, all things and light move at the straight lines in spacetime. If they have a mass, then they can never reach the speed of light, but all the massless ones are constantly traveling at the speed of light.

Now, with photons it's easy to understand, that is: curvature of spacetime around the giant mass can be so big that they are eventually getting "trapped" within certain area, being unable to run away. HOWEVER, the curvature so big causes an "event horizon", i.e. we have a black hole now.

So, I recently learned from some youtube videos that gluons are massless, but only today I noticed this paradox:

  1. Gluons are massless

  2. They are massless, thus they should travel at the speed of light. That's what I heard many times, that massless things always travel at the speed of light.

  3. Participating in strong interactions between the quarks, they are "trapped" within a very tiny region of spacetime that we call "hadron". We don't see some of the gluons running away or spilling outside of proton, resulting in breaking the "trap" and, for example, making the photon to just decay, right? So they are truly trapped there in some way, even though they should move at the speed of light.

  4. Now, to make the light trapped within a small region of spacetime, we need curvature so big that it causes an event horizon, so now we have a Black Hole

  5. So, is there a connection between the hadrons and black holes? Are they like a mini black holes, trapping gluons inside? If not, then how are they trapping something that travels at the speed of light without a curvature so big that it causes an event horizon?

Are some of my premises above wrong? Maybe some of the information I learned from science videos on youtube is false or I misunderstood it?

Where is the flaw in my reasoning above?

Or maybe gluons actually have some mass?

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    $\begingroup$ Your question is based on a wrong premise that the ordinary (hadronic) matter contains gluons. It doesn’t. It contains virtual gluons. Virtual gluons always fly from one quark to another. Your question is the same as to ask why magnets don’t shine in the dark since the magnetic field is made of “trapped” (virtual) photons. $\endgroup$
    – safesphere
    Commented Jan 26, 2023 at 14:55
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    $\begingroup$ Gravity isn't the only force. You can trap things using forces other than gravity, if those things are affected by those forces. $\endgroup$ Commented Jan 27, 2023 at 1:18
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    $\begingroup$ Huhh, that is funny thing. If I would not know that QFT has strong and deep math roots, I would not believe it. It consequently contradicts intuition. Note, there is no such thing as gravitational event horizon in QFT, because no one knows, how can it work. I think this guy might be close to that. $\endgroup$
    – peterh
    Commented Jan 27, 2023 at 12:42

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That quarks and gluons are trapped inside hadrons is called color confinement. As far as I know: it is unrelated to black holes but I don't read Phys Rev D... it's possible it has been suggested somewhere. (My PhD advisor caught me reading said journal in the library and laughs, "What you reading that for...it's physics porn". True story).

Color confinement is very technical, but the simple explanation is the QCD (aka: the color force) increases with range (where the range is roughly the size of a hadron). For quarks: when they become sufficiently separated, it's energetically favorable to produce a $q\bar q$ pair, with each new particle binding to a preexisting quark (or antiquark), thereby producing two regions of confinement. Since gluons carry color (that is, they interact with each other), the same principle applies to a gluon trying to escape confinement.

Note that this is very different from photons, which do not interact with each other (to 1st order, or below the Schwinger Limit $~10^{18}\, {\rm V/m}$). Nevertheless, the phenomenon of pair production in strong fields (say near a nucleus with $Z \approx 1/\alpha \approx 137$, which can be assembled briefly in heavy ion collisions) may occur. This is called "sparking of the vacuum".

Back to gluons. Gluons attempting to escape hadron has been observed in 3-jet events.(See figure).

enter image description here

In this figure, an escaping gluon has dressed itself with quarks in a process called hadronization. That there are 3 is unique to gluon-gluon coupling, and was considered a major validation of QCD.

Also: above the Hagedorn temperature $1.7 \times 10^{12}\,$K), it's believed confinement breaks down and hadrons phase transition to quark matter.

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    $\begingroup$ How is Phys Rev B physics porn? I never heard that. :-D $\endgroup$
    – Koschi
    Commented Jan 27, 2023 at 14:00
  • $\begingroup$ My advisor also thought work like the last Nobel Prize was "so what, quantum mechanics works...who woulda thunk?" ...was it B? what ever had string theory in it. $\endgroup$
    – JEB
    Commented Jan 27, 2023 at 17:23
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    $\begingroup$ No that it really matters, but work on foundations of quantum mechanics would typically go in PRA. Work related to string theory would probably end up in PRD. $\endgroup$
    – d_b
    Commented Jan 27, 2023 at 17:48
  • $\begingroup$ I'll edit my answer accordingly. This was 30 years an ago. D, B, all I know is it's not C, and if you're trying to validate the R.H.S> of the Bjorken Sum Rule experimentally, all that laser table stuff just doesn't impress. $\endgroup$
    – JEB
    Commented Jan 28, 2023 at 4:37
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Now, to make the light trapped within a small region of spacetime, we need curvature so big that it causes an event horizon, so now we have a Black Hole

Photons do not carry an electric charge. So photons cannot create photons (directly). As a result, photons can travel off into space and will continue to do so until they hit something that does have a charge.

Toy model follows:

So one might imagine standing in front of a wood stove and the electrons in the atoms of the steel are relaxing back to ground state and giving off IR photons which travel through space until they hit you, at which point they excite electrons in your skin and those relax thermally and warm you up. The photons in question "disappear" as part of this reaction.

Gluons do have a color charge. That means gluons will react with other gluons, and even form glueballs (at least in theory), in a highly non-linear and complex fashion.

So, unlike a photon which is free to fly off into space, gluons will react with each other and the quarks that most likely caused them to come into existence. When they do try to fly off, the resulting increase in energy becomes so great that entire new particle pairs are created and the gluons are "used up" in that interaction (sort of). Those particles then react with the other quarks and that's what's holding the nucleus together, the nuclear force.

So the gluons are "bound" due to these many interactions. There's simply no analog of these with photons. There's nothing to do with gravity and event horizons in either case, particles appear and disappear all the time.

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    $\begingroup$ Regarding your last paragraph: I'm not very good at QFT but I think that an electron bound to a proton (=hydrogen atom) by the electromagnetic force is a nice analog that uses photons. The photons are not free but just exist to mediate the electromagnetic force. Photons inside a medium can also form quasiparticles that behave as if the photons have mass $\endgroup$ Commented Jan 27, 2023 at 15:14
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    $\begingroup$ @AccidentalTaylorExpansion - actually yes, I should have used that example after the wood stove, sort of a series expansion. $\endgroup$ Commented Jan 29, 2023 at 19:38

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