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Is there any way in which a bound state could consist only of massless particles? If yes, would this "atom" of massless particles travel on a light-like trajectory, or would the interaction energy cause it to travel on a time-like trajectory?

Lior
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  • An exotic strictly massless particle accessible as a bound state at an end of a p-wave superconductor is thw celebrated Majorana fermion (search for Kouwenhoven/Majorana) – Slaviks May 04 '13 at 09:09

3 Answers3

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Yes, or at least probably. Glueballs, if they exist, are bound states of two massless gluons. However glueballs (are calculated to) have a non-zero mass because their binding energy contributes to their mass, so they would travel on timelike trajectories.

I think the glueball is a special case because the strong force is confining. I'm not sure what would happen for a hypothetical massless system bound by the electromagnetic force.

John Rennie
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  • "I'm not sure what would happen for a hypothetical massless system bound by the electromagnetic force." That's related to my question here (no answers yet though). The Bohr radius blows up so I'm confident that no two body system would be bound, but for many body states I don't know. Then again there is no clean seperation between two and many body states without a mass gap, so I could be wrong. – Michael May 04 '13 at 08:45
  • So this means that a glueball could be at rest in my laboratory frame, and then if I give it just enough energy to break the bound state, the gluons would immediately accelerate to the speed of light. Interesting. (I know that this comment contains errors in understanding and interpretation, but I'm interested to see if there are any comments on this) – Lior May 04 '13 at 13:32
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    It would take infinite energy to separate the gluons to infinity, so you can't break the bound state. It is this property of the strong force, i.e. confinement, that allows the massless gluons to be bound. In practice as you increased the separation the energy would create more gluons and quarks, and you'd get a couple of jets of hadrons not separated gluons. – John Rennie May 04 '13 at 13:36
  • In addition to glueballs, there is also the possibility of geons: http://en.wikipedia.org/wiki/Geon_%28physics%29 –  May 04 '13 at 14:27
  • @MichaelBrown: you can't use non-relativistic QM to discusss massless particles. – Zo the Relativist May 04 '13 at 14:41
  • @JerrySchirmer I know that. I'm talking about the limiting process $m\to 0$, and I'm saying that I don't really know what the relativistic behaviour is. But if it turned out the massless case was bound I would be surprised (and delighted)! – Michael May 04 '13 at 14:46
  • One should note that the statement that glueballs consist of two massless gluons is just valid in the constituent picture and that the number of "actual" gluons is not determined. Furthermore one should mention that in the constituent picture, glueballs consisting of a higher number of gluons, e.g. 3, are also possible. – Frederic Brünner Mar 25 '14 at 17:38
  • Can an accumulation of glueballs exert a gravitational field? – Len Feb 07 '18 at 17:20
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John Rennie has answered the first part of the question. The second part was this:

If yes, would this "atom" of massless particles travel on a light-like trajectory, or would the interaction energy cause it to travel on a time-like trajectory?

The answer is that it would have a timelike world-line, and this is independent of any (probably uncertain) details of the system's dynamics or binding energy.

Mass is not additive. Mass is defined (in units with $c=1$) by $m^2=E^2-p^2$, where $E$ is the mass-energy and $p$ is the momentum. $(E,p)$ is the momentum four-vector, and the squared mass is its squared norm. For a massless particle, the momentum four-vector is lightlike. If four-vectors $p$ and $p'$ are both lightlike and future-directed, but not parallel, then $p+p'$ is timelike. Therefore a system of interacting, massless particles is guaranteed to have a nonzero mass.

  • Should be $m^2$. – Stan Liou May 04 '13 at 14:16
  • "Therefore a system of interacting, massless particles is guaranteed to have a nonzero mass." but can they exert a gravitational pull on mass? – Len Feb 07 '18 at 17:21
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    @Len Yes, anything with mass (i.e. anything with energy in a frame where it has no momentum) attracts other bodies gravitationally. – Chris Feb 07 '18 at 20:22
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The Standard Model, as validated by a large number of measurements, extrapolates all particles to 0 mass at energies larger than symmetry breaking energies. I have never heard of bound states in the early cosmology models : with symmetry breaking, one gets quark gluon plasma and with further cooling the quarks bind into the protons etc as we know them.Before symmetry breaking the particles are free. One would have to propose a different theory for anything like this, which would manifest exactly as the SM at low energies; then also the interpretation of early cosmology would be different.

anna v
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  • There are lots of structures that can exist but that don't occur naturally. Cars don't exist naturally, but that doesn't mean they're impossible. –  May 04 '13 at 16:18
  • @BenCrowell cars exist because atoms and molecules exist following the SM. Cars are a meta level. Zero masses binding into a stable configuration would be a fundamental level manifestation, describable by a mathematical theory. – anna v May 04 '13 at 19:09