Do gluons interact via virtual photons?

On a video on Youtube, I commented how a PBS Space Time episode helped me understand the speed of light by calling it the speed of causality. In response, I received the following comment:

"Let's check your learning: Why can we consider light speed to be the speed of causality?"

"If I understand correctly, it's because it is the fastest speed at which information can travel. So, it is the fastest speed at which someTHING can interact with another THING. Is that right?"

To which they responded:

"Well it is certainly true, but it's missing the cause/mechanism. Its the speed at which the electric and magnetic fields interact. A photon is the result of a changing magnetic field inducing a changing electric field, and a changing electric field induces a changing magnetic field. That interaction of the permittivity and permeability of "free space" is the speed at which the field interact and that is c, or the speed of light."

This didn't sit right, because gluons travel at c as well, and as far as I knew did not require the electromagnetic force. So, it would seem to me that the speed of photons transcends merely the electromagnetic force because it applies to gluons as well. So, I responded back:

"Hmmm. That may be partially true, but would fail to explain the gluon, which also moves at the speed of light and, as far as I know, carries the strong force. So causation is the same speed for the strong field too."

And they responded thus:

"That is because gluons interact with virtual photons. What is the strong field without the electric and magentic [sic] fields, what is a proton without electromagnetism? You are right to point out other forces, but they all interact at c for the same reason."

Now, the first thing I find confusing is when they say that gluons interact with virtual photons. This to me sounds like they are saying that photons carry the strong force between quarks and gluons, but I always thought gluons were the virtual particles moving the strong force between quarks and gluons. Then the ending sentence has me with more questions.

They say, "They all interact at c for the same reason." And that reason, I can presume is the reason given before: "Its the speed at which the electric and magnetic fields interact." But how do we know that c is derived from the speed at which electromagnetic fields can interact and not based on how strong nuclear fields can interact.

I lack the knowledge to assess these claims. Is what they are saying making sense? I would ask the commenter questions about what he has said, but I have zero faith in the reliability of a random Youtuber who comes off a tad smug. If you don't have proper stack credentials, your words are meaningless on questions like this. I would appreciate any help you could provide.

• My answer here may help: physics.stackexchange.com/a/291346/123208 Commented Sep 24, 2022 at 7:17
• Don't get confused, you had it right. Anything massless will travel at the speed of light, gravitational waves being another example.
– rfl
Commented Sep 24, 2022 at 13:43

You are correct not to trust the youtube contributor. He/she seems to be confusing classical electrodynamics and quantum physics concepts.

The speed of light was defined in classical electrodynamics where Lorentz transformations are inherent in the Maxwell equations. Lorentz transformations are imposed on quantum field theory at the particle level, and thus c is the velocity of photons and gluons as it is imposed by the theory on all zero mass particles, independent of interactions.

Gluons may interact with virtual photons in complicated Feynman diagrams( example here) where charged virtual particles exist.

In this answer I will discuss two things:

The reason - as I perceive it - why there is a multitude of opinions when it comes to concepts such as the speed of light.

How I prefer to think of what the context of the speed of light is.

There are parallels between doing theoretical physics and reverse engineering.

Let's say a team has decided to reverse engineer some firmware. The team has no access to the actual implementation. The information that they have is how the device firmware behaves; how the device firmware responds to various inputs.

Kepler's laws of celestial motion are quite close to the raw observation data.

Significantly different from that: the inverse square law of gravity is an inferred concept. We infer that the motions of the celestial bodies are due to an inverse square law of attraction. The law of gravity is corroborated beyond reasonable doubt.

(Of course, Newton's law of gravity has been superseded by Einstein's General Relavity, but as we know: in non-relativistic circumstances the mathematics of GR simplifies down to the inverse square law of gravity.)

In theoretical physics we assume there is an actual underlying implementation, and we tend to assume that if we probe hard enough then eventually we will be able to reverse engineer the underlying implementation.

In my opinion that is why when it comes to concepts such as the speed of light there is a multitude of opinions.

How I prefer to think:

We have that the speed of light is something that is common to several different phenomena. The LIGO observatories have yielded strong corroboration that light and gravitational waves propagate at the same speed; the speed of light.

Since the speed of light is found also in contexts other than electromagnetism it doesn't make sense to me to think of the speed of light purely in terms of electromagnetism.

I prefer to think that the speed of light is a property of spacetime. Of course, in order to make that kind of attribution it is necessary to grant that spacetime has physical properties.

(If one grants that spacetime is such that curvature of spacetime is possible: that is implicitly granting that spacetime has physical properties.)

I prefer to think that among the physical properties of spacetime is causality structure. There is a speed of causality.

I'm aware that other people may well have the point of view that causality and spacetime are intrinsically distinct concepts.

When it comes to making inferences: there are the obvious inferences, but as you start addressing deeper and deeper questions the decisions become judgement calls more and more.

A free gluon would “spend part of its time” as a virtual $$\bar qq$$ pair, to which photons do couple in higher-order computations. This is analogous to photons “spending part of their time” as virtual electron-positron pairs. Whether it makes sense to discuss a “free gluon” is left as an exercise.
The misconception that the color force is just a special case of electromagnetism remains common among people who haven’t yet gone deep into their study of modern physics. In relativity, $$c$$ is the speed of all massless particles.