Photons speed limit

Question

Is there any reason why the speed limit (light speed) is what it is?

Also, doesn't gravity and electromagnetism travel at the speed of light? What can we infer from this. (Is gravity massless?)

Answer 1

Your questions:

1) why is the speed limit (light speed) what it is?

Three parts of this answer:

a) what is light speed: light speed, c, is the propagation speed of electromagnetic (EM) waves. Light speed was measured (not perfectly accurately but good enough) before it was known that it was an electromagnetic phenomena. When Maxwell's equations showed that EM waves traveled at a speed that, from electric and magnetic measurements, were close (close enough) to the speed of light, it was an important moment identifying light as EM waves. So, c came from measurements on light, other EM waves, and electric and magnetic constants (electrical permittivity and magnetic permeability, which together give us that same number c).

b) why is it the speed limit? That came from special relativity (SR). SR and Michelson Morley's experiment determined that light traveled at speed c in any inertial reference frame. SR further derived from that that nothing can reach the speed of light, except for light and any other particles that have no mass. The presumed graviton also has zero mass, just like the photon.

c) how does that make sense, how can there be zero mass particles? Quantum Electrodynmaics is the theory that unified EM and quantum theory. The theory has it that the disturbances of the EM field are carried by the photon field, and since it is consistent with SR travels at speed c in any inertial reference frame. Einstein got the Nobel prize for the photoelectric effect that proved that light came in discrete entities; he did not develop quantum theory, but people who did knew that light was carried by photons, and had zero mass.

2) What about gravity also traveling at the same speed, c?

a) yes, gravitational waves (GW) travel at speed c. GWs are predicted by general relativity (GR), and incorporated c in the equations because the theory needed to reduce to standard SR in a local inertial frame, in a small (local) area. The equations then predicted that GWs travel at speed c. GWs are presumed to be carried by the graviton, but the quantum theory of gravity does not exist as an accepted theory, there are still issues. Still, in the weak gravitational field limit (still good for our galaxy and at some distance from black holes), a first order wave approximation reduces to a linear theory similar to Maxwell's waves (but with spin 2, the photon had spin 1), and in that linear domain the graviton has to have mass zero and travel at speed c. Even in general relativity two events separated by distances and times such that light can not reach one event from the other are not causally connected.

b) what does it mean? Well, that special relativity is an important part of the way the laws of nature (I.e., physics)work. When quantum theory was developed and set on a firm standing, it did not at first account for special relativity, it did not work for high speeds. Physicists spent a lot of time trying to unify special relativity and quantum theory, and finally did it in Quantum Electrodynamics, and more generally (relativistic) quantum field theory (QFT). Further developments in QFT and observations of a large number of new particles eventually also led to the unification of EM and the weak nuclear field in electroweak theory, and now more inclusively (but only partially unified) with the strong nuclear force, in the so called Standard Model that accounts for EM, the wel and the strong force. Gravity is accounted for by general relativity, but a quantum theory of it, and unification with the other force, is still an elusive goal. The speed of light being to the maximum causal propagation of any effect in physics (nothing can affect anything else any faster, since physics is consistent with all effects being local I.e., any effect is transmitted by a quantum field which must act locally and which cannot travel faster than c) is one of the facts that brings it all together. That what it means.

c) from a technical physics point of view the speed of light brought in also the transformations of inertial frames of reference not affecting physics, I.e., invariance of the laws of physics in different inertial a frames), the generalization to all frames of reference in general relativity explaining why the curvature of spacetime is the way gravity is manifested, and later to more general symmetry transformations that conserve other more abstract entities like spin, flavor, and parity, and later symmetry breaking, and which all led to the understanding of the electroweak forces, strong forces, and the mass-giving Higgs boson.

Answer 2

Physics never explains "Why?" but "How?", and in this formulation it's impossible to give you a clear answer. Let's maybe clear the second part of the question first.

You maybe know there are 2 types of particles and 4 interactions in the Universe. We distinguish the particles between the Fermions (obeying the Fermi statistics) and the Bosons (obeying the Bose statistics). There are a few differences between them but the most evident one is the Pauli exclusion principle. Two fermions cannot occupy the same point in the Space-Time. Bosons can. The 4 interactions are the Electro-magnetic, Weak, Strong and Gravitational interactions. They establish the rules between the different types of "collisions" allowed between the fermions and the bosons, but one remarkable thing, the four interactions use a vector of interaction and those vectors are themselves Bosons. For example Electromagnetism uses Photons as a vector of interaction, in other words, every electro-magnetical interaction produces or absorbs a photon somewhere. The Photon, Gluon (strong-interaction) and the Graviton are massless and therefore travel at the speed of light.

As we said, electromagnetism uses photons, this is an intuitive way to understand why you can write $c_0=\frac{1}{\sqrt{\mu_0 \epsilon_0}}$ but it's not really a reason why.

Well, now it's more my own interpretation, it might be wrong but satisfies me in a way. You know $\epsilon_0$ and $\mu_0$ describes the permittivity in the vacuum. But vacuum is still something lying in the space-time and photons have the remarkable property to travel along lines in the curved space-time. Meaning that if the space-time has a curvature, from the point of view of the photon, he is still following a straight line. In my interpretation $c$ is just a property of the space time itself. If you imagine space-time as a grid, $c$ is just the ratio between one unit of space over one unit of time. I'm not able to explain why it's gridded this way but it somehow satisfies my curiosity.

All the technical words I used are well explained on Wikipedia. I hope this will help you.