# Why is the speed of causality equal to the speed of light?

I heard that the most fundament concept is Causality, and also that it is turn out that speed of light has nothing special in it so that It is ultimate speed limit but because it is happen to be speed of causality. So why it is so that speed of causality is equal to speed of light?

Yes, causality is fundamental. If you assume that the speed of causal signals has some upper limit which is a fundamental property of the universe, then that must be the same in all inertial frames; you can call it $$c$$ and deduce the whole of special relativity (contraction, dilation, Lorentz transformation, twin paradox...) talking about 'maximum velocity causal messages' rather than 'light signals', and all the formulae come out the same, without any mention of light.

Then you can introduce electrostatics. But you will discover that the relativistic effects you derived earlier mean that there must be more than Coulomb's Law - for instance, two co-moving like charges repel less than two stationary ones because of time dilation. The extra forces are what we know as magnetism. If you introduce some of Maxwells' equations you have to introduce all of them to preserve Lorentz Invariance. (This is the reverse of usual argument method, which deduces the Lorentz Transformation as Maxwell's equations are not covariant under the Galilean transformation, but it works. both ways.)

From Maxwell's equations you then discover (standard undergraduate exercise) that there are wave solutions with speed $$1 \over \sqrt {\mu_0 \epsilon_0}$$ which turns out, inevitably, to be the speed $$c$$ that appears in the Lorentz transformations.

So: starting from a fundamental causal signal speed $$c$$, you get the Lorentz transformations, which give you Maxwell's equations, whose wave solutions happen to have a particular velocity $$c$$.

That's just a reference to the fact that the speed of light is really a characteristic of space-time itself, and that any disturbances of space-time (to include disturbances to any fields that pervade space-time) propagate outward at the speed of light. So therefore it can be thought of as a limit on the speed at which information can flow, which is the tie to causality.

Edit: to elaborate slightly on causality, one of the requirements for event A to have caused event B is that A occurred before B. The concept of "before" and "after" gets a little tricky under Special Relativity, because events that are simultaneous for one observer in one inertial reference frame are not simultaneous for another observer in a different reference frame.

Nevertheless, there is an absolute dividing line between events that are "time like separated" (A always occurs before B, regardless of the reference frame) and "space like separated" (A may or may not have occurred before B; it depends on the reference frame of the observer). The speed of light is the main parameter that defines this dividing line. More detail can be found in other answers, such as here and here.

Causality is a fundamental concept in thermodynamcs and statistical mechanics. If one event causes another and event A comes before B then we say both that A causes B and that A occurs in time before B. "Before" and "after" are inextricably wedded to both causality and time. Thus, thermodynamics is the study of causal systems, i.e. systems which evolve through time.

The speed of light is just a number. But it happens to be the speed at which distortions in space propagate and, since everything distorts space, nothing can travel faster.

As a causal system evolves in time, nothing in it can, as it were, carry causality with it faster than light.

Quantum entanglement is thought to create exceptions, including a highly controversial phenomenon known as quantum retrocausality, but it is probably not relevant to your query.

It isn't. It is only in special relativity. In general there is no known upper bound to the speed of causality simply because there is no known well tested theory with such generality that it applies to all phenomenon across all the scales of reality. With so much unexplained problems in physics there is no logic behind putting such general constraints on the universe.

• If someone has a problem with this answer let me know with a comment.. Feb 6 '20 at 21:00