Why is the speed of light exactly $299,792.458$ m/s and not faster or slower? [duplicate]

Why is the speed of light $299,792,458$ metres per second, and not faster or slower.

Why not $500$ trillion kilometers per second or $120$ miles per hour?

This has been 'bothering' me for a while. Googling it usually found answers about why isn't '$c$' infinite et cetera, and the answers were usually saying (from my interpretation) that if $c$ were infinite, then matter couldn't exist.

I recently found this reference, but despite its blatantly obvious attempt to explain to laymen, I still don't understand why $c$ is (roughly) $300$ million meters per second.

A 'dummy's' guide to my understanding why '$c$' is the number/speed that it is, would be greatly appreciated by me and all others who will read your answer in the future.

marked as duplicate by Emilio Pisanty, Kyle Kanos, CR Drost, Danu, ACuriousMind♦Feb 12 '16 at 0:44

• No one knows the answer to that. It could be that there are multiple universes in which c has a different value, and so it's not meaningful to ask 'why' it's the value we measure it to be. – lemon Feb 11 '16 at 18:03

The basic question is, "how do we measure that something is this fast at all?" which is, "we measure the distance something goes, we measure the time it took to travel there, we divide the two."

How do we know how far it traveled? Well, we use these things called "rulers." But how do we know that those rulers maintain a constant length, rather than getting larger or smaller? At some point in practice we normal experimenters just trust them, but for the international committee which decides how to measure such things, this is a real problem! In fact their most reliable measurements are measurements of time, and the velocity of light: therefore their definition of the meter is phrased as "the distance light goes in X seconds." Therefore the speed of light is exactly 1/X meters per second, by the definition of the meter itself!

That probably seems very unsatisfying for you, since this is a socially arbitrary choice. Originally the meter was instead defined as one 10-millionth of the distance from the Earth's pole to its equator on a line that went over the surface of the Earth through a city in France. The committee tried to make the new-meter roughly the same size as the old-meter by choosing X very precisely, so that nobody would need to change their tables of measurements. Before that, there was probably an unofficial measurement much like the Imperial yard, about the distance that you step if you make very large "paces", and so they were trying to pin down this idea of one "pace" and it happened to be that 10 million such steps would let you get from the equator to the North Pole, so they were refining that. And so forth.

So the questions stop being about why the speed of light is what it is, and start being about us: why are we 1-2 meters high and why is our reaction time 0.1-0.2 seconds long? The ratios of these numbers then dictate how fast the speed of light is relative to the speeds we're prepared for. We chose our units based on these speeds and times that we're prepared for, and the speed of light doesn't care about that, but we do.

Furthermore it turns out that we cannot answer some of these questions because if the speed of light were any faster, how would we know? What if the speed of light were twice as fast, but as a consequence, all of our rulers (which are built out of the electromagnetic forces in atoms -- mediated by the photon, which is the particle of light!) were twice as long? Well, we might not see anything! So it turns out that when we get down to it we cannot detect these unit variations in isolation but only by combining them all together into unit-less numbers that we call "dimensionless." (The study of units and how they interact with physical quantities is called "dimensional analysis", doesn't have anything to do with the "dimensions" of our 4D-spacetime or "other dimensions" in sci-fi.)

The important dimensionless constant for how big we are is called the "fine-structure constant." It is a smidge less than 1/137.036, and essentially says how strong the electromagnetic force is. And if you ask me, "why is it the way it is, so that atoms are possible and molecules have the size that they have and we are the relative size we are compared to light over the time-frames that atoms vibrate?" and all of those questions, I can firmly tell you nobody knows. People have been trying to find a mystical understanding of this number ever since they discovered that it was approximately 1/137, and were not stopped when they discovered that it was actually closer to 1/137.036, but those mystical understandings have never led to scientific theories with testable predictions which we could then confirm with actual evidence. We simply don't know.

• Actually we would notice if the speed of light doubled and rules grew in length by a factor of 2 as long as other changes such as our size and the size of building's didn't change. Some changes we don't notice like the speed of light is slower in Earth's gravitational field but atomic clocks are also slower by the same amount so we don't notice. That's one reason we should do the math to check whether the theory predicts something and not just assume it predicts it without checking just because it was observed in experiment. – Timothy Sep 24 '18 at 2:06

The speed of light in natural units is 1. The value in SI units depends on the reasons why we chose the units in the way we did. Now, SI units were chosen to match older units that were defined to match the scales appropriate for daily life purposes. So, the meter is of the order of our length, the second is a small time interval that we can still perceive reasonably well.

So, the order of magnitude of the speed of light as expressed in Si units reflects our size compared to the minimum time needed for us to perceive new information.

• and the sky is blue but this doesnt answer the question – Yossarian Feb 11 '16 at 18:51