### Why is the speed of light 299,792,458 meters/sec?

• Ok, I am majoring in physics (4th year) and I never understood this fundamental (kinda) question. Maybe I haven't explored it enough.

For example, why does it take 8min20sec for the light from the sun to get to us?
I know the answer to this question on a 'surface' scale. The sun is 1AU away, c=3E8 m/s, and d=v/t to get approx 8 min 20 sec.

my question is on a deeper level.

Say you could "ride a photon" I KNOW THIS IS IMPOSSIBLE, but just say you could. Or a better question: what does a photon experience? The photon, as per my understanding, would leave the sun and (if it is on the right trajectory) hit the Earth instantaneously. A photon leaving Alpha Centauri would see the universe all at once, in a infinitesimal small unit of time (if directed out to space).

If a photon sees everything all at once, why do we perceive it to have a speed? I am sure this has something to do with frames of reference, special relatively, Lorentz transforms? but just seems strange. why is the speed of light finite to us... if it was infinite would this be problematic?

Since 1983, the meter has been defined as the distance traveled by light in a vacuum in 1/299,792,458 of a second, so that number is exact by definition. Of course that doesn't answer your question, but it's interesting. https://en.wikipedia.org/wiki/Speed_of_light

If you haven't read Feynmann's QED I'd really recommend it for more perspective on this.

It is theorized that other multi-verses may have different constants than the ones we have in this universe. For example, the constant of gravity might be different, the speed of light might be different, etc. These universes would look entirely different than our universe.

The speed of light is 299792458 meters per second because The universe works the way it does and also: the speed of light was defined much after the meter was. Hence in order to retain the original meter measure SI decided that the speed of light to be 299792458 m/s just in older to retain the old meter measure which earlier was defined to be equal to one ten-millionth of the distance from the equator to the pole measured on a meridian which passed through Paris France

The actual value of a physical constant with dimensions is merely a product of our unit system. That there is a finite speed for light arises from some simple symmetry considerations - e.g. allowing the laws of physics to be unchanged by translations in space and time.

If you need in-depth explanations, check Michael Stevens videos about lightspeed such as Would Headlights Work at Light Speed?. Beware that you will end up with more questions than before watching.

8 years ago

Speed of light being finite is one of the fundamentals of our Universe.

If it were infinite, this would have a major implication in causality.

Besides, in non-quantum physics, light is just an electromagnetic wave. Eelectromagnetic field is described by Maxwell's equations, which predict that the speed $c$ of electromagnetic waves propagating through the vacuum depends on the dielectric permittivity $ε_0$ and the magnetic permeability $μ_0$ by the equation $c = {1\over\sqrt{ε_{0}μ_{0}}}$ so you can not have an infinite speed of light unless electric permittivity or magnetic permeability were zero, which in turn would cause all sorts of odd things to electromagnetical attraction (and thus, to matter existence beyond elemental particles).

Ok, but why 300,000km/sec? I know km and sec are human inventions - but whatever your units of measure are - why that speed? what is so special about that number? and what about the other part of my question: if a photon experiences everything all at once - how can it be that it leaves the sun and hits earth in t=0 but to us t=8min20sec ?

That speed (297000Km/s) comes from the formula I posted above: 1 over the square root of ε0μ0. About the photon experiencing everything at once, that is due to relativistic time dilation. For a photon, time is infinitely dilated so one instant extends infinitely long.

oh ya.. that's the stuff. intellectual satisfaction. Thanks! I like that answer a lot.

This answer is just a sophisticated version of "it is because it is"

I have the same question. Why a finite no. I was studying transformation of relativistic kinematics and realized light particles would not feel the journey if they were living.Everything would happen in an instance for them. the Value 299792458 comes from the permittivity and permeability that's okay. It's a cause that speed is finite. But why finite, to know that I think more advancement is needed.