# 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?

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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. en.wikipedia.org/wiki/Speed_of_light –  Keith Thompson Feb 13 at 20:09
If you haven't read Feynmann's QED I'd really recommend it for more perspective on this. –  adrianmcmenamin Feb 14 at 10:55

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).

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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 ? –  Andrew H Feb 13 at 9:19
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. –  Envite Feb 13 at 9:30
oh ya.. that's the stuff. intellectual satisfaction. Thanks! I like that answer a lot. –  Andrew H Feb 13 at 9:32
This answer is just a sophisticated version of "it is because it is" –  adrianmcmenamin Feb 14 at 10:54
@Envite I think there needs to be more explanation of the formula c equals one over the square root of epsilon nought mu nought and how the speed of light relates to electric permittivity and magnetic permeability. –  called2voyage Feb 19 at 15:33

Why is the speed of light 299,792,458 m/s, and not (for instance) 3,1 or 4,3 x 10^44 m/s?

The answer is that all those numbers are consequences of arbitrary choices of the units of measure. In fact there is nothing special about the number 299,792,458, so much so that one can correctly write that the speed of light is:

• 1079252848.8 [km/h]
• 0.3 [pc/year]
• 1 [lightyear/year]

So much so, that in particle physics it is common to use the speed of light as the unit of measure of speed, so that it is effectively equal to unity. You would write that the speed of light is 1 [c], and that the speed of that particle was 0.99998 [c], while I typically get to work at a speed of 1. x 10^{-8} [c].

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In so-called "natural units" the speed of light is 1 (dimensionless) –  Envite Feb 14 at 12:00
astabada, I think you missed the level of the question I was asking. I was asking whatever unit of measure you are using why is it that speed. For example if the meter and second stayed the same why is it 3E8 m/s and not 6E8m/s, Envite answered the quesiton nicely. Although, of course you can go on to ask why are electric and magnetic permeability the way they are...and even deeper question: why is any constant the value it is?!?! Is there a 'natural' optimization in the universe? or are these values related to the least amount of energy being used? –  Andrew H Feb 14 at 12:05
@Envite I wanted to be clear, that is why I specified 1 [c]. I agree that if c = 1 the expression is redundant, much like writing "8 x 1" rather than just "8"... –  astabada Feb 17 at 9:54
@AndrewH yes, there is a reason for which all these universal constants have the value they have. It is called the Anthropic Principle: If they had any other value, we will not be here to observe them. –  Envite Feb 17 at 9:58
@AndrewH I had already seen that you had accepted Envite 's answer. However, I stress that - as you have acknowledged - Envite's is not a full answer as it moves the question onto permeabilities. You might answer for example why the ratio between two speeds (e.g. light vs sound) is such and such, but not about a single value, without any comparison. –  astabada Feb 17 at 9:59

One answer is that it isn't. When physicists work out equations in relativity they often set the speed of light to one: c = 1. This makes the equations more tidy. It amounts to defining natural units of measurement in which the speed of light is exactly one unit. For example, if the second is kept as the basic unit of time, then the unit of length must be equal to exactly 299792458 metres. This unit is called the light-second because it is the distance travelled by light in one second. The speed of light is then one light-second per second.

This is not a complete answer. The speed of light is high when measured in our standard units such as metres per second or miles per hour. Those units are defined by arbitrary conventions which have their roots in ancient ways of keeping time and measuring distances. It is probably no accident that the second is about the average duration of a heart beat and the metre or yard is the distance of one human step. So the real question is "Why is the speed of light so high in terms of familiar every day measurements?" or "Why are the speeds at which we normally move so slow compared to the natural units in which the equations of physics take the most tidy form?"

These are very meaningful questions but ones to which we have only partial answers. The speeds at which we walk and live are limited by the amounts of energy E available to us from the chemical processes which drive our muscles compared to the amount of mass m which is to be moved. Kinetic energy at low speed is given by the formula E=(1/2)mv2. So the order of magnitude of velocities we obtain when powered by chemical energy might be given by the square root of E/m. Actually it will be much less than that because we are very inefficient in our use of energy, allowing most of it to be released slowly and dissipated as heat. Our speeds might also be related to the strength of gravity on Earth g = 9.81m/s2 in relation to our own size. It is no coincidence that g takes a moderate value in conventional units, unlike c.

It is a consequence of relativity deduced by Einstein that the amount of energy available from a mass m is given by E = mc2 so the question now becomes (in part at least) "Why is so little of the energy of matter available in the form of chemical energy?" If our metabolisms worked using nuclear reactions instead of chemical reactions we might move much faster (other factors permitting) and then our units of length and time would be different, and the speed of light would not seem so high. These relative scales of energy are determined by such parameters as the coupling constants of the natural forces and the masses of particles. We know from observation that these take values which vary widely in scale over many orders of magnitude. We do not yet know why this is. It may be that the values are arbitrary and their differing values have to be put down to something ontological such as the anthropic principle, or it may be that they are determined without ambiguity from a unified theory of forces which split naturally at different scales. The strength of gravity on Earth comes from similar parameters in cosmology and similar principles may apply to the question of why hospitable planets have moderate gravitational fields. Until more is known about the fundamental parameters and how they derive from deeper principles, a complete answer cannot be given.

Reference: Why is the speed of light so high?

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There is no answer to your question as per Why? That assumes there is a purpose for light waves to travel at that speed. And there is not. The laws of physics are an accident of this universe. For what we know there could exist other universes where the speed of light is different, where all the laws of physics are different.

If you ask Why? in the sense of purpose then you are assuming the answer before you ask the question, you are assuming that there is a purpose, and as far as we know there is not. (Unless you believe in God, which I hope you don't)

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-1: Asking "why" is a request for reason, explanation, or purpose. Two of those three have a perfectly valid place in science, but this answer pretends the question is purely teleological, whereas the OP's clarifications make it clear it is not. –  Stan Liou Apr 23 at 2:17
Then he should have used How instead of Why. Anyways I did answer his question asuming what he meant by Why was really a How. So I dont see reason for your negative vote. –  harogaston Apr 23 at 2:25
"Why" is standard English usage for all of those, so no. –  Stan Liou Apr 23 at 2:31
I don't see how. In any case, I would downvote Krauss for this answer as well. –  Stan Liou Apr 23 at 3:38
Well apparently you will never get to the point that: ""I did answer his question assuming what he meant by Why was really a How. So I don't see reason for your negative vote." –  harogaston Apr 23 at 3:46