Why 186,282?

[thetexan]

TL;DR Summary

Why this speed

Is there an explanation for why the speed of light tops out at 186,282 miles per second? Of course that number depends on our definition of miles and seconds. If a mile was 3000 feet then c would be a different number.

But whatever speed it is…. Why that speed? In other words… there is something tangible that limits c to a top limit of some speed. Again, why 186,282? Why is it not 231,655? If it were then that would be the speed beyond which we could not speed.

It’s like the photons give out at 186,282 and say “I just can’t go any faster”. No… there must be some physical reason the speed of light only goes 186,282, and not faster, such as 188,476?

Tex

 

[jedishrfu]

In Maxwell's theory of electromagetism there is a prediction of the existence of an electromagnetic wave with that exact velocity when traveling in the vacuum of free space that comes out of the equations.

One could say the speed is derived from and depends on the measured electric and magnetic constants that are the basis for Maxwell's theory, The next question would be why these constants are measured to be the values they are.

The answer is we don't know but we hope someday a greater theory will come along and explain that. The greater theory will likely have fewer but equally mysterious constants.

 

[Ibix]

A finite invariant speed drops out of the maths if you assert the principle of relativity and work out the consequences. All massless fields propagate at that speed. The EM field is massless so light travels at the invariant speed.

Attempting to explain why the invariant speed has the value it does in any unit system eventually leads you through a tangle of metrology to the answer "because you chose that value by the definitions of your unit system". The SI is actually explicit about this - $c$ is a defined constant and the meter is defined from it. Other systems may disguise it more, but the answer is still the same.

 

[Dale]

TL;DR Summary: Why this speed

that number depends on our definition of miles and seconds

This is the answer.

Physically, what is important about $c$ is that it is invariant. Its numerical value is only an artifact of the choice of units.

No… there must be some physical reason the speed of light only goes 186,282, and not faster, such as 188,476?

If we had defined the mile to be shorter or the second to be longer then the speed of light could certainly be 188,476 mps. Because we have complete freedom to define our units, we can give $c$ any numerical value we like. Usually we choose $c=1$ for convenience in relativity problems.

 

[pines-demon]

Why that speed? In other words… there is something tangible that limits c to a top limit of some speed. Again, why 186,282? Why is it not 231,655?

Usually physics is very bad at answering "why" questions. As others have suggested you can derive it from a couple of principles, but then you can ask "why" we have those principles. In the end $c$ turns out to be what it is because it confirms what we measure. Try to reformulate your question without using why.

 

[Baluncore]

The speed of light is defined to be exactly 299792458 metres per second.
That can be converted to 186282.3970512209 miles per second.

 

[pines-demon]

The speed of light is defined to be exactly 299792458 metres per second.
That can be converted to 186282.3970512209 miles per second.

or about 1 foot/nanosecond (0.9836 ft/ns if you want to be exact).

We can even go weirder, $c=1.8026$ terafurlong/fortnight in FFFF units.

 

[Baluncore]

or about 1 foot/nanosecond (0.9836 ft/ns if you want to be exact).

The beauty of the integer definition is an exact value.
The inch is defined to be exactly 25.4 mm, so the foot is exactly 304.8 mm
0.9836 ft/ns is not exact. Try 0.9835710564304462

 

[Mister T]

N. David Mermin defines the phoot to be exactly 0.299 792 458 m. Thus light speed is exactly 1 phoot per nanosecond.

Note that the foot is 0.3048 m, which differs from the phoot by less than 2%.

 

[Svein]

As far as I remember the speed of light in vacuum is determined by the formula$c= \frac{1}{\sqrt{\epsilon_{0}\cdot \mu_{0}}}$. The actual numerical value follows from that.
BTW the speed of light in any environment is given by $c = \frac{1}{\sqrt{\epsilon \cdot \mu}}$ where ε is the dielectric constant of the environment and μ the magnetic constant of the environment.

 

[Ibix]

As far as I remember the speed of light in vacuum is determined by the formula$c= \frac{1}{\sqrt{\epsilon_{0}\cdot \mu_{0}}}$. The actual numerical value follows from that.

Depends on your unit system. In SI, the speed of light in vacuum is a defined constant and the values of $\epsilon_0$ and $\mu_0$ follow from that (and other unit definitions). If you pick a system in which $c$ is a derived constant, its value just tracks back to your unit definitions.

There genuinely isn't an answer here. You can ask why light travels at $c$ (it's because it's massless, and "massless" and "travels at $c$" are synonyms), but asking why $c$ has the value it does will always boil down to "because that's how we defined our length and time units" or "because we defined it directly".

 

[Dale]

Depends on your unit system. In SI, the speed of light in vacuum is a defined constant and the values of ϵ0 and μ0 follow from that (and other unit definitions). If you pick a system in which c is a derived constant, its value just tracks back to your unit definitions.

And some unit systems don’t even have $\epsilon_0$ or $\mu_0$.

 

[Vanadium 50]

<sigh> Once again, this question goes swirling down the metrology drain.

The speed of light does not come out of ε₀ and μ₀. If anything, its the reverse. The c in the Lorentz force is the same c you get out of ε₀ and μ₀. It comes about when we take the electromagnetic field and try and define an electric part and a magnetic part.

 

[sandy stone]

If I might chime in here as an interested layman, I think when someone asks here, "Why is the speed of light what it is", what they are really asking is, "Why is the speed of light so slow compared to the enormous distances between stars (not to say galaxies), making it all but impossible to contemplate exploring even the nearest star systems?" Of course, the answer must be, "That's what we measure, and that's just how it is. There is no explanation beyond that. Sorry."

 

[Mister T]

TL;DR Summary: Why this speed

Is there an explanation for why the speed of light tops out at 186,282 miles per second?

It may help you to understand the answers you've been given by looking differently at the question you're asking. When we say the speed of light is 186 282 mi/s what we really mean is that compared to something that has a speed of 1 mi/s, light has a speed that is 186 282 times greater. (Note that is really what it means to assign a numerical value to anything with dimensions.)

So, the answer is simply that it follows from the assigned values of the length of the mile and the duration of the second.

The more profound consideration IMO is that this speed is invariant. In other words if you were to chase after something traveling at this speed, you would find that no matter how fast you move in your attempt to catch up, it will always recede from you at this same speed.

It is this fact that leads to all the strange and unfamiliar consequences in Einstein's theory of relativity.

 

[russ_watters]

If I might chime in here as an interested layman, I think when someone asks here, "Why is the speed of light what it is", what they are really asking is, "Why is the speed of light so slow compared to the enormous distances between stars (not to say galaxies)....

Well:

 

[Dale]

If I might chime in here as an interested layman, I think when someone asks here, "Why is the speed of light what it is", what they are really asking is, "Why is the speed of light so slow compared to the enormous distances between stars (not to say galaxies), making it all but impossible to contemplate exploring even the nearest star systems?" Of course, the answer must be, "That's what we measure, and that's just how it is. There is no explanation beyond that. Sorry."

That is at least a more interesting question. But then the question is less about physics than about engineering (what engineering considerations limit our maximum speed) and biology (what biological effects limit our lifespan).

In my answer I tried to refocus on what actually makes $c$ interesting. Its value is largely irrelevant. What is interesting and physically important about $c$ is that it is invariant. All inertial reference frames agree on that speed, even though they disagree on all other speeds.

 

[DaveC426913]

We're all concentrating on the value in different measuring systems, but it seems to me the question is really about 'why is it not slower or faster'?

Doesn't the answer the OP is looking for have something to do with the permittivity of space or somesuch?

 

[Ibix]

We're all concentrating on the value in different measuring systems, but it seems to me the question is really about 'why is it not slower or faster'?

That's why I keep saying there isn't really an answer.

One way to look at it is that the natural way of measuring speeds in a relativistic universe is in fractions of $c$. Then asking why $c$ isn't slower or faster reduces to asking why 1 isn't bigger or smaller.

 

[DaveC426913]

That's why I keep saying there isn't really an answer.

One way to look at it is that the natural way of measuring speeds in a relativistic universe is in fractions of $c$. Then asking why $c$ isn't slower or faster reduces to asking why 1 isn't bigger or smaller.

But ... vacuum permittivity...

 

[Ibix]

But ... vacuum permittivity...

...is derived from the value of $c$ in modern SI and isn't even present in some unit systems. You can chase your tail through the metrology as much as you like, but the values are always an artefact of unit choice.

 

[russ_watters]

We're all concentrating on the value in different measuring systems, but it seems to me the question is really about 'why is it not slower or faster'?

I share your...dissatisfaction(?) with these answers. It's not a question of units it's a question of relationships. It's not a question why is the value 1 or 186,000, it's a question of why it's "only" Mach 874,000 or 27,000x escape velocity or whatever. What parameters establish these ratios?

 

[DaveC426913]

...is derived from the value of $c$ in modern SI and isn't even present in some unit systems. You can chase your tail through the metrology as much as you like, but the values are always an artefact of unit choice.

But one doesn't care about the number - the value; one cares about the principle - the phenomenon - of permittivity.

(Unless what you're saying is that permittivity isn't a factor - a cause; it is simply another cool named term which is derived from the only fact we observe: c. IOW: a tautology.)

 

[Dale]

But ... vacuum permittivity...

The vacuum permittivity doesn’t even exist in some systems of units.

 

[Dale]

27,000x escape velocity or whatever. What parameters establish these ratios?

Yes, these questions are physical. But now you are asking things about coincidental things like the amount of mass in the dust cloud that formed the earth.

As far as I know the only “fundamental” ratio winds up being the fine structure constant.

 

[Ibix]

What parameters establish these ratios?

You're just picking an arbitrary value as your unit of speed. The result is that $c$ has some different numerical value (874,000, or 27,000 or whatever). There isn't a deeper "why" than "because you picked that speed to call 1 unit of speed".

The escape velocity in particular turns out to be $c\sqrt{R_S/R_E}$ - just $c$ times the square root of the Earth's radius expressed in terms of its Schwarzschild radius. Quite closely related to the original definition of the metre, which was a fraction of the Earth's circumference, and with the same issues of poor precision.

Dale beat me to mentioning that the thing you can meaningfully muck around with is the fine structure constant. And you can ask why it is 1/137ish and not some other value. The answer is that we don't know, but the dimensionless constants don't drive you round in metrological tautologies so it's at least possible that there will be an answer one day. Changing the fine structure constant right now (assuming you can do that without messing around with other constants) would change things like "how long does it take to get to another galaxy".

 

[russ_watters]

You're just picking an arbitrary value as your unit of speed. The result is that $c$ has some different numerical value (874,000, or 27,000 or whatever). There isn't a deeper "why" than "because you picked that speed to call 1 unit of speed".

Again, the point is the ratio, not the units. The ratio is the same regardless of what units you use.

 

[russ_watters]

Yes, these questions are physical. But now you are asking things about coincidental things like the amount of mass in the dust cloud that formed the earth.

As far as I know the only “fundamental” ratio winds up being the fine structure constant.

Yes, that's what I'm getting at, thanks. The answer of "this universe happens to have a fine structure constant of 0.007" is the sort of answer I'm looking for. It's not a "why", it's just a "what".

This article has an that answer plus an interesting additional one:

There needed to be some sort of glue, some connection that allowed us to translate between movement in space and movement in time. In other words, we need to know how much one meter of space, for example, is worth in time. What's the exchange rate? Einstein found that there was a single constant, a certain speed, that could tell us how much space was equivalent to how much time, and vice versa.

https://www.space.com/speed-of-light-properties-explained.html

If I may paraphrase, I think it's saying 'C is a conversion/ratio between amounts of space and time'. Thoughts?

 

[Field physics]

Famous quote:
" To infinity and beyond!!!"
- Buzz light-year
Take what you want from this but I find it very important and helpful.

 

[Ibix]

Again, the point is the ratio, not the units. The ratio is the same regardless of what units you use.

But that's exactly what a unitful value is - a ratio of a quantity to some standard value. You are defining a unit system (or part of one, anyway) based on an artifact, the escape velocity of Earth, similar to the old school "bar in a box in Paris" definition of the metre. The reason the ratio of light speed to escape velocity is 27,000 (i.e. that light speed is 27,000 in your unit system) is because you chose to use Earth's escape velocity as a comparator, and the reason Earth's escape velocity is what it is is an accident of history, one that varies depending where you launch from.

If I may paraphrase, I think it's saying 'C is a conversion/ratio between amounts of space and time'. Thoughts?

Yes. It's like the ratio between fathoms (a unit of depth) and nautical miles (a unit of horizontal distance). It's arbitrary and can be eliminated by using units where it's 1.

You might object that time and space are different in a way depth and distance aren't. But we're talking about spacetime. A direction you call "only moving in time" a different frame calls"moving in space and time". So there's less of a distinction than you might think, and using different units for the two is a choice.

The dimensionless constants are definitely the way to go (and if you scratch any press release thst talks about "looking for changes in the speed of light" you'll find in bleeds $\alpha$s). We don't know why they are what they are, but the answer doesn't disappear in a spiral of metrology.

 

[russ_watters]

But that's exactly what a unitful value is - a ratio of a quantity to some standard value. You are defining a unit system (or part of one, anyway) based on an artifact, the escape velocity of Earth, similar to the old school "bar in a box in Paris" definition of the metre. The reason the ratio of light speed to escape velocity is 27,000 (i.e. that light speed is 27,000 in your unit system) is because you chose to use Earth's escape velocity as a comparator, and the reason Earth's escape velocity is what it is is an accident of history, one that varies depending where you launch from.

Yes. It's like the ratio between fathoms (a unit of depth) and nautical miles (a unit of horizontal distance). It's arbitrary and can be eliminated by using units where it's 1.

No. My example is not an artifact of unit choice and isn't a unit conversion factor between units - it happens that you can use the two speeds as units too, but that's not what I'm referring to. The ratio is the same whether you are using mph, kph, mps, mach, c, etc as your base unit. heck, I calculated it from kps: 300,000 / 11.2 = 27,000. You can redo the calculation in mph if you want and you'll still get 27,000.

Your example is not the same as my example. You are - again, incorrectly - ratioing the units of fathoms and nm and I'm talking about this ship being twice as long as that ship.

[edit]
I find it hard to understand why this question is so hard to understand and/or recognize why it might matter. Alpha Centuari is 4.4 light years away which means if we could travel there at almost the speed of light it would take about 4.4 Earth years to travel there and 8.8 years to get pictures back to Earth. If the speed of light were twice as fast, it would take 2.2 and 4.4 years, respectively. The speed of light being "slow" is a barrier to space travel.

 

[Ibix]

If the speed of light were twice as fast, it would take 2.2 and 4.4 years, respectively. The speed of light being "slow" is a barrier to space travel.

When you decided that the speed of light was twice as fast, why did you assume that Alpha Centauri was only 2.2 "new" light years away and not 4.4? Are you assuming that the speed of light has doubled but distances haven't?

 

[russ_watters]

When you decided that the speed of light was twice as fast, why did you assume that Alpha Centauri was only 2.2 "new" light years away and not 4.4? Are you assuming that the speed of light has doubled but distances haven't?

Yes.

[Edit: And based on the article I quoted, I think that this answer may be invalid.]

 

[Ibix]

Yes.

[Edit: And based on the article I quoted, I think that this answer may be invalid.]

It's problematic, certainly. Imagine a rod that fits between here and Alpha Centauri. If you double the speed of light without changing $\alpha$ you have to change one or more of the constants $e$, $\hbar$ or $\epsilon_0$, and the consequence of that on the electrostatic force or the size of electron orbitals will double your calculation of the length of the rod. So it'll still take light 4.4 years each way, because really all you did was mess around with your unit system (or, if you prefer, whatever you did was indistinguishable from messing around with your unit system). It's only if you change $\alpha$ that you get a change in the flight time of the light, because that messes around with the strength of electromagnetic forces.

 

[Vanadium 50]

But ... vacuum permittivity...

Please read #13.