# Why c is ~299,793 km/s ?

1. Aug 30, 2010

### wondercosmos

I know that the speed of light has been measured with great precision and used successfully in many calculations.
I just wonder why this specific speed. What is the deep reason?

I am aware that if the strength of the fundamental forces is not what they are, we Earthlings would not be here; we would not exist. Is there a link between these forces and c that imposes the speed limit to c?

I have heard of the Tachyon whose lowest speed is c, but has never been detected, so I tend to ignore it.

As a product of the above questions: What would happen to the universe if the speed of c is less or more than ~186,282 mi/s in the vacuum?

2. Aug 30, 2010

### PhanthomJay

I urge you to search this forum for a year's worth of reading on this topic. It seems to boil down to:
The speed of light is what it is because the dimensionless fine structure constant of the Universe, which is a function of the speed of light, the electric charge, the permittivity and permeability of space, and Planck's constant, and which is equal to 1/137.035999..., is what IT is, and no one yet knows why that dimensionless constant equals 1/137.035999.... at least I don't think ...so maybe I shouldn't talk.

3. Aug 30, 2010

### Creator

That is the speed in a vacuum basically because the permittivity of free space, e, is 8.8541878 x 10^-12, and the vacuum permeability, u, is defined as 4 (pi) x 10^-7.

And since ... c = 1 / sq.rt.(e X u) (thank you Mr Maxwell)

Then plugging in the values ... c = 2.9972... X 10^8 m/sec.

IOW, According to Maxwell's eqns. the speed of light is determined by two electromagnetic properties of the vacuum, namely, its electric permittivity and its magnetic permeability.

;))

Last edited: Aug 30, 2010
4. Aug 30, 2010

### Chronos

In other words, no one know why c is what it is. Permittivity and permeability are not empirical [measured] values.

5. Aug 31, 2010

### Staff: Mentor

But why do $\epsilon_0$ and $\mu_0$ have the values that they do?

(We define $\mu_0$ to have a particular value as part of a system of electromagnetic units that is commonly used, but that system is not the only one that has been used.)

Last edited: Aug 31, 2010
6. Aug 31, 2010

### Chalnoth

I'm pretty sure it's $c$, not $\epsilon_0$ or $\mu_0$ that is the fundamental value. Basically, we now know that space and time are both part of the same thing, and it was only our particular history of evolving in a situation where we don't typically move (or witness) objects moving at anywhere near the speed of light that we ever thought that space was different from time.

And if space and time are part of the same thing, then one can use the exact same units to describe both. That is, it is sensible to talk of meters of time, or seconds of distance. The speed of light is only the unit conversion factor we use between them. Since the unit conversion factor is between distance and space, its units come up as a speed. This unit conversion factor is only called the speed of light because light is the first thing we ever measured that traveled at this speed (anything with zero mass must travel at the same speed).

7. Aug 31, 2010

### PhanthomJay

I like this. It reminds me of Brian Greene's now ancient interpretation, which I loosely (probably incorrectly) describe as this:
"We live in a 4-dimensional spacetime universe. Massless particles, like Photons, always travel at the speed of light...through space. They do not travel through time (time is naught for the photon). On the other hand, we mortals, sitting stationary on a chair (with respect to the chair) travel at the speed of light through time, and not at all through space'. When we move with respect to the chair, we travel through both, using the conversion factor noted above.

For more on the value of the speed of light, see

Enjoy.

8. Aug 31, 2010

### Chalnoth

Well, this is nitpicking a little bit, but photons always travel along what are called "null geodesics". That is, they always travel along paths whose metric distance is zero. This means that the spatial part of the distance traveled and the time part of the distance traveled must cancel exactly (distance traveled across space has an opposite sign from distance traveled across time).

From our perspective, then, light travels in equal parts across space and time. From the perspective of the photon, however, light travels across neither space nor time (with infinite time dilation, a hypothetical photon observer always takes zero time to get anywhere, and "sees" the universe as a pancake infinitely contracted along its direction of motion so that it doesn't need to take any time to get anywhere).

The statement that from our perspective, we are moving through time and not space is reasonable. However, I just don't know if you can sensibly talk about a speed of motion through time in this context.

9. Aug 31, 2010

### Dickfore

The reason why the numerical value of the speed of light is exactly:

$$c = 299,792,458 \, \frac{\mathrm{m}}{\mathrm{s}}$$

is because the speed of light is used today to define the unit of length through the unit of time and all uncertainty in its determination is attributed to the uncertainty with which the standard of length had been defined. It is chosen this specific value so that it coincides with the old etalon of length in the metric system chosen to be:

"one ten millionth of the length of the Earth's meridian from the North Pole to the Equator passing through Paris..."

and the unit of time (the second) chosen to be:

"1/86,400 part of the mean Solar day"

Today, the second is defined by counting a particular number of periods in the line of a particular isotope:

"the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom."

Again, the weird numerical factor is because of the tendency to adhere to the old etalon of time.

These units are terrestrial and have no deep cosmological meaning.

All mechanical quantities have dimensions with respect to length, time and mass. Therefore, there can be no more than 3 freely definable fundamental constants. In principle, one can then choose these constants to be exactly equal to 1 (or another convenient numerical factor, but, nevertheless, dimensionless).

The modern theories developed in the XX century, the Theory of Relativity and Quantum Mechanics naturally establish two such constants: the speed of light in vacuum and the Planck constant. In natural units, the values of these are chosen to be exactly $\hbar = c = 1$. Because of the dimensions of these constants in SI:

$$[c] = \mathrm{L} \, \mathrm{T}^{-1}$$
$$[\hbar] = \mathrm{M} \, \mathrm{L}^{2} \, \mathrm{T}^{-1}$$

we see that by choosing these constant to be dimensionless, we choose a particular relation between the base physical quantities' dimensions:

$$\mathrm{L} = \mathrm{T} = \mathrm{M}^{-1}$$

(Almost) all electric units have an additional dimension with respect to electric current (in SI). However, because of the way the unit of current is defined - through specifying what the force, a mechanical quantity, between a particularly simple arrangement of conductors is - there is a "fundamental constant", permeability of free space (the magnetic constant of classical vacuum), with an exact value:

$$\frac{\mu_{0}}{4 \pi} = 10^{-7} \, \frac{\mathrm{N}}{\mathrm{A}^{2}}$$

This constant is used to just make the equations of (classical) electrodynamics dimensionally consistent. There is another related quantity, permittivity of free space (the dielectric constant of classical vacuum) $\epsilon_{0}$. According to Maxwell's equations, the speed of electromagnetic waves in free space is exactly:

$$c = \frac{1}{\sqrt{\epsilon_{0} \, \mu_{0}}} \Rightarrow \epsilon_{0} = \frac{1}{\mu_{0} \, c^{2}}$$

According to the electromagnetic theory of light, light is nothing more but electromagnetic waves with specific frequency (of wavelength). Therefore, this speed must be also the speed of light in vacuum. But, as we just saw, this quantity is a fundamental constant with an exact value. It follows that the permittivity is also an exact numerical factor. In equations of electrostatics, this constant enters in a different combination:

$$k_{0} = \frac{1}{4 \pi \epsilon_{0}} = \frac{\mu_{0}}{4 \pi} \, c^{2}, \; [k_{0}] = \mathrm{M} \, \mathrm{L}^{3} \, \mathrm{T}^{-4} \, \mathrm{I}^{-2}$$

the Coulomb constant.

Another fundamental quantity is the electron charge e ($[e] = \mathrm{T} \, \mathrm{I}$). We can use the above Coulomb constant to construct a "mechanical quantity" by canceling the dimensions of electric current. Specifically, the combination $k_{0} \, e^{2}$. The dimensions of this combination are $[k_{0} e^{2}] = \mathrm{M} \, \mathrm{L}^{3} \, \mathrm{T}^{-2}$, which is a dimensionless quantity in natural units. Actually the dimensionless quantity is the following combination:

$$\alpha = \frac{k_{0} \, e^{2}}{\hbar \, c} \approx \frac{1}{137.0}$$

the fine structure constant.

Last edited: Aug 31, 2010
10. Aug 31, 2010

### jackmell

I think you guys can't see the forest for the trees. I bet any money it's that speed because of how the Universe was created and if it was created differently, I suspect the speed of light as well as other constants of Nature would be different.

11. Aug 31, 2010

### Dickfore

How can we verify your bet?

12. Aug 31, 2010

### jackmell

Well, I don't want to be any more speculative else my post get deleted. I'm simply offering what I believe is the best answer to the OP's question and if I may leave him with my hope that one day we will learn how to create Universes and thus provide the verification you seek.

13. Aug 31, 2010

### Creator

I agree .

Creator ;))

-- "The works of the Lord are great, studied by all who have pleasure therein" - Inscribed in the Archway of doorway to James Clerk Maxwell's Cavendish Laboratory - Cambridge.

14. Aug 31, 2010

### Chalnoth

Sort of.

The speed of light is a dimensionful quantity. It only takes on its meaning once we define what we mean by "distance" and "time". Change our measure of "distance" or "time", and we change the measured speed. Thus the speed of light itself cannot possibly be a fundamental quantity. It only takes on meaning once we define what we mean by "space" and "time", and then the constant itself only exists when we attempt to claim that "space" and "time" are not part of the same thing.

The sorts of things that are fundamental quantities are dimensionless constants. The fine structure constant which sets the strength of the electromagnetic force, for instance, is a pure number: $\alpha= 1/137$. It is this sort of number that changes in the early universe can potentially effect. But quantities like the speed of light are too arbitrary to have a grounding in the behavior of our early universe. Yes, one could write down a situation where the speed of light comes out different, but that wouldn't be particularly meaningful when the terms "meter" and "second" wouldn't be well-grounded in this other hypothetical universe.

15. Aug 31, 2010

### epenguin

We have done this question before as pointed out, even over the last year.

The only form in which this question can have a sense would be something like "Can you explain why the physiology of these intelligent creatures on earth is such that a photon could bounce between the head and feet of the order of 2.108 times during one of its heartbeats?". You probably can, starting with explanation of why, say, a hydrogen molecule an atom has the size it that can be traversed by light in (however many times it is) during one vibration in its lowest energy.

Not joking!

16. Sep 1, 2010

### twofish-quant

The speed of light is 1. 1 is a very nice number and there isn't anything to explain.

Now you may have heard that on planet earth, they use the number 299,792,458 for the speed of light, but that happens because the length unit they use started with some fraction of the size of their planet, and the time unit they use happens to be some fraction of how quickly their planet spins.

I've heard that on planet Kosbane, they use the number 402,343,434. Because their length unit is based on the sign of King Fazoks fourth leg, and the time unit ultimately came from how long it takes to drop a quartzball from the top of Spire Mountain.

The fact that different beings on different planets use different numbers for the speed of light tells you a lot about history. But from the point of view of a physicist that doesn't care about the details of planet Kosbane, the speed of light is 1.

Nothing to explain there. The speed of light is one. Since one is a nice number, we don't have any issues here.

Now there happens to be another number called the fine structure constant which about 1/137.

Explaining that is a deeper question since we aren't dealing with the details of planet Kosbane.

17. Sep 1, 2010

### twofish-quant

It often happens in physics that the opposite happens, which is that if you change some constant then nothing changes.

Imagine that you do to sleep tonight, and you wake up and while you were asleep, everything doubled in size. Everything would change, but nothing would change, because when you woke up, all the rulers would also double in size.

There are a lot of situations physics like that. You change one thing, but the rules are set up so that everything else reacts to give you the same situation that you started out with. It happens often enough so that one strategy for theorists is to assume that the laws of physics are set up so that there is some basic symmetry (i.e. if everything doubles in size, no one notices, if the entire universe just suddenly moves one foot to the left no one will notice, etc. etc.) and then see what rules you come up with.

For example, you can come up with a set of rules saying "I want to be able to set up the speed of light to be anything I want and still have the universe to be the same." If you work through the math, you find out to have everything workout, you have to add some fudge factor to have everything work out. The theory that you come up with is general relativity and the fudge factor you have to put in so that you can set the speed of light at anything anywhere and still come out with the same universe is gravity.

18. Sep 1, 2010

### jackmell

Ok, that sounds interesting. You guys know way more about this than me and I want to believe and trust what you and the others say. However I can't help but remain skeptical that our Universe is the only one possible but rather suspect it is only one of an infinite number of possibilities, some of which perhaps would be vastly different with entirely different physical properties, for example, one in which there is no speed of light. Carl Sagan wanted so much to know if other forms of life existed in the Universe. Me, I'd rather know how the Universe was created.

19. Sep 1, 2010

### Chalnoth

It is perfectly reasonable that there may well be many other regions of space-time with very different properties. We currently don't even know the possible variations on effective physical law.

However, some prescriptions for how another universe might behave just don't make sense, and a universe with no speed of light is one of them. Now, if you want to accept the possibility of a universe with only spatial dimensions and no time dimension, then you wouldn't have a speed of light, because you'd have no speed! There would be no motion of any sort, for that matter: such a universe would just be a static configuration.

By contrast, if you have a universe that has one dimension of time, then you necessarily have a speed limit (which we call the speed of light). There are a couple of ways to look at this. One is from the relativity standpoint posted earlier, where the speed of light is just the unit conversion factor between space and time. Another is to consider it from the quantum mechanical direction and consider that all of the microscopic laws of physics are local laws: they deal with behavior that happens at a specific location. If you make a change in a system in one place, then that change has to take time to propagate to another place. If the change didn't take time to propagate, if changes could happen instantaneously with respect to some observers, then you'd just have to move with respect to those observers and suddenly you'd see effects happening before causes! Such a universe without a speed limit, therefore, is a nonsensical universe.

That speed limit might not be the "speed of light" in another universe, mind you, because there might not be "light" in the other universe. But it would still be the speed of massless particles.

20. Sep 1, 2010