# Why 186,282?

1. Nov 1, 2012

### thetexan

I feel a little like the kid that, when his dad tells him that he has to water the plants, asks 'why daddy'...to which dad replies 'because the plants need water to live'...to which the kid asks 'why daddy'...and it goes on and on. Why? Why? Why?

Here is my confusion and my question. If for the purpose of this question I grant that the top speed of light is 186282mps can anyone tell me why it is 186282? Is it simply that that is what nature ended up with as the top speed of the photon? Or, it there a limiting factor that prevents the photon from going faster if it wanted to?

Could it have just as easily ended up being 200000mps? Or is there something that stops the photon from going faster?

This seems a bit like trying to use a word for which we are looking for a definition in the definition itself. It seems to me that to say that the photon cannot be pushed beyond 186282 then that means there is a force or limiting cause that stops the added speed. That's fine for me but then the question becomes...why is that 'stopping or limiting thing' locked in at 186282? Why not 213765? Or 543998? What is special about 186282?

We know the speed limit exists...but why 186262?

Here is another way of asking the question. Relativity requires that there be a speed limit. Does relativity care that it is 186282 or just that there is A LIMIT of some value? If the value was 200000 would it be allowed by the theory?

tex

2. Nov 1, 2012

### Muphrid

You could say relativity doesn't set a speed limit for light in itself, just for massless particles, and light so happens to transmitted by massless particles. Any massless particle would travel at that speed.

The theory does not say what particular value that speed should be. All relativity cares about is that there is such a speed.

As a dimensioned quantity (that is, it has units of speed, as opposed to being a pure number), the speed of light's numerical value is, to some extent, not meaningful. The speed of light takes on a whole range of values depending on different unit systems (from SI to imperial and more), and often, relativists will choose a unit system in which $c=1$ precisely because they are free to do so and because it is convenient. So in some ways, asking why the speed of light isn't larger or smaller is to ask why we don't use a different unit system.

Put it this way: if the speed of light were actually twice as fast, but we used a definition of the mile that were twice as large, that wouldn't yield any difference in the measured value of the speed of light.

3. Nov 1, 2012

### bobc2

One way of looking at this is to consider the problem in the context of a 4-dimensional universe. Consider all objects, including a photon of light, to be 4-dimensional objects having very small X1, X2, and X3 measurements while extending some 10^13 miles along their 4th dimensions. These long time-like paths through the 4-dimensional universe are often referred to as world lines.

And along with that, consider the strange and curious way in which nature has worked out the instantaneous 3-D cross-section views of the universe experienced by observers moving about at various speeds relative to each other. The sequence of space-time diagrams below shows observers (blue coordinate inertial frames) moving at ever increasing relativistic speeds relative to the black rest frame (increase in clockwise rotations corresponds to increasing speed along the black X1 axis--time increasing along the X4 axis). The slanted X4 axes represent the world line paths through 4-D space while the X1 axes represent the instantaneous cross-section views across the 4-D space experienced by the observers (the 3-D worlds the observers live in at a given instant of time).

The photon is always represented by a world line slanted at a 45-degree angle with respect to the black rest frame. It always bisects the angle between the X4 and X1 axes for any observer (no matter what his speed, i.e., the slant of his X4 axis). Thus, the 4-dimensional photon has THE unique orientation among all 4-dimensional particles. It's angle-bisecting slant is unique--giving a ratio of dX4/dX1 = 1 in the inertial frame for any and all observers. The arbitrary accidental calibration assignment of clocks (sec, min, hours, days, years, etc.) along the X4 axis results in our numerical value for c.

Why and how did nature manage to work out such a rule of rotating X1 axis to provide the 3-D world that an observer should experience? Who knows. But, one thing that is accomplished by that (in addition to having the same c for all observers) is that the laws of physics then are naturally the same in all inertial frames (no matter how X4 is slanted).

Last edited: Nov 1, 2012
4. Nov 1, 2012

### lightarrow

I would like to advocate the OP a little. Ignatowsky showed us that it's possible, with acceptable assumptions, to prove that the relativity principle alone leads to the existence of a maximum speed of signals, that is a signal' speed which is measured with the same value in all inertial frames.
But no one tells us how much this value should be, experiments only can.
One can say that light speed value is determined by the electromagnetic properties of the void space, but it's not quite satisfying, anyway.

5. Nov 1, 2012

### pervect

Staff Emeritus

Or perhaps a simpler answer - the natural value of c is one. It's our choice of units based on our history, that determine the numerical value of 'c'.

Last edited by a moderator: May 6, 2017
6. Nov 1, 2012

### PAllen

If you take that approach, then the thing to ask next is what is the mass of a photon? If 0, it must travel at that invariant speed (this follows from the same assumptions). So then you probe experimentally whether light is best described as the field of a massless particle. This is verified to a high precision, but extremely slight nonzero mass is not excluded.

Similarly, the speed of neutrinos puts an upper bound on their mass (let's not bring up OPERA).

7. Nov 2, 2012

### DiracPool

Perhaps we may want to try to answer Tex's actual question. First of all, the issue of the speed of light not being a "round" number is just one of convention. I think they tried to even this later on by switching to meter-SI units in an attempt to give it a round number of 300K meters per second, but somehow it ended up being a little short of that. In any case, those units are contrived and arbitrary, and, as I believe another commenter posted, many researchers simply set the value to one light second in a dimensional-analysis usage of that velocity.

The fundamental issue I think the OP is getting at, though, is why is there a fundamental speed limit at all, and, even more puzzling, why would it have some finite value. I think that is an interesting and valid question. The only answer is that this speed limit relates to Maxwells equations in the sense that the speed limit is determined by the properties of the medium that light propogates through. Simply from experiment, we know that this medium has certain permissive qualities which are quantified by the electric and magnetic constants. These constants serve as the electromagnetic counterpart of tension and density acting to determine the velocity of wave propogation in a physical medium. Why these constants have the value they do is just as mysterious as why the gravitational constant has the value it does, and why E=mc^2. These are the riddles we do not yet know but are tying to uncover, and the reason why physics is so fun.

8. Nov 2, 2012

### lightarrow

But let's say I'm not interested in photons, just in classical electromagnetic radiation. We know that light speed in the void is 299,792,458 m/s but there is no prove that in some sort of a "modified" kind of void, let's say in the presence of extremely high em fields (just as an example, not a possibility), light speed would be the same. If such a situation could really happen, then it would be meaningful to ask "why that value and not another one".

9. Nov 2, 2012

### PAllen

If classical EM were not Lorentz invariant, we would have a big problem and never invented SR. Then, assumption of classical EM is equivalent to assumption of massless photon. Given an invariant speed, it is then required that light moves at this speed. The key: classical EM is Lorentz invariant if and only if the c in Maxwell's equations is the invariant speed.

10. Nov 2, 2012

### lightarrow

Yes, given an invariant speed in a specific class of frame of references: the inertials ones. We don't know if a "modified" void of the kind I was speculating would belong to the same class. Inertial frames, if I remember correctly, are related to the "space homogeneity" described by Noether's theorem, that is from the fact lagrangian is invariant for translations in space; if could exist regions of space with different electromagnetic properties, this would probably introduce a breaking in that symmetry.
Forgive me if I'm writing stupid things...

11. Nov 2, 2012

### AlexGTV

This belongs to the greater question of why some 200 natural constants are what they are. We don't have an answer as they seem independent of one another.

12. Nov 2, 2012

### grav-universe

We could modify the length of a meter or the period of a second to make the speed of light anything we want. But more simply, we can just call it c and define all other speeds as fractions of c. Kinematics tells us that such a limiting speed must exist, but if reduced to Galilean kinematics, c is infinite. For any non-Galilean kinetics, however, c is finite. That is really the only surprising thing, that c is finite, that the universe is non-Galilean. So the real question would be "Why is c finite and not infinite?"

13. Nov 2, 2012

### PAllen

SM+GR has 'only' 23 arbitrary fundamental constants, not 200.