# Why is the speed of light?

1. Apr 17, 2007

### rogerp

Hi

I'm a confused layman, and was hoping to get some answers to the question: why is the speed of light? That's not a typo - I mean, why is it what it is? The questions below are specific ways to ask essentially the same question.

1. The speed of light is 299,792,458 metres per second. What stops it from reaching 299,792,459 m/s?

2. If light has no mass, what stops it from having infinite speed? What’s slowing it down?

3. Light from the sun takes 8 minutes 24 seconds to reach the earth – why can’t it get here faster?

.

Last edited: Apr 17, 2007
2. Apr 17, 2007

### HallsofIvy

Staff Emeritus
I'm not sure what your question is. Is "why is the speed of light that particular number and not some other number?"

The speed of light happens to be that number because of a particular choice of the length of a meter- which is completely arbitrary. If you measure distance in km and time in hours, or distance in feet and time in minutes, you would get some other number. Nothing very deep about that!

3. Apr 17, 2007

### Staff: Mentor

The Universe has a fundamental symmetry, called Lorentz symmetry, which causes to exist an asymptotic upper limit on all relative speeds. Objects with mass can never reach that upper limit. Massless objects (such as photons) must travel at that limiting speed, and no other. These are consequences of the mathematics of Lorentz symmetry.

This obviously begs the question, "why does the universe have Lorentz symmetry?" Nobody knows. (Or at least there is no generally accepted answer, as far as I know.) This is the ultimate answer to all "why?" questions in physics, by the way. The answer to any "why?" question leads to another "why?" question, and ultimately we always come to one that we cannot answer in the context of physics, at least not yet.

4. Apr 17, 2007

### Gib Z

1. We defined light to go that distance in 1 second. If somehow miraculously, and it cant, light went faster, that new distance is still 299,792,458m.

2. Nothings "slowing" it down, thats the fastest it can go. It can't have an infinite speed because the fabric of spacetime, and infact everything, has 2 quantities. Permittivity and Permeability. The former is sort of a measure of how well Electric fields transmit in the material, in this case spacetime. The latter is a similar measure, except of magnetic fields. Both these quantities must be finite, by definition. Something can't transmit something infinity well.

Since Light is just magnetic and electric fields travelling through space, the speed must be finite as the ability for the spacetime to transmit it is finite.

It may interest you that this equation holds:

$$c= \frac {1} {\sqrt{\varepsilon_0\mu_0}}$$

Where c is the speed of light, episilon_0 is the permittivity of free space, and mu_0 is the permeability.

3. As I said, light can't go faster than spacetime allows it to. To find out why spacetime has the values of permeability and permittivity that it does, you would need to do some serious study into both physics and mathematics so you can Understand Maxwells Famous Equation and Einsteins General Relativity.

5. Apr 17, 2007

### Gib Z

Didn't you read my post >.<
EDIT: or jtbells...he's got it in the first line lol.

6. Apr 17, 2007

### rogerp

Yes, thanks Gib , I did! That's why I deleted my reply.

May I ask one more question?

I'm really interested by this idea of the Permittivity and Permeability of the fabric of spacetime. But am I right that this is a circular theory - i.e. that the speed of light is defined by the Permittivity and Permeability of spacetime, and the Permittivity and Permeability of spacetime are defined by the speed of light?

I'm not sure that physics is explaining here so much as describing. I suspect this question may have been answered by the second paragraph in jtbell's post.

Can I also just thank you both for your answers.

.

7. Apr 17, 2007

### Gib Z

It is somewhat circular, good spot :D

However, only in its definitions. I only when I say "only" you're thinking I'm quite an idiot :) You see, Permittivity and Permeability can be experimentally measured!

The Permittivity and Permeability of Space are defined exactly, as a consequence of the mathematical relation I posted previously. However, one can experimentally measure Permittivity and Permeability without measuring the speed of light, and use the equation to find the speed of light. Measurements are not definitions, but they do show us approximations and that the speed of light, what ever it is, in finite.

8. Apr 17, 2007

### rogerp

Gib, thanks again - believe me, I think you're very, very far from an idiot; after all, you just explained some very difficult concepts to a layman in a way which he understood.

I've got to think about this some more, and come back with further impertinent questions later. One is likely to be about how there can ever be 'inertial observers' (which, as I understand it, is a postulate of special relativity) when we're all falling towards one massive body or another by the operation of gravity...

I thought of this while reading this paper:

http://www.cfa.harvard.edu/Walsworth/pdf/PhysicsWorld_2004.pdf

Anyway, thanks again

.

9. Apr 17, 2007

### reilly

The plain fact is that nobody knows why c is what it is. It is built into physics from the beginning -- Maxwell's equations require knowledge of the speed of light. All the stuff about Permittivity and Permeability is after the fact, and provides no clue about c.

In short, like the charge of the electron, the gravitational constant, ... , nobody knows from c -- Nature gives us things for which we have no explanation.

Regards,
Reilly Atkinson

10. Apr 17, 2007

### exponent137

good question

...Which we have no explanation, but one explanation should be.

In next reference there are clues.

Last edited: Apr 17, 2007
11. Apr 17, 2007

### rbj

the gravitational constant, the speed of propagation (EM, gravitation, information, whatever is your "instantaneous" action), Planck's constant, permitivity of free space, these are all numbers that are purely human constructs resulting on how humans chose to define units of time, length, mass, and charge. note the 4 constraints and the 4 unknowns (that are eventually measured in terms of these anthropometric units). i know that the meter is now defined to be the distance traversed by light in 1/299792458 second, but that wasn't the original definition, for the sake of illustration, let's revert the definition of the meter back before 1960.

now, if instead, you measure everything in terms of Planck units, the values for all these constants become 1, 1, 1, and $1/(4 \pi)$. the only numbers given to us by Nature are dimensionless numbers. so, to ask "why is the speed of light equal to 299792458 meters per second?" causes us to ask the more basic questions that are "why are there about 6.1821 x 1034 Planck lengths in a meter?" and "why are there about 1.8549 x 1043 Planck times in a second?" those are the meaningful questions.

you see, if we measure and describe everything in Planck units, there simply is no c, or G, or $\hbar$, or $4 \pi \epsilon_0$. those numbers just go away from all of our algebraic equations of physical law.

we know that the meter and second are determined to be related to our experience of reality. a meter is approximately how big we are. and a second is, well, not the absolute shortest period of time in our bioological perception, but close to it. somewhere i read that, at our prime, we can do about 20 basic logical operations or computations (crude compare operations) per second in our conscious mind, dunno if that is true or not. when we get older, our CPU slows down but we got a better database.

so then we might start asking, why are there about 1025 Planck lengths in the Bohr radius (about the size of atoms)? and why are there about 105 atoms in the length of a biological cell? and why are there about the same number of cells in the length of a sentient organism like us?

you could construct similar questions about physiological processes regarding why it takes about 1040 Planck times for us to do anything with our bodies (without tools). there is a relationship of the speed of our consciousness and the time around a second. if we were tiny insects, a second might seem like a long period of time. but then we wouldn't be thinking about why the speed of light is what it is. suppose we lived for 1000 years and it took us what we now consider a minute to think every new thought. we wouldn't be manuvering cars at 100 km/hr and i don't think a second would be our unit time and the speed of light would seem even faster to us.

you answer those questions, then you'll get close to why the meter and the second are as big as they are (relative to some Natural units), and, from that, you'll have an idea why the speed of light (which as far as Planck units are concerned is just 1, not some dumb and arbitrary number like 299793458) is what it is, from our perspective.

the speed of light (and of all things instantaneous) is just the natural speed of things in the universe of which to reference all other speeds against.

now the Elementary Charge, that's something else, since the natural unit of charge is already defined. it's interesting (to me at least) that the electron charge, relative to the Planck charge, is just $$\sqrt{\alpha}$$. one can say that e is what it is because of the value of the fine-structure constant (this important dimensionless number that the universe does give us), or (what i prefer) the fine-structure constant is what it is because of the amount of charge that Nature has bestowed upon electrons and other charged particles. because i think that they should have normalized $\epsilon_0$ and $4 \pi G$ instead of $4 \pi \epsilon_0$ and $G$, i think the most natural units would come out slightly different than the Planck units (but be the same order of magnitude) and then, measured in these natural units, the electron charge would be $\sqrt{4 \pi \alpha}$ which is about 0.30282212 . VERY close (as far as orders of magnitude go) to unity. i think 0.30282212 is the number theoretical physicists should put on their walls instead of 137.035999679 . i think the latter flows from the former.

those are the sorta numerical "why?" questions i would be wondering about.

Last edited: Apr 17, 2007
12. Apr 17, 2007

### rbj

i took a look at it. G is not dimensionless and i agree with Michael Duff (and a bunch of other physicists who dispute VSL and varying-G) about the meaninglessness of the varying G or c or any other dimensionful parameter in and of themselves. it's only the dimensionless parameters (which often come out as ratios of like dimensioned quantities) that matter. variable $\alpha$ has meaning. if the fine-structure changed, we would actually notice, but not if G did or c.

as stated previously, you measure everything in Planck units and there simply is no G or c or $\hbar$ to vary. they're just not there in physical law.

here's a nice quote from John Barrow:

Last edited: Apr 17, 2007
13. Apr 17, 2007

### windscar

I think if you were to answer the question; Why does all matter move exactly the speed of light slower than light?; would give more insight into this matter. What property of matter makes everything with mass travel exactly the speed of light slower than light, that travels at one truely constant speed.

14. Apr 18, 2007

### HallsofIvy

Staff Emeritus
What?? That doesn't even make sense. It is not true that all matter moves "exactly the speed of light slower than light". Literally interpreted that would mean that everything has speed 0! I presume you mean "everything travels slower than the speed of light", not "exactly the speed of light slower".

I'm not sure you will accept it as a property of mass, by the Lorentz formula an object moving at speed v has mass
$$\frac{m0}{\sqrt{1- v^2/c^2}}$$
where m0 is the "rest mass" or "invariant mass". As long as m0 is not 0, an object cannot move at the speed of light because that would mean infinite mass. Or, since acceleration= force/mass, the increasing mass requires constantly increasing force to accelerat further. Close to the speed of light requires almost infinite force to accelerate any more.

15. Apr 19, 2007

### windscar

Everything with mass measure's the speed of light being exactly the speed of light. It is one of the basis that started relativity. So if every object see's light traveling exactly the speed of light, then the difference in velocity of every object relative to light is exactly the speed of light. I did not say that matter can travel the speed of light, but all matter travel's the speed of light slower than light. Because they all measure the speed of light to be C.

16. Apr 19, 2007

### cristo

Staff Emeritus
Correct.

This is an invalid comment. I can measure the speed of light in my rest frame, and I will find it to be c. But, you are saying that light can measure my velocity relative to itself. However, this is not true, since light has no inertial frame of reference, and so the notion of travelling on a photon and measuring a body's speed relative to the photon does not make sense.

Last edited: Apr 19, 2007
17. Apr 19, 2007

### windscar

You don't have to sadle up on any photons to see this. All you must do is realize that light is always the speed of light faster than you. The difference in velocity of light and matter is always C. And I was just putting a brain teaser out there that matter always travels a speed of zero relative to light when traveling at a constant speed.

18. Apr 19, 2007

### masudr

In which reference frame?

19. Apr 19, 2007

### Gib Z

In its own.

20. Apr 20, 2007

### masudr

Good, good.

Also, what does it mean when a username has a line through it in these forums (as windscar's appears to now do in all of his/her posts)?