# Speed of light limitation

1. Nov 20, 2007

### bens

I'm a non physicist and I wonder if someone can explain why the light speed is limited.
I'll precise my question...

There is a limit, something, somehow limit the speed, we say it's propagating in fact. I don't know what 'propagating' in a vaccum can mean!

How does this appear in theories, is it a input?
is it demonstrated the physics law?
...

Any explanations are welcome, thanks

2. Nov 20, 2007

### mgb_phys

I will attempt an explanation - although you are probably better off buying some books by proper scientists!

There is nothing that says light is the limit - it's just that a lot of physical theories work quite well if we assume it is and a lot of stuff we think is right fails if it isn't!

Maxwell's equation describe how electricity and magnetism work, this includes light.
They say that the speed of ligth is the same whatever the speed of the thing emitting the light.
Einstein added to this by showing that if Maxwell was to be right then lots of other things about speed, distance and time we think are obvious (like 10mph + 10mph = 20mph) must be wrong.
A side effect of this is that if any information can be sent faster than light causality would be violated - that is you would be able to send a message saying something had happened BEFORE it happened.
Since this is widely believed to be impossible, then if Eisntein and Maxwell are right then the speed of light is the limit.

Last edited: Nov 20, 2007
3. Nov 20, 2007

### CompuChip

Hi bens, welcome to PF.

Since you indicated you do not have a physics background, I'm going to explain some ideas to you, without trying to be very precise. So I might say something here and there which is technically not entirely correct.

Also, from your question I cannot clearly make out if you mean to ask why the speed of light is finite, or why nothing (massive) can travel faster than light. So if you could clarify that?

As for the rest: "Propagating", in this context, is basically just a fancy word for "moving" (instead of saying that the light ray moves from one place to another, we say that the photons propagate through space ). This does not have anything to do with the limit you are talking about, light just propagates through a medium (e.g. vacuum, air, glass, etc) much like a sound wave does (except of course, light can propagate through vacuum while sound can't, but that's just because sound is molecules vibrating which aren't there in vacuum; though we describe light as a wave and it behaves like a wave, there is not actually anything "waving" like in a sound wave or on a string).

In Einsteins special theory of relativity, there is a postulate saying that the light speed is constant for all observers (in a certain position, namely: moving with constant velocities relative to each other). It doesn't say anything about the value of this speed (that was found experimentally and though it's very large by most standards, it's most certainly finite). Also the fact that things with mass which initially move slower than the speed of light can never reach or cross this velocity, follows from this postulate.

Additional dimensions have nothing to do with it, it (relativity, that is) all works perfectly in 4 dimensions (three space, and one time). All the cool stuff you probably heard about with 6, 11 and 26 dimensions refers to string theory, which tries to explain gravity as a consequence of a more basic thing instead of something fundamental in nature. But if we are not interested in where gravity comes from, just in how it works, and affects things, Einsteins theories of relativity (special and general) describe that perfectly.

Hope that gets the questions started

Last edited: Nov 20, 2007
4. Nov 20, 2007

### Mephisto

one weird thing also about it is that speeds don't exactly add up. mgb_phys didn't elaborate too much on this, but i think its really spooky and interesting :)

if you are traveling in your car at 60km/hr, and there is a car coming against you at 50 km/hr, to you it appears that he is raveling towards you at 60+50 = 110 km/hr.... right? however, if you are in a spaceship traveling at 75% speed of light, and there is another spaceship traveling towards you at say, 60% speed of light, you will NOT see it approaching you at 135% speed of light, because NOTHING can EVER travel faster than speed of light, in no reference frame... If you do the math, it would come out that you would actually see him approaching at something like 99.9% speed of light, instead of the 135%. kinda weird :)

5. Nov 20, 2007

### CompuChip

The even weirder thing is that this is so for any two velocities. So even in the example with the cars traveling at very low speeds compared to the speed of light, you would actually have to do a little more complicated calculation and you'd find that the relative speed is a little off from the 110 you'd expect. Now that's weird

Luckily, this "correction" to the "classical" way of adding speeds is so small that we won't even notice it for speeds like the ones we encounter in everyday life (go figure: even a plane flying at 1000 km/hr will only travel 0.3 km/s, which is far less than the 300 000 km/s of light).

6. Nov 20, 2007

### Claude Bile

One thing relativity showed us is that space and time are not separate entities, they are intertwined with one another (hence the term space-time). The existence of a universal speed limit is a characteristic of space itself!

Claude.

7. Nov 21, 2007

### bens

Go further on

Thanks all of you, can we go further on?
I can remerber this from my lessons

first one, why the speed of light is finite, or just why speed of light in vacuum?

Vacuum is quite a strange medium, what is emptyness if there is energy 'moving' in it?

I guess we touch the point!

if light can cross pure vacuum (imagine) it undergoes no attenuation ever, TRUE?
OK it's vacuum, none mass is moving but just electromagnetic forces => no attenuation.

NO medium, NO mass movements NO attenuation, what kind of propagation is it !?

8. Nov 21, 2007

### mgb_phys

It's wrong to think of light as a wave in the same way as sound wave or a wave on a string, it's more useful to think of it as a little ball of energy. It has a wavelength - but so does everything, a golf ball has a wavelength calculated in exactly the same was as the wavelenght of light. It's only because light has such little energy that it's wavelength is large enough to notice.

Relativity says that there is a maximum speed that information can move. Maxwell's equations say that it is the speed of light in vacuum.

Light travelling in empty space isn't attenuated because there is no process to lose energy to. In practice space isn't that empty and light is attenuated by hitting any free particles or dust.

In fact the best at travelling through space unattenuated are neutrinos, very low mass neutrla particles which interact with almost nothing. It takes a photon about 250,000 years to get from the centre of the sun to the surface because it bounces of all the matter in there - it takes a neutrino seconds.

9. Nov 21, 2007

### Chris Hillman

Law of addition of tangents in elliptic, parabolic, hyperbolic trig

Do you also consider the law of addition of tangents from high school trig "spooky"? See [post=1502170]this post[/post] and [post=1513092]this one[/post].

Last edited: Nov 21, 2007
10. Nov 26, 2007

### bens

May I have a last question?
What prevents the light, but also information if I understood correctly, to go faster than the speed of light?

11. Nov 26, 2007

### Chris Hillman

Trigonmetrically speaking, in Minkowski geometry the "slope" of a null line is always +/-1. Timelike curves must always have tangents which fit inside the "light cones" attached to each event on the curve, which is another way of saying the positive mass particles cannot move at or faster than light. A massless particle OTH must always have a world line which is a null line. The remainder are spacelike lines; a hypothetical particle (tachyon) which moved faster than light would be seen to be moving into the past by some observers, and into the future by others. This alone leads to all kinds of problems, and there other reasons why physicists reject the idea that a signal could propagate faster than light.

12. Nov 26, 2007

### Coin

bens, I think something that helps is if you think of c not as "the speed of light" but as "the fastest it is possible to go". Light in a vacuum goes as fast as it is possible to go, therefore we expect light in a vacuum to move at c.

As for why c is "the fastest it is possible to go", see what Claude and Chris said-- space and time are part of the same structure, and the way that structure is "shaped" means that there's a "fastest possible speed", which we call c.

I *THINK* ( I may be about to say something wrong! ) that the specific reason why the "shape" of spacetime causes there to be some universal speed limit is that one of the attributes of that "shape" (at least according to GR) is that spacetime is "lorentz invariant", which says that the relation

$$\Delta t^2 - \Delta x^2 - \Delta y^2 - \Delta z^2 = 0$$

is preserved in all reference frames. If you think about this, since t has opposite sign from xyz, you can rewrite this as:

$$\Delta t^2 = \sqrt{\Delta x^2 + \Delta y^2 + \Delta z^2}$$

Which basically says "distance in time is equal to distance in space". So if you want to move across an infinite amount of distance in space, it will take you an infinite amount of time...

13. Nov 26, 2007

### Chris Hillman

Hi, Coin, make that "gtr models a spacetime, which provides the geometric setting for all non-gravitational physics, and whose curvature models all gravitational phenomena, as a Lorentzian manifold, and the tangent spaces to a Lorentzian manifold are endowed with the structure of a Lorentzian inner product space, which guarantees that str holds in the small, including infinitesimal Lorentz invariance very near any event".

IOW the stuff about infinitesimal lightcones and timelike/null/spacelike curves is built into gtr at a fundamental level.

14. Nov 26, 2007

### Staff: Mentor

That question is a logically meaningless: whatever speed light propagates at is the speed of light. It can't go faster than itself any more than you can be beside yourself.

If what you really mean is is the speed of light constant, the answer is not really: it depends on the properties of the medium it is travleing in - the permeability and permittivity (its ability to pass electric and magnetic fields). It also just so happens that a vacuum has a measurable permeability and permittivity, which then allows you to calculate the speed of light in a vacuum. That speed, then, is constant.

What prevents information from traveling faster than the speed of light is that the fastest way to send information of any kind is with light. People often ask about pushing on a long, rigid bar, but the rigidity of a bar is limited by the elecromagnetic forces holding it together. And those electromagnetic forces propagate at....you guessed it.... the speed of light.

15. Nov 27, 2007

### Coin

That sounds like a much more accurate way of putting it, yeah :)

16. Nov 27, 2007

### JesseM

I don't think it's logically meaningless, the question can be interpreted as "why does light have a fixed speed in a vacuum"--we could easily imagine a universe where it didn't, where there was no upper limit on the speed of any particle (as would be true in a Newtonian universe). However, what this comes down to is asking why the laws of physics are the way they are, and physics can't answer those sorts of questions.

17. Nov 27, 2007

### deSitter

Actually the entire point is that, yes, there is a physical limit with dimensions of a velocity, and light happens to go at that speed because it is mediated by a field with no mass. See this for an explanation requiring nothing more than algebra to understand - no mirrors, no trains, no barns, no elevators.

http://membrane.com/sidd/wundrelat.txt

The point of this is - simple arguments based on homogeneity and isotropy of space and time lead inevitably to the existence of a universal parameter with dimensions of a velocity. It is either finite or not, and experience shows that it is finite. The most important thing is that this parameter has nothing to do with light as such - it's built into the very geometry of the world, which is really 4-dimensional (at this level at least).

-drl

18. Nov 27, 2007

### Staff: Mentor

That isn't what the question asked, but yes, that's what I presume was meant....and how I answered.

19. Nov 27, 2007

### rbj

i think that what the physics is, is this:

1. whether it's gravity, EM, or any other "instantaneous" interaction, the effect of that interaction, when some causal agent at point A changes, any reflection at point B (not at the same location as point A) of that change, does not happen immediately as perceived by an observer as some third location that is equidistant from points A and B. that observer will see a time delay in the effect of that interaction that is proportional to the distance that point B is from point A. we can call that constant of proportionality "1/c". and it is clear that c is the speed of propagation of this "instantaneous" interaction.

2. from a POV of Nature, it doesn't matter what the value of c is. any value attached to it is a human construct (or a Zogian construct for the aliens who live on the planet Zog). all the physics says is that c is finite. what particular finite value is not primary. whatever c is defines the natural unit of speed. all other physical reality are scaled accordingly.

20. Nov 27, 2007

### deSitter

Yes this is an excellent point - one could go so far as to say "c" should be banned from equations!

There is another way of looking at this that goes very deep into the heart of the geometry. In relativity, propagation is elevated to a primitive fact by welding space and time into a geometric unity via the fundamental speed. There is no longer any logical necessity for introducing a medium of propagation at all! The precise geometrical expression of this is one of the great beauties in physics.

Euclidean geometry can be interpreted as a projective metric (Google for examples) with the fundamental quadric being the so-called "circular points at infinity" (or isotropic points in modern terms) - these are the idealized points satisfying the relation

x^2 + (ay)^2 = 0

which can be factored

(x + iay)(x - iay) = 0

Minkowski geometry likewise is characterized by taking as fundamental quadric the "light cone"

x^2 - (ct)^2 = 0

or

(x + ct)(x - ct) = 0

The isotropic points are no longer "idealized", but very real, the locus of an expanding wavefront from, say, a light pulse.

Thus in very real sense, pure Euclidean geometry is, like Minkowski geometry, characterized by a fixed, finite value - in natural units where a=1, the imaginary unit i! This is probably the most primitive expression of complex numbers in reality.

-drl