# Why is speed of light constent at a given place

1. Apr 15, 2012

### abhishek002

i dont know this question goes at the right place
but i would like to know why speed of light remains constant

what i mean is simple
suppose you throw a ball
and then consider you are throwing the ball by running yourself
the ball acquires more speed in the 2nd case

i would like to know why this does not happen in the case of light
be descriptive

2. Apr 15, 2012

### HallsofIvy

First this is a question about relativity, not quantum physics so I am moving it.

Second, the basic answer to any physics question is: because that is what the experimental evidence shows!

Light does, in fact, follow the same laws of motion as other objects. But the law may be different than what you are used to. A crucial difference between relativity and classical mechanics is this (derived from experimental evidence as I said)- if a person running toward you at speed u (relative to you) and throws a ball toward you at speed v, the speed of the ball relative to you is NOT given by u+ v. It is, rather,
$$\frac{u+ v}{1+ \frac{uv}{c^2}}$$
where c, of course, is the speed of light.

In particular if v= c (the person running toward you at speed u shines a light at you) the speed of the light relative to you will be
$$\frac{u+ c}{1+ \frac{uc}{c^2}}= \frac{u+ c}{1+ \frac{u}{c}}$$
multiplying both numerator and denominator by c,
$$\frac{c(u+ c)}{c+u}= c$$

3. Apr 15, 2012

### Naty1

yes. In other words, the impression we are given in elementary math is that 'u + v' is 'the way the world works' when in fact it is an approximation which is really, really good at everyday baseball, automobile, running [slow] speeds....but inadequate [not accurate] when we consider speeds at a significant proportion of 'c'....rocketship, atomic particle, electromagnetic, gravitational field,etc,etc, speeds...

Perhaps a more fundamental reason, but not a final answer, is that space and time vary with speed rather than the speed of light. It's a crazy situation when you first learn about it, but,for example, you can read about time dilation [time slowing down] in Wikipedia describing the GPS system: clocks on earth run slower than orbiting satellite clocks....so frequent corrections must be made to maintain position accuracy.

And another interesting feature of 'c' is that nothing can go faster; unlike other slower velocities, as in a car race, you can't even get to 'c' let alone go faster. No matter how fast you go, light always passes you at 'c'....so you can't even begin to catch up!!

When gravity is present, space and time also vary as a result...so things get more complicated to describe.

Last edited: Apr 15, 2012
4. Apr 15, 2012

### harrylin

First of all, if you throw the ball by running yourself, the ball does not acquire more speed with respect to yourself; but it does acquire more speed with respect to the road (or wherever you are running).

Now, there are two facts about the speed of light that seemed to contradict each other, and these two facts are at least historically important for special relativity:

1. light propagation is more like sound in air than like a ball in air: the speed of light is, similarly as the speed of sound, a constant that is independent of the motion of the source.
That is also called the second postulate.

The main difference with sound, which is related to what is called the first postulate, is with measurements of the speed of light with different systems:

2. It's important to understand that in relativity "the speed of light" merely means the ratio of distance divided by time as measured with a certain reference system; and this ratio is the same (invariant) when measured with different systems. Explanations for how that is possible depend somewhat on interpretation, but it's in any case related to the fact that systems that move at different velocities measure such things as time and distance differently.

5. Apr 15, 2012

### Staff: Mentor

Its because light is different than throwing a ball. The speed a ball is thrown at depends on the speed you are moving at and the speed you throw the ball relative to you. However the speed light propagates at is determined by Maxwell's equations which are exactly the same in any internal frame regardless of how fast it is moving relative to another inertial frame - ie the speed of the source does not come into it. It's like making waves in a pond - the speed of the waves does not spend on how fast what ever is making the waves moves at.

When looked at this way its quite reasonable but has far reaching conseqences for our conception of space and time.

In fact the speed of light thing really is not what relativity is about - its really about symmetry - namely the symmetry implied by the principle of relativity which says the laws of physics are the same in any inertial frame. Check out:
http://www.scribd.com/doc/86454982/17/Relativity-without-c [Broken]

Thanks
Bill

Last edited by a moderator: May 5, 2017
6. Apr 15, 2012

### rbj

please use punctuation. i also am sorta recalcitrant regarding caps (as was e.e.cummings), but if you ditch both caps and punctuation, your sentences have nothing left to separate them.

first, light and thrown balls are not the same thing, but the physical universe they exist in are the same.

as mentioned by Halls, velocities do not add linearly, like you would expect to. but that is a result, not a first principle, which is what i think you're asking about. also it isn't just about light (or the EM interaction). any of these ostensibly "instantaneous" interactions act on objects at a distance with the same speed of propagation we call "c".

now the answer to your original question is because of this basic principle of relativity:

In every inertial frame of reference, the laws of physics are identical in every respect.

an inertial frame of reference is one that is unaccelerated, at constant velocity. you see, you can have two different observers with one flying through space, even at a high velocity with respect to the other and both observers have equal claim to being the guy who isn't moving (at rest) pointing to the other guy as the object in motion. they are both at rest from the own perspective and it's the other guy who's moving. there is no absolute frame of reference that is "at rest". (this was confirmed in the 19th century with the Michaelson-Morley experiment.) this means, unlike sound, there is no medium, no nothing that blows across your face as you fly through a vacuum at great speed. there is no meaning to the speed of the vacuum moving past you. so, no matter which observer you are, there is no sense of any physical thing moving past you (except for the other observer).

now suppose one of these observers is holding a flashlight and points it "ahead" of him (from the perspective of the other observer that considers himself at rest). now, once this light leaves the flashlight, it propagates only because of Maxwell's equations for EM (not because there is any medium carrying it). that EM wave we call "light" is propagating because this changing E field is causing a changing B field which is causing a changing E field, etc. so when the guy with the flashling measures the speed of the beam of light coming out if his flashlight, he says the speed is c. but, even though the flashlight is whipping past the other observer at high speed, when the "at rest" observer observes the same beam of light, it's the same Maxwell's equations and the same $\epsilon_0$ and the same $\mu_0$. and c is a quantity totally defined by $\epsilon_0$ and $\mu_0$.

if Maxwell's equations were different for one inertial observer than the other (both having equal claim to being "at rest"), including the values of $\epsilon_0$ and $\mu_0$, then this first principle that these two observers, both who have equal claim to being the observer at rest, would be violated and these two observers would have different laws of physics. but then, if any consistency were to be considered, if one observer's c (or $\epsilon_0$ and $\mu_0$) was different from the other's c, which of these two observers should get the faster one and which should get the slower one?

long winded answer. but it's essentially a case by contradiction. your laws of physics would be less consistent if you allowed them to be different for different inertial frames of reference.