# Fundamental c

## Main Question or Discussion Point

I've recently read a short intro to SR and am quite curious to learn more but there are some things that bother me. One such issue is the fundamental speed of light (or is it properly 'velocity' even for light? English is not my mother tongue). I understand that time dilation would be impossible without the speed of light being constant to any observer irrespective of the observer's movement in reference to the light source but why is it constant? For me it seems sort of counter-intuitive. Has it been proven empirically? Or is it just a dogma?

Here's an example that got me thinking: Suppose you're in a train (that's moving in reference to Earth) with a flashlight in your hand and a mirror on ceiling above you. You turn on the flashlight, put it on the floor and direct it to the mirror. Now the light beam goes up to the mirror and comes down to the floor. You know the distance the light beam has traveled (2 times the height of the carriage you're in) and so you can calculate the time (because you know c) it took for the beam to be reflected on the floor. Now suppose an observer, from outside the train, standing on the ground, is watching. If the train is moving with a constant velocity, than the observer sees the light beam forming two sides of an isosceles triangle, hence, traveling a longer distance than observed by the person in the train and taking more time to do so. This is true, if the speed of light is constant to any observer.

So, why is it constant (or why it is widely accepted that it is constant)?

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DrGreg
Gold Member
I've recently read a short intro to SR and am quite curious to learn more but there are some things that bother me. One such issue is the fundamental speed of light (or is it properly 'velocity' even for light? English is not my mother tongue). I understand that time dilation would be impossible without the speed of light being constant to any observer irrespective of the observer's movement in reference to the light source but why is it constant? For me it seems sort of counter-intuitive. Has it been proven empirically? Or is it just a dogma?

Here's an example that got me thinking: Suppose you're in a train (that's moving in reference to Earth) with a flashlight in your hand and a mirror on ceiling above you. You turn on the flashlight, put it on the floor and direct it to the mirror. Now the light beam goes up to the mirror and comes down to the floor. You know the distance the light beam has traveled (2 times the height of the carriage you're in) and so you can calculate the time (because you know c) it took for the beam to be reflected on the floor. Now suppose an observer, from outside the train, standing on the ground, is watching. If the train is moving with a constant velocity, than the observer sees the light beam forming two sides of an isosceles triangle, hence, traveling a longer distance than observed by the person in the train and taking more time to do so. This is true, if the speed of light is constant to any observer.

So, why is it constant (or why it is widely accepted that it is constant)?
Your example does indeed show that if the speed of light is constant then there must be time dilation.

For experimental results to confirm that the speed of light really is constant, follow the link within the "Sticky: FAQ: Experimental Basis of Special Relativity" at the top of this Special & General Relativity forum, and in particular look at sections 3.1, 3.3 and 3.4.

Your example does indeed show that if the speed of light is constant then there must be time dilation.

For experimental results to confirm that the speed of light really is constant, follow the link within the "Sticky: FAQ: Experimental Basis of Special Relativity" at the top of this Special & General Relativity forum, and in particular look at sections 3.1, 3.3 and 3.4.
Thanks for the input. But is there any way to theoretically (by some deduction or using other information as a basis) prove that c=const? Or it has just been proved empirically? I'm curious because this is something that's hard to grasp, at least for me. The constancy of c seems a bit counter-intuitive. If it is so, can light even be defined as a particle (photon)? Because then it should move just as any rigid body, shouldn't it? If a I throw a rock, then it's velocity is relative, it differs if you change the frame of reference, however the speed of light is absolute. All this is a bit confusing for me, though it raises curiosity.

NWH
The thing about light is that it acts as both a particle and a wave, it can have both properties... Look into the double slit experiment, it gives insight into just how much of a weird phenomenon light is...

Personally I think it speaks for it's self. If no matter what constant speed you're traveling at, the laws of physics are exactly the same in all frames of reference (this can and has been tested to a certain degree), those rules must also apply to light somehow. I believe Maxwell said that you can't have static light, meaning that it's not possible, in any frame of reference, to see a beam of light at rest beside you. It was with this theory Einstein came to the realisation that in order for this to be possible, time must adjust it's self so light can fly past you accordingly (keeping the laws of physics the same in all frames of reference).

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DrGreg
Gold Member
Thanks for the input. But is there any way to theoretically (by some deduction or using other information as a basis) prove that c=const? Or it has just been proved empirically? I'm curious because this is something that's hard to grasp, at least for me. The constancy of c seems a bit counter-intuitive. If it is so, can light even be defined as a particle (photon)? Because then it should move just as any rigid body, shouldn't it? If a I throw a rock, then it's velocity is relative, it differs if you change the frame of reference, however the speed of light is absolute. All this is a bit confusing for me, though it raises curiosity.
Rocks and photons don't really behave differently. If you are travelling at 30 mph in a car and you throw a rock forward at 10 mph relative to the car, pre-relativistic Newtonian theory says that the rock goes at (30+10) mph relative to the ground. But relativity says the rock goes slightly slower at

(30 + 10) / (1 + 30×10/c2) mph​

relative to the ground. This formula applies to everything, rocks and photons. If you make one of the speeds c, you get an answer of c. (Of course that doesn't prove anything, as I haven't told you where my formula came from.)

One way of thinking about it is that c isn't so much the speed of light, it's the universal speed limit (and light just goes as fast as it can without breaking the limit). Either there is or there isn't a universal speed limit, and if you accept the principle of relativity that all inertial observers have equal status, then if the limit is finite then everyone has to agree on its value. Only experiment can tell us whether the limit is finite or infinite.

I've recently read a short intro to SR and am quite curious to learn more but there are some things that bother me. One such issue is the fundamental speed of light (or is it properly 'velocity' even for light? English is not my mother tongue). I understand that time dilation would be impossible without the speed of light being constant to any observer irrespective of the observer's movement in reference to the light source but why is it constant? For me it seems sort of counter-intuitive. Has it been proven empirically? Or is it just a dogma?

Here's an example that got me thinking: Suppose you're in a train (that's moving in reference to Earth) with a flashlight in your hand and a mirror on ceiling above you. You turn on the flashlight, put it on the floor and direct it to the mirror. Now the light beam goes up to the mirror and comes down to the floor. You know the distance the light beam has traveled (2 times the height of the carriage you're in) and so you can calculate the time (because you know c) it took for the beam to be reflected on the floor. Now suppose an observer, from outside the train, standing on the ground, is watching. If the train is moving with a constant velocity, than the observer sees the light beam forming two sides of an isosceles triangle, hence, traveling a longer distance than observed by the person in the train and taking more time to do so. This is true, if the speed of light is constant to any observer.

So, why is it constant (or why it is widely accepted that it is constant)?
If you're in a moving boat and drop a stone into the water, the waves move radially away from the point where the stone contacts the water. You move away from that point, but the waves move at a constant speed relative to the water, and independently of your boat.
With material objects, the projected object acquires the speed of the parent object, but photons do not.

From the perspective of the person on the train, if you remove all his horizontal motion, which he does not detect by internal measurement, you are left with only vertical motion. Time dilation prevents his detection of a longer transit time for light, i.e. his observations are the same as if he is not moving.

Dale
Mentor
is there any way to theoretically (by some deduction or using other information as a basis) prove that c=const? Or it has just been proved empirically?
The short answer is that it has just been proved empirically.