# Why is the speed of light the same for all observers?

I never understand why the speed of light is the same for all observers irrespective of their motion relative to the source of light. Now suppose I am sitting at the back of a vehicle which is travelling at the speed of 0.999999999999c and light approaches me from behind the vehicle. i.e. I am going away from the source of light while I can still see the light. Now I attach an instrument to my car for measuring the speed of light. Won't it measure 0.000000000001c.

Please help me understand why will the instrument still record 0.999999999999c and not 0.000000000001c according to the theory of relativity.

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Saw
Gold Member
I suppose you may now be asking yourself why velocities add in a different way in relativistic physics. if you want to answer yourself this, just look at the way that the relativistic formula for addition of velocities is derived.

I know we use the lorentz transformation to add velocities but doesn't it seem a bit absurd?

Saw
Gold Member
Why? You may be thinking that the Galilean alternatives (c+v) and (c-v) are self-evident but they are aren't. They are also derived. Think of it: how do you derive them?

(Will go to play tennis now...:)

tom.stoer
In physics we cannot explain why nature is the way it is. We can only try to find a mathematical representation which describes how it works, and we can derive predictions.

In this specific case we find experimentally that electromagnetic waves travel at the speed of light, and we find that this is true for all observers (all reference frames). Then we find theoretically that Maxwell's equations predict exactly this behavior. In addition we can use special relativity (including Lorentz transformations, relativistic addition of velocities, ...) to formulate a comprehensive theoretical framework.

So we know how to describe nature. And we should believe in this description b/c it makes correct predictions.

Unfortunately this is all we can say in physics.

In physics we cannot explain why nature is the way it is. .......
So we know how to describe nature.
so true!
Just to emphasize those points, everybody who studies special and then general relativity and especially quantum mechanics must change their way of thinking.

It turns out you probably think space and time are fixed and immutable; turns out they are not, but 'conspire' together in such as way that enables all observations of lightspeed to be the same. It turns out the speed of light that is fixed and immutable...

I know we use the lorentz transformation to add velocities but doesn't it seem a bit absurd?
yes, it took an 'Einstein' to recognize that, so don't feel bad about it not seeming natural to you. If you are not familiar with the struggles of the greatest minds of the early 1920's, look up 'luminiferous ether'......

It’s nature that is bizarre, not the presentation.
A. Zee

I never understand why the speed of light is the same for all observers irrespective
for clarity: nobody knows.

Nobody even knows why light exists.

ghwellsjr
Gold Member
I never understand why the speed of light is the same for all observers irrespective of their motion relative to the source of light. Now suppose I am sitting at the back of a vehicle which is travelling at the speed of 0.999999999999c and light approaches me from behind the vehicle. i.e. I am going away from the source of light while I can still see the light. Now I attach an instrument to my car for measuring the speed of light. Won't it measure 0.000000000001c.
Would you please describe this instrument that measures the speed of light. How does it work? Do you know of a place where you can buy one?

Please help me understand why will the instrument still record 0.999999999999c and not 0.000000000001c according to the theory of relativity.
Are those the only two choices? If I bought an instrument that measures the speed of light and it gave me one of those results, I'd want my money back. I could sell you an instrument that measures the speed of light. It would be a little box with a hole in one end. When you shine a light in it, a photo detector inside powers a little display that says "c".

But if you actually wanted to measure the speed of light you would have to start a timer when the light reached you, then put a mirror in front of you some measured distance away and stop the timer when the reflection got back to you. Since the light traveled twice the distance to the mirror, you would calculate the speed of light to be that double distance divided by the reading on the timer. As long as you are not changing your speed while you're doing this, you will always get the same answer, c. Why? That's just the way the universe is.

Bill_K
But if you actually wanted to measure the speed of light you would have to start a timer when the light reached you, then put a mirror in front of you some measured distance away and stop the timer when the reflection got back to you. Since the light traveled twice the distance to the mirror, you would calculate the speed of light to be that double distance divided by the reading on the timer.
Then there are the people who measure the speed of neutrinos. They obviously don't use a mirror! ghwellsjr
Gold Member
Then there are the people who measure the speed of neutrinos. They obviously don't use a mirror! Aren't they comparing the speed of neutrinos to the speed of light? We can also compare the speed of light coming from two different sources that are traveling at different speeds and determine that the speed of the light does not depend on the speed of
the source. These are both examples of races to see which one wins or if it is a tie but they don't measure the absolute one-way speed, don't you agree?

tiny-tim
Homework Helper
don't we have an FAQ on this? I never understand why the speed of light is the same for all observers irrespective of their motion relative to the source of light. Now suppose I am sitting at the back of a vehicle which is travelling at the speed of 0.999999999999c and light approaches me from behind the vehicle. i.e. I am going away from the source of light while I can still see the light. Now I attach an instrument to my car for measuring the speed of light. Won't it measure 0.000000000001c.

Please help me understand why will the instrument still record 0.999999999999c and not 0.000000000001c according to the theory of relativity.
Yes, all experiments showed this and so we believe in this. But Special relativity did provide an answer for that. Length contraction and time dilation are nothing but an explanation for this phenomenon, is what I have known.

Your instrument will calculate speed of light, by using distance of the source and time taken by light to reach it. Since both the values decrease while in motion, when you will calculate the speed, it will turn out to be 'c'.

But even I'm still not able to use and calculate it mathematically. I am not sure who's length and time we would consider and how exactly the 'instrument' will find it. Maybe anyone would like to help in that?

• mtworkowski@o
Gold Member

jtbell
Mentor
But even I'm still not able to use and calculate it mathematically. I am not sure who's length and time we would consider and how exactly the 'instrument' will find it. Maybe anyone would like to help in that?
If you post a specific example of a situation which confuses you, and your attempt in calculating it, with some description of what exactly is confusing you, we can help you with it. Please start a new thread for it rather than hijack this one.

I could sell you an instrument that measures the speed of light. It would be a little box with a hole in one end. When you shine a light in it, a photo detector inside powers a little display that says "c".
:rofl:

ghwellsjr
Gold Member
Yes, all experiments showed this and so we believe in this. But Special relativity did provide an answer for that. Length contraction and time dilation are nothing but an explanation for this phenomenon, is what I have known.

Your instrument will calculate speed of light, by using distance of the source and time taken by light to reach it.
No, that is not right. There is no instrument that can measure the one-way speed of light that you are describing here. You cannot measure the time it takes for light to travel a distance. I already described how you measure the round-trip speed of light in post #9:

But if you actually wanted to measure the speed of light you would have to start a timer when the light reached you, then put a mirror in front of you some measured distance away and stop the timer when the reflection got back to you. Since the light traveled twice the distance to the mirror, you would calculate the speed of light to be that double distance divided by the reading on the timer. As long as you are not changing your speed while you're doing this, you will always get the same answer, c. Why? That's just the way the universe is.
Since both the values decrease while in motion, when you will calculate the speed, it will turn out to be 'c'.
Where did you get the idea that both the length and the time decrease while in motion? Please tell me what you are thinking.

But even I'm still not able to use and calculate it mathematically. I am not sure who's length and time we would consider and how exactly the 'instrument' will find it. Maybe anyone would like to help in that?
Even if you had such an instrument that you calibrated to work correctly in one inertial state (by synchronizing two clocks some distance apart), it would no longer work if you accelerated it to a new inertial state or pointed it in a different direction.

Where did you get the idea that both the length and the time decrease while in motion? Please tell me what you are thinking.
I refered to the time dilation and length contraction. But not sure how it applied to that example. Equally confused.

But if you actually wanted to measure the speed of light you would have to start a timer when the light reached you, then put a mirror in front of you some measured distance away and stop the timer when the reflection got back to you. Since the light traveled twice the distance to the mirror, you would calculate the speed of light to be that double distance divided by the reading on the timer. As long as you are not changing your speed while you're doing this, you will always get the same answer, c.
I don't think practically it is possible to do this, due to the high speed of light. Do you know experiments that are actually done? Do they have the same set up or some other techniques?

ghwellsjr
Gold Member
Where did you get the idea that both the length and the time decrease while in motion? Please tell me what you are thinking.
I refered to the time dilation and length contraction. But not sure how it applied to that example. Equally confused.
Are you aware that Dilation means "expansion", not "contraction"?

Even if you had such an instrument that you calibrated to work correctly in one inertial state (by synchronizing two clocks some distance apart), it would no longer work if you accelerated it to a new inertial state or pointed it in a different direction.
I don't think practically it is possible to do this, due to the high speed of light. Do you know experiments that are actually done? Do they have the same set up or some other techniques?

Are you aware that Dilation means "expansion", not "contraction"?
Yes it does, but that also means there are fewer 'ticks' while moving a fixed distance at a slower speed.

ghwellsjr
Gold Member
Yes it does, but that also means there are fewer 'ticks' while moving a fixed distance at a slower speed.
I think you mean "at a faster speed"? But even without Special Relativity there will be fewer 'ticks' the faster a clock moves a fixed distance. I don't understand how this helps interpreting rushikesh's comment:
Length contraction and time dilation are nothing but an explanation for this phenomenon, is what I have known.

Your instrument will calculate speed of light, by using distance of the source and time taken by light to reach it. Since both the values decrease while in motion, when you will calculate the speed, it will turn out to be 'c'.
Are you supporting his comment?

You had asked me how my contraction comment applied to light approaching at a 90 degree angle in the closed thread. What is the comparative speed to the light source in that situation? you call time dilation "expansion" just because of the comparative of proper time over the same distance across spacetime.

For the made up calculations you don't see a problem with this statement you made were you double the distance because the ruler is contracted 50%?

If we have a length contracted ruler, say to 50%, then we will think that the distance to the mirror is 20 feet [double the length?] and we will calculate the speed of light to be 40 feet per 20 nsec or 2 feet per nsec.

ghwellsjr
Gold Member
You had asked me how my contraction comment applied to light approaching at a 90 degree angle in the closed thread. What is the comparative speed to the light source in that situation?
Your comment was similar to rushikesh's in that the calculation of the speed of light (length divided by time) would come out the same because both parameters were equally "retarded" and I just wanted you to think about the situation where the length for a calculation applied at 90 degrees to the direction of motion would not be retarded and yet the speed of light still comes out to be c. The light source never has any bearing on the speed of light. It is defined to be c in all inertial reference frames.

you call time dilation "expansion" just because of the comparative of proper time over the same distance across spacetime.
I was talking about comparing the spacing of the Proper Time tick marks on a spacetime diagram to the coordinate time markings.

For the made up calculations you don't see a problem with this statement you made were you double the distance because the ruler is contracted 50%?

If we have a length contracted ruler, say to 50%, then we will think that the distance to the mirror is 20 feet [double the length?] and we will calculate the speed of light to be 40 feet per 20 nsec or 2 feet per nsec.
No, I don't see a problem. If you are measuring the round-trip speed of light to a mirror that is 10 feet away and your ruler is actually only six inches long but claims to be 12 inches long, then you will measure the distance to be 20 feet in one direction or 40 feet for the round trip.

All I'm trying to point out is that if we recognize that time gets "dilated" (or expanded, because that's what the word means) and length gets contracted, then it's less likely that someone will jump to the conclusion that the calculation of the speed of light (being length divided by time) remains at c simply because the effects "cancel out".

I think you mean "at a faster speed"? But even without Special Relativity there will be fewer 'ticks' the faster a clock moves a fixed distance. I don't understand how this helps interpreting rushikesh's comment:

Are you supporting his comment?
My comment poorly worded. Should be something like "the converse of time dilation is fewer ticks".

As to the op:

Using a=v/c and substituting based on x=ct

x' = Î³(x-vt) = Î³x(1-a)

t' = Î³(t-vx/cc) = Î³t(1-a)

x'/t' = x/t

The moving frame is a scaled version of the 'rest' frame, therefore
the expressions involving x and t are equivalent (including light speed).
This requires x and t to change by the same proportion (Î³).

also refer to the drawing

View attachment 64995

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ghwellsjr
Gold Member
As to the op:

Using a=v/c and substituting based on x=ct
If you are going to limit x to be equal to ct, then you are only concerned with events that are light-like.

x' = Î³(x-vt) = Î³x(1-a)

t' = Î³(t-vx/cc) = Î³t(1-a)

x'/t' = x/t
You should add that both of these factors are equal to c (because you made that limitation to begin with).

The moving frame is a scaled version of the 'rest' frame, therefore
the expressions involving x and t are equivalent (including light speed).
You should say that this is true only for light speed.

This requires x and t to change by the same proportion (Î³).
But that proportion is not equal to Î³. In fact, you can derive it if you just added a couple more steps:

t' = Î³t(1-a)

t'/t = Î³(1-a)

So, for example, at a=0.6, Î³=1.25 and t'/t = 1.25(1-.6) = 1.25(.4) = 0.5.

This is actually the relativistic Doppler factor (or its reciprocal) and not gamma.

also refer to the drawing

View attachment 64995