Constancy of the speed of light

[Beetroot]

Hi

I'm having trouble understanding why the speed of light must be constant.

Consider a torch resting on a bench with light shining outwards. Some distance away I have a watch and a metre rule and wish to measure the speed of light.

First I stand perfectly still and someone turns on the torch. I note on my watch the exact times when light hits the zero and end point of the rule. Because the speed of light is distance divided by time, I calculate the speed of light.

Now, for the second experiment I walk towards the torch with a certain velocity. Someone turns on the torch and again I note the times that the light hits the zero and end points on the rule.

Why is it that in the second experiment I would measure the same speed of light? The watch and rule are always at rest relative to me.

Many of the textbooks I have read don't address this properly. They simply mention that there is experimental evidence that indicates that light travels with constant velocity.

Can someone provide an explanation?

Thank you

Beetroot

 

[christensen]

We don’t know why. All of relativity is based first on the fact that the speed of light is observed to be the same in all frames of reference. Experiments have determined this to be true, but we don’t know why. If you want to learn about some of the history leading up to this, look into the "ether".

 

[Peeter]

I'd guess that anybody new to relativity (like me) has some trouble with this idea. It seemed to me that my old E&M and intro dynamics texts (which I have dusted off and am re-reading;) glossed over this too somewhat.

An idea that I personally found helpful was to consider the wave equation for a (source free) electromagnetic field (light) :

$$(\nabla^2 - \mu_0 \epsilon_0 \frac{\partial^2}{\partial t^2}) F = 0$$

Where F is an electric field or magnetic field or a combination of the two that satisfies the rest of Maxwell's equations. I was more comfortable with the idea that light satifies this wave equation, and light is "wavy" regardless of our state of motion. If that is to be the case, what types of changes of variables between (x,y,z,t) can you perform that maintain the wave equation in that precise form (ie: with no cross partial terms.)

If you calculate this for linear transformations, a strictly mechanical exersize in the chain rule, you'll find that rotations and lorentz boosts are two such transformations. Also, if you accept that the wave equation holds for light regardless of the motion of observer (ie: that boosts transform between observers), then the propagation speed is also fixed by the \mu_0 \epsilon_0 = 1/c^2 term in the wave equation. Those two constants that define the wave propagation speed and do not vary with the speed of the observer.

I don't say that I neccessarily understand relativity any better with this as a starting point instead of the expanding sphere of light equation in my old dynamics book. I'm hand waving at least as much as my dynamics book especially since I needed to invoke higher level abstractions like the wave equation and electromagnetism ... regardless, this happens to be a a way that acceptably-to-me motivated the Lorentz transformation, so I share in case it helps.

Once you can arrive at the Lorentz transformation from some means that you are comfortable with, then you can then also do the velocity addition exersize. You will also find that this also "says" the speed of light remains the same regardless of the state of motion, which is exactly the point of the Lorentz transformation (ie: maintains the wave equation unchanged with a space/time change of variables).

 

[rbj]

i think, with really just one fundamental axiom (people have disagreed with me about whether it's one or two fundamental axioms) that for any inertial observer all of the laws of physics are exactly the same. that two inertial observers that are moving past each other at a constant velocity, that both of these observers have equal claim to being the guy "at rest" (and it's the other guy who is moving). i tried to lay it out here: https://www.physicsforums.com/showthread.php?p=1556816#post1556816

 

[JesseM]

Hi

I'm having trouble understanding why the speed of light must be constant.

Consider a torch resting on a bench with light shining outwards. Some distance away I have a watch and a metre rule and wish to measure the speed of light.

First I stand perfectly still and someone turns on the torch. I note on my watch the exact times when light hits the zero and end point of the rule. Because the speed of light is distance divided by time, I calculate the speed of light.

Now, for the second experiment I walk towards the torch with a certain velocity. Someone turns on the torch and again I note the times that the light hits the zero and end points on the rule.

Why is it that in the second experiment I would measure the same speed of light? The watch and rule are always at rest relative to me.

Many of the textbooks I have read don't address this properly. They simply mention that there is experimental evidence that indicates that light travels with constant velocity.

Can someone provide an explanation?

When people say that the speed of light is constant, they mean that if any inertial (non-accelerating) observers measures the speed of light using rulers and clocks at rest relative to themselves, with the clocks synchronized using the Einstein synchronization convention, they will all find it moves at c. So to understand how it works that they all get the same speed, you have to keep in mind that in relativity each observer will measure moving rulers to be shrunk relative to their own by a factor of $$\sqrt{1 - v^2/c^2}$$ (length contraction), and moving clocks to be ticking slower than their own by the same factor (time dilation), and moving clocks which were synchronized using the Einstein synchronization convention in their own rest frame, and were a distance x apart in their own rest frame to be out-of-sync in the observer's frame by a time of vx/c^2 (the relativity of simultaneity, discussed here and illustrated with an animation here). I gave an example showing how all these factors work together on this thread:

Say there's a ruler that's 50 light-seconds long in its own rest frame, moving at 0.6c in my frame. In this case the relativistic gamma-factor (which determines the amount of length contraction and time dilation) is 1.25, so in my frame its length is 50/1.25 = 40 light seconds long. At the front and back of the ruler are clocks which are synchronized in the ruler's rest frame; because of the relativity of simultaneity, this means that in my frame they are out-of-sync, with the front clock's time being behind the back clock's time by vx/c^2 = (0.6c)(50 light-seconds)/c^2 = 30 seconds.

Now, when the back end of the moving ruler is lined up with the 0-light-seconds mark of my own ruler (with my own ruler at rest relative to me), I set up a light flash at that position. Let's say at this moment the clock at the back of the moving ruler reads a time of 0 seconds, and since the clock at the front is always behind it by 30 seconds in my frame, then in my frame the clock at the front must read -30 seconds at that moment. 100 seconds later in my frame, the back end will have moved (100 seconds)*(0.6c) = 60 light-seconds along my ruler, and since the ruler is 40 light-seconds long in my frame, this means the front end will be lined up with the 100-light-seconds mark on my ruler. Since 100 seconds have passed, if the light beam is moving at c in my frame it must have moved 100 light-seconds in that time, so it will also be at the 100-light-seconds mark on my ruler, just having caught up with the front end of the moving ruler.

Since 100 seconds passed in my frame, this means 100/1.25 = 80 seconds have passed on the clocks at the front and back of the moving ruler. Since the clock at the back read 0 seconds when the flash was set off, it now reads 80 seconds; and since the clock at the front read -30 seconds, it now reads 50 seconds. And remember, the ruler was 50 light-seconds long in its own rest frame! So in its frame, where the clock at the front is synchronized with the clock at the back, the light flash was set off at the back when the clock there read 0 seconds, and the light beam passed the clock at the front when its time read 50 seconds, so since the ruler is 50-light-seconds long, the beam must have been moving at 50 light-seconds/50 seconds = c as well! So you can see that everything works out--if I measure distances and times with rulers and clocks at rest in my frame, I conclude the light beam moved at 1 c, and if a moving observer measures distance and times with rulers and clocks at rest in his frame, he also concludes the same light beam moved at 1 c.

If you want to also consider what happens if, after reaching the front end of the moving ruler at 100 seconds in my frame, the light then bounces back towards the back in the opposite direction towards the back end, then at 125 seconds in my frame the light will be at a position of 75 light-seconds on my ruler, and the back end of the moving ruler will be at that position as well. Since 125 seconds have passed in my frame, 125/1.25 = 100 seconds will have passed on the clock at the back of the moving ruler. Now remember that on the clock at the front read 50 seconds when the light reached it, and the ruler is 50 light-seconds long in its own rest frame, so an observer on the moving ruler will have measured the light to take an additional 50 seconds to travel the 50 light-seconds from front end to back end.

 

[Beetroot]

Hi Jesse

You cannot use time dilation and length contraction to explain the constancy of the speed of light in this example. The rule and watch are always at rest relative to me and I am the one observing them in both examples. Therfore, they will always look and act the same to me.

This is the weird thing.

Beetroot

 

[Narayanan.S]

I will make a try.
1) Sound or water waves travel through a physical medium Air,water molecules solids and different material medium can permit different velocities
and for a (moving source) or (a moving observer) or (the relative velocity between the two) can be known are subjected to normal Doppler effect since we have reference common to both the "Earth" ( the pitch of the sound from a source varies in accordance with all 3 above).This happens to electromagnetic radiation too but slightly a modified relation. With reference to Earth moving objects may have (c+v) and (c-v) effect
2)Whereas electromagnetic radiation does not need a medium and hence can travel through Vacuum or Ether assuming it so subtle with non material properties that it is hard to differentiate between the two and therefore since the Earth does not have any reference frame "we are limited only to relative velocity between the two frames"
3) The speed of light does not inherit the velocity of the source and once say a photon is emitted it travels at a constant speed of 3x10^8m/s.Now consider two sources one from Jupiter the other from Moon and if the two sources were to be switched on simultaneously through some instant signal between the two,we will see the light from the Moon first and later from Jupiter. This is because of the speed limit (In other words constant speed of light in vacuum)
4)Now consider a moving source and let that be moving away from us.For any photon to be created during an electron jump (cannot be instantaneous) from one higher level to the lower energy needs some finite time and this process is taking place in a moving frame.
Once the electron starts to move from higher energy level the process of creation of a photon also starts and this process of creation will last until the electron reaches the lower energy level.
During this duration the source at velocity "V" would have moved by a distance of
"V[t0-t1]" at the same duration the photon would have moved by "C[t0-t1] by comparing the two lengths (that is the ratio of the two velocities) will reflect as relativity Doppler effect from which we can find the wavelength/frequency of the photon/wave.
The wavelength/frequency would have been the true wavelength/frequency of the source if both were to be stationary with respect to each other that we would see.
But when the source is moving away or we moving away from the source we see a lower frequency and only the relative velocity between the two can be found if we know the source frequency(known as red shift) that is stars etc are moving away from us. This is what is my understanding from the book.
“Concepts of Modern Physics-McGrawHill Inc-Arthur Beiser" which could be useful for other references too.
We can be happy as long as we keep seeing red shift
Cheers

 

[JesseM]

Hi Jesse

You cannot use time dilation and length contraction to explain the constancy of the speed of light in this example. The rule and watch are always at rest relative to me and I am the one observing them in both examples. Therfore, they will always look and act the same to me.

This is the weird thing.

But I think you are implicitly referring to two frames--you seem to be thinking that if you are moving relative to the ruler and clock, then the light you send out should move at c relative to your current rest frame, and should therefore not move at c relative to the rest frame of that ruler and clock. If this is not what you are thinking, then what is the source of the problem? Why do you think the speed of light should be different for source moving relative to the ruler/clock than one at rest relative to it?

 

[Gear300]

It is probably because it defies common sense and experience. If instead of light, we were measuring the velocity of the bullet in your mentioned experiment, we would notice a difference in the measured velocities. Thus, if it happens for the bullet, then it should also happen for light. However, for some reason, light seems somewhat special and excluded from this.

Apparently, this sort of contradiction occurs simply because we are comparing two velocities that could be said to be largely different (one being much greater than the other). What applies to light also applies to the bullet - there is a space-time distortion for objects in motion...but this sort of phenomenon is not very noticeable at speeds slower than the speed of light (such as the speed of the bullet, which is comparably much slower than light)...you would have to be rather close to the speed of light to notice it. What is more is that we are not used to being able to observe the velocities of objects close to the speed of light with our naked eye...our daily experience is with objects that are much slower (making it more difficult to become used to this phenomenon). Basically, there was no justification to the method of adding velocities (in the case of your experiment, it would be adding the speed of the ruler to the speed of light) other than that the phenomenon seems to work that way. It turned out that this justification was oversimplifying the situation.

 

[JesseM]

It is probably because it defies common sense and experience. If instead of light, we were measuring the velocity of the bullet in your mentioned experiment, we would notice a difference in the measured velocities. Thus, if it happens for the bullet, then it should also happen for light.

Yes, but the reason for this is because the bullet always has a constant speed in the rest frame of the gun, so we'd expect the speed of the bullet to be different in the ruler/clock frame depending on whether the gun is at rest or moving relative to this frame. So again, our expectations here have to do with a comparison of two frames, and yet Beetroot seemed to deny that the "problem" pointed to in the original post was meant to have anything to do with comparing multiple frames.

 

[diazona]

You cannot use time dilation and length contraction to explain the constancy of the speed of light in this example. The rule and watch are always at rest relative to me and I am the one observing them in both examples. Therfore, they will always look and act the same to me.

Well, if the ruler and watch are always at rest relative to you, and you are the only one making observations, there's only one reference frame involved in the problem. So in that case, your question is sort of equivalent to this: a light beam travels past you at speed c. Another light beam travels past you at speed c. Why do they have the same speed? Well, hopefully you're thinking, why on Earth wouldn't they? ("Duh...") So there isn't even any question of the invariance (what you've been calling "constancy" is actually "invariance") of the speed of light.

You only see weird effects when you compare observations from two observers who are moving relative to each other.

 

[Max™]

Technically they have the right of it, at least in part.

It isn't about the speed being constant, if the speed of light varied from moment to moment, two observers measuring it at the same instant would still measure the same value.

It is simply used as a yard stick to explain motion through spacetime properly, the point of Relativity isn't the constant speed of light, no more than the point of QFT is the mass of the Electron.

 

[D H]

a light beam travels past you at speed c. Another light beam travels past you at speed c. Why do they have the same speed? Well, hopefully you're thinking, why on Earth wouldn't they? ("Duh...")

Even in this simple case the answer is not "Duh". Suppose I see persons A and B each fire a gun and I measure the speed of the bullets. If person A is moving in one direction and person B in another, the observed velocities will not be the same. The speed of light is quite a different beast. It is the same for all sources; the velocity of the source does not come into play.