# Speed of light for different observers

1. Sep 12, 2011

### sisoev

He everybody :)

I guess I am not the only one who cannot comprehend the idea that the light has same speed for all observers, regardless of the velocity between the source and the observer.
In an attempt to get a picture of the idea, I constructed a thought experiment which I think could be performed.

[PLAIN]http://onegative.org/light1.jpg [Broken]

(the image above) Lets imagine that a truck traveling with high speed has attached a light source in its front and a detector "A" on its back.
As the truck is moving with constant speed the light source emits a light pulse or a single photon if you prefer so.
Knowing the speed of the truck we can calculate after what traveled distance the light will reach detector "A" and on the same line we place detector "B".
Now both detectors will detect the light at the same time (simultaneously)

[PLAIN]http://onegative.org/light2.gif [Broken]

The second image shows the position of the truck when the light hits both detectors.
We can see the difference in the distance traveled by the light to the two detectors for the same amount of time.

Initially I built this experiment with the truck moving in the right direction, but I found out that it is kind of deceiving to figure out the distance traveled for the light for both detectors.
I can post the other images if you think that it would be easier to explain the problem.

Respectfully looking forward for your explanation and help.

P.S. I'd like to ask Janus to make an animation for the above, which will make it easier for us to imagine the full path of the light as traved to both detectors.

Last edited by a moderator: May 5, 2017
2. Sep 12, 2011

### ghwellsjr

It is not possible to determine or measure the one-way speed of a light pulse or a photon. We can only measure the round-trip time it takes for a light pulse to start from a source, traverse to a mirror, reflect off the mirror and traverse back to the source. This is experimental evidence for the universal constant value of the speed of light.

In Einstein's Special Relativity, a Frame of Reference is defined in which the two halves of the trajectory of the aforementioned experiment are assigned equal times. This is Einstein's second postulate. Read his 1905 paper.

3. Sep 12, 2011

### Staff: Mentor

Your diagrams are misleading because they mix together distances defined using different rules. In particular, in your second diagram, the "distance covered by light for detector A" is defined using different rules than the "distance covered by light for detector B". The A distance assumes that the truck is motionless; the B distance assumes that the truck is moving. These are inconsistent assumptions, so the two distances are not consistently defined and you can't conclude anything by comparing them.

More precisely, you are assuming that, even though the distances in your second diagram are different, the *times* for A and B are the same. But since the distance definitions are not consistent, you can't assume that the time definitions are either. That is called the "relativity of simultaneity", and once it is taken into account, it becomes clear that, if you define the A distance as you have in your second diagram, so that it is longer than the B distance, then if you define A's time consistently with that definition of distance, you will find that A's time is longer as well, by just enough to make the speed of light, distance divided by time, the same for both.

To properly analyze this situation, you need to draw a spacetime diagram. I don't have the tools handy to do that right now, but doing so makes what I've said above clearer and easier to see since it is visually obvious from the diagram.

4. Sep 12, 2011

### Staff: Mentor

Note that the second image incorrectly shows the distance covered by the light for detector A. The light travels a distance from the location of the source at the time of emission to the location of the detector at the time of detection. It does not travel from the location of the source at the time of detection to the location of the detector at the time of detection, which is what you have drawn. The distance traveled is the same for A and B.

That said, other than that small error I am not sure what your point is. You don't seem to be proposing any measurement that could even in principle distinguish between relativity and Newtonian mechanics, nor any other theory.

Last edited: Sep 12, 2011
5. Sep 13, 2011

### sisoev

I am well aware of that, ghwellsjr, but the experiment does not measure speed of light.
It measures difference in the speed.

6. Sep 13, 2011

### sisoev

It is not correct to use in your explanation inconsistency with theory of relativity.
Time and simultaneity will differ only if the speed of light is the same for all observers.
This experiment puts that in doubt an it requires explanation which does not involve "relativity laws".
Otherwise there is no way to prove inconsistency in the theory in question.

7. Sep 13, 2011

### sisoev

The light source and detector A are in rest relative to each other.
The light has to travel the full length of the truck in order to reach detector A.

I agree that the place of emission for detector A does not match the position of the light source, but that is only when we compare them from outside of their own frame of reference.
We should not do that mistake in our comparison.
Remember that we are comparing the speed of light for two observers, which can be done only if we compare the distance traveled in their frames with the time for that travel.

We can easily predict that the light interference seen on both detectors will be different.

Last edited: Sep 13, 2011
8. Sep 13, 2011

### ghwellsjr

You started off your thread by stating that you "cannot comprehend the idea that the light has same speed for all observers, regardless of the velocity between the source and the observer."

Are you interested in comprehending this idea?

9. Sep 13, 2011

### sisoev

Ha-ha :D
That's the point, ghwellsjr
If I agree with everything you say, I shouldn't have the problem of comprehending the idea.
Measuring speed and measuring difference in a speed are two different things to me.

We may still not know what the speed of the light is, but its difference for A and B can be determent by the above experiment.

10. Sep 13, 2011

### harrylin

Hi sisoev,

Did you actually try to calculate (with simple numbers) what each will measure? Often such an exercise answers all questions.

11. Sep 13, 2011

### A.T.

Nonsense. To show that a theory is inconsistent, you have to use only the laws of that theory, and show a contradiction between them.

12. Sep 13, 2011

### Staff: Mentor

Yes, clearly.

No, this is not correct in any frame where the truck is moving. If the truck is moving in the opposite direction of the light then the distance will be shorter than the length of the truck and if the truck is moving in the same direction of the light then the distance will be longer than the length of the truck.

Note, this is not a distinction between Newtonian physics and relativity. Your drawing is incorrect regardless of which theory of physics you are using.

Both drawings are done from the ground frame, and not the truck frame. If you wish to do a drawing in the truck's frame I would be glad to look at that also.

What interference? You have to have two different light paths going to the same detector to get interference. Each detector has a single light path, there will not be any interference. Again, this is not a distinction between Newton and Einstein. Both theories would predict no interference for either.

In order to determine the interference expected you need to calculate the difference in the phase between the two different paths that reach the same detector from the same emitter.

Last edited: Sep 13, 2011
13. Sep 13, 2011

### PAllen

I am going to be generous and interpret your drawings the way I think you intended.

Someone in the truck would measure the speed as c = L / t (all measurements made in the truck frame). Someone on the ground outside the truck would measure (same) c = L'/t' where L' < L, t' < t. Identically constructed clocks at A and B (moving relative to each other) would disagree on both rate and synchronization. That is, if A and B were synchronized with each other at emission time according to ground observer, they would not be synchronized according truck observer; and vice versa.

You will complain I have used relativity to explain what would be observed. Well, relativity is the theory that does explain what is observed here. You can say you don't like it, just like the person in ancient times who might believe that heavier objects must fall faster than light objects. However, reality is what it is. In a vaccuum, all object fall at the same speed; what I described in the prior paragraph is what would actually happen in your experiment.

Last edited: Sep 13, 2011
14. Sep 13, 2011

### sisoev

You are absolutely right A.T.
Now try to show the inconsistency in Newton's theory by explaining the above experiment with Newton's theory and show where it has flaws.
(Where the theory contradicts itself in the proposed experiment?)

15. Sep 13, 2011

### PAllen

If the speed of light is assumed to behave like the speed of a material body, then Galilean relativity for your experiment makes the following predictions (among others):

1) The speed of light measured in the truck will be different from the speed measured on the ground.

2) Maxwell's equations will not hold inside the truck

Both of these are known to be false. The contradiction is with reality. Galilean relativity is mathematically self consistent.

16. Sep 13, 2011

### sisoev

It will be shorter of longer for your frame of reference but in the inertial frame the path of the light will be the same (from the source to the detector) , no matter in which direction is moving the truck.
I think we need animation here.

The experiment is the same as if it was done with a ball.
The ball would arrive to observer B with slower speed compared to observer A and would release less energy.

I meant pattern, not "interference".
As I said above, a ball will release less energy for detector B compared to the energy released for A.
Same will be observed with photon or light pulse; the pattern for both detectors will be different.
Imagine the experiment in laboratory; one photon released, splits and hits two detectors at the same time and it will leave two different patterns on the two detectors.
Can we say that in one of the reference frames the photon was trapped in different time.

17. Sep 13, 2011

### sisoev

Where did I say that t' < t ?
The whole point is that we set the experiment with t = t'

18. Sep 13, 2011

### Denius1704

Let me ask a simple enough question. We have two identical trucks, one moving and the other one stationary and they both emmit a light from the one end and then a detector which is put on the other end of the truck, detects that light.

My question is, would both detectors detect that light for the same interval of time from the moment of emission? Meaning would it take both of them, let's say 1 second to detect the light (Yes that's a very long truck i know :) )?

19. Sep 13, 2011

### PAllen

Except it would not come out that way. Speed is measured by distance traveled in a time interval. The time interval between emission and reception in the truck, measured with clocks moving with the truck would come out greater than the time interval measured between emission and absorption for the ground observer using ground clocks [and using your particular set up, where the truck observer measures truck length, and the ground observer uses a shorter length to measure light speed]. Making the absorption events simultaneous between the two frames does not control for differences in measured interval. So you can claim t=t', just like you can claim heavy objects fall faster than light objects. Both claims are false. It's that simple.

20. Sep 13, 2011

### Staff: Mentor

Your scenario differs from the OP because you stipulate that in each case, the light emitter and the light detector are both not moving relative to the truck. The only difference is in whether the whole assembly, truck, emitter, and detector together, is "moving". So as you pose the question, yes, both detectors would detect the light for the same interval of time, as measured by clocks traveling with the respective trucks.