Speed of light for different observers

[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

(the image above) Let's 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

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.

 

[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.

 

[PeterDonis]

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.

 

[Dale]

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.

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.

 

[sisoev]

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.

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

 

[sisoev]

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.

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.

 

[sisoev]

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.

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.

 

[ghwellsjr]

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

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?

 

[sisoev]

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?

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.

 

[harrylin]

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.
[..]

Hi sisoev,

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

 

[A.T.]

it requires explanation which does not involve "relativity laws".
Otherwise there is no way to prove inconsistency in the theory in question.

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

 

[Dale]

The light source and detector A are in rest relative to each other.

Yes, clearly.

The light has to travel the full length of the truck in order to reach detector A.

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.

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.

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.

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

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.

 

[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.

 

[sisoev]

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

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?)

 

[PAllen]

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?)

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.

 

[sisoev]

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.

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.

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

Explain that please.
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.

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.

I don't understand your point.

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.

Excuse my English, please.
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.

 

[sisoev]

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.

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

 

[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 :) )?

 

[PAllen]

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

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.

 

[PeterDonis]

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 :) )?

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.

 

[Denius1704]

I wasn't trying to make any point yet. My point is coming now :) If there is no difference between the measurement of the stationary and moving objects since their frame of reference is the same that would mean that in his example the detector A is actually detecting the full length of the truck and not shorter length as DaleSpam suggested. That is all i wanted to understand and clear up.
Now it comes down to the fact that according to Pallen (i believe), sisoev's conclusion of detector B detecting the light at that place at the same time as A would be wrong. So according to you, do we have to put B back as many times as A has moved forward so that they both see the light at the same time?

 

[PAllen]

I wasn't trying to make any point yet. My point is coming now :) If there is no difference between the measurement of the stationary and moving objects since their frame of reference is the same that would mean that in his example the detector A is actually detecting the full length of the truck and not shorter length as DaleSpam suggested. That is all i wanted to understand and clear up.
Now it comes down to the fact that according to Pallen (i believe), sisoev's conclusion of detector B detecting the light at that place at the same time as A would be wrong. So according to you, do we have to put B back as many times as A has moved forward so that they both see the light at the same time?

My understanding of the OP set up does achieve the following: Both A and B agree that the absorption event is simultaneous and colocated between them. What it fails to achieve is that their measurement of time interval between emission and absorption agree. OP seems to think that the first statement implies the second.

 

[ghwellsjr]

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 :) )?

As I responded to sisoev in post #2:

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.

This is the essence of the problem. You cannot measure the time interval of the one-way speed of light.

If instead of detectors at the far end of both trucks, you placed mirrors there and measured how long it took for the light to make the trip to the rear of the trucks and back to the front of the trucks, you would get the same answer for both trucks. Let's say that answer is two seconds (yes, very long trucks).

Both truck drivers have no way to know if it took one second for the light to make the trip from the front of the truck to the rear. Einstein's brilliant idea was to say that either one could arbitrarily assign the time interval to be one second and you build a Reference Frame based on that assumption. But that means that it does not take one second for the other truck. You can use any Reference Frame you want but there is no Reference Frame in which it takes one second for both trucks.

 

[PAllen]

As I responded to sisoev in post #2:

This is the essence of the problem. You cannot measure the time interval of the one-way speed of light.

If instead of detectors at the far end of both trucks, you placed mirrors there and measured how long it took for the light to make the trip to the rear of the trucks and back to the front of the trucks, you would get the same answer for both trucks. Let's say that answer is two seconds (yes, very long trucks).

Both truck drivers have no way to know if it took one second for the light to make the trip from the front of the truck to the rear. Einstein's brilliant idea was to say that either one could arbitrarily assign the time interval to be one second and you build a Reference Frame based on that assumption. But that means that it does not take one second for the other truck. You can use any Reference Frame you want but there is no Reference Frame in which it takes one second for both trucks.

This is a long debated, interesting, philosophic debate, but it is not much related to the OP conclusions. We can assume, for example, that prior to the trucks arrival 'at the scene', still moving at constant speed relative to the ground, someone inside synchronized two identical clocks next to each other and walked one over the far end. Yes, you can turn around and argue about the hidden assumptions of slow clock transport, but this is really not related to the very basic misunderstanding involved in the OP.

 

[Denius1704]

You guys are so confusing :)

ghwellsjr are you saying that it's impossible to measure the truck's length by just sending an impulse from the one side to the other side? (and when i say "length" i mean it is measured in time needed for the pulse to come from the emission's point to the absorption point)

Pallen are you saying that at the absorption event the moving truck's detector would read let's say 1 sec and the stationary detector would read 0.8 sec?

 

[sisoev]

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.

I need help on this one, please :D
If the time interval differs for A and B, that would mean that the simultaneity set in the experiment will be lost for them. Is that correct?

 

[PAllen]

You guys are so confusing :)

ghwellsjr are you saying that it's impossible to measure the truck's length by just sending an impulse from the one side to the other side? (and when i say "length" i mean it is measured in time needed for the pulse to come from the emission's point to the absorption point)

Pallen are you saying that at the absorption event the moving truck's detector would read let's say 1 sec and the stationary detector would read 0.8 sec?

If you're trying to measure the speed of light, you certainly don't want to define distance in terms of light. Use rulers.

I'm saying if the an observe in the truck measured its length ahead of time using rulers, then, after it was moving at desired speed, but before reaching the experiment setup, they walked a clock from one end to the other; then, recorded the time the front clock passed the emission event, and then the time for the signal to reach the back clock, they would get a different time then someone on the ground measuring the time between emission and absorption.

 

[PAllen]

I need help on this one, please :D
If the time interval differs for A and B, that would mean that the simultaneity set in the experiment will be lost for them. Is that correct?

In my very first post on this, I emphasized the following:

- ground and truck clocks will disagree on rate.
- if the ground observer synchronized clocks across some distance, the truck observer will see them out of synch; thus events at different places deemed simultaneous by the ground observer will not be simultaneous observed from the truck
- In the above statement, replace ground->truck, truck->ground, and the same statement is true.

 

[sisoev]

.......
......... will not be simultaneous observed from the truck

I like the "observed" used in the context of "simultaneity", but since I know that you are referring to the relativity of simultaneity I'd like to ask; if the simultaneity is universal and only observed differently, would that equalize the time for both observers? I mean, then we could really measure time and distance according to the simultaneity we set in the experiment?

 

[PAllen]

I like the "observed" used in the context of "simultaneity", but since I know that you are referring to the relativity of simultaneity I'd like to ask; if the simultaneity is universal and only observed differently, would that equalize the time for both observers? I mean, then we could really measure time and distance according to the simultaneity we set in the experiment?

You could choose to do all measurements in one frame. However, you have to do all of them that way, not mix and match. Then it is trivial that you get the same speed for light for A and B, because for (e.g. the ground frame) the light has traveled the same distance in both cases and the same time interval. But if you want to use length of truck as measured in the truck, then you need clocks synchronized in the truck to measure the time interval. If you mix and match, you just get nonsense.