Special relativity, light direction and wave source.

[Banana Joe]

If the speed at which light waves propagate in vacuum is independent both of the motion of the wave source and of the inertial frame of reference of the observer, why isn't the direction? Shouldn't the light travel directly upward from the point of emission and not diagonally, following the rocket?

I was under the impression that "time" doesn't exist... Isn't it just something we created to measure the succession of events? Past and future exist only in our minds, the only thing that actually exists is the present, the now, and that is true simultaneously anywhere in the Universe. If we decide that one second is one 86400th of Earth's rotation on its axis at current speed, isn't that measure absolute and unchangeable? How can a rocket slow it down?

How does speed slow down the oscillation of the atoms, cellular reproduction and decay (and everything else)? And even if it does, does it necessarily mean that "time" has slowed down? If "time" did slow down, shouldn't everything be affected, including light?

Thanks for the clarifications!

 

[Mentz114]

If the speed at which light waves propagate in vacuum is independent both of the motion of the wave source and of the inertial frame of reference of the observer, why isn't the direction? Shouldn't the light travel directly upward from the point of emission and not diagonally, following the rocket?

For a spherical wavefront the emission/absorption looks something like this. The light is the sphere emitted by the botton dot and absorbed by the top dot which moves wrt to the emission point. The light appears in the stationary frame to have traveled diagonally.

http://www.blatword.co.uk/space-time/wavemove.mpeg

 

[Banana Joe]

For a spherical wavefront the emission/absorption looks something like this. The light is the sphere emitted by the botton dot and absorbed by the top dot which moves wrt to the emission point. The light appears in the stationary frame to have traveled diagonally.

http://www.blatword.co.uk/space-time/wavemove.mpeg

The light reached the moving top dot after it reached the stationary one, so it covered more space in more time, where is it that "the time slows down"? If I were in the rocket why wouldn't I be able to tell that it took longer to complete one period?

 

[Mentz114]

The light reached the moving top dot after it reached the stationary one, so it covered more space in more time, where is it that "the time slows down"?

I thought you were asking why the light appears to be diagonal in the moving frame. In the clip, the line joining the bottom dot with the (upper) moving dot is the light vector.

Please look up 'Light-clock' to see how we can deduce the slowing down of moving clocks.

The wiki article is OK. Scroll down fro the light clock.

http://en.wikipedia.org/wiki/Time_dilation

 

[Banana Joe]

I thought you were asking why the light appears to be diagonal in the moving frame. In the clip, the line joining the bottom dot with the (upper) moving dot is the light vector.

Please look up 'Light-clock' to see how we can deduce the slowing down of moving clocks.

The wiki article is OK. Scroll down fro the light clock.

http://en.wikipedia.org/wiki/Time_dilation

I get why for the moving clock it takes longer to complete one period, the light has to travel more space at the same speed, but why wouldn't I notice that if I was on the rocket?

 

[Mentz114]

I get why for the moving clock it takes longer to complete one period, the light has to travel more space at the same speed, but why wouldn't I notice that if I was on the rocket?

On the rocket the light is moving vertically. There's nothing to notice.

 

[Banana Joe]

On the rocket the light is moving vertically. There's nothing to notice.

The light wave is traveling diagonally at c from the point of origin, but from my perspective on the rocket wouldn't it seem to go up and down slower than c?

 

[Ibix]

No. You, in the rocket, explain that by saying the light is going straight up and down (1ms for a round trip, say). I, on Earth, say the light is traveling on a longer diagonal trajectory, so takes longer (1.1ms, say). But I also notice that your wristwatch is ticking slower than mine. That means I'm fine with the notion that you claim that the light is only taking 1ms, because I can see that your idea of time is slower than mine.

That's a bit of a mess. The clearer explanation is this:

Einstein asserted that the speed of light is constant for all inertial observers. He worked out (Mentz already suggested googling the light clock) that this implies length contraction and time dilation. Lots of people went out to see if reality matched his predictions - and it does so far.

 

[WannabeNewton]

Your question was asked previously, see here: https://www.physicsforums.com/showthread.php?t=731306&highlight=light+clock

 

[Mentz114]

The light wave is traveling diagonally at c from the point of origin, but from my perspective on the rocket wouldn't it seem to go up and down slower than c?

Why would you think that ?

 

[Banana Joe]

No. You, in the rocket, explain that by saying the light is going straight up and down (1ms for a round trip, say). I, on Earth, say the light is traveling on a longer diagonal trajectory, so takes longer (1.1ms, say). But I also notice that your wristwatch is ticking slower than mine. That means I'm fine with the notion that you claim that the light is only taking 1ms, because I can see that your idea of time is slower than mine.

That's a bit of a mess. The clearer explanation is this:

Einstein asserted that the speed of light is constant for all inertial observers. He worked out (Mentz already suggested googling the light clock) that this implies length contraction and time dilation. Lots of people went out to see if reality matched his predictions - and it does so far.

From Earth I see the light travel diagonally and measure that it takes 1ms to complete a period. On the rocket I see it going up and down in what I know is 1ms, so from the rocket's perspective it seems that the light traveled a shorter up/down path at less than c, while it actually traveled the longer diagonal path at c.

 

[Ibix]

There is no "actually traveled". Either perspective is valid - the light goes up and down according to one observer and it follows a zig-zag path according to the other. Neither is less "actual" than the other.

This is an extension of the fact that you can pour a drink on a moving train without having to correct for the 120mph you are moving along the ground. You can consider yourself to be stationary, and the Earth to be passing backwards at 120mph. Thus you can pour the drink without thinking. Seen from the platform, however, you did really well to hit a cup that was traveling at 120mph - I couldn't do it.

 

[Banana Joe]

There is no "actually traveled". Either perspective is valid - the light goes up and down according to one observer and it follows a zig-zag path according to the other. Neither is less "actual" than the other.

This is an extension of the fact that you can pour a drink on a moving train without having to correct for the 120mph you are moving along the ground. You can consider yourself to be stationary, and the Earth to be passing backwards at 120mph. Thus you can pour the drink without thinking. Seen from the platform, however, you did really well to hit a cup that was traveling at 120mph - I couldn't do it.

I can pour a drink in a train without problem thanks to inertia, the drink and the cup are moving with the train.

The rocket did travel away from the emission point, or the light source and detector would have stayed at the center of the spherical wavefront and would have picked up the light that traveled straight up and down in less than 1ms, not the one that traveled diagonally in 1ms.

 

[Mentz114]

The rocket did travel away from the emission point, or the light source and detector would have stayed at the center of the spherical wavefront and would have picked up the light that traveled straight up and down in less than 1ms, not the one that traveled diagonally in 1ms.

That is the difference that results in the different tick rate. It is only a kind of analogy though, because the exact nature of the light source is irrelevant.

The fact is that the light hits the mirror and is reflected, and this must be seen from any POV because it happened.

 

[Banana Joe]

That is the difference that results in the different tick rate. It is only a kind of analogy though, because the exact nature of the light source is irrelevant.

The fact is that the light hits the mirror and is reflected, and this must be seen from any POV because it happened.

If in the rocket I see the light travel up and down in 1ms, while it actually traveled the longer diagonal path, shouldn't I see the light travel at less than c?

 

[Mentz114]

If in the rocket I see the light travel up and down in 1ms, while it actually traveled the longer diagonal path, shouldn't I see the light travel at less than c?

No, light travels at the same speed for everyone, irrespective of the relative velocity between the emitter and receiver.

 

[bahamagreen]

It is confusing.

Looking at the link with the animation of the spherical wavefront, it looks like the part of it that goes straight up the screen would miss a moving mirror, but the part of it that goes in the right upward direction could hit a moving mirror.

That explanation seems to suggest that the mover and observer might identify the light hitting the mirror as originating from two different parts of the light's wavefront, depending on reference frame; but I'm sure that is not meant to be thought as true, is it?.

If that were true, then a detector on the mirror would be detecting one part of the wavefront as detected by the mover, but the same mirror and detector would be detecting a different part of the wavefront for the stationary observer.

I'm assuming there are wavefronts that can have, or have imposed on them, some variable attribute with respect to direction. If the spherical wavefront could be made to have variable phase with respect to direction of propagation, or some other measurable feature, the mover and observer would be able to tell which angle the light traveled by measuring this attribute at the mirror... What prevents that?

Is there something like the Doppler correction in SR that eliminates or "hides" this so that both observers' detections are always identical?

 

[Banana Joe]

No, light travels at the same speed for everyone, irrespective of the relative velocity between the emitter and receiver.

Light does travel at c from the point of emission, to the observer on the rocket it would just seem to go slower, because he sees only the vertical movement.

 

[Mentz114]

Light does travel at c from the point of emission, to the observer on the rocket it would just seem to go slower, because he sees only the vertical movement.

Every point on the wavefront is moving at c. I can't follow your logic. The light seems to travel further when the clock is moving wrt you.

I'm signing off now because it is late in my timezone. Try to understand the Wiki article, or do a Google search.

 

[Banana Joe]

Every point on the wavefront is moving at c. I can't follow your logic. The light seems to travel further when the clock is moving wrt you.

I'm signing off now because it is late in my timezone. Try to understand the Wiki article, or do a Google search.

Every point on the wavefront is moving at c away from the point of emission. In the video you linked, if the stationary observer looking from the side follows the point of the wavefront that will intercept the mirror, he will see that point traveling at c along the hypotenuse of the triangle, but another stationary observer placed on the route of the rocket (and the one on the rocket) would see that point going straight up, like it was traveling along h at a slower speed than c, because they would see it cover less space in the same time.

 

[Mentz114]

I'm assuming there are wavefronts that can have, or have imposed on them, some variable attribute with respect to direction. If the spherical wavefront could be made to have variable phase with respect to direction of propagation, or some other measurable feature, the mover and observer would be able to tell which angle the light traveled by measuring this attribute at the mirror... What prevents that?

Is there something like the Doppler correction in SR that eliminates or "hides" this so that both observers' detections are always identical?

Doppler frequnecy shift won't affect the outcome. Phase is Lorentz invariant so both observers will detect the same phase change, if there is any. The wavefront represented by the circle is a line of constant phase in any case.

 

[Mentz114]

Every point on the wavefront is moving at c away from the point of emission. In the video you linked, if the stationary observer looking from the side follows the point of the wavefront that will intercept the mirror, he will see that point traveling at c along the hypotenuse of the triangle, but another stationary observer placed on the route of the rocket (and the one on the rocket) would see that point going straight up, like it was traveling along h at a slower speed than c, because they would see it cover less space in the same time.

I just don't get it. The observer on the rocket sees the light travel distance h, so this takes h/c seconds. The 'stationary' observer sees the light travel a longer distance, and therefore thinks the clock is running slower.

I can only point you again at this calculation.

http://en.wikipedia.org/wiki/Time_d...nce_of_time_dilation_due_to_relative_velocity

This is an generally accepted conclusion and I think I've done all I can to explain it.

 

[Nugatory]

If in the rocket I see the light travel up and down in 1ms, while it actually traveled the longer diagonal path, shouldn't I see the light travel at less than c?

The problem here is that word "actually". Would rocket-guy be wrong to insist that the light is "actually" traveling up and down, and the longer diagonal path measured by earth-guy is just an artifact of way that the Earth is moving?

Before you answer "yes, he's wrong because it's him and not earth-guy who's actually moving", think about it for a moment... Earth-guy and the "stationary" ground he's standing on are going around the sun, the sun is moving through space at a many kilometers per seconds, so what justifies earth-guy's claim that it's the rocket and not him that's moving? Or imagine that somebody on Mars (also going around the sun, but at a different speed than Earth) was watching the proceedings through a telescope, and was asked whether it was earth-guy or rocket-guy who was "actually" moving... What would Mars-guy say was "actually" the path of the light?

Experiments have confirmed that all of these observers will agree that when they take their notion of the distance the light travels, divide it by their notion of the time it took the light to cover that distance, they'll all get the same value, $c$, for the speed of light.

 

[jartsa]

If the speed at which light waves propagate in vacuum is independent both of the motion of the wave source and of the inertial frame of reference of the observer, why isn't the direction? Shouldn't the light travel directly upward from the point of emission and not diagonally, following the rocket?

Yes, our intuition says light should not travel diagonally. But light travels diagonally, because the light source sends the light into that direction, because it is a moving light source ... I will not go into details of different moving light sources.

I was under the impression that "time" doesn't exist... Isn't it just something we created to measure the succession of events? Past and future exist only in our minds, the only thing that actually exists is the present, the now, and that is true simultaneously anywhere in the Universe. If we decide that one second is one 86400th of Earth's rotation on its axis at current speed, isn't that measure absolute and unchangeable? How can a rocket slow it down?

Well maybe the constant linear motion caused the bouncing and rotating motions inside of all kinds of gadgets to slow down, the light clock is one example of this.

How does speed slow down the oscillation of the atoms, cellular reproduction and decay (and everything else)? And even if it does, does it necessarily mean that "time" has slowed down? If "time" did slow down, shouldn't everything be affected, including light?

Cells travel fast and reproduce and decay slowly.
Light travels fast and bounces slowly. Very simple

 

[Banana Joe]

The problem here is that word "actually". Would rocket-guy be wrong to insist that the light is "actually" traveling up and down, and the longer diagonal path measured by earth-guy is just an artifact of way that the Earth is moving?

Before you answer "yes, he's wrong because it's him and not earth-guy who's actually moving", think about it for a moment... Earth-guy and the "stationary" ground he's standing on are going around the sun, the sun is moving through space at a many kilometers per seconds, so what justifies earth-guy's claim that it's the rocket and not him that's moving? Or imagine that somebody on Mars (also going around the sun, but at a different speed than Earth) was watching the proceedings through a telescope, and was asked whether it was earth-guy or rocket-guy who was "actually" moving... What would Mars-guy say was "actually" the path of the light?

Experiments have confirmed that all of these observers will agree that when they take their notion of the distance the light travels, divide it by their notion of the time it took the light to cover that distance, they'll all get the same value, $c$, for the speed of light.

And why is that? How are we sure that they'll get the same value?
Let's forget the "stationary" observer and think about the light source, when it fires an impulse a spheric wavefront is originated, in which every point on it is moving away from the point of emission.
If the light source stays at the center of that sphere than we know it didn't move, if it doesn't then it's moving, and rocket guy would be incorrect in insisting that it traveled up and down, because the actual movement of the wavefront has to be calculated considering the point of emission as a reference frame, not the rocket.

Let's assume we have a light source and a sensor at the opposite extremes of the base of an isosceles triangle and a mirror at the third vertex, all stationary. We also have two stationary observers, one looking from the side, the other far away positioned on the extension of the triangle's base, so that he only sees a line which coincides with the height of the triangle. Now, if the light source fires an impulse so that it travels up along the oblique side of the triangle, hits the mirror and travels down along the other oblique side and hits the sensor, I would expect the observer on the side to see the impulse travel on this diagonal path at c, but I would expect the other to see the impulse go straight up and down like it was traveling along the height of the triangle, at a lower speed than c. Or why not?

 

[Nugatory]

And why is that? How are we sure that they'll get the same value?

At the top of this forum, there's a pinned thread on the experimental support for relativity: https://www.physicsforums.com/showthread.php?t=229034. We're as sure as experiments and empirical evidence can ever make us that inertial observers will measure the same value for the speed of light.

I would expect the other to see the impulse go straight up and down like it was traveling along the height of the triangle, at a lower speed than c. Or why not?

if he knows the exact position of the sensors (maybe he examined the experimental setup and then moved far away, or maybe he has accurate range-finding equipment) then he'll be able to calculate the distance between the vertices and when he does "speed=distance divided by time" he'll get c. If not, this is a simple case of experimental error - his experiment to measure the speed of light failed because he started with an incorrect measure of the distance.

It's worth noting that you cannot actually SEE a flash of light traveling through space; we just get to detect when it is emitted and when it hits something. Thus, we can get rid of both observers who (in your new scenario are at rest relative to each other and the vertices of the triangle) and replace them with three machines, one at each vertex, which print out a time-stamped log of what happened at their location. Now we can gather up the logs afterwards, and from the timestamps and the known positions of the machines accurately calculate the speed of light from the timestamps of the emission, reflection, and detection events. But - and this is essential to understanding relativity! - this procedure only works when the machines are all at rest relative to one another.

 

[Banana Joe]

if he knows the exact position of the sensors (maybe he examined the experimental setup and then moved far away, or maybe he has accurate range-finding equipment) then he'll be able to calculate the distance between the vertices and when he does "speed=distance divided by time" he'll get c. If not, this is a simple case of experimental error - his experiment to measure the speed of light failed because he started with an incorrect measure of the distance.

It's worth noting that you cannot actually SEE a flash of light traveling through space; we just get to detect when it is emitted and when it hits something. Thus, we can get rid of both observers who (in your new scenario are at rest relative to each other and the vertices of the triangle) and replace them with three machines, one at each vertex, which print out a time-stamped log of what happened at their location. Now we can gather up the logs afterwards, and from the timestamps and the known positions of the machines accurately calculate the speed of light from the timestamps of the emission, reflection, and detection events. But - and this is essential to understanding relativity! - this procedure only works when the machines are all at rest relative to one another.

I know you can't see the flash traveling, but let's say you can, and let's say the observer hasn't seen the setup, then from his perspective the light will seem to travel slower than c, because he (like the rocket man) erroneously thinks that the light only traveled up and down the height of the triangle, and not along the oblique sides.

 

[A.T.]

I know you can't see the flash traveling, but let's say you can, and let's say the observer hasn't seen the setup, then from his perspective the light will seem to travel slower than c,

No, it’s c for every observer.

because he (like the rocket man) erroneously thinks that the light only traveled up and down the height of the triangle, and not along the oblique sides.

That is no error. The light does travel only up and down in his frame.

The movement of the light source is irrelevant. See:
http://en.wikipedia.org/wiki/Emission_theory#Refutations_of_emission_theory

 

[bahamagreen]

Doppler frequnecy shift won't affect the outcome. Phase is Lorentz invariant so both observers will detect the same phase change, if there is any. The wavefront represented by the circle is a line of constant phase in any case.

I had a feeling it might be like that, but just to be complete and eliminate all loop holes, there are no such attributes whose variation with direction of emission could be measured at different parts of the wavefront? Frequency, amplitude, wave shape, ...?

So it would be impossible to create a spherical waveform that has some "encoding" impressed into one or more combined attributes such that a measurement could identify the direction from which the measuring detector was relative to the source?

Maybe emitting the light from a "magnetic bubble" or some other contrivance so that some attribute(s) are skewed and detection reveals the source direction?

Even if the answer to all these is no... what about an emission that comprised a series of wavefront bursts sent in different directions, each direction series coded by differential attributes... maybe using an array of lasers on the surface of a ball to approximate the wavefront?

Or is it that there might be such a thing in principle, but SR always invokes invariance so there is null measured difference?

 

[Mentz114]

I had a feeling it might be like that, but just to be complete and eliminate all loop holes, there are no such attributes whose variation with direction of emission could be measured at different parts of the wavefront? Frequency, amplitude, wave shape, ...?

So it would be impossible to create a spherical waveform that has some "encoding" impressed into one or more combined attributes such that a measurement could identify the direction from which the measuring detector was relative to the source?

Maybe emitting the light from a "magnetic bubble" or some other contrivance so that some attribute(s) are skewed and detection reveals the source direction?

Even if the answer to all these is no... what about an emission that comprised a series of wavefront bursts sent in different directions, each direction series coded by differential attributes... maybe using an array of lasers on the surface of a ball to approximate the wavefront?

Or is it that there might be such a thing in principle, but SR always invokes invariance so there is null measured difference?

As long as the light can reach the mirror and bounce back in the rest frame of the light and mirror - then it will do this in all frames, whatever is done to the light.

As you no doubt know, the light hitting the mirror is an event, the meeting of the worldline of the light and the worldline of the mirror. Nothing related to motion can un-happen it.

 

[Ibix]

I know you can't see the flash traveling, but let's say you can, and let's say the observer hasn't seen the setup, then from his perspective the light will seem to travel slower than c, because he (like the rocket man) erroneously thinks that the light only traveled up and down the height of the triangle, and not along the oblique sides.

There is no "erroneous" here. Either viewpoint is perfectly valid. When you add the requirement that lightspeed be constant for all observers, you can derive the equations for time dilation and length contraction.

To see the point about both viewoints being valid, imagine two identical rockets with lightclocks, traveling in opposite directions. According to one rocket, its own lightclock is working vertically and the other is working on the diagonal. The other rocket can say the same thing the other way round. Which one is right? There's nothing to choose. Both viewpoints are equally valid.

 

[Ibix]

Nothing related to motion can un-happen it.

It would be double plus ungood if it could. Cause could be effect and effect, cause.

 

[Nugatory]

That is no error. The light does travel only up and down in his frame.

You've misread the conditions that Banana Joe proposed:

Let's assume we have a light source and a sensor at the opposite extremes of the base of an isosceles triangle and a mirror at the third vertex, all stationary. We also have two stationary observers, one looking from the side, the other far away positioned on the extension of the triangle's base, so that he only sees a line which coincides with the height of the triangle. Now, if the light source fires an impulse so that it travels up along the oblique side of the triangle, hits the mirror and travels down along the other oblique side and hits the sensor, I would expect the observer on the side to see the impulse travel on this diagonal path at c, but I would expect the other to see the impulse go straight up and down like it was traveling along the height of the triangle, at a lower speed than c.

Here all of the observers, mirrors, sources, and detectors are at rest relative to one another, and Banana Joe is trying to use the projection of the distance traveled onto a plane not parallel to the direction of travel as the distance.

 

[A.T.]

Banana Joe is trying to use the projection of the distance traveled onto a plane not parallel to the direction of travel as the distance.

I see. He is confusing the visual impression of the observer due to perspective with what happens in the rest frame of the observer. I blame the use of the words "observer/observes/sees" instead of "reference frame/measures" for such misconceptions.

 

[Nugatory]

I see. He is confusing the visual impression of the observer due to perspective with what happens in the rest frame of the observer. I blame the use of the words "observer/observes/sees" instead of "reference frame/measures" for such misconceptions.

Many people, myself included, share the blame for that confusion

 

[jartsa]

I had a feeling it might be like that, but just to be complete and eliminate all loop holes, there are no such attributes whose variation with direction of emission could be measured at different parts of the wavefront? Frequency, amplitude, wave shape, ...?

So it would be impossible to create a spherical waveform that has some "encoding" impressed into one or more combined attributes such that a measurement could identify the direction from which the measuring detector was relative to the source?

Maybe emitting the light from a "magnetic bubble" or some other contrivance so that some attribute(s) are skewed and detection reveals the source direction?

Even if the answer to all these is no... what about an emission that comprised a series of wavefront bursts sent in different directions, each direction series coded by differential attributes... maybe using an array of lasers on the surface of a ball to approximate the wavefront?

Or is it that there might be such a thing in principle, but SR always invokes invariance so there is null measured difference?

Of course we can mark different parts of the wave front. By putting a fancy lamp shade over the light source, for example.

If we do that, we notice that a certain part of the wave hits a certain part of the rocket wall. If we change the velocity of the rocket, the pattern on the wall does not change.

(A lamp attached to rocket wall is shining light to the opposite rocket wall in this scenario)
(Or: A source of a wave front attached to rocket wall is sending a wave to the opposite rocket wall)

 

[Mentz114]

Of course we can mark different parts of the wave front. By putting a fancy lamp shade over the light source, for example.

If we do that, we notice that a certain part of the wave hits a certain part of the rocket wall. If we change the velocity of the rocket, the pattern on the wall does not change.

(A lamp attached to rocket wall is shining light to the opposite rocket wall in this scenario)
(Or: A source of a wave front attached to rocket wall is sending a wave to the opposite rocket wall)

The sphercal wave analogy breaks down here. There is no way to distinguish the light that hits the mirror in the rest frame and the moving frame. It is the same mirror and the same light. If we could detect a difference due to motion this would violate the principles of relativity.

Maybe this is what you are saying ... not sure though.

 

[Banana Joe]

Let’s consider this experiment: we have a straight rail with a rocket attached, on the rocket we have two arms (in the same orientation of the track) with a light source in the middle, each arm has at its extreme a light detector, plus we have one stationary detector at each end of the track. The rocket starts at one end of the track, reaches the maximum speed possible, and then the light source fires an impulse exactly in the middle of the track. If the speed of light was affected by the motion of the light source, I would expect the two sensors on the rocket to detect the light at the same time, and the stationary sensor at the end of the track in the rocket’s direction to detect it before the other one. If instead the light traveled at c from the point of emission regardless of the speed of the light source, I would expect the two stationary sensors to receive the light at the same time, and the sensor on the back of the rocket to receive it before the one in the front. According to relativity, instead, not only the moving sensors detect it simultaneously, but also the stationary ones do, correct? Doesn’t that mean that light would be traveling at two speeds at the same time, at c relative to the track and the stationary sensors, and at c relative to the moving sensors (so at (c + the velocity of the rocket) relative to the track)?

If I’m in the rocket and everything is slower and I can’t notice, and I see the light traveling at c, shouldn’t that mean that it’s actually moving slower? If it was actually moving at c relative to me, shouldn't it appear to move faster than c?

 

[Mentz114]

Let’s consider this experiment: we have a straight rail with a rocket attached, on the rocket we have two arms (in the same orientation of the track) with a light source in the middle, each arm has at its extreme a light detector, plus we have one stationary detector at each end of the track. The rocket starts at one end of the track, reaches the maximum speed possible, and then the light source fires an impulse exactly in the middle of the track. If the speed of light was affected by the motion of the light source, I would expect the two sensors on the rocket to detect the light at the same time, and the stationary sensor at the end of the track in the rocket’s direction to detect it before the other one. If instead the light traveled at c from the point of emission regardless of the speed of the light source, I would expect the two stationary sensors to receive the light at the same time, and the sensor on the back of the rocket to receive it before the one in the front. According to relativity, instead, not only the moving sensors detect it simultaneously, but also the stationary ones do, correct? Doesn’t that mean that light would be traveling at two speeds at the same time, at c relative to the track and the stationary sensors, and at c relative to the moving sensors (so at (c + the velocity of the rocket) relative to the track)?

If I’m in the rocket and everything is slower and I can’t notice, and I see the light traveling at c, shouldn’t that mean that it’s actually moving slower? If it was actually moving at c relative to me, shouldn't it appear to move faster than c?

I think it is simpler to analyse this if there is a light emitter in center of the rocket and a sensor at each end. Someone in the rocket will conclude that the light hits both sensors at the same time by his clock. If the rocket is moving ( inertially) along the track, then an observer on the ground ( the track frame) will see the back sensor detect the light before the front sensor. It is easy to calculate those times if we write equations for the motion of back of the rocket, the light moving towards the back, the light moving forwrd and the front of the rocket.
Using x and t in the ground frame, and with the end of the rocket being at x=0 at t=0 ( the time of the light emission) we get

back of rocket x = v*t
light going back x = L/(2*γ) - c*t

front of rocket x = L/γ + v*t
light forward x = L/(2*γ) + c*t

From which I get from t₀ = L/(2*γ*(v+c)) and t₁ = L/(2*γ*(c-v))

L is the rest length of the rocket, v is the relative velocity of rocket and ground, γ is the usual factor.

If v = 0 then t₀ = t₁ = L/(2*γ*c)

This does not prove anything but it is correct to keep c in both frames as the speed of light, and this makes the times different in the moving frame.

If you repeat the calculation with additive velocities, the times will be the same t₀ = t₁ .

So we get non-simultaneity if the speed of light is the same in both frames.

 

[Ibix]

If instead the light traveled at c from the point of emission regardless of the speed of the light source, I would expect the two stationary sensors to receive the light at the same time, and the sensor on the back of the rocket to receive it before the one in the front.

Correct, for an observer stood on the track. For one stood on the rocket, the rocket is stationary and the track is moving backwards, so the logic is reversed, and you would expect the pulses to arrive simultaneously at the rocket sensors and not at the track sensors.

According to relativity, instead, not only the moving sensors detect it simultaneously, but also the stationary ones do, correct?

No. There can exist observers who see one pair of detections as simultaneous, and observers who see the other pair as simultaneous. There are no observers who see both as simultaneous. That there is no global notion of "simultaneous" is a key concept in relativity. You need to say who sees something as simultaneous, just like you need to say who sees something as "here".

Doesn’t that mean that light would be traveling at two speeds at the same time, at c relative to the track and the stationary sensors, and at c relative to the moving sensors (so at (c + the velocity of the rocket) relative to the track)?

No. It means that two observers in motion with respect to each other do not agree on the distance between two events or the time between them. They do not always agree on whether or not they are simultaneous, or even which one happens first. They do agree on the speed of light.

This is basically what Mentz proves in his post above. It's been extensively checked by experiment - check out the sticky thread at the top of this forum.

You seem to me to be stuck on the notion that one of the observers is stationary and the others are moving. This is not correct. Any time you are not accelerating, you can say you are stationary. Everybody else is moving.

 

[ghwellsjr]

Let’s consider this experiment: we have a straight rail with a rocket attached, on the rocket we have two arms (in the same orientation of the track) with a light source in the middle, each arm has at its extreme a light detector, plus we have one stationary detector at each end of the track. The rocket starts at one end of the track, reaches the maximum speed possible, and then the light source fires an impulse exactly in the middle of the track.

Here's a spacetime diagram depicting your scenario. The rocket starts out stationary at the left end of the track. The ends of the rocket are shown in blue and red. The ends of the track are shown in black and green. The middle of the rocket and the track are shown as separate grey lines. The dots mark off hundred nanosecond intervals of Proper Time for each end of each object and their middles. The speed of light is one foot per nanosecond.

The Proper Length of the rocket is 600 feet when at rest and it is accelerated to 60%c such that it's Proper Length is maintained at 600 feet. The Proper Length of the track is 1800 feet:

When the middle of the rocket reaches the middle of the track (the two grey lines intersect), the light source at the middle of the rocket emits a short burst of light which travels at c in both directions in the Inertial Reference Frame depicted in the diagram. As you can see, the light reaches the two detectors at each end of the track 900 nsecs later.

If the speed of light was affected by the motion of the light source, I would expect the two sensors on the rocket to detect the light at the same time, and the stationary sensor at the end of the track in the rocket’s direction to detect it before the other one.

Or if the speed of light was affected by the Inertial Reference Frame (IRF) you choose to depict your scenario in, specifically, if it is defined to propagate at c in all directions, then you would expect the two sensors on the rocket to detect the light at the same time, just like when we transform to the IRF in which the rocket is at rest:

As you can see, the light reaches both rocket detectors in 300 nanoseconds. And note that the Proper Length of the rocket is still 600 feet when at rest in this IRF.

If instead the light traveled at c from the point of emission regardless of the speed of the light source, I would expect the two stationary sensors to receive the light at the same time, and the sensor on the back of the rocket to receive it before the one in the front.

Or if the light travels at c no matter what IRF you depict the scenario in, then in the rest IRF of the track, the detectors at the ends of the track receive the light at the same time, as shown in the first diagram above.

According to relativity, instead, not only the moving sensors detect it simultaneously, but also the stationary ones do, correct?

That is not the best way to say it. A better way to say it is in the rest IRF of the rocket, the rocket sensors detect it simultaneously and in the rest IRF of the track, the track sensors detect it simultaneously. So whichever sensors are at rest (stationary) in the IRF are the ones that detect the light simultaneously.

Doesn’t that mean that light would be traveling at two speeds at the same time, at c relative to the track and the stationary sensors, and at c relative to the moving sensors (so at (c + the velocity of the rocket) relative to the track)?

No, you need to pick one IRF at a time, not two IRF's at the same time. Observers cannot measure the propagation of light. They cannot tell which IRF you are using to describe the scenario.

If I’m in the rocket and everything is slower and I can’t notice, and I see the light traveling at c, shouldn’t that mean that it’s actually moving slower? If it was actually moving at c relative to me, shouldn't it appear to move faster than c?

You cannot see the light traveling at all. It's not a bullet that you can shine a light on to see where it is at any given moment and then plot its position as a function of time. How would you light up the light to see where it is? Instead, the best you can do is reflect the light off an object and then measure its "average" round trip time. When we apply Einstein's convention, we assume that the light takes the same amount of time to get to the target as its reflection takes to get back in any IRF and that allows us define the time it takes for the light to reach both stationary detectors in each IRF to be the same.

Pretty simple, isn't it? Does it make sense? Any questions?