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Isotropy of light velocity and Einstein’s postulate


Vilas Tamhane

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To my previous question, whether light pulse acquires transverse velocity of the source, there was no answer. Therefore in this post I will assume both the possibilities.

 

Consider a spaceship moving with some velocity, which we will consider as zero. Spaceship is in the frame O1.

 

Observer in the spaceship arranges a source that can direct a light pulse in the direction perpendicular to the length of the spaceship. He arranges a detector D at the top to receive the pulse.

 

Spaceship is now accelerated lengthwise to the new velocity v, which the observer detects on his instrument. Now he is in frame O2. He again sends the pulse. Will the pulse miss the detector? In this thought experiment only the view of the observer in the ship is considered.

 

Case 1: Light pulse does not move along the source.

 

In this case the light pulse is bound to miss the target. It will fall back and its path will be in the diagonal direction, inclined backwards. So in order to hit the target, the observer will have to shift the target to left and by measuring the shift, he can measure his own velocity (w.r.t. frame O1).

 

Case 2: Light pulse moves along with the source:

 

If the pulse is ballistic, then like any other material object, it will have velocity greater than ‘c’. Since this is not possible, we assume that it is ‘c’. In this case the pulse will move diagonally forward and its velocity will be ‘c’ in the diagonal direction. Therefore its vertical component will be lesser than ‘c’ and it will go on reducing with the increasing speed of the spaceship. Although observer in the spaceship will not notice horizontal component of the light pulse, as he too is moving along with it, he will find that vertical velocity of the light pulse is reduced and with this light clock he will be able to measure his own velocity.

 

 

According to Einstein’s postulate, whatever might be the velocity of the spaceship, light pulse will always hit the detector with a velocity ‘c’. However this postulate can be assumed to be correct only if we disregard cases 1 and 2. However these cases are most fundamental and are based on the observation of velocity of light. So should we assume that Einstein’s basic postulate is wrong?

 

 

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To my previous question, whether light pulse acquires transverse velocity of the source, there was no answer. Therefore in this post I will assume both the possibilities.

 

Consider a spaceship moving with some velocity, which we will consider as zero. Spaceship is in the frame O1.

 

Observer in the spaceship arranges a source that can direct a light pulse in the direction perpendicular to the length of the spaceship. He arranges a detector D at the top to receive the pulse.

 

Spaceship is now accelerated lengthwise to the new velocity v, which the observer detects on his instrument. Now he is in frame O2. He again sends the pulse. Will the pulse miss the detector? In this thought experiment only the view of the observer in the ship is considered.

 

Case 1: Light pulse does not move along the source.

 

In this case the light pulse is bound to miss the target. It will fall back and its path will be in the diagonal direction, inclined backwards. So in order to hit the target, the observer will have to shift the target to left and by measuring the shift, he can measure his own velocity (w.r.t. frame O1).

 

Case 2: Light pulse moves along with the source:

 

If the pulse is ballistic, then like any other material object, it will have velocity greater than ‘c’. Since this is not possible, we assume that it is ‘c’. In this case the pulse will move diagonally forward and its velocity will be ‘c’ in the diagonal direction. Therefore its vertical component will be lesser than ‘c’ and it will go on reducing with the increasing speed of the spaceship. Although observer in the spaceship will not notice horizontal component of the light pulse, as he too is moving along with it, he will find that vertical velocity of the light pulse is reduced and with this light clock he will be able to measure his own velocity.

 

 

According to Einstein’s postulate, whatever might be the velocity of the spaceship, light pulse will always hit the detector with a velocity ‘c’. However this postulate can be assumed to be correct only if we disregard cases 1 and 2. However these cases are most fundamental and are based on the observation of velocity of light. So should we assume that Einstein’s basic postulate is wrong?

 

Have you accounted for time dilation?

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No. Time dilation and length contractions are the effects which are based on the postulate and I am considering validity of the postulate based on the nature of light velocity

 

So you are assuming no time dilation and have come upon a contradiction?

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So you are assuming no time dilation and have come upon a contradiction?

 

Yes. I am considering pre-relativistic validity of the postulate. In any case, there cannot be time dilation for the observer in the ship. Once more note that I am not considering any frame other than the ship.

 

 

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Yes. I am considering pre-relativistic validity of the postulate. In any case, there cannot be time dilation for the observer in the ship. Once more note that I am not considering any frame other than the ship.

 

Except while accelerating the observer will not be aware of any changes between the original inertial frame and the later one, unless he looks out the window and uses the same reference points. He/she will interpret light speed as being the same as it was.

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According to Einstein’s postulate, whatever might be the velocity of the spaceship, light pulse will always hit the detector with a velocity ‘c’. However this postulate can be assumed to be correct only if we disregard cases 1 and 2. However these cases are most fundamental and are based on the observation of velocity of light. So should we assume that Einstein’s basic postulate is wrong?

I don't see how this requires that you disregard anything. You have done a thought experiment, and it cannot negate anything. A thought experiment tells you what you expect to see, under a set of conditions and assumptions. You need to do an actual experiment to see if you are right.

 

In the observer's frame, s/he is at rest. There is no transverse velocity the light may obtain. One can actually do this experiment by sending a light to a target and then changing the velocity of the system, such as a free-space laser into a single-mode fiber, which requires better than micron-level alignment. As the earth rotates, and orbits, the velocity changes. No transverse velocity is acquired — the light stays aligned.

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Except while accelerating the observer will not be aware of any changes between the original inertial frame and the later one, unless he looks out the window and uses the same reference points. He/she will interpret light speed as being the same as it was.

 

 

Your reply is not clear to me. All inertial frames are equivalent for mechanical laws because all material bodies acquire velocity of the object in which they are contained. If this is not the property of light then it is bound to behave in a different way in a moving system. One and only one criteria for light velocity to be same in the moving system is that it should behave the way all other material particles behave.

 

 

 

I don't see how this requires that you disregard anything. You have done a thought experiment, and it cannot negate anything. A thought experiment tells you what you expect to see, under a set of conditions and assumptions. You need to do an actual experiment to see if you are right.

 

In the observer's frame, s/he is at rest. There is no transverse velocity the light may obtain. One can actually do this experiment by sending a light to a target and then changing the velocity of the system, such as a free-space laser into a single-mode fiber, which requires better than micron-level alignment. As the earth rotates, and orbits, the velocity changes. No transverse velocity is acquired — the light stays aligned.

 

I am not conversant with lasers. In any case, based on any observation, light can be proved to possess only three types of behavior.

 

1. Light behaves like material objects. In this case its velocity cannot be constant ‘c’.

 

2. Velocity vector of light is constant ‘c’ but it moves along with the source.

 

3. Once a pulse is propagated in a particular direction, it keeps the direction and moves with velocity ‘c’ in that direction.

 

Any of the three propositions go against Einstein’s postulates.

 

 

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Here is the way to think about it under special relativity:

 

Let's say that we have a spaceship which emits photons in the x-direction. Then in the frame of the spaceship, the path of the photons is the set of all points (t, ct, 0, 0) for positive t.

 

We now take a look in the frame in which the spaceship is moving at a rate v in the y-direction.

 

If we have an event (t, x, y, z) in the frame of the spaceship, the event becomes

 

[MATH](t', x', y', z') = (\gamma (t + v/c^2 y), x, \gamma (y + vt), z)[/MATH]

 

So the event (t, ct, 0, 0) becomes

 

[MATH](t', x', y', z') = (\gamma t, ct, \gamma vt, 0)[/MATH]

 

If we scale t, we get [MATH]t*(1, c/\gamma, v, 0)[/MATH]

 

We then get that the speed is [MATH]\sqrt{(c/\gamma)^2 + v^2} = \sqrt{(c^2 - v^2) + v^2} = c.[/MATH]

 

So no problem with relativity.

 

In short, the answer is that it moves with the same transverse velocity as the source, but the parallel velocity is changed.

=Uncool-

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Here is the way to think about it under special relativity:

 

Let's say that we have a spaceship which emits photons in the x-direction. Then in the frame of the spaceship, the path of the photons is the set of all points (t, ct, 0, 0) for positive t.

 

We now take a look in the frame in which the spaceship is moving at a rate v in the y-direction.

 

So no problem with relativity.

 

In short, the answer is that it moves with the same transverse velocity as the source, but the parallel velocity is changed.

=Uncool-

 

We don’t go anywhere and remain in the spaceship. We of course don’t know relativity yet because we are stuck up at the basic postulate.

 

 

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I am not conversant with lasers. In any case, based on any observation, light can be proved to possess only three types of behavior.

 

1. Light behaves like material objects. In this case its velocity cannot be constant ‘c’.

 

2. Velocity vector of light is constant ‘c’ but it moves along with the source.

 

3. Once a pulse is propagated in a particular direction, it keeps the direction and moves with velocity ‘c’ in that direction.

 

Any of the three propositions go against Einstein’s postulates.

 

If they disagree with the postulate then they are wrong. Why is that a problem? One obvious possibility is that your three propositions do not cover the entire spectrum of possibilities, making it a false trichotomy.

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If they disagree with the postulate then they are wrong. Why is that a problem? One obvious possibility is that your three propositions do not cover the entire spectrum of possibilities, making it a false trichotomy.

 

 

Postulate can never be sacrosanct. I think the 3rd proposition is true, since all observed orbits of binary stars follow Kepler’s law. Thus once light is emitted in particular direction, it will not have any relationship with the velocity of the source. I do not know of any fourth observed possibility.

 

 

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Postulate can never be sacrosanct. I think the 3rd proposition is true, since all observed orbits of binary stars follow Kepler’s law. Thus once light is emitted in particular direction, it will not have any relationship with the velocity of the source. I do not know of any fourth observed possibility.

 

But relativity works, and so does electrodynamics (the constancy of c appears in Maxwell's equations). So unless you have experimental data that overturns both of these quite large chunks of physics, you have to go with the postulate being correct. Anyway, I'm not seeing the conflict with #3 that you apparently think is there.

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But relativity works, and so does electrodynamics (the constancy of c appears in Maxwell's equations). So unless you have experimental data that overturns both of these quite large chunks of physics, you have to go with the postulate being correct. Anyway, I'm not seeing the conflict with #3 that you apparently think is there.

 

 

If #3 is correct then in the spaceship light pulse will fall back and path of light will be diagonal backward. Interestingly, for the observer in the ship as well as for the observer outside the ship (at rest), path of light will be same. It will be diagonal. This will make everything topsy-turvy.

 

I am not questioning experimental data. It can fit to some other theory not yet known. Even if a particular apparently erroneous theory is used to explain experiments then I do agree that the theory should be used. At the same time I would insist that inconsistencies in the present theory must be examined. This is the only way which gives birth to new theories, more correct than the existing ones.

 

And in SR there are many inconsistencies.

 

 

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If #3 is correct then in the spaceship light pulse will fall back and path of light will be diagonal backward. Interestingly, for the observer in the ship as well as for the observer outside the ship (at rest), path of light will be same. It will be diagonal. This will make everything topsy-turvy.

 

I am not questioning experimental data. It can fit to some other theory not yet known. Even if a particular apparently erroneous theory is used to explain experiments then I do agree that the theory should be used. At the same time I would insist that inconsistencies in the present theory must be examined. This is the only way which gives birth to new theories, more correct than the existing ones.

 

Then it is inconsistent with observation and therefore wrong. Since none of the scenarios agrees with reality, there must be a fourth: The speed of light is a constant in all inertial frames.

 

And in SR there are many inconsistencies.

No, not really.

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We don’t go anywhere and remain in the spaceship. We of course don’t know relativity yet because we are stuck up at the basic postulate.

Let me make sure that I have your initial ideas correct.

 

So you start in a spaceship which has velocity (0, 0, 0) relative to an inertial frame O1. This spaceship lets out a light pulse in the x-direction (relative to O1) towards a stationary (still relative to O1) detector at (x, 0, 0), right?

 

The spaceship then acquires a y-velocity of v, giving it a velocity of (0, v, 0). Then there is another inertial frame O2, relative to which the spaceship is stationary (but then the detector is moving at (0, -v, 0)). This spaceship lets out a light pulse in the x-direction (relative to O2)

 

Is that the situation so far?

 

ETA: Or is the detector inside the spaceship?

=Uncool-

Edited by uncool
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Let me make sure that I have your initial ideas correct.

 

So you start in a spaceship which has velocity (0, 0, 0) relative to an inertial frame O1. This spaceship lets out a light pulse in the x-direction (relative to O1) towards a stationary (still relative to O1) detector at (x, 0, 0), right?

 

The spaceship then acquires a y-velocity of v, giving it a velocity of (0, v, 0). Then there is another inertial frame O2, relative to which the spaceship is stationary (but then the detector is moving at (0, -v, 0)). This spaceship lets out a light pulse in the x-direction (relative to O2)

 

Is that the situation so far?

 

ETA: Or is the detector inside the spaceship?

=Uncool-

 

 

Yes the detector is in the spaceship.

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Yes the detector is in the spaceship.

Ahh. That is what I misunderstood.

 

Case 2: Light pulse moves along with the source:

 

If the pulse is ballistic, then like any other material object, it will have velocity greater than ‘c’.

Only if you assume Galilean relativity. In other words, you have made two contradicting assumptions; one must give. Unless "ballistic" means the same thing as "Galilean" to you.

Since this is not possible, we assume that it is ‘c’. In this case the pulse will move diagonally forward

Relative to which frame? The original frame (O1) or the new frame (O2)?

and its velocity will be ‘c’ in the diagonal direction. Therefore its vertical component will be lesser than ‘c’ and it will go on reducing with the increasing speed of the spaceship. Although observer in the spaceship will not notice horizontal component of the light pulse, as he too is moving along with it, he will find that vertical velocity of the light pulse is reduced

Only once you make the assumption that there is no time dilation (or sideways spatial dilation, although that happens to be true even in special relativity); in other words, you've proven (again) from the assumptions that there must be time dilation.

and with this light clock he will be able to measure his own velocity.
Only if you discard one of the key components of special relativity - time dilation. In other words, you are specifically assuming that special relativity has contradictions to prove it has contradictions.

=Uncool-

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Ahh. That is what I misunderstood.

Only if you assume Galilean relativity. In other words, you have made two contradicting assumptions; one must give. Unless "ballistic" means the same thing as "Galilean" to you.

Relative to which frame? The original frame (O1) or the new frame (O2)?

Only once you make the assumption that there is no time dilation (or sideways spatial dilation, although that happens to be true even in special relativity); in other words, you've proven (again) from the assumptions that there must be time dilation.

Only if you discard one of the key components of special relativity - time dilation. In other words, you are specifically assuming that special relativity has contradictions to prove it has contradictions.

=Uncool-

 

I have taken two steps. First is to find out about the velocity of light. How a light pulse will travel in space, after it is emitted in a particular direction (say by a laser). I raised a question about it in my last post but could not get confident reply. Therefore I assumed three possible pictures. It is my belief that 3rd is true. In that case once light is emitted in a particular direction by the moving source, it keeps the direction and in that direction velocity of the pulse will be ‘c’.

 

However there can be two more options which I have stated.

 

We now take a second step. In this we consider only one frame. A train compartment or a spaceship. In this, an observer sends a pulse vertically up, in the y-direction. (This is a normal notation, so I have interchanged your x and y directions).

 

Please note that we are considering only one frame and not two. However any object that is in uniform speed can be considered to have zero velocity. Therefore we have to consider two situations.

 

In the spaceship, whatever might be the velocity of the ship, consider it zero (frame O1). Observer arranges target to receive the light pulse sent vertically up. Observer sends a pulse and is satisfied to see that the pulse hits the target fixed at a ceiling.

 

Now the ship is accelerated to uniform speed v, w.r.t. O1. Ship is now in the frame O2. However for the observer in the ship, he will be always at zero speed unless he has some other object to compare his velocity with.

 

There is another way for him to ascertain the fact that he is in frame O2. A velocity meter (which would actually take a reading of acceleration and record the velocity after making calculations) in his ship will tell him that he is in the frame O2. He again sends a pulse. Will the pulse hit the target and if yes, at what speed?

 

Remember that we are considering some real situation and we are not considering any laws of SR. To make a statement we just have a law about emission of light pulse. Now you have to apply (2) or (3) to find out how the pulse will travel in the spaceship when the spaceship is moving with a velocity v. (Note that observer in the ship cannot notice it without referring his meter. But light pulse knows.)

 

With this set up I am not considering SR at all. Einstein’s postulate, time dilation etc will appear only after we decide behavior of light pulse in the moving frame.

 

Note that we have to reject #1, because we know that velocity of light is always ‘c’. Now consider #2 or #3 (these are the only other possibilities) and tell me what observer in the moving ship should note about the path and speed of light pulse.

 

Behavior of light emission has to be a basic law which should override any postulate.

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I have taken two steps. First is to find out about the velocity of light. How a light pulse will travel in space, after it is emitted in a particular direction (say by a laser). I raised a question about it in my last post but could not get confident reply. Therefore I assumed three possible pictures. It is my belief that 3rd is true. In that case once light is emitted in a particular direction by the moving source, it keeps the direction and in that direction velocity of the pulse will be ‘c’.

 

However there can be two more options which I have stated.

 

We now take a second step. In this we consider only one frame. A train compartment or a spaceship. In this, an observer sends a pulse vertically up, in the y-direction. (This is a normal notation, so I have interchanged your x and y directions).

 

Please note that we are considering only one frame and not two. However any object that is in uniform speed can be considered to have zero velocity. Therefore we have to consider two situations.

 

In the spaceship, whatever might be the velocity of the ship, consider it zero (frame O1). Observer arranges target to receive the light pulse sent vertically up. Observer sends a pulse and is satisfied to see that the pulse hits the target fixed at a ceiling.

 

Now the ship is accelerated to uniform speed v, w.r.t. O1. Ship is now in the frame O2. However for the observer in the ship, he will be always at zero speed unless he has some other object to compare his velocity with.

 

There is another way for him to ascertain the fact that he is in frame O2. A velocity meter (which would actually take a reading of acceleration and record the velocity after making calculations) in his ship will tell him that he is in the frame O2. He again sends a pulse. Will the pulse hit the target and if yes, at what speed?

 

Remember that we are considering some real situation and we are not considering any laws of SR. To make a statement we just have a law about emission of light pulse. Now you have to apply (2) or (3) to find out how the pulse will travel in the spaceship when the spaceship is moving with a velocity v. (Note that observer in the ship cannot notice it without referring his meter. But light pulse knows.)

 

With this set up I am not considering SR at all. Einstein’s postulate, time dilation etc will appear only after we decide behavior of light pulse in the moving frame.

 

Note that we have to reject #1, because we know that velocity of light is always ‘c’. Now consider #2 or #3 (these are the only other possibilities) and tell me what observer in the moving ship should note about the path and speed of light pulse.

 

Behavior of light emission has to be a basic law which should override any postulate.

The light always hits the target, and in all frames. There can be no disagreement on whether or not that occurs.

 

The light is always measured to be traveling at c in all frames.

 

You cannot assign a velocity to any frame, because you cannot tell if you are at rest. If you accelerate, you don't know if you are at rest at the beginning of the acceleration or at the end, so there is no way to say that one frame represents being at rest. The behavior has to be the same in both frames. Speed is not absolute. It is always in reference to something else.

 

You can't ignore the effects of relativity, because they will be present. If you ignore them and the thought experiment gives you a contradiction, then it is one of the assumptions that could be wrong.

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I have taken two steps. First is to find out about the velocity of light. How a light pulse will travel in space, after it is emitted in a particular direction (say by a laser). I raised a question about it in my last post but could not get confident reply. Therefore I assumed three possible pictures. It is my belief that 3rd is true. In that case once light is emitted in a particular direction by the moving source, it keeps the direction and in that direction velocity of the pulse will be ‘c’.

 

However there can be two more options which I have stated.

 

We now take a second step. In this we consider only one frame. A train compartment or a spaceship. In this, an observer sends a pulse vertically up, in the y-direction. (This is a normal notation, so I have interchanged your x and y directions).

 

Please note that we are considering only one frame and not two. However any object that is in uniform speed can be considered to have zero velocity. Therefore we have to consider two situations.

 

In the spaceship, whatever might be the velocity of the ship, consider it zero (frame O1). Observer arranges target to receive the light pulse sent vertically up. Observer sends a pulse and is satisfied to see that the pulse hits the target fixed at a ceiling

 

Now the ship is accelerated to uniform speed v, w.r.t. O1. Ship is now in the frame O2. However for the observer in the ship, he will be always at zero speed unless he has some other object to compare his velocity with.

 

There is another way for him to ascertain the fact that he is in frame O2. A velocity meter (which would actually take a reading of acceleration and record the velocity after making calculations) in his ship will tell him that he is in the frame O2. He again sends a pulse. Will the pulse hit the target and if yes, at what speed?

The pulse will hit the target, at speed c.

Remember that we are considering some real situation and we are not considering any laws of SR.

SR is real. The laws of SR are real.

To make a statement we just have a law about emission of light pulse. Now you have to apply (2) or (3) to find out how the pulse will travel in the spaceship when the spaceship is moving with a velocity v. (Note that observer in the ship cannot notice it without referring his meter. But light pulse knows.)

 

With this set up I am not considering SR at all. Einstein’s postulate, time dilation etc will appear only after we decide behavior of light pulse in the moving frame.

 

Note that we have to reject #1, because we know that velocity of light is always ‘c’. Now consider #2 or #3 (these are the only other possibilities) and tell me what observer in the moving ship should note about the path and speed of light pulse.

The correct answer is that the light will hit the target, moving at c on a diagonal path relative to O1, but the person in the ship will still see it moving at c in the y-direction. You are saying that that is impossible because you have an unstated assumption about how velocities add, which contradicts SR.

Behavior of light emission has to be a basic law which should override any postulate.

Except that your "analysis" of light emission is making assumptions itself that you aren't noticing. Note all of your assumptions whenever you make a conclusion here - you are assuming that there is no time dilation and coming up with a contradiction.

=Uncool-

Edited by uncool
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The pulse will hit the target, at speed c.

SR is real. The laws of SR are real.

The correct answer is that the light will hit the target, moving at c on a diagonal path relative to O1, but the person in the ship will still see it moving at c in the y-direction. You are saying that that is impossible because you have an unstated assumption about how velocities add, which contradicts SR.

Except that your "analysis" of light emission is making assumptions itself that you aren't noticing. Note all of your assumptions whenever you make a conclusion here - you are assuming that there is no time dilation and coming up with a contradiction.

=Uncool-

 

If you consider SRT as sacrosanct, then there is nothing left for me to discuss.

 

 

 

The light always hits the target, and in all frames. There can be no disagreement on whether or not that occurs.

The light is always measured to be traveling at c in all frames.

You cannot assign a velocity to any frame, because you cannot tell if you are at rest. If you accelerate, you don't know if you are at rest at the beginning of the acceleration or at the end, so there is no way to say that one frame represents being at rest. The behavior has to be the same in both frames. Speed is not absolute. It is always in reference to something else.

You can't ignore the effects of relativity, because they will be present. If you ignore them and the thought experiment gives you a contradiction, then it is one of the assumptions that could be wrong.

 

 

Light will always hit the target only if it moves along the source.

If light velocity is always c in the vertical direction then this is possible only if light behaves like any other material object and its velocity c will no more be constant. At this point I wish to make it clear that I am considering light pulse, a package of photons. In the moving frame velocity of light can be c only in the diagonal direction.

All frames are equivalent is the fundamental concept of Galilean relativity. This is true because when spaceship or rail compartment moves, all objects in it move with that velocity. (All mechanical laws are same in all inertial frames).<BR style="mso-special-character: line-break">I think I am not wrong if I consider first, the way light is propagated before I consider any postulate about velocity of light. I have a problem here. I do not have any law that defines photon emission.

 

 

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Light will always hit the target only if it moves along the source.

If light velocity is always c in the vertical direction then this is possible only if light behaves like any other material object and its velocity c will no more be constant.

 

It's not constant in the vertical direction. Nobody has claimed that it is.

 

At this point I wish to make it clear that I am considering light pulse, a package of photons. In the moving frame velocity of light can be c only in the diagonal direction.

All frames are equivalent is the fundamental concept of Galilean relativity. This is true because when spaceship or rail compartment moves, all objects in it move with that velocity. (All mechanical laws are same in all inertial frames).<BR style="mso-special-character: line-break">I think I am not wrong if I consider first, the way light is propagated before I consider any postulate about velocity of light. I have a problem here. I do not have any law that defines photon emission.

How is "light moves at a constant speed in all frames" not a law that defines photon emission?

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If you consider SRT as sacrosanct, then there is nothing left for me to discuss.

 

I consider it to be correct, not sacrosanct, because I understand how it is proven from the postulates, and why the postulates are assumed.

 

 

Light will always hit the target only if it moves along the source.

If light velocity is always c in the vertical direction

It is not. It is always c in total. It is only c in the vertical direction when there is no other component to the velocity.

=Uncool-

Edited by uncool
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