What Happens to Light Speed When Measured from a Fast-Moving Space Station?

[zoobyshoe]

I'm on a space station in deep space. I depart in a rocket and accelerate to .5 c then level off to that speed. No longer accelerating, I now define myself to be stationary. I define the speed of anything I percieve to be in motion as relative to my own stipulated-to-be-unmoving inertial frame

On board I have a Michelson-Morley (or better) apparatus for measuring the speed of light. However, I am not going to measure the speed of any light that originates on my own ship. I am going to measure the speed of a beam of light that comes from the space station I just left.

At a prearranged time the space station sends this beam of light in exactly the same direction I am traveling.

When it catches up to me I measure it to be going:

A. c?

B. .5 c?

c. other ?

 

[jcsd]

A. c

second postulate

 

[Nereid]

On board I have a Michelson-Morley (or better) apparatus for measuring the speed of light. However, I am not going to measure the speed of any light that originates on my own ship. I am going to measure the speed of a beam of light that comes from the space station I just left.

At a prearranged time the space station sends this beam of light in exactly the same direction I am traveling.

When it catches up to me I measure it to be going

How, exactly, do you measure the speed of light from the space station?

 

[zoobyshoe]

I assumed it could be done since people have measured the speed of light from stars.

You're saying it can't be done?

 

[Nereid]

There are several methods by which one could measure the speed of light. Many of those who find SR hard to understand (or accept) feel that part of the 'problem' is the actual method of measuring the (local) speed of light.

In the case of your hypothetical experiment, I was wondering if you were getting at something special about the space station you had left (or would any distant source do)?

 

[zoobyshoe]

Any source would do, actually.

 

[zoobyshoe]

Another Speed Of Light Question

In the above situation (space station, rocket ship) my speed away from the station is .5 c. The speed of the light departing the space station in my direction is c.

If I am, say, 300,000 km away from the station ( a distance selected for convenience) when the light is emitted from the station, what math do I use to determine 1.) how long it will take for the light from the station to catch up to me and 2.) How far away from the station I will be when it does catch up?

 

[Doc Al]

Assuming you are 300,000 km away from the station as measured in your frame, then:

(1) The light must travel 300,000 km to reach you, so T = D/c = 1 sec.
(2) During that 1 sec the station has traveled a distance D = VT = 0.5cT = 150,000 km. So when the light reaches you you'll be a total of 450,000 km from the station.​

 

[Janus]

In the above situation (space station, rocket ship) my speed away from the station is .5 c. The speed of the light departing the space station in my direction is c.

If I am, say, 300,000 km away from the station ( a distance selected for convenience) when the light is emitted from the station, what math do I use to determine 1.) how long it will take for the light from the station to catch up to me and 2.) How far away from the station I will be when it does catch up?

As measured by you or the space station? If measured by you, the light will reach you in one sec and the station will be 450,000 km away when it reaches you.

If measured by the space station, then the light will reach you in 2 sec and you will be 600,000 km away from the station.

 

[zoobyshoe]

Sorry I wasn't clear.

In the second question I meant to change my definition of myself as being motionless to being in motion at .5c relative to the source of the light - the space station.

So, If I am traveling at .5 c away from the station, and the beam of light is emitted from the station when I am a distance of 300,000 km away, how long will the light take to reach me, and how far away will I be from the station?

 

[Janus]

Sorry I wasn't clear.

In the second question I meant to change my definition of myself as being motionless to being in motion at .5c relative to the source of the light - the space station.

So, If I am traveling at .5 c away from the station, and the beam of light is emitted from the station when I am a distance of 300,000 km away, how long will the light take to reach me, and how far away will I be from the station?

Doc Al and I both gave you the answer already: 1 sec and 450,000 km, assuming that you are making the measurements.

 

[zoobyshoe]

Doc Al and I both gave you the answer already: 1 sec and 450,000 km, assuming that you are making the measurements.

OK, What math did you use to arrive at the 2 sec, 600,000 km figures?

 

[Janus]

OK, What math did you use to arrive at the 2 sec, 600,000 km figures?

From the space stations perpective, the relative speed between the light it emits and you is .5c. Since it the distance between you and the station is 1 light sec at the time of emission, it takes 2 sec for the light to close the distance. If the light travels for 2 secs, it travels 600,000 km.

 

[zoobyshoe]

OK the space station viewpoint makes sense to me, but I don't understand how there could be a difference from my perspective.

If the light is emitted from the station when I am 300,000 km away from it, it will take the light one second to reach that point. Once that second has elapsed and the light has reached that point, I will no longer be there. It will be one second later, and at .5c, I will be 150,000 km farther away, the light will not have caught up with me yet. In the half second it takes the light to reach that point 150,000km away, I will have traveled yet further, and won't be there when it arrives. And so on, such that I'm thoroughly confused as to why it isn't also 2 seconds 600,000 km viewed from my perspective as well.

 

[Doc Al]

view from the ship

If the light is emitted from the station when I am 300,000 km away from it, it will take the light one second to reach that point.

The light travels at speed c with respect to you. And, with respect to you, "that point" is you! The fact that you are also moving with respect to something else (the spaceship) is irrelevant. No matter what speed you are moving, if the light flashes when it's 300,000 km away from you, it will reach you in one second.

Once that second has elapsed and the light has reached that point, I will no longer be there.

In your frame, you don't move. (You are at rest in your own frame.) In the frame of the station you are moving, but that doesn't matter.

It will be one second later, and at .5c, I will be 150,000 km farther away, the light will not have caught up with me yet.

Yes, you will be 150,000 km further from the station. And yes the light will have caught up with you!

Just remember that in your frame light travels 300,000 km/sec with respect to you.

 

[GOD__AM]

Hi, I'm new so please excuse me if I'm butting in. This is all very interesting but I'd like to add another observer to the seudo experiment. Assuming what Doc Ai and Janus are saying is correct (as far as I understand they are) then we get the following senario.

Let's say there are 2 space stations 450,000k apart. The rocket leaves the first station (call it "a") as outlined already heading towards space station "b". The light is still turned on when the rocket is 300,000k from space station "a".

Now the observer in the rocket sees the light from space station "a" when he is right beside space station "b" . Space station "b" cannot see the light for another 1/2 second.

Now let's suppose that the observer in the rocket has a mirror set up that aligns the light source from space station "a" with our observer at space station "b" as it passes so that he sees the light reflected from the rocket nearly a 1/2 second before he sees the light from space station "a". :surprise:

Hope I didn't botch that up too bad. It makes perfect sense to me (the experiment not the results that is).

 

[zoobyshoe]

The light travels at speed c with respect to you.And, with respect to you, "that point" is you! The fact that you are also moving with respect to something else (the spaceship) is irrelevant.

The light is moving at c in its direction of propagation. That is: at any given time, the tip of the beam of light is propagating away from the point in space from which it was emitted, at speed c.

My speed in the same direction is relevant with respect to the tip of that beam of light. The light cannot reach me in one second, because I am moving away from its approaching tip. And: I cannot be aware of the beam of light to calculate anything about its time until it first catches up with me. Were I able, by magic, to see the tip of the beam of light, I would not see it closing the distance between us at c. The time it takes for the light to reach me from the time I was at 300,000 km from the station must be greater than 1 sec.

Just remember that in your frame light travels 300,000 km/sec with respect to you.

If, once the light has caught up with me, I measure its speed, I will clock it to be going at c regardless of my speed in any inertial frame. Jcsd confirmed this above, and I believe this is the agreed result. Einstein used this mysterious fact as his second postulate.

That, however, is a separate issue from the fact that the tip of a beam of light is limited to propagation at c from its point of origin. It is for this reason that the space station could determine that there was a difference of .5 c between my speed, and the speed of the beam of light as it is on its way toward me.

 

[Doc Al]

The light is moving at c in its direction of propagation.

The light is moving at speed c with respect to the observer.

That is: at any given time, the tip of the beam of light is propagating away from the point in space from which it was emitted, at speed c.

No. From the viewpoint of the spaceship, the separation distance between the tip of the light beam and the space station increases at only 0.5 c. (It is only from the view of the space station that the light travels at speed c with respect to the space station.)

My speed in the same direction is relevant with respect to the tip of that beam of light. The light cannot reach me in one second, because I am moving away from its approaching tip.

Not true. You are moving away from the space station, but the light is still moving towards you at speed c. This is what "invariant speed of light" means.

And: I cannot be aware of the beam of light to calculate anything about its time until it first catches up with me. Were I able, by magic, to see the tip of the beam of light, I would not see it closing the distance between us at c. The time it takes for the light to reach me from the time I was at 300,000 km from the station must be greater than 1 sec.

The only way to measure the speed at which the light got to you is to know when and where it started. You'll have to imagine an extended spaceship frame--or another spaceship moving along with yours but located next to the space station at the very moment the light is emitted. Your sister spaceship has its clock synchronized to yours, and it is 300,000 km away from you. When the light reaches you, you note the time. Later you compare notes with the other ship, which tells you the time the light flashed: you will find that the light took 1 second to reach you, according to the synchronized clocks in the two ships.

If, once the light has caught up with me, I measure its speed, I will clock it to be going at c regardless of my speed in any inertial frame. Jcsd confirmed this above, and I believe this is the agreed result. Einstein used this mysterious fact as his second postulate.

Exactly right. But in your frame, the light only traveled 300,000 km to get to you. So it took 1 second.

That, however, is a separate issue from the fact that the tip of a beam of light is limited to propagation at c from its point of origin. It is for this reason that the space station could determine that there was a difference of .5 c between my speed, and the speed of the beam of light as it is on its way toward me.

The speed of light will always be c with respect to whatever observer is making the measurement. That does not mean that from your point of view that light cannot separate from a moving object at some speed less than c. Of course it can.

 

[zoobyshoe]

Thanks for your patience, Doc Al. I have never explored this in such detail, and these answers are not what I expected.

If I reverse the direction of the rocket in the set up, then, to be headed toward the station, I take it that a beam of light emitted from the station when I am 300,000 km from the station will also reach me in one second, from my viewpoint, however: I will be only 150,000 km from the station when I detect it?

 

[plover]

If I reverse the direction of the rocket in the set up, then, to be headed toward the station, I take it that a beam of light emitted from the station when I am 300,000 km from the station will also reach me in one second, from my viewpoint, however: I will be only 150,000 km from the station when I detect it?

Linguistic point:
The phrasing used here (e.g. "headed toward the station") carries the connotation that the rocket is moving and the station is stationary, which is, of course, the familiar setup - vehicles move and destinations don't. However, part of the essence of special relativity is that describing events for a given observer must always presume that observer as being at rest.

Thus while the mindset of a person on the rocket might be "I am approaching the station at .5c", the necessary viewpoint for setting up any special relativistic calculations is "the rocket is at rest, the station is approaching the rocket at .5c".

Once that framework is established, it becomes easier to see that a photon emitted from a station 300k km away takes 1 second to reach the rocket (since the rocket is at rest) no matter the velocity of the station.

My point is that it's easy for intuitive descriptions of a situation to carry assumptions that conflict with the requirements of the formal model.

 

[zoobyshoe]

My point is that it's easy for intuitive descriptions of a situation to carry assumptions that conflict with the requirements of the formal model.

Point taken.

So, If I am at rest in my rocket with the station approaching me at .5 c and it emits a beam of light when it is 300,000 km away, I take it I will detect the light one second later, but the station will be 150,000 away at the moment I detect the light?

 

[plover]

Yes.

And you now have one second left to figure out how to avoid a collision...

 

[Olias]

Moral:
Dont try and signal the incoming station with some kind of " Morse-flashlight"!

Switch off all non essential onboard lighting, close one's eyes and hope that Shroedinger's Cat exists as a physical process!

 

[zoobyshoe]

Yes.

And you now have one second left to figure out how to avoid a collision...

Not sure it can be avoided:

The one second time for my reception of the light signal seems to me to be directly at odds with Einstein's understanding of the same situation as laid out in chapter IX of SR, The Relativity of Simultaneity

Here Einstein says:

"Are two events (e.g. the two strokes of lightning A and B) which are simultaneous with reference to the railway embankment also simultaneous relatively to the train.? We shall show directly that the answer must be in the negative.

When we say that the lightning strokes A and B are simultaneous with respect to the embankment, we mean: the rays of light emitted at the places A and B, where the lightning occurs, meet each other at the mid-point M of the length A ---->B of the embankment. But the events A and B also correspond to the positions A and B on the train. Let M' be the mid-point of the distance A---->B on the traveling train. Just when the flashes¹ of lightning occur, this point M' naturally coincides with the point M, but it moves toward the right in the diagram with the velocity v of the train. If an observer sitting in the position M' in the train did not possesses this velocity, then he would remain permanently at M, and the light rays emitted by the flashes of lightning A and B would reach him simultaneously, i.e. they would meet just where he is situated. Now in reality (considered with reference to the railway embankment) he is hastening toward the beam of light coming from B, whilst he is riding on ahead of the beam of light coming from A. Hence the observer will see the beam of light emitted from B earlier than he will see that emitted from A.

_{1 As judged from the embankment.}

If we substitute the situation where the space station is approaching me (from my perspective) for the situation where the observer on the train is approaching the flash of light from point B, you can see that Einstein would not reakon the time between the flash and when I detect it to be one second, rather, less than a second.

Likewise, if we substitute the situation where the station is moving away from me for the situation where the observer on the train is moving away from the flash of light at point A, you can see that Einstein would not reakon the time between the flash of light and when I detected it to be one second, but something greater than one second.

If, I detect the time of the light's travel to be one second coming or going, then Einstein has no basis on which to build his case for what he calls The Relativity of Simultaneity

Chapter 9. The Relativity of Simultaneity. Einstein, Albert. 1920. Relativity: The Special and General Theory
Address:http://www.bartleby.com/173/9.html

 

[plover]

The observer in the rocket is the equivalent of the person on the railway embankment who sees the flashes simultaneously.

It is often the case that effects in relativity can appear paradoxical if only some of the effects are accounted for. When the mathematical formalism is used, these problems tend to disappear.

I assume the situation presented by Einstein is thus:

Points A and B are two points on a perfectly straight rail track. Observer X is at the midpoint between A and B. The midpoint of a train which X would measure as having a length equal to the distance from A to B is passing X at .5c. At the same moment (as measured in the rest frame of X and the track) photons are emitted at A and B. Observer Y is positioned at the midpoint of the train.​

I will assume it is uncontroversial that these photons reach X simultaneously.

I will also assume that it is uncontroversial that the back of the train is at A when the photon is emitted at A, and that the front of the train is at B when the photon is emitted at B.

Now in order to see why these flashes do not reach Y simultaneously we first note that the train appears length contracted to X. Thus the length of the train at rest is actually longer than distance between A and B. Y, being at rest relative to the train, experiences the train as having that longer length. In addition, an observer on the train would measure the track as length contracted, so A and B are closer together for Y than for X.

So, according to Y, when the front of the train reaches B and the photon is emitted at B, the back end of the train is still (if I'm remembering my formulas right) 1/4 the length of the train away from A.

Thus, though Y would say that the photons traveled equal distances to reach the train's midpoint, Y would not say they were emitted at the same moment.

 

[zoobyshoe]

The observer in the rocket is the equivalent of the person on the railway embankment who sees the flashes simultaneously.

This is incorrect. The observer on the train is the counterpart to me in the rocket.

Please go to the link I edited in in my post above for the complete text of that chapter written by Einstein as well as the diagram referred to.

 

[plover]

The observer on the train is the counterpart to me in the rocket.

It is, of course, possible to construct an analogy where the observer on the train corresponds to the person in the rocket. In doing this, however, it is also necessary to state what the station(s) and any other relevant objects correspond to in the train scenario.

If you think the scenario I laid out in my previous post is somehow unfaithful to Einstein's thought experiment, could you explain?

I also note that the quote you give from the article describes what X predicts that Y will see (i.e. it is not a statement from the point of view of Y).

Chapters 10-12 of the Einstein article go over more about length contractions.

 

[Doc Al]

If I reverse the direction of the rocket in the set up, then, to be headed toward the station, I take it that a beam of light emitted from the station when I am 300,000 km from the station will also reach me in one second, from my viewpoint, however: I will be only 150,000 km from the station when I detect it?

That is absolutely correct. If the light flashes when it's 300,000 km from you, then it will reach you in 1 second regardless of your speed with respect to the light source. (Note that all measurements are made from your rocket frame.)

 

[Doc Al]

Einstein's train

If we substitute the situation where the space station is approaching me (from my perspective) for the situation where the observer on the train is approaching the flash of light from point B, you can see that Einstein would not reakon the time between the flash and when I detect it to be one second, rather, less than a second.

Right! As measured by observers on the space station, the light reaches you in less than a second.

Likewise, if we substitute the situation where the station is moving away from me for the situation where the observer on the train is moving away from the flash of light at point A, you can see that Einstein would not reakon the time between the flash of light and when I detected it to be one second, but something greater than one second.

Right again! As measured by observers on the space station, in this case the light takes more than a second to reach you.

If, I detect the time of the light's travel to be one second coming or going, then Einstein has no basis on which to build his case for what he calls The Relativity of Simultaneity

Not so fast. Einstein's train example had two events (lightning strikes) happening simultaneously when observed in one frame and he showed that they must happen at different times according to the other frame. Nothing in your example contradicts this.

Everything you've said so far agrees with Einstein. To see how simultaneity fits in, consider how you measured the time between when the light was emitted and when you detected it in your rocket: Remember that you needed a second rocket in your frame (moving at the same speed as you) that just happens to pass the station when the light flashes. That rocket measures the time when the light was emitted, and you find out that the light reaches you 1 second later. But what does the space station think about the clocks in your frame? For one thing, the station frame does not agree that your two clocks are synchronized! According to measurements made in the space station frame: (1) your rocket clocks are out of synch, (2) your rocket clocks are operating slowly compared to station clocks (time dilation), and (3) the distance that you think is 300,000 km is really smaller (length contraction).

To really understand how to compare measurements made in the different frames, you need to consider all of those relativistic effects operating together. But everything is perfectly consistent with the reasoning we used from the rocket frame in determining that the light took 1 second (rocket time) to get from the station to the rocket. We didn't need to take all that stuff into consideration because we assumed that all measurements were made by the rocket frame: the distance the light traveled (measured by rocket rulers), the time light traveled (measured by rocket clocks). Of course these better combine to get the proper speed of light--measured by the rocket!

 

[zoobyshoe]

That is absolutely correct. If the light flashes when it's 300,000 km from you, then it will reach you in 1 second regardless of your speed with respect to the light source. (Note that all measurements are made from your rocket frame.)

This seems to be at odds with what Einstein understood would happen, as I pointed out above.

 

[zoobyshoe]

Right! As measured by observers on the space station, the light reaches you in less than a second.

Incorrect. The light from point B reaches me in less that one second as measured by me on the train (rocket). Einstein: "Hence the observer will see the beam of light emitted from B earlier than he will see that emitted from A." He is talking about the observer on the train (rocket). If you go to the link you'll see that he specifies this in the next sentence: "Obervers who take the railway train as their reference-body must therefore come to the conclusion that the lightning flash B took place earlier than the lightning flash A." The train, moving relative to the flashes of lightning, is the inertial frame which sees the flash it is "hastening toward" before the one it is "riding on ahead of".

Right again! As measured by observers on the space station, in this case the light takes more than a second to reach you.

Incorrect. As perceived by the observer on the train (rocket). You have argued that the observer on the train will percieve both flashes to take the same amount of time to reach him ( 1 sec, coming or going). Einstein is saying something else. Einstein is saying the observer on the train will ascribe a time of less than 1 sec for the flash he is "hastening toward", and a time greater than 1 sec for the flach he is "riding on ahead of".

Not so fast. Einstein's train example had two events (lightning strikes) happening simultaneously when observed in one frame and he showed that they must happen at different times according to the other frame. Nothing in your example contradicts this.

Yes, I am demonstrating by direct quotation from Einstein, that you do not agree with him on what the observer on the train will see. You have argued that the observer on the train will see the flashes of lightning as simultaneous: 1 sec coming or going. Einstein said: "Hence the observer will see the beam of light emitted from B earlier than he will see that emitted from A." In all cases the light has been emitted at exactly the same distance from the observer, train or rocket.

Everything you've said so far agrees with Einstein. To see how simultaneity fits in, consider how you measured the time between when the light was emitted and when you detected it in your rocket:...

None of that is relevant to which flash of light is seen first.

To really understand how to compare measurements made in the different frames, you need to consider all of those relativistic effects operating together...

Yes, but not relevant here. What is relevant is that Einstein believed that the observer on the train will see the flash he is "hastening toward" before the flash he is "riding on ahead of" despite the fact they were both emitted at the same distance from him.

If you argue that I, in my rocket ship, will see the flash of light 1 sec after it is emitted when the station is 300.000 kms away regardless of whether the station is "hastening toward" me, or whether it is "riding on ahead of" me, then Einstein has no basis on which to build his argument for what he calls The Relativity of Simultanaity. By your argument, the observer on the train will judge the flashes as simultaneous.

 

[zoobyshoe]

It is, of course, possible to construct an analogy where the observer on the train corresponds to the person in the rocket. In doing this, however, it is also necessary to state what the station(s) and any other relevant objects correspond to in the train scenario.

I did this in my post above:

If we substitute the situation where the space station is approaching me (from my perspective) for the situation where the observer on the train is approaching the flash of light from point B, you can see that Einstein would not reakon the time between the flash and when I detect it to be one second, rather, less than a second.

Likewise, if we substitute the situation where the station is moving away from me for the situation where the observer on the train is moving away from the flash of light at point A, you can see that Einstein would not reakon the time between the flash of light and when I detected it to be one second, but something greater than one second.

If you think the scenario I laid out in my previous post is somehow unfaithful to Einstein's thought experiment, could you explain?

I didn't respond to the bulk of your post because it started with the false premise that the observer in the rocket corresponded to someone on the embankement in Einstein's version. That is false.

I also note that the quote you give from the article describes what X predicts that Y will see (i.e. it is not a statement from the point of view of Y).

This is false. The quote from Einstein does not contain any predictions by one observer about what another will see.

 

[Doc Al]

your example differs from Einstein's

For some reason, you are mixing up Einstein's train example with your rocket example. They are not identical. (For one, the train embankment observers see two events happen simultaneously.) But if you understand Einstein's reasoning, then you can certainly apply it to your rocket and space station example as appropriate.

Don't make the naive comparison that since the train is "moving" that the train corresponds to the rocket in your example. It's not that simple.

Incorrect. The light from point B reaches me in less that one second as measured by me on the train (rocket). Einstein: "Hence the observer will see the beam of light emitted from B earlier than he will see that emitted from A." He is talking about the observer on the train (rocket). If you go to the link you'll see that he specifies this in the next sentence: "Obervers who take the railway train as their reference-body must therefore come to the conclusion that the lightning flash B took place earlier than the lightning flash A." The train, moving relative to the flashes of lightning, is the inertial frame which sees the flash it is "hastening toward" before the one it is "riding on ahead of".

There is nothing wrong with Einstein's reasoning, but you misapply it to your rocket example. In Einstein's example, embankment observers see the light from B approach them at speed c. And they also see the train moving towards B. So they agree that the light from B reaches the train before it reaches the midpoint of the embankment. Everyone agrees that the train sees the light from B before the light from A.

What do the train observers think? If the lights were switched on just at the moment they passed the midpoint, then they would agree that the light from A and B would reach them at the same time. (To them, the light approaches at speed c.) After all, it's just the distance that the light source is from them when it flashes that matters, not how fast the light source is moving. But we know that the light from B reaches the train first, so the train observers deduce that in their frame the lights were not turned on simultaneously.

Now let's turn to your rocket example. What do we know? All we know is that according to the rockets the light was switched on when the light was 300,000 km from your rocket. And the rocket measures the speed of light to be c, so it takes 1 second for the light to reach the rocket. Where's the problem? All measurements are in the rocket frame. Now it is certainly true that the space station observers see the rocket approach them while the light moves away from them at speed c. So what? They measure different times and distances as well.

Incorrect. As perceived by the observer on the train (rocket). You have argued that the observer on the train will percieve both flashes to take the same amount of time to reach him ( 1 sec, coming or going). Einstein is saying something else. Einstein is saying the observer on the train will ascribe a time of less than 1 sec for the flash he is "hastening toward", and a time greater than 1 sec for the flach he is "riding on ahead of".

Again, you seem to naively compare Einstein's example to your own. They are not the same. Einstein is merely saying that the observers on the embankment can deduce that the light will take less time to reach the train because the train is moving towards the light source. So what?

Yes, I am demonstrating by direct quotation from Einstein, that you do not agree with him on what the observer on the train will see. You have argued that the observer on the train will see the flashes of lightning as simultaneous: 1 sec coming or going. Einstein said: "Hence the observer will see the beam of light emitted from B earlier than he will see that emitted from A." In all cases the light has been emitted at exactly the same distance from the observer, train or rocket.

Again, you take a statement I made about your rocket example and misapply it to Einstein's train example. They are not the same. I assure you that Einstein would agree that any observer will measure light to move at speed c (with respect to themselves) regardless of the motion of the light source.

None of that is relevant to which flash of light is seen first.

Again, you mix examples. In Einstein's example there are two flashes; in yours only one.

Yes, but not relevant here. What is relevant is that Einstein believed that the observer on the train will see the flash he is "hastening toward" before the flash he is "riding on ahead of" despite the fact they were both emitted at the same distance from him.

The reason that the train observers see the lights arrive at different times is that according to the train clocks light B was turned on first!

If you argue that I, in my rocket ship, will see the flash of light 1 sec after it is emitted when the station is 300.000 kms away regardless of whether the station is "hastening toward" me, or whether it is "riding on ahead of" me, then Einstein has no basis on which to build his argument for what he calls The Relativity of Simultanaity. By your argument, the observer on the train will judge the flashes as simultaneous.

Well I certainly make that argument in analyzing your rocket example. But you mistakenly think it directly applies to Einstein's train as well. But the train observers see light B turn on first: when the train passes the midpoint, the light from B is well on its way--and the light at A hasn't even turned on yet!

You may want to strengthen your understanding of Einstein's train gedanken experiment.

 

[zoobyshoe]

For some reason, you are mixing up Einstein's train example with your rocket example. They are not identical. (For one, the train embankment observers see two events happen simultaneously.) But if you understand Einstein's reasoning, then you can certainly apply it to your rocket and space station example as appropriate.

There is no mixup: they are identical. The lighning flashes are simultaneous, not to the embankment in general, but at one specific spot: the exact midpoint M between point A and point B. Einstein: "When we say that the lightning strokes A and B are simultaneous with respect to the embankment, we mean: the rays of light emitted at the places A and B, where the lightning occurs, meet each other at the mid-point M of the length A---->B of the embankment."

This mid-point M corresponds to the distance 300,000 kms from the space station in my rocket example because the light is emitted, in the train scenario, exactly at the moment the observer on the train is at the mid-point M between the two points. The observer continues to move and encounters the flash from B before the flash from A by his own reckoning not as seen from the embankment. The flash he perceives from point B corresponds to the flash from the space station as my rocket approaches it, (or it approaches my rocket if you want to define it that way) and the flash from point A corresponds to the flash from the space station as I am moving away from it (or it away from me).

The mid point M in the train scenario corresponds to the distance 300,000 kms in the rocket scenario because it is the same distance in the example where the station is approaching me, and also in the example where the station is moving away from me. In both cases the station emits light when the distance bewteen the station and my ship is 300,000 kms.

To make this as clear as possible let's say that when the distance between point A and point B in the train scenario was measured it proved to be exactly 600,000 kms. The midpoint, therefore, is located 300,000 kms from both A and B. Any value for the distance will do as long as point M is exactly midway between A and B. Using 300,000 kms helps you to see how the rocket example is the same as the train.

In Einstein's example, embankment observers see the light from B approach them at speed c. And they also see the train moving towards B. So they agree that the light from B reaches the train before it reaches the midpoint of the embankment. Everyone agrees that the train sees the light from B before the light from A.

In Einstein's example any observation anyone on the embankment might have about what the observer on the train sees is unimportant, and Einstein doesn't even mention it. What is important about any person on the embankment is that they will see the flashes of light from both directions at exactly the same time. That is important because Einstein wants to contrast it with what the observer on the train will see.

It is important to note that when the flashes occur, the observer on the train is located at the midpoint M between the two flashes. However, he moves away from that spot before the flashes arrive. The result is that he detects flash B before flash A, in spite of the fact he was at the midpoint when they occured!

By this reasoning, I would not detect the light beam from the space station, emitted when the distance between my rocket and the station was 300,000 kms, to be 1 sec, in any case of relative motion toward or away from the station (or it toward or away from me) By Einstein's reasoning, I will detect it in less than a second when the distance between my ship and the station is closing at .5c, and I will detect it in some time greater than 1 sec. when the distance between my ship and the station is widening at .5 c.

Again, If I detect it to be 1 sec coming or going Einstein has no basis upon which to build his case for what he calls The Relativity of Simultaneity.

 

[jcsd]

I don't see ythe problem here, the confusion here is 1 sec for who? and 300,000 km, in whose reference frame? It's clear that the person on the rocket ship who measures the distnace to the spacestaion to be 300,000 km when the light is emitted, will measure the time taken for that light to cover that distance will be 1 second. It doesn't need any calculations or any thought experimnets to prove as it's a postulate of special relativity.

 

[zoobyshoe]

I don't see ythe problem here, the confusion here is 1 sec for who? and 300,000 km, in whose reference frame? It's clear that the person on the rocket ship who measures the distnace to the spacestaion to be 300,000 km when the light is emitted, will measure the time taken for that light to cover that distance will be 1 second. It doesn't need any calculations or any thought experimnets to prove as it's a postulate of special relativity.

True, a postulate is a postulate. However, in this case, going by the postulate leads to a situation where there is no Relativity of Simultaneity. Going by the postulate, Einstein's observer on the train should see both light flashes as simultaneous. Einstein says he won't, however.

 

[jcsd]

No, it's not inconsistent with the relativity of simulatneoty I think what you're missing is what the observer on the space station sees:

When the light is emitted, the rocket is approximately 340,000 km away, when it arrives at the rocket it is approximately 170,000 km away as viewed by the space station, and thus took approximately 0.6 secs to arrive at the rocket. You cannot ignore the fact that length and time change with reference frame when comparing the two examples.

 

[Doc Al]

There is no mixup: they are identical. The lighning flashes are simultaneous, not to the embankment in general, but at one specific spot: the exact midpoint M between point A and point B. Einstein: "When we say that the lightning strokes A and B are simultaneous with respect to the embankment, we mean: the rays of light emitted at the places A and B, where the lightning occurs, meet each other at the mid-point M of the length A---->B of the embankment."

You are mixed up. In Einstein's example, the lightning flashes are simultaneous in the frame of the embankment. I have no idea what you mean by simultaneous at one specific spot.

This mid-point M corresponds to the distance 300,000 kms from the space station in my rocket example because the light is emitted, in the train scenario, exactly at the moment the observer on the train is at the mid-point M between the two points.

In Einstein's example the midpoint M is a fixed distance from the source B in the embankment frame. So, by analogy, your rocket frame corresponds to the embankment frame. (Sort of.) You've gotten them mixed up.

The observer continues to move and encounters the flash from B before the flash from A by his own reckoning not as seen from the embankment. The flash he perceives from point B corresponds to the flash from the space station as my rocket approaches it, (or it approaches my rocket if you want to define it that way) and the flash from point A corresponds to the flash from the space station as I am moving away from it (or it away from me).

The moving train corresponds to your space station frame. At least it would if your example were comparable to Einstein's, but it's not.

The mid point M in the train scenario corresponds to the distance 300,000 kms in the rocket scenario because it is the same distance in the example where the station is approaching me, and also in the example where the station is moving away from me. In both cases the station emits light when the distance bewteen the station and my ship is 300,000 kms.

It would make more sense if there was a moving observer at that midpoint. But there isn't is there?

To make this as clear as possible let's say that when the distance between point A and point B in the train scenario was measured it proved to be exactly 600,000 kms. The midpoint, therefore, is located 300,000 kms from both A and B. Any value for the distance will do as long as point M is exactly midway between A and B. Using 300,000 kms helps you to see how the rocket example is the same as the train.

The example with the train is very clear. What's not clear is what it has to do with your rocket? If the "rocket" is the midpoint, where's the moving train that passes by at just the right moment?

In Einstein's example any observation anyone on the embankment might have about what the observer on the train sees is unimportant, and Einstein doesn't even mention it. What is important about any person on the embankment is that they will see the flashes of light from both directions at exactly the same time. That is important because Einstein wants to contrast it with what the observer on the train will see.

No, Einstein uses the observations from the embankment to conclude draw conclusions about what actually happens and what the train sees. He deduces from what the embankment must see that the light reaches the moving train at different times. (Both frames agree with this.) And then the observers on the train use that fact to deduce that those lights cannot have been flashed simultaneously.

It is important to note that when the flashes occur, the observer on the train is located at the midpoint M between the two flashes.

Careful! To the observer on the train the flashes do not occur at the moment he passes the midpoint--they can't, since they happen at different times. Only from the embankment are the flashes observed to be simultaneous.

However, he moves away from that spot before the flashes arrive. The result is that he detects flash B before flash A, in spite of the fact he was at the midpoint when they occured!

It would be a contradiction to the basic assumption of the invariant speed of light if this were true. But it's not. In his frame, the flashes did not occur when he was at the midpoint.

By this reasoning, I would not detect the light beam from the space station, emitted when the distance between my rocket and the station was 300,000 kms, to be 1 sec, in any case of relative motion toward or away from the station (or it toward or away from me) By Einstein's reasoning, I will detect it in less than a second when the distance between my ship and the station is closing at .5c, and I will detect it in some time greater than 1 sec. when the distance between my ship and the station is widening at .5 c.

Your reasoning is incorrect, as I have explained. Don't blame Einstein.

Again, If I detect it to be 1 sec coming or going Einstein has no basis upon which to build his case for what he calls The Relativity of Simultaneity.

Sorry, but you don't seem to understand Einstein's argument. And, on top of that, you are misapplying Einstein's argument in comparing it to your rocket example.

I recommend that you work to understand Einstein's simple argument for the relativity of simultaneity. Maybe this will help: https://www.physicsforums.com/showpost.php?p=229410&postcount=2

 

[plover]

I did this in my post above

If we substitute the situation where the space station is approaching me (from my perspective) for the situation where the observer on the train is approaching the flash of light from point B, you can see that Einstein would not reakon the time between the flash and when I detect it to be one second, rather, less than a second.

Likewise, if we substitute the situation where the station is moving away from me for the situation where the observer on the train is moving away from the flash of light at point A, you can see that Einstein would not reakon the time between the flash of light and when I detected it to be one second, but something greater than one second.

Ok, I see that you want to set stations as being at the points A and B on the train tracks. As Doc Al noted, you have to be careful here. To fill out the analogy, we can stick someone else in a rocket that's half way between the stations, and at rest with respect to the stations. We'll call this observer X. Now, the original specification of the scenario is that the flashes are simultaneous in X's reference frame - not yours.

Suppose you have a long rigid filament stretched out to the front and back of your rocket to correspond to the rest of the train. X says that each station emitted a flash at the same moment that you passed him, and that this is the same moment as the ends of the filament passed the stations.

Now remember, since you're in motion with repect to X, the filament appears length contracted to X. In your frame of reference the filament is not length contracted. Thus if X says that the length of the filament corresponds to the distance between the two stations, then to you, the filament must have a length that is greater than that, and therefore if each flash originates just as the end of the filament passes the station, then to you the flashes could not have originated simultaneously.

(See also below for warnings about the observer on the train regarding themself as being in motion.)

I didn't respond to the bulk of your post because it started with the false premise that the observer in the rocket corresponded to someone on the embankement in Einstein's version. That is false.

The bulk of my post contains no direct comparison to the rocket scenario. Its logic can be analyzed without reference to any outside analogy.

This is false. The quote from Einstein does not contain any predictions by one observer about what another will see.

The form that Einstein's argument takes over the course of the essay is to present the conclusions that can be drawn by a person on the embankment, and to show which common assumptions must be discarded in order to remove apparent contradictions that arise. It is not until the later sections of the essay (starting in Ch 11) that he starts showing what removing these assumptions implies for how time and space measurements differ for the observer on the train compared to the person on the ground.

You quote:

Now in reality (considered with reference to the railway embankment) he is hastening towards the beam of light coming from B, whilst he is riding on ahead of the beam of light coming from A.​

Note that the "hastening towards" and "riding ahead" going on here are "considered with reference to the railway embankment". Remember - an observer on the train must regard the train as being at rest. An observer in special relativity can never describe themself as "hastening" or "riding" anywhere!

The quote continues:

Hence the observer will see the beam of light emitted from B earlier than he will see that emitted from A. Observers who take the railway train as their reference-body must therefore come to the conclusion that the lightning flash B took place earlier than the lightning flash A.
​

These statements are a conclusion (note the "hence") that can be drawn by the observer on the embankment (X) about what the observer on the train (Y) will see.

Thus Einstein is noting that X can conclude from his own space and time measurements that Y will see the photon from B before seeing the photon from A, but there is nothing that yet describes how time and space are arranged from Y's perspective.

One thing to keep in mind here is that observers in any inertial reference frame will agree on the order of events for any given spatial coordinate in other reference frames (thus both X and Y will agree on the order of events that each will see as X occupies a specific coordinate in X's reference frame and Y occupies a specific coordinate in Y's reference frame. What observers disagree on is whether events that are separated spatially in both frames are simultaneous (a difference which can lead to changes in the overall order of events depending on the particular reference frame).

 

[zoobyshoe]

No, it's not inconsistent with the relativity of simulatneoty I think what you're missing is what the observer on the space station sees:

In the Einstein train scenario transferred to space, there is no observer at the space station. Nothing observed by any observer in the space stations inertial frame is of importance except to confirm, I suppose, that the observer in the rocket is located at exactly 300.000 kms from the station when the station emits light. We really don't need an observer for that because Einstein stipulates it.

When the light is emitted, the rocket is approximately 340,000 km away...

I have no idea where you are getting 340,000 km. It is stipulated that when the light flashes the observer in the rocket is 300,000 away from the station. It is a stipulation in both Einstein's train scenario (the observer on the train is at the midpoint when the light flashes) and the rocket scenario.

You cannot ignore the fact that length and time change with reference frame when comparing the two examples.

We can't take length and time dilation into account at all yet. Einstein is setting up his case for the existence of time dilation with this very scenario. Relativity of Simultaneity preceeds time and length dilation. He must first demonstrate Relativity of Simultaneity, in order to show why there is a need for time and length dilation. No Relativity of Simultaneity, no different reckoning of time in different reference frames.

Somehow, the postulate that light always propagates at c in all reference frames has gotten in the way of The Relativity of Simultaneity. I am surprised. This is passing strange.

 

[zoobyshoe]

Now remember, since you're in motion with repect to X, the filament appears length contracted to X.

This filament and midpoint observer are completely unnecessary since Einstein stipulates that the flashes occur when the train observers position coincides with the midpoint between A and B. Also, as I pointed out to jcsd, at this point we aren't concerned with any time or length dilations. We have no need of them. They are immaterial to his point.

The form that Einstein's argument takes over the course of the essay is to present the conclusions that can be drawn by a person on the embankment,

In this chapter Einstein's point is to show there will be a difference of perception of when the flashes of light occur between the two reference frames: the moving train, and the embankment. He is not describing the embankment observers notion of what the observer on the train will see. He describes what the embankment observer will see, and separately, what the train observer will see. Neither speculates about what the other sees.
You quote:

The quote continues:

Hence the observer will see the beam of light emitted from B earlier than he will see that emitted from A. Observers who take the railway train as their reference-body must therefore come to the conclusion that the lightning flash B took place earlier than the lightning flash A.
​

These statements are a conclusion (note the "hence") that can be drawn by the observer on the embankment (X) about what the observer on the train (Y) will see.

I am astonished that you can accurately quote him as saying "Observers who take the railway train as their reference-body must therefore come to the conclusion that the lightning flash B took place earlier than the lightning flash A," and maintain he is talking about something an observer on the embankment is speculating about. Are you just yanking my chain?

Thus Einstein is noting that X can conclude from his own space and time measurements that Y will see the photon from B before seeing the photon from A, but there is nothing that yet describes how time and space are arranged from Y's perspective.

If what you just said here were true Einstein would have had no reason to write this chapter and call it The Relativity of Simultaneity. Where's the story, if all we're talking about is what the embankment observer sees vs what he thinks the train observer sees?

Back to the problem: If the calculation of 1 sec, 150,000 km for one flash, and 1 sec 450,000 km for the other flash is correct, then: 1 sec = 1 sec, and both the train observer and the embankment observer detect the flashes to be simultaneous. This leads to the conclusion there is no Relativity of Simultaneity. How can that be?

 

[jcsd]

In the Einstein train scenario transferred to space, there is no observer at the space station. Nothing observed by any observer in the space stations inertial frame is of importance except to confirm, I suppose, that the observer in the rocket is located at exactly 300.000 kms from the station when the station emits light. We really don't need an observer for that because Einstein stipulates it.

Clearly the train scenario relies on two different inertial observers, otherwise the relativity on simultaneity cannot be demonstrated. Indeed if we're only talking about 1 inertial observer we needn't really bring in relativity to such a simple problem as long as we remember than the speed of light for that inertial observer will be c.

I have no idea where you are getting 340,000 km. It is stipulated that when the light flashes the observer in the rocket is 300,000 away from the station. It is a stipulation in both Einstein's train scenario (the observer on the train is at the midpoint when the light flashes) and the rocket scenario.

A got the the figures of 340,000 and 170,000 by simply applying a Lorentz transformation to the 4-vector postion of the space station a) when the light is emitted b) when it arrives. I think this is the vital point that you're missing that the distance between the rocket and the space station are NOT the same for the two different observers.

We can't take length and time dilation into account at all yet. Einstein is setting up his case for the existence of time dilation with this very scenario. Relativity of Simultaneity preceeds time and length dilation. He must first demonstrate Relativity of Simultaneity, in order to show why there is a need for time and length dilation. No Relativity of Simultaneity, no different reckoning of time in different reference frames.

No time dialtion and length contraction do not require the relativity of simultaneity to be demonstarted, they can be demonstrated with two events that have a definite ordering in 2 different reference frames. Indeed in the situation we describe there is no need to consider the relativity of simulatenoty (and if there was it would arise naturally out of considering time dialtion and length contraction) as both observers observe the light to be emitted before it hits the spaceship.

Somehow, the postulate that light always propagates at c in all reference frames has gotten in the way of The Relativity of Simultaneity. I am surprised. This is passing strange.

It doesn't get in the way it is easy to demonstare that both situations are consistent with relativity.

 

[zoobyshoe]

Clearly the train scenario relies on two different inertial observers,

Agreed.

otherwise the relativity on simultaneity cannot be demonstrated.

Indeed if we're only talking about 1 inertial observer we needn't really bring in relativity to such a simple problem as long as we remember than the speed of light for that inertial observer will be c.

Right.

Lets ask though, if we need an observer at the space station? What would the space station correspond to in Einsteins's train scenario? It would correspond to point A or point B. These are the points at which the lightning hits the tracks. As space stations they are the points at which light is emitted. Did Einstein put any observers at points A or B? He did not. This is why I said we don't need an observer at the space station.

We do need an observer in the space station's inertial frame, though, as you pointed out. Where do we put him? Where did Einstein put him? At point M, the mid point between lightning flash A and lightning flash B.

What is that observer going to see? We don't have to calculate this or figure it out in any way. Einstein has carefully controlled everything in order that the observer at point M sees the two flashes of light as simultaneous. That is: he has carefully measured the distance from point A--->M and from B---->M, and determined them to be the same, and then he has stipulated that light will always travel at the same speed, regardless of direction of travel.

Because the two distances the light will travel are the same, and because light has been stipulated by Einstein to always travel at the same speed, there is no doubt whatever that the light from both lightning strikes will arrive at point M simultaneously.

That is why I said we don't need an observer at the space station: for the same reason we don't need an observer at the points where lightning strikes the rails. Einstein didn't have any observers at the point where lightning struck the rails. Why do we need anyone at the space station?

As for the observer who is at point M I said "We don't really need an observer for that because Einstein stipulates it." This was not incorrect. I am saying that Einstein has controlled all the conditions so carefully that there is no doubt about what an actual person at point M will see. He can't see anything but simultaneous flashes of light from A and B. That being the case, we don't actually have to station a person there to know what he'd see.

So we don't need an observer at the space station, and we have taken care of what the potential observer at point M (which would be a point 300,000 km from the space station on the rockets path in that example) will see by stipulation. There we have our two different inertial frames: one observer on the train, and one at point M.

I'll stop here to see if you understand and agree or disagree.

 

[jcsd]

Agreed.


Right.

Lets ask though, if we need an observer at the space station? What would the space station correspond to in Einsteins's train scenario? It would correspond to point A or point B. These are the points at which the lightning hits the tracks. As space stations they are the points at which light is emitted. Did Einstein put any observers at points A or B? He did not. This is why I said we don't need an observer at the space station.

By saying that the light strikes simulatenously on the tracks he tacitly includes an observer in the rest frame of the tracks.

We do need an observer in the space station's inertial frame, though, as you pointed out. Where do we put him? Where did Einstein put him? At point M, the mid point between lightning flash A and lightning flash B.

It's not of great import where the obsrever is spatially locatedd as where only in differences in distances and times rather than definign a co-ordinate system.

What is that observer going to see? We don't have to calculate this or figure it out in any way. Einstein has carefully controlled everything in order that the observer at point M sees the two flashes of light as simultaneous. That is: he has carefully measured the distance from point A--->M and from B---->M, and determined them to be the same, and then he has stipulated that light will always travel at the same speed, regardless of direction of travel.

Because the two distances the light will travel are the same, and because light has been stipulated by Einstein to always travel at the same speed, there is no doubt whatever that the light from both lightning strikes will arrive at point M simultaneously.

That is why I said we don't need an observer at the space station: for the same reason we don't need an observer at the points where lightning strikes the rails. Einstein didn't have any observers at the point where lightning struck the rails. Why do we need anyone at the space station?

As for the observer who is at point M I said "We don't really need an observer for that because Einstein stipulates it." This was not incorrect. I am saying that Einstein has controlled all the conditions so carefully that there is no doubt about what an actual person at point M will see. He can't see anything but simultaneous flashes of light from A and B. That being the case, we don't actually have to station a person there to know what he'd see.

So we don't need an observer at the space station, and we have taken care of what the potential observer at point M (which would be a point 300,000 km from the space station on the rockets path in that example) will see by stipulation. There we have our two different inertial frames: one observer on the train, and one at point M.

I'll stop here to see if you understand and agree or disagree.

Ok, so the obsrever at M is tin the rest frma eof the space staitons right? and in the rest frame of the space staions the two flashes are emitted simulatneously? As I said before though the observer at M will be 340,000 km from the two space stations due to the effects of length contraction. Or are you changing it now so that in the space stations' rest frame rtaher than the rocket's the distance is 300,000 km. It cannot be the same for both observers.

 

[zoobyshoe]

Ok, so the obsrever at M is tin the rest frma eof the space staitons right?

Right.

and in the rest frame of the space staions the two flashes are emitted simulatneously?

Absolutely. That's the way Einstein worked so hard to set it up.

As I said before though the observer at M will be 340,000 km from the two space stations due to the effects of length contraction.

Confusion. The observer at M is the one in the rest frame of the stations. He is at the mid point between the stations. The stations are 600,000 km apart. Therefore the observer at M is always located 300,000 km from both stations in the station's rest frame. (M stands for midpoint)

The observer in the rocket/train is the one in relative motion to the stations. He is different than the observer at M. We shouldn't refer to the guy in the rocket as "the observer at M."

Or are you changing it now so that in the space stations' rest frame rtaher than the rocket's the distance is 300,000 km. It cannot be the same for both observers.

I haven't changed any distance or anything else. What, in fact, I have done is to forget that at .5c the observer on the train will not see the 300,000 km distance as 300,000 kms, and I have erroneously referred to it as 300,000 even when speaking about his perspective. Sorry for that confusion.

Now, my reading of the Einstein leads me to conclude that he believes there is an instant in time when both the observer on the rocket/train and the observer at point M will agree that the observer on the rocket/train is located at point M and that it is at this instant the lights flash. I am not completely sure, but I get the impression that you have an objection to this, and that you don't think there can be an instant where both observers agree that the observer on the rocket is at point M. Do you have such an objection?

 

[plover]

[The Einstein quotes in the following are taken from Chapter 9 of the essay Relativity: The Special and General Theory.]
​

When we say that the lightning strokes A and B are simultaneous with respect to the embankment, we mean: the rays of light emitted at the places A and B, where the lightning occurs, meet each other at the mid-point M of the length A--->B of the embankment.

[§ 1]
This reiterates the definition of simultaneity given in Ch 8. As stated here, it uses observations taken at M as an indicator to define simultaneity specifically for events at A and B and only in the embankment frame. Under the definition of "'time' in physics" given in Ch 8, we may also say that any observer who shares the embankment frame (i.e. is at rest with respect to the observer at M) will agree that the flashes are simultaneous in that reference frame by making use of clocks or of some other suitable extension to the mechanism established in the footnote to Ch 8.

But the events A and B also correspond to positions A and B on the train.

[§ 2]
This could be confusing. Let's call the points on the train A' and B' to distinguish them from the points A and B on the embankment.

Further quotes from the Einstein essay are edited to reflect this change.

Let M' be the mid-point of the distance A'--->B' on the traveling train.

[§ 3]
Let's have a diagram:

[motion of train]________---->
[train ] ... ==== A'======= M'======= B'==== ...
[ground] ... ____ A _______ M _______ B ____ ...

Just when the flashes [as judged from the embankment] of lightning occur, this point M' naturally coincides with the point M ...

[§ 4]
The footnote interpolated here in brackets is not strictly necessary as there is only one reference frame (i.e. the embankment frame) for which we have established that the flashes are simultaneous, and thus only one reference frame in which the phrase "Just when the flashes ... occur" has any meaning.

In particular, we have no basis to assert that the three events - 1) flash at A, 2) flash at B, and 3) M' passes M - are simultaneous to an observer in the reference frame of the train.

There are two sets of events that can be asserted as simultaneous in both frames as they have been defined as such -- this definition being possible because the events occur (for the purposes of the argument) at the same location.

The first set is: 1) flash at A, 2) A' passes A.
The second set is: 1) flash at B, 2) B' passes B.

There is, of course, one other set of events which we can assert are simultaneous in the embankment frame: 1) flash from A arrives at M, and 2) flash from B arrives at M. (This assertion follows from the mechanism through which simultaneity of events separated in space was defined.)

...but it moves towards the right in the diagram with the velocity v of the train. If an observer sitting in the position M' in the train did not possesses this velocity, then he would remain permanently at M, and the light rays emitted by the flashes of lightning A and B would reach him simultaneously, i.e. they would meet just where he is situated.

[§ 5]
So, an observer in the reference frame of the train moves with the same velocity as the train, and consequently such an observer cannot be in the frame of the embankment.

Now in reality (considered with reference to the railway embankment) he is hastening towards the beam of light coming from B, whilst he is riding on ahead of the beam of light coming from A.

[§ 6]
Since the observer on the train at M' (the "he" of the preceding quote) is not at rest with respect to the observer at M (i.e. not at rest in the embankment frame), the observer at M will say that the observer at M' moved toward B during the period when light from the flashes was traveling from A and B to M, and thus that the observer at M' was moving toward the flash from B and away from the flash from A.

Hence the observer will see the beam of light emitted from B earlier than he will see that emitted from A.

[§ 7]
Therefore, the observer at M may conclude, since the flash from B passed M' sometime before reaching M, and the flash from A will pass M' sometime after reaching M, an observer positioned at M' will witness the flash from B prior to witnessing the flash from A.

And if the preceding conclusion about an observer at M' is true, then, using the same procedures from Ch 8 mentioned above, the following conclusion may be made about any observers in the reference frame of the train:

Observers who take the railway train as their reference-body must therefore come to the conclusion that the lightning flash B took place earlier than the lightning flash A.

[§ 8]
Or in other words, events (separated in space) that are determined to be simultaneous by observers in the frame of the embankment could not be determined to be simultaneous by observers in the frame of the train.

If one were to work through all these steps again, only exchanging the assumption that the flashes are simultaneous in the embankment frame for the assumption that the flashes are simultaneous in the frame of the train, the complementary conclusion would be reached: that events (separated in space) that are determined to be simultaneous by observers in the frame of the train could not be determined to be simultaneous by observers in the frame of the embankment.

These two complementary conclusions comprise the definition of Relativity of Simultaneity given by Einstein. In his words:

Events which are simultaneous with reference to the embankment are not simultaneous with respect to the train, and vice versa (relativity of simultaneity).

Zoobyshoe:

[§ 9]
I don't know what upsets you about this argument. At this point in history, however, trying to proclaim this argument to be false falls under the rubric of "Extraordinary claims require extraordinary proof".

I doubt that a comparison with the rocket scenario that you worked out is useful - nobody giving answers in the early part of this thread was limiting themselves to the assumptions employed by Einstein in Ch 1-9 of this essay, they were employing whatever knowledge of Special Relativity seemed appropriate. So it is likely that whatever conclusions you have made about the rocket scenario would need to be rejected on the same basis that you reject any mention of length contraction.

I will point out that it was not until post #43 of this thread that you made it explicit enough (at least to me - I can't be sure of what Doc Al and jcsd were thinking, but from their answers I doubt the assumption was clear to them either) that the reason that you insist that the person in the rocket should correspond to the observer on the train is that because the stations are emitting the photons and the lightning strikes the ground in the embankment frame, the stations need to be in the embankment frame.

It is not actually relevant what frame the photon emitters are in, what matters is that the observer in the embankment frame at M sees the flashes at the same moment. The constant velocity of light makes the velocity of the source irrelevant (and the reference frame of the source irrelevant) to when the flashes arrive at M. In addition, Einstein gives this as an empirical result in Ch 7.

It is much more important to have a thorough and explicit listing of the assumptions that are made about each frame. And to make sure that knowledge gained with reference to one frame is not applied to the other in unwarranted ways.

 

[zoobyshoe]

Plover,

Excellent, excellent breakdown of the train scenario! You are an extremely patient, persistent, and articulate poster.
Good to have you here.

You have pointed out that the observer on the embankment will suppose the observer on the train sees one flash before the other. However, there is doubt in my mind as to whether you think Einstein is asserting that the man on the train will see one flash of light before the other in his reference frame on the train.

His wording is iffy at many points, but since he comes to the conclusion "Events which are simultaneous with reference to the embankment are not simultaneous with respect to thr train, and vice versa (relativity of simultaneity)." it seems unbelievable to me that he could only be talking about what the observer on the embankment thinks the observer on the train might be experiencing. If he were, why would he go on to conclude "Every reference-body (co-ordinate system) has its own particular time; unless we are told the reference-body to which the statement of time refers, there is no meaning in a statement of time." It would make no sense whatever for him to draw that conclusion unless he believed an actual observer seated on the train would actually see one flash before the other.
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It never occurred to me that the flashes could come from the ends of the train just as well as from fixed points on the rails, but now that you point it out, I see that it is another valid possibility.
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I'm not claiming Einstein's argument is false.

Janus, Doc Al and you answered my questions about the rocket in such a way that it seems to me the observer on the train will see the flashes of light as simultaneous. If there is anything about the train scenario that I failed to carry over to the rocket questions, I am still not aware of what it was. If there is a different method that should be used to calculate how much time the man on the train will judge to have elapsed between the instant he is at the midpoint and when he detects the light and what should be used to determine the time that will elapse for the rocket man between the instant he hits the 300,000 km mark and when he detects the light, I will be very surprised: all the distances and speeds are the same.


I don't object to length contraction or time dilation being brought in if it can be used to explain that the observer on the train will see one flash of light before the other. He seemed to be on his way to use it to say something about how the rocket looks to station.
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I've reread your explanation of the reason the observer on the train might see one flash before the other. It is quite interesting, but is dependent on point M of the track and point M' of the train not actually corresponding when the light flashes for it to work. That would be fine except Einstein is, it seems to me, explicit about the fact that point M' of the train must correspond to point M of the embankment when the flashes occur. (I don't know why he even bothers to mention what the ends of the train are doing when he is so exacting in his description of the midpoints lining up.) It seems to me he is trying very hard to describe a situation exactly like what would happen if a rod sticking out from the outside of the train beside the observer on the train were to trip a switch located at point M on the embankment causing the flashes (the signal getting from the switch to the lights instantaneously, by magic, of course). Does that not seem to be the case to you?

 

[jcsd]

Right.

Absolutely. That's the way Einstein worked so hard to set it up.

Confusion. The observer at M is the one in the rest frame of the stations. He is at the mid point between the stations. The stations are 600,000 km apart. Therefore the observer at M is always located 300,000 km from both stations in the station's rest frame. (M stands for midpoint)

The observer in the rocket/train is the one in relative motion to the stations. He is different than the observer at M. We shouldn't refer to the guy in the rocket as "the observer at M."

I haven't changed any distance or anything else. What, in fact, I have done is to forget that at .5c the observer on the train will not see the 300,000 km distance as 300,000 kms, and I have erroneously referred to it as 300,000 even when speaking about his perspective. Sorry for that confusion.

Right so that is cleared up.

Now, my reading of the Einstein leads me to conclude that he believes there is an instant in time when both the observer on the rocket/train and the observer at point M will agree that the observer on the rocket/train is located at point M and that it is at this instant the lights flash. I am not completely sure, but I get the impression that you have an objection to this, and that you don't think there can be an instant where both observers agree that the observer on the rocket is at point M. Do you have such an objection?

The problem is time is relative, there will be an instant in M's refernce frame where the rocket ship is at M and there will be an instant in the rocket ship's frame when he is at M. The problem is at the instant in M's frame that the rocket ship is at M this will be the instant the two lights flash, BUT in the rocket ship's frame at the instant that he is at M, one of the lights will already of flashed and the other light will not of yet flashed.

 

[Doc Al]

Janus, Doc Al and you answered my questions about the rocket in such a way that it seems to me the observer on the train will see the flashes of light as simultaneous.

I'm still not seeing how you conclude this based on what we have explained. You are drawing a confused analogy between Einstein's train and your rocket.

But in any case, I'd still like to know what you think is wrong with the simple calculation, done by the folks in your rocket, that shows that according to the rocket clocks the light takes 1 second to reach them from the time it leaves the station. You agree that the rocket frame has measured the distance from the station to the rocket to be 300,000 km at the time of emission, right? (That's given in the problem.) And you must also agree that the rocket frame observes the light to travel towards the rocket at speed c, right? (That's a postulate of relativity.) Since all measurements are made in the same frame, the conclusion follows from D = VT: The time (measured by rocket clocks) must be 1 second. There is no need whatsoever to invoke any measurements made in other frames. But you must think something is wrong with this calculation. What is it?

I've reread your explanation of the reason the observer on the train might see one flash before the other. It is quite interesting, but is dependent on point M of the track and point M' of the train not actually corresponding when the light flashes for it to work.

Einstein's conclusion is that it physically impossible for that condition to be satisfied.

That would be fine except Einstein is, it seems to me, explicit about the fact that point M' of the train must correspond to point M of the embankment when the flashes occur.

What Einstein arranges is that M' pass by the midpoint M exactly at the moment that the lights go off according to the embankment clocks. How can this be arranged? Imagine three synchronized clocks in the embankment frame: at A, M, and B. Exactly when those clocks each read 12:00 noon, the lights will flash. So M' is to pass M exactly when the M' clock reads 12:00 noon. That's the scenario.

Einstein argues that the observers on the train must conclude that according to their own clocks, those clocks on the embankment must not be synchronized because those flashes could not have occurred simultaneously at the moment M' passed M according to observations made on the train.

 

[Janus]

Maybe the attached images will help.

Let's assume that you have two space stations and a rocket. the rocket is traveling from one space station to another. Leading and trailing the rocket is a line that extends an equal distance in both directions. on the end of each line is a device that will trigger a flash of light from each station as it passes the station. The length of the lines are such that, from both station's frame of reference, each end of a line touches a station when the rocket is midway between the stations (first image of the attachment).

Now let's look at the same situation from the frame of the rocket. Length contraction has shortened the distance between the stations, so now the ends of the lines extend past the stations positions when the rocket is at the midpoint. (second image) Since the stations will not emit the flashes of light until triggered by the ends of the line(the ends of the line physically trigger the flash), they do not do so when the rocket is at midpoint (according to the rocket).

Instead we see what is shown in the next two images. First the leadiing end of the wire triggers a flash from the station ahead of the rocket, and then sometime later, the trailing end of the line triggers the station behind the rocket.

Thus the events of the station emitting the flashes are simultaneous in the station frame, but not simultaneous in the rocket frame.