Simultaneity of Relativity
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From: mpc755 on 9 Oct 2009 13:26 On Oct 9, 1:17 pm, PD <thedraperfam...(a)gmail.com> wrote: > On Oct 9, 12:08 pm, mpc755 <mpc...(a)gmail.com> wrote: > > > > > On Oct 9, 12:30 pm, PD <thedraperfam...(a)gmail.com> wrote: > > > > On Oct 9, 10:06 am, mpc755 <mpc...(a)gmail.com> wrote: > > > > > On Oct 9, 10:52 am, PD <thedraperfam...(a)gmail.com> wrote: > > > > > > On Oct 9, 8:53 am, mpc755 <mpc...(a)gmail.com> wrote: > > > > > > > On Oct 9, 8:57 am, PD <thedraperfam...(a)gmail.com> wrote: > > > > > > > > On Oct 8, 8:34 pm, mpc755 <mpc...(a)gmail.com> wrote: > > > > > > > > > > > > > > > > > > Sorry, I've fouled this up. > > > > > Yes, the light from A and B reaches M' at different times, but the > > > > light from A' and B' reaches M' simultaneously. > > > > A and A' are a single strike. B and B' are a single strike. > > > Yes, A and A' are a single strike but A and A' are two different > > locations in three dimensional space. A in on the embankment and A' is > > on the train. > > No, they are not. You have not read the gedanken carefully. A lighting > strike hits in ONE place, not two. A and A' are two labels for the > same point. In the original gedanken, A and A' label the point where > the train meets the track at one end of the train. That is ONE POINT. > > Please reread it and pay more attention than what you have been doing > so far. > The lightning strike leaves marks at A, A', B, and B'. This is four different locations in three dimensional space. A and A' and B and B' were co-located at the time of the strikes, but they are four different locations. If A and A' are two labels for the same point, why does the Observer at M measure to A and B and the Observer at M' measure to A' and B'? The measure to the appropriate marks because there are four marks. Please try and understand if you have four marks at four locations that is four points. > > > > > The light from A/A' travels through the *same medium* that the > > > embankment and the open flatbed train cars are immersed in. The light > > > from B/B' does the same thing. > > > So how does the light, coming from a single lightning strike (A/A'), > > > traveling through a common medium, arrive at the same observer M' both > > > simultaneously and not simultaneously as the light from B/B'? > > > It doesn't. If the train contains open flatbed cars, then you are > > implying the medium is stationary relative to the embankment. > > No, I'm not. There's no such implication at all. What you know is true > is that there is ONE medium, not two. > If there is one medium that is stationary relative to one of the frames of reference in Einstein's train thought experiment then that means it is moving relative to the other frame of reference which means there is a preferred frame of reference. > > > > Meaning > > the light travels from B to M' and from A to M'. The marks made by the > > lightning strikes are A' and B' are meaningless in this scenario. Even > > with the marks made at A' and B', since the medium is stationary > > relative to the embankment, all of the light associated with the > > lightning strikes travels from A to M' and from B to M'. > > > > The observer M' either sees the flashes from the strikes at his eyes at > > > the same time or he doesn't. He can't do both. > > > Incorrect. If the medium is stationary relative to the embankment in > > the embankment frame of reference and the medium is stationary > > relative to the train in the train frame of reference the observer at > > M' will see the light from the lightning strikes at A' and B' > > simultaneously. The light from A and B will have to transition from > > the embankment frame of reference to the train frame of reference and > > will arrive at M' at different times. > > > > > > The train observer has to agree with that. > > > > > Yes, the train observer agrees the light from A and B reaches him at > > > > different times, but the light from A' and B' reaches him > > > > simultaneously. > > > > A and A' are ONE lightning strike. B and B' are ONE lightning strike. > > > Yes, they are one lightning strike but they occur at two different > > locations. A on the embankment and A' on the train. Likewise for the > > lightning strike at B/B'. > > > > Let's say that the ONE lightning strike at A/A' is greenish, and the > > > lightning strike at B/B' is yellowish. > > > > The question is simple. There is a guy M' who is going to see the two > > > lightning flashes. Does he see the yellowish and greenish ones at the > > > same time or at different times? There can only be one answer, as this > > > is something that the guy can write down when it happens. > > > If the medium is stationary relative to the train in the train frame > > of reference and the medium is stationary relative to the embankment > > in the embankment frame of reference the observer at M' is going to > > see the yellowish light from A' and the greenish light from B' arrive > > simultaneously. He will also see the yellowish light from A and the > > greenish light from B arrive at different times. > > OK, and this is where you get a little loony. > > You say that the observer M' will see the green flash and the yellow > flash at the same time AND not at the same time? > Yes, because the medium is stationary relative to the embankment in the embankment frame of reference and the medium is stationary relative to the train in the train frame of reference. Therefore, the light from the lightning strikes on the train travel from A' and B' to M' and the light from the lightning strikes on the embankment travel from A and B to M'. > This kind of odd behavior you describe has never been observed in > experiment. > > > > > > > If the medium is stationary relative to the train in all reference > > frames, then the Observer at M' will see a single lighting strike from > > A' and a single lightning strike at B' both arrive simultaneously. > > > If the medium is stationary relative to the embankment in all > > reference frames, the Observer at M' will see a single lightning > > strike from A and a single lightning strike at B arrive at different > > times. > > > > > > Nature doesn't produce two > > > > > different measurable outcomes at the same time. There is only one.. > > > > > Either the light arrives at the same time at M' or it doesn't. The > > > > > embankment observer and the train observer have to agree which one of > > > > > those two it was. > > > > > > It appears that you are having a slow time getting a grip on what the > > > > > Einstein gedanken really says. > > > > > > > > > The water is stationary relative to the train. Pebbles are dropped at > > > > > > > > A/A' and B/B'. The wave from A' reaches M. The waves from A' and B' > > > > > > > > reach M' simultaneously. The wave from B' reaches M. A and B are > > > > > > > > irrelevant in this scenario. > > > > > > > > OK, but there are really only two lightning strikes, and the water > > > > > > > doesn't really have time to switch from being stationary relative to > > > > > > > the embankment to being stationary relative to the train. > > > > > > > The water doesn't have to switch. The water is stationary relative to > > > > > > the embankment in the embankment frame of reference and the water is > > > > > > stationary relative to the train in the train frame of reference. > > > > > > But these aren't two different sequences of events. It's the same > > > > > train, the same two lightning strikes, and there is only one pool of > > > > > water surrounding the embankment and the open train cars. So you tell > > > > > me, how can the water be stationary relative to the train AND > > > > > stationary relative to the embankment? > > > > > It's the same two lightning strikes, but it is occurring at A on the > > > > embankment and A' on the train. > > > > So? > > > > > You can have a bucket of water that is stationary on the embankment > > > > and a bucket of water that is stationary on the train. > > > > Same body of water that the train is immersed in and the embankment is > > > immersed in. > > > If it's not the same body of water, then there has to be a boundary > > > between the two bodies of water. Where is that boundary? > > > If the train contains open flatbed cars, then the water will be > > stationary relative to the embankment and the light from the lightning > > strikes at A/A' and B/B' will travel from A to M' and from B to M'. > > > If the train is enclosed and the water is moving with the train in the > > train frame of reference and the water on the embankment is stationary > > relative to the embankment, then it is the train that is the boundary. > > There is no enclosure implied in the gedanken. Please reread it > carefully. > There is no enclosure implied in Einstein's train thought experiment because he did not realize the mistake he was making. Einstein states the speed of light is 'c' regardless of the speed of the source. What Einstein failed to realize is the speed of light is 'c' relative to the medium it is propagating through: 'Fizeau experiment' http://en.wikipedia.org/wiki/Fizeau_experiment > > > > > > > > Pebbles are dropped at A, A', B, and B' simultaneously as determined > > > > by observers. > > > > That's just it. Whether they are simultaneous or not depends on the > > > signals they actually receive at their locations. That is, the > > > observers M and M' are not AT the locations A, A', B, B'. They are at > > > the places marked M and M'. What they know is what happens where they > > > are, and THAT tells them what happens at A, A', B, and B'. They have > > > no other way of knowing. > > > There are observers at A, A', B and B' and they all have clickers and > > they all click their clickers when the pebbles hit the water. It is > > determined all four observers hit their clickers at the same time. > > How is it determined that they hit their clickers at the same time? > What procedure would you need to ensure that? > I want you to think about this very carefully... There are observer as close to each contact point between the pebble and the water as possible. The length of wire from the clicker to the clicker response unit is the same for all observers. If the clicks are determined to be simultaneous at the clicker response unit, then the pebbles each hit the water simultaneously.
From: mpc755 on 9 Oct 2009 13:29 On Oct 9, 1:22 pm, PD <thedraperfam...(a)gmail.com> wrote: > On Oct 9, 12:17 pm, mpc755 <mpc...(a)gmail.com> wrote: > > > > > On Oct 9, 1:11 pm, PD <thedraperfam...(a)gmail.com> wrote: > > > > On Oct 9, 11:54 am, mpc755 <mpc...(a)gmail.com> wrote: > > > > > On Oct 9, 12:35 pm, PD <thedraperfam...(a)gmail.com> wrote: > > > > > > On Oct 9, 11:01 am, mpc755 <mpc...(a)gmail.com> wrote: > > > > > > > On Oct 9, 11:06 am, mpc755 <mpc...(a)gmail.com> wrote: > > > > > > > > On Oct 9, 10:52 am, PD <thedraperfam...(a)gmail.com> wrote: > > > > > > > > > > > > > > > > > > > > > Sorry, I've fouled this up. > > > > > > > I missed where you say it is an open train car. If it is an open train > > > > > > car, which implies the water is stationary relative to the embankment > > > > > > and not stationary relative to the train, > > > > > > Well, hold on a second. Why isn't it possible the water is stationary > > > > > relative to the train and not stationary relative to the embankment? > > > > > The water could be stationary relative to the train and not stationary > > > > relative to the embankment. In that case, the light from the lightning > > > > strike at B/B' will travel from B' to M and the light from the > > > > lightning strike at A/A' will travel from A' to M. The light from A' > > > > and B' will reach M' simultaneously. > > > > And if this were so, then you'd be able to measure a different speed > > > of propagation of the signal someplace. > > > > Remember that for BOTH observers M and M', the distance between the > > > strikes and where the observer is standing is identical. That is, A--M > > > = M--B, and A--M' = M'--B. > > > Correct, at the time of the lightning strikes. > > Or any time. The track observer could do it all afterwards if he > wanted to. He just marks the location where he was standing and then > goes to look for the scorch mark on the track and he measures the > distance from where he was standing to the scorch mark. Then he does > the same for the other scorch mark. > The train observer can do the same thing. > Yes, for the scorch marks in their frame of reference. The light from the other frame of reference travels different distances to them. > > > > > And so if the speed of the signal propagating from A to M and from B > > > to M is the same, then the time of propagation has to be the same. > > > So what the observer M SEES (simultaneous or not simultaneous) > > > determines completely whether the strikes are REALLY simultaneous or > > > not. > > > And the same statements hold true for M'. > > > Correct, for M' and the lightning strikes at A' and B'. > > A' and B' happen at the same locations as A and B. A and A' are two > different labels applied to the same point. Same for B and B'. > If they are the same point, then why are there four marks? > > > > > And here is what is REALLY seen in experiment (or analogous > > > experiment): M sees the flashes at the same time and M' sees the > > > flashes at different times. > > > M sees the flashes at the same time if the medium is stationary > > relative to him. > > > M' sees the flashes at different times from A and B because the light > > has traveled different distances from A and B to M'. M' is moving > > relative to A and B. > > M' cannot see the flashes at the same time AND at different times. It > has to be one or the other. There is only one green flash and he will > see it only once, and there is only one yellow flash and he will see > it only once. When he sees the green and yellow flashes, does he see > them at the same time or at different times? He doesn't see the green > flash twice or the yellow flash twice. > Take another look at the animation and you can see how M' sees the flashes from A' and B' at the same time and the flashes from A and B at different times: http://www.youtube.com/watch?v=jyWTaXMElUk > > > > > The only way this can be true is if the speed of propagation from A is > > > somehow different than the speed of propagation from B. > > > Incorrect. M' sees the light from B prior to the light from A because > > M' is hastening towards B and away from A. > > > > But measurements in REAL LIFE show that this isn't the case. The speed > > > is always the same. > > > Yes, the speed of light is always 'c'. But what you do not understand > > is where the light emanates from is dependent on the relative motion > > of the medium it was created in and is traveling through. See Fizeau > > experiment (http://en.wikipedia.org/wiki/Fizeau_experiment) > > > > I see that this simple gedanken continues to cause you problems and > > > you're having trouble understanding the point. > >
From: paparios on 9 Oct 2009 14:23 On 9 oct, 13:26, mpc755 <mpc...(a)gmail.com> wrote: > On Oct 9, 1:17 pm, PD <thedraperfam...(a)gmail.com> wrote: > > > There is no enclosure implied in the gedanken. Please reread it > > carefully. > > There is no enclosure implied in Einstein's train thought experiment > because he did not realize the mistake he was making. Einstein states > the speed of light is 'c' regardless of the speed of the source. What > Einstein failed to realize is the speed of light is 'c' relative to > the medium it is propagating through: That is, of course, totally wrong. Einstein clearly wrote in his 1905 paper: "...In agreement with experience we further assume the quantity 2AB/ (t'_A-t_A)=c to be a universal constantthe velocity of light in empty space." So the train gedanken, which was a pedagogical example for people like you, is clearly setup in deep space and far away from any gravitational mass. The two events could be two nuclear blasts, observer M just floating in space on a small ship and observer M' moving at a speed v in a small ship. So all your Aether nonsense is totally useless in this example. Einstein himself also clearly wrote about it: "The introduction of a luminiferous ether will prove to be superfluous inasmuch as the view here to be developed will not require an absolutely stationary space provided with special properties, nor assign a velocity-vector to a point of the empty space in which electromagnetic processes take place." Miguel Rios
From: PD on 9 Oct 2009 14:29 On Oct 9, 12:26 pm, mpc755 <mpc...(a)gmail.com> wrote: > On Oct 9, 1:17 pm, PD <thedraperfam...(a)gmail.com> wrote: > > > On Oct 9, 12:08 pm, mpc755 <mpc...(a)gmail.com> wrote: > > > > On Oct 9, 12:30 pm, PD <thedraperfam...(a)gmail.com> wrote: > > > > > On Oct 9, 10:06 am, mpc755 <mpc...(a)gmail.com> wrote: > > > > > > On Oct 9, 10:52 am, PD <thedraperfam...(a)gmail.com> wrote: > > > > > > > On Oct 9, 8:53 am, mpc755 <mpc...(a)gmail.com> wrote: > > > > > > > > On Oct 9, 8:57 am, PD <thedraperfam...(a)gmail.com> wrote: > > > > > > > > > On Oct 8, 8:34 pm, mpc755 <mpc...(a)gmail.com> wrote: > > > > > > > > > > > > > > > > > > > Sorry, I've fouled this up. > > > > > > Yes, the light from A and B reaches M' at different times, but the > > > > > light from A' and B' reaches M' simultaneously. > > > > > A and A' are a single strike. B and B' are a single strike. > > > > Yes, A and A' are a single strike but A and A' are two different > > > locations in three dimensional space. A in on the embankment and A' is > > > on the train. > > > No, they are not. You have not read the gedanken carefully. A lighting > > strike hits in ONE place, not two. A and A' are two labels for the > > same point. In the original gedanken, A and A' label the point where > > the train meets the track at one end of the train. That is ONE POINT. > > > Please reread it and pay more attention than what you have been doing > > so far. > > The lightning strike leaves marks at A, A', B, and B'. This is four > different locations in three dimensional space. A and A' and B and B' > were co-located at the time of the strikes, but they are four > different locations. A and A' are colocated but they are two different locations? Listen to yourself! LOL! Lightning strikes at ONE POINT at the end of the train, where one end of the train meets the track. There is a scorch mark left on the track (A) and a scorch mark left on the train (A') where this ONE spot occurred. Another lightning bolt strikes at ONE point at the other end of the train, where that end of the train meets the track. Here's another way you can think of it. Set up a graph with an x and y axis. The x and y axis meet at ONE POINT. That point is labeled (y=0) for the y-axis and is labeled (x=0) for the x-axis. Does the fact that there are two labels mean that it is ONE point or TWO points where the axes meet? > > If A and A' are two labels for the same point, why does the Observer > at M measure to A and B and the Observer at M' measure to A' and B'? > The measure to the appropriate marks because there are four marks. I'm sorry, but you are REALLY poor at reading comprehension. Try reading it again. > > Please try and understand if you have four marks at four locations > that is four points. > > > > > > > The light from A/A' travels through the *same medium* that the > > > > embankment and the open flatbed train cars are immersed in. The light > > > > from B/B' does the same thing. > > > > So how does the light, coming from a single lightning strike (A/A'), > > > > traveling through a common medium, arrive at the same observer M' both > > > > simultaneously and not simultaneously as the light from B/B'? > > > > It doesn't. If the train contains open flatbed cars, then you are > > > implying the medium is stationary relative to the embankment. > > > No, I'm not. There's no such implication at all. What you know is true > > is that there is ONE medium, not two. > > If there is one medium that is stationary relative to one of the > frames of reference in Einstein's train thought experiment then that > means it is moving relative to the other frame of reference which > means there is a preferred frame of reference. If there is a medium, yes. But there isn't a preferred frame of reference, is there? And how do you know that if there is a medium then it is stationary with respect to the embankment and not with respect to the train? What if it's not stationary with respect to either one? > > > > > > Meaning > > > the light travels from B to M' and from A to M'. The marks made by the > > > lightning strikes are A' and B' are meaningless in this scenario. Even > > > with the marks made at A' and B', since the medium is stationary > > > relative to the embankment, all of the light associated with the > > > lightning strikes travels from A to M' and from B to M'. > > > > > The observer M' either sees the flashes from the strikes at his eyes at > > > > the same time or he doesn't. He can't do both. > > > > Incorrect. If the medium is stationary relative to the embankment in > > > the embankment frame of reference and the medium is stationary > > > relative to the train in the train frame of reference the observer at > > > M' will see the light from the lightning strikes at A' and B' > > > simultaneously. The light from A and B will have to transition from > > > the embankment frame of reference to the train frame of reference and > > > will arrive at M' at different times. > > > > > > > The train observer has to agree with that. > > > > > > Yes, the train observer agrees the light from A and B reaches him at > > > > > different times, but the light from A' and B' reaches him > > > > > simultaneously. > > > > > A and A' are ONE lightning strike. B and B' are ONE lightning strike. > > > > Yes, they are one lightning strike but they occur at two different > > > locations. A on the embankment and A' on the train. Likewise for the > > > lightning strike at B/B'. > > > > > Let's say that the ONE lightning strike at A/A' is greenish, and the > > > > lightning strike at B/B' is yellowish. > > > > > The question is simple. There is a guy M' who is going to see the two > > > > lightning flashes. Does he see the yellowish and greenish ones at the > > > > same time or at different times? There can only be one answer, as this > > > > is something that the guy can write down when it happens. > > > > If the medium is stationary relative to the train in the train frame > > > of reference and the medium is stationary relative to the embankment > > > in the embankment frame of reference the observer at M' is going to > > > see the yellowish light from A' and the greenish light from B' arrive > > > simultaneously. He will also see the yellowish light from A and the > > > greenish light from B arrive at different times. > > > OK, and this is where you get a little loony. > > > You say that the observer M' will see the green flash and the yellow > > flash at the same time AND not at the same time? > > Yes, because the medium is stationary relative to the embankment in > the embankment frame of reference and the medium is stationary > relative to the train in the train frame of reference. Woah! The same medium is stationary with respect to the train in one reference frame and stationary with respect to the embankment in the other reference frame? It's ONE medium being looked at from two different reference frames at the same time? How can anything do that? If you had a bird, a car, and a street sign, could you explain how the bird could be moving along with the car from the street sign's frame of reference, and moving along with the street sign from the car's frame of reference???? LOL! > Therefore, the > light from the lightning strikes on the train travel from A' and B' to > M' and the light from the lightning strikes on the embankment travel > from A and B to M'. > > > This kind of odd behavior you describe has never been observed in > > experiment. > > > > If the medium is stationary relative to the train in all reference > > > frames, then the Observer at M' will see a single lighting strike from > > > A' and a single lightning strike at B' both arrive simultaneously. > > > > If the medium is stationary relative to the embankment in all > > > reference frames, the Observer at M' will see a single lightning > > > strike from A and a single lightning strike at B arrive at different > > > times. > > > > > > > Nature doesn't produce two > > > > > > different measurable outcomes at the same time. There is only one. > > > > > > Either the light arrives at the same time at M' or it doesn't. The > > > > > > embankment observer and the train observer have to agree which one of > > > > > > those two it was. > > > > > > > It appears that you are having a slow time getting a grip on what the > > > > > > Einstein gedanken really says. > > > > > > > > > > The water is stationary relative to the train. Pebbles are dropped at > > > > > > > > > A/A' and B/B'. The wave from A' reaches M. The waves from A' and B' > > > > > > > > > reach M' simultaneously. The wave from B' reaches M. A and B are > > > > > > > > > irrelevant in this scenario. > > > > > > > > > OK, but there are really only two lightning strikes, and the water > > > > > > > > doesn't really have time to switch from being stationary relative to > > > > > > > > the embankment to being stationary relative to the train. > > > > > > > > The water doesn't have to switch. The water is stationary relative to > > > > > > > the embankment in the embankment frame of reference and the water is > > > > > > > stationary relative to the train in the train frame of reference. > > > > > > > But these aren't two different sequences of events. It's the same > > > > > > train, the same two lightning strikes, and there is only one pool of > > > > > > water surrounding the embankment and the open train cars. So you tell > > > > > > me, how can the water be stationary relative to the train AND > > > > > > stationary relative to the embankment? > > > > > > It's the same two lightning strikes, but it is occurring at A on the > > > > > embankment and A' on the train. > > > > > So? > > > > > > You can have a bucket of water that is stationary on the embankment > > > > > and a bucket of water that is stationary on the train. > > > > > Same body of water that the train is immersed in and the embankment is > > > > immersed in. > > > > If it's not the same body of water, then there has to be a boundary > > > > between the two bodies of water. Where is that boundary? > > > > If the train contains open flatbed cars, then the water will be > > > stationary relative to the embankment and the light from the lightning > > > strikes at A/A' and B/B' will travel from A to M' and from B to M'. > > > > If the train is enclosed and the water is moving with the train in the > > > train frame of reference and the water on the embankment is stationary > > > relative to the embankment, then it is the train that is the boundary.. > > > There is no enclosure implied in the gedanken. Please reread it > > carefully. > > There is no enclosure implied in Einstein's train thought experiment > because he did not realize the mistake he was making. LOL! So what if we do the experiment where there is no isolation of the medium into two chunks? > Einstein states > the speed of light is 'c' regardless of the speed of the source. What > Einstein failed to realize is the speed of light is 'c' relative to > the medium it is propagating through: > > 'Fizeau experiment'http://en.wikipedia.org/wiki/Fizeau_experiment > > > > > > > > Pebbles are dropped at A, A', B, and B' simultaneously as determined > > > > > by observers. > > > > > That's just it. Whether they are simultaneous or not depends on the > > > > signals they actually receive at their locations. That is, the > > > > observers M and M' are not AT the locations A, A', B, B'. They are at > > > > the places marked M and M'. What they know is what happens where they > > > > are, and THAT tells them what happens at A, A', B, and B'. They have > > > > no other way of knowing. > > > > There are observers at A, A', B and B' and they all have clickers and > > > they all click their clickers when the pebbles hit the water. It is > > > determined all four observers hit their clickers at the same time. > > > How is it determined that they hit their clickers at the same time? > > What procedure would you need to ensure that? > > I want you to think about this very carefully... > > There are observer as close to each contact point between the pebble > and the water as possible. The length of wire from the clicker to the > clicker response unit is the same for all observers. If the clicks are > determined to be simultaneous at the clicker response unit, then the > pebbles each hit the water simultaneously.
From: PD on 9 Oct 2009 14:38
On Oct 9, 12:26 pm, mpc755 <mpc...(a)gmail.com> wrote: > > > > > That's just it. Whether they are simultaneous or not depends on the > > > > signals they actually receive at their locations. That is, the > > > > observers M and M' are not AT the locations A, A', B, B'. They are at > > > > the places marked M and M'. What they know is what happens where they > > > > are, and THAT tells them what happens at A, A', B, and B'. They have > > > > no other way of knowing. > > > > There are observers at A, A', B and B' and they all have clickers and > > > they all click their clickers when the pebbles hit the water. It is > > > determined all four observers hit their clickers at the same time. > > > How is it determined that they hit their clickers at the same time? > > What procedure would you need to ensure that? > > I want you to think about this very carefully... > > There are observer as close to each contact point between the pebble > and the water as possible. The length of wire from the clicker to the > clicker response unit is the same for all observers. And the speed of the signal is the same through the wire in both cases. So if the speed in the wire is the same, and the length of the wire is the same, then you know that the time propagation through the wires would be the same, right? And if this is the case, then you know the following: 1. If the clicker response unit records signals from the clickers at the same time, THEN you know that the pebbles landed at the same time. 2. If the clicker response unit records signals from the clickers at different times, THEN you know that the pebbles landed at different times. Right? This is how you determine from the clicker and clicker response system whether the pebbles really landed at the same time or not. OK, so here's the situation with the lightning strikes: You've got ONE lightning strike at one end of the train, and ONE lightning strike at the other end of the train. The path length (just like the wire length) from one lightning strike to the observer M is the same as the path length from the other lightning strike to the observer M. Equal path lengths, just like equal wire lengths. The path length (just like the wire length) from one lightning strike to the observer M' is the same as the path length from the other lightning strike to the observer M'. Equal path lengths, just like equal wire lengths. And you know the speed of the signal from one lightning strike to M is the same as the speed of the signal from the other lightning strike to M. And you know the speed of the signal from one lightning strike to M' is the same as the speed of the signal from the other lightning strike to M'. The problem is, in experiment, M says he received the signals at the same time (clicker case (1)), and M' says he received the signals at different times (clicker case (2)). > If the clicks are > determined to be simultaneous at the clicker response unit, then the > pebbles each hit the water simultaneously. |