Questions relating to time dilation

[salzrah]

1. Is there anyway we can measure time without depending on or using light? If we can, what are they and do special relativistic effects still take place in "close to c" relative velocity situations by using this method of time keeping?

2. My second question relates to relative movement. Time dilation suggests that the time measured in two different reference frames moving with a relative velocity to each other is different. This conclusion then suggests that the time measured in a moving reference frame relative to a stationary one is less than the time measured by the stationary observer for the moving reference frame. Because both frames are moving relative to each other, doesn't the reference frame which we originally dictate to be the one moving see that time actually slows down in the reference frame that we considered to be stationary? This is because the velocity that we assumed one reference frame had relative to another can be applied to the other reference frame in the opposite direction. Therefore, we can assume both reference frames believe the other reference frame has a slower passage of time. If what I said so far is true, then at any instant the amount of time that has passed for each observer in their own reference frame is the same and each observer believes less time has passed in the other reference frame. (This contradiction relates to the twin paradox, without the acceleration part that many use as a "solution" to the paradox.) Now I want to know, is what I have said a paradox? If it is, what does this suggest? One thing it can suggest is that the way we measure time is flawed. But what else can be said about the nature of time?

 

[bcrowell]

1. Is there anyway we can measure time without depending on or using light?

Yes, e.g., a mechanical clock, or the Earth's rotation.

do special relativistic effects still take place in "close to c" relative velocity situations by using this method of time keeping?

Yes.

 

[Erland]

The second question has to do with the relativity of simultaneity.
See https://www.physicsforums.com/showthread.php?t=468826

The first question, I leave to our one-way and two-way measurement experts to sort out. :)

 

[Nugatory]

2. My second question relates to relative movement. Time dilation suggests that the time measured in two different reference frames moving with a relative velocity to each other is different. This conclusion then suggests that the time measured in a moving reference frame relative to a stationary one is less than the time measured by the stationary observer for the moving reference frame. Because both frames are moving relative to each other, doesn't the reference frame which we originally dictate to be the one moving see that time actually slows down in the reference frame that we considered to be stationary? This is because the velocity that we assumed one reference frame had relative to another can be applied to the other reference frame in the opposite direction. Therefore, we can assume both reference frames believe the other reference frame has a slower passage of time. If what I said so far is true, then at any instant the amount of time that has passed for each observer in their own reference frame is the same and each observer believes less time has passed in the other reference frame. (This contradiction relates to the twin paradox, without the acceleration part that many use as a "solution" to the paradox.) Now I want to know, is what I have said a paradox? If it is, what does this suggest? One thing it can suggest is that the way we measure time is flawed. But what else can be said about the nature of time?

The bolded words in the quote above are the crux of the problem.

You have to consider not only time dilation but also the relativity of simultaneity, and when you do that the apparent paradoxical inconsistency goes away. There are a number of more thorough explanations in other threads here and on the web - try googling for "relativity of simultaneity", see what you find, and if that doesn't clear things up for you, come back with a more specific question and we can help.

 

[salzrah]

Ben, how can we theoretically prove that time measuring techniques that do not rely on light still have special relativistic effects? An explanation of why you said "yes" would be great.

Erland, the example post you provided suggests that both the train master and the train driver accuse each other of aging slower and "that is no contradiction." But the contradiction is that the train master/driver age slower in one reference frame and faster in another. How is that not a contradiction?

 

[bcrowell]

Ben, how can we theoretically prove that time measuring techniques that do not rely on light still have special relativistic effects? An explanation of why you said "yes" would be great.

Theoretically, it follows from the fact that SR is a description of time and space themselves, not of specific measuring sticks or types of clocks. SR doesn't predict different length contractions for wooden rulers than for aluminum rulers, and we can see this because SR doesn't have any descriptions of wood or aluminum, just space. Ditto for a wound-spring clock versus a light clock.

Experimentally, a good example is decay of relativistic muons, Bailey at al., Nucl. Phys. B150(1979) 1. Description here: http://www.lightandmatter.com/html_books/lm/ch23/ch23.html#Section23.1 (example 4).

You may have gotten the wrong impression from the common pedagogical use of the "light clock" as a way of introducing SR. The light clock doesn't actually exist, and it plays no fundamental role in relativity. You may also have gotten the impression that light itself plays some fundamental role in relativity. The modern point of view is that it doesn't. The fact that Einstein's 1905 postulates referred to light was just an artifact of people's limited understanding of fundamental particles and fields in 1905.

 

[Erland]

Erland, the example post you provided suggests that both the train master and the train driver accuse each other of aging slower and "that is no contradiction." But the contradiction is that the train master/driver age slower in one reference frame and faster in another. How is that not a contradiction?

Because they have different opinions of which events are simultaneous and not.
The event when the clock at the west end (where the station master is located) shows 2 and the event when the clock at the east end shows 2 are simultaneous wrt the platform. Since at the second of these events, the clock in the locomotive (which arrives to the east end at this precise moment) shows 1, the station master says that the train driver has been aging slower. Notice that we must talk about two events here, since the station master and the train driver are not located at the same point in space. For the station master to reach his conclusion, it is necessary that the two events are simultaneous, according to him.

But, according to the train driver, these two events are not simultaneous. The train driver must use two other events, which are simultaneous wrt the train, to find out which one is aging slower, and these two events are not simultaneous wrt the platform (and the station master). It is therefore not a contradiction that they reach different conclusions about who is aging slower.

 

[salzrah]

Ben, if we used a wound-spring clock, then how can you theoretically prove time dilation still occurs. Everyone suggests time dilation occurs independently of the way we measure time, but I have not found any theoretical proof of time dilation without using light clocks. Atomic clocks use microwaves, which is why they are compared to light clocks -- both rely on the propagation of EM waves, which I agree should show time dilation at high speeds. The experiment you cite uses atomic clocks as well. I have read on decaying muons for some time and have yet to find one experiment where atomic clocks are not used.

I understand the relativity of simultaneity much better now. Erland, I completely understand why the train driver and master think the other has aged more which is a direct consequence of time dilation. However, in Erland's example you simply say the west end clock in the train shows t=4. Why does it show t=4? Why would it show any time different that the other clock on the train?...
Other explanations of this idea use the lightning bolt example on the front end and back end of a train. Like this -- .
But, if the lady on the train accounts for her speed relative to the lightning bolt and how long it takes to reach her eyes, can't she calculate the proper time of the lightning bolt and find when it actually occurred? The part I don't understand is that just because she SEES the lightning at different times does not imply that in her reference frame the lightning bolts struck at different times. The same way when we see stars that are already dead doesn't mean they are alive to us because we are seeing them right now.

I hope readers understand that I am not arguing against time dilation, but want proof of time dilation that doesn't rely on EM waves. And I am not arguing against the relativity of simultaneity, but asking why there can't be an event that two observers in different moving reference frames experience at their own respective instantaneous present.

Nugatory, why can there not be a NOW when the times on both clocks are measured? If there is an observer that sees two objects moving relative to each other and measures the clocks at an instantaneous moment in the present state then how does the relativity of simultaneity apply?

 

[Erland]

I understand the relativity of simultaneity much better now. Erland, I completely understand why the train driver and master think the other has aged more which is a direct consequence of time dilation. However, in Erland's example you simply say the west end clock in the train shows t=4. Why does it show t=4? Why would it show any time different that the other clock on the train?...

This can be calculated by the Lorentz transformation.

Other explanations of this idea use the lightning bolt example on the front end and back end of a train. Like this -- .
But, if the lady on the train accounts for her speed relative to the lightning bolt and how long it takes to reach her eyes, can't she calculate the proper time of the lightning bolt and find when it actually occurred? The part I don't understand is that just because she SEES the lightning at different times does not imply that in her reference frame the lightning bolts struck at different times. The same way when we see stars that are already dead doesn't mean they are alive to us because we are seeing them right now.

According to the passenger, she is at rest, so she has no speed to account for. Also, light speed is c relative to her, no matter in what direction it propagates. (We have now applied both fundamental postulates of SR.) The light from both flashes travel the same distance according to her, half the length of the train (although in opposite directions). Since she sees the front flash before the back flash, she must therefore conclude that the front flash struck before the back flash (and of course, she knows that each flash strikes before she sees it).

I hope readers understand that I am not arguing against time dilation, but want proof of time dilation that doesn't rely on EM waves.

I'm afraid that's not possible, since the invariance of light speed (that is, the speed of EM waves) is a fundamental postulate of SR.

 

[Nugatory]

Nugatory, why can there not be a NOW when the times on both clocks are measured? If there is an observer that sees two objects moving relative to each other and measures the clocks at an instantaneous moment in the present state then how does the relativity of simultaneity apply?

The problem is that all the observers have their own equally valid NOW.

Say I'm floating in space, and suddenly two spaceships zoom past me, each traveling at .6c, one moving left to right and the other moving right to left. As they pass in front of me, all three of us set our clocks to zero.

Then I wait for 100 seconds by my clock. At the exact moment that my clock reads 100 seconds, both of the spaceship clocks will read 80 seconds, for me, using my frame's notion of simultaneity. (How I actually know what their clocks say is a non-trivial problem - we can go there later). So I'll say that at the exact moment that the left-mover's clock reads 80, my clock reads 100. I also say that his clock is running slower than mine, because his ticked off 80 seconds since they were synchronized while mine ticked off 100.

But what about the guy on the left moving spaceship? For him, at the exact moment that his clock reads 80, my clock reads 64 and he says that my clock is running slow. That's relativity of simultaneity at work: to him, 80 on his clock and 64 on mine are simultaneous, while for me 80 on his clock and 100 on mine are simultaneous.

Meanwhile, we've still got this other spaceship zooming off to the right. I'll say that when my clock reads 100, his clock reads 80, just like left-mover's clock. But when right-mover sees his clock reading 80, he won't say that mine reads 100 and left-mover's reads 80. He'll say that my clock reads 64 at the moment that his reads 80, and that left-mover's reads something less than 64.

So we all end up seeing everyone else's clock running slow relative to ours, yet there is no paradox.

 

[salzrah]

So the amount of time progressed at the back end of the train is different from the time progressed at the front of the train? How does that even intuitively make sense?

The only reason she sees the front flash first is because of her velocity relative to the flash. She is traveling towards the front flash so she sees it before. If she accounts for her speed relative to the flashes she will determine the flashes occurred at the same time but she saw one first. This does not mean it occurred first.

Oh my...I know light speed is invariant. I know it is a fundamental postulate of SR. I am talking about proving time dilation without using EM waves to measure that time.

 

[salzrah]

Nugatory, how can "all the observers have their own equally valid NOW."?
Isn't the present an all encompassing instantaneous event for everything in the universe. One object can not, not be in the present while another is in the present. I like your example, and yes I understand that we observe the time in another reference frame to move slower if that frame is moving with a velocity relative to you. However, the contradiction is still there. In one reference frame the time progressed in one reference frame is less than what an observer in another reference frame measures it to be. The reason I brought up this "contradiction" is that when people say time moves slowly at close to c speeds, it does not mean that things in the "moving" reference frame will actually move slower to the "stationary" reference frame. Just the time the "stationary" frame measures to pass will be different then the time measured in the "moving" frame. The actual time passed will be equal if both reference frames measure their own time passage.

 

[Nugatory]

The part I don't understand is that just because she SEES the lightning at different times does not imply that in her reference frame the lightning bolts struck at different times.

Just as you say, she must allow for the time for light to travel between the point of the strike and her eyes, and adjust her notion of when the strike happened accordingly.

But if light always travels at the speed c, and if both strikes happened at the same distance D from her... Then that travel time will be D/c for both strikes, so she makes the same adjustment for both strikes. With the same adjustment, there's no way that the light can reach her eyes at different times if the strikes were simultaneous.

 

[salzrah]

Yes, but while the two light flashes are traveling towards her, she is not still. She is moving away from one light flash and towards another. So she sees the front one first, even though they occurred at the same time.
To better put it -- the back light flash must travel a greater distance than the front flash.

 

[Nugatory]

Isn't the present an all encompassing instantaneous event for everything in the universe?

No. It's weird, it's counter-intuitive, it goes against everything we've learned in a lifetime experiencing speeds that are small compared with the speed of light... But nonetheless, there are no all-encompassing instantaneous events for everything in the universe.

That's what "relativity of simultaneity" means. You can't say that two things happen "now" without also implying that they're happening at the same time (that time being now, of course). If "at the same time" is relative, then there's no universal now.

 

[Erland]

Isn't the present an all encompassing instantaneous event for everything in the universe.

No, it is not so! An event is given by three space and one time coordinate (x,y,z,t), although the coordinates depend of the reference system. If we change the space coordinates of an event, we get another event, even if the time coordinate remains unchanged. If I am sleeping in my bed the very moment you read this, these (my sleeping and your redaing) are different events even if they are simultaneous (wrt us observers on Earth). An observer in a reference system moving with a high speed wrt us will not consider these two events as simultaneous.

There is no such thing as "an all encompassing instantaneous event for everything in the universe". The present, wrt us, is an infinite set of events which are simultaneous wrt us but not wrt observers in motion wrt us. Such an observer has another "present".

 

[Nugatory]

Yes, but while the two light flashes are traveling towards her, she is not still. She is moving away from one light flash and towards another. So she sees the front one first, even though they occurred at the same time.
To better put it -- the back light flash must travel a greater distance than the front flash.

But suppose I choose a point of view in which she's not moving? She and the train are at rest, while the ground is moving backwards. So a lightning flash hits both ends of this stationary train, and the lady in the middle of the train will see the flashes if and only if they happened at the same time. But the the observer on the platform, which is moving backwards while the train is at rest, will not see the flashes at the same time.

What makes the platform observer's assertion that the flashes were not simultaneous any more right than the train lady's assertion that they were?

 

[Erland]

Yes, but while the two light flashes are traveling towards her, she is not still.

But she is still! In the reference system at rest wrt the train, that is. And this reference system is precisely as valid as the one at rest wrt the platform. This is what the special principle of relativity says.

 

[salzrah]

"You can't say that two things happen "now" without also implying that they're happening at the same time"

Time is relative because of the way we measure time. The present is independent of time. If one event occurs NOW, it occurs NOW for every frame of reference. We just MEASURE the time that the event occurs differently. An event can not happen in the present for a reference frame while it has already happened or will happen in another frame.
I may be wrong in saying what I have stated, but every example I see disregards that the object that is moving has to account for its movement relative to the light flashes to see when the light flashes ACTUALLY occurred. If you can provide me a better example proving the relativity of simultaneity it would be great!

 

[salzrah]

She is not still relative to the light flashes. I don't know if you watched the youtube video I posted, but the flashes of light hit the ground from the sky. The train/lady has a velocity with respect to the flashes.

 

[Nugatory]

She is not still relative to the light flashes. I don't know if you watched the youtube video I posted, but the flashes of light hit the ground from the sky. The train/lady has a velocity with respect to the flashes.

Careful - she may be moving relative to the points where the lightning bolts hit, but that's not what we're talking about. We're talking about the light traveling from the point of the strike to her eyes, and that light is traveling at c relative the lady no matter what her speed is.

 

[salzrah]

Yes, that is correct. But let me try to better convey what I am saying--

Let's assume the speed of light is 5 m/s. The train is 10 m long moving with a velocity of 1 m/s relative to the ground. Now, both lightning strikes occur and the flashes of light propagate towards the midpoint of the train where the lady is sitting. If the lady and train are moving at 1 m/s away from where they originally were, the back lightning flash will need to move through a larger distance to catch up to the lady who is now in a position further away. Likewise, the front flash will have to cover a smaller distance to reach the lady because she will be closer to the front flash than she originally was.
Now to numerically justify this- let's say the lightning strikes occur at x=0 and x=10. After one second, the front lightning flash will be at x=5 and the back flash will also be at x=5. However, the lady will have moved to x=6. So the front flash will have hit her, but not the back flash. After 1.x seconds the lady will see the second flash. Now, just because she SEES the lightning flashes at different times doesn't mean that they actually occurred at different times in her reference frame.

 

[Nugatory]

Yes, that is correct. But let me try to better convey what I am saying--

Let's assume the speed of light is 5 m/s. The train is 10 m long moving with a velocity of 1 m/s relative to the ground. Now, both lightning strikes occur and the flashes of light propagate towards the midpoint of the train where the lady is sitting. If the lady and train are moving at 1 m/s away from where they originally were, the back lightning flash will need to move through a larger distance to catch up to the lady who is now in a position further away. Likewise, the front flash will have to cover a smaller distance to reach the lady because she will be closer to the front flash than she originally was.
Now to numerically justify this- let's say the lightning strikes occur at x=0 and x=10. After one second, the front lightning flash will be at x=5 and the back flash will also be at x=5. However, the lady will have moved to x=6. So the front flash will have hit her, but not the back flash. After 1.x seconds the lady will see the second flash. Now, just because she SEES the lightning flashes at different times doesn't mean that they actually occurred at different times in her reference frame.

Try doing the same calculations, but assuming that the train is at rest and the ground is moving at a velocity of -1 m/s relative to the train. What results do you get?

Is there any difference between the two cases, or any reason why you should prefer one answer over the other?

 

[salzrah]

If you do that, the lady will see the lightning flashes at the same time and they actually occurred at the same time. However, the person on the ground will be moving away one flash and towards another so he will SEE the lightning flashes at different times, but can perform calculations including the relative -1 m/s to see that the lightning strikes happened at the same time.
You get the same answer in both situations - the lightning strikes are simultaneous in both reference frames.

 

[Nugatory]

If you do that, the lady will see the lightning flashes at the same time AND they actually occurred at the same time. However, the person on the ground will be moving away one flash and towards another so he will SEE the lightning flashes at different times, but can perform calculations including the relative -1 m/s to see that the lightning strikes happened at the same time.
You get the same answer in both situations - the lightning strikes are simultaneous in both reference frames.

Why should the guy on the ground include the relative -1 m/s at all? Maybe he has his back to the tracks so he doesn't see the train at rest so can't know that he's moving at 1 m/s relative to the train.

Or maybe he's looking up at the sky, where there's an airplane zooming by at 300 m/s (relative to the train, hence 301 m/sec relative to the platform guy), also being hit at both ends by the same two lightning bolts. Why shouldn't he apply a correction of 301 m/s instead of 1 m/s?

 

[salzrah]

Let's say the lightning strikes occur in mid-air right above the ground with the guy standing in the middle of the two strikes. The ground/guy is moving at -1 m/s relative to the train and the lightning flashes. I think you're not accepting that the observer that is moving is moving with a relative velocity with respect to the lightning strikes. Yes, he sees the light propagate at c, but he himself is also moving away from his original position between the two lightning strikes. So, he is moving closer to the left lightning flash and further from the right lightning flash while both are approaching him.
Basically -- the lightning flashes have to travel different distances to reach the guy so he SEES them at different times.

 

[Erland]

If you do that, the lady will see the lightning flashes at the same time and they actually occurred at the same time. However, the person on the ground will be moving away one flash and towards another so he will SEE the lightning flashes at different times, but can perform calculations including the relative -1 m/s to see that the lightning strikes happened at the same time.
You get the same answer in both situations - the lightning strikes are simultaneous in both reference frames.

Here you are saying that the passenger will SEE the flashes at the same time if she considers herself being at rest and that she will SEE them at different times if she considers herself being in motion. This contradicts the special relativity principle, which, as you know, is a fundamental postulate of SR. She either sees the flashes at the same time or at different times, and that must be independent of her motion relative to the platform.

Now, suppose that the flash that hit the ground at the point to which the front of the train just arrives also hit the front of the train (that would be no problem, since the distance between that point on the ground and the front of the train at that moment is neglible, we effectively talk about one and the same event here). Suppose also that there is a detector at the front of the train which, in the moment when it detects the flash (with neglible time lapse) sends a light signal backwards in the train, which the passenger will see when it reaches midtrain.

Likewise, the back flash also hits the back of the train, where there is a similar detector sending a light signal forward in the train.
Notice that these detectors, which are the sources of the light signals, are at rest relative to the train.
The passenger on the train sees both the flashes hit the ground and the signals sent by the detectors. Now:

1. Does the passenger SEE the front flash and the signal from the front detector at the same time or at different times?

2. Same question for the back flash and the signal from the back detector?

If your answers to these questions are "different times", then this contradicts the invariance of light speed, which says that the light speed will be measured to the same independently of the velocity of the light source relative to the observer.

If your answer is "same time" (to both questions) then you must admit that she sees the signal from the front detector before she sees the signal from the back detector (it is the observer at the platform who sees them simultaneously), and since she is at rest relative to the detectors, and the light from the detectors has traveled the same distance according to her, she must conclude that the flashes did not strike simultaneously.

So, according to the observer at the platform, the flashes strike simultaneously, but not according to the train passenger. And by the special relativity principle, there is NO WAY we can say that one of them is more right than the other.

 

[Erland]

I don't know if you watched the youtube video I posted, but the flashes of light hit the ground from the sky. The train/lady has a velocity with respect to the flashes.

You are complicating things unnecessarily. It is clear from the video that the light that is interesting here is the parts of the flashes striking the front and the back of the train. This light originate at these very places, not up in the sky. The parts of the flashes in the sky are not of interest here. Presumably, the lightning is caused by electrons in motion due to electrical disharge, and there are many electrons all the way from the sky to the ground, so light is originating at several places. But the physics of lightnings is not really interesting here. The important thing is the parts of the flashes which hit the front and the back of the train.

In my opinion, they made a small mistake in the video, when they placed the observer on the platform at a perpendicular distance from the rail. I would have placed him next to the rail, at a very short (neglible) distance from it. This way we don't need to bother about a light speed components perpendicular to the motion of the train relative to the platform. This doesn't change the conclusion, though.

 

[Nugatory]

The ground/guy is moving at -1 m/s relative to the train and the lightning flashes. I think you're not accepting that the observer that is moving is moving with a relative velocity with respect to the lightning strikes. Yes, he sees the light propagate at c, but he himself is also moving away from his original position between the two lightning strikes. So, he is moving closer to the left lightning flash and further from the right lightning flash while both are approaching him.
Basically -- the lightning flashes have to travel different distances to reach the guy so he SEES them at different times.

We agree that because the observer is moving the light from the to impacts has to travel different distances to reach the observer, and that the observer can compensate (light from this flash traveled distance D1 so took time D1/c to get from point of strike to my eye; light from that flash traveled distance D2, so took time D2/c to get from point of strike to my eye). But that's not the point of relativity of simultaneity; the point of relativity of simultaneity is that we cannot use the corrections to arrive at a global "at the same time" that can be shared all observers.

Let's consider not two lightning strikes but three. I'll call them A, B, and C. A and B hit on opposite sides of the ground observer, placed and timed so that the light from these strikes reaches his eyes together. We know, therefore, that train-lady will see the light from these two flashes at different times because of her motion relative to ground observer. Now, train-lady knows about her relative velocity, so the two flashes had to travel different distances to get to her eyes, so you might think that she can calculate when they "really" happened and conclude that just as platform-guy says, they really happened at the same time even though she saw them at different times. You might think that.

But...
Suppose there's a third flash, which we'll call C. It also lands the same side as B, but it is placed and timed so that the light from its flash reaches train-lady's together with the light from flash A. Of course because of the relative motion between the train-lady and the platform-guy we know that this means that the light from A and C will not reach platform-guy's eyes at the same time. And if we try telling platform-guy that this is an illusion of motion, that A and C "really" happened at the same time and the light from the two events just had to travel different distances to get to his eyes, he'll laugh at us, for two reasons:
1) What motion? As far as platform-guy is concerned, he's not moving while A and C are happening around him.
1) We've already agreed that A and B happened at the same time; if we then claim that A and C also happen at the same time we're forced to the absurd conclusion that B and C happened at the same time as well.

So we're left with two different but equally reasonable ways of describing what happened:
a) Platform-guy says A and B happened at the same time, and C happened a bit later.
b) Train-lady says A and C happened at the same time, but a bit after B.

Which of these is right? You can't say that it depends on which one of the them is "really" moving, because it's just as reasonable to consider the train at rest and the platform moving backwards as the platform at rest and the train moving forward.

The answer, according to relativity of simultaneity, is that they are both right: "at the same time" and "now" mean different things to observers moving at different speeds relative to one another. And this is why when when back in post #8 you asked "Isn't the present an all encompassing instantaneous event for everything in the universe?" we answered NO.

------
(BTW, even though one of our observers sees B happen before C and the other sees B happen after C, no matter how you twist and turn you won't be able to construct a paradox in which an effect happens before its cause. Relativity of simultaneity is surprising and counter-intuitive, but it is not illogical).

 

[salzrah]

Erland, I don't get why you're trying to blow up what I said. Kind of ironic that you write all that and blame me for over complicating things. I was just trying to paint a visual of what happened and to make sure you saw the video; no where do I discuss the phenomena later as any justification for my argument...Either way, yes the way the lightning happened doesn't matter, only the flashes at the front and back are important...

If your answer is "same time" (to both questions) then you must admit that she sees the signal from the front detector before she sees the signal from the back detector (it is the observer at the platform who sees them simultaneously), and since she is at rest relative to the detectors, and the light from the detectors has traveled the same distance according to her, she must conclude that the flashes did not strike simultaneously.

My answer to the two questions you posted is "same time." Can you explain to me why she sees the signal from the front detector before she sees the signal from the back detector?

 

[Erland]

Erland, I don't get why you're trying to blow up what I said. Kind of ironic that you write all that and blame me for over complicating things. I was just trying to paint a visual of what happened and to make sure you saw the video; no where do I discuss the phenomena later as any justification for my argument...Either way, yes the way the lightning happened doesn't matter, only the flashes at the front and back are important...

I am glad we agree about that. I didn't mean to make you upset. Please, accept my apology if you were. I just wanted to point out that there is no point in considering the light originating up in the sky. Since we agree on this, let's continue:

My answer to the two questions you posted is "same time." Can you explain to me why she sees the signal from the front detector before she sees the signal from the back detector?

If she sees the two signals from the detectors at the same time, mustn't she then also see the two flashes at the same time?

 

[salzrah]

Nugatory-
In regards to the third signal C, you say that the light flash/signal is timed so that it reaches the lady's eyes at the same time as flash A. This inherently means that C and A did NOT happen at the same time. In the reference frame of the light flashes themselves, A occurs at a different time than C so they reach the lady's eyes at the same time (which she can calculate and find out didn't actually happen at the same time even though she sees them at the same time).
Because the light flashes are independent of the motion of the train, the man on the ground will see the light flashes at different times as well. He will see flash C, then flash A. When you say -
"a) Platform-guy says A and B happened at the same time, and C happened a bit later.
b) Train-lady says A and C happened at the same time, but a bit after B. "

a) is right, but in b) train-lady should NOT say A and C happened at the same time. Because just as you agreed with me, she can calculate that A and C did not happen at the same time but it was because of her motion she saw it that way. So they are BOTH right.

 

[salzrah]

If she sees the two signals from the detectors at the same time, mustn't she then also see the two flashes at the same time?

Yes, but you said she sees the two flashes at different times, correct? I was wondering what your justification is to conclude that she sees the flashes at different times. I agree with this, I just want to see how you're looking at the situation.

 

[Erland]

Yes, but you said she sees the two flashes at different times, correct? I was wondering what your justification is to conclude that she sees the flashes at different times. I agree with this, I just want to see how you're looking at the situation.

Well, it follows from the original setup of the problem, and is explained in the video, that the passenger sees the front flash before she sees the back flash. I thought you agreed on this. Don't you?

 

[salzrah]

Erland, I think the underlying difference between us is that I am saying the lady/train has motion relative to the reference frame of the platform AND motion relative to the reference frame of the light flashes. I don't think you are accepting that she has motion relative to the origin of the light flashes. Or vis versa -- looking through the reference frame of the light flashes, you're not accepting that the lady is moving.