Still learning about special relativity, .

[Wattever]

I'm reading Einstein's book about relativity and having some trouble - two to be specific.

1. You all probably know this experiment already but I'll copy and paste it from the book just in case.There's a moving train and an embankment, with respect to the embankment two flashes of lightning happen at A and B simultaneously.

"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 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 flashes 1 of lightning occur, this point M' naturally coincides with the point M, 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. 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. Hence the observer will see the beam of light emitted from B earlier than he will see that emitted from A."

As far as my understanding goes, the difference in the judgment of simultaneity is only because the observer is at M' (by the time light reaches M' AM' will have become larger and BM' will have become shorter), but if we place some sort of light detectors at the exact points where the lightning strikes, there shouldn't be any difference. Is that correct?

2. A person on a moving train walks a distance from A to B, why is this distance different when it is judged from the embankment that when it is judged by a passenger?

 

[bucher]

For issue #1, placing light detectors at the points of the train where the lightning strikes would show simultaneity (the light would have to travel the same distance towards the moving detector).

Simultaneity is relative to the observer. What may happen at the same time for one may happen at different times for another.

For issue #2, think about length contraction of the train relative to the embankment.

 

[Wattever]

1. But wouldn't that just be a mistake on the observer's part? Taking into acount the velocity of light and that of the train, an observer at M' should make the conclusion that the lightning could have happened at A at the same time it did at B, and that it could have happened at a point closer to M' than A, after it had happened at B. But the books says: "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."

2. Am I supposed to know about length contraction at this point? Nothing has been mention about it so far but it is implied that I should already understand the difference in measurement:
"In the first place we require to determine the points A and B of the embankment which are just being passed by the two points A' and B' at a particular time t—judged from the embankment. These points A and B of the embankment can be determined by applying the definition of time given in Section VIII. The distance between these points A and B is then measured by repeated application of the measuring-rod along the embankment.
A priori it is by no means certain that this last measurement will supply us with the same result as the first." (emphasis not mine)

 

[bucher]

1. What the book is trying to convey is that, according to the observers on the train, the two lightning strikes happened at different times. The observers could very well think that it was simultaneous to someone else. But to those observers on that train the two events were not simultaneous. Again, simultaneity is a concept on relativity. It is different to each observer. There is no absolute scenario of what really happened. There are just observations of the scenario from different points of view; each view can be completely different from one another and still be deemed as the correct view at that reference point.

2. I'm not quite sure what the book is trying to say but I think that it may be getting into length contraction. I would read Section VIII, maybe it has some clue.

 

[Wattever]

1. OK, but for example we, here on earth, know perfectly well that things we see happening in stars far off are not happening at the time we see them! In the book this is how Einstein defines simultaneity: "If the observer perceives the two flashes of lightning at the same time, then they are simultaneous." That just doesn't seem right :/ Why then do we say that this star or that might be dead at a time when we can still see it? Isn't that the same thing? I understand that there doesn't have to be any absolute scenario, but each scenario has to be formed correctly!

2. Section VIII is about simultaneity/time, simultaneity is defined as in the quote above.

 

[Integral]

1. OK, but for example we, here on earth, know perfectly well that things we see happening in stars far off are not happening at the time we see them! In the book this is how Einstein defines simultaneity: "If the observer perceives the two flashes of lightning at the same time, then they are simultaneous." That just doesn't seem right :/ Why then do we say that this star or that might be dead at a time when we can still see it? Isn't that the same thing? I understand that there doesn't have to be any absolute scenario, but each scenario has to be formed correctly!

2. Section VIII is about simultaneity/time, simultaneity is defined as in the quote above.

Flashes is a key word in that definition, you must know that distant galaxys do not flash.

 

[Wattever]

I don't understand the significance, isn't it just something that happens that we could see?

 

[bucher]

Though the observers on the train see the lightning as non-simultaneous. They can still calculate to see what the embankment would observe. It's not like they are barred from thinking that someone else could have observed something differently. The book is stating that when an observer sees two events happen at the same time then those two events are simultaneous to the observer. These event times can be adjusted to any reference frame. If someone were running on top of the train were to see the flash, their perception of the events would be different than those in the train and those on the embankment. These events are adjusted to each observers inertial reference frame. We know that it takes roughly 8 minutes for light to go from the Sun to Earth. But if the Sun were to stop emitting light, we would know that the Sun stop emitting light 8 minutes ago because we adjusted for the distance it took for light to reach us. The event is not simultaneous, but we can still adjust to see what other observers saw.

 

[ZikZak]

1. OK, but for example we, here on earth, know perfectly well that things we see happening in stars far off are not happening at the time we see them!

An "observation" in Relativity is what you get after light-travel times are taken into account. You look through your telescope, say "what I am seeing is 2 light-seconds away," and then subtract 2 seconds from the time read out on your watch when you log the time of the event you see.

Einstein was saying that since the passenger on the train is in the MIDDLE of the train, having previously measured very carefully that the distances to the front and back of the train were exactly equal, and knowing that the speed of light is always c, that he is in a special position on the train, such that the time it takes a signal to get to him from the front is the same as the time from the back. So if he sees one flash before the other, he can only conclude--- he MUST conclude--- that the actual time of that event was earlier.

It does NOT help the passenger to place lightning detectors in front and back and let them do the observing for him. For he must synchronize the clocks on those detectors with is own in the middle of the train, and he does this by making his clock flash a light when it reads, say, zero, and knowing the distances to the detectors, programming them to reset their clocks to the time it will take that sync-flash to get there. Thus the clocks are all synchronized based on the perfect, constant, speed of light (but in the reference frame of the platform observer will still suffer from the same problems the lightning-flashed did) and thus the clocks will read differently when the lightning flashes hit.

 

[jtbell]

It does NOT help the passenger to place lightning detectors in front and back and let them do the observing for him. For he must synchronize the clocks on those detectors with is own in the middle of the train, and he does this by making his clock flash a light when it reads, say, zero, and knowing the distances to the detectors, programming them to reset their clocks to the time it will take that sync-flash to get there.

You don't actually have to use light for this synchronization procedure. You could also use very precise baseball-shooting machines which always shoot baseballs at the same known speed (in the machine's rest frame of course). It's simply more convenient conceptually to use light, since we know its speed (by assumption at least).

 

[Wattever]

It's not like they are barred from thinking that someone else could have observed something differently.

But it's not observation that we're concerned with. Suppose we're on the train, and at time t there was to be a cat at point A and we want to know if it had been struck by the lightning we saw. If we were to make the assumption that the lightning had struck A at time t+some, we would come to the conclusion that the lightning hadn't struck the cat, when in fact it had. So this would be a mistake we're making regardless of other reference frames.

such that the time it takes a signal to get to him from the front is the same as the time from the back.

But this is wrong, the distance from one will decrease and the other will increase because the train is moving, and the velocity of light is the same, so obviously the time the signals take to reach him from each end will be different.
OK now I'm confused. Why doesn't this happen on the embankment as well since the Earth is moving?

 

[bucher]

Suppose we're on the train, and at time t there was to be a cat at point A and we want to know if it had been struck by the lightning we saw. If we were to make the assumption that the lightning had struck A at time t+some, we would come to the conclusion that the lightning hadn't struck the cat, when in fact it had. So this would be a mistake we're making regardless of other reference frames.

If the cat was struck by lighting at time t according to the embankment, then it would be struck at time t' according to the people in the train. You have to account for relativity due to the train's speed and the distance that the light needs to cover to reach the train's observers.

 

[Wattever]

I'm assuming that we can't see the cat, it's on the roof or something. We'll conclude that the lightning happened at t', and we know the cat was only there at t (not because we see), therefore it was not struck by lightning, which is incorrect.

 

[bucher]

The two times observed (embankment and train) are different. The cat was struck by lighting at t according to the embankment and it was struck at time t' according to the train. The two times are different when compared. The reason why they are different is because the train was moving relative to the embankment. The two reference frames are not the same so the time the cat was struck would not be the same.

 

[JazzFusion]

Try this one:

(Clip from a NOVA special describing exactly this issue with exactly this scenario)

 

[Wattever]

The two times observed (embankment and train) are different. The cat was struck by lighting at t according to the embankment and it was struck at time t' according to the train. The two times are different when compared. The reason why they are different is because the train was moving relative to the embankment. The two reference frames are not the same so the time the cat was struck would not be the same.

Except we're not calculating the time it was struck, only whether or not it was struck at all given that it magically appears at A at a specified time t (we had a revelation that it will, doesn't matter) and disappears just after that, and that we cannot see it. (You overlooked my previous post)

I'll watch the video, but I got to go now - making this post in a haste.

 

[Wattever]

I watched the video, it doesn't add anything to what the book says :(

 

[ZikZak]

Except we're not calculating the time it was struck, only whether or not it was struck at all given that it magically appears at A at a specified time t (we had a revelation that it will, doesn't matter) and disappears just after that, and that we cannot see it. (You overlooked my previous post)

I'll watch the video, but I got to go now - making this post in a haste.

There is no "global" universal absolute clock ticking away the universe. If the cat appears at time t in the embankment frame and is struck by lightning, then in the train's frame it appears at time t' (NOT t) and is still struck by the lightning. There is no absolute sense in which one observer's clock is "correct" and the other is not. That is why it is called "Relativity."

 

[Wattever]

There is no "global" universal absolute clock ticking away the universe. If the cat appears at time t in the embankment frame and is struck by lightning, then in the train's frame it appears at time t' (NOT t) and is still struck by the lightning. There is no absolute sense in which one observer's clock is "correct" and the other is not. That is why it is called "Relativity."

In what sense will it appear at t' and not t? Even if we cannot see it? Same as with the lightning, assume there's a detector that detects the presence of the cat there at time t, we do not see it appear. And also a lightning detector that detects the flash of lightning at time t. Now keep the cat detector and replace the lightning detector with the observer, we'll have two different time t and t'! Ergo, we'll make an incorrect conclusion as whether or not it was struck, making our perception of time incorrect to begin with - not because it doesn't agree with another reference frame but because it leads to incorrect conclusions (also, we cannot attribute the error to the fact that we used two different methods of knowing time-- it could be as ordinary as a person who steps on A when his wrist watch strikes t).

 

[bucher]

Now keep the cat detector and replace the lightning detector with the observer, we'll have two different time t and t'!

The detectors on the train will be affected by time delay as well. Everyone/everything on that train will be affected.

In order to see the cat, photons will have to bounce off the cat and reach an observer. It takes time for the light to reach that observer. When the cat is struck by lightning, it will take time to observe the flash. The observers/detectors on that train will still observe/detect the cat being struck by lightning at point A. The only discrepancy is at what time. The observers on the train will experience time delay along with extra waiting for the light to reach them. The observers on the embankment will have to wait for the light to reach them as well (it will be a shorter distance). Even the cat (if it had a detector) would have recorded a different time. This is not simultaneity because it's one event now; but some of its principles still apply. Observers/detectors when in different positions and/or velocities will observe an event to happen at different times.

 

[ZikZak]

In what sense will it appear at t' and not t? Even if we cannot see it? Same as with the lightning, assume there's a detector that detects the presence of the cat there at time t, we do not see it appear. And also a lightning detector that detects the flash of lightning at time t. Now keep the cat detector and replace the lightning detector with the observer, we'll have two different time t and t'! Ergo, we'll make an incorrect conclusion as whether or not it was struck, making our perception of time incorrect to begin with - not because it doesn't agree with another reference frame but because it leads to incorrect conclusions (also, we cannot attribute the error to the fact that we used two different methods of knowing time-- it could be as ordinary as a person who steps on A when his wrist watch strikes t).

Once again, it makes no difference whether you are using cat detectors or not. If the observer on the embankment observes (via light waves, with a cat detector, or in any way whatsoever) the cat to appear and be struck by lightning at time t, then the observer on the train observes the cat to appear and be struck by lightning at time t'. Special Relativity does not "lead to incorrect conclusions." That is why it is an accepted theory.

 

[Wattever]

You guys, you're not even reading! Yes, the observer on the train will see it struck at t', but I'm pretty sure I've said over and over that the observer cannot see it at all! The observer can see the lightning, but not the cat! It's a transparent cat, ok?

In order to see the cat

I did mention that the observer doesn't see the cat, more than once.

Even the cat (if it had a detector) would have recorded a different time.

Why would the detector record a different time? The detector is exactly at point A, and it records the time as t. Then maybe after half an hour I go pick it up and check the reading, I do not take the reading when I'm at M' but when I've walked over to A.

then the observer on the train observes the cat to appear and be struck by lightning at time t'.

The observer on the train does not observe the cat at all. It's transparent cat.

Special Relativity does not "lead to incorrect conclusions." That is why it is an accepted theory.

:/ So? I still don't understand this, which is why I'm posting in this forum asking for help.

 

[JesseM]

But it's not observation that we're concerned with. Suppose we're on the train, and at time t there was to be a cat at point A and we want to know if it had been struck by the lightning we saw. If we were to make the assumption that the lightning had struck A at time t+some, we would come to the conclusion that the lightning hadn't struck the cat, when in fact it had. So this would be a mistake we're making regardless of other reference frames.

This scenario is very vague--why would we assume the lightning had struck A at time t+some, as opposed to time t? And since there is no universal time, do t and t+some refer to the time in our own frame? In any case, it's definitely true in relativity that different frames always make the same predictions about whether different events coincide at a single point in spacetime (like whether a cat was at A at the moment lightning struck A), so there must be some mistake in your thinking here.

But this is wrong, the distance from one will decrease and the other will increase because the train is moving

There is no absolute way to define "moving" in relativity--all velocity is relative, which is one of the reasons it's called "relativity". For any non-accelerating object, you can pick an inertial frame where that object is considered to be at rest, and one of the two basic postulates of relativity is that all the laws of physics work the same way in every inertial frame (so if two observers perform the same experiment within ships moving relative to each other, they will each get identical results). The other postulate, of course, is the one that says that light has the same speed of c in every inertial frame. This second postulate is more like a definition of how to define simultaneity in different frames than an empirical postulate (we define two clocks as 'synchronized' in a given frame if light from a flash at the midpoint reaches each clock when it shows the same reading), the empirical part is that if you define inertial coordinate systems such that light has the speed of c in every frame, then the laws of physics are such that the first postulate will be satisfied, i.e. the equations of the laws of physics will be the same when expressed in any inertial coordinate system. If you defined simultaneity differently than many basic laws of physics like Maxwell's equations would not hold in every inertial coordinate system.

So, we are free to pick a frame where the train is at rest, and light must move at c in this frame. So if the light from each end reaches the center simultaneously, the lightning must have struck each end simultaneously in this frame.

OK now I'm confused. Why doesn't this happen on the embankment as well since the Earth is moving?

In the embankment frame the embankment is at rest. Again, there is no absolute way to define whether anything is "moving", speed can only be defined relative to some choice of reference frame.

 

[matheinste]

Hello Wattever.

JesseM replied while I was writing this and covered the parts I have not covered. My reply just addresses the cat scenario but is relevant in a wider sense.

I hope another perspective may help. First you need to be sure of the basic definitions in Special Relativity. I have made a not very rigorous attempt at some of them below.

First of all the word observer is used as any data recording or collection device, human or otherwise, which assigns to an event a time and a place with respect to some coordinate system. An event is a happening at a certain place and a certain time. It has no duration in either space or time. If an event is not observed it did not happen. Events e.g. the appearance of a cat are not invisible, but of course they may be hidden from human view. It is also understood that these observers take into account light travel time. It is often useful to use an observer present at an event who makes a recording of time and place for later inspection and use in calculations. This removes the necessity of taking into account light travel times. Usually the word “see” describes what a remote observer, that is one not actually present at an event, actually sees and does not take into account light travel times. Also, an event either occurs or does not occur. If it occurs it occurs for all observers and if it does not occur it does not occur for all observers.

If you consider the lightning strike at a certain point at a certain time as event 1 and the appearance of the cat a certain point and a certain time as event 2, then the lightning striking the cat is the simultaneous happening or coincidence of these two events. Because these two events occur at the same place and the same time (this is important) in one reference frame, then they must happen at the same time and place in all reference frames. This just says that if two events coincide in one reference frame then they coincide in all reference frames. So the striking of the cat occurs for all observers. However, although each observer regards these events 1 and 2 as simultaneous in their respective frames, the coordinates they assign to these events may not agree, hence the assignment two different times in this example.

Matheinste.

 

[Wattever]

This scenario is very vague--why would we assume the lightning had struck A at time t+some, as opposed to time t?

For the same reason the two flashes of lightning appear not to be simultaneous to an observer at M'.

(we define two clocks as 'synchronized' in a given frame if light from a flash at the midpoint reaches each clock when it shows the same reading)

Yes, this is what's bothering me. The scenario I gave is to explain why this definition doesn't make sense to me.

First of all the word observer is used as any data recording or collection device

Sure. What I wanted to clarify is that there are two observers on the train (they're both on the train): one at A observing the cat, and one at M' observing the lightning (and the lightning alone). Would it be their conclusion that the lightning strikes the cat? If not, they would be absolutely wrong, because the effect of the strike of lightning would be apparent on the cat afterwards. If they do reach that conclusion, then they must've taken into account that the distance light has to travel in order to get from A to M' is not the same as the actual distance from A to M' (as measured by people on the train), no?

 

[matheinste]

What I wanted to clarify is that there are two observers on the train (they're both on the train): one at A observing the cat, and one at M' observing the lightning (and the lightning alone). Would it be their conclusion that the lightning strikes the cat? If not, they would be absolutely wrong, because the effect of the strike of lightning would be apparent on the cat afterwards. If they do reach that conclusion, then they must've taken into account that the distance light has to travel in order to get from A to M' is not the same as the actual distance from A to M' (as measured by people on the train), no?

Just to clarify. Two observers are on the train, and therefore can regard themselves at rest in the same inertial reference frame. One observer watches the event of the lightning strike and notes the times. The second observer watches the event of the cat cat momentarily appearing and notes the time. If the lightning strikes the cat then both observers, if they have previously synchronized their clocks with each other, will record the same time because they are in the same reference frame.

In other words two observers with previously synchronized clocks, wherever they are located, as long as they are not moving relative to each other, that is in the same inertial reference frame, will each assign the same time value to each event.

If the lightning strikes the cat, if two observers in another reference frame, who have synchronized their clocks with each other, one watching lightning flash and the other watching the appearance of the cat, will also record the same times as each other but not the same time as the other two observers in the other frame. The readings that the observers record, unless they are colocated with the events, are assumed to have taken into account light travel times. This adjustment takes into account distances from the events in both frames.

If two observers in the same frame of reference record different times, after adjustment, then they must conclude, correctly, that the lightning did not strike the cat.

Matheinste.

 

[JesseM]

For the same reason the two flashes of lightning appear not to be simultaneous to an observer at M'.

That doesn't make sense--the reason they appear to be non-simultaneous to the train observer is that in his frame the two strikes occurred at different distances from himself (at rest at the midpoint of the train), so if he assumes the light from both flashes traveled at the same speed towards him, the only way to explain the fact that both rays of light reached him at the same time is to infer that the light from the more distant flash occurred at an earlier time (for each flash, he infers that the time the flash occurred can be calculated by [time light reached him] - [c*distance of flash from him]). How is anything like this supposed to apply to the cat scenario? Naturally if the event of the cat being at A coincided with the lightning striking A, then the distance between any observer and the event [cat at A] will be the same as the distance between that observer and the event [lightning strikes A].

Sure. What I wanted to clarify is that there are two observers on the train (they're both on the train): one at A observing the cat, and one at M' observing the lightning (and the lightning alone). Would it be their conclusion that the lightning strikes the cat?

If indeed it struck the cat, sure. Why would you imagine otherwise? The observer at A will obviously see the lightning strike A at the same time the cat reaches A, say at some time T, while the observer at M' will see the light from the lightning at time T + cD, where D is the distance between T and M' (and assuming the two observers have clocks which are synchronized in their frame), so after subtracting for the light's travel time he will conclude the lightning hit A at (T + cD) - cD = T. Since you want the cat to be invisible to him I guess he can't say anything one way or another about whether the cat was at A at time T just based on his own observations, but if he later learns of the fact that the observer at A saw the cat there at time T, then he will conclude the lightning must have hit the cat.

If they do reach that conclusion, then they must've taken into account that the distance light has to travel in order to get from A to M' is not the same as the actual distance from A to M' (as measured by people on the train), no?

No, why do you say that? If they are both on the train, and they measure the distance between them as D, then if their clocks are synchronized in the train's frame, that means that if the observer at A sees the lightning strike A when his clock reads T, then the observer at M will see the light from this event when his own clock reads T + cD.

Perhaps you are thinking in terms of the perspective of the embankment observer? But in this case we must keep in mind that from his perspective, the clocks of the two observers on the train are out-of-sync by a constant amount vD/c^2, where D is the distance between them in their own frame and v is the speed they are moving in the embankment frame. Let's look at an example with some specific numbers. Suppose in the train's frame the distance from A to M' is 20 light-seconds, and the train is moving at 0.6c relative to the embankment. Because of the length contraction effect in relativity, this means the distance between the two observers on the train is only $$20*\sqrt{1 - 0.6^2}$$ = 20*0.8 = 16 light-seconds in the embankment frame. Further, suppose that the lightning hits the train-observer at A when his clock reads T=30 seconds. In the embankment frame, the two observer's clocks are out-of-sync by (0.6c)*(20)/c^2 = 12 seconds, so at the moment the lightning hits the observer at A, the clock of the observer at M' already reads 30 + 12 = 42 seconds (in the embankment frame). At this moment this second clock is 16 light-seconds away from the lightning flash in the embankment frame, and it's rushing towards the position of the lightning flash at 0.6c while the light from the flash rushes towards it at 1c, so it will take 16/(0.6c + 1c) = 10 seconds for the light to catch up to the observer at M' in the embankment frame. But the clock of the observer at M' was slowed down by a factor of $$\sqrt{1 - 0.6^2}$$ = 0.8 in the embankment frame (the time dilation effect), so in those 10 seconds it only ticked forward by 8 seconds, and since it read 42 seconds when the lightning first struck, it must read 50 seconds when the light from the strike catches up to it.

So, to sum up, looking at things from the perspective of the embankment frame, we find that if the lightning struck the clock at A when it read 30 seconds, the embankment observer predicts that the light from this strike must reach the clock at B when it reads 50 seconds. But since we know the distance between the two train observers was 20 light-seconds, then you can see that this is exactly what the train-observers will predict if they assume that both of them are at rest and that light moves at exactly 1c in their frame.

 

[Wattever]

Yes, I think we're finally talking about the same thing now!

But in this case we must keep in mind that from his perspective, the clocks of the two observers on the train are out-of-sync by a constant amount vD/c^2

I did not know that. I didn't know about time dilation either, and the length contraction hasn't been explained yet; I'm guessing these come furthur in the book. Hopefully I'll understand this when I get to them.

Thank you all for taking the time with me!

 

[DRMOKADI]

IF TWO OBSERVERS SEE AN EVENT AT A TIME(t),,THEY WUDNT SEE IT SIMILARLY...THE OTHER WILL SEE IT DIFFERENTLY FROM THE OTHER

 

[DRMOKADI]

yes, i think we're finally talking about the same thing now!


I did not know that. I didn't know about time dilation either, and the length contraction hasn't been explained yet; I'm guessing these come furthur in the book. Hopefully i'll understand this when i get to them.

Thank you all for taking the time with me!

u r ryt understanding the concept of time dilation and length will help u...try to read even sumthing on doppler effect(the red shift and blue shift)

 

[DRMOKADI]

Imagine a car cuming toward u and ur friend...your friend is at position 'a' and u are at position 'b'...u r going to hear the sound of the car first or he's going to hear it first because of the shift in the wavelength and frequency when the car approaches both of u