Explaining Relative Simultaneity

[Grimble]

Ref:http://www.bartleby.com/173/9.html"

I am having a little bother with this and hope that someone will be able to explain it for me

If lightning strikes A & B simultaneously then, as those strikes are space-time 'events' they have no motion, only a time and a place. OK?

Then, as they also occur adjacent to points A' & B' on the train, and, if the light were reflected by mirrors attatched to those points, it would travel at 'c' relative to the train, in which co-ordinate system the observer at M' is not moving!:(

Therefore the two lightning strikes at A & B, A' & B', are also simultaneous to the observer on the train, as perceived by that observer

Einstein wrote that is the observer on the train
Then was he not saying that the lightning strikes were not simultaneous with respect to the train, as perceived from the embankment?

 

[ZikZak]

Ref:http://www.bartleby.com/173/9.html"
If lightning strikes A & B simultaneously then, as those strikes are space-time 'events' they have no motion, only a time and a place. OK?

No, you're equivocating a specific "time and place" with "spacetime event." A spacetime event is a specific geometrical location in spacetime, which to any given observer will be at a specific time and place. But different observers will *disagree* on the particular time and place of the event.

In other words, yes, spacetime events are specific locations in spacetime, but the actual x and t coordinates assigned to them by different observers will differ.

The example is meant to illustrate that the strikes cannot be simultaneous in both frames, because if the light flashes reach M simultaneously (a single event, since it happens at a specific time and place), then they cannot have reached M' simultaneously (since M' is not at M at the event when both signals arrive).

There is only one event where the light flashes meet, and in the example, this is given to be at observer M. Since observer M' is not at that event, the light flashes cannot have reached him simultaneously.

Since the light flashes did not reach M' simultaneously, even though he is equidistant from A' and B', where the lightning struck, he can only conclude that the flash at B' (=B) happened first. Thus in his reference frame the lightning flashes are not simultaneous. i.e., even though observer M assigns the same value of the time coordinate t to the two lightning flashes, observer M' does not.

 

[HallsofIvy]

I might add that you go off the track when you start with "If lightning strikes A & B simultaneously". There is no such thing without stating a frame of reference in which the two events are simultaneous.

 

[Rasalhague]

In Einstein's example, the lightning strikes are simultaneous in the rest frame of the embankment, and therefore not simultaneous in the rest frame of the train:

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

In fact they can't be simultaneous in the rest frame of the train if they're simultaneous in the rest frame of the embankment. Likewise, if another pair of lightning bolts struck A and B simultaneously in the rest frame of the train, then this second pair of lightning strikes would not be simultaneous in the rest frame of the embankment.

If the train stopped relative to the embankment, then the rest frames of train and embankment would coincide and be the same frame; only then could lightning strike A and B simultaneously in the rest frame of the train and the embankment. But the lightning strikes could only be simultaneous in all frames moving at some nonzero velocity relative to each other if the two bolts of lightning struck the same place as each other and at the same time as each other. This is what "relativity of simultaneity" means; in general, whether two events are simultaneous depends on which frame of reference they're described with respect to.

Here are three animations illustrating the relativity of simultaneity.

http://video.google.co.uk/videoplay?docid=4820883104387202016&ei=QnjiSteyONOg-Aai6LyoAg#

(Animation begins at 08:00 minutes.)
http://video.google.co.uk/videoplay?docid=-6328514962912264988&ei=EXziSoGiI9yf-AbftsDzBw#

(Animation begins 01:16.)
http://video.google.co.uk/videoplay?docid=6322511432077219124&ei=OoHiSvT3Msnm-AbmtOTRDA

I found it very confusing when I first saw these. I remember watching the animation in The Mechanical Universe again and again as I tried to get some intuition for it, but I think they're well worth a study, even if it's not obvious at first. Also worth scrutinising spacetime diagrams.

A personal way I have of imagining it that I have is to think of a line (or plane) of simultaneity in a Minkowski spacetime diagram as being like a speedboat that tilts upwards in the direction that the speedboat is going (and down at the back). But that's just my personal way of remembering which way round it goes. So if that makes no sense, just ignore this paragraph!

 

[Rasalhague]

I might add that you go off the track when you start with "If lightning strikes A & B simultaneously". There is no such thing without stating a frame of reference in which the two events are simultaneous.

Yes, this is the source of a lot of apparent paradoxes. For the statement "A and B are simultaneous" to be meaningful, you have to say in which frame of reference they're simultaneous - because if they're simultaneous in one frame of reference, they won't be in others.

 

[Grimble]

OK, sorry, take out

If lightning strikes A & B simultaneously

No, let's start again.

Einstein wrote in http://www.bartleby.com/173/9.html"

UP to now our considerations have been referred to a particular body of reference, which we have styled a “railway embankment.” We suppose a very long train traveling along the rails with the constant velocity v and in the direction indicated in Fig. 1. People traveling in this train will with advantage use the train as a rigid reference-body (co-ordinate system); they regard all events in reference to the train. Then every event which takes place along the line also takes place at a particular point of the train. Also the definition of simultaneity can be given relative to the train in exactly the same way as with respect to the embankment.

But then he writes,

Now in reality (considered with reference to the railway embankment) he

that is the observer on the train

is hastening towards the beam of light coming from B, whilst he is riding on ahead of the beam of light coming from A.

Was he not saying that the lightning strikes were not simultaneous with respect to the train, as perceived from the embankment?

 

[Grimble]

And again, if we were to consider the observer in the train, what does he perceive?

Again I quote

People traveling in this train will with advantage use the train as a rigid reference-body (co-ordinate system); they regard all events in reference to the train. Then every event which takes place along the line also takes place at a particular point of the train. Also the definition of simultaneity can be given relative to the train in exactly the same way as with respect to the embankment.

And

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

And it is surely not unreasonable to suppose that at night, for instance, the traveller is completely unaware of the embankment. No all he perceives is himself and his reference-body, the train.

Now when the lightning strikes he will see the light from A and the light from B, each traveling at c relative to the train reach him at the same time. For him, only his own reference-body exists and to him, this reference-body is not moving.

I do understand what Einstein was saying, the relativity of simultaneity; but it is, for one observer, between his own reference-body and his perception of another reference body; where he will of course also perceive length contraction and time dilation, not that they are relevant to this discussion.

 

[Rasalhague]

Was he not saying that the lightning strikes were not simultaneous with respect to the train, as perceived from the embankment? [...] And again, if we were to consider the observer in the train, what does he perceive?

In the first example, lightning strikes A and B simultaneously with respect to a coordinate system in which the embankment is still and the train moving, but these strikes are not simultaneous with respect to a coordinate system in which the train is still and the embankment moving. An observer sitting on the embankment at M will see the flashes at the same time, whereas an observer sitting on the train at M' will see the flash from B before the flash from A. This is no illusion. In the latter observer's rest frame (the rest frame of the train), the lightning will really have struck B before it struck A, even though in the rest frame of the observer at M (the rest frame of the embankment), both strikes happened at the same time as each other.

It's completely cointerintuitive. I'm sure everyone finds this a confusing idea when they first encounter it.

In the second example, Einstein imagines a different pair of lightning strikes which happen to be simultaneous with respect to the train's rest frame, in which case they're not simultaneous in the rest frame of the embankment. In this example, it's the train passenger at M' who sees the flashes at the same time, while the person sitting on the embankment at M will see the lightning strike A before it strikes B. In this case, in the rest frame of the embankment, the lightning really does strike A first, even though the strikes were simultaneous in the train's rest frame.

And it is surely not unreasonable to suppose that at night, for instance, the traveller is completely unaware of the embankment. No all he perceives is himself and his reference-body, the train.

This is a good idea to think about.

Now when the lightning strikes he will see the light from A and the light from B, each traveling at c relative to the train reach him at the same time. For him, only his own reference-body exists and to him, this reference-body is not moving.

This is not what will happen if the lightning strikes are simultaneous in the rest frame of the (invisible) embankment. Even at night and even if there is no embankment there at all, so long as the lightning strikes A and B simultaneously according to a frame in which the train is defined as moving, these events will not be simultaneous in a reference frame defined such that the train is at rest in it.

The choice of reference frame is arbitrary, a matter of convenience. We can define a frame in terms of some object being at rest in that frame, but we don't have to. We could just as well define a frame moving at some velocity relative to the train even if we didn't know of any object which was at rest in such a frame, or of any literal observer at rest with respect to it. Or if there was only an embankment and no train, we could just as easily define a frame moving at some velocity relative to the embankment and calculate time, distances and the order of events in such a frame, regardless of whether there is any physical object at rest with respect to that frame.

 

[Grimble]

Yes but...

Let me simplify my understanding to the very basics as I see them:

We have two entities, the embankment and the train which are moving relative to one another.

Each is stationary wth respect to its own reference-body and each is moving with respect to the other's reference body.

Lightning strikes points A & B which exist in both reference bodies.

Observers in each reference-body will surely see the same effects with respect to their own reference-body; which, at the expense of repeating myself, is stationary with respect to that observer.

The light will travel from A & B at the speed of light c relative to the observer's reference-body and so will meet at either M or M' depending on which reference-body the observer is in.

It is all a completely self contained, symmetrical, set of circumstances.

From the above, please tell me how one can determine that one case is simultaneous and the other is not

As far as I can see each would say that the lightning strikes were simultaneous for him but not for the other. What is it I am missing here

 

[Doc Al]

Lightning strikes points A & B which exist in both reference bodies.

Think of A and B as fixed points on the embankment. Both reference frames agree that the lightning strikes A and B, but the train frame will measure the positions differently. Think of a position A' fixed in the train that coincides with A at the instant the lightning strikes A; similarly, think of train location B' coinciding with B at the instant the lightning strikes B.

Observers in each reference-body will surely see the same effects with respect to their own reference-body; which, at the expense of repeating myself, is stationary with respect to that observer.

Not sure what that means.

The light will travel from A & B at the speed of light c relative to the observer's reference-body and so will meet at either M or M' depending on which reference-body the observer is in.

No. M' coincides with M at the moment the lightning strikes according to the embankment frame. Light traveling from A & B will meet at M, but not at M'. By the time that the light reaches M, M' has moved along.

It is all a completely self contained, symmetrical, set of circumstances.

Not symmetric at all.

From the above, please tell me how one can determine that one case is simultaneous and the other is not

The embankment frame sees the light go from A and B and meet in the middle at M. So they surely think that the lightning strikes were simultaneous. The train, on the other hand, sees the lightning striking at point A' and B' (equidistant from M'), but the light does not meet in the middle of the train at M'. So they must conclude that the lightning strikes did not occur simultaneously.

 

[Bob_for_short]

If in one reference frame you have a solution Acos(ωt) (a long horizontal rod oscillating up and down as a whole), in a moving RF (with velocity V) you will see it as a wave: A'cos(ω't'-kx') with k being dependent on V.

 

[Doc Al]

If in one reference frame you have a solution Acos(ωt) (a long horizontal rod oscillating up and down as a whole), in a moving RF (with velocity V) you will see it as a wave: A'cos(ω't'-kx') with k being dependent on V.

Well, that's true. But I'm not sure how helpful it will be in sorting out the specific example being discussed in this thread.

 

[ZikZak]

Lightning strikes points A & B which exist in both reference bodies.

But not simultaneously in both. The example demonstrates how assuming that the strikes occur simultaneously in both reference frames leads to an inescapable contradiction.

Observers in each reference-body will surely see the same effects with respect to their own reference-body; which, at the expense of repeating myself, is stationary with respect to that observer.

The light will travel from A & B at the speed of light c relative to the observer's reference-body and so will meet at either M or M' depending on which reference-body the observer is in.

The light does indeed travel at c relative to either reference body. Therefore, the fact that the flash from B' reaches M' before the flash from A' does requires that M' conclude that the strikes were not simultaneous.

It is all a completely self contained, symmetrical, set of circumstances.

No it isn't. You are forgetting the givens. The given is that the flashes reach M simultaneously. There is no such given for M'. The assumption of complete symmetry you are trying to make leads to a logical contradiction. That is the point of the exercise.

From the above, please tell me how one can determine that one case is simultaneous and the other is not

As far as I can see each would say that the lightning strikes were simultaneous for him but not for the other. What is it I am missing here

In the example, it is given that the flashes are received simultaneously by M. There is one event at which the world-lines of both flashes and M himself meet. Because all the worldlines meet at one event, all observers must agree that this event occurred. This is the basic assumption of reality in science: that observers might disagree on when and where an event happened, but they should always agree that it did.

Therefore, M' also observes that the light rays meet with observer M at a single event. If an external reality exists, this is it. There is no escaping this. Things that happen, happen. M' may label the "both light rays hit M" event with different coordinate values than M does, but it is one single event with one single set of coordinates in any particular reference frame.

Working in the reference frame of M, M observes the flash from B hit M' at a different time (different event) from the flash from A. Two separate events. Changing reference frames cannot possibly combine two different events into one. In other words, M observes that when flash A reaches M', flash B is not there at that event. When flash B reaches M', flash A is not there. When the two flashes meet each other, M' is not there. Merely changing reference frames cannot magically stitch all these different events together. M' therefore observes the flashes at two different times (two different events). He must conclude that the bolts were not simultaneous.

Summary: assuming that the bolts were simultaneous in M *forbids* them from being simultaneous in M'. Both observers agree on the events that occur: light flashes A and B reach M at a single event, and M' at two different events. All observers in the universe must agree that both light flashes and M meet at some event, while M' meets the light flashes separately at two different events.

You could do the same argument starting from the assumption that the flashes reach M' simultaneously, which would forbid M from seeing them simultaneously, but that would be a different universe. The two situations would be two completely different sets of events. Only one of them can occur, not both.

EDIT: And I should add, that since the given is that the light rays reach M simultaneously, and not that the bolts were simultaneous in all frames, that the correct calculation to make in the M' frame would be to ask when the bolts must occur in order for their flashes to meet at M, NOT at M'. Since M is traveling backwards, bolt B must occur before bolt A in order for the flashes to meet at M as given.

 

[Rasalhague]

We have two entities, the embankment and the train which are moving relative to one another.

Yes.

Each is stationary wth respect to its own reference-body and each is moving with respect to the other's reference body.

I'm more familiar with the synonyms "reference frame" and "coordinate system", but this is what the book says "reference body" means, a coordinate system. Bear in mind that although the names train and embankment can be given to these two coordinate systems, the coordinate systems themselves are abstract entities. There doesn't have to be a physical embankment present for us to define a coordinate system moving relative to the train.

Lightning strikes points A & B which exist in both reference bodies.

Yes.

Observers in each reference-body will surely see the same effects with respect to their own reference-body; which, at the expense of repeating myself, is stationary with respect to that observer.

They won't see the same effect if lightning strikes A and B simultaneously in one frame. If this was the case, there would be no need for a theory of relativity. It's because the effects referred to one coordinate system differ from the effects referred to another, traveling at some velocity relative to it, that we need to take care to specify which coordinate system events are simultaneous in. If they're simultaneous in one frame, they can't be in the other (except in the trivial cases where A = B or the frames are the same).

The light will travel from A & B at the speed of light c relative to the observer's reference-body and so will meet at either M or M' depending on which reference-body the observer is in.

The light travels at c in both frames. If the strikes were simultaneous in the rest frame of the embankment, the light from each strike will reach M at the same time. According to this frame, the light from B will reach M' first. In this frame, the light reaches B first because M' is moving to meet the light from B and away from the light from A, so the light from A has further to go to get to M' and so takes longer to reach M'. Likewise in the rest frame of the train, the light from B will reach M' first. This couldn't happen if the strikes were simultaneous in this frame too unless the light from B was approaching M' at a different speed than the light from A. But we know the light always travels at speed c, so that can't be the reason. Instead we conclude that B must have been struck first, since the light from this strike arrived first, and the only way it could arrive first is if it set off first.

It is all a completely self contained, symmetrical, set of circumstances.

The symmetry becomes apparent when you compare what happens in the case of a pair of lightning strikes at A and B which are simultaneous in one frame with the case of a different pair of lightning strikes, this latter pair being simultaneous in the other frame. The amount of time that M' will have to wait in the first case after seeing the light from B till the light from A arrives will be the same as the amount of time that M will have to wait in the second case after seeing the light from A till the light from B arrives.

Did you look at the videos I linked to? They might not make it immediately clear. They certainly didn't for me. But I think that poring over them did eventually help get me a little closer to understanding. But it was really when I learned about spacetime diagrams that the concept of relative simultaneity began to sink in.

EDIT: The book talks about "two strokes [sic] of lightning A and B", which we could think of as points in spacetime (events). Alternatively, we can think of a space coordinate A (constant in the embankment's rest frame) and distinguish it from a space coordinate A' (constant in the train's rest frame), so A makes a line in spacetime, as does A', such that their intersection is the point in spacetime where and when the lightning strikes on the left. And we can define B and B' likewise.

 

[Grimble]

Observers in each reference-body will surely see the same effects with respect to their own reference-body; which, at the expense of repeating myself, is stationary with respect to that observer.

Not sure what that means.

What that means is that as each observer is stationary within his own reference-body and the points A&B are stationary with respect to each body of reference they will experience similar phenomena. Light from A&B will meet at the mid-point between A&B in each reference frame. i.e. at M or M' depending on which frame the observer is in.

No. M' coincides with M at the moment the lightning strikes according to the embankment frame. Light traveling from A & B will meet at M, but not at M'. By the time that the light reaches M, M' has moved along.

But not according to the train the train's frame where it is permanently midway between A&B

Look, I am not saying that M and M' remain adjacent, They are in different reference-bodies.
Light is traveling at c within each reference body, relative to each reference body, so it will meet at two separate points in two separate reference bodies. Surely that is fundamental to Relativity.

The embankment frame sees the light go from A and B and meet in the middle at M. So they surely think that the lightning strikes were simultaneous. The train, on the other hand, sees the lightning striking at point A' and B' (equidistant from M'), but the light does not meet in the middle of the train at M'.

But why not? It is traveling at c from A' and from B' to M', MIDWAY, and permanently midway, between A' & B', from the train's reference body.

 

[Doc Al]

What that means is that as each observer is stationary within his own reference-body and the points A&B are stationary with respect to each body of reference they will experience similar phenomena. Light from A&B will meet at the mid-point between A&B in each reference frame. i.e. at M or M' depending on which frame the observer is in.

Note that A & B are stationary with respect to the embankment; while A' & B' are stationary with respect to the train. The light meets at M, not at M'!

But not according to the train the train's frame where it is permanently midway between A&B

Wrong: M is a fixed point in the embankment that is permanently midway between A & B. M' is a fixed point in the train that is permanently midway between A' and B'. M is not fixed from the train's viewpoint, just like M' (the middle of the train) is not fixed from the embankment's view.

Look, I am not saying that M and M' remain adjacent, They are in different reference-bodies.
Light is traveling at c within each reference body, relative to each reference body, so it will meet at two separate points in two separate reference bodies. Surely that is fundamental to Relativity.

The light meets at point M--not M'. Everyone agrees on that. M is midway between the A and B (as it always is). M is not midway between A' and B' at the moment the light reaches M.

But why not? It is traveling at c from A' and from B' to M', MIDWAY, and permanently midway, between A' & B', from the train's reference body.

No. Light does not travel from A' and B' and meet at M'--the light meets at M. Which is the entire point. Since everyone agrees that the light meets at M, and since M is much closer to the rear of the train when the light reaches M, the train observers conclude that the lightning strikes could not have been simultaneous. (If the lightning strikes were simultaneous according to train observers, then the light would meet in the middle of the train--at M', not M--since the lightning struck at points A' and B' which were equidistant from the middle of the train. But that doesn't happen.)

 

[ZikZak]

Look, I am not saying that M and M' remain adjacent, They are in different reference-bodies.
Light is traveling at c within each reference body, relative to each reference body, so it will meet at two separate points in two separate reference bodies. Surely that is fundamental to Relativity.

No, a universe which would permit real paradoxes (M is not equal to M' and the light beams meet at M and the light beams meet at M') is anathema to Relativity, and all of science.

 

[Rasalhague]

If there's a spacelike separation between two events (i.e. the sum of the squares of each space components of the separation vector is greater than the square of the time component (when space and time are measured in the same units)), then--given that nothing can go faster than c--it's never possible for a single particle to be present at both events, and so neither event can have an effect on the other. The lightning strikes are two such events. And when there is a spacelike separation between two events, there's no absolute way of ordering them in time; we can only say which happens first and how far apart they are in time with respect to a particular coordinate system, knowing that there are infinitely many other coordinate systems we could chose to describe them, in some of which the other event will happen first. Although bizarre and counterintuitive to us humans, these rules are consistent with causality because events which have no absolute order can't influence each other, so the contradiction of cause preceding effect never arises.

But if there's a timelike separation between two events (i.e. the square of the time component of the separation vector is greater than the sum of the squares of the space components), or a lightlike separation (i.e. the square of the time component equals the sum of the squares of the space components), then it is possible for a particle to be present at both events. There is a causal connection between the two events: one can have an effect on the other. Events which a single particle is present at are said to lie on the particle's worldline. Worldline means a trajectory through spacetime. Consider the light from the lightning strike at B = B' reaching M' as one event, and the light from the lightning strike at A = A' reaching M' as another event. Both events lie on the worldline of M' because M' is present at both events. It doesn't matter which coordinate system we describe this pair of events in, this pair of events will always happen in the same order, otherwise there would be a genuine contradiction: no way of ordering cause and effect. If there wasn't an absolute order to events on a worldline, then we'd lose the causal structure of Minkowski spacetime. So if this pair of events (the light from each strike reaching M') happens in one order in the rest frame of the embankment, it must happen in the same order in all frames (coordinate systems), including the rest frame of the train.

Likewise the simultaneous arrival of the light from A and B at M. When things happen simultaneously at the same location in one frame, they must happen simultaneously in all frames otherwise there'd be a contradiction about real physical events.

 

[Grimble]

No. Light does not travel from A' and B' and meet at M'--the light meets at M. Which is the entire point. Since everyone agrees that the light meets at M, and since M is much closer to the rear of the train when the light reaches M, the train observers conclude that the lightning strikes could not have been simultaneous. (If the lightning strikes were simultaneous according to train observers, then the light would meet in the middle of the train--at M', not M--since the lightning struck at points A' and B' which were equidistant from the middle of the train. But that doesn't happen.)

OK OK, let us examine what you are saying here:

Everyone agrees (which somehow gives it authority?) that the lightning strikes at A & B are simultaneous as observed from the embankment. . . . . . (1)

At the instant that the lightning strikes hit, points A' & B' are adjacent to points A & B, so the lightning strikes them too. . . . . . (2)

In order to establish whether this appears to be simultaneous as observed from the train, we need to establish when the light from those lightning strikes reaches an observer at M', midway between A' and B'. . . . . . (3)

If the distance between the points A' & B' is 2L the light has to travel the distance L to reach M'. . . . . . (4)

Then the time it will take from A' to M' t = \frac{L}{c} where c is the speed of light in the train's reference-body. . . . . . (5)

And the time it will take from B' to M' is also t = \frac{L}{c}.. . . . . (6)

So the transit times for the light to travel from A' to M' and from B' to M' are equal - (5),(6) above. . . . . . (7)

And as we saw in (2) above the lightning struck A' and B' at the same time as it struck A & B which strikes we have established was simultaneously - (1)

So if the light started from A' and B' at the same instant and the travel times were equal - (7)

The light must meet at point M' in the Train's reference-body! - in the same way that it meets at M in the embankment's reference-body.

That surely is relativity - What happens is relative to where it is viewed from.

Or is there something wrong with my maths?

It has to be straightforward and logical, there is nothing mysterious about relativity, it is not some sort of dark magic only known to a few initiates

Please note that my last comment is intended to be humerous and is in no way intended to be sarcastic.

Grimble

 

[Rasalhague]

If the distance between the points A' & B' is 2L the light has to travel the distance L to reach M'. . . . . . (4)

Here's where the problem is. It's not an algebraic mistake, but a logical one. A' and B' are indeed equidistant from M', but when you use (4) in your argument for simultaneity, you assume the conclusion you expect, namely that the lightning strikes are simultaneous in the rest frame of M' (the rest frame of the train). But if this was the case, we'd have a contradiction because, according to M (in the rest frame of the embankment), the light from the right reaches M' before the light from the left, not at the same time. In the rest frame of the embankment this is because M' has moved closer to B (while B' has moved further to the right beyond B). But M' hasn't moved in the train's rest frame. The light from B can't both arrive first at M' and not arrive first at M', nor (according to observation and Einstein's second postulate) can its speed be different. The only remaining alternative is that in the train's rest frame, the light struck B' first, before it struck A', and that's why it arrives first at M'.

This conclusion offends our intuition, and seems superficially like a contradiction too. But the fact that information can't travel faster than c ensures that causality is respected, i.e. that cause always precedes effect. The only events whose order isn't frame invariant are events which can't be affected by each other because there isn't time in any frame for information to travel from one to the other at speed c or less.

Similarly, if the light from both strikes does reach an observer simultaneously in one frame, it must reach that observer simultaneously in all frames. When two things happen at the same time and place, we call them a "spacetime coincidence". Anything that's a spacetime coincidence in one frame is a spacetime coincidence in all frames, and would have to be for causality to be preserved.

It has to be straightforward and logical, there is nothing mysterious about relativity, it is not some sort of dark magic only known to a few initiates

It is logical, but I think it's only natural that most people find it far from obvious at first (I certainly did, and there's lots of concepts I still struggle with). That's because it's so counterintuitive. In our everyday experience, at the human scales we're used to, simultaneity is not relative, and there's nothing directly comparable to this effect. But of course what one person can learn, another can, and with determination you'll get there in the end!

 

[Doc Al]

Everyone agrees (which somehow gives it authority?) that the lightning strikes at A & B are simultaneous as observed from the embankment. . . . . . (1)

That's a basic stipulation of the setup. (The lightning strikes must be simultaneous according to somebody, otherwise we don't have much of a thought experiment.)

At the instant that the lightning strikes hit, points A' & B' are adjacent to points A & B, so the lightning strikes them too. . . . . . (2)

Careful here. More accurate to make these two statements: (2a) When lightning hits A, A' is adjacent to A. (2b) When lightning hits B, B' is adjacent to B. Of course--by stipulation--the embankment observers claim that those strikes were simultaneous, thus they say A & A' and B & B' were adjacent at the same time.

In order to establish whether this appears to be simultaneous as observed from the train, we need to establish when the light from those lightning strikes reaches an observer at M', midway between A' and B'. . . . . . (3)

If the distance between the points A' & B' is 2L the light has to travel the distance L to reach M'. . . . . . (4)

Then the time it will take from A' to M' t = \frac{L}{c} where c is the speed of light in the train's reference-body. . . . . . (5)

And the time it will take from B' to M' is also t = \frac{L}{c}.. . . . . (6)

So the transit times for the light to travel from A' to M' and from B' to M' are equal - (5),(6) above. . . . . . (7)

All good.

And as we saw in (2) above the lightning struck A' and B' at the same time as it struck A & B which strikes we have established was simultaneously - (1)

Careful here: Those strikes were simultaneous according to the embankment frame. You cannot assume that they were simultaneous from the train frame.

So if the light started from A' and B' at the same instant and the travel times were equal - (7)

The light must meet at point M' in the Train's reference-body! - in the same way that it meets at M in the embankment's reference-body.

Your reasoning is correct, but that's a big if! IF the lightning strikes were simultaneous according to the train observers, then the light would meet at M'. Absolutely!

Note that this reasoning works the other way around: If the light does not meet at M', then the lightning strikes could not have been simultaneous according to the train observers. (7a)

That surely is relativity - What happens is relative to where it is viewed from.

Actually, no. "What happens" generally does not depend on where it is viewed from.

Consider these questions:
Do you agree that the light meets at M? (You must agree, because it was stipulated that according to the embankment frame, the lightning strikes were simultaneous. Using the same math you used above, that means the light must meet at M.) This is a physical fact agreed to by everyone. For example, I can place a bomb at M with a light detector on each side and set it to explode if a signal is detected on both sides within some arbitrarily small time interval. Either it explodes or it doesn't--everyone will observe or not observe the explosion.

When the light reaches M, is M' still adjacent? Of course not. M' & M were adjacent (according to embankment observers) when the lightning struck. So by the time the light reaches M, M' is long gone. Note that the light from B/B' reaches M' before it reaches M. (And if we put a similar bomb on the train at M', it would not explode.)

Thus we must conclude that the light does not meet at M'. And then, using the reasoning of 7a above, we conclude that according to train observers the lightning strikes could not have been simultaneous.

Or is there something wrong with my maths?

Your math is fine; it's your premise that is incorrect.

It has to be straightforward and logical, there is nothing mysterious about relativity, it is not some sort of dark magic only known to a few initiates

Logical? Absolutely. Straightforward? I'd say it's pretty tricky stuff since it goes against the intuitions we've built from dealing with things at non-relativistic speeds.

If it were easy and obvious, where would be the fun?

 

[ZikZak]

Everyone agrees (which somehow gives it authority?)

What authority is there in science, besides observation?

 

[matheinste]

Originally Posted by Grimble
Everyone agrees (which somehow gives it authority?) hat the lightning strikes at A & B are simultaneous as observed from the embankment.

In the text Einstein asks---
Are two events (e.g. the two strokes of lightning A and B) which are simultaneous with reference to the railway embankment also simultaneous relatively to the train? ----

So they are defined as being simultaneous in the embankment frame. No more authority required.

He then continues----
We shall show directly that the answer must be in the negative. -----

The statement, by Einstein himself, is pretty unambiguous. I used to have problems with it as well but realized that, given the scenario and its unambiguous answer, it might be a sensible option to try to understand it rather than disagree with it. Many things which follow, although a little odd and seemingly complicated at first, will eventually make sense and you will wonder why you ever had a problem with it.

Matheinste.

 

[Grimble]

Originally Posted by Grimble
Everyone agrees (which somehow gives it authority?) hat the lightning strikes at A & B are simultaneous as observed from the embankment.

In the text Einstein asks---
Are two events (e.g. the two strokes of lightning A and B) which are simultaneous with reference to the railway embankment also simultaneous relatively to the train? ----

So they are defined as being simultaneous in the embankment frame. No more authority required.

He then continues----
We shall show directly that the answer must be in the negative. -----

The statement, by Einstein himself, is pretty unambiguous. I used to have problems with it as well but realized that, given the scenario and its unambiguous answer, it might be a sensible option to try to understand it rather than disagree with it. Many things which follow, although a little odd and seemingly complicated at first, will eventually make sense and you will wonder why you ever had a problem with it.

Matheinste.

But I have absolutely no problem with what Einstein says!

1)

Also the definition of simultaneity can be given relative to the train in exactly the same way as with respect to the embankment.

2)

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

3)

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.

4)

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

It all makes sense to me

 

[Grimble]

Please accept my apologies for the state of this thread, good people, it is so easy to be diverted by arguments of minutiae.

Let me say that I have come to SR on my own using the Einstein paper that I quote from.

I found that to be clear, concise and easy to understand.

I then looked further, on the web, principally in Wikipedia etc. and was intersted to find things that did not match what I had learned from Einstein.

I do not pretend (honestly) to know the answers, but for me, just being told 'thats the way it is' doesn't satisfy, I like to know WHY and HOW.

One of the major problems I find is the constant pulling apart every statement I make and telling me to rephrase it or disecting what the words mean!

I have been told (not just in this thread) that proper time is the term to use and that there is no such thing as proper time...

that there is no need to use A' and B', but that A & B will do: then I am told that I should use A' and B'...

having experienced so much criticism for using the wron terms, I tried defining my own - inertial and transformed units, and earning immediate criticism despite attempting to define exactly what I meant by the use of those terms.

No matter how I try and ask questions or address the points that don't seem to add up for me all I get is constant critical disection of the language I am trying to use.

And it is not just that I am unused to the particular terms you use, but you can't even agree amongst yourselves about the use of the terms.

Top this with a tendency to read into what I am saying, what you expect me to be saying, without bothering, it seems, to actually reading it, and the whole exercise becomes frustrating.

One thing which I find particularly annoying (and which I am sure will annoy anyone who experiences it) is to be told what I am thinking, when what I am told is not, and sometimes is the very opposite, of what I am thinking.

Moaning over!

My background is scientific, I studied physics at university, many years ago, followed by 25 years in computing, where I spent many years solving problems, designing systems and in support work, where the prime skill was to be able to take written documents, designs, and complete software systems and find the bugs in them.

I have come to you for assistance in understanding SR and answering questions that arise where the modern understanding seems to fit uneasily with what Einstein wrote.

So I ask for your patience and your help

Thank you, Grimble

 

[JesseM]

OK OK, let us examine what you are saying here:

Everyone agrees (which somehow gives it authority?) that the lightning strikes at A & B are simultaneous as observed from the embankment. . . . . . (1)

At the instant that the lightning strikes hit, points A' & B' are adjacent to points A & B, so the lightning strikes them too. . . . . . (2)

In order to establish whether this appears to be simultaneous as observed from the train, we need to establish when the light from those lightning strikes reaches an observer at M', midway between A' and B'. . . . . . (3)

If the distance between the points A' & B' is 2L the light has to travel the distance L to reach M'. . . . . . (4)

Only in the frame where M' is at rest, i.e. the train's frame. In the embankment frame, M' is moving towards the point where one strike occurred (let's say this is B) and away from the point where the other strike occurred (say this is A), so naturally the light from B will hit the observer on the train at position M' before the light from A hits him.

Then the time it will take from A' to M' t = \frac{L}{c} where c is the speed of light in the train's reference-body. . . . . . (5)

And the time it will take from B' to M' is also t = \frac{L}{c}.. . . . . (6)

Again, these results only hold in the train's rest frame.

So the transit times for the light to travel from A' to M' and from B' to M' are equal - (5),(6) above. . . . . . (7)

Yes, in the train's frame the transit times were equal, but you can't assume the strikes were simultaneous in this frame, and thus can't assume that equal transit times implies the light from each strike reaches M' at the same moment.

And as we saw in (2) above the lightning struck A' and B' at the same time as it struck A & B which strikes we have established was simultaneously - (1)

They were only simultaneous in the embankment frame, again you can't assume they were simultaneous in the train frame.

So if the light started from A' and B' at the same instant

But you have no reason to assume that it "started from A' and B' at the same instant" in the train's frame, and in fact Einstein's whole point was to show that it must not have. The idea is that different frames can never disagree on coincidences of local events (this is a very crucial idea in relativity), like what two clocks read when they pass next to each other, or whether two light beams coming from different directions strike a single observer at the same moment or at different moments. If they did, it would be easy to settle which frame's predictions were correct by experiment (thus defining a preferred frame and violating the first postulate), since it's impossible to have different truths about local events without invoking parallel universes or something of the sort. To see this, suppose one frame predicted a given clock would read 30 seconds when it passed an observer, and another frame predicted it would read 60 seconds when it passed that observer. Well, we could easily see which frame's prediction was objectively correct by attaching a bomb to the clock which was set to go off at 60 seconds--one frame could then predict the clock would already have passed the observer and gotten far enough away that the explosion wouldn't harm him, while the other would predict the observer would be right next to the bomb when it went off and would be killed. To see which frame's prediction is correct, you need only check whether the guy is alive or dead--they can't both be right! Similarly with the train thought experiment, it would be easy enough to put a small device at the center of the train which would sound an alarm (or set off a bomb) only if light detectors on opposite sides of the device detected bright light simultaneously (the detectors could convert light above a certain threshold into electrical signals which would be channeled through an AND gate, for example)--if different frames made different predictions about whether this device goes off, it would be easy enough to check which prediction was correct and thus establish a preferred frame, since again they couldn't both be right.

Einstein didn't explicitly state this point about different frames needing to agree on local events, but it's understood as a basic point in physics that different predictions about local events are mutually exclusive, and thus different frames cannot disagree in these predictions. We already know that the embankment frame predicts that the light from the flashes will reach the observer at the center of the train at different moments (a purely local prediction), so Einstein's point was that the only way this can also be true in the train's rest frame, without violating the assumption that the light from each flash should travel at c in this frame too (so the travel times for the light to get from the strike to the center must be equal in this frame), is if the strikes were not simultaneous in this frame. Hence the "relativity of simultaneity".

Please read the above carefully and then reread the text by Einstein to see if there is anything he says that is incompatible with this interpretation of his meaning (this is how every physicists since has interpreted him, and the fact that events which are simultaneous in one frame are non-simultaneous in others is built into the Lorentz transformation, so it seems a priori pretty unlikely that everyone has been misunderstanding him). And if after doing so you still think that somehow Einstein was saying that the strikes at A' and B' were simultaneous in the train frame just like they were in the embankment frame, how can you possibly make sense of this statement by Einstein?

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

 

[Grimble]

But you have no reason to assume that it "started from A' and B' at the same instant" in the train's frame, and in fact Einstein's whole point was to show that it must not have. The idea is that different frames can never disagree on coincidences of local events (this is a very crucial idea in relativity), like what two clocks read when they pass next to each other, or whether two light beams coming from different directions strike a single observer at the same moment or at different moments. If they did, it would be easy to settle which frame's predictions were correct by experiment (thus defining a preferred frame and violating the first postulate), since it's impossible to have different truths about local events without invoking parallel universes or something of the sort.

Hello Jesse, I have been re-reading and considering this as you suggested and it seems to me that you are saying on the one hand

that different frames can never disagree on coincidences of local events (this is a very crucial idea in relativity),

And then, on the other hand, that the two strikes of lightning that coincide (are simultaneous) in the embankment frame do not coincide in the train's frame.

Which could imply that the embankment is a preferred frame

And I agree that Einstein said:

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

But he also implies that this is only from the point of view of the embankment:

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

That which frame we are viewing from is an essential piece of information:

Every reference-body (co-ordinate system) has its own particular time; unless we are told the reference-body to which the statement of time refers, there is no meaning in a statement of the time of an event.

And he says near the start of this chapter that:

Also the definition of simultaneity can be given relative to the train in exactly the same way as with respect to the embankment.

And I think you can see how confused I am for when I studied this, the understanding that I formed, was that Einstein was saying that there was one event (no, wrong use of that word); one coincidence - the simultaneous strikes of lightning, that could only be simultaneous from the frame it is being viewed from, which ever that was, and that from any other frame it would be asynchronous.

That reading seems to me to answer all your criteria:
The two frames would both agree that it was simultaneous, but only to the viewing frame;
Neither frame would be in any way a preferred frame;
That from the embankment frame that the observer on the train is hastening towards the beam of light coming from B, whilst he is riding on ahead of the beam of light coming from A;
That the two frames are agreeing about what happened locally within their two frames, whilst agreeing that the other would see it differently, as would be expected; For as Einstein said

Every reference-body (co-ordinate system) has its own particular time; unless we are told the reference-body to which the statement of time refers, there is no meaning in a statement of the time of an event.

I am not trying to be difficult here, Jesse, I am only trying to shew how I have become confused, as I like to dot every I and cross every T!

I am going over and over all that you and the other kind contributers to my threads, say and looking at all the references; it does take a little time, but it is fascinating.

I may seem a bit of a recalcitrant old fuddy-duddy, but, wanting to be clear in my understanding, I like everything to fit neatly into place.

Thank you for your patience, your humble student, Grimble

 

[JesseM]

Hello Jesse, I have been re-reading and considering this as you suggested and it seems to me that you are saying on the one hand

But you have no reason to assume that it "started from A' and B' at the same instant" in the train's frame, and in fact Einstein's whole point was to show that it must not have. The idea is that different frames can never disagree on coincidences of local events (this is a very crucial idea in relativity), like what two clocks read when they pass next to each other, or whether two light beams coming from different directions strike a single observer at the same moment or at different moments. If they did, it would be easy to settle which frame's predictions were correct by experiment (thus defining a preferred frame and violating the first postulate), since it's impossible to have different truths about local events without invoking parallel universes or something of the sort.

And then, on the other hand, that the two strikes of lightning that coincide (are simultaneous) in the embankment frame do not coincide in the train's frame.

You misunderstand, when I said "coincidences of local events" I was referring to events that coincide right next to each other in both space and time--all my examples were of that sort (that's why I keep talking about bombs going off, only if you're right next to the bomb in space at the time it explodes are you going to be killed, and all frames should agree about whether or not you get killed!) That's also what "locally" always means in relativity, "in the same local neighborhood of spacetime" (for the purposes of idealized problems, this means that the separation in space and time is treated as zero). The two lightning strikes happen at the same time in one frame, but they do not happen at the same position in space in any frame, so this is not what I meant by a "coincidence of local events". On the other hand, the event of the lightning hitting point A on the tracks and point A' on the end of the train is treated as happening at the same point in both time and space, so these events would coincide locally. Likewise, if two light beams coming from different directions strike a single observer at the same moment, the events of each beam striking him would coincide locally, so all frames would have to agree on this; and the converse of this is that if one frame predicts they hit an observer at different times, then all frames must agree these events do not locally coincide. So, Einstein was using the fact that in the embankment frame, we predict that the light from the strikes will hit the observer at the center of the train (at position M') at different times to show that in order for the train frame to agree that the light hits the observer at the center of the train at different moments, it must judge that the strikes happened non-simultaneously in this frame.

Does this help?

And I agree that Einstein said:

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

But he also implies that this is only from the point of view of the embankment

How could it only be from the point of view of the embankment? He's explicitly comparing simultaneity in two frames here, the embankment frame and the train frame, and saying that if they are simultaneous in the first frame ('simultaneous with reference to the railway embankment') then they are not "simultaneous relatively to the train". It doesn't make any sense that a statement about what is true "relatively to the train" could be from the perspective of the embankment frame, the phrase "relatively to the train" is synonymous with "in the train's frame".

In the section you quote next, "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", he was talking about what is true in the embankment frame, but the point of doing this was to show that the embankment frame predicts the light strikes the observer at the center at different moments, which is an objective fact that must be true in all frames (that's why he next says 'Hence the observer will see the beam of light emitted from B earlier than he will see that emitted from A', without bothering to specify a frame). This implies (by the principle that all frames must agree on coincidences of local events, as understood above) that the train frame must also predict the light strikes the observer at the center of the train at different moments, which is why he goes on to say "Observers who take the railway train as their reference-body must therefore come to the conclusion that the lightning flash B took place earlier than the lightning flash A".

And he says near the start of this chapter that:

Also the definition of simultaneity can be given relative to the train in exactly the same way as with respect to the embankment.

He is not saying that all frames agree on simultaneity, just that they all define simultaneity in their own frame using the physical procedure given in the previous section of the book, i.e. they say two events are simultaneous if an observer at the exact midpoint between the position of those events receives light-signals from each event at the same moment. The train thought experiment shows that if observers in both frames use this definition, then a pair of events which one observer defines to be simultaneous must not be judged to be simultaneous by the other; if the light from each flash reaches an embankment observer at M at the midpoint of A and B at the same moment, then the light from each flash will reach the train observer at M' at the midpoint of A' and B' at different moments.

And I think you can see how confused I am for when I studied this, the understanding that I formed, was that Einstein was saying that there was one event (no, wrong use of that word); one coincidence - the simultaneous strikes of lightning, that could only be simultaneous from the frame it is being viewed from, which ever that was, and that from any other frame it would be asynchronous.

That reading seems to me to answer all your criteria:
The two frames would both agree that it was simultaneous, but only to the viewing frame;

This phrase doesn't make any sense to me. How can they both "agree that it was simultaneous" if it was only simultaneous in the viewing frame? If the events aren't simultaneous in the train frame, then by definition both frames do not "both agree it was simultaneous". When physicists use anthropomorphic language about frames, like talking of frames making judgments or agreeing about things, they do not mean to imply that frames can "think" about any other frame besides themselves and form opinions about what is true in that other frame; a "judgment" made by a frame is just a fact which you arrive at by making an analysis that involves the coordinates of that frame alone, like the judgment that two events are simultaneous in that frame (they happen at the same t-coordinate), and for two frames to "agree" on something just means that a thing which is true when you analyze it from one frame's perspective is also true when you analyze it from another frame's perspective. So it would be stretching the anthropomorphism to the point of absurdity to talk of frames making "judgments" about what is true in other frames besides themselves, or of two frames A and B "agreeing" that two events are simultaneous in A (even though they are not simultaneous in B). Trust me, physicists never talk this way.

Neither frame would be in any way a preferred frame;

If different frames made different predictions about whether the light from each strike would reach the observer at the center of the train at the same moment or at different moments (a disagreement about whether two events happen at the same local point in both space and time), then surely you agree only one frame's prediction can be empirically correct, and whichever one had made the correct prediction would be preferred over the one that made the incorrect prediction? Again consider the apparatus I imagined in the earlier post:

Similarly with the train thought experiment, it would be easy enough to put a small device at the center of the train which would sound an alarm (or set off a bomb) only if light detectors on opposite sides of the device detected bright light simultaneously (the detectors could convert light above a certain threshold into electrical signals which would be channeled through an AND gate, for example)--if different frames made different predictions about whether this device goes off, it would be easy enough to check which prediction was correct and thus establish a preferred frame, since again they couldn't both be right.

 

[matheinste]

Hello Grimble,

This may be of some use.

Consider the scenario where the strikes are simultaneous in the embankment frame. We know they are simultaneous in the embankment frame because the light from the strikes meets at the location of an observer, on the embankment, midway between the points where the lightning struck. This is the requirement for simultaneity.

Now consider an observer at rest in the train frame at the mid point of the train, which is also midway between the points at which the lightning struck. He will not consider the strikes to be simultaneous in the train frame because the light from the strikes did not meet at his location as would be necessary for the requirements of the definition of simultaneity to be met.. HOWEVER, with the information available to him, and with an understanding of the postulates of relativity, he can calculate that the events WERE simultaneous in the embankment frame. So we could say that that although the strikes were not simultaneous in both frames, observers in both frames can conclude that they were simultaneous in the embankment frame. The opposite applies if the strikes were simultaneous in the train frame.

As a little extra comment, which can be ignored for the present purposes if it in any way adds to the confusion, any observer at any point at rest in the embankment frame can, by knowledge of data which is available to him, also conclude that the strikes were simultaneous in the embankment frame but not in the train frame. The observer does not have to be at the mid point between the strikes to be able to decide upon simultaneity. The same reasoning applies with regards to the train frame.

Matheinste

 

[Grimble]

Thank you, both, that is a great help to understand what you are saying, I must re-think and understand it now.

Grimble