I Relativity of simultaneity doubt

[lukka98]

TL;DR Summary

My question is about on of the "famous" Einstein's mental experiment: the train and the lightnings, i don't understand why the result is what it is, I thought for day but I don't understand this particular case, If you can help me to understand I'll very grateful.

(excuse me for my english, but I'm studying physics and I am not a native English speaker)
One observer OE, is on the ground, we take him as the fixed frame of reference.
The other OT is on the train that is moving relatively to the OE at a costant velocity ( they are both inertial frame of reference).
So, two lighning strike the two points A and B when the train is with back and end in the same points ( A and B) and the two observer are aligned.

The observer OE is at equal distance from A and B, so the light, which travel at constant speed c, arrive at the same time at his eyes, the two events are simultaneous.
The observer OE anyway see OT traveling to B and move away from A, the speed of light is always c, so he conclude that OT observers first the light from B and then the light from A.
The result: OT see first ligh from B and then from A in his frame of reference.( like what think OE)

I agree with that, but now there is the problem( more than one):
1- If the speed of light is the same in EVERY inertial frame of reference, in the reference of OT that speed is c, so i think when the two lightning strike in A and B, they are equal distance from the center where there is OT 'cause the first assumption (when A and B are ALIGNED) so i think light will arrive at OT at the same time also in his frame of reference, if i don't observe that i think light speed is greater than c from B to OT and lower from A to OT, but this is a contradiction, and I don't understand how to escape from that my surely wrong interpretation.

2-If A and B are fixed with OE, and they arrive at OE in the same time, when I am OT, I see OE traveling in the opposite direction so I see light from A arrive first to OE and the B, ( because always c is the speed of light), but in this case OT see the "same" event but from different perspective and this for me is clear, also with Minkowskii diagrams, i see two events simultaneous for OE and for the OT perspective they're not.

3-If A and B are fixed with OT, they are simultaneous for OT but OE see what the original experiment say: OT see first A and then B, this time I am totally agree with that.

So what is the difference between 1 and 3, and why if the speed of light is the same, c, OT see first B and then A, if they are aligned and equal distance from OT.

Thank for answer.

 

[PeroK]

Would you consider learning about the relativity of simultaneity from a different experiment?

I find this Einstein experiment confusing and unsatisfactory. There are easier ways!

 

[Dale]

1- If the speed of light is the same in EVERY inertial frame of reference, in the reference of OT that speed is c, so i think when the two lightning strike in A and B, they are equal distance from the center where there is OT 'cause the first assumption (when A and B are ALIGNED) so i think light will arrive at OT at the same time also in his frame of reference, if i don't observe that i think light speed is greater than c from B to OT and lower from A to OT, but this is a contradiction, and I don't understand how to escape from that my surely wrong interpretation.

You are making an incorrect assumption here. The two light pulses arrive to OT at the same time if all three of the following conditions are met:

IF
1) OT is equidistant from where the flashes occurred
AND
2) The speed of both flashes are the same
AND
3) The flashes occurred at the same time
THEN
The flashes arrive at OT at the same time

We know that 1) and 2) are true, but we do not know 3). In fact, since we know that the flashes do not arrive at OT at the same time, we know that at least one of 1), 2), or 3) must be false. And since we know that 1) and 2) are true, that implies that 3) must be false.

 

[PeroK]

So what is the difference between 1 and 3, and why if the speed of light is the same, c, OT see first B and then A, if they are aligned and equal distance from OT.

I don't know if this is an answer to your question.

The time that light signals take to travel from an event to reach an observer is irrelevant. Signal delay has nothing to do with relativity. This is one of the things I don't like about this experiment. It suggests that signal delay is part of the theory of SR.

The time of an event in a inertial frame of reference is determined by a local observer; or, by a distant observer who takes the signal delay into account.

 

[lukka98]

Would you consider learning about the relativity of simultaneity from a different experiment?

I find this Einstein experiment confusing and unsatisfactory. There are easier

You are making an incorrect assumption here. The two light pulses arrive to OT at the same time if all three of the following conditions are met:

IF
1) OT is equidistant from where the flashes occurred
AND
2) The speed of both flashes are the same
AND
3) The flashes occurred at the same time
THEN
The flashes arrive at OT at the same time

We know that 1) and 2) are true, but we do not know 3). In fact, since we know that the flashes do not arrive at OT at the same time, we know that at least one of 1), 2), or 3) must be false. And since we know that 1) and 2) are true, that implies that 3) must be false.

Thank you for the answer, but i don't understand one thing, we know that 3) must be false, but from observation made by OE which is in motion,
so for example if there are two flash light at the end of the train instead of lightnings, in this case the observation of OE is the same, they don't arrivere at same time but for OT there are simultaneous...
Is possible to replace lightning with two flash light? Because this will be more clear but result will not the same...
And last question: if i had two flash light at the same distance from me and I go to one of that and away from the other, if i think of light as a ball, I say " first I met one and then the other, but because light has a constant velocity of c, if I met one before the other i think it go faster than the other...

What a confusion I had, thanks for reply

 

[PeroK]

Thank you for the answer, but i don't understand one thing, we know that 3) must be false, but from observation made by OE which is in motion,
so for example if there are two flash light at the end of the train instead of lightnings, in this case the observation of OE is the same, they don't arrivere at same time but for OT there are simultaneous...
Is possible to replace lightning with two flash light? Because this will be more clear but result will not the same...
And last question: if i had two flash light at the same distance from me and I go to one of that and away from the other, if i think of light as a ball, I say " first I met one and then the other, but because light has a constant velocity of c, if I met one before the other i think it go faster than the other...

What a confusion I had, thanks for reply

I'm not sure I really understand your question. One of the things I think is most important in learning SR is to be able to transform an experiment (set of events) from one reference frame to another. In this case, let's first describe the experiment in the platform frame:

1) Platform Frame of reference:

There are two markers on the platform at points A and B. These are a distance $L$ apart, say.

The train has length $L$, so that the front of the train is at $B$ when the rear of the train is at $A$. We can call this time $t = 0$.

At $t = 0$ two lightning strikes hit $A$ and $B$ (and the front and rear of the train).

NOTE: the time of both events in the platform frame is $t = 0$.

At time $t = L/2c$ the light from the lightning strikes reaches the midpoint between A and B, where OE is standing. NOTE: this is largely irrelevant.

2) Train frame of reference.

The train is longer than $L$ (as it is length contracted in the platform frame).

The distance between A and B is shorter than $L$ (as the platform is length contracted in the train frame).

When the front of the train is at $B$, the rear of the train is still not at $A$. The point $A$ is somewhere near the middle of the train. Because the train is (much) longer than the platform.

At this time, let's call this time $t' = 0$, a lightning strike hits B (and the front of the train).

Later, the rear or the train reaches point A. At this time a lightning strike hits point A and the rear of the train.

So, we can see that the lighteing strikes are not simultaneous in the train frame.

NOTE: the whole experiment looks very different in the train frame from the platform frame.

 

[PeroK]

PS part of the problem here is when you rely on a diagram drawn in the platform frame. You are trying to think in the train frame, but the diagram is always the platform frame. This is confusing.

The first thing I would do is draw a new diagram for the train frame.

 

[Dale]

we know that 3) must be false, but from observation made by OE which is in motion

No, 3) is false regardless of who is making the observation. It is merely easiest to see in OE's frame.

For clarity, suppose that OT carries an accurate clock, and that clock has optical sensors that detect exactly when a flash arrives at OT and prints on a piece of paper a permanent record of that time. All frames must agree on what is printed on that piece of paper. In this case, all frames agree that the two times are different.

So in any frame OE receives both flashes at some point in time. At that point in time OT is to OE's right. That means that the flash from the right has already passed OT and thus been received by OT. That also means that the flash from the left has not yet reached OT and therefore has not been received by OT. Therefore in every frame there exists some time when OT has received the flash from the right but has not received the flash from the left.

Therefore the flashes are not received at the same time and all frames must agree that the two times printed on the paper are different. The analysis holds in any frame. They may disagree that the times are correct, but they agree what is printed and that it is different.

 

[PeroK]

PPS If we accept length contraction, then we can simplify this experiment:

We don't need the lightning strikes. We don't need observers OE and OT. We don't need accurate clocks or optical sensors.

In the platform frame the events: "front of train at B" and "rear of train at A" are simultaneous.

In the train frame the event ""front of train at B" occurs before "rear of train at A".

Therefore: simultaneity is relative.

 

[Janus]

Thank you for the answer, but i don't understand one thing, we know that 3) must be false, but from observation made by OE which is in motion,
so for example if there are two flash light at the end of the train instead of lightnings, in this case the observation of OE is the same, they don't arrivere at same time but for OT there are simultaneous...
Is possible to replace lightning with two flash light? Because this will be more clear but result will not the same...
And last question: if i had two flash light at the same distance from me and I go to one of that and away from the other, if i think of light as a ball, I say " first I met one and then the other, but because light has a constant velocity of c, if I met one before the other i think it go faster than the other...

What a confusion I had, thanks for reply

From the ground observer view, the train is moving away from strike A and towards strike B.
By the time he sees the light from both strikes, the train observer has moved to a point closer to strike B and further from strike A, in other words, the light from strike B will have already passed the train observer on its way to our Ground observer, but the light from Strike A will not have yet reached the train observer, and won't reach him until the train observer has moved even closer to where strike B occurred.
This means that the train observer had to be next to two different points of the tracks when each light flash reached him.
Now, here's the important part. The train observer must agree to this fact. You can't have the ground observer say that that light flash B reached the observer when he was next to point C of the tracks and Light flash A reached him while next to point D while the train observer says that both flashes reached him when he was next to point E. That would involve a physical contradiction.
So we are forced to accept that the train observer must see the flashes at different times, And, being at the midpoint of the train, with the strikes hitting the ends, and light traveling at the same speed from each flash, he must conclude that the lightning strikes that produced those flashes could not have occurred simultaneously in the rest frame of the train.

 

[cianfa72]

So we are forced to accept that the train observer must see the flashes at different times, And, being at the midpoint of the train, with the strikes hitting the ends, and light traveling at the same speed from each flash, he must conclude that the lightning strikes that produced those flashes could not have occurred simultaneously in the rest frame of the train.

I think an important point is that when the lightning strikes occur each of them leaves actually two co-located 'marks'. A mark on the tracks and a mark on one end of the train (strike A at the rear end and strike B at the front end of the train).

The observer in the midpoint of the train knows the strikes are originated from the rear end and the front end hence he must conclude lightning strikes that produced those flashes could not have occurred simultaneously in its rest frame.

 

[Nugatory]

, in this case the observation of OE is the same, they don't arrivere at same time but for OT there are simultaneous...
Is possible to replace lightning with two flash light? Because this will be more clear but result will not the same...

In that case the train observer will find the two flashes to be simultaneous but the platform observer will find that they are not. It will be easier to analyze this variation if we imagine that the train is standing still while the platform is moving backwards (and if you are not satisfied that that's an equivalent way of describing the situation you'll want to back up and learn about Galilean relativity, discovered a few centuries before Einstein).

 

[lukka98]

Okay I have two last doubts,
1)The speed of light is c, for all inertial frame of reference, so what I'll see if I run to a flash light? And there is difference from a stationary observer at the same distance when the light will turn on?
I think no because the speed is the same, but intuitively i think if i move towards the light i see it first, but first than who...?

2)When I did SR, I found always trasformation from event occurs in a frame of reference to another frame of reference to see what different observes see, but I think my miss-understanding of the "Einstein train lightnings" became from the fact that I don't understand if the two lightning "occurs" in the "rest" or "stationary" observer or in the train frame.

Maybe the main problem that I don't understand Is that:
If I think they occur in the "stationary" frame of reference, they met the observer simultaneous but when I change frame of reference and go in the train frame, usually what I do is to see the same event from that perspective, and i will see that the observer at the rest see one first and then the other and I think the two event are not simultaneous, but In the explanation I found is different I think, because is what the train observer see about "his event"

 

[PeroK]

Okay I have two last doubts,
1)The speed of light is c, for all inertial frame of reference, so what I'll see if I run to a flash light? And there is difference from a stationary observer at the same distance when the light will turn on?
I think no because the speed is the same, but intuitively i think if i move towards the light i see it first, but first than who...?

2)When I did SR, I found always trasformation from event occurs in a frame of reference to another frame of reference to see what different observes see, but I think my miss-understanding of the "Einstein train lightnings" became from the fact that I don't understand if the two lightning "occurs" in the "rest" or "stationary" observer or in the train frame.

Maybe the main problem that I don't understand Is that:
If I think they occur in the "stationary" frame of reference, they met the observer simultaneous but when I change frame of reference and go in the train frame, usually what I do is to see the same event from that perspective, and i will see that the observer at the rest see one first and then the other and I think the two event are not simultaneous, but In the explanation I found is different I think, because is what the train observer see about "his event"

I think you are very confused here. I think the advice I gave in post #2 is valid. The Einstein lightning experiment is so complicated and confusing that it is a potential disaster for many students.

Note that events do not occur in one reference frame or another. Events are events - the things that happen. They occur in all reference frames. Each reference frame assigns spacetime coordinates to each event.

Your problems are also caused by having an observer at rest in each reference frame and having light from every event be transmitted to that observer. What happens if you do an experiment in a dark room? Is the physics different if you switch the lights off?

In general, the time that a single observer sees an event (in terms of receiving a light signal directly from an event) is not relevant. That's another confusion that you need to overcome - and that's a confusion that the Einstein experiment has directly caused.

I would rewind, rethink and learn SR without this crazy, complicated, confusing experiment.

 

[Dale]

I don't understand if the two lightning "occurs" in the "rest" or "stationary" observer or in the train frame.

All events occur in every frame. Different frames merely disagree about their coordinates, but not their existence.

It always bothers me when you read things like “Bob is in an inertial frame”. What they mean is “Bob is at rest in an inertial frame”. Everything and every event is in all frames. They may be moving in some and at rest in others, but they are all in every frame.

 

[Hans de Vries]

One observer OE, is on the ground, we take him as the fixed frame of reference.
The other OT is on the train that is moving relatively to the OE at a constant velocity
So, two lightning strike the two points A and B when the train is with back and end in the same points ( A and B) and the two observer are aligned.
View attachment 289031
The observer OE is at equal distance from A and B, so the light, which travel at constant speed c, arrive at the same time at his eyes, the two events are simultaneous.
The observer OE anyway see OT traveling to B and move away from A, the speed of light is always c, so he conclude that OT observers first the light from B and then the light from A.
The result: OT see first ligh from B and then from A in his frame of reference.( like what think OE)

Once you understand non-simultaneity it is really not that complicated. It is also very natural: Just what you would expect.

You can also already see why non-simultaneity occurs without any reference to relativistic effects like Lorentz contraction and Time dilation. This because at low speeds non-simultaneity is proportional to the velocity $v$ and therefor it is already relevant while the other effects can still be neglected.

Addressing the misunderstanding:

If the two propagated light flashes meet each other at one point then any observer at that point will see them (receive the light flashes in his eyes) at the same time. This is totally independent of the velocity of the observer. However, they draw different conclusions about the simultaneity of the light flashes.

​

So both observers see two flashes at the same time. Nevertheless, your observer at rest concludes that they happened at the same time, while your moving observer concludes that the flash in front of him occurred earlier then the one behind them.

Why?

Say you see two flashes at house b and c at the same time. Your conclusion is that the flash at house b occurred earlier because, from the size, you conclude that house b is further away.

This is the whole point. The moving observer sees a bigger flash in front of him and a smaller flash behind him, so he concludes that the flash in front of him occurred later.

The explanation for this effect is (without any need to involve special relativity) just a simple vector addition in the rest frame. You need to add the speed vector of the observer to the light ray vectors coming from the light source.

The angle of the light rays change depending on the relative velocity and the apparent size changes.
The image above illustrates this effect. Now let's go into more detail using your image.

What does the OT observer see if he moves at 1% of the speed of light? We take the formula for $t'$ and for low speeds we can set $\gamma\approx 1$ so we have for the non-simultaneity:

$$t' = t - vx/c^2$$
Now the light rays coming of an object are wave-fronts build up from emitted light over a period of time. So a wavefront from a moving object is different than from an object at rest.

- OT will see the house B blue-shifted by 1% and larger by 1%.
- OT will see the house A red-shifted by 1% and smaller by 1%
- OT sees no red or blue shifting in the wavefront from both ends of the train.
- OT neither sees an apparent change in size of both ends of the train.

Because OT sees the objects in the frame at rest changed in size by 1% he concludes that there is a 1% shift in simultaneity as expressed by the formula above. This is all still without Special Relativity.

In more detail: House A and B have clocks. The light from clocks A and B reaches the eyes of OT (and OE) and will show the exact same time since both observers are in the middle. However, OT knows about propagation speed so he assumes that the clocks must have ticked further during the propagation. Now, OT assumes that clock B is closer as clock A so he assumes that clock B has progressed less than clock A and concludes their actual times are different. He assumes they are different as given by the non-simultaneity formula given above.

-------​

If you want to understand Special Relativity and the beautiful way in which this non-simultaneity effect perfectly reverses the relativistic effects of Lorentz contraction and Time dilation I can recommend to this chapter of my book:
http://www.physics-quest.org/Book_Chapter_Non_Simultaneity.pdf

It involves the ellipsoids of simultaneity. The ellipsoids on the top are defined as simultaneous by our moving observer by the effect described above. The ellipsoids in the middle reverses the vector addition in a non-relativistic way. The lower spheres are corrected for Lorentz contraction: Because we end up with spheres the moving observer concludes that the speed of light is still C in any direction, even after changing to a new reference frame.

Other chapters:
Lorentz contraction: http://www.physics-quest.org/Book_Chapter_EM_LorentzContr.pdf
Time dilation: http://www.physics-quest.org/Book_Chapter_Time_Dilation.pdf

The first one may be too technical since it involves Liénard Wiechert potentials. The start of the second is very readable though.

 

[cianfa72]

If the two propagated light flashes meet each other at one point then any observer at that point will see them (receive the light flashes in his eyes) at the same time. This is totally independent of the velocity of the observer. However, they draw different conclusions about the simultaneity of the light flashes.

I would say they (the two propagated light flashes) meet each other at the same spacetime point (event). This is frame independent.

 

[Chris S]

Summary:: My question is about on of the "famous" Einstein's mental experiment: the train and the lightnings, i don't understand why the result is what it is, I thought for day but I don't understand this particular case, If you can help me to understand I'll very grateful.

View attachment 289031

1- If the speed of light is the same in EVERY inertial frame of reference, in the reference of OT that speed is c, so i think when the two lightning strike in A and B, they are equal distance from the center where there is OT 'cause the first assumption (when A and B are ALIGNED) so i think light will arrive at OT at the same time also in his frame of reference, if i don't observe that i think light speed is greater than c from B to OT and lower from A to OT, but this is a contradiction, and I don't understand how to escape from that my surely wrong interpretation.

Lukka98, Perhaps this may help resolve your problem #1: OT observes the light from each lightning strike at different times because OT was no longer at a location equidistant from both lightning strikes at the time the light from both strikes reached OT.

Let's stop time when the lightning strikes occur so we can establish what is occurring at that time. When the two lightning strikes occur, the light has not traveled toward OT yet because light takes time to travel. When the lightning strikes occur, OT is at a certain location we will call LOCATION 1. OT has not seen the light yet because light takes time to travel.

Now, let's start time moving very slowly so we can observe events in order. Let's first consider OT's relation to only the lightning strike at the front of the train. The light from the lightning strike is traveling toward OT, and OT is traveling away from LOCATION 1 (where OT was when the lightning strike occurred), and OT is traveling toward the light. The light reaches OT sooner than it reaches LOCATION 1 because OT has been moving toward the light while the light was traveling toward OT. The light traveled a shorter distance, which took less time to reach OT than it would have if OT was back at LOCATION 1, so OT observes the light sooner than if OT was back at LOCATION 1 when the lighting struck.

If we look at what happens with the lightning strike at the back of the train in the same manner, we notice that OT was moving away from that lightning strike while the light from it was moving toward OT, and OT was moving away from LOCATION 1, where he was when the lightnings struck. By the time the light from the back of the train reached OT, OT had traveled farther away from the light and farther away from LOCATION 1, so the light took longer to travel the longer distance to reach OT. So, OT observed the light from the back of the train at a later time than if OT were back at LOCATION 1.

Therefore, OT observes the light from each lightning strike at different times because OT was no longer at a location (LOCATION 1) equidistant from both lightning strikes at the time the light from both strikes reached OT.

 

[PeroK]

Therefore, OT observes the light from each lightning strike at different times because OT was no longer at a location (LOCATION 1) equidistant from both lightning strikes at the time the light from both strikes reached OT.

This whole analysis simply makes the platform frame a universal frame of reference. As fas as OT is concerned, the lightning strikes hit either end of the train, from which OT is permanently equidistant. As fas as OT is concerned it is OE and the platform that are moving relative to the locations that the lightning struck.

 

[LBoy]

- If the speed of light is the same in EVERY inertial frame of reference, in the reference of OT that speed is c, so i think when the two lightning strike in A and B, they are equal distance from the center (LBoy: but they are niot simultaneous) where there is OT 'cause the first assumption (when A and B are ALIGNED) so i think light will arrive at OT at the same time also in his frame of reference

Bold: here you have made the implicit assumption that both events are simultaneous for the OT on the train. And they aren't. That's where the misunderstanding comes from.

In the OE frame A and B are simultaneous (obvious I suppose). The OT has the same distance to the beginning and end of the train, where the lightning strikes, but by the time he sees the light from B (the beginning) a certain amount of time will have passed in which he approaches B and moves away from A.

The point or time at which it receives the light is crucial - that point is moving toward B and away from A.
Therefore, if the speed of light is constant for both observers - OE will see the light from B earlier and the light from A later, because distance from B to him is shorter due to movement, and bigger from him to A.

For him A and B are not simultaneous.

 

[David Lewis]

OE will see the light from B earlier and the light from A later, because distance from B to him is shorter due to movement, and bigger from him to A.

Why would OE see the light from B earlier and the light from A later? Doesn't OE see both flashes at the same time?

 

[LBoy]

Why would OE see the light from B earlier and the light from A later? Doesn't OE see both flashes at the same time?

Thank you, my bad! There should be OT (observer in the train) instead of OE of course, I will change it immediately.

 

[LBoy]

The point or time at which it receives the light is crucial - that point is moving toward B and away from A.
Therefore, if the speed of light is constant for both observers - OT (in my previous post there was an error, it was OE instead of OT) will see the light from B earlier and the light from A later, because distance from B to him is shorter due to movement, and bigger from him to A.

For him A and B are not simultaneous.

As I see I cannot edit my previous post,OK, so I'm doing it here.

 

[PeroK]

This particular thought experiment is good and bad at the same time.

This thought experiment, IMO, is simply bad. It confuses everyone who is new to SR. It over-emphasises a single observer over a reference frame, and creates misunderstanding about the need for light signals. It also over-emphasises the platform frame over the train frame and requires so many physical coincidences that it is genuinely quite complicated. It gets SR off on the wrong foot altogether.

Relativity of simultaneity can be shown much more simply.

I would advise students to steer clear of it, but obviously they are wowed by the fact that it was Einstein's original thought experiment and can't resist.

 

[LBoy]

Relativity of simultaneity can be shown much more simply.

I would advise students to steer clear of it, but obviously they are wowed by the fact that it was Einstein's original thought experiment and can't resist.

I would like to see it if you wouldn't mind, train experiment works for me, however I see the whole environment, a galaxy of possibilities of making an error due to a lot of irrelevant effects present. I can filter it out I suppose however I see that Hans might have a problem with this, he focuses on the less relevant things.

Maybe I can use something new, simpler to explain the essence of simultaneity.

 

[Dale]

A large number of misinformed posts and responses were deleted. I sincerely apologize for those who wrote good informative responses to the incorrect posts. I had to delete the good with the bad. But we decided that there was such a large disruption that cleanup was needed.

The thread is now reopened.

 

[LBoy]

So both observers see two flashes at the same time. Nevertheless, your observer at rest concludes that they happened at the same time, while your moving observer concludes that the flash in front of him occurred earlier then the one behind them

No, because that would mean that for both of them A and B occurred simultaneously. We explained this many times before.

The rest of explanation below is wrong. For example - the OT will not see flash B (front) as bigger and A smaller, velocity doesn't change the intensity (I assume that you meant intensity instead of size?) of the flash, it changes the frequency of light, so OT will see blue and redshift of light.

I am not sure about all following discussion about size, all other shapes, lengths adnd spatial relations, including size don't change for perpendicular coordinates at all in relativistic motion, so the light cone will not be bigger in space but exactly the same (sidenote: there will be no cone at all in case of lightning).

The same problem follows: in STR we have contraction of length (space in fact) along the direction of the move (simplified version) so simultaneous points in space time for a given observer lie on:
1. straight lines (two dimensial space time)
2. and are three - dimensional in case of 4 dimensional space time.

And in no reference frame surfaces of simultaneity are ellipsoidal, not in this metric.

In conclusion - the whole post is misleading too, these are imho pretty basic errors too, sorry.

And now comes the book: let us look at the page 11 from the chapter: "Non-simultaneity from the classical wave equation"

 

[PAllen]

No, because that would mean that for both of them A and B occurred simultaneously. We explained this many times before.

No, @Hans de Vries is correct and you are wrong. If two flashes of light arrive simultaneously, but you know one source is further away, then you conclude that the one further away occurred first, even though they arrived simultaneously.

The rest of explanation below is wrong. For example - the OT will not see flash B (front) as bigger and A smaller, velocity doesn't change the intensity (I assume that you meant intensity instead of size?) of the flash, it changes the frequency of light, so OT will see blue and redshift of light.

The rest of the explanation is completely correct (arguably, though, a lot more information than the OP needs).

Please look up aberration and beaming in special relativity. These effects, all derived in Einstein's 1905 paper (unlike prior work by Lorentz and Poincare) are in addition to redshift/blue shift. They cause increase/decrease in perceived size and intensity of a body image, depending on relative motion.

And in no reference frame surfaces of simultaneity are ellipsoidal, not in this metric.

You misunderstand the argument. If you allow for light delays but do not account for specifically relativistic effects (simultaneity, length contraction, etc.) a sphere moving rapidly relative to you would appear as an ellipse. When the other effects are taken into account, it again looks like a sphere. This is all well known, and a search keyword for literature on this is Penrose-Terrell rotation.

In conclusion - the whole post is misleading too, these are imho pretty basic errors too, sorry.

As far as I can tell, there are no errors in the referenced post.

And now comes the book: let us look at the page 11 from the chapter: "Non-simultaneity from the classical wave equation"

Quote:

"The right hand side of same figure shows a very fast forward moving cabin. Light from the front passenger reaches the middle passenger much faster with a relative speed of c+v, while the light from the back passenger goes relatively slower with c − v."

And my comment to that: Sweet Baby Jesus.

No, that is correct. Implicit is that it is description of the cabin in a frame in which it is moving. c+v, for example, is difference in velocity of a wave front and a body, in that frame in which the cabin is moving at v. This is different from relative velocity as determined within the cabin.

I do not necessarily like the presentation in the book, but, again, I don't see any error in the section referenced.

 

[LBoy]

Thank you for your answer. Lots to think about :)

1. First comment about simultaneity of flashes. Original idea,the starting thought-experiment describes situation in and out of the train. For the observer in the train flashes at the front (B) and at the back (A) are not simultaneous so in his reference frame he will not see them both as simultaneous (contrary to what Hans says).

Hans: "So both observers see two flashes at the same time." They don't. The point where the two flashes meet is outside OT's head towards the back of the train.

2. Relativistic beaming. As far as I know this effect amount of energy "perceived" (measured) by the observer so in this case my use of word "intensity" is wrong, thanks for pointing that out, however I don't quite get how the observer will measure changes of size of the object. If there is an orthogonal rod along y-axis at length of 1 meter we still see 1 meter, not less nor more in the train. So no "bigger" nor "smaller" flashes unless we define big and small in terms not size but intensity/amount of energy measured in time. I have just realized that Hans might use this colloquialism, however in our case this double meaning is very misleading.

3. Penrose-Teller rotation. In Minkowski space we have only three types of object that can be parametrized as simultaneous: a line in 2 dimensions, a plane in 3 d spacetime and finally a 3-d space when spacetime is 4 dimensional. All defined as orthogonal to the versor of time.

Now, however I see that Hans might use the term in 3-d space not in 4-d, and in this context "sphere of simultaneity" to an observer may mean a wavefront of e-m wave traveling from him in 3-d space, in vacuum this will indeed form a sphere in his rest frame and an ellipsoid in Minkowski space. I think there is a way of using this idea to explain events here, however in my opinion, this is a bit too much as it may complicate the picture in this quite difficult thought experiment. If I have time today I will re-read Hans explanations however I don't think 'spherical simultaneity" will add clarity to the picture, but of course I can be wrong.

Thank you again for your comments.

 

[italicus]

Hi

a similar discussion took place some months ago. I put a drawing in message #9:

https://www.physicsforums.com/threa...nt-demonstrate-relativity.998322/post-6442172

some more details:

the train passenger, Who knows that the speed of light is c for every IO, concludes that the event B happened for him before event A;

The train length for him is the proper length, while for the IO on Earth is the contracted one.

This is not one of the best examples by Einstein, but at least shows that two events, simoultaneous for the Earth IO, aren’t such for the IO moving past the previous.

 

[LBoy]

Hi

a similar discussion took place some months ago. I put a drawing in message #9:

https://www.physicsforums.com/threa...nt-demonstrate-relativity.998322/post-6442172

From the diagram we clearly see that light lines from A and B intersect blue skewed t' line in two separate points Q and P respectively. Thus for the OT both events are not simultaneous. It means that pulse from B arrives first and from A second. OT really sees B first and A as the second pulse, therefore it is not true (Hans) "So both observers see two flashes at the same time."

Hans, please analyze diagram in the post above.

Q is the event that light from B reaches OT.

P is the event that light from A reaches OT.

These events are separate in time along the blue worldline of the observer OT (the middle one). OT sees them both as separated in time - not simultaneous.

 

[PAllen]

From the diagram we clearly see that light lines from A and B intersect blue skewed t' line in two separate points Q and P respectively. Thus for the OT both events are not simultaneous. It means that pulse from B arrives first and from A second. OT really sees B first and A as the second pulse, therefore it is not true (Hans) "So both observers see two flashes at the same time."

Hans, please analyze diagram in the post above.

Q is the event that light from B reaches OT.

P is the event that light from A reaches OT.

These events are separate in time along the blue worldline of the observer OT (the middle one). OT sees them both as separated in time - not simultaneous.

Are you possibly confused by 'see' versus 'model'? If two detectors are colocated at some moment (present at the same event), irrespective of their relative state of motion, it is physically impossible and absurd to claim that one receives two signals at that event and the other does not. That is the sense of both see simultaneous signal arrival time. How you model simultaneity of the distant emission events is a separate question and is fundamentally one of convention, not physics. Frame dependent is not enough of a statement to capture the issue. More precisely, the only invariant statements that can be made about distinct events is whether one is in the causal future, past, or neither (acausal, "possibly now") from the other. The only further statement that can be made is that if two observers use the same convention meeting certain properties (e.g. the Einstein convention) for assigning simultaneity to spacelike separated events, and one is in motion relative to the other, then they will disagree on simultaneity assignment. But simultaneity of distinct events is never an observable, per se.

 

[PeroK]

Are you possibly confused by 'see' versus 'model'? If two detectors are colocated at some moment (present at the same event), irrespective of their relative state of motion, it is physically impossible and absurd to claim that one receives two signals at that event and the other does not. That is the sense of both see simultaneous signal arrival time. How you model simultaneity of the distant emission events is a separate question and is fundamentally one of convention, not physics. Frame dependent is not enough of a statement to capture the issue. More precisely, the only invariant statements that can be made about distinct events is whether one is in the causal future, past, or neither (acausal, "possibly now") from the other. The only further statement that can be made is that if two observers use the same convention meeting certain properties (e.g. the Einstein convention) for assigning simultaneity to spacelike separated events, and one is in motion relative to the other, then they will disagree on simultaneity assignment. But simultaneity of distinct events is never an observable, per se.

This analysis goes way beyond the purpose of the train experiment or any other introductory treatment of the RoS.

I'm not sure what @LBoy has said to warrant this. The nonsense that had to be deleted from this thread was not posted by him.

 

[PAllen]

This analysis goes way beyond the purpose of the train experiment or any other introductory treatment of the RoS.

I'm not sure what @LBoy has said to warrant this. The nonsense that had to be deleted from this thread was not posted by him.

This is what @Hans de Vries says:

"
If the two propagated light flashes meet each other at one point then any observer at that point will see them (receive the light flashes in his eyes) at the same time. This is totally independent of the velocity of the observer. However, they draw different conclusions about the simultaneity of the light flashes.
"

This is trivially true, yet it seems to me that @LBoy rejects this. @LBoy also questions many other statements in @Hans de Vries post that are clearly true. I don't see my responses as having any other tone than factual discussion. I am trying to understand the conceptual disconnect between these two posters. ('point' here is taken to mean event).

 

[PeroK]

This is what @Hans de Vries says:

"
If the two propagated light flashes meet each other at one point then any observer at that point will see them (receive the light flashes in his eyes) at the same time. This is totally independent of the velocity of the observer. However, they draw different conclusions about the simultaneity of the light flashes.
"

This is trivially true, yet it seems to me that @LBoy rejects this. @LBoy also questions many other statements in @Hans de Vries post that are clearly true. I don't see my responses as having any other tone than factual discussion. I am trying to understand the conceptual disconnect between these two posters. ('point' here is taken to mean event).

You are at the disadvantage of not seeing what was posted yesterday!

 

[PAllen]

You are at the disadvantage of not seeing what was posted yesterday!

Oh well, but thread posts should not really take account of what is no longer present, even if I had seen it. Otherwise the thread becomes incomprehensible to a future reader.

 

[Dale]

Please focus only on what remains. I deleted the deleted stuff precisely to NOT discuss it. If you continue discussing the deleted stuff then I will have to delete the new discussion and keep the thread closed. Just leave Hans alone, he recognized the mistake and doesn’t need to be hassled about it further.

 

[italicus]

How you model simultaneity of the distant emission events is a separate question and is fundamentally one of convention, not physics. Frame dependent is not enough of a statement to capture the issue.

First of all, excuse me for my bad English.
I’d like to consider the following, which “is” physics, and there is no frame dependence, IMHO. Maybe I haven't well understood your observation, if this is the case please correct me.
Let us suppose that two light signals hit me ( enter my eyes) at the very same moment of my wristwatch, one coming from the explosion of a Supernova in Andromeda, and the other coming from an asteroid that hits the Moon.
Of course, I see them at the same wristwatch time. But the two events are not contemporary : the first one happened some 2.5 millions years ago ( apart from relative motion of Andromeda and our Galaxy...: let’s imagine that Andromeda and me are in the same inertial r.f. ), the second one happened a little more than a second ago.
The 4-spacetime interval of both events, each calculated from the happening event and the light entering my eyes, are both equal to zero.
Well, here I see physics at work, and no convention about simultaneity.
Is it possible that other inertial observers receive the light from the two events at the same moment (of their wristwatch ) ? Yes, it is. There are a lot.
I hope I explained my idea well.

 

[cianfa72]

More precisely, the only invariant statements that can be made about distinct events is whether one is in the causal future, past, or neither (acausal, "possibly now") from the other.

If the second event is not in the causal future or past then it is actually spacelike separated from the first, I believe.

 

[PAllen]

First of all, excuse me for my bad English.
I’d like to consider the following, which “is” physics, and there is no frame dependence, IMHO. Maybe I haven't well understood your observation, if this is the case please correct me.
Let us suppose that two light signals hit me ( enter my eyes) at the very same moment of my wristwatch, one coming from the explosion of a Supernova in Andromeda, and the other coming from an asteroid that hits the Moon.
Of course, I see them at the same wristwatch time. But the two events are not contemporary : the first one happened some 2.5 millions years ago ( apart from relative motion of Andromeda and our Galaxy...: let’s imagine that Andromeda and me are in the same inertial r.f. ), the second one happened a little more than a second ago.
The 4-spacetime interval of both events, each calculated from the happening event and the light entering my eyes, are both equal to zero.
Well, here I see physics at work, and no convention about simultaneity.
Is it possible that other inertial observers receive the light from the two events at the same moment (of their wristwatch ) ? Yes, it is. There are a lot.
I hope I explained my idea well.

Yes, of course, most of what you say is true. Let me further assume the asteroid strike is in the opposite direction from the Andromeda explosion. This ensures that the emission events are spacelike in separation. Then, for an observer moving near lightspeed relative to Earth in the direction away from Andromeda, passing you at the moment both signals arrive (thus also seeing them arrive at the same time), would conclude (using standard Minkowski coordinates) that the asteroid strike occurred before the Andromeda explosion. For any spacelike separated events there is no invariant time ordering of them.

 

[PAllen]

@cianfa72 asked "If the second event is not in the causal future or past then it is spacelike separated from the first, I believe."

Yes, in SR this is an unambiguous equivalence. In GR, there are some complications (e.g. there can be both timelike and spacelike geodesics connecting the two events; using the notion of causal future, past, or neither, resolves such ambiguities; the scenario where this can happen is CTCs). So I used the most general wording, which is certainly overkill in SR.

 

[italicus]

For any spacelike separated events there is no invariant time ordering of them.

Absolutely correct !
But for now I’d leave GR aside. I’m aware of the complications that can be introduced here... !
This thread is about a doubt regarding the relativity of simultaneity , for which A.E. introduced the (not so happy...) example of two lightings that strike the embankment (and head and tail of the train...) : we are at a very basic level !
The drawing I reported was intended to show that , while the strikes are simultaneous for the Earth observer (OE=M in the drawing) , the aren’t such for the train observer (OT=M’ in the drawing) , because he is moving with speed v w.r.t. the embankment.

 

[cianfa72]

Sorry, CTCs what does it mean ?

 

[PAllen]

Sorry, CTCs what does it mean ?

closed timelike curve. These are present in many GR solutions. Many, but not all, physicists consider such solutions unphysical. For example, one of the interior regions of a spinning (Kerr solution) BH has them. However, it is generally believed that this section of the interior would never be physically realized because there would never be exact axial symmetry, and chaotically perturbing the collapse dynamics by a tiny amount would eliminate the CTC region. However, while I 'believe' this, to my knowledge, this has never been proven.

 

[PAllen]

Thank you for your answer. Lots to think about :)

1. First comment about simultaneity of flashes. Original idea,the starting thought-experiment describes situation in and out of the train. For the observer in the train flashes at the front (B) and at the back (A) are not simultaneous so in his reference frame he will not see them both as simultaneous (contrary to what Hans says).

Hans: "So both observers see two flashes at the same time." They don't. The point where the two flashes meet is outside OT's head towards the back of the train.

I read the explanation as that there is an observer in the train who visually sees the flashes arrive at the same time, this observation in the train is effectively colocated in space and time with the ground observer seeing the flashes arrive at the same time. However, the train observer models that the emission events are not simultaneous, while the ground observer models them as simultaneous. Neither of these statements about simultaneity represent anything that can be observed.

2. Relativistic beaming. As far as I know this effect amount of energy "perceived" (measured) by the observer so in this case my use of word "intensity" is wrong, thanks for pointing that out, however I don't quite get how the observer will measure changes of size of the object. If there is an orthogonal rod along y-axis at length of 1 meter we still see 1 meter, not less nor more in the train. So no "bigger" nor "smaller" flashes unless we define big and small in terms not size but intensity/amount of energy measured in time. I have just realized that Hans might use this colloquialism, however in our case this double meaning is very misleading.

Relativistic beaming is the effect that if you are moving towards an EM source at near the speed of light, then, compared to a colocated observer at rest with respect to the source, you measure an intensity (power per sq. centimeter, for example) on the order of $\gamma ^3$ times greater. The causes of the are a combination of aberration reducing the angular diameter of the object, and the Lorentz transform of amplitute of a wave (which implies energy). In the classical treatment, there is no coupling between wave amplitude and wave frequency. It happens that they both transform in the same way, so the Doppler factor applies to both. But classically, these are independently derived facts, which happen to be coupled in a quantum theory. Thus, looking at photons, you might think there is just Doppler and aberration. However, classically, Doppler has nothing to do with energy - that is determined by amplitude transformation.

3. Penrose-Teller rotation. In Minkowski space we have only three types of object that can be parametrized as simultaneous: a line in 2 dimensions, a plane in 3 d spacetime and finally a 3-d space when spacetime is 4 dimensional. All defined as orthogonal to the versor of time.

Now, however I see that Hans might use the term in 3-d space not in 4-d, and in this context "sphere of simultaneity" to an observer may mean a wavefront of e-m wave traveling from him in 3-d space, in vacuum this will indeed form a sphere in his rest frame and an ellipsoid in Minkowski space. I think there is a way of using this idea to explain events here, however in my opinion, this is a bit too much as it may complicate the picture in this quite difficult thought experiment. If I have time today I will re-read Hans explanations however I don't think 'spherical simultaneity" will add clarity to the picture, but of course I can be wrong.

Thank you again for your comments.

I don't understand what your are getting at here. One traditional analysis of the case of a moving sphere is to consider that light always travels at c in some chosen frame, but that no relativistic effects are present (relativity of simultaneity, length contraction, or time dilation). Then, you find that due to which light rays (simplifying to a geometric optics approximation) arrive at the same time, the sphere is elongated to an ellipse. However, then assuming that what was a sphere in its rest frame must be considered as a squashed in a frame in which it is moving (due to length contraction), then, redoing the arrival time analysis, you find an exact sphere is what will be observed. Member @A.T., I believe, has links to nice visualizations of all this.

Penrose-Terrell rotation is a completely general phenomenon in special relativity which can be most elegantly approached in terms of aberration, because then you need not consider arrival times or simultaneity, and can immediately see that it applies to objects of any shape. The analysis, in brief, is as follows.

First, what is aberration? In SR, it is simply the way the angle of a light ray transforms in SR under a Lorentz transform. Conceptually, this has nothing in common with the Bradley derivation, which requires a corpuscular model of light as well as the false assumption that light speed depends on the motion of the source (even though the two different formulas are currently indistinguishable due to observational precision limitations). The general rule is simple. Consider two colocated observers, A and B. Suppose B is moving in the +x direction relative to A. Suppose A observes a light ray (using geometric optics approximation, rather than plane waves) arriving at some $\theta$ relative to the x axis. Then B will observe this light ray arriving at an angle closer to the +x axis. The amount depends on speed, and in the limit of near c, even a ray A perceives as arriving from near the direction of the -x axis, B will observe as coming from near the +x axis.

Consider an arbitrary object moving relative relative to observer B as described above, but at rest relative to A. In the rest frame of A, you can analyze the image without considering simultaneity or arrival times. The situation is completely static. But then, in B rest frame, the set of rays arriving cannot be different. Their angles can be different, as can the frequency and energy. Thus, if you want to know the image B sees when the object looks orthogonal to x, per B, you compute the image per A when the object is back towards -x by the appropriate amount. For an object not too large in angular size, aberration then simply rotates this image towards +x, so it appears to come orthogonal to x per B. This means B sees an image of the object as if it is rotated towards B. In particular, even for a ruler with markings, the image looks just like the ruler was simply turned towards B, and this 'explains' the decrease in angular size (length contraction). Especially, if you imagine B able to image the object continuously despite high speed, it would look like the object, of whatever shape, is rotating as it moves, without any first order change in size or shape.

 

[PeterDonis]

here I see physics at work, and no convention about simultaneity.

Yes, there is a simultaneity convention implicit in what you said, specifically, here:

the two events are not contemporary : the first one happened some 2.5 millions years ago ( apart from relative motion of Andromeda and our Galaxy...: let’s imagine that Andromeda and me are in the same inertial r.f. ), the second one happened a little more than a second ago.

You cannot derive these statements just from the light signals that you received; light signals contain no inherent "how long it took the signal to get to you". That "how long" is frame dependent--i.e., it depends on your choice of simultaneity convention. When you say the Andromeda signal took 2.5 million years to get to you, but the one from the Moon took only a little more than a second, you have adopted a particular simultaneity convention. Other such conventions would give different propagation times for the two light signals.

 

[italicus]

When you say the Andromeda signal took 2.5 million years to get to you, but the one from the Moon took only a little more than a second, you have adopted a particular simultaneity convention. Other such conventions would give different propagation times for the two light signals.

I am a bit perplexed here. Isn’t the speed of light equal to c , for all IO ? This is the second postulate of SR . The signal from Andromeda takes 2.5 million years to get to me, because d = ct, hence t = d/c . Which particular simultaneity convention have I adopted? The easiest and most natural one is that by Einstein, who writes : “ When you say that a train has arrived at 7.00 o’clock , you are just stating that the arrival of the train is simultaneous to such and such position of your clock hands” (something like that...I don’t remember exactly!).
How is it possible that another simultaneity convention gives a different propagation time ? But, first of all : which other simultaneity convention could be adopted here?

 

[PAllen]

I am a bit perplexed here. Isn’t the speed of light equal to c , for all IO ? This is the second postulate of SR . The signal from Andromeda takes 2.5 million years to get to me, because d = ct, hence t = d/c . Which particular simultaneity convention have I adopted? The easiest and most natural one is that by Einstein, who writes : “ When you say that a train has arrived at 7.00 o’clock , you are just stating that the arrival of the train is simultaneous to such and such position of your clock hands” (something like that...I don’t remember exactly!).
How is it possible that another simultaneity convention give a different propagation time ? But, first of all : which other simultaneity convention could be adopted here?

How do you know d?

There is no fundamental reason to use a reference frame based on you being at rest. Suppose you consider that some object of cultural significance should be the basis of coordinates, and that object has high speed relative to you. Then you might conclude the asteroid colliding with the moon happened at the same time as the Andromeda explosion (or even before it).

 

[italicus]

There is no fundamental reason to use a reference frame based on you being at rest

Well, the reason for me is that it is the simplest reference frame! Nobody moves with respect to himself, no ? If I am sitting in a fast (not accelerating) train, I prefer the reference frame of the train for my observation of physical phenomena, and say that the landscape is moving towards me.
Galileo implicitly suggests me this : “ Shut yourself under deck of a big ship...” and let butterflies fly, drops of water fall vertically from a vase...

{ Dear friends, my life in this moment is simultaneous with 01:20 of Sept 24 ...Excuse me, I am tired and will go to sleep. See you later ! }

 

[PAllen]

Well, the reason for me is that it is the simplest reference frame! Nobody moves with respect to himself, no ? If I am sitting in a fast (not accelerating) train, I prefer the reference frame of the train for my observation of physical phenomena, and say that the landscape is moving towards me.
Galileo implicitly suggests me this : “ Shut yourself under deck of a big ship...” and let butterflies fly, drops of water fall vertically from a vase...

{ Dear friends, my life in this moment is simultaneous with 01:20 of Sept 24 ...Excuse me, I am tired and will go to sleep. See you later ! }

Yes and no. Do astronomers each use their own personal rest frames, with all different relative velocities depending on latitude and longitude? In fact, they rarely use Earth an Earth centric frame (GPS does, but not astronomers). Instead they may use sun centric frame (actually, solar system barycenter is most common for solar system phenomena), Milky Way centric frame, or CMB frame, for different purposes. All would have different definitions of simultaneity.