# Simultaneity of Events

Dear PF Forum,
What does "at the same time" mean for two observers?
1. Does "At the same time" mean different for two COMOVING observers than two REST observers?

2. Can we say in picture 1 that E1 and E7 are at the same time?
3. Or do we have to convert it to picture 2 then we'll know that it's E1 and E2 are at the same time?
4. Regarding Pic 2. If E1 and E2 are at the same time, Blue (B) will never now about E2 until E2A will it?
5. Is at the same time for B is E2A and E2?
6. Is at the same time for B is E1 and E2?
Thanks for any help

you have to be careful what you mean by "an observer". usually, in relativity texts, an observer actually means an inertial frame. an inertial frame is a set of clocks at the intersection of a set of rulers that are synchronized accordingly and all at rest relative to each other. having defined "observer" this way it is clear that any frame which has clocks or rulers at rest relative to this frame is an equivalent frame or "comoving observer". in this language, a comoving observer would ALWAYS label two events with the SAME coordinates in spacetime with the exception of the possibility that their spatial origins may be translated. it's important here to understand that the TIME coponent of a spacetime event is NOT the time read off by some clock at the origin when a "literal observer (a person at the origin, say)" SEES the event happen, rather it is the time the clock, located AT THE EVENT, read when the event occured. For example, an event occuring in my frame at time t=0 and a distance 1 light second away from me means the LIGHT reaches me a time t=1 second, but the actual event is labeled in spacetime by the point (t=0,x=1) in the proper units. So, to answer your questions, events that are simultaneous in one frame are simultaneous to all other frames at rest relative to this frame.

For example, an event occuring in my frame at time t=0 and a distance 1 light second away from me means the LIGHT reaches me a time t=1 second, but the actual event is labeled in spacetime by the point (t=0,x=1) in the proper units. So, to answer your questions, events that are simultaneous in one frame are simultaneous to all other frames at rest relative to this frame.
So events that are simultaneous for E1 is E1A?

you need more information to tell. is pic 2 the blue line and the green line's rest frame?

you need more information to tell. is pic 2 the blue line and the green line's rest frame?
Well, the lines are vertical, right. Aren't they at rest in Pic 2?

if that is their rest frame, then E1 is simultaneous to E2 for those 2 comoving observers. the rest of the events are not simultaneous in that frame

if that is their rest frame, then E1 is simultaneous to E2 for those 2 comoving observers. the rest of the events are not simultaneous in that frame
What about pic 1. For blue and green, they wouldn't know that they are moving, right? Motion is relative. All Blue see is Green at the same distance with Blue all the time.
Perhaps in Pic 2, for a REST observer other than Blue and Green, the simulaneus event is E1 and E2?
And for a REST observer in pic 1, the simultaneus event is E1 and E7?

that's correct. in picture 1, that frame sees events E1 and E7 as simultaneous. but those events ARE NOT simultaneous for the blue and green observers, themselves.

I'll continue later. Driving home. Thanks.

that's correct. in picture 1, that frame sees events E1 and E7 as simultaneous. but those events ARE NOT simultaneous for the blue and green observers, themselves.
Ok, so simultaneous for whom?

pervect
Staff Emeritus
Dear PF Forum,
What does "at the same time" mean for two observers?

You might also try reading Einstein's original remarks, http://www.bartleby.com/173/9.html, Specifically:

When we say that the lightning strokes A and B are simultaneous with respect to the embankment, we mean: the rays of light emitted at the places A and B, where the lightning occurs, meet each other at the mid-point M of the length A —> B of the embankment.

or try wiki https://en.wikipedia.org/w/index.php?title=Relativity_of_simultaneity&oldid=672017033. I prefer both to the thread you quoted.

1. Does "At the same time" mean different for two COMOVING observers than two REST observers?

Basically, the answer is yes, but it's usually expressed in different language. This is basically what we mean when we talk about simultaneity depending on the frame of reference, though.

View attachment 86251
2. Can we say in picture 1 that E1 and E7 are at the same time?

As always, we need to qualify this statement. Your drawing is a drawing of two co-moving observers - and you've just noticed/stated that simultaneity means something different when we talk about two co-moving observers than when we talk about two at-rest observers. The language issue here is that while the two observers in your drawing are comoving in the frame of reference of the drawing, we can easily imagine or make a different drawing of the same physical situation, in which the blue and green are at rest.

Einstein makes basically the same point in his remarks, where he talks about using the train as a "rigid reference-body". We really need to introduce the concept of a frame of reference (what Einstein means by rigid reference-body) to understand this properly, but I'm not sure that when I say those words, you associate my intended meaning with them :(. I have never yet seen you specify which "reference frame" you are using when you talk about simultaneous events, or even talk about frames of reference at all. But we need those underlying concepts (which I have used liberally throughout this post and others) to understand the problem. If there isn't a common understanding about what those concepts mean, obviously, there will be some communication issues :(.

Nugatory
Mentor
Here's an easy way of understanding what "at the same time" means when you're looking at a space-time diagram:

First, draw the x and t axes for one or more frames of reference. They may or may not intersect at right angles on your sheet of paper, doesn't matter. (But you should try to break yourself of the habit of thinking that the one frame in which they meet at right angles is different from any of the others)

Now, draw a line between two events. If that line is parallel to the x axis of some frame, then the two events are happened at the same time in that frame. If it's not, they aren't.

Equivalently, when you draw a line parallel to the x-axis for a given frame, then all events on that line are happened at the same time in that frame.

Stephanus
Here's an easy way of understanding what "at the same time" means when you're looking at a space-time diagram:

First, draw the x and t axes for [..]
But, that would be cheating, right.
We'll know about simultaneity of events, because we are OUTSIDE the ST diagram, watching it on the computer screen. What if we put ourselves at event AV1 as indicated by the "eye" icon.
Consider this space-diagram:

Here, at AV1. Green (G) at AV1 wouldn't see the big picture. The only thing that G sees at AV1, see zoomed picture is Avn1 and Born happens at the same time.
The blue lines (B1 and B2) is the world line of twins co moving. I know, I know when I drew this picture I didn't think that two twins can't be born at separate distance. One is born at B1 and the other is born at B2. But, I've already drawn the picture when I realize the impossible.
My question is:
1. Is AV1 can determine Anv1 and Born speed? I thinks, yes. Because of doppler effect.
2. Is AV1 can determine Anv1 and Born distance? I think so, if using some calculations and signal bouncing as in

Can I ask again regarding simultaneity of events?
=========== PIC 1 =======================
3. What is the event that happens"AT THE SAME TIME" as Anv1? Is the question complete.? Or should I say
4. What is the event that happens at the same time as Anv1 according G at G's moving frame, as in Pic 1?
Here, G at AV1 will see Anv1 and Born. Is that the same events according to G?
5. Or G has to wait until AV2 and say, "Aha, Anv2 is coming. So using some calculation G can determine that Anv1 and Anv2 are at the same time.
=========== PIC 1 =======================
I could have asked more combination question. Perhaps I should shorten it to this.

What is the events that happens at the same time as Anv1?
A. Anv2?
B. Born?
C. Anv1X?

Thanks for any trouble answering me.

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You might also try reading Einstein's original remarks, http://www.bartleby.com/173/9.html, Specifically: or try wiki https://en.wikipedia.org/w/index.php?title=Relativity_of_simultaneity&oldid=672017033.
And regarding to Einstein's original remarks.
I remember this post.

This is the post that allow me to devise Lorentz factor (gamma) and realize about length contraction, time dilation and that there IS simultaneity of events. But foolishly, I don't know what does "HAPPENS AT THE SAME TIME" mean.

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..., I don't know what does "HAPPENS AT THE SAME TIME" mean.

It means 'having the same time coordinate'. In Pic 1, Anv1 and Anv2 have the same time coordinate ( as far as one can tell ).

It means 'having the same time coordinate'. In Pic 1, Anv1 and Anv2 have the same time coordinate ( as far as one can tell ).
And in Pic 2, it's Anv1 and Anv1X happens at the same time. Is that so?
Btw, I'm discarding cartesian, I'm using Lorentz Transformation now to draw the ST diagram. Cartesian is very tedious and lengthy! But still using spread sheet. So I can draw precisely.

And in Pic 2, it's Anv1 and Anv1X happens at the same time. Is that so?
If Anv1 and Anv1X have the same time coord in green coords then they are simultaneous in green coords.

If Anv1 and Anv1X have the same time coord in green coords then they are simultaneous in green coords.
Ah, yes actually this is very simple. I understand now. When reading the ambulance case in this link.
But how to calculate event at the same time?

1. Does G as in Pic 2 have to turn/calculate his world line to calculate simultaneity of events for Blue (B1 and B2) as in Pic 1?
In short.
If we want to calculate simultaneity of event, we to calculate the event/object at their rest frame? Is that how we have to do it to get the correct answer as in Pic 1?
2. When G sees AV1, G will now B1 speed through doppler and B1 distance through bouncing signal, so G has to wait until AV2 then G calculate that Anniversary 2 (Anv2) is actually the same time for Blue as Anniversary 1 (Anv1).

In short what I mean is this:
G doesn't see any of the space time diagram. We are the one who see it on the computer screen, right?
At AV1, all G see is this, right?
1. G time,
2. B1 speed according to Doppler ##f = \sqrt{\frac{1+\beta}{1-\beta}} f0; \beta = \frac{f^2 - f0^2}{f^2+f0^2}##,
3. B1 distance according to signal bouncing.
And based on all these data, when G reaches AV2, G will know that Anv1 and Anv2 happens at the same time, right?

G doesn't see any of the space time diagram. We are the one who see it on the computer screen, right?
Yes. We can see the past and future. G and B can only see along the x-axis. They are aware of their own clock time and will receive light/radio signals sent towards them.
They can also bounce a signal off another thing on the x-axis.