Are Observers on the Plane of Simultaneity Experiencing Events Simultaneously?

[jainabhs]

Hi
Please explain following on simulataneity..
Two far removed relatively at rest observers are on the plane of simultaneity.But if some event occurs in the close vicinity of observer1, he will see it immediately whereas it will take years for oberserver2 to see that event; and vice versa. So the events are not simultaneous for them (unless they happen at the middle of the line joining both obeservers ). are they still on the plane of simultaneity (Given that their clocks are synchronised)?

OR being on the plane of simultaneity just means that time of the event (by the clock located at the location where event occurres) and time that both relatively at rest observers' clocks show is same, but they may not see the event ??

And also please tell me where I can read more on this plane of simultaneity and effect of distance on time dilation??

Thanks a lot
Abhishek

 

[JesseM]

Simultaneity has nothing to do with when you see events, it has to do with when you calculate they occurred in your rest frame, given the assumption that light travels at c in your frame. For example, if in 2007 I look through my telescope and see an event taking place 7-light years away according to my rest frame's definition of distance, and then in 2008 I see an event taking place 8-light years away, once I take into account the time the light from each event took to reach me, I'll conclude both events happened "simultaneously" in my frame in 2000.

 

[Entropia]

The concept of the plane of simultaneity is an important concept in the theory of relativity. It refers to a hypothetical plane that contains all events that occur at the same time according to a specific observer. This means that if two events occur at the same time according to this observer, they will both lie on this plane.

In the scenario you described, both observers are on the plane of simultaneity because their clocks are synchronized and they both see the event happening at the same time according to their own clocks. However, as you correctly pointed out, the event may not be seen simultaneously by both observers due to the distance between them. This is because the speed of light is finite, so it takes time for the light from the event to reach the observers. Therefore, the event may appear to happen at different times for each observer.

This concept is closely related to the effects of distance on time dilation. Time dilation is the phenomenon where time passes at different rates for observers in different frames of reference. In this case, the distance between the observers causes a difference in the time that they perceive the event to occur, even though their clocks are synchronized.

To learn more about the plane of simultaneity and its implications in relativity, I suggest reading about the thought experiment known as the "train and platform paradox" or the "barn and pole paradox". These examples illustrate the concept in a more concrete way and can help deepen your understanding. Additionally, there are many resources available online and in textbooks that discuss the effects of distance on time dilation and the concept of the plane of simultaneity in more detail.

I hope this helps to clarify the concept for you. Happy learning!