Simultaneity of events in 2 dimensions

[techdirect]

Hi all,

I am not a physicist. Some engineer friends of mine and I have a question about special relativity in two dimensions. To set it up, there are 2 lights floating in space parallel to the x-axis and a spaceship is traveling at .8c flying parallel to the y-axis towards the midpoint of the line connecting the lights. Then at some time, t, an observer, o1, between the lights at the midpoint flashes both of them simultaneously.

I drew a quick diagram which is attached.

1. The observer o1 will see both flash simultaneously

2. At a different time t', the crew of the spaceship will also see both flash simultaneously because of the symmetry of the problem.

Is our understanding correct?

 

[tiny-tim]

Welcome to PF!

Hi techdirect! Welcome to PF!

1. The observer o1 will see both flash simultaneously

2. At a different time t', the crew of the spaceship will also see both flash simultaneously because of the symmetry of the problem.

Is our understanding correct?

Completely!

(and, more generally, even if the spaceship was not in line with o, but was still moving parallel to the y-axis, even though it would not see the flashes at the same time, it would calculate that they happened at the same time)

 

[Entropia]

Hi there,

Your understanding is correct. In special relativity, simultaneity is relative and depends on the observer's frame of reference. In this scenario, the observer o1 is at rest relative to the lights, so they will see both lights flash simultaneously. However, the crew on the spaceship is moving at .8c, so they will experience time dilation and length contraction. This means that from their perspective, the distance between the lights will appear shorter and time will appear to pass slower. As a result, they will also see both lights flash simultaneously at a different time t'. This is known as the relativity of simultaneity.

The key concept here is that events that appear simultaneous to one observer may not appear simultaneous to another observer in a different frame of reference. This is one of the fundamental principles of special relativity and has been confirmed through numerous experiments and observations.

I hope this helps clarify your understanding of the simultaneity of events in two dimensions. If you have any further questions, please don't hesitate to ask. Thank you for bringing up this interesting topic!