Understanding Relativity of Simultaneity

[Cobalt101]

I am having a bit of trouble with understanding a basic point re the concept of relativity of simultaneity. I get the point of observers seeing events at different times, due to the passage of time of light traveling to them from the event. But I don't understand why this precludes events being known as occurring simultaneously. One might not actually observe this, but knowing the speed of light, each observer can gain an understanding of when the event actually happened by deducting the time that the light took to reach them. Thus an event at C may have taken 1 week to be seen at B and 2 weeks to be seen at A, but both A and B can calculate that it took place at the same time. I am clearly missing something.

 

[andrewkirk]

,

both A and B can calculate that it took place at the same time.

The question is 'what does "at the same time" mean'.

Einstein answered this question by postulating that a person A determines that spacetime events X and Y occur at the same time iff clocks that were at spacetime events X and Y and moving with the same velocity as A and were synchronized with a clock that A is holding, both showed the same time.

Note how this definition depends on the velocity of A - see the underlined bit. So A and B will have different definitions of simultaneous because the clocks they use are moving at different velocities.

 

[Nugatory]

IOne might not actually observe this, but knowing the speed of light, each observer can gain an understanding of when the event actually happened by deducting the time that the light took to reach them. Thus an event at C may have taken 1 week to be seen at B and 2 weeks to be seen at A, but both A and B can calculate that it took place at the same time.

You are right about how we determine when an event happened - we subtract the light travel time from when the light reaches us, so if it happened one light-minute away and the light reaches us at noon, we know the it happened one minute before noon at 11:59.

However, observers in motion relative to one another will not agree about the simultaneity of spatially separated events when they make this correction for light travel time.

Your should start by working carefully through Einstein's thought experiment showing this - Google for "Einstein train simultaneity" and see how it is that if the two lightning flashes are simultaneous for the train observer they are not simultaneous for the platform observer and vice versa when they both allow for the light travel time.

 

[pixel]

The results of relativity apply even when the travel time of light ("lookback time") is accounted for. They are an additional effect. In Einstein's famous train thought experiment, the light flash from the front of the train reaches the observer in the center before the light from the rear of the train. It is precisely because the observer takes into account the equal distances and the constant speed of light that he concludes the light flashes are not simultaneous.

 

[Herman Trivilino]

One might not actually observe this, but knowing the speed of light, each observer can gain an understanding of when the event actually happened by deducting the time that the light took to reach them. Thus an event at C may have taken 1 week to be seen at B and 2 weeks to be seen at A, but both A and B can calculate that it took place at the same time. I am clearly missing something.

Let's say that (with an appropriate safety lens) you see a solar flare and note the time is 11:29. You conclude that the flare occurred at 11:21. What this really means is that to you there are two events. Your clock reading 11:21 and the emission of the flare. In your frame of reference these events are simultaneous. To observers in other frames of reference they may not be simultaneous.

Let's consider a third event, the arrival of the light at 11:29 notifying you of the flare. To you, 8 minutes elapsed between the emission of the flare and this third event. But to other observers the elapsed time between these two events may not be 8 minutes.

Relativistic effects like these are not a consequence of the delay in time that occurs because of light travel. They are a consequence of the fact that the speed of light is the same for all observers.