Frame of reference and relativity.

[bayan]

Homework Statement

You are flying your personal rocketcraft at 0.9c from Star A toward Star B. The distance between the stars, in the stars' reference frame, is 1.0 ly. Both stars happen to explode simultaneously in your reference frame at the instant you are exactly halfway between them.

The question asked of the aforementioned scenario is "Do you see the flashes simultaneously?"

Homework Equations

Conceptual question, no equations needed.

The Attempt at a Solution

I answered the question with a no, my reasons were, if the rocket is at midway in his frame of reference when both stars explode, (the light from star B would reach the rocket first as it is traveling towards star B, i.e at .9c the distance of 1ly would be reduced to .44ly the midway of which would be .22ly) however it turns out the answer is yes. My relativity lecturer had a same view (on a similar question, he stated that the flashes would be observed at same time).

Could someone explain explain why my answer was wrong?

 

[collinsmark]

Homework Statement

You are flying your personal rocketcraft at 0.9c from Star A toward Star B. The distance between the stars, in the stars' reference frame, is 1.0 ly. Both stars happen to explode simultaneously in your reference frame at the instant you are exactly halfway between them.

The question asked of the aforementioned scenario is "Do you see the flashes simultaneously?"

Homework Equations

Conceptual question, no equations needed.

The Attempt at a Solution

I answered the question with a no, my reasons were, if the rocket is at midway in his frame of reference when both stars explode, (the light from star B would reach the rocket first as it is traveling towards star B,

That would be true if the stars exploded simultaneously in the stars' frame of reference.

If somebody not moving relative to the stars (i.e that observer shares the same reference frame as the stars) observes the stars explode simultaneously, then you (who is moving with respect to the stars at 0.9 c) would see (and observe) star B explode first. But that's not what the problem statement describes. The problem statement says that the stars explode simultaneously in your frame of reference (not the stars' frame of reference).

however it turns out the answer is yes. My relativity lecturer had a same view (on a similar question, he stated that the flashes would be observed at same time).

Could someone explain explain why my answer was wrong?

There is no such thing as absolute simultaneity in relativity. Events which are simultaneous in one frame of reference are not necessarily simultaneous in another frame. Not only does the time difference of events change depending on one's frame of reference, but also the spatial difference. This is true even for different inertial frames of reference, (different inertial frames in special relativity have different relative velocities, even though they are constant velocities).

In your inertial frame of reference, you are the one standing still. According to your frame of reference, the stars are the things that are moving at 0.9 C (star B is moving toward you and star A away from you). Now try the same thought process.

 

[bayan]

Thanks for your reply, I understand it now :)