Making sure events are simultaneous in S'

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In summary, the conversation discusses using inverse Lorentz transformations to determine the timing of events in different reference frames. The speaker proposes defining events in the asteroid's reference frame to ensure simultaneity and asks for confirmation that this approach is correct. The responder agrees and explains the concept of inverse transformations. The speaker then questions the results they are getting and the responder suggests they check for arithmetic errors.
  • #1
Shaybay92
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I have a problem where it requires me to find when a laser should be fired at an asteroid to ensure that in the reference frame of the asteroid, the laser hits the back and front within 1 millisecond. I thought that I could define events in S' such that the front and back are hit at t' = 0, and then see what events this would correspond to in S. Thus I would know when the events must happen in S to ensure simultaneity. Is this correct?
 
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  • #2
Shaybay92 said:
I have a problem where it requires me to find when a laser should be fired at an asteroid to ensure that in the reference frame of the asteroid, the laser hits the back and front within 1 millisecond. I thought that I could define events in S' such that the front and back are hit at t' = 0, and then see what events this would correspond to in S. Thus I would know when the events must happen in S to ensure simultaneity. Is this correct?
Yes, that would work.
 
  • #3
It seems logical to me, however when I try and use inverse lorentz transformations on those events to get the coordinates in S and then re-transform those S coordinates back into S' it says that those events are not simultaneous in S'. I thought this was a 'closed loop'. I should get the original events I defined back right?
 
  • #4
Yes. That is what it means for a transform to be an inverse. You must have made an arithmetic error.
 

1. What is the concept of simultaneity in S'?

Simultaneity in S' refers to the idea that two events occurring in different locations can be considered to happen at the same time in the frame of reference of an observer in S'. This concept is based on the theory of special relativity, which states that the perception of time and space is relative to the observer's frame of reference.

2. How can we ensure events are simultaneous in S'?

To ensure events are simultaneous in S', we must synchronize the clocks of observers in different locations. This can be done by sending a signal from one observer to another, which is then used to adjust their respective clocks. This synchronization process is essential in the theory of special relativity to maintain consistency in the measurement of time and distance.

3. What is the role of the speed of light in determining simultaneity in S'?

The speed of light is a fundamental constant in the theory of special relativity. It is the same for all observers, regardless of their frame of reference. This means that the perception of time and space is distorted at high speeds, as the speed of light is constant and cannot be exceeded. Therefore, the speed of light plays a crucial role in determining simultaneity in S' as it is used to calculate the time difference between events.

4. Can events be simultaneous in different frames of reference?

Yes, events can be simultaneous in different frames of reference. However, this is only possible if the frames of reference are in relative motion with constant velocity and are not accelerating. This is because the perception of time and space is relative to the observer's frame of reference. In other words, two events deemed simultaneous in one frame of reference may not be simultaneous in another.

5. How does the concept of simultaneity in S' impact our understanding of time and space?

The concept of simultaneity in S' challenges our traditional understanding of time and space as absolute and universal. It suggests that the measurement of time and distance is relative to the observer's frame of reference and is affected by factors such as speed and gravity. This has significant implications for our understanding of the universe and has been confirmed by various experiments and observations in the field of physics.

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