Temporal order of events seen by different Lorentz observers

In summary, the problem presents three events, A, B, and C, seen by two different observers in different orders. While some placements of the events on a spacetime diagram can produce these orders, not all do. To determine if a third observer sees the events in the order ACB, it is necessary to correctly project the events onto the t'-axis using Minkowski diagrams or other tools.
  • #1
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Homework Statement



Three events, ##A##, ##B##, ##C##, are seen by observer ##\mathcal{O}## to occur in the order ##ABC##. Another observer, ##\mathcal{\bar{O}}##, sees the events to occur in the order ##CBA##. Is it possible that a third observer sees the events in the order ##ACB##? Support your conclusion by drawing a spacetime diagram.

Homework Equations



The Attempt at a Solution



Here's a particular placement of the events ##A##, ##B##, ##C## in the order ##ABC## as seen by observer ##\mathcal{O}## (##t##-##x## coordinate system) and in the order ##CBA## as seen by observer ##\mathcal{\bar{O}}## (##t'##-##x'## coordinate system):

IMAG0113.jpg


I find that not all placements of the events ##A##, ##B##, ##C## on the spacetime diagram simultaneously produce the orders ##ABC## and ##CBA## as seen by two different observers ##\mathcal{O}## and ##\mathcal{\bar{O}}##.

How I proceed with demonstrating whether or not a third observer sees the events in the order ##ACB##?
 
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  • #2

1. What is the "temporal order of events seen by different Lorentz observers"?

The "temporal order of events seen by different Lorentz observers" refers to the order in which events occur as perceived by observers in different frames of reference, based on the principles of special relativity. This means that the order of events can differ for different observers depending on their relative motion and position in space and time.

2. How does the theory of special relativity explain the concept of temporal order?

The theory of special relativity explains that time is a relative concept and is influenced by an observer's frame of reference. This means that the temporal order of events can appear different to different observers based on their relative motion and position in space and time. The theory also states that the speed of light is constant and the same for all observers, regardless of their frame of reference.

3. Can the temporal order of events ever be reversed for different Lorentz observers?

No, the temporal order of events cannot be reversed for different Lorentz observers. The principles of special relativity state that the speed of light is constant for all observers, meaning that the order of events can only appear different due to the differences in relative motion and position in space and time.

4. How does the concept of time dilation affect the temporal order of events seen by different Lorentz observers?

Time dilation, a phenomenon predicted by the theory of special relativity, states that time appears to pass slower for objects or observers in motion compared to those at rest. This means that the temporal order of events can appear different for observers in different frames of reference, as time may seem to pass at a different rate for each observer.

5. Are there any practical applications of understanding the temporal order of events for different Lorentz observers?

Yes, understanding the temporal order of events for different Lorentz observers has practical applications in fields such as space travel, telecommunications, and satellite navigation. Knowledge of how time and the order of events can appear different for different observers is crucial in accurately measuring and coordinating events and signals between different frames of reference.

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