A question about Alice and Bob in SR

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Discussion Overview

The discussion revolves around the scenario of Alice and Bob in the context of special relativity, specifically focusing on Alice's constant acceleration and the implications for their respective time measurements when they meet. Participants explore the calculations related to proper time, coordinate time, and the synchronization of watches, as well as the number of signals received by Alice from Bob.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • Bob is at rest in Minkowski space, while Alice experiences constant proper acceleration.
  • Participants discuss the proper time ##\tau## for Alice and the coordinate time ##t## for Bob, emphasizing the need to calculate these values at the times they meet.
  • There is uncertainty regarding the relationship between the time intervals ##\Delta t## and the proper times measured by Alice and Bob.
  • Some participants suggest that the time elapsed for Bob can be computed from the difference in coordinate times at the events of their meetings.
  • There is confusion about the relevance of the light pulses sent by Bob and how they relate to the calculation of elapsed time.
  • Participants propose using the equations of motion for Alice to find the times at which she meets Bob and to derive the corresponding times for Bob.
  • Discussions include the need to clarify the definitions and roles of ##\Delta t## in the context of the problem.

Areas of Agreement / Disagreement

Participants express differing views on the necessity and role of the light pulses in calculating elapsed time. While some suggest they are irrelevant, others question how to compute the time differences without them. The discussion remains unresolved regarding the correct approach to calculating the elapsed times for both Alice and Bob.

Contextual Notes

There are limitations in the clarity of how ##\Delta t## is defined and its connection to the calculations of proper times. The discussion also highlights the need for careful consideration of the world line intersections and the implications of proper acceleration on time measurements.

  • #31
Ibix said:
It is. But whose time interval? Alice and Bob don't agree on the duration.

When answering the question, think whose clock is responsible for measuring ##\Delta t##.
Bob's, because ##\Delta t## is according to his clock.

So if I am not mistaken the number of pulses arriving to Alice are: ##(2/a\Delta t)\sqrt{L^2-1/a^2}##.
 
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  • #32
MathematicalPhysicist said:
Bob's, because ##\Delta t## is according to his clock.

So if I am not mistaken the number of pulses arriving to Alice are: ##(2/a\Delta t)\sqrt{L^2-1/a^2}##.
Exactly - the same number as emitted.
 
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