A question about Alice and Bob in SR

  • Context: Undergrad 
  • Thread starter Thread starter MathematicalPhysicist
  • Start date Start date
  • Tags Tags
    Sr
Click For Summary
SUMMARY

The discussion centers on the relativistic scenario involving Alice and Bob, where Bob remains stationary in Minkowski space while Alice moves with constant proper acceleration. The key equations governing their interactions are Alice's trajectory, described by ##X(\tau)=\frac{1}{a}\cosh(a\tau)## and ##T(\tau)=\frac{1}{a}\sinh(a\tau)##. The participants clarify how to compute the times shown on their watches when they meet again and the number of pulses Alice receives from Bob. The correct answers are: Alice's watch shows ##\tau = \frac{1}{a}\sinh^{-1}(aL)##, Bob's watch shows ##2\sqrt{L^2 - \frac{1}{a^2}}##, and Alice receives a number of pulses equal to the time interval divided by ##\Delta t##.

PREREQUISITES
  • Understanding of Minkowski space and proper time.
  • Familiarity with hyperbolic functions, specifically ##\sinh## and ##\cosh##.
  • Knowledge of special relativity concepts, including time dilation and simultaneity.
  • Ability to solve equations involving hyperbolic functions and their inverses.
NEXT STEPS
  • Study the derivation of proper time in accelerated frames using the Rindler coordinates.
  • Learn about the implications of constant proper acceleration in special relativity.
  • Explore the relationship between coordinate time and proper time in different inertial frames.
  • Investigate the physical interpretations of negative time solutions in relativistic contexts.
USEFUL FOR

Physicists, students of relativity, and anyone interested in understanding the dynamics of accelerated frames in Minkowski space.

  • #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}##.
 
Physics news on Phys.org
  • #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.
 
  • Like
Likes   Reactions: MathematicalPhysicist

Similar threads

High School Metric Line Element Use: Do's & Don'ts for Accelerated Dummies?
  • · Replies 29 ·
Replies
29
Views
2K
High School Why Do Bob and Alice Disagree on Astronomical Measurements?
  • · Replies 25 ·
Replies
25
Views
1K
High School A well defined thought experiment
  • · Replies 55 ·
2
Replies
55
Views
4K
Undergrad The Lorentz factor gamma and proper time
  • · Replies 31 ·
2
Replies
31
Views
3K
Undergrad Twin Paradox with accelerated Motion
  • · Replies 15 ·
Replies
15
Views
3K
Undergrad Request for Input: 2D Minkowski Spacetime Diagram Generator
  • · Replies 6 ·
Replies
6
Views
3K
Undergrad Twin paradox for (accelerated) dummies?
  • · Replies 36 ·
2
Replies
36
Views
6K
Graduate Stumped by a Lagrangian in Einstein's 1916 paper
  • · Replies 3 ·
Replies
3
Views
467
High School Rookie question about proper time
  • · Replies 20 ·
Replies
20
Views
2K
Undergrad Confusion regarding acceleration in SR
  • · Replies 62 ·
3
Replies
62
Views
5K