Twin Paradox: How Do We Calculate Ages and Coordinates in Different Frames?

Click For Summary
SUMMARY

The discussion centers on the Twin Paradox, specifically calculating ages and coordinates in different inertial frames for Anna, Bob, and Carl, who are traveling at 0.9c. The key events are defined as follows: Event A is Anna passing Earth, Event B is Anna passing Planet Z, and Event C is Carl passing Earth. The equations used include Lorentz transformations: x' = gamma(x - vt) and t' = gamma(-v/c² * x + t), which are essential for determining the coordinates and ages in each frame. The participants express confusion regarding the application of these transformations to derive the necessary values.

PREREQUISITES
  • Understanding of special relativity concepts, particularly time dilation and length contraction.
  • Familiarity with Lorentz transformations and their applications in different inertial frames.
  • Basic knowledge of spacetime diagrams and how to interpret them.
  • Ability to perform calculations involving gamma (γ) factor in relativistic contexts.
NEXT STEPS
  • Study the derivation and application of Lorentz transformations in special relativity.
  • Learn how to construct and interpret spacetime diagrams for relativistic scenarios.
  • Explore the implications of time dilation and simultaneity in different inertial frames.
  • Investigate the concept of proper time and its calculation in various frames of reference.
USEFUL FOR

Students of physics, particularly those studying special relativity, educators teaching these concepts, and anyone interested in understanding the implications of relativistic travel on aging and coordinate systems.

Lucille
Messages
31
Reaction score
0

Homework Statement


Anna is born in a spaceship, Bob is born on Earth (at the same time t=t'=0) just as Anna's spaceship passes Earth at 0.9c (EVENT A)

Planet Z is 45 ly away at rest in Bob's frame. Anna flies past plant Z (event B)

Meanwhile, Carl was born at the same time (t=t'=t''=0) on a spaceship traveling 0.9c towards Earth and passes planet z at event b

event C is when he passes earth.

bobs frame: x,ct
anna's: x',ct'
carl's: x'',ct''

a) what are the coordinates of a,b,c in the rest frames of anna, bob, carl
b) how old is bob in his rest frame when carl passes earth?
c) what is the sum of anna's age when she passes planet Z with the amount carl ages in going from planet z to Earth as measured in x,ct
d)what is the sum of anna's age when she passes planet z as in her rest frame with the amount carl ages going from planet z to Earth in his rest frame?

Homework Equations


x'=gamma(x-vt)
t'=gamma (-v/c^2*x + t)

The Attempt at a Solution


a)

Anna's frame
A (0,0)
B <-- I'm not sure how to get to this using the 45 ly from bob's frame :/

This question as a whole confuses me, I'm not sure where to start.
 
Physics news on Phys.org
Here is my space time diagram

Phys.jpg
 

Similar threads

Time Dilation and Length Contraction Problem
  • · Replies 1 ·
Replies
1
Views
3K
(Introductory SR) Light sent from a spaceship received by Earth
  • · Replies 6 ·
Replies
6
Views
2K
Reference Frames with Different Origins
  • · Replies 4 ·
Replies
4
Views
1K
Special Relativity Spaceship Question
  • · Replies 3 ·
Replies
3
Views
3K
Undergrad Twin Paradox Resolution
  • · Replies 4 ·
Replies
4
Views
1K
How to Solve the Twin Paradox Problem Using Lorentz Transformations
  • · Replies 1 ·
Replies
1
Views
2K
Twin Paradox from Moving Reference Frame- Return Journey
  • · Replies 2 ·
Replies
2
Views
1K
Undergrad Twin Paradox: Aging Slower with Continuous Acceleration?
  • · Replies 13 ·
Replies
13
Views
3K
Undergrad Twin paradox for (accelerated) dummies?
  • · Replies 36 ·
2
Replies
36
Views
6K
Undergrad Twin Paradox with accelerated Motion
  • · Replies 15 ·
Replies
15
Views
3K