Basic Relativity Question (Time Dilation)

Click For Summary
SUMMARY

The discussion revolves around a basic relativity question concerning time dilation and distance perception when traveling to Proxima Centauri at 0.24c. According to the equations provided, the time experienced by the spaceship's pilot differs from that measured by a stationary observer on Earth due to time dilation effects. The pilot measures a shorter travel time and perceives the distance to Proxima Centauri as less than 4.2 light years due to Lorentz contraction. The key equations used are d = v/t and t' = t/sqrt(1-(v/c)^2).

PREREQUISITES
  • Understanding of special relativity concepts
  • Familiarity with Lorentz transformations
  • Basic knowledge of speed as a fraction of the speed of light (c)
  • Ability to manipulate algebraic equations
NEXT STEPS
  • Study the implications of Lorentz contraction in special relativity
  • Learn about time dilation effects in different frames of reference
  • Explore advanced applications of the equations d = v/t and t' = t/sqrt(1-(v/c)^2)
  • Investigate real-world examples of relativistic travel scenarios
USEFUL FOR

Students of physics, educators teaching special relativity, and anyone interested in understanding the effects of high-speed travel on time and distance perception.

CSGuy123
Messages
9
Reaction score
0

Homework Statement



Proxima Centauri, the star nearest our own, is some 4.2 ly away. (a) If a spaceship could travel at a speed of 0.24c, how long would it take to reach the star according to the spaceship's pilot? (b) What would someone in the frame that moves along with the spaceship measure as the distance to Proxima Centauri?


Homework Equations



d = v/t
t' = t/sqrt(1-(v/c)^2)


The Attempt at a Solution



I know this question is probably very basic, but I'm having a hard time trying to see reason in the way that the question is asked. If the pilot is moving in the frame of reference of the spaceship, would not the time taken to reach the star just be (v/d)? Wouldn't time only be dilated for a stationary observer?

As for part (b), would not a person moving along with the spaceship's frame of reference perceive the same time? Wouldn't this imply that the perceived distance is still 4.2 ly?
 
Physics news on Phys.org
I know this question is probably very basic, but I'm having a hard time trying to see reason in the way that the question is asked. If the pilot is moving in the frame of reference of the spaceship, would not the time taken to reach the star just be (v/d)? Wouldn't time only be dilated for a stationary observer?
v/d, where d is calculated in the system of the spaceship. This is not 4.2 light years.

As for part (b), would not a person moving along with the spaceship's frame of reference perceive the same time?
The same time as the spaceship, but not the same time as we on earth.
 
That cleared things right up! Thanks!
 

Similar threads

Length Contraction & Time Dilation
  • · Replies 5 ·
Replies
5
Views
2K
Proper Time and Time Dilatation
  • · Replies 1 ·
Replies
1
Views
1K
Length contraction and Time dilation for LIGHT?
  • · Replies 8 ·
Replies
8
Views
2K
Time Dilation and Length Contraction Problem
  • · Replies 1 ·
Replies
1
Views
3K
Special Relativity: Time dilation
  • · Replies 5 ·
Replies
5
Views
2K
Time dilation and length contraction for a rocket
  • · Replies 12 ·
Replies
12
Views
3K
How do proper time and time dilation differ?
  • · Replies 21 ·
Replies
21
Views
6K
Intro special relativity problem regarding time dilation
  • · Replies 4 ·
Replies
4
Views
2K
Question on special relativity from "Basic Relativity"
  • · Replies 67 ·
3
Replies
67
Views
5K
(Introductory SR) Light sent from a spaceship received by Earth
  • · Replies 6 ·
Replies
6
Views
2K