Theory of relativity -- Car and Garage Paradox

  • Thread starter Groovy2
  • Start date
In summary, the Car and Garage Paradox is a thought experiment that illustrates the implications of the theory of relativity, particularly concerning simultaneity and length contraction. It involves a scenario where a car that is longer than a garage attempts to enter it while moving at a relativistic speed. According to an observer outside the garage, the car contracts in length and can fit inside, while an observer inside the garage sees the car as too long to fit. This paradox highlights how different observers can have conflicting perceptions of the same event due to the effects of relativity, emphasizing the complexities of time and space in Einstein's theory.
  • #1
Groovy2
7
0
Homework Statement
Theory of relativity
Relevant Equations
Delta(t)=tA-tB
Hey everyone!

Im new here so im not really familiar with this forum. But nice to meet yal! Btw im not really sure if this problem fits in the "Advanced Phyics Homework Help". But heres my problem:

Assume that the car and the garage in the garage paradox have the same rest length L0
and that they move at a speed of 0.53c relative to each other. Call the event when the front of the car reaches the end of the garage A and the event when the end of the car reaches the beginning of the garage B. What is the time difference delta(t)=tA-tB
between these events in the garage rest system?

Tried to solve it a couple of times and gotten nowhere. I appreciate all the help!
 
Physics news on Phys.org
  • #2
Please show your work in your attempt
 
  • #3
phinds said:
Please show your work in your attempt
Alright so heres what i did:

stept 1: Lorentz abbreviation

L=L0*sqrt(1−(0.53)^2)=L0*(1−0.2809)=L0sqrt(0.7191)≈L0⋅0.847

Step 2:
Δt=L/v
Δt=L0*0.847/0.53c

Therefore
(0.847/0.53)*(Lo/c)= approx 1.598
 
  • #4
What happened to ##L_0##?

Is that supposed to be approximately ##1.6## seconds? It's considered very ungroovy to omit units after a numerical quantity.
 
  • #5
PeroK said:
What happened to ##L_0##?

Is that supposed to be approximately ##1.6## seconds? It's considered very ungroovy to omit units after a numerical quantity.
Sorry, forgot to mention. They want the answere to be in L0/c. So therefor my answere is 1.6*Lo/c
 
  • #6
More importantly, which event happens first: A or B?
 
  • #7
PeroK said:
More importantly, which event happens first: A or B?
According to the question? I assume A
 
  • #8
Groovy2 said:
According to the question? I assume A
Better to check that with a diagram. 1.6 doesn't look right.
 
  • #9
PeroK said:
Better to check that with a diagram. 1.6 doesn't look right.
I honestly dont know how to solve this more than this. The answere needs to be as a multiple of L0/c
 
  • #10
Groovy2 said:
I honestly dont know how to solve this more than this. The answere needs to be as a multiple of L0/c
In the rest frame of the garage, the car is shorter than the garage.
 
  • #11
PeroK said:
In the rest frame of the garage, the car is shorter than the garage.
Im very new to this whole theory of relativity, so what does that really mean?
 
  • #12
Groovy2 said:
Im very new to this whole theory of relativity, so what does that really mean?
Shorter simply means its length is less. I.e. it fits inside the garage.
 
  • #13
PeroK said:
Shorter simply means its length is less. I.e. it fits inside the garage.
Yeah i got that. Am I suppose to draw anything to see the big picture? Im just using formulas at the moment, so thats why i dont really understand what that means
 
  • #14
Groovy2 said:
Am I suppose to draw anything to see the big picture? Im just using formulas at the moment, so thats why i dont really understand what that means
Let O be an observer in the garage frame.

A couple of diagrams showing the car’s positions (as seen by O) at events A and B should help.

From the description, it sounds like O should see event B before event A. And that you are being asked to find the time for the car (of contracted length ##L’##) to travel a distance ##L_0 – L’##. This corresponds to the time the car is entirely inside the garage (as measured by O).
 
  • Like
Likes PeroK

FAQ: Theory of relativity -- Car and Garage Paradox

What is the Car and Garage Paradox?

The Car and Garage Paradox is a thought experiment that illustrates the effects of length contraction in special relativity. It involves a scenario where a car that is longer than a garage is moving at a significant fraction of the speed of light. When the car enters the garage, it appears to fit inside due to the relativistic effect of length contraction, which leads to a paradoxical situation regarding the simultaneity of events in different frames of reference.

How does length contraction affect the Car and Garage Paradox?

Length contraction states that an object moving relative to an observer will appear shorter in the direction of motion. In the case of the Car and Garage Paradox, from the perspective of a stationary observer, the moving car contracts in length as it approaches the garage, allowing it to fit inside. However, from the perspective of someone inside the garage, the car is longer than the garage, leading to confusion about whether the car can fit inside without colliding with the garage walls.

What role does simultaneity play in resolving the paradox?

Simultaneity in special relativity is relative, meaning that two events that appear simultaneous in one frame of reference may not be simultaneous in another. In the Car and Garage Paradox, observers in different frames will disagree on when the front and back of the car are inside the garage. This relativity of simultaneity helps resolve the paradox, as it shows that the events of the car entering and fitting in the garage can be perceived differently depending on the observer's frame of reference.

Can the Car and Garage Paradox be resolved logically?

Yes, the paradox can be resolved by understanding the principles of special relativity, particularly length contraction and the relativity of simultaneity. By analyzing the scenario from different frames of reference and recognizing that measurements of time and space can differ, the paradox can be logically explained without contradiction. Each observer's measurements are valid within their own frame, leading to a consistent understanding of the situation.

What are the implications of the Car and Garage Paradox in physics?

The Car and Garage Paradox highlights the counterintuitive nature of relativistic physics and emphasizes the importance of frame of reference in understanding motion and measurements. It serves as an educational tool to illustrate key concepts of special relativity, such as length contraction and the relativity of simultaneity, which have profound implications for our understanding of space, time, and the behavior of objects at high velocities.

Similar threads

Can a Limo Fit into a Smaller Garage with Special Relativity?
Replies
2
Views
3K
Special Relativity of Train Problem
Replies
8
Views
3K
Ladder Paradox: Understanding the Contradictory Length Contraction Phenomenon
Replies
24
Views
6K
Special Relativity Conceptual Question
Replies
4
Views
2K
Simple Special Relativity Problem of Length Contraction
Replies
1
Views
2K
Special Relativity - Relativity of Simultaneity?
Replies
4
Views
1K
Relativistic Shooting Paradox: Does A Hit B?
Replies
11
Views
1K
Help with Kinematics Problem (Two bodies in motion; one direction)
Replies
4
Views
4K
Modified Twin Paradox in Special Relativity
Replies
6
Views
2K
I Three inertial particles: Separating the twins from the paradox
2
Replies
40
Views
3K

Hot Threads

Recent Insights

Back
Top