Translations

Code	Language		Translator	Run

Credits

Fu-Kwun Hwang - Dept. of Physics,National Taiwan normal Univ.; Loo Kang Wee

1. Overview:

This resource is a JavaScript HTML5 applet simulation designed to illustrate the concepts of length contraction and the Lorentz transformation within the context of special relativity. The classic "bus in garage" thought experiment is used as a visual aid. The simulation allows users to manipulate parameters and observe the effects on the perceived length of the bus and garage from different frames of reference.

2. Main Themes and Important Ideas:

• Length Contraction (Lorentz Contraction): The primary focus is on demonstrating how the length of an object moving at relativistic speeds appears shorter in the direction of motion to an observer in a different inertial frame. This is a direct consequence of Einstein's theory of special relativity.
• Relativity of Simultaneity: While not explicitly stated, the simulation implicitly touches upon the concept of the relativity of simultaneity. The "bus fits in the garage" paradox arises because the events of the front of the bus entering and the back of the bus entering are not simultaneous in all reference frames.
• Interactive Learning: The resource is designed to be interactive, allowing users to explore the concepts by adjusting parameters and observing the results. This hands-on approach can enhance understanding compared to passive learning methods.
• Visualization of Abstract Concepts: Special relativity can be challenging to grasp due to its counter-intuitive nature. The simulation provides a visual representation of length contraction, making the concept more accessible.

3. Key Features and Functionality (Based on the Description):

• Garage/Bus Ratio Slider: Allows users to change the relative sizes of the garage and the bus, setting up different scenarios for the thought experiment.
• V Slider (Velocity Slider): Controls the relative speed between the bus and the garage, a crucial parameter in determining the extent of length contraction. Higher speeds will result in more noticeable contraction.
• Car Moving Frame Check Box: This is a very important feature. Checking this box changes the frame of reference, allowing the user to see the scenario from the bus's perspective (where the garage is moving towards the bus). This directly addresses the paradox.
• Visual Representation: The applet visually displays the bus and garage, dynamically adjusting their lengths according to the chosen parameters and frame of reference.
• HTML5 and JavaScript: The use of HTML5 and JavaScript ensures that the simulation can run in modern web browsers without the need for plugins like Flash.

4. Intended Audience and Learning Goals:

• Teachers: The resource includes "Sample Learning Goals For Teachers," indicating that it is intended to be used in educational settings.
• Students: The interactive nature and visual aids make it suitable for students learning about special relativity, likely at the high school or undergraduate level.
• Learning Goals: The primary learning goal is to understand and visualize length contraction and the Lorentz transformation. A secondary goal is likely to promote conceptual understanding of special relativity, going beyond rote memorization of formulas.

5. Quotes from the Source:

• "(Adjusts the size of the garage to the bus.)" - Description of the Garage/Bus Ratio Slider
• "(Adjusts the speed and size of the bus/garage)" - Description of the V Slider
• "(Checking the box will cause the garage to appear moving towards the bus)" - Description of the Car Moving Frame Check Box

6. Related Resources:

The resource provides a link to another educational website about special relativity: http://propg.ufabc.edu.br/mnpef-sites/relatividade-restrita/relatividade-restrita/ This suggests that the "Bus in Garage" simulation is intended to be part of a broader learning experience. The numerous other links on the page also hint at an ecosystem of physics simulations available on the OER/OSP site.

7. Conclusion:

The "Bus in Garage Relativity Length Lorentz Transformation JavaScript Simulation Applet HTML 5" appears to be a valuable educational tool for teaching and learning about special relativity. Its interactive nature, visual representations, and focus on the "bus in garage" thought experiment make it a potentially engaging and effective way to grasp the concepts of length contraction and the relativity of simultaneity. The simulation's accessibility via HTML5 enhances its usability in various learning environments.

 

Relativity and Length Contraction: A Study Guide

I. Study Guide Outline

1. Introduction to Special Relativity: Briefly review the postulates of special relativity.
2. Length Contraction: Focus on the concept of length contraction and its relationship to relative motion.
3. Lorentz Transformation: Understand how to use the Lorentz transformation to relate measurements in different inertial frames of reference.
4. The "Bus in Garage" Thought Experiment: Understand the paradox in this thought experiment.
5. Using the Simulation: Instructions on how to use the simulation to explore length contraction and the relativity of simultaneity.
6. Applications and Implications: Think about the broader implications of length contraction in relativistic scenarios.

II. Quiz (Short Answer)

1. What are the two postulates of Einstein's special relativity?
2. Define length contraction. In what direction does the contraction occur?
3. What is an inertial frame of reference? Give an example.
4. Explain how the relative speed between two objects affects the observed length contraction.
5. According to the reference material, what two parameters can be changed in the simulation?
6. In the "bus in garage" thought experiment, what is the key question that leads to the paradox?
7. How does the simulation allow you to visualize length contraction?
8. What is the role of the Lorentz transformation in understanding length contraction?
9. How does the simulation address the relativity of simultaneity?
10. Give an example of a real-world application (theoretical) where length contraction might be significant.

III. Quiz Answer Key

1. The laws of physics are the same for all observers in uniform motion (inertial frames). The speed of light in a vacuum is the same for all observers, regardless of the motion of the light source.
2. Length contraction is the phenomenon where the length of an object moving relative to an observer is measured to be shorter along the direction of motion than its proper length (the length in its rest frame). The contraction occurs along the direction of motion.
3. An inertial frame of reference is a frame in which an object not subject to forces is observed to move at constant velocity (either at rest or in a straight line). A car moving at a constant speed on a straight road can be considered an inertial frame.
4. As the relative speed between the object and the observer increases, the observed length contraction becomes more significant. The closer the relative speed approaches the speed of light, the more pronounced the contraction.
5. The Garage/Bus Ratio and the V Slider.
6. The key question is whether the bus is entirely inside the garage at the same time according to different observers.
7. The simulation visualizes length contraction by displaying how the length of the bus appears to change as its speed increases relative to the garage.
8. The Lorentz transformation provides the mathematical framework for calculating how length measurements change between different inertial frames of reference, thus quantifying length contraction.
9. The simulation shows how events that are simultaneous in one frame of reference may not be simultaneous in another, depending on their relative motion.
10. High-energy particle physics experiments, such as those conducted at CERN, where particles are accelerated to speeds close to the speed of light.

IV. Essay Questions

1. Explain the concept of length contraction and how it arises from the postulates of special relativity. Discuss the implications of length contraction for our understanding of space and time.
2. Describe the "bus in garage" thought experiment. How does the concept of the relativity of simultaneity resolve the apparent paradox?
3. Using the provided simulation as a guide, explain how changing the speed of the "bus" affects the observed length of the bus and the garage from different frames of reference.
4. Discuss the relationship between length contraction and the Lorentz transformation. How does the Lorentz transformation provide a mathematical description of length contraction?
5. Critically evaluate the claim that length contraction is a "real" phenomenon. Is it simply a consequence of measurement, or does it reflect a fundamental property of spacetime?

V. Glossary of Key Terms

• Special Relativity: A theory developed by Albert Einstein that describes the relationship between space and time. It's based on two postulates: the laws of physics are the same for all observers in uniform motion, and the speed of light in a vacuum is the same for all observers, regardless of the motion of the light source.
• Length Contraction: The phenomenon in which the length of an object moving at relativistic speeds appears to be shorter in the direction of motion to an observer who is stationary relative to the object.
• Lorentz Transformation: A set of equations that describe how space and time coordinates transform between different inertial frames of reference, taking into account the effects of special relativity.
• Inertial Frame of Reference: A frame of reference in which an object that is not subject to any external forces moves with constant velocity (i.e., either remains at rest or moves in a straight line at a constant speed).
• Relativity of Simultaneity: The concept that simultaneity is not absolute but depends on the observer's frame of reference. Two events that are simultaneous in one frame may not be simultaneous in another frame that is moving relative to the first.
• Proper Length: The length of an object as measured in its rest frame (the frame in which the object is stationary). This is the maximum length of the object that can be measured.
• Applet: A small application, often written in Java or JavaScript, that can be run within a web browser. The "Bus in Garage" simulation is an example of an applet.

Sample Learning Goals

 

For Teachers

 

Relativity Length Lorentz Transformation JavaScript Simulation Applet HTML 5

Instructions on how to use the applet

Garage/Bus Ratio Slider

 

V Slider

 

Car Moving Frame Check Box

Simulation Mechanism

Research

 

Video

 

 Version:

Other Resources

1.  http://propg.ufabc.edu.br/mnpef-sites/relatividade-restrita/relatividade-restrita/

Frequently Asked Questions

What is the "Bus in Garage" simulation about?

The "Bus in Garage" simulation is a JavaScript HTML5 applet that visually demonstrates the concept of length contraction in special relativity. It explores how the observed length of a moving object (the bus) changes depending on its speed relative to a stationary observer (the garage).

How does the "Garage/Bus Ratio" slider work?

The "Garage/Bus Ratio" slider allows users to adjust the relative sizes of the garage and the bus within the simulation. This helps visualize different scenarios where the garage may appear larger or smaller than the bus, especially when relativistic effects are considered.

What does the "V Slider" control?

The "V Slider" controls the velocity of the bus. As the velocity increases, the simulation demonstrates length contraction, causing the bus to appear shorter in the direction of motion. This allows users to observe how length changes with increasing speed according to special relativity.

What does checking the "Car Moving Frame" checkbox do?

Checking the "Car Moving Frame" checkbox changes the frame of reference in the simulation. Instead of the bus moving towards a stationary garage, the garage appears to move towards the bus. This helps illustrate that motion and length contraction are relative, depending on the observer's frame of reference.

What is the Lorentz transformation in the context of this simulation?

The Lorentz transformation is a mathematical relationship that describes how space and time coordinates change between different inertial frames of reference. In the simulation, the Lorentz transformation is implicitly used to calculate the observed length of the bus as its velocity changes. The simulation provides a visual representation of these transformations.

What are some other resources related to special relativity?

The resource links to other materials on special relativity, such as content hosted at propg.ufabc.edu.br, providing users with additional learning materials beyond the simulation itself.

What is Easy JavaScript Simulations (EJS) and how is it related to this simulation?

Easy JavaScript Simulations (EJS) is a tool used to create interactive physics simulations. The "Bus in Garage" simulation is built using EJS, making it accessible in web browsers through HTML5. EJS allows educators and developers to create and share interactive learning resources in physics and other fields.

What license governs the use of this simulation and related resources?

The contents are licensed under the Creative Commons Attribution-Share Alike 4.0 Singapore License. Commercial use of the EasyJavaScriptSimulations Library is governed by a separate license, requiring users to read the linked license information and contact fem@um.es directly.