Time Stops at the Speed of Light. What Does that Mean?

Step-by-Step Tutorial: Understanding Time Stops at the Speed of Light

Step 1: Introduction to Special and General Relativity

• Special and general relativity theories are based on the concept that time is a coordinate that must be combined with the three dimensions of space to form a four-dimensional SpaceTime.
• Both theories emphasize that the speed of light in a vacuum is constant.

Step 2: Understanding Different Notions of Time

• Special and general relativity introduce two notions of time: coordinate time and personal time.
• Coordinate time is a measurement on a diagram, while personal time is the time that passes for an observer.

Step 3: Visualizing Time with a Spacetime Diagram

• Use a Spacetime diagram with space on the horizontal axis and time on the vertical axis to visualize an observer's motion.
• An observer at rest is represented by a vertical line, while an observer in motion at a constant velocity is shown by a diagonal line.
• The angle of 45° on the diagram represents the speed of light.
• The path that an observer takes on the Spacetime diagram is called their world line.

Step 4: Proper Time vs. Coordinate Time

• Proper time is the physically meaningful time measured by the length of an observer's world line in the Spacetime diagram.
• Coordinate time is arbitrary and does not hold physical significance.

Step 5: Calculating Proper Time in Spacetime

• In Spacetime, the length of a path is calculated using the Lorenzian distance formula, which involves the square of the distance in space and time.
• The proper time for an observer between two instances of coordinate time is determined by calculating the length of their world line using the Lorenzian distance.

Step 6: Time Stops for Light at the Speed of Light

• As an object approaches the speed of light, the proper time measured for it gets shorter.
• When an object moves at the speed of light, the proper time measured is always zero, indicating that time stops for light.
• The concept of time stopping for light is philosophical and relates to the experience of light moving at the speed of light.

Step 7: Interpretation of the Mathematical Concepts

• Moving at the speed of light implies that everything along the path happens in the same instant.
• The duration of a trip across the universe at the speed of light would be perceived as instantaneous.
• Light, being made of photons, is the only known entity that can move at the speed of light.

Step 8: Further Exploration and Resources

• Consider exploring more topics in science, mathematics, and physics to deepen your understanding.
• Check out courses on platforms like Brilliant for interactive learning experiences in various scientific fields.
• Engage in discussions and share your thoughts on the concepts of time and light in the comments section of related videos or forums.

By following these steps, you can gain a better understanding of the concept of time stopping at the speed of light and its implications in the theories of relativity.