Overview
This lecture discusses the challenges and conventions around measuring the speed of light, especially the difference between the one-way and two-way (roundtrip) speed, and examines why only the roundtrip speed is experimentally measurable.
Measuring Speed: General Concepts
- Speed is typically measured by dividing distance by travel time between two points.
- Measuring the speed of light the same way as other objects (with two clocks) is problematic due to synchronization issues.
Problems with Measuring One-Way Speed of Light
- Synchronizing two distant clocks requires sending a signal that itself travels at (unknown) speed of light.
- Moving clocks cause relativistic time dilation, making synchronization impossible without assumptions.
- All practical methods end up measuring the roundtrip (two-way) speed, not the one-way speed.
Historical Context & Experiments
- Fizeau’s 1849 experiment measured the roundtrip speed of light using a gear, a distant mirror, and roundtrip timing.
- Experimental results provide the two-way speed of light, which matches the defined value ‘c’.
Einstein Synchronization Convention
- Einstein defined that the speed of light is the same in all directions by convention, not by empirical evidence.
- This convention is necessary for defining simultaneity at different locations.
Implications of Direction-Dependent Light Speed
- Theoretically, speed could differ in each direction (e.g., c/2 one way, instantaneous the other) without observable consequences.
- Clocks synchronized using Einstein’s convention can be out of sync if the one-way speed differs.
- Physical laws remain unchanged as long as the roundtrip speed equals ‘c’.
Failed Ideas for One-Way Measurement
- High-speed cameras, fiber optic cables, and GPS-based synchronization all rely on assumptions about light’s speed.
- Any method requiring clock synchronization presupposes the very value it seeks to measure.
Philosophical and Physical Consequences
- The inability to measure one-way light speed raises questions about simultaneity and the nature of time.
- Most physicists accept the convention for practicality, though it's not an empirical fact.
Key Terms & Definitions
- Speed of Light (c) — Defined as 299,792,458 meters per second, the distance light travels in a vacuum in 1/299,792,458 seconds.
- Roundtrip (Two-Way) Speed of Light — The average speed measured for light traveling to a point and back.
- One-Way Speed of Light — The (theoretical) speed of light in a single direction; not directly measurable.
- Einstein Synchronization Convention — The assumption that light’s speed is the same in all directions, used to synchronize clocks.
- Simultaneity — The concept of events occurring at the same time in different locations, which depends on the chosen convention.
Action Items / Next Steps
- Review concepts of relativity, especially time dilation and simultaneity.
- Consider thought experiments about measurement conventions and their implications for physics.