Light travels at a constant speed, regardless of how fast you're moving. This mind-bending fact shook up our understanding of physics. It led to Einstein's special relativity theory, which changed how we think about space and time.

Experiments like Michelson-Morley's tried to measure light speed differences but found none. This discovery threw out old ideas about light traveling through a special substance called aether. Instead, it showed light speed is always the same for everyone.

Speed of Light Experiments

Measuring the Speed of Light

• Speed of light (c) represents the universal speed limit at which all massless particles and waves travel through a vacuum
  • Measured to be approximately 299,792,458 meters per second or 186,282 miles per second
  • Remains constant regardless of the motion of the light source or observer
• Michelson-Morley experiment aimed to detect the motion of the Earth relative to the hypothetical luminiferous aether
  • Used an interferometer to compare the speed of light in perpendicular directions
  • Expected to observe a difference in light speed due to Earth's motion through the aether
  • Results showed no significant difference in the speed of light, contradicting the existence of the aether

Luminiferous Aether and Invariance of c

• Luminiferous aether was a hypothetical medium thought to be necessary for the propagation of light waves
  • Believed to permeate all space and provide a reference frame for light propagation
  • Expected to cause variations in the speed of light relative to Earth's motion through the aether
• Invariance of c refers to the constant speed of light in all inertial reference frames
  • Michelson-Morley experiment provided strong evidence for the invariance of c
  • Contradicted the concept of the luminiferous aether and classical notions of absolute space and time
  • Laid the groundwork for Einstein's special theory of relativity

Theoretical Foundations

Einstein's Second Postulate

• Einstein's second postulate states that the speed of light in a vacuum is the same for all observers, regardless of their motion relative to the light source
  • Extends the principle of relativity to include the invariance of c
  • Implies that the laws of physics, including the speed of light, are the same in all inertial reference frames
  • Challenges classical notions of absolute space and time, leading to counterintuitive consequences such as time dilation and length contraction

Maxwell's Equations and the Speed of Light

• Maxwell's equations describe the behavior of electric and magnetic fields and their interactions
  • Consist of four fundamental equations: Gauss's law for electric fields, Gauss's law for magnetic fields, Faraday's law of induction, and Ampère's circuital law with Maxwell's correction
  • Predict the existence of electromagnetic waves that propagate at the speed of light
• Maxwell's equations provide a theoretical foundation for the invariance of c
  • Speed of light emerges naturally from the equations as a constant determined by the permittivity and permeability of free space
  • Suggest that the speed of light is a fundamental property of the universe, independent of the motion of the source or observer

Thought Experiments

Light Clock and Time Dilation

• Light clock is a hypothetical device used to illustrate the concept of time dilation in special relativity
  • Consists of two mirrors facing each other with a light pulse bouncing between them
  • Each bounce constitutes a tick of the clock, with the time between ticks determined by the distance between the mirrors and the speed of light
• Time dilation occurs when a light clock is observed from a moving reference frame
  • From the perspective of a stationary observer, the light pulse in the moving clock must travel a longer path due to the clock's motion
  • Since the speed of light is invariant, the moving clock appears to tick more slowly compared to a stationary clock
  • Demonstrates that time is relative and depends on the relative motion between the observer and the clock

Relativity of Simultaneity

• Light clock thought experiment also illustrates the relativity of simultaneity
  • Two events that are simultaneous in one reference frame may not be simultaneous in another frame moving relative to the first
  • Consider two light clocks at opposite ends of a moving platform, synchronized in the platform's frame
  • From the perspective of a stationary observer, the light pulses in the moving clocks will not arrive at the mirrors simultaneously due to the platform's motion
  • Events that are simultaneous in the moving frame (light pulses hitting the mirrors) are not simultaneous in the stationary frame