Einstein's special relativity revolutionized our understanding of space and time. His two postulates - the laws of physics are the same in all inertial frames, and light's speed is constant - led to mind-bending consequences like time dilation and length contraction.

These ideas challenged classical physics and paved the way for modern concepts. The constancy of light speed, supported by experiments like Michelson-Morley, has far-reaching implications. It sets a universal speed limit and requires us to rethink our notions of simultaneity and causality.

Einstein's Postulates and Special Relativity

Postulates of special relativity

• First postulate states the laws of physics are identical in all inertial reference frames (Galilean relativity)
  • No experiment can distinguish between different inertial frames, such as a stationary lab and a smoothly moving train
  • All inertial observers measure the same values for physical quantities like mass, charge, and force
• Second postulate asserts the speed of light in a vacuum is constant and independent of the motion of the source or observer
  • Light always travels at $c = 3 \times 10^8$ m/s in a vacuum, whether emitted by a stationary or moving source (flashlight)
  • Contradicts the classical notion of velocity addition, where light should appear faster or slower depending on the observer's motion
• Implications of the postulates revolutionize our understanding of space, time, and mass-energy
  • Simultaneity is relative events simultaneous in one reference frame may not be simultaneous in another (lightning strikes viewed from a moving train)
  • Time dilation moving clocks run slower than stationary clocks (muon decay, twin paradox)
  • Length contraction objects in motion appear shorter along the direction of motion (Lorentz contraction of a spacecraft)
  • Mass-energy equivalence mass and energy are interchangeable, as expressed by the equation $E = mc^2$ (nuclear reactions, particle collisions)

Inertial frames of reference

• An inertial frame of reference is a coordinate system in which Newton's first law of motion holds true
  • In an inertial frame, an object at rest remains at rest, and an object in motion remains in motion with a constant velocity, unless acted upon by an external force (a ball rolling on a frictionless surface)
• Non-inertial frames are accelerating or rotating reference frames
  • In non-inertial frames, fictitious forces appear to act on objects (centrifugal force in a rotating space station, Coriolis force on Earth)
• Special relativity is formulated in the context of inertial reference frames
  • Einstein's postulates apply only to inertial frames (a smoothly moving train, a spacecraft in deep space)
  • The laws of physics are the same in all inertial frames, but they may differ in non-inertial frames (a rotating platform, an accelerating elevator)
• Lorentz transformations describe how space and time coordinates change between inertial frames

Constancy of light speed

• The constancy of the speed of light is a fundamental postulate of special relativity
• Experimental evidence supports this postulate
  • The Michelson-Morley experiment demonstrated that the speed of light is independent of the Earth's motion through space
  • Subsequent experiments have confirmed this result with increasing precision (modern Michelson-Morley experiments, Kennedy-Thorndike experiment)
• The constancy of the speed of light has several consequences
  • Requires a revision of the classical concepts of space and time (absolute space and time vs. spacetime)
  • Leads to the relativity of simultaneity, time dilation, and length contraction (as observed in particle accelerators and GPS satellites)
  • Sets an upper limit on the speed at which information and matter can travel (causality, light cones)
• The speed of light is a universal constant, denoted by $c$, with a value of approximately $3 \times 10^8$ m/s in a vacuum
  • This value is independent of the motion of the source or observer (Doppler effect does not apply to light in vacuum)
  • It is the same in all directions and in all inertial reference frames (isotropic and homogeneous universe)
• The invariance of Maxwell's equations in all inertial frames supports the constancy of light speed

Spacetime and Relativity

• Minkowski spacetime combines space and time into a four-dimensional continuum
• General relativity extends special relativity to include non-inertial frames and gravity
• The principle of invariance states that the laws of physics should have the same form in all coordinate systems