8.1 Einstein's equivalence principle

Einstein's equivalence principle is a cornerstone of general relativity. It states that the effects of gravity are indistinguishable from those of acceleration, linking inertial and gravitational mass. This idea revolutionized our understanding of gravity.

The principle has far-reaching consequences. It predicts phenomena like gravitational time dilation and redshift, which have been experimentally confirmed. These effects show how gravity influences the fabric of spacetime itself.

Equivalence Principles

Weak and Strong Equivalence Principles

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• Weak equivalence principle states that the trajectory of a freely falling test body depends only on its initial position and velocity, not on its composition or structure
  • Implies all objects fall at the same rate in a gravitational field regardless of their mass or composition (feathers and bowling balls)
  • Supported by Galileo's famous Leaning Tower of Pisa experiment
• Strong equivalence principle extends the weak equivalence principle to include all the laws of physics, not just mechanics
  • States that in a freely falling reference frame, the laws of physics are the same as in an inertial frame in the absence of gravity
  • Implies that gravitational mass and inertial mass are equivalent

Reference Frames and Equivalence

• Local inertial frame is a reference frame that is freely falling under the influence of gravity
  • In a local inertial frame, an observer experiences weightlessness and the laws of physics are the same as in an inertial frame without gravity
• Freely falling reference frame is equivalent to an inertial frame without gravity according to the equivalence principle
  • An observer inside a freely falling elevator would not be able to distinguish between being in the elevator or being in deep space far from any gravitational sources
• Uniformly accelerated reference frame is equivalent to a uniform gravitational field according to the equivalence principle
  • An observer in a uniformly accelerated elevator would experience the same effects as an observer stationary in a uniform gravitational field (standing on Earth's surface)

Gravitational Effects on Light

Gravitational Redshift and Time Dilation

• Gravitational redshift is the shift of light towards longer wavelengths (redder colors) when it moves out of a gravitational potential well
  • Light loses energy as it climbs out of a gravitational field, resulting in a decrease in frequency and increase in wavelength
  • Observed in the Pound-Rebka experiment using the Mössbauer effect to measure the redshift of gamma rays moving upwards in Earth's gravitational field
• Gravitational time dilation is the effect where time passes more slowly in the presence of a strong gravitational field compared to a weaker field
  • Clocks at different heights in a gravitational field will tick at different rates, with clocks closer to the source of gravity ticking more slowly
  • Demonstrated by the Hafele-Keating experiment using atomic clocks on airplanes traveling around the world

Thought Experiments

Einstein's Elevator Thought Experiment

• Einstein used the thought experiment of an observer inside an elevator to illustrate the equivalence principle
• An observer in a stationary elevator on Earth's surface experiences a downward force equal to their weight due to gravity
  • If the elevator cable is cut, the observer will experience weightlessness as they freely fall with the elevator
  • The freely falling elevator is equivalent to an inertial frame without gravity
• An observer in an elevator accelerating upwards in empty space will experience a downward force indistinguishable from gravity
  • The uniformly accelerated elevator is equivalent to a uniform gravitational field
• The thought experiment demonstrates that an observer cannot distinguish between the effects of gravity and acceleration based on local observations alone