An astronaut in a sealed, windowless laboratory measures that all objects accelerate toward the floor at 9.8 m/s². Which of the following can the astronaut conclude from local experiments alone?
AThe laboratory is on the surface of Earth
BThe laboratory is accelerating upward at 9.8 m/s² in deep space
CEither scenario is possible — local experiments cannot distinguish between them
DThe laboratory must be in a gravitational field because tidal forces would reveal acceleration
The equivalence principle states that a uniform gravitational field and uniform acceleration are locally indistinguishable. In a sufficiently small lab (where tidal effects are negligible), no experiment can determine which scenario applies. Option D is incorrect for a sufficiently small laboratory — tidal forces are a second-order effect that vanishes in the local limit.
Question 2 True / False
The equivalence principle implies that light must bend in a gravitational field.
TTrue
FFalse
Answer: True
If an accelerating elevator is equivalent to a gravitational field, then a light beam crossing the elevator must curve downward in the elevator frame (since the elevator accelerates upward while the light travels in a straight line in the inertial frame). By the equivalence principle, the same bending must occur in a gravitational field. This was one of Einstein's earliest predictions from the equivalence principle, confirmed during the 1919 solar eclipse.
Question 3 Short Answer
Explain why the equivalence principle implies that clocks at different heights in a gravitational field tick at different rates.
Think about your answer, then reveal below.
Model answer: Consider two clocks at different heights in a uniform gravitational field. By the equivalence principle, this is equivalent to two clocks at different positions in a uniformly accelerating rocket. The rear clock (lower, closer to the engine) experiences a greater accumulated velocity relative to a momentarily co-moving inertial frame than the front clock (higher) by the time light signals arrive. By the relativistic Doppler effect, signals from the lower clock appear redshifted to the upper clock. Since this frequency shift is persistent and observer-independent in the equivalence-principle framework, lower clocks must genuinely tick slower — this is gravitational time dilation.
The equivalence principle converts a gravitational problem into an acceleration problem where special-relativistic effects (Doppler shift, time dilation) can be applied directly. The result — gravitational time dilation — was confirmed by the Pound-Rebka experiment in 1959 and is essential for GPS accuracy.
Question 4 Short Answer
The strong equivalence principle extends the weak equivalence principle by asserting what additional claim?
Think about your answer, then reveal below.
Model answer: The weak equivalence principle states only that gravitational and inertial mass are equal, so all test bodies fall identically in a gravitational field. The strong equivalence principle extends this to all laws of physics: in a freely falling reference frame over a sufficiently small region, the outcome of any local non-gravitational experiment is independent of the frame's velocity and position in the gravitational field. This includes self-gravitating bodies and local gravitational experiments — the laws of special relativity hold in the local freely falling frame.
The distinction matters because the strong form constrains not just how test particles move but how all physics — electrodynamics, thermodynamics, nuclear physics — behaves in a gravitational field. It is what forces gravity to be described by spacetime geometry rather than by a force on a flat background.