A photon is emitted from the surface of a neutron star and observed by a distant astronomer. Compared to the same atomic transition measured in the astronomer's laboratory, the neutron-star photon appears:
ABlueshifted, because the strong gravitational field accelerates the photon
BRedshifted, because the photon loses energy climbing out of the deep gravitational potential
CUnchanged, because photons are massless and unaffected by gravity
DRedshifted or blueshifted depending on the photon's direction of emission
A photon climbing out of a gravitational well is redshifted — its frequency decreases. For a neutron star with r_s/R ≈ 0.4, the redshift factor (1 - r_s/R)^{1/2} ≈ 0.77, meaning the observed frequency is about 77% of the emitted frequency — a substantial 23% redshift. The photon does not 'lose energy' in the Newtonian sense (there is no well-defined local gravitational potential energy for photons in GR), but the relationship between the emitter's proper time and the observer's proper time produces the frequency shift.
Question 2 True / False
Gravitational time dilation and gravitational redshift are two descriptions of the same physical phenomenon.
TTrue
FFalse
Answer: True
A clock at lower gravitational potential ticks slower relative to a clock at higher potential — this is gravitational time dilation. A photon emitted by the lower clock (which oscillates at the lower clock's rate) arrives at the upper clock with fewer oscillations per unit of the upper clock's time — this is gravitational redshift. They are the same effect described from different perspectives: one in terms of clock rates, the other in terms of photon frequencies. The fractional frequency shift equals the fractional difference in clock rates.
Question 3 Short Answer
In the Pound-Rebka experiment, gamma rays were sent vertically through a height difference of 22.6 meters in Earth's gravitational field. Calculate the expected fractional frequency shift and explain why this experiment was feasible despite the tiny effect.
Think about your answer, then reveal below.
Model answer: The fractional frequency shift is Δν/ν = gΔh/c² = (9.8)(22.6)/(3×10⁸)² ≈ 2.46 × 10⁻¹⁵. This extraordinarily small shift was measurable because Pound and Rebka used the Mossbauer effect — nuclear gamma-ray resonance with ⁵⁷Fe, which has a natural linewidth narrow enough (Δν/ν ~ 10⁻¹³) to resolve the gravitational shift. By moving the source at a controlled velocity (Doppler compensation), they could scan across the resonance line and measure the gravitational frequency shift to about 10% accuracy, later improved to about 1% by Pound and Snider.
The Pound-Rebka experiment was the first direct measurement of gravitational redshift in a laboratory setting. The key enabling technology was the Mossbauer effect, discovered in 1958, which provided the spectral precision needed to detect a shift of parts in 10¹⁵.
Question 4 Short Answer
GPS satellites orbit at about 20,200 km altitude and carry atomic clocks. In what direction does gravitational time dilation shift the satellite clocks relative to ground clocks, and by approximately how much per day?
Think about your answer, then reveal below.
Model answer: Satellite clocks at higher gravitational potential tick faster than ground clocks. The gravitational time dilation effect causes the satellite clocks to gain about 45 microseconds per day relative to ground clocks. (There is a competing special-relativistic time dilation of about -7 microseconds/day due to the satellites' orbital speed, giving a net gain of about 38 microseconds/day.) Without correction, this would cause position errors accumulating at about 10 km per day, rendering GPS useless for navigation.
GPS is one of the most tangible everyday consequences of general relativity. The 38 μs/day net correction is pre-programmed into the satellite clocks by adjusting their frequency before launch. The fact that both special-relativistic and general-relativistic corrections are needed, and that they act in opposite directions, makes GPS a beautiful demonstration of both theories.