About Gravitational Redshift
This simulation shows a photon climbing out of the gravitational well of a massive body and losing energy, so its frequency drops and its wavelength stretches towards the red. It models the effect using the Schwarzschild metric: the received-to-emitted frequency ratio is √(1 − Rs/remit) divided by √(1 − Rs/rrecv), where Rs = 2GM/c² is the Schwarzschild radius.
You choose the central body (Earth, Sun, white dwarf, neutron star or a 10-solar-mass black hole), then set the emission radius, reception radius and emitted wavelength using the sliders. Live readouts show Rs, the redshift z, the fractional shift Δλ/λ, the frequency ratio and the clock rate. Gravitational redshift is real and measurable: GPS satellites correct for it, and it shifts spectral lines from white dwarfs and neutron stars.
Frequently Asked Questions
What is gravitational redshift?
Gravitational redshift is the loss of energy a photon suffers as it climbs away from a massive body. Because a photon's energy is proportional to its frequency, losing energy lowers its frequency and lengthens its wavelength, shifting the light towards the red end of the spectrum. It is a direct prediction of Einstein's general theory of relativity.
What equation does the simulation use?
It uses the Schwarzschild result frecv/femit = √(1 − Rs/remit) / √(1 − Rs/rrecv), with the Schwarzschild radius Rs = 2GM/c². The redshift parameter is z = femit/frecv − 1, and the received wavelength is just the emitted wavelength divided by that frequency ratio.
What do the controls actually do?
The Massive Body dropdown sets the mass M, which fixes the Schwarzschild radius. The emission and reception height sliders set remit and rrecv in units of Rs, and the wavelength slider sets the emitted colour from 380 to 750 nm. The stats panel and spectrum strip then update to show z, the shift and the received wavelength.
Why does the redshift diverge as the photon approaches the Schwarzschild radius?
As remit approaches Rs, the factor √(1 − Rs/remit) tends to zero, so the frequency ratio collapses and z grows without bound. Physically, light emitted exactly at the event horizon is infinitely redshifted and can never reach a distant observer, which is why the simulation caps the emission slider just above 1 Rs.
Is the simulation physically accurate?
The frequency ratio, redshift and clock rate are computed from the exact Schwarzschild formulae using the real values of G and c, so the numbers are quantitatively correct for a static, non-rotating, uncharged mass. The photon animation and the smooth colour change along its path are illustrative rather than literal, since the colour shift in reality is fixed by the endpoints, not by the position en route.
How is gravitational redshift related to time dilation?
They are two views of the same effect. A clock at radius r ticks at rate dτ/dt = √(1 − Rs/r) relative to a distant clock, so a deeper clock runs slow. Because a wave's frequency is a clock, light emitted by that slow clock arrives with a correspondingly lower frequency, which is exactly the redshift the simulation displays as the clock ratio.
What was the Pound-Rebka experiment?
In 1959 Robert Pound and Glen Rebka measured gravitational redshift in a 22.6 m tower at Harvard, using 14.4 keV gamma rays from iron-57 and the Mossbauer effect to detect a tiny shift of about z = gh/c² ≈ 2.46×10−¹⁵. Their result confirmed Einstein's prediction to within about 10 percent, later tightened to roughly 1 percent by Pound and Snider in 1965.
Does the Sun's light reach us redshifted?
Yes, slightly. Light leaving the Sun's surface climbs out of its gravitational well and arrives with a fractional shift of about 2×10−⁶, equivalent to a Doppler velocity of roughly 0.6 km/s. The effect is small but has been measured in solar spectral lines, and the Solar Escape preset in this simulation reproduces this regime.
What is the difference between redshift and blueshift here?
The sign depends on direction. A photon moving outwards, to a larger radius, loses energy and is redshifted; a photon falling inwards, to a smaller radius, gains energy and is blueshifted. This simulation focuses on the outward case with rrecv greater than remit, which always produces a redshift with z greater than zero.
Why are neutron stars and white dwarfs interesting for this effect?
They are compact, so their radius is only a few times their Schwarzschild radius, making the redshift large enough to see directly in their spectra. The Neutron Star preset places the surface at about 1.69 Rs, giving a redshift of tens of percent, whereas the same mass spread over a normal star would produce a negligible shift.
Why do GPS satellites have to correct for gravitational redshift?
Satellite clocks sit higher in Earth's gravitational well than ground clocks, so they tick faster by about 45 microseconds per day from this effect alone. Without correcting for that, plus the smaller special-relativistic slowing from orbital speed, positioning errors would accumulate at roughly 10 km per day, rendering the system useless.