Light is often described as something that travels at a constant speed, and in a vacuum, it always moves at the speed of light, regardless of the strength of gravity. Yet gravity can change the energy of light as it travels. When light moves away from a massive object, such as a planet, star, or black hole, its frequency decreases and its wavelength increases. This phenomenon is called gravitational redshift.
Gravitational redshift occurs because gravity affects the passage of time. Light traveling from a region of stronger gravity to a region of weaker gravity is measured at a lower frequency by an observer farther from the massive object. Since lower-frequency light has a longer wavelength, its color shifts toward the red end of the electromagnetic spectrum. The light has not slowed down, but its energy, as measured by the distant observer, is lower.
This effect is one of the important predictions of Albert Einstein’s general theory of relativity. It reveals that gravity influences not only the motion of matter but also the behavior of light and the relationship between time, space, and energy.
What gravitational redshift means
To understand gravitational redshift, it helps to start with the relationship between light’s frequency, wavelength, and energy.
Light travels in waves. Its frequency describes how many wave cycles pass a given point each second, while its wavelength is the distance between successive wave peaks. These two properties are connected by the speed of light:
c = fλ
Here, c represents the speed of light, f is frequency, and λ is wavelength.
Because the speed of light in a vacuum remains constant, a decrease in frequency corresponds to an increase in wavelength.
Light also carries energy. According to quantum physics, the energy of an individual light particle, called a photon, is:
E = hf
In this equation, E is photon energy, h is Planck’s constant, and f is frequency.
A photon with a higher frequency carries more energy than one with a lower frequency. Therefore, when light undergoes gravitational redshift, its frequency and photon energy decrease while its wavelength increases.
The term redshift comes from visible light. Red light has a longer wavelength than blue or violet light. However, gravitational redshift is not limited to visible light. It can affect radio waves, infrared radiation, ultraviolet light, X-rays, and other forms of electromagnetic radiation.
Why gravity changes the frequency of light
The key to understanding gravitational redshift is Einstein’s discovery that gravity affects time itself.
In Newtonian physics, gravity is generally treated as a force that attracts objects with mass. Einstein’s general theory of relativity provides a deeper explanation: mass and energy curve spacetime, and objects move through this curved spacetime.
Spacetime combines the three dimensions of space with the dimension of time. According to general relativity, the presence of a massive object changes the geometry of spacetime around it. One consequence is that clocks run at different rates depending on their position in a gravitational field.
A clock closer to a massive object ticks more slowly than an otherwise identical clock farther away, where gravity is weaker. This difference is known as gravitational time dilation.
The relationship between gravitational time dilation and gravitational redshift explains why light changes frequency as it travels through a gravitational field.
Imagine a source of light near the surface of a massive planet. The source emits successive wave peaks at regular intervals according to a clock located nearby. A distant observer receives those wave peaks and measures the time between their arrivals using a clock farther from the planet.
Because time passes at different rates at the two locations, the distant observer measures a longer interval between successive wave peaks than the local observer does.
Fewer wave cycles arrive each second, so the distant observer measures a lower frequency. The wavelength is correspondingly longer, producing a redshift.
The important point is that gravitational redshift is not simply a result of light being slowed by gravity. Light still travels at the same local speed in a vacuum. Instead, gravity changes how time is measured at different locations, which affects the frequency measured by observers in those locations.
Why light loses energy when climbing out of gravity
The phrase “light loses energy climbing out of gravity” is a useful way to describe gravitational redshift, but it requires some explanation.
In a familiar example, a ball thrown upward loses kinetic energy as it rises. Gravity slows the ball, converting its kinetic energy into gravitational potential energy. When the ball falls back down, that potential energy becomes kinetic energy again.
Light behaves differently because it always travels at the speed of light in a vacuum. It does not gradually slow down as it moves away from a massive object.
Instead, the energy of a photon, as measured by a stationary observer, depends on the gravitational environment in which the measurement takes place.
When a photon moves outward from a region of stronger gravity to one of weaker gravity, a distant observer measures it as having less energy. Its frequency is lower, and its wavelength is longer.
This is the gravitational redshift.
The change can be understood through energy conservation in a gravitational field. In a static gravitational environment, a photon has a conserved energy associated with the spacetime’s time symmetry. However, observers at different gravitational potentials measure that conserved energy differently because their clocks run at different rates.
This distinction is important. It is not quite accurate to imagine a photon continuously surrendering energy to gravity in the same way that a moving object transfers energy while climbing a hill. Rather, the measured photon energy changes with the gravitational conditions at the observer’s location.
For a photon traveling outward, its energy measured by an observer at the destination is lower than the energy measured by an observer at the point of emission.
If the photon travels back down into a stronger gravitational field, the reverse occurs: its measured frequency increases and its energy is higher.
How gravitational redshift works mathematically
General relativity provides a precise way to calculate gravitational redshift.
For a simple case involving a nonrotating, spherical object, such as an idealized planet or star, the gravitational time dilation experienced by a stationary clock outside the object can be expressed using:
dτ = dt√(1 − 2GM/rc²)
Here:
- dτ is the time measured by a clock at a particular distance from the object’s center.
- dt is the corresponding time coordinate measured relative to an observer very far away.
- G is the gravitational constant.
- M is the mass of the object.
- r is the distance from its center.
- c is the speed of light.
As the distance r decreases, the gravitational field becomes stronger, and the clock runs more slowly relative to a distant clock.
For light emitted at a distance rₑ and received at a greater distance rᵣ, the relationship between the emitted and received frequencies is:
fᵣ/fₑ = √[(1 − 2GM/rₑc²)/(1 − 2GM/rᵣc²)]
The subscripts e and r refer to emission and reception.
When the light travels outward, rᵣ is greater than rₑ. The received frequency is therefore lower than the emitted frequency.
This equation describes an idealized situation in which the source and receiver remain stationary relative to the massive object. More complicated situations, including rotating objects and moving observers, require additional considerations.
For weak gravitational fields, such as those near Earth’s surface, the fractional frequency shift can be approximated by:
Δf/f ≈ −ΔΦ/c²
Here, ΔΦ is the change in gravitational potential between the emission and reception locations. When light moves upward to a higher gravitational potential, ΔΦ is positive, and the frequency shift is negative.
The approximation shows that the effect becomes stronger when the difference in gravitational potential is greater. It also explains why gravitational redshift is usually very small near Earth but becomes much more significant near extremely compact objects.
Gravitational redshift near Earth
Earth’s gravitational field is relatively weak compared with that of a neutron star or black hole. Nevertheless, gravitational redshift occurs even here.
Light traveling upward from Earth’s surface to a higher altitude experiences a tiny gravitational redshift. Its frequency, measured by an observer at the higher altitude, is slightly lower than the frequency measured by an observer near the surface.
The effect is extremely small under everyday conditions, which is why people do not notice it.
However, modern scientific instruments can measure such small frequency differences. Extremely precise atomic clocks make it possible to detect gravitational time dilation across surprisingly modest differences in height.
For example, two highly accurate clocks placed at different elevations will gradually disagree because the clock at the higher elevation runs slightly faster than the clock closer to Earth’s center.
This is the same underlying effect responsible for gravitational redshift. The difference in clock rates determines the difference in the frequencies they measure.
The phenomenon has also been tested through experiments involving light traveling vertically in Earth’s gravitational field. These experiments demonstrate that the frequency of light changes in the way general relativity predicts.
Gravitational redshift near stars and black holes
Gravitational redshift becomes much more pronounced near extremely dense and massive objects.
A star has a gravitational field that affects light escaping from its surface. Light emitted near the surface must travel through the star’s gravitational environment before reaching a distant observer. The stronger the gravitational field at the emission point, the greater the redshift.
For ordinary stars, the effect is generally modest. For compact stellar remnants, such as neutron stars, it can be substantial.
Neutron stars form when the cores of certain massive stars collapse during supernova explosions. They pack enormous amounts of mass into a remarkably small volume, creating an extremely strong gravitational field near their surfaces.
Light escaping from a neutron star can therefore experience significant gravitational redshift. By studying the radiation emitted from these objects, astronomers can investigate their gravitational fields and gain information about their physical properties.
Black holes represent an even more extreme case.
A black hole has an event horizon, a boundary beyond which nothing, including light, can escape to distant space. As light emitted from outside the event horizon travels outward, it can undergo increasingly strong gravitational redshift as its point of emission approaches that boundary.
For a distant observer, light emitted very close to the event horizon can appear dramatically redshifted and weakened. In the idealized description of a stationary source approaching the horizon of a nonrotating black hole, the observed frequency approaches zero as the emission point approaches the horizon.
This does not mean that light emitted outside the event horizon is necessarily destroyed. It means that its energy, measured by a distant stationary observer, becomes increasingly small.
The event horizon itself is not a physical surface that light must climb across. It is a boundary in spacetime that separates regions from which signals can reach distant observers from regions where they cannot.
How gravitational redshift differs from ordinary Doppler redshift
Gravitational redshift is sometimes confused with Doppler redshift because both can make light appear redder.
However, the two effects have different causes.
Doppler redshift occurs because of relative motion between a light source and an observer. When a source moves away from an observer, the observer measures a lower frequency and a longer wavelength. When the source moves toward the observer, the measured frequency increases, producing a blueshift.
The familiar example is an ambulance siren. As the ambulance moves away, its sound appears lower in pitch. Light behaves similarly in terms of frequency, although electromagnetic waves do not require a medium through which to travel.
Gravitational redshift, by contrast, occurs because of differences in gravitational potential and the resulting differences in the passage of time. A source and observer can remain stationary relative to one another and still measure a gravitational frequency shift.
In astronomy, both effects can occur simultaneously. A star might emit light that is gravitationally redshifted because of its strong surface gravity, while its motion relative to Earth produces an additional Doppler shift.
Astronomers must account for these effects when interpreting the light they receive from distant objects.
How scientists detect gravitational redshift
Gravitational redshift can be detected by comparing the frequency or wavelength of light measured at different gravitational potentials.
One important method involves examining the spectral lines produced by atoms.
Atoms absorb and emit light at particular frequencies determined by their internal energy levels. These frequencies provide recognizable patterns, much like fingerprints. When light from an astronomical object is analyzed, scientists can identify these patterns and compare them with measurements made under controlled laboratory conditions.
If the light has traveled out of a sufficiently strong gravitational field, its spectral lines may appear shifted toward longer wavelengths.
This allows researchers to investigate the gravitational effects near stars and other massive objects.
Another method uses extremely precise atomic clocks. Because the frequencies associated with atomic transitions are affected by gravitational time dilation, clocks at different elevations can measure the difference in gravitational potential.
The famous Pound–Rebka experiment, conducted in the late 1950s at Harvard University, provided an important direct test of gravitational redshift. Researchers measured the frequency shift of gamma rays traveling vertically in Earth’s gravitational field over a height of approximately 22.5 meters.
The experiment confirmed that light experiences the gravitational frequency shift predicted by general relativity.
Modern clock technology has made it possible to detect even smaller gravitational differences, strengthening the connection between gravitational redshift and time dilation.
Why gravitational redshift matters for GPS and modern technology
Gravitational redshift is more than an interesting feature of theoretical physics. Its underlying principle has practical consequences for technologies that rely on precise timekeeping.
The Global Positioning System, or GPS, uses satellites carrying highly accurate atomic clocks. These satellites orbit Earth at altitudes where gravity is weaker than at the planet’s surface.
As a result, their clocks run faster than comparable clocks on the ground because of gravitational time dilation.
There is also a competing effect: the satellites move rapidly relative to observers on Earth’s surface. According to special relativity, this motion makes their clocks run more slowly.
The two effects act in opposite directions. For GPS satellites, the gravitational effect is larger than the motion-related effect, so their clocks gain time relative to clocks on the ground.
The system must account for these relativistic differences to maintain accurate positioning. Without the necessary corrections, timing errors would accumulate and navigation accuracy would deteriorate significantly.
Although GPS is not simply a gravitational redshift detector, its operation demonstrates why understanding how gravity affects time is essential in modern technology.
The same physical principle connects the frequency of light to the rates of clocks in different gravitational environments.
Does gravitational redshift violate conservation of energy?
At first, gravitational redshift can seem to create a puzzle.
If a photon loses energy while traveling away from a massive object, where does that energy go? Does it transfer the energy to the gravitational field? If so, how can energy be conserved?
The answer requires distinguishing between local energy measurements and global energy conservation.
In ordinary situations involving a static gravitational field, there is a well-defined conserved energy associated with the time symmetry of the spacetime. However, the energy measured locally by an observer depends on that observer’s gravitational position.
A photon measured near a massive object has a higher locally measured energy than the same photon measured farther away. These measurements differ because the observers’ clocks run at different rates.
This does not mean that energy conservation has failed.
In general relativity, energy conservation is expressed through precise mathematical relationships involving spacetime geometry. In some situations, particularly in expanding or dynamic universes, there may not be a single globally conserved energy that applies to the entire system.
That is why the question of where a redshifted photon’s energy goes cannot always be answered by imagining a simple transfer of energy to a gravitational reservoir.
For gravitational redshift around a static massive object, the conserved quantity associated with the spacetime’s time symmetry provides the consistent description. The locally measured photon energy changes, even though the conserved energy remains constant.
What gravitational redshift reveals about the universe
Gravitational redshift demonstrates that light is affected by gravity even though photons have no rest mass.
This is one of the major differences between Newtonian gravity and general relativity. In Newtonian physics, gravity is traditionally described as a force acting on objects with mass. General relativity instead describes gravity as the curvature of spacetime, which influences the paths of light as well as matter.
Gravitational redshift also shows that time is not universal. Two observers in different gravitational environments can experience different rates of time, and those differences can be measured through the frequencies of light they exchange.
The phenomenon connects several important ideas in modern physics: the relationship between energy and frequency, the geometry of spacetime, gravitational time dilation, and the behavior of electromagnetic radiation.
Most importantly, it provides a measurable way to test Einstein’s theory of general relativity.
When light climbs out of a gravitational field, it does not slow down or lose energy through friction. Instead, the changing gravitational environment alters how its frequency and energy are measured. Its wavelength becomes longer, and a distant observer sees it as redshifted.
That subtle change in light carries a profound message: gravity does not merely shape the paths objects follow through space. It also changes the rate at which time passes, and light provides one of the clearest ways to observe that effect.