Few scientific theories are as important in today’s society as Einstein’s theory of relativity. Until Einstein, space was regarded as an axiom, a given, but his theory offered an alternative which has turned out to be much more accurate. It also discovered the relationship between space, time, matter and energy. The theory consists of two theories, the one of special relativity introduced in 1905 and the one of general relativity introduced in 1915. Today, scientists continue to test and investigate the theory over 100 years later. This paper aims to discuss Einstein’s theory of relativity and present some recent scientific papers that have been published and illustrate how it is continually evolving.
Understanding Special and General Relativity
Special relativity has two principles which are easy to state. The first principle is that the laws of physics are the same for all observers moving at a constant speed with respect to each other. The second principle says that the speed of light in a vacuum is the same for any observer and doesn’t depend on the motion of the light source or the observer. The two postulates are very simple, but have bizarre consequences. Time stretches, for instance, when an object is moving at a high velocity, near the speed of light, with respect to an observer. The length of a moving object is contracted, according to an observer. The most famous consequence is that E = mc² so that a small amount of mass is equivalent to a huge amount of energy. The effects are negligible, as Newton’s laws of motion are accurate enough for most purposes, at speeds characteristic of everyday life.
γ = 1 / √(1 − v²/c²)Δt = γ · Δt₀L = L₀ / γ
- Lorentz factor, γ
- 1.667
- When the moving clock shows 1 hour
- the stationary clock shows 1 h 40 min
- After 24 hours on the stationary clock
- the moving clock is 9 h 36 min behind
- A 1 m rod moving along its length
- measures 0.600 m (40 cm shorter)
At 0.800 times the speed of light, one hour on the moving clock lasts 1 h 40 min for a stationary observer.
Or pick a speed that comes with a source:
NASA gives the station’s speed as about 28,000 km/h, which is 7.78 km/s. NASA, Spot the Station FAQ
Ashby gives the speed of GPS satellite SV43 on 22 July 2000 as 3.874 km/s. Ashby (2003)
Bailey and colleagues kept muons circling at γ = 29.33. At rest a muon lasts about 2.2 μs; the circling muons lasted about 64.4 μs. Bailey et al. (1977)
This explorer shows the effect of speed alone. Gravity changes a clock’s rate too, which is general relativity; the chart that follows puts the two together for a GPS satellite.
Calculated by Writers Per Hour from the Lorentz factor, as given in OpenStax, University Physics Volume 3, section 5.3 and section 5.4, with the speed of light fixed at 299,792.458 km/s (NIST). The essay does not cite these figures.
Show the figures for the reference speeds and round fractions of the speed of light
| Speed | km/s | v/c | γ | One hour on the moving clock lasts | Moving clock behind after one day |
|---|---|---|---|---|---|
| International Space Station | 7.778 | 2.59 × 10⁻⁵ | 1 + 3.37 × 10⁻¹⁰ | 1 h + 1.21 μs | 29.1 μs |
| GPS satellite | 3.874 | 1.29 × 10⁻⁵ | 1 + 8.35 × 10⁻¹¹ | 1 h + 301 ns | 7.21 μs |
| Muon in the CERN storage ring | 299,618 | 0.99942 | 29.33 | 29 h 20 min | 23 h 11 min |
| 0.1 c | 29,979 | 0.100 | 1.005 | 1 h + 18.1 s | 7 min 13 s |
| 0.5 c | 149,896 | 0.500 | 1.155 | 1 h 9 min | 3 h 13 min |
| 0.8 c | 239,834 | 0.800 | 1.667 | 1 h 40 min | 9 h 36 min |
| 0.9 c | 269,813 | 0.900 | 2.294 | 2 h 18 min | 13 h 32 min |
| 0.99 c | 296,795 | 0.990 | 7.089 | 7 h 5 min | 20 h 37 min |
Special relativity is also a geometrical theory, and there is a way to write laws of physics which work in space-time. For instance, Ganesan (2024) is working on a special relativity theory that is based on a “dual” Minkowski metric from which the Lorentz transformation factors that represent time dilation and length contraction are derived. The article itself is a complicated piece of work, but it was written, so physics continues to be the search for new physical laws using Einstein’s theory of relativity. Special relativity is only valid for observers moving at constant speed with respect to one another and it does not take gravity into account. It took Einstein approximately ten years to develop the theory of gravity and he published the general theory of relativity in 1915. This theory also makes the assumption of space-time but also asserts that gravity is a result of matter and energy that bends space-time and that objects in motion react to this bending. The easiest way to explain this is to imagine a bowling ball on a rubber membrane: the ball forms a dent in the membrane, and other balls roll towards the dent, rather than away.
General relativity makes predictions for the bending of light near massive objects, for clocks running slower in the presence of gravity, for the possibility of black holes, and for the generation of gravitational waves by accelerating masses. Gravitational waves are a phenomenon that is predicted by general relativity, but not by Newton’s law of universal gravitation. Krishnendu and Ohme (2021) write that in Newtonian gravity “the orbital period is constant over time,” while in general relativity “the binary orbit shrinks due to the emission of energy” through gravitational waves. The first indirect evidence of gravitational waves was the observation of a binary pulsar PSR B1913+16 that was found to be losing energy in its orbit at the rate expected by general relativity, and for which Hulse and Taylor were awarded the 1993 Nobel Prize (Krishnendu & Ohme, 2021). On September 14, 2015, the gravitational waves from the merger of two black holes were detected for the first time by the LIGO scientists, and the number of observations of gravitational waves from black hole mergers has since grown to over fifty (Krishnendu & Ohme, 2021).
The study of gravitational waves is not the only way to test general relativity. The status of general relativity “cannot be thought of as isolated from the rest of fundamental physics,” write Giulini and Jetzer (2022). So, the authors discuss the testing of general relativity in the highest gravity fields, such as those of stars orbiting Sgr A*, radio pulsars, lunar laser ranging, and gravitational waves. They continue that “solar system and near-Earth gravity research is by no means closed,” and that relativistic geodesy and inertial sensing “can, conversely, be used for high-precision tests of [general relativity].” In addition to being a problem of distant celestial mechanics, space-time is also a problem of everyday life: Relativistic effects had to be considered when designing satellite positioning systems.
- Runs slower
- Runs faster
- Net change
Microseconds (μs) gained or lost in one day
- Orbital speed (special relativity): −7.2 Microseconds (μs) gained or lost in one day. At about 3.9 km/s the satellite’s clock runs slow, as the explorer above shows.
- Weaker gravity at its height (general relativity): +45.8 Microseconds (μs) gained or lost in one day. Far from the Earth gravity is weaker, and a clock in weaker gravity runs fast.
- Net change: +38.6 Microseconds (μs) gained or lost in one day. The satellite clock gains about 38.6 μs a day.
GPS measures distance by signal travel time, so a clock error of 38.6 μs is a distance error of about 11.6 km (38.6 μs times the speed of light) after a day. The satellite clocks are therefore tuned before launch to run slow by 4.4647 parts in ten billion (10.22999999543 MHz instead of 10.23 MHz); in orbit they then keep the right time for an observer on the ground.
Chart by Writers Per Hour from Ashby (2003), Eq. (35) and (36) (Living Reviews in Relativity, CC BY 4.0): the satellite clock’s net rate offset is 4.4647 × 10⁻¹⁰, which is 6.9693 × 10⁻¹⁰ (gravity at the ground clock) less 2.5046 × 10⁻¹⁰ (the orbit: a third from speed, two thirds from gravity at its height), times 86,400 seconds in a day, rounded to 0.1 μs. The essay does not cite these figures.
Show the figures as a table
| Effect | μs per day |
|---|---|
| Orbital speed (special relativity) | −7.2 |
| Weaker gravity at its height (general relativity) | +45.8 |
| Net change | +38.6 |
Conclusion
Einstein’s theory of relativity has revolutionized mankind’s knowledge of the universe. Special relativity gave a new interpretation of time and space being relative to the observer and that mass and energy are equivalent, while general relativity gave a new interpretation of the nature of gravity as a property of space-time. More than a century after Einstein made his predictions, his theory is being put to the test in more extreme environments, such as binary pulsars and black hole collisions, and new mathematical formulations are being discovered for the theory. This essay illustrates the fact that relativity is a living and developing theory, and an understanding of it is an understanding of Einstein’s genius and the development of physics in this century.
