# Einstein, Friedmann & Relativity

## Albert Einstein (1879 - 1955)

Albert Einstein is probably the most recongnisable and famous scientist in the world today even though he died six decades ago. 2005 was celebrated as the World Year of Physics to commemorate the centenary of the papers he wrote in 1905 on three key topics in Physics:

**The photoelectric effect and the photon**. Einstein applied the concept of the discrete package of energy, the quantum, discovered by the German physicist**Max Planck**to explain the*photoelectric effect*. Attempts to explain this effect, in which ultraviolet or blue light knocked electrons off a metal plate when even high levels of red light could not, using classical physics had all failed.

By considering light to behave as discrete particles called*photons*rather than as a wave Einstein was able to successfully account for the observations. Light therefore was quantised, with the energy of a photon being proportional to its frequency. It was for his work on this topic and not relativity that Einstein was awarded the Nobel Prize in Physics in 1921.**Brownian motion and the size of atoms**. In 1827 the Scottish botanist**Robert Brown**observed and described the random motion of tiny grains of pollen under a microscope. This motion was subsequently termed*Brownian motion*defied attempts by scientists to satisfactorily explain it until 1905. Einstein accounted for this motion by stating that minute atoms move randomly in a liquid and collide with the pollen grains. He proposed a means to measure both the size and average speed of the atoms. This work was instrumental in convincing scientific sceptics of the reality of atoms.**The special theory of relativity**. Einstein's work on special relativity changed the way we view time and mass. The term 'special' in his theory refers to the fact that Einstein limited his discussion to the special case of non-accelerated objects, that is objects moving in a straight line at constant speed. The key concept in special relativity is that the speed of light,*c*, is the same for any observer in an*inertial*(ie unaccelerated) frame of reference. Two observers, one moving much faster then the other, both measure the speed of light to be the same. from this premise we get some interesting phenomena.

Rather than being fixed, the mass of an object is dependent on its speed. As an object approaches the speed of light, its mass increases. This*relativistic*mass increase has been measured to high precision in many situations. Einstein also realised that a direct realtionship existed between energy and mass, indeed that the two were interchangeable. This gave rise to his famous equation:

`E`=`mc`(^{2}**2.1**)

where`E`is energy,`m`is the mass of an object and`c`is the speed of light in a vacuum.The importance of this relationship is that a small amount of mass can be converted into a large amount of energy. The realisation of this ultimately led other scientists to the discovery of nuclear

*fission*(the splitting of the atom) and the development of atomic weapons in the Second World War. It also provided an explanation for the source of energy in stars such as our Sun. Nuclear*fusion*, in which light nuclei such as hydrogen fuse together produce a new, heavier nucleus in which the mass is slightly less than the sum of the original nuclei. A small amount of mass is converted into high energy gamma ray photons.

Special relativity also introduces the concepots of*time dilation*and*length contraction*. These can be used to explain the detection at the Earth's surface of muons from cosmic ray showers even though they should decay before they have time to reach it.

## General Relativity

By 1916 Einstein had extended his earlier work on relativity to encompass more general situations including gravity and accelerated motion. This became known as the general theory of relativity and is a theory of gravity, the key long-range force in the Universe. He derived it from a key postulate, the *principle of equivalence* between inertial and gravitational forces. An object with mass not only possesses inertia but actually warps or curves space around it. It affects spacetime. The concept of four-dimensional *spacetime* had been applied to relativity by **Minkowki** in 1908. Motion and forces act along straight lines but where space is curved due to the presence of matter, the path followed by an object or light thus also appears curved.

The predicted curvature of light around a massive object was dramatically verified by the British astrophysicist, **Sir Arthur Eddington** in 1919. Observations made by his teams in Brazil and West Africa measured the apparent shift in light from a star close to the Sun during a solar eclipse, fitting Einstein's predictions. This successful confirmation was largely responsible for the rapid acceptance of Einstein's work and his global fame.

Einstein showed that Newton's theory of gravity was really a subset of more general conditions covered by general relativity. General relativity can account for the observed precession of the perihelion of Mercury about the Sun and the observed difference in hydrogen maser clocks in satellites orbiting Earth compared with those on the ground.

General Relativity has been tested to incredible precision. The recent discovery of a double pulsar system J0737-3039 using the Parkes radio telescope in which two pulsars orbit each other provides an outstanding natural laboratory for testing general relativity in extreme conditions. Numerous examples of gravitational lensing have now been observed by astronomers. Gravity Probe B, launched in 2004, uses gyroscopes in a polar-orbiting satellite space to test the concept of frame-dragging. This was a previously untested aspect of general relativity.

General relativity is not just on interest to astrophysicists and gravitational wave physicists. The modern GPS satellite system can only function due to the application of general relativistic corrections to the orbits of each of the over twenty satellites in the system. The growing commercial, military and safety applications of such navigation systems show the relevance of general relativity in the modern world.

## Aleksandr Friedmann (1888 - 1925)

Friedmann was a Russian mathematician and meteorologist who lived a short but eventful life. During the revolution of 1917 whilst besieged by White Russian forces in Petrograd (now St. Petersburg) he heard about Einstein's work on general relativity. He started to derive solutions, publishing his findings in 1922. His key insight was to realise that there was no unique solution to Einstein's equations, rather there was a whole family of solutions possible. This family of solutions thus allowed for different cosmological models of the Universe.

In Friedmann's models the only force that is considered is gravitation. His model universes are *homogeneous* (the same everywhere on a large enough scale) and *isotropic* (look the same in every direction). Most importantly they incorporate the concept of *expansion* and in some cases, contraction. Einstein himself had viewed the Universe as static. Friedmann thus provided the theoretical framework for an expanding Universe within the spaceteime and mathematics of general relativity. Unfortunatley he contracted typhoid and and died in 1925 during the Russian civil war before his work became widely known.

Friedmann's work was independently verified in 1927 when the Belgian astrophysicist and priest **Georges Lemaître** derived the same solutions, unaware of Friedmann's earlier work. Lemaître also realised that the newly discovered galaxies could be used to show the expansion of the Universe.

The observational evidence for this was forthcoming through the work of Edwin Hubble.

Lemaître went on to apply thermodynamics and quantum theory to consider the entropy or state of order of the Universe. He realised that if the disorder increased over time then the converse should also apply if one went back in time. This led him in 1927 to propose the concept that the Universe began as a *primeval atom.* His theory suggested that all of the mass-energy (10^{51} kg) of the universe was concentrated in a single super-atom about one astronomical unit across. The primeval atom would then fragment and the universe expand. Lemaître's concept was a precursor of the big bang model.