The Star Garden
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By 1907, Einstein had already predicted that gravity would create an effect similar to the Doppler effect, which causes light to be redshifted if it is moving away from an observer and blueshifted if it is moving towards them (Einstein, 1907). From the point of view of a stationary observer, light appears to be redshifted as it moves away from a strong gravitational force and blueshifted if it moves towards one. This change corresponds to the fact that time appears to run slower for observers in a stronger gravitational field.
Gravitational time dilation was first observed in 1971 when American physicists Joseph Hafele and Richard Keating flew four atomic clocks twice around the world on a commercial plane and then compared their time to clocks on Earth. All satellite navigation systems, including Global Positioning Systems (GPS), have to take the effects of gravitational time dilation into account in order to be accurate.
Using equations developed by German mathematician Bernhard Riemann in the 1850s (Ferraro, pp.234), Einstein showed that mass would curve Minkowski's flat spacetime. A model of the universe can be specified by two mathematical objects; the manifold, which represents unstructured spacetime and the metric field tensor, which represents the geometry. The manifold consists of the set of all possible events in the universe and is mathematically modelled by abstract spacetime points. The metric field was introduced to define all observable properties including the spatial and temporal intervals between events and the distribution of energy and matter. The spacetime structure of the metric is, partly shaped by what it contains.
Einstein suggested that general relativity does away with Newton's idea that space and time exist independently of matter and energy as a type of substance. This is because the metric interacts with matter and energy and the manifold does not exist independently of the metric. The manifold represents a choice of coordinate systems yet any system will give the same solution to relativistic equations and so there is no way to know which is 'correct'. This means that space and time would not exist if there was no matter or energy in universe. Einstein concluded that general relativity "takes away from space and time the last remnant of physical objectivity" (Einstein, 1916, pp.117).
Newton argued that absolute space can be derived from the fact that acceleration is absolute, we can always determine if we are accelerating. If we were to tie a rope between two rocks in space and then rotate the system, the rope will become taut, in an otherwise empty universe this does not make sense as it cannot be said to be rotating with respect to anything. There is still debate as to whether general relativity can resolve this problem without invoking the notion of absolute space and so some continue to argue that spacetime must be absolute.
Proponents of absolute spacetime must face the hole argument. This shows that if you accept that coordinate systems do represent true representations of the manifold, then there is no reason why there could not be a 'hole', where spacetime suddenly follows another coordinate system. There is no way to determine when a hole will appear and so proponents of absolute spacetime must argue that general relativity possess the same objective uncertainty as quantum mechanics. If we remove the idea that spacetime is absolute then we do not face this problem.
General relativity implies that planets do not appear to travel in perfect ellipses, as German astronomer Johannes Kepler had suggested, because the ellipse itself is rotating. This effect is most noticeable in Mercury as it is the closest planet to the Sun.
General relativity makes a number of other unique predictions; because gravity curves space, light will travel in a curved path as it approaches a massive object. This means that we are sometimes able to see objects which would otherwise be obscured from our view. Einstein calculated that the gravitational force of the Sun would cause starlight to deflect by up to 1.75 arc seconds (0.0005 degrees). The first observation of the deflection of light was confirmed by English physicist Arthur Stanley Eddington after the 1919 Solar eclipse. Because light is deflected by mass, it is possible for the same image to be projected more than once as its image is deflected in different directions. This effect is known as gravitational lensing, it was first considered by Swiss astrophysicist Fritz Zwicky in 1937 and was observed by Dennis Walsh, Robert Carswell, and Ray Weymann at the Kitt Peak National Observatory in America in 1979.
Eddington's depiction of the 1919 eclipse
Gravitational waves are a consequence of general relativity because a massive moving object creates a 'wave' as the curvature of spacetime changes at the speed of light. Black holes are another consequence, these occur when an object becomes so massive that even light, which has no rest mass, cannot escape. It is now known that supermassive black holes reside in the centre of most galaxies, these are millions of times the mass of the Sun.
If mass curves space then it will also curve time, and in 1949, Austrian mathematician Kurt Godel suggested that time travel is possible because 'closed timelike curves' can occur. These are regions where time is curved so that an observer would find themselves in an earlier time (Godel, pp.447-450). Time travel would violate our notion of causality and so there is still much debate on whether it is possible.
Gravitational lensing
In order to apply his theories to the universe as a whole, Einstein applied the cosmological principle, this assumes that the universe is homogeneous and isotropic when averaged over very large scales. Homogeneity assumes that our observations are representational of the whole universe and isotropy means that the universe is the same in whichever direction we look. These ideas were formulised by English astrophysicist Edward Milne in 1933 and verified by the WMAP satellite, launched in 2001.
For Einstein, the most startling consequence of general relativity was that it shows the shape of the universe depends upon its energy density. If mass is not sufficiently distributed then everything will fall in on itself and the universe will end in a 'big crunch'. Einstein devised the cosmological constant in order to counterbalance this force and create a static universe. In 1922, Russian mathematician Alexander Friedmann showed that it is also possible that the universe is expanding (Tropp et al., pp.169). This could occur if it begun at an extremely high density and temperature, if this was the case, and if mass is distributed too sparsely, then matter will continue to move apart forever.
References
Einstein, A., 1907, 'On the relativity principle and the conclusions drawn from it', Jahrbuch der Radioaktivitaet und Elektronik, Vol.4, pp.411, from 'The collected papers of Albert Einstein, Vol.2: The Swiss years', 1989, Beck, A., (trans.), Princeton University Press, Princeton
Einstein, A., 1916, 'The Foundation of the General Theory of Relativity', Annalen der Physik, Vol.49, from 'The principle of relativity: a collection of original memoirs on the special and general theory of relativity', Dover Publications, Mineola, pp.109-164
Ferraro, R., 2007, 'Einstein's space-time: an introduction to special and general relativity', Springer, New York
Godel, K., 1949, 'An Example of a New Type of Cosmological Solutions of Einstein's Field Equations of Gravitation', Reviews of Modern Physics, Vol.21
Tropp, E.A., Frenkel, Y.Va. and Artur Davidovich Chernin, A.D., 1993, 'Alexander A. Friedmann: the man who made the universe expand', Cambridge University Press, Cambridge
Einstein's theory of General Relativity (1916)
German-American physicist Albert Einstein devised his theory of general relativity after realising that the force felt in a uniform gravitational field is equivalent to the force felt during acceleration. Gravity can be equated with acceleration because the effects of a gravitational field can be produced by accelerating. In a closed room, a person cannot tell if objects are falling because they are experiencing the gravitational force of the Earth or because they are in deep space, accelerating at the same rate. This allowed Einstein to consider the affect of acceleration on spacetime and apply his findings to gravitation.