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published on 17 October 2013 in space

The Theory of Relativity

The Theory of Relativity can be divided into Special and General Relativity. The former was introduced in 1905 in an article that combined the principle of Galilean relativity with Maxwell’s equations for electromagnetic waves. The Theory of General Relativity was published in a series of articles from 1915 onwards. Although the theory was not supported by empirical findings, it incorporated Newton’s law of universal gravitation and the Special Relativity Theory. This was the reason for which it was readily accepted. In 1919 it was proven empirically with three tests which went down in history as the classical tests of General Relativity.
Today the Theory of Relativity has been confirmed by a number of experiments and is essential to explain not only the macro world but also specific phenomena such as the mean lifetime of a muon.
Let’s proceed step by step and learn more about the three classical tests that confirmed the accuracy of the Theory of Relativity.

Deflection of light by the Sun
According to the Theory of General Relativity, light is bent when it passes close to a massive body. Before this the physicists Henry Cavendish in 1784 and Johann Georg von Soldner in 1801 had claimed that a massive object, or one that has mass, was capable of deviating light coming from the stars. Einstein was the first who measured the value of this deflection with precision.
In 1919 the English astrophysicist Arthur Eddington, during an expedition to the island of Principe off the west coast of Africa, found evidence in favour of General Relativity while observing a solar eclipse.

Image of the 1919 solar eclipse taken by Sir Arthur Eddington during the expedition that confirmed the deflection of light by the Sun predicted by Einstein's General Relativity Theory.  Source: Wikipedia

Image of the 1919 solar eclipse taken by Sir Arthur Eddington during the expedition that confirmed the deflection of light by the Sun predicted by Einstein’s General Relativity Theory.
Source: Wikipedia

The experiment had to be able to observe the deviation of the light from a star when passing close to a massive body such as the Sun. In fact, according to the Theory of Relativity, since the light from a visible star is deflected as it passes near the Sun, the star should appear slightly further away (apparent position) with respect to its true position.

The presence of a massive body, in this case the Sun, deflects the path of starlight by a certain angle. From the Earth the star appears in a different position (apparent) with respect to its true position. Source: www.castfvg.it

The presence of a massive body, in this case the Sun, deflects the path of starlight by a certain angle. From the Earth the star appears in a different position (apparent) with respect to its true position. Source: www.castfvg.it

Eddington took many photographs of the event, but due to unfavourable weather conditions, the results were not very accurate and were criticised for a long time. However, they represented the first empirical evidence of light deflection and gave enormous prestige to Einstein’s theory, making it well-known all over the world.
It is said that when Einstein was asked what his reaction would have been had Eddington’s experiment not confirmed his theory, he answered ironically: “Then I would feel sorry for the dear Lord. The theory is correct anyway.”
Subsequent tests have fully confirmed Einstein’s predictions and today light deflection has become an important tool in astrophysics. For example, the phenomenon of gravitational lenses (see the Special Report, The phenomenon of gravitational lenses)  can be explained solely with the deflection of light. In fact, the distorted images are produced when light coming from a distant celestial body is deflected by the gravitational field of a galaxy or a group of galaxies.

Precession of the perihelion of Mercury
According to Newtonian physics, in a two-body system consisting of a lone object orbiting a spherical mass, as in the case of Mercury’s orbit around the Sun, the shape of the orbit is an ellipse, with the Sun as one of the two focuses.  However, it is observed that due to various factors, the perihelion of the planets, the point closest to the Sun,  shifts.  One of the main reasons is the gravitational attraction of the other planets. In the case of Mercury, the phenomenon is substantially due to the attraction of the Earth, Venus and Jupiter, and it is even more curious. In fact, from the very first observations, the planet presented a decidedly anomalous precession, so that, in 1859 it was considered one of the problems in celestial mechanics.

The perihelion of Mercury, the point closest to the Sun, shifts 574” per century. 531” are mainly due to the gravitational perturbation of the Earth, Venus and Jupiter, while the remaining 43” can be explained with The Theory of General Relativity. Source: bo.astro.it

The perihelion of Mercury, the point closest to the Sun, shifts 574” per century. 531” are mainly due to the gravitational perturbation of the Earth, Venus and Jupiter, while the remaining 43” can be explained with The Theory of General Relativity. Source: bo.astro.it

Measurements of the perihelion precession of Mercury were carried out by observing the transits of Mercury across the face of the Sun. The result was that the value of the said precession differed from the amount calculated with Newtonian mechanics, by about 43” (arcseconds). However, the Theory of General Relativity was able to estimate the shifting of the perihelion exactly, and for this reason it was immediately accepted by the scientific community.

Gravitational redshift of light
Gravitational  redshift (i.e. when the wavelength moves towards the red end of the light spectrum), is the variation in the wavelength and therefore in the colour of the spectrum produced by radiant light in the presence of a gravitational field. When the light produced by a celestial body moves away from the gravitational field, it loses energy and therefore its frequency decreases. The more intense the gravitational field is, the redder its spectrum will be.

A ray of light (a photon)  loses energy as it shifts away from the gravitational field.  The result is a decrease in light frequency and consequently a shift toward the red end.   Source: www.introni.it

A ray of light (a photon) loses energy as it shifts away from the gravitational field. The result is a decrease in light frequency and consequently a shift toward the red end. Source: www.introni.it

The gravitational redshift was measured precisely only in 1959, with the Pound-Rebka experiment at Harvard University.  In the experiment the redshift of two sources of 57 Fe gamma rays, positioned respectively on top and at the base of the Jefferson Tower, was measured. The results confirmed what was predicted by the Theory of General Relativity.

A modern test: the strange case of the mean lifetime of a muon
Out of the many modern tests that support the Theory of Relativity, one of the most curious ones regards the mean life of a mu meson, known as a muon.
A muon is produced by the interaction of cosmic rays from space and particles of the atmosphere. These are fundamental, unstable particles with a mean life of approximately 1.5 microseconds (μs), after which they decay into an electron and a neutrino-antineutrino pair.
Muons travel at extremely high speeds that are very near to the speed of light (300,000 km/s). If we consider the mean lifetime of a muon and multiply it by its speed, we discover that before disintegrating, the particles travel approximately 450 metres in the atmosphere.
And this is the particular characteristic of the muon: if the Earth’s atmosphere is approximately 15 kilometres thick, then, how is it possible to measure the arrival of muons on the Earth? Shouldn’t they disintegrate in the atmosphere after having travelled 450 metres?
The explanation is very simple if we use the concept of time related to an observer of the Theory of Relativity,  according to which, if two observers are in relative motion i.e. they move in relation to the each other, and they measure an event, it will occur that what they measure is not the same. The phenomenon is always valid but  it is evident to observers that  they are moving at speeds that are close to the speed of light.
So let us consider the muons that cross the higher layers of the atmosphere. According to the Special Theory of Relativity  an event that occurs in a place, seen by an observer who is standing still in that place will have a certain duration, defined the proper time of the event. In the case of the muon, the proper time is the mean lifetime of the muon (1.5 μs).
For an observer on the Earth, the decay rate will dilate, i.e. it will become much bigger. Time dilation depends on the speed of the object. The greater the speed, the bigger the time dilation. In the case of the muon, time dilates 25 times. This means that for an observer on the Earth, the decay rate becomes 37.5 μs. Again, multiplying this time interval by the speed of the muon it can be observed that the muon has travelled approximately 11 km, a distance that is much greater than 450 metres. So  this explains the mystery of why about 40% of the muons reach the Earth.
Let us now observe what happens from the point of view of the muon, or better of an observer moving along with the muon. In its reference system, the muon lives 1.5 μs. how then does it reach the Earth in such a short amount of time?
The Special Theory of Relativity comes to our aid again. This time, however, let us consider the length contraction. A certain length L. measured in a reference system in which L is at rest, will contract if looked at from a system that is moving, respect to this one.
The result is that according to the muon, the thickness of the atmosphere (L=15 km) is diminished by a γ factor, or Lorentz factor. The atmosphere will therefore appear to be 600 metres thick.

Edited by Simona Romaniello
Astrophysicist, scientific divulger, for the Planetarium in Turin, she is in charge of training and development and display of museum exhibits.

 
 
 
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