Einstein's theory of Special Relativity (1905)
In 1905, German-American physicist Albert Einstein combined the idea that experiments performed at a constant velocity will give the same results as experiments that are stationery, with the idea that the speed of light will remain constant from both perspectives (Einstein, 1905). The first assumption is a result of Galileo's relativity. In 1632, Galileo showed that there is no experiment which can distinguish if we are moving at a constant rate or if we are stationary. We do not feel the movement of the Earth, for example, because we are moving at the same rate. The second assumption comes from the Michelson-Morley experiment of 1887, this disproved the idea that absolute space is at rest relative to the aether.
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Albert Einstein
The Michelson-Morley experiment showed that the speed of light appears to be the same whether we are moving towards or away from it. In 1842, Austrian physicist, Christian Doppler had discovered the Doppler effect, this shows that a waves apparent frequency will change, depending on whether it is moving towards you or away from you. Doppler had tried to apply his principle to light waves, but it was French physicist, Armand Fizeau who, in 1848, suggested that light changes colour - and hence wavelength - not frequency as its velocity changes (Harrison, pp.76).
Light is unlike everything else because it does not obey Galileo's principle for adding velocities. We would expect that if we moved away from something, then its speed would appear to equal its original speed minus the speed with which we move away. If we move towards something, then we expect to measure a speed equal to our own plus the speed of the object. It is this principle which compels us to run towards the things we want and away from things we wish to avoid. Light is different to this, is appears to be travelling at the same speed from both perspectives.
Einstein realised that if these two ideas were combined then the speed of light must be measured to be the same by two observers who are moving relative to each other. In order to accommodate this, either of the two properties that velocity relies upon, time or space, must differ between observers.
The first consequence of special relativity is known as the relativity of simultaneity, this shows that events which appear simultaneous in one reference frame, may not do so in another. It removes all objectivity to the concept of 'now'. What we perceive as the present corresponds only to what is occurring simultaneously to us in our reference frame.
The second consequence of special relativity is length contraction. Einstein showed that an object will appear to be longer if we measure it whilst we are moving parallel to it than if we are stationary. The length which we measure when we are stationary with respect to an object is known as the 'proper' length.
The third consequence of special relativity is time dilation, the time that a clock takes between ticks appears to be longer when the clock is moving relative to our observations. Moving clocks appear to run slower than ones that are stationary relative to us. This can be illustrated by imagining that we bounce a beam of light from two mirrors and observe it from both perspectives, one which is moving with respect to it and one which is stationary. To the stationary observer, the light will travel vertically, up and down. To the moving observer, the mirrors will appear to be moving and so the light will have to travel further. The speed of light, like all speeds, is equal to the distance the light travels divided by the time it takes and so, in order for the speed to remain the same in both cases, time has to appear to pass more slowly for the moving observer, from the perspective of the stationary observer. This effect cannot be due to length contraction because the contraction is perpendicular to the direction of motion. As with length contraction, the time we measure between events that are stationary with respect us is known as 'proper' time.
The faster an object accelerates, the larger its relativistic mass becomes. An infinite amount of energy is required to accelerate an object to the speed of light because of the resistance created by this increase.
Some argue that special relativity implies that mass and energy are the same, English physicist Arthur Stanley Eddington stated that "it seems very probable that mass and energy are two ways of measuring what is essentially the same thing, in the same sense that the parallax and distance of a star are two ways of expressing the same property of location" (Eddington, 1929). This is because the speed of light is equal to one if the distance is measured in light years, and so e = m, although there has been considerable debate about the meaning of the energy-mass relationship.
In 1908, German mathematician Hermann Minkowski showed that special relativity is best described using the concept of a four dimensional spacetime, this unites the time dimension with the three spatial dimensions we observe (Harrison, pp.207). Minkowski showed that events take place in a point in spacetime specified by four numbers in any coordinate system. The worldline of an object is the path that it takes though this spacetime.
The concept of mass was not fully understood until Einstein reconciled his theory of special relativity with Newton's law of universal gravitation. He finally achieved this in 1916, with his theory of general relativity (Einstein, 1916).
References
Eddington, A., 1929, Space, Time, and Gravitation, Cambridge University Press, Cambridge
Einstein, A., 1905, 'On the electrodynamics of moving bodies', Annalen der Physik, Vol.17, from 'The principle of relativity: a collection of original memoirs on the special and general theory of relativity', Dover Publications, Mineola, pp.35-66
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
Harrison, E.R., 2000, 'Cosmology: the science of the universe', Cambridge University Press, Cambridge
Time dilation and the relativity of simultaneity lead to the twin paradox, this shows that if one twin travelled away from the other at near to the speed of light, and then turned around and came back again, they would not have aged as much as their sibling on Earth. If the first twin travelled at 86.6% the speed of light, they will be ten years younger than their sibling when they return. This appears to be a paradox because Galileo's relativity states that there is no absolute state of rest and so the twin on Earth could equally consider themselves to be moving away from their sibling at this speed. The paradox is resolved by the fact that the moving twin turns around and travels back to Earth. As they turn around they are forced to accelerate and this breaks the symmetry. Newton showed that acceleration is unlike velocity because we can always tell if we are not accelerating at a constant rate.
Einstein's theory of special relativity also alters our understanding of mass. The mass of an object measured by an observer who is stationary with respect to it, is referred to as its rest mass. This can be calculated using Newton's second law, force = mass x acceleration. Special relativity shows that an object that is moving from a stationary observers perspective, will also have a mass associated with it. This is different from the Newtonian concept of mass and is related to the objects momentum.