ASTRONOMY (HERSCHEL)

Einstein’s Three Revolutionary Papers of 1905

Meeting chaired by Richard Phillips

Drs. Peter Ford & Vincent Smith

Institute of Physics

6 May 2005

Einstein was born in Ulm on 14 March 1879. This was momentous year in many respects: Bismark became the German Chancellor, leading to rapid industrialisation of that country; both Trotsky and Stalin were born; the Treaty of Gandomak brought Afghanistan under British control: Tay Bridge disaster.

In Physics, 1879 saw the birth of Otto Hahn who discovered fission of heavy elements in 1938 and of Owen Richardson who discovered thermionic emission and photo-electricity. The same year James Clerk Maxwell died. (Maxwell had discovered light, and Herschel’s infra-red radiation, to be an electromagnetic phenomenon which suggested the presence of an ‘aether’ for its waves to travel in. The failure to detect the aether by Michelson and Morley was critical in Einstein’s later work.). Joseph Swann and Thomas Eddington developed the electric light bulb, Siemens the electric train in 1879, Edwin Hall discovered the Hall effect, later to be important in developing semiconductor technology and Stefan and Boltzmann discovered that the energy of radiation from a hot body was proportional to the fourth power of the temperature.

Einstein’s father ran a small electro-chemical plant. Albert was slow at school but read books on science. However, he ‘kicked over the traces’ in his late teens and ended up in the Patent Office in Bern. he married a Serbian girl, Mileva Maric in 1903 and obtained a doctorate from the University of Zurich in 1905, the year of his three revolutions in science:

Revolution 1: Explanation of Brownian Motion

The British botanist Robert Brown had noticed that pollen grains suspended in a liquid were in constant random movement. This became know as ‘Brownian motion’ and was attributed to a ‘life force’ (but not by Brown himself).

In 1877 Desaulx suggested that the motion was the result of buffeting by molecules in the liquid. Although molecules were used to explain chemical reactions and Maxwell had used them to explain the behaviour of gases, molecules were not considered ‘real’.

In 1900 F. M. Exner showed that Brownian motion depended on temperature and particle size.

Einstein’s contribution was to use statistical mechanics to show that the average energy of the particles was equal to the average energy of the molecules and that the distance a particle moved was equal to the square-root of the time from taken.

This relationship, nick-named the ‘Drunkard’s walk’ relationship is similar to that which governs diffusion in gases, ‘derivatives’ or ‘futures’ in stocks and shares and even the game of ‘Snakes and Ladders’!

Revolution 2: The Photo-electric Effect

When light falls on a metal, electrons are knocked out of it. Classical mechanics would suggest that the energy imparted to the electrons would depend on the intensity of the light beam. However, this does not happen. For electrons to be knocked out, the frequency of the light has to be high enough (the wavelength short enough) - there is a threshold frequency.

Above this threshold, the energy of the electrons is proportional to the frequency of the light. It is the electric current (that is the number of electrons knocked out) which is determined by the light intensity.

Einstein explained this using Planck’s idea that energy is transferred in packets or ‘quanta’ and that each light ‘quantum’ has an energy E = h x f where E = energy, f = frequency and h is a constant, known as ‘Planck’s constant.

One might imagine light as a series of particles of energy fixed by E = hf, each one knocking out one electron by giving up its packet of energy.

The reason why there is a threshold frequency is because each electron needs a minimum amount of energy to overcome the forces holding it in the metal. Below this energy (i.e. frequency) an electron cannot escape.

An analogy is a coconut shy - the coconut will not be knocked out of its holder unless the ball has sufficient energy to do so. If there are heavy blue balls and small red ones (blue light has a higher frequency), it is better to choose a blue ball as a more massive ball will have more energy (= ½ m v ²) for the same speed. The number of coconuts won is only proportional to the number of balls thrown - you don’t get more coconuts by throwing harder (i.e. giving the ball more energy)!

Einstein’s use of Planck’s quantum theory serve to confirm it and it was especially for this that Einstein received the Nobel Prize for physics in 1921.

Revolution 3: The Special Theory of Relativity

Einstein introduced the democratic principle of ‘all inertial observers are equal’ into physics. An inertial observer has no acceleration - if he releases an object it will not change its position with respect to him. Einstein applied this principle to electromagnetic radiation (light) as well as to mechanics - that is, all inertial observers measuring the speed of light arrive at the same value. This goes against the grain of classical science - it is not true of waves (water or sound) - the value you get depends on your speed with respect to the medium the waves are travelling in and other observers will get different results depending on their speed.

Michelson and Morley tried to find out their speed in relation to the ‘aether’ and failed and others (Fitzgerald and Lorentz) had derived equations to explain this failure but they were really ‘fudges’. Einstein realised that his postulate that the speed of light is ‘absolute’ required a reappraisal of time and distance.

The speed of light of 300,000 km per second means that you can rely on the fact that a flash of laser light directed at a mirror 300,000 km away will come back to you in 2 seconds.

However, if you watch another experimenter doing the same thing on another planet travelling at right angles to your light beam at a speed of 225,000 km per second, you will see his light flash travel 375,000 km there and back. By your clock, it will take 2½ seconds but if you glance at his clock, it would show only 2 seconds!

After all, by the democratic principle he has every right to consider himself ‘stationary’ and it is you who is ‘moving’ and therefore use the same argument as you. If his clock showed anything but 2 seconds to him he would have to consider that the speed of light was not 300,000 km per second.

You would therefore come to the conclusion that his clock is running slow!

More generally, if c is the speed of light (which you both agree on) and the other observer’s speed with respect to you is v, while his time measurement is t´ and yours is t, then half the path length by your reckoning is ct and his is ct´. By applying Pythagoras’ theorem to one of the right triangles in the diagram:

(ct)² = (ct´)² + (vt)²

c²t² = c²t´² + v²t²

t²(c² - v²) = c²t´²

t = Ö t´²/(c² - v²)

t/ t´ = Ö 1/(c² - v²)

This equation enables you to calculate the comparison of your time measurement (t) with that of another inertial observer (t´) who is travelling at speed v with respect to you. This is the "time dilation" of relativity.

Einstein’s Later Years

1909 Associate lecturer of physics at the University of Zurich

1915 Published a General Theory of Relativity.

Although he was central to the development of quantum mechanics, he was troubled by its later development.

The design of the Einstein Tower in Potsdam is based on his ideas of curved space-time. His ideas also were influential in the development of cubism in art.

‘L’imagination est plus importante que le savoir.’

Richard H Phillips