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Einstein's Legacy: 100 Years Later

Compiled by Frikkie de Bruyn

E-mail: [debruyn1@telkomsa.net]

 

Introduction

The year 2005 is the World Year of Physics. We commemorate the 100th year of the three seminal Einstein papers of 1905. Six papers were published in that year. In this short paper I will deal only with the three papers of Einstein published in 1905 and their scientific importance as seen by a layman and, most important, pay tribute to Einstein as a scientist and a human being.

The greatest tribute to Einstein is perhaps that the scientific importance and wonders of his theories are still emerging a century after the publication of his papers. Einstein laid the foundation of a pillar of modern physics, special relativity and he helped establishing a second pillar of modern physics, quantum mechanics.

The basic tenet of quantum mechanics is uncertainties of nature at the atomic level and smaller. Certainties were replaced by probabilities. Einstein maintained that behind the apparent uncertainties of quantum mechanics, the universe is ultimately ruled by the rules of classical physics. Later in 1915 with the publication of his general theory of relativity, he created a new theory of gravity.

Today we refer to the "Einsteinian" universe; a universe of relativities. Einstein described a causal universe in which incidents in the past of the universe are direct causes of future events, provided that the information, travelling at the finite speed of light, had enough time to reach and influence the future events. Time and space are not absolute. Time is relative and its temporal flow depends on the observer.

Special Relativity

Einstein began thinking about how motion and gravity interact. He startled the world by showing that Newton's laws of motion and gravity were only partially correct. He revised Newton's laws by publishing two relativity theories. I will not deal with general relativity since this paper was published in 1915. The paper requiring our attention is special relativity.

In the theory of special relativity a physical happening is called an event. An event, such as the launch of a spacecraft, occurs at a specific place and time. The observer watching the launch uses a reference frame consisting of the place where the launch takes place, called a co-ordinate system and a clock. He uses the co-ordinate system to specify where the launch takes place and the clock to specify the time. The observer watching the launch and the astronaught in space are at rest each relative to his own reference frame. But they are moving relative to each other and so are their reference frames.

The reference frame in special relativity is a special kind of reference frame called an inertial reference frame. In an inertial reference frame the body either remains at rest or moves in constant speed when the net force acting on the body is zero. The acceleration of such a body is therefore zero when measured in the inertial reference frame. It follows that rotating or otherwise accelerating reference frames are not inertial reference frames. The acceleration of the earth as it spins on its axis and revolves around the sun is so small that they can be ignored and the reference frame of the observer on the ground can be regarded as an inertial reference frame. But why are inertial reference frames so important in relativity?

 

Postulates

To understand relativity we must, like Einstein, think about how moving observers (the astronaught and the observer on the ground) see events around them. From this perspective Einstein formulated the first postulate of relativity also known as the principle of relativity:

                 Observers can never detect their
                 uniform motion except relative to
                 other objects.

This is easy. You may have experienced the first postulate when you are aboard a ship in the harbour and the ship began to move very slowly. You would argue that it is not the ship moving but the land and buildings. It is only after a few moments that you realize the ship is moving. Take another example. Suppose you are floating in a spaceship in outer space and another spaceship comes floating by. You might conclude that your spaceship is not moving but that the other spaceship is moving, but the astronaught in the other spaceship might be equally convinced that you are moving and it is not. The principle of relativity states that there is no experiment you or the other astronaught can perform to decide which spaceship is moving and which is not. From this Einstein concluded that there is no such thing as absolute rest - all motion is relative. Since no experiment can be performed to determine absolute motion through space, the laws of physics must be the same in both spaceships. The first postulate can therefore be stated to refer to the laws of physics:

                     (alternate version) The laws of
                     physics are the same for all observers,
                     no matter what their motion, so long as
                     they are not accelerated.

The words uniform and accelerated are important. If one of the spaceships were to fire its rockets, its velocity would change. The astronaught would be aware of it because he would feel the acceleration. Accelerated motion is different since we can tell which ship is moving and which is not. The postulates of relativity discussed above apply only to observers in uniform motion. That is why it is called special relativity.

The first postulate fit in with Einstein's conclusion that the speed of light is constant for all observers. No matter how you move, your measurement of the speed of light must always be the same. This forms the second postulate of special relativity:

                 The velocity of light is constant
                 and will be the same for all observers
                 independent of their motion relative
                 to the light source.

The acceptance by Einstein of the basic postulates of relativity led him to some amazing discoveries. Newton's laws on motion and relativity are approximations; they work well at small distances and low velocities. At very large distances and very high velocities Newton's laws are inadequate to describe what happens. Then we have to use relativistic physics. Special relativity shows that the mass of a moving particle depends on its velocity. That is, the higher the particle's velocity the greater it's mass. At low velocities this effect is insignificant but it becomes very important at velocities approaching the speed of light. This effect becomes apparent when particles are accelerated to high velocities.

This discovery led to another insight. The relativistic equations describing the energy of a moving particle predict that the energy of motionless particle (particle at rest) is not zero. Rather the rest energy of a particle is m_o c^2. From this insight Einstein arrived at his famous equation:

                               E = m_o c^2

In this equation c is the speed of light and mo is the mass of the particle at rest. Mass has to be specified this way because one of the consequences of relativity is that the mass of a particle depends on its velocity. Einstein showed, therefore, that mass and energy are related. This is how nature can convert one into the other inside stars.

Suppose we convert one kilogram of matter into energy. We express the velocity of light as 3 x 108 m/s and the answer is 9 x 1016 joules (J). That is approximately equal to a 20-megaton nuclear bomb.

Other relativistic effects are the slowing of moving clocks (time dilation) and the shrinkage of lengths measured in direction of motion (Lorentz contraction).

We must, however move on to the other two Einstein papers published in 1905.

 

The Photoelectric Effect

To understand what the photoelectric effect is about we must go back to what Max Planck said about black body radiation. All bodies, no matter how hot or cold, continuously radiate electromagnetic waves. A very hot object glows because it emits electromagnetic waves in the visible region of the spectrum. The sun, which has a surface temperature of about 6 000 K, appears yellow, while the cooler star Betelgeuse has a red orange appearance due to its lower surface temperature of 2 900 K.

What does all this mean? At a given temperature, the intensities of the electromagnetic waves emitted by an object vary from wavelength to wavelength throughout the visible, infrared and other regions of the electromagnetic spectrum. Planck showed that an electromagnetic wave could have energies of only certain definite values. That means that whenever the energy of a system can have only certain definite values, and nothing in between, the energy is said to be quantized.

Experimental evidence that light consists of photons comes from the photoelectric phenomenon, in which electrons are emitted from a metal surface if the light used has a sufficiently high frequency. In 1905 Einstein presented an explanation for the photoelectric effect by making use of Planck's work on black body radiation. He proposed that light of frequency f could be regarded as a collection of discrete packets of energy (photons). Each packet contains an amount of energy E given by:

Energy of a photon       E = hf  

Where h is Planck's constant. The brighter the light on a given area (higher intensity), the greater is the number of photons that strike the area. Einstein showed that if the photon has enough energy to remove the electron from the metal (energising the electron), the electron can be ejected. The amount of energy required to eject the electron depends on how strongly the electron is held. If a photon has more energy than needed to eject the electron, the excess appears as kinetic energy of the electron. The photon picture as used by Einstein provides an explanation of certain features of the photoelectric effect which are difficult to explain without photons. It was found, for instance, that only light with a frequency above a certain minimal value, denoted fo , will eject electrons. If the frequency of the light is below this value, no electrons are ejected, regardless of how intense the light is.

We know that a photon sometimes behave like a particle and sometimes like a wave. It is, however, Einstein's photon model of light that explains satisfactorily the photoelectric effect, whereas the electromagnetic wave picture of light does not. We must recognize that the wave picture does not explain all the characteristics of light. In addition the photon model makes an important contribution to our understanding of the way light behaves when it interacts with matter. The photon can eject an electron because it has energy. However a photon is different from another particle. A normal particle cannot exceed the speed of light. A photon, on the other hand, travels at the speed of light in a vacuum and does not exist as an object at rest. The energy of a photon is entirely kinetic in nature, because it has no rest energy and no mass. Einstein was awarded the Nobel Prize in physics in 1921 primarily for his theory of the photoelectric effect.

 

Brownian Motion

The English Botanist Robert Brown (1773 - 1858) observed through a microscope that pollen grains suspended in water move on very irregular, zigzag paths. You can also observe this Brownian motion with other particle suspensions such as fine smoke particles in the air. It was Einstein who showed in 1905 that Brownian motion could be explained as the large suspended particles, such as the pollen grains, moving because of impacts from the moving molecules of the fluid medium (such as water or air). He further proved that, as a result of the impacts, the suspended particles have the same kinetic energy as the fluid molecules. Many people before Einstein studied and performed experiments on the Brownian motion, but could not obtain any decisive results. It was Einstein who predicted in his paper "motions of such magnitudes that they can easily be observed with a microscope".

 

Einstein in our everyday lives

Einstein's theories are of enormous importance to science. But even the lives of ordinary people would have been very different without Einstein. His descriptions of how light can act as particles, the emission of radiation by atoms and the influence of gravity on clocks are very important for the devises we use everyday. Sensors used to open doors automatically and to close it again make use of the photoelectric effect. Einstein did not discover the photoelectric effect, which was first discovered in France in 1839. He was, however, the first to explain the phenomenon correctly.

Einstein postulated that Planck's constant, h, was not a mere mathematical tool. He argued that light travels in packets, rather than flowing as a continuous wave of energy. He showed that light can behave as a stream of particles knocking electrons out of metal. He further showed that the velocity of the liberated electron does not depend on the number of photons, but rather on the colour of light. He concluded that the energy of a photon depends on its frequency multiplied by Planck's constant h. For this explanation Einstein won the Nobel Prize in 1921.

The photoelectric effect is used to turn on street lights at dusk, regulate the density of the toner in photostat machines and govern the exposure time of cameras. It is even used in breathalyzers - the photocell picks up a colour change occurring after a test has reacted with alcohol. Solar cells make use of the photoelectric effect. Solar cells convert 30 to 50 percent of the incident light into electricity for homes power calculators, watches and orbiting satellites. The invention of the maser and subsequently the laser follows Einstein's paper on "On the Quantum Theory of Radiation". The Global Positioning System uses relativistic corrections based on Einstein's discovery that time is relative, that clocks on board satellites run slower than clocks on earth. Without Einstein our lives would indeed be very different.

 

Frikkie de Bruyn (on the right) of the Natal Midlands Centre poses with a photograph of Albert Einstein in the Natal Society Library, where he helped organize a display to celebrate the World Year of Physics. Photographed by Nash Narrandes (not shown here).

 

 

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