General Background Notes

Special Relativity is based on two postulates:

The Principle of Relativity: The laws of physics are the same in all inertial reference frames. One cannot tell by any experiment whether one is at rest or moving uniformly (that is, moving in a straight line with constant velocity). In other words, there is no such thing as absolute rest. All motion or rest is only in relation to other observed objects (i.e. I can consider myself not to be moving with respect to the earth while at the same time I am moving very rapidly with respect to the sun).

The Principle of the Constancy of the Speed of Light (c= 2.99*10⁸ m/s): The speed of light in free space has the same value c in all inertial frames.

• Effect of E=mc² present at all speeds. On earth the effect is tiny but unnoticeable. This holds true for ‘time dilation’, length contraction etc.

• Einstein also renewed conservation laws – Energy is not conserved; mass is not conserved. BUT any mass gained is always balanced by an equivalent amount of energy being lost.

• Du Chatelet pitted Newton’s mv against Leibniz’s mv². Newton believed that God replenished lost energy (after a collision, per say). Leibniz believed that energy was not cancelled out, but added up, and energy was conserved (Einstein corrected that). Hence the world runs on its own.

• Electron derives from: Elektron, Greek word for amber. It was known that after rubbing amber, the amber would attract light objects, like paper etc.

• In 1676 Danish astronomer Ole Roemer discovered that the speed of light was finite. He found this by studying the orbit of the moon Io around Jupiter. Two years later Dutch physicist Christian Huyghens used Roemer’s data to estimate the speed of light.

• Nucleus of any atom follows the Water Drop Model: The exterior of the water provides for a binding energy that keeps the water molecules in. In the nucleus, despite abundance of positive charges, the binding energy levels out the repulsive mass. Hence, when neutrons are fired into the nucleus, the inversely proportional relationship causes the mass to increase, binding energy to decrease (this is in order to maintain same level of energy for the nucleus). Therefore unstable isotopes split.

• People who came close to relativity: Hendrik Antoon Lorentz (1853 – 1928); Henri Poincare. Einstein acknowledged their roles in relativity.

• What Einstein then discovered was that in order for all observers to measure the same velocity for a beam of light, time would have to "flow" differently for different observers, and space would sometimes have to contract.

• A mathematical formulation of the special theory of relativity is based on the idea that an event is specified by four co-ordinates: three spatial co-ordinates and one time co-ordinate.  These co-ordinates define a four-dimensional space and the motion of a particle can be described by a curve in this space. (refer to Examples and Analogies For Special Relativity).

• Mass Increase

A moving object weighs more than an object which isn't moving. It can be shown that if an object travels at the speed of light, it must either weigh nothing (which is only true for light) or it is infinitely heavy. This implies nothing can travel at the speed of light… other than photons, which are the massless ‘particles’ that make up light. Having said that a photon is really just a description of a process, the process of electrical and magnetic fields inducing each other and moving forward.

• Speed of light is the effective speed limit

There is nothing in the theory of relativity which prevents an object from travelling faster than the speed of light, although such objects can never slow down to below the speed of light or they would violate special relativity. Any particle which travels faster than the speed of light is called a TACHYON (imaginary).

· Differences between Special and General Relativity

General deals with space and time, how objects interact with each other on a greater scale. It deals with problems presented by E=mc2 in more detail – Energy is mass; as well as energy’s part in gravity. Special is useful for problems in everyday life and ‘local’ interactions. Where General Relativity is needed is in the presence of heavy objects or large amounts of energy. It also deals acceleration in more detail than Special.

The special theory of relativity is concerned with relative motion between non-accelerated frames of reference. The general theory deals with general relative motion between accelerated frames of reference.  In accelerated systems of reference, certain fictitious forces are observed, such as the centrifugal and Coriolis forces found in rotating systems.  These are known as fictitious forces because they disappear when the observer transforms to an non-accelerated system.

Tez Asfaw