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## Special relativity
The
## Motivation for the theory of special relativity
Before the formulation of special relativity, Hendrik Lorentz and others had already noted that electromagnetics differed from Newtonian physics in that observations by one of some phenomenon can differ from those of a person moving relative to that person at speeds nearing the speed of light. For example, one may observe
While Lorentz suggested the Lorentz transformation equations as a mathematical description that accurately described the results of measurements, Einstein's contribution was to
Special relativity is usually concerned with the behaviour of objects and observers which remain at rest or are moving at a constant velocity. In this case, the observer is said to be in an ## Status of Special RelativitySpecial relativity is now universally accepted by the physics community, unlike General Relativity which is still insufficiently confirmed by experiment to exclude certain alternative theories of gravitation. However, there are a handful of people opposed to relativity on various grounds and who have proposed various alternatives, mainly Aether theories. One alternative theory is doubly-special relativity, where a characteristic length is added to the list of invariant quantities. ## Invariance of the speed of lightSR postulated that the speed of light in vacuum is the same to all inertial observers, and said that every physical theory should be shaped or reshaped so that it is the same mathematically for every inertial observer. This postulate (which comes from Maxwell's equations for electromagnetics) together with the requirement, successfully reproduces the Lorentz
- The time lapse between two events is not invariant from observer to another, but is dependent on the relative speeds of the observers' reference frames.
- The twin paradox is the "story" of a twin who flies off in a spaceship travelling near the speed of light. When he returns he discovers that his twin has aged much more rapidly than he has (or he aged more slowly).
- Two events that occur simultaneously in different places in one reference frame may occur one after the other in another reference frame (relativity of simultaneity).
- The dimensions (e.g. length) of an object as measured by an observer may differ from those by another.
- The mass of a particle increases as it's velocity increases. This led to the famous equation E = mc
^{2}. See below.
## Lack of an absolute reference frame
Special Relativity rejects the idea of any absolute ('unique' or 'special') frame of reference; rather physics must look the same to ^{th} Century, some physicists suggested that the universe was filled with a substance known as "aether" which transmited Electromagnetic waves. Aether constituted an absolute reference frame against which speeds could be measured. Aether had some wonderful properties: it was sufficiently elastic that it could support electromagnetc waves, those waves could interact with matter, yet it offered no resistance to bodies passing through it. The results of various experiments, culminating in the famous Michelson-Morley experiment, suggested that either the Earth was always 'stationary', or the notion of an absolute frame of reference was mistaken and must be discarded. ## Equivalence of mass and energy
As the velocity of an object increases, so does it mass, and the increase in mass is equal to 1/c
m = γ m, , _{0}E is the energy of the object, m is the rest mass, _{0}c is the speed of light, v is the velocity of the object. The term γ occurs frequently in relativity, and comes from the Lorentz transformation equations.The equivalence of mass and energy turns out to be fundamental. The destruction of mass in nuclear reactions releases vast amounts of energy.
It is worth noting that if
m_{0}c^{2}, plus the Newtonian kinetic energy, m_{0}v^{2}/2. This is just one example of how the two theories coincide when velocities are small.
As the velocity approaches The speed of light is approximately 300,000 kilometers per second or 186,300 miles per second. The theory implies that there is an upper limit to the speed at which gravitational influences can travel (the speed of light). This is inconsistent with the classic theory of gravity formulated by Isaac Newton The name "tachyon" has been used for hypothetical particles which would move faster than the speed of light, but to date evidence of the actual existence of tachyons has not been produced. ## Simultaneity and Causality## The Geometry of Space-time in Special RelativitySR uses a 'flat' 4 dimensional Minkowski space, usually referred to as space-time. This space, however, is very similar to the standard 3 dimensional Euclidean space, and fortunately by that fact, very easy to work with.
The differential of distance(
defined by the equation r=c*dt.
If we extend this to three spatial dimensions, the null geodesics are
continuous concentric spheres, with radius = distance = c*(+ or -)time.
d/c seconds in the past. For this reason the null dual cone is also known as the 'light cone'. (The point in the lower left of the picture below represents the star, the origin represents the observer, and the line represents the null geodesic "line of sight".)
The cone in the ## Tests of postulates of special relativity- Michelson-Morley experiment - ether drift
- Hamar experiment - obstruction of ether flow
- Trouton-Noble experiment - torque on a capacitor
- Kennedy-Thorndike experiment - time contraction
- Forms of the emission theory experiment
## Related TopicsPeople: Physics and Math: Philosophy:- Actualism
- Convensionalism
- Formalism
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