Special theory of relativity
Special Relativity (SRT) is a generalization of classical mechanics. In contrast to General Relativity, Special Relativity deals with processes observed in so called inertial frames (frames of observation without the influence of acceleration or gravity). It is based on two main observations from different experiments.
- The speed of light is constant for all (inertial) observers, regardless of their velocities relative to each other.
- The laws of physics are identical in all inertial reference frames.
The three most prominent SRT effects are time dilation, length contraction and the equivalence of mass and energy.
The central equations of special relativity are the Lorentz transformations:
These are the transformations from one coordinate system to another system, , moving past this one at speed u, and with and axes colinear.
The Lorentz factor, occurs frequently all over special relativity and is
- , where:
- is the difference in speed between the frames of reference
- is the speed of light
When , the speed of the object in question, is low relative to , approaches , causing the Einstein-Lorentz relativity equations to be equivalent to Newton's equations. This is why classical mechanics, governed by Isaac Newton's laws of motion, works for particles at low mass and low speed. However, at higher velocities, diverges, causing relativity to be essential.
Electromagnetism, including for light and gamma radiation, where the quanta (photons) travel at light speed have no rest mass, is always relativistic.
Universal speed limit
At the other extreme, when approaches , approaches . Since infinite means an object would have infinite kinetic energy, no object with mass can ever travel at the speed of light. Relativity does not however forbid particles from traveling faster then , rather that it is impossible to cross the speed of light barrier. Some theorists have postulated hypothetical tachyons, which would always travel faster than the speed of light. No evidence has been found for them.
- Michelson-Moreley experiment
- GPS clocks - there are two effects here and both are time dilation. The first is due to special relativity caused by the fact the satellite is in an inertial frame of reference moving past the ground. The other is due to general relativity since the craft is further out than someone on the ground of the earth's gravitational well. The overall effect is for clocks on the satellite to run faster by approximately 38 ms per day.
- Lifetimes of fast traveling particles such as muons produced by cosmic rays (see muon)
In the beginning of the last century the two assumption mentioned before where found experimentally in the form of the Maxwell equations, which describe electromagnetic waves. The general idea at that point was that any wave is carried by some medium, called the luminiferous aether. However, as the earth is moving through space, there should be a difference in the interferometrically determined light wavelength, when measured at noon, at evening and at night at the same geographic location. However the Michelson-Morley experiment did reject the aether hypothesis. With this rejection it became an inevitable fact that equations describing physics, which where fitting to a three dimensional space with a single timeframe for all observers exist. The mathematical framework and physical significance was developed by Henri Poincaré and Hendrik Lorentz. Albert Einstein gave an alternate derivation in terms of postulates. Many other scientists contributed modifications of this theory. In particular, the Irish Physicist Fitzgerald proposed that the failure of the Michelson Morley experiment was as a result of a length contraction effect. This idea was taken up by Hendrik Lorentz and shown by others to be a useful mechanism by which theory could be forced into conformance with experimental results. However, in 2005, Michael Strauss a computer engineer invalidated much of Special Relativity theory by showing clear contradictions in the theory. Special Relativity
Spin as a relativistic effect
The relativistic extension of Quantum Mechanics, described by the Dirac Equation allows, due to the symmetry of the equation in 4-space, an additional quantum number to exist, called spin. electron spin was known from chemistry before relativity arose.
Interpretation and paradoxes
Some consequences of the SRT are:
- It is impossible ever to transmit information faster than the speed of light.
- The laws of physics are identical, without any variation, in every location throughout the universe.
- The laws of physics are identical, without any variation, no matter how fast something is traveling (in an inertial reference frame).
Special relativity alters Isaac Newton's laws of motion by assuming that the speed of light will be the same for all observers, despite their relative velocities and the source of the light. (Therefore, if A sends a beam of light to B, and both measure the speed, it will be the same for both, no matter what the relative velocity of A and B. In Newtonian/Galilean mechanics, If A sends a physical object at a particular velocity towards B, and nothing slows it, the velocity of the object relative to B depends on the velocities of the object and of B relative to A.)
In the framework of special relativity, several thought experiments can be constructed, which lead to apparent paradoxes. The most striking one is the twin paradox. If you take twins, one on earth, and one in traveling to the next star with high speed and back, their biological age will not be the same, even though you could redefine the system of the traveling twin to be resting. This paradox is resolved because the second twin is not in an inertial frame - he has accelerated, most significantly at his turn-around point. This points out, that while neglected in special relativity, acceleration has a non-trivial role. This is considered in the General theory of relativity.
- ↑ http://www2.slac.stanford.edu/vvc/theory/relativity.html
- ↑ http://www.math.ucr.edu/home/baez/physics/ParticleAndNuclear/tachyons.html
- ↑ http://www.astronomy.ohio-state.edu/~pogge/Ast162/Unit5/gps.html
- ↑ This assumption is commonly restated in this manner. For example, a discussion of hypothetical tachyons talks "about using tachyons to transmit information faster than the speed of light, in violation of Special Relativity." However, there is some question whether the Theory of Special Relativity really restricts faster-than-light communication of information.
Mass Energy Equivalence Example