Special Relativity, Physics tutorial

Introduction:

Special relativity is the scientific theory describing how matter moves through time and space. When it was initial published in 1905 by Albert Einstein, special relativity caused the revolution in physics community. Special relativity is one of the most well-confirmed physics theories of all time, and its forecast have been confirmed to more than twenty decimal places of accuracy.

Two essential postulates of special relativity are that laws of physics are same despite of absolute velocity, and that speed of light is constant for all observers. If you are in the closed box moving at steady velocity, special relativity forecasts that no experiment you perform inside box can tell how fast box is moving. Similarly, speed of light will remain same for the observer inside box, even if box itself is moving at the large fraction of speed of light.

Special relativity abandons notions of absolute space and absolute time developed by Newton. Under special relativity, there is no such thing as the single universal time; rather, time is different for every observer. There is also no single universal measure of space; a single ruler can be longer or shorter depending on who measures it. Lastly, special relativity unifies concepts of space and time into the single four-dimensional structure known as spacetime.

According to special relativity, if the object is moving at high speed relative to you, object will seem to act strangely. Its mass will increase, so that it becomes harder and harder to accelerate as it approaches speed of light. It will seem to shrink in direction of motion, becoming more and more distorted as it travels faster. Object's time will also become distorted; if there is a clock on object, it will seem to tick more slowly. These effects occur to every object, but they only become visible once objects approach speed of light.

Special relativity forbids any object from traveling faster than speed of light. If the object seems to go faster than light speed for one observer, it should be likely to find the observer who observes object traveling backward in time. As the object's velocity approaches that of light, its mass and kinetic energy go to infinity. Even information may not travel faster than light, as this would permit messages to be sent backward in time as well.

Einstein's theory was based on two key principles:

  • The principle of relativity: Laws of physics do not change, even for objects moving in inertial (constant speed) frames of reference.
  • The principle of the speed of light: Speed of light is same for all observers, despite of their motion relative to light source.

Unifying space and time:

Einstein's theory of special relativity developed the fundamental link between space and time. Universe can be observed as having three space dimensions - up/down, left/right, forward/backward - and one time dimension. 4-dimensional space is referred to as space-time continuum.

If you move fast enough through space, observations that you make about space and time vary somewhat from observations of other people, who are moving at different speeds.

Unifying mass and energy:

Most famous work of Einstein's life also dates from 1905 when he applied ideas of his relativity paper to come up with equation E=mc2 which represents relationship between mass (m) and energy (E).

In the nutshell, Einstein found that as the object approached speed of light, c, mass of object increased. Object goes faster, but it also gets heavier. If it were really able to move at c, object's mass and energy would both be infinite. The heavier object is harder to speed up, so it is not possible to ever really get particle up to a speed of c.

Round-Trip Tests of Light-Speed Isotropy:

Speed of light is said to be isotropic if it has same value when estimated in any/every direction.

Michelson-Morley Experiment (the MMX):

Michelson-Morley experiment (MMX) was intended to compute velocity of Earth relative to "luminiferous aether" which was at time presumed to carry electromagnetic phenomena. Failure of it and other early experiments to actually observe Earth's motion through aether became important in promoting acceptance of Einstein's theory of Special Relativity, as it was appreciated from early on that Einstein's approach (via symmetry) was more elegant and parsimonious of assumptions than were other approaches.

Time dilation:

One of the most dramatic predictions of Special Relativity is time dilation. Time dilation means that clocks in the frame moving with respect to you appear to run slow. You and I are never likely to be moving at near the speed of light but many elementary particles can hardly help themselves from doing so.

Tests of Einstein's two Postulates:

One-Way Tests of Light-Speed Isotropy:

Experiments clearly use one-way light path and find isotropy, they are inherently not capable to rule out the large class of theories in which one-way speed of light is anisotropic. These theories share property that round-trip speed of light is isotropic in any inertial frame, but one-way speed is isotropic only in the aether frame. In all of the theories the effects of slow clock transport accurately offset effects of anisotropic one-way speed of light (in any inertial frame), and all are experimentally interchangeable from SR. All of the theories forecast null results for the experiments.

Tests of Light Speed from Moving Source:

If light emitted from the source moving with velocity v toward observer has the speed c+kv in observer's frame, then the experiments place the limit on k. Many but not all of the experiments are subject to criticism because of Optical Extinction.

Measurements of the Speed of Light, and Other Limits on it:

In 1983 international standard for meter was redefined in terms of definition of second and the defined value for speed of light. Defined value was chosen to be as reliable as possible with earlier metrological definitions of meter and second.  As then it is not possible to determine speed of light using current metrological standards, but one can still measure any anisotropy in its speed, or use the earlier definition of meter if essential.

Tests of Time Dilation and Transverse Doppler Effect:

The Doppler Effect is observed variation in frequency of the source when it is seen by detector that is moving relative to source. This effect is most pronounced when source is moving directly toward or away from detector, and in pre-relativity physics its value was zero for transverse motion (motion perpendicular to source-detector line). In SR there is non-zero Doppler effect for transverse motion, because of relative time dilation of source as observed by detector. Measurements of Doppler shifts for sources moving with velocities approaching c can test validity of SR's prediction for such observations that varies significantly from classical predictions; experiments support SR and are in complete disagreement with non-relativistic predictions.

Other Experiments:

The Fizeau Experiment:

Fizeau estimated speed of light in moving mediums, most notably moving water.  Fresnel suggested the drag coefficient which putatively explained how strongly the moving material medium dragged aether.  SR forecasts no aether but predicts that speed of light in the moving medium varies from speed in medium at rest, by the amount consistent with the experiments and with Fresnel drag coefficient.

Special Relativity is developed into framework of modern physics. Its results are utilized all time and areas of physics which use the results work very well. Though some results of Special Relativity are counter-intuitive, in hindsight what Einstein did now appears natural. He realized that incompatibility between Newtonian Mechanics and Electricity & Magnetism must and could be determined by re-writing old mechanics and not new Electricity & Magnetism.

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