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The basic concept of relativity is that that motion can only be measured relative to other objects and not in any absolute sense. Another basic concept of relativity is that the laws of physics are unaffected by relative motion such that all inertial observers experience the exact same laws of physics. One of the results of this is the fact that you never see your self moving but you do see the world moving by you. Relativity has profound affects on our understanding of space and time making it one of the most significant discoveries of modern science.
The theory of relativity described by Galileo Galilei in 1632. Its basic concept was that the fundamental laws of physics are the same in all inertial frames. He also considered space and time as being absolutes. One of the short comings of Galilean Relativity was the failure to consider the speed of light. This was because Galileo lacked the ability to measure the speed of light even though he tried. When this short coming was dealt with the result was the modern theory of relativity.
Newton’s laws of motion were first published in Philosophiae Naturalis Principia Mathematica in 1687 and they were based in part on Galilean Relativity and they are foundational to all of physics. His 3laws are: the Law of inertia, the Law of acceleration and the Law of action reaction.
The Law of inertia is that objects in motion tend to stay in strait line motion unless acted on by a force. 

When a force is applied to an object is acceleration is inversely proportional to its mass
Law of acceleration is that when a force is applied to an object its acceleration is inversely proportional to its mass.  
F = MA  F = Force  M = Mass  A = Acceleration 


Law of action reaction is that for every action there is an equal and opposite reaction such that total momentum is conserved. 
Objects of equal mass are pushed apart at the same speed and objects of unequal mass are pushed apart such that the smaller one goes faster.
A physicist that lived 1831 – 1879 who developed the statistical means of describing the kinetic theory of gases called the Maxwell distribution which helped the development of Quantum Mechanics. Ironically given the above picture he made the first true color photograph and showed light to be Electromagnetic waves.
Maxwell's equations 

These quasions mathematically describes electromagnetism and
electromagnetic waves thta is light.
They also mathematically produces the speed of light in a vacuum, from the
electromagnetic properties of free space.(Permittivity, Permeability)
Led Einstein to his conclusion that the speed of light constant for all observers.
A theoretical medium in which light was thought to propagate that was general accepted in 19th century. The idea was that light propagated through the aether like sound in air.
An experiment intended to detect the aether was conducted by Albert
Michelson and Edward Morley in 1887.
It used a split light beams sent at 90 degrees in an attempt to measure.
The small variation is the light travel time in different directions caused
by the Earth’s motion through the aether.


Formula for relativistic length contraction. v is the relative velocity. c is the speed of light. L is the rest length. L' is length at velocity v. 

Similar to the length contraction of Special relativity but described as an electromagnetic affect. 
The degree of length contraction exactly counters expected variation in the light travel time.It was independently developed by George Fitz Gerald and Hendrik Lorentz and it's pupose was to keep the concept of Luminiferous aether alive. It was described as an electrodynamic affect resulting from motion through the aether. However it was considered an ad hoc explanation the failure of MichelsonMorley. Ultimately it was a forerunner of Special relativity and helped led to its development.
Published by Albert Einstein in 1905 Special Relativity deals with a special case where gravity can be ignored resulting in its name. Gravity was later incorporates into the theory of General Relativity. Special Relativity has two basic assumptions or postulates.
Observation of physical phenomena are the same for all inertial observers
The speed of light in a vacuum (c) is the same to all inertial observers., that is it is the same in all directions regardless of the velocity of the source or the observer.
http://en.wikipedia.org/wiki/Minkowski_diagram
How assumption 2nd can be true is shown by a SpaceTime Diagram. It shows the relationship between inertial reference frames. Such that observer S' is moving with a speed v in relation to S. The superposition has the axes of S' tilted so that the slope of the time axis is c / v and the slope of the apace axis is v / c.
The space axis of observer X’ moving relative to observer X is tilted such that observers X and X’ each see the same point at different times. Observer X’ sees light cone past two points at the same time and observer X sees light cone past same points at different times.


Formula for relativistic length contraction. v is the relative velocity. c is the speed of light. L is the rest length. L' is length at velocity v. 

Space time diagram showing relativistic length contraction.
The affect is caused by a tilting relationship between two reference frames in spacetime.
The yellow area is a light cone.
The black lines are the space (x) and time (t) axes of the S reference frame and the Blue line is the time axis of S' the reference frame .
The purple line is the space axis of a ship in the S' frame of reference.
In frame S' the light cone reaches both ends of a ship at
the time but they don't in frame S. This is because observer S is looking at
both ends of a ship at different points in the frame S' time line.
The forward end of the ship has not moved as far as the trailing end so the
ship is foreshortened to observer S. Furthermore an observer in frame S' sees frame S
objects with same length contraction.
Time Dilation 

Light clock at rest Time = t 
Light clock in relative motion. Time = t’ 

v is the relative velocity. c is the speed of light. t is the time at rest. t' is time at velocity v. 
Here is an illustration of time dilation in Special Relativity
General Relativity is an extension of Special Relativity into the general case of noninertial frames, resulting in a theory of gravity that extends and corrects Newtonian gravitation. Gravity results from a spacetime distortion caused by the presence of a mass like placing a weight on a rubber sheet. The mathematics of both are basically the same. To date it has passed every experimental test devised for it. making it one the best verified theories in Physics.
From: http://en.wikipedia.org/wiki/General_relativity
Twodimensional visualization of this spacetime distortion. The presence of matter bends spacetime, this bending is what is interpreted as gravity. One of the affects of General Relativity is gravitational time dilation, it is the slowing of time by a gravitational field Because the gravitational constant is so small, it takes a large mass with a small radius to produce significant time dilation. Using atomic clocks it is possible to detect the effect on Earth.
t' = Time inside the gravitational field. t = Time outside the gravitational field. m = The mass causing the gravitational field. r = The distance from the center of the gravitational field. c = the speed of light in a vacuum. G = The gravitational constant = 6.6742 X 10^{11} N m2 kg^{2} 
Identical atomic clocks exist in Greenwich England and Boulder Colorado. Boulder Colorado is a miles above sea level while Greenwich England is at sea level. The one in Greenwich England ticks 5 microseconds / year slower however according to General Relativity both clocks are right in their respective frames of reference.
Basic Concept of Relativity Theory is that all motion is
relative. Relativity Theory was first described by Galileo but he kept absolute
Space and Time Newton’s laws of motion built on Galilean Relativity. James
Maxwell showed light to be electromagnetic waves. Luminiferous
aether was theoretical medium in which light was thought to propagate. The
MichelsonMorley experiment tried to detect the aether but failed.
This eventually led to the development of Special relativity. Expanding
Special relativity led to General relativity.
Galilean Relativity 
Newton to Einstein 
Special Relativity 
General Relativity 
Biblical Significance Relativity 
Relativity and Creation Science 
Generalized, General Relativistic Metric 

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