bullet Special Relativity

 

The Special Theory of Relativity was proposed in 1905 by Albert Einstein (1879-1955). The reason it is "special" is because it is part of, or a "special case" of, the more comprehensive and complex General Theory of Relativity. The latter, General Theory, was proposed by Einstein in 1915.

The theory is based on two principles (postulates):

  1. Physical laws are the same in all frames of reference. That is; any event within a portion of space (a frame) can be specified by three spatial dimensions (east-west, north-south, up-down) and one temporal dimension (time). Also, the laws that apply to us in everyday circumstances (Newton's laws) also apply within each frame of reference.

  2. The speed of light is constant. By this it is meant that in a vacuum, such as in space, the speed of light is always the same, regardless of the speed of someone observing it.

 

Albert Einstein
(1879-1955)

 

 

bullet Equivalence of Electromagnetic Forces

 

Carl F. Gauss
(1777-1855)
Andre M. Ampere
(1775-1836)
Michael Faraday
(1791-1867)

The electric and magnetic phenomena can be described by the laws of Gauss (includes Coulomb's law), Ampere (generalized law), and Faraday.

James Clerk Maxwell as a young man; holding his top, showing how colours can be mixed to give white

The two electric charges are at rest, what are the forces between the charges detected by the two observers?

James C. Maxwell
(1831-1879)

Although the laws of electricity and of magnetism according to Gauss, Ampere, and Faraday worked remarkably well, there was a glaring problem: taken together, these laws did not "conserve charge". Maxwell modified Ampere's Law by adding a single term to it. This was what was needed to make the laws consistent with the conservation of charge.

The addition of this term led to a remarkable prediction: the existence of electromagnetic waves. With the full set of equations, Maxwell was able to calculate the speed of these waves. He found that their speed was a constant, independent of the nature of the electric and magnetic fields. What Maxwell found was that electromagnetic waves traveled at the speed of light. Maxwell had just discovered a fundamental constant of nature: the speed of light.

1 nanometer = 1nm = 10-9 m

 

bullet Luminiferous Aether

 

In the late 19th century the luminiferous aether ("light-bearing aether"), or ether, was a substance postulated to be the medium for the propagation of light. Later theories, including Einstein's Theory of Relativity, demonstrated that an aether did not have to exist, and today the concept is considered "quaint".

(The word "aether" stems via Latin from the Greek αιθηρ, from a root meaning "to kindle/burn/shine", which signified the substance thought in ancient times to fill the upper regions of space, beyond the clouds.)

The luminiferous aether: it was hypothesized that the Earth moves through a "medium" of aether that carries light

Each year, the Earth travels a tremendous distance in its orbit around the sun, at a speed of around 30 km/second, over 100,000 km per hour. It was reasoned that the Earth would at all times be moving through the aether and producing a detectable "aether wind". At any given point on the Earth's surface, the magnitude and direction of the wind would vary with time of day and season. By analyzing the effective wind at various different times, it should be possible to separate out components due to motion of the Earth relative to the Solar System from any due to the overall motion of that system. The effect of an aether wind on a beam of light would be for the beam to take slightly longer to travel round-trip in the direction parallel to the "wind" than to travel the same round-trip distance at right angles to it.

 

bullet Michelson-Morley Experiment

The Michelson-Morley experiment studies the possible variation of the speed of light due to the motion of the Earth with respect to the proposed luminiferous aether. As mentioned before, the Earth has several combined motions that result in the Earth having relative velocities with respect to different celestial bodies; and as postulated by the theory of the luminiferous aether, the Earth will have a relative velocity with respect to this media. If the speed of light and the speed of the Earth would add as quantities obeying Galileo Galilei transformation, the experiment would detect the variation on the speed of light as related to the direction of motion. Michelson-Morley apparatus is basically an interferometer where a single ray of light is slipped at a semi transparent mirror, M, into two rays moving perpendicular to each other. The two sub rays travel toward two different mirrors, M1 and M2, where they reflect back to the semi transparent mirror crossing it and ending up on the screen D. Since the Earth moves with respect to the Aether with a velocity v, the ray traveling toward mirror M1 will take a different time as the ray traveling to mirror M2. Therefore, at the screen, interference fringes should be observed.

 
The time needs for the ray of light to travel back an for mirror M2 is calculated accordingly with
  1. Ray going to mirror: since the the Earth (with the mirror) is following the ray, classically, the speed of light with respect to this direction is c - v.

  2. Ray returning from the mirror: in this case the semi transparent mirror is moving toward the ray of light which, classically, means that the ray appears to move faster when returning to the semi transparent mirror. Thus, classically, the speed of light with respect to this direction is c + v.

Therefore, the total time needed for this ray to travel back an for is

 

The time needs for the ray of light traveling to the mirror M1 is calculated accordingly with

  1. Ray going to the mirror: this ray needs to travels the distance D at the classical velocity . Classically, the ray of light has a velocity in the direction of motion of the Earth v even before is emitted (just like a ball before being released from a hand). Looking at the diagram on the left, the distance D can be calculated also from the Pythagorean theorem, .

  2. Ray returning from the mirror: The velocity of the ray as well as the distance to travel are the same as for the ray going to the mirror.

Therefore, the time needed for this ray to go back an for to the semi transparent mirror is

Thus, classically, the difference in time for the two rays when arriving to the screen is just the difference between the previous two calculated times. In addition, the instrument is constructed such that the length of the two arms of the interferometer are the same, L1 = L2 = L. Therefore, the time difference is

 

The following link presents a Flash simulation of the M-M experiment

http://galileoandeinstein.physics.virginia.edu/more_stuff/flashlets/mmexpt6.htm

 

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by Luis F. Sez, Ph. D.    Comments and Suggestions: LSaez@dallaswinwin.com