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Article ABUT simultaneity

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DEMONSTRATION OF LORENT'S EQUATION AND GALILEO'S EQUATION

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DEMONSTRATION OF LORENT'S EQUATION AND GALILEO'S EQUATION

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Initially we have two overlapped with source systems, then S 'moves with a speed v. if it is much smaller than the speed of light, then the equations of Lorents and Galileo may be considered the same.

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the time dilation can be expanded in a binomial expansion to get the approximate expression:

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What aether is?

Eather is an invisible massless nothing. It is very rarified and highly elastic substance formerly believed to permeate all spaces including the interstices between the particles of matter. Maxwell believed electromagnetic waves, such as light, to be vibration in the aether. It's only physical property is that allows light propagate through.

Why aether was introduced?

If a sound wave travels through air, light waves must travel through a medium as well. As the sound requires air so the light requires the aether to move from a place to another.

When aether was introduced?

When the measure of speed of light became possible, testing the predicted effect of the aether on the speed of light become possible to.

Who?

In 1887 Michelson and Morley conduct an experiment and they needed an experimento presition never had before. The idea was: the earth orbits around the sun at the speed of 30 km/s and it moves inside the  aether so the speed of light have to be different when the earth moves in the same direction of the light in the aether or in a transverse direction, I.E. perpendicularly. Their results were inconsistent with the existence of the aether, but they were consistent with the point of view of Einstein and this is the beginning of modern physics.

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By rotating the spectrometer 90 degrees, one can compare the effect of speed through the putative æther on one of the beams. Then by making measurements six months apart, one can add or subtract the speed of the Earth through the æther. The speed of the Earth in its orbit around the sun is v = 30 km/s. Substituting in the equations above (and using l = 11 m - for an optical spectrometer, it was a seriously large) the phase difference expected would be: Δφ = 2πΔt(c/λ) = 2.3 radians = 0.4 fringes.
But Michelson and Morley never observed that.

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Schematically, a beam of monochromatic light is divided by a beam splitter (a transparent sheet at an angle). The divided beams reach two mirrors, are returned and recombined by respectively transmission and reflection at the beam splitter. Schematically the experiement was: a beam of light (actually continuous) is split when it strikes a transparent plate: part is transmitted, part is reflected. When the two divided beams return to the block, partial reflection and partial transmission also combines them.
Following Galilean/Newtonian Physics, let us suppose that light travels (at c) with respect to a "stationary" medium (called the aether). For our purposes, suppose that it be set up with L1 = L2 and that the whole spectrometer be stationary with respect to the æther. Let's consider a point in the interference pattern at which the phase difference is zero. This is the situation shown at left. Now suppose that it move to the right at speed v with respect to æther. The transit times are no longer equal, but for the horizontal and near verticaldirections are given by:

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WHAT WAS THE MICHELSON-MORLEY EXPERIMENT?

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WHAT WAS THE MICHELSON-MORLEY EXPERIMENT?

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The Michelson-Morley experiment was an attempt to measure the motion of the Earth through the luminous ether. Thought often called the Michelson-Morley experiment, the phrase actually refers to a series of experiment carried out by Albert Michelson in 1881 and then again (with better equipment) at Case Western University in 1887 along with chemist Edward Morley. Although the ultimate result was negative, the experiment key is that it opened the door for an alternative explanation for the strange wave-like behavious of light.

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According to Einstein's, two phenomena that take place in the points P1 and P2 are simultaneous if the light they emit comes at the same time at a point P equidistant from P1 and P2.

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This definition does not always allow to make an absolute judgment on the simultaneity of two events. This is reflected in a concrete example: two firecrackers explode at the same distance from the two observers, one on a train and the other one on the ground. To the observer on the train explosions are not simultaneous: the flash of light coming from the left before than the right. To the observer on the ground explosions are simultaneous: the two flashes of light arriving at the point where is located him at the same instant. Both statements are correct infact the train on which there was an observer moved to the left, so we can understand that the concept of simultaneity depends on the reference system and considered the concept of absolute time has no physical meaning, because the speed of propagation of the light is finite.

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-The Newtonian dynamics appered to have definitively solved the question of describing motion and its causes.
-In classical mechanics speed is not absolute but always relative to a reference frame.
-If a law of mechanics is valid in a reference grame K, it must be valid an all reference frames K' moving with uniform linear motion in relation to K.
-Galileian law for the addition of velocities is also valid.
-Maxwell developed the theory of electromagnetism around 1870.
-In electromagnetism the speed of light in vacuum is constant.
-This is the fundamental postulate of special relativity, called invariance of the speed of light.

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DILATATION: the act of expanding.
CONTRACTION: the act of contracting.
REFERENCE FRAME: a set of coordinate axes in terms of which position or movement may be specified.
INERTIAL FRAME: a reference system in which the Newton's 1st law is valid.
GALILEAN TRANSFORMATION OF COORDINATES: relation between the coordinates of an event as observed from two intertial rederence frames.
MEDIUM: an intervening substance through which something is transmitted or carried on.
ETHER: an all-pervading, infinitely elastic, massless medium.
VACUUM: absence of matter.
SIMULTANEITY: happening at the some time.
ELEMENTARY PARTICLE: any of the subatomic particle that compose matter and energy.
REST FRAME: the coordinate system in which the particle is at rest.
STATIONATY: a time-invariant quantity, such as a constant position or temperature.

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An object will continue to remain at rest unless acted upon by an external unbalanced force.
This is the first law of dynamics; it was understood by Galileo Galilei that described it in 1632 and then it was enunced by Newton in 1687. The law also states that an object will stay in a state of costant velocity, called uniform motion, in the absence of an unbalanced force.
It means if there was no frictional or any other force the body would never stop.

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THE THEORY OF SPECIAL RELATIVITY

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When the position of a body with respect to its surroundings doesn't change with time it is said to be "at rest". If the position of an object is changing, it's "in motion".