astrohysics-theory of relativity

8/2/2019 Astrohysics-Theory of Relativity

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Armando Mateo

Astrophysics-Theory of relativity


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What is time?


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What is Lorentz transformation?

In physics, the Lorentz transformation describes how,according to the theory of special relativity, two observers'varying measurements of space and time can be convertedinto each other's frame of reference.

The Lorentz transformation was the result of attempts by theeponymous Hendrik Lorentzand others to explain observed

properties of light propagating in what was presumed to be theluminiferous aether;


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Its frame of reference is the aether


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Influential person to Albert Einstein

career.

Hendrik Antoon Lorentz(1853-1928) a Dutch physicistand mathematician who describe the movement of objectapproaching the velocity of light in aether using Minkowskispace.

Hermann Minkowski, German mathematician whoelegantly described using a four-dimensional spacetime,which combines the dimension of time with the threedimensions of space.


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Graphical representation Minkowskispace


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What the difference between MinkowskiSpace and Euclidean Space?

Minkowski space has four dimension which includespacetime use in theory of relativity while Euclideanspace has only 3 dimension of space used in

classical mechanics.


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What the difference between Galilean

transformation and Lorentz transformation?

The Galilean transformation is used to transformbetween the coordinates of two coordinate systems inconstant relative motion in Newtonian physics. There is

no limitation of speed up to infinity.

The Lorentz transformation describe the coordinate ofevent in quantum mechanics started by Max Plank and

Albert Einstein that velocity of light is the maximumvelocity and its constant.


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Example of velocity addition in thetransformation

In Galilean velocity addition, the total velocityV of an object moving opposite to thedirection of light is V1 + c.

In Lorentz velocity addition , the total velocity Vof an object moving opposite of the direction oflight is still value of c.

The velocity of light is about 300,000,000meter per second.(Appx) is the speed limitin the universe.


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What is inertial frame of reference?

An inertial reference frameis a space-time coordinatesystem that neither rotates nor accelerates. In real life,such frames of reference are purely theoretical, becausegravitational force (and thus acceleration) exists

everywhere in the known universe. However, they may beapproximated very well in intergalactic space, or to alesser extent within the confines of a coasting spacecraft.

For an observer, the region in space where hisvelocity is constant or zero.


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Diagram of length contraction

Length contraction, according to Hendrik Lorentz, is thephysical phenomenon of a decrease in length detected byan observer in objects that travel at any non-zero velocityrelative to that observer.


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The Lorentz factor


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Diagram of time dilation

Time dilation, according to Hendrik Lorentz, is the physicalphenomenon of a decrease in time detected by an observerin objects that travel at any non-zero velocity relative to thatobserver.


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Postulates of Special Relativity

First Postulate

The speed of light in vacuum is the same to allinertial observers. This postulate has been verified

experimentally.

NOTE: Einstein changes the reference of

Lorentz from aether to speed of light.


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In the late 19th Century, some physicistssuggested that the universe was filled with a

substance known as "aether" whichtransmited Electromagnetic waves. Aetherconstituted an absolute reference frameagainst which speeds could be measured.

Aether had some wonderful properties: it wassufficiently elastic that it could supportelectromagnetic waves, those waves couldinteract with matter, yet it offered no resistance

to bodies passing through it. The results ofvarious experiments, including the Michelson-Morley experiment, suggested that the Earthwas always 'stationary' relative to the Aether -


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Second Postulate

Observation of physical phenomena by more thanone inertial observer must result in agreementbetween the observers as to the nature of reality.

Or, the nature of the universe must not change foran observer if their inertial state changes.

Every physical theory should look the samemathematically to every inertial observer.


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Albert Einstein 14March 1879 18April 1955 atheoretical physicist.He is best known for

his theories ofspecial relativity andgeneral relativity.


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Einstein received the 1921 Nobel Prize inPhysics "for his services to Theoretical Physics,

and especially for his discovery of the law of thephotoelectric effect."


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