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Relativity (Special and General) 2012

Page history last edited by Parker Gardner 9 years, 7 months ago

By Parker G. and Siddhartha J.

 

Einstein’s Special Relativity
Orig
ins of Relativity:

The co
ncept of Relativity itself was not new.  As early as the 16th and 17th centuries, Galileo Galilei formulated the idea of relativity.  Galileo argued that motion in space was relative, depending on what frame of reference one used.  For instance, imagine a situation in which two cars are passing each other on the highway, each at 60mph, one going north and the other going south.  In this case, the people in the northbound car could think of themselves as stationary, and would see the southbound car going at 120mph, their combined speed, and the same holds for the southbound car.  That is, for two objects in motion the speeds of the objects can only be given relative to a reference frame, not absolutely.  Stated more precisely, the reference frame must be an inertial one, that is, the reference frame itself cannot be accelerating.

Michelson-Morley Experiment:

Upon the discovery that light was a wave that traveled at a finite speed, and even through empty space / vacuum, the main question in 19th century physics became: What does light travel through?  It was already well known that other waves needed to propagate through other materials, for instance sound cannot go through vacuum, as it needs to vibrate atoms and molecules to get from one place to another.  Therefore, scientists proposed that light too needed a substance to pass through, and it would be called ether.  Therefore, ether became the theoretical substance that was spread uniformly throughout the universe; although not scientifically observed, the theory was a big hit.

In 1887, Albert Michelson and Edaward Morley decided that they would once and for all prove the existence of the ether.  To do this, they proposed, what would later be called the Michelson-Morley experiment.  In this Experiment, an interferometer was used to split a light beam at a right angle, this would cause one beam of light coming from the laser to bounce of the Beam-splitter and go off at a right angle and bounce of the mirror, while the other beam would

go straight through the splitter and bounce of the mirror straight ahead.  Once they got back to the beam-splitter, they would once again be redirected to the screen at the bottom.  The screen was made so that it would light up in different ways, signifying whether or not the two beams of light got back at the same time.

Michelson who believed in the existence of ether, hypothesized that the two beams would take different amounts of time, with the light bouncing of the mirror opposite to the laser taking longer, as the two beams are moving relative to the ether.  That is, since the earth is rotating (relative to the all pervasive ether), and thereby the interferometer, which is on the earth, is rotating relative to the ether, the light beam that reflects upwards makes goes in a triangle, and the light beam going straight has farther to go one way than the other way.  Therefore, if there was ether, the light beam that got reflected upwards would always be faster than the other.



However, to the dismay of Michelson and Morley, the two light beams took the same time to travel back to the detector, regardless of how many trials they did.  This proved that ether could not exist.  The Michelson-Morley experiment along with Maxwell’s equations on electro-magnetism suggested that light traveled at the same speed, regardless of the relative speed of the observers.  That is, if person A released a light beam, while person B was going away from A at some speed, they would both clock the speed of the beam to be the same c, the speed constant speed of light; this contradicts classical relativity and was just the ingredient Einstein needed to propose his special relativity.


Special Relativity:

The main idea in Einstein’s Special theory of relativity can be stated as follows:

Objects moving at constant velocities follow the same laws of physics that stationary objects follow.  And, the constant speed of light is one of the laws of physics.

Combining the above idea with the Galileo, and Newton’s classical relativity, Einstein came up with a model in which not only space, but time was also not absolute.  That is, different entities clock different times.  In Einstein’s Special relativity, if two identical objects, for example, spaceships, are flying through space, with each going at a relative velocity to the other, two things happen.  For the sake of the example, let us think of one of the ships as A, and the other is B.  The order of assignment does not matter, as the relative motion between the two would be similar regardless.  Now, imagine that you are in spaceship A.  Therefore, you see B going past you in space.  In this case two things will happen in order to keep the speed of light constant for the two ships:

1) Time will slow down for B (from the viewpoint of A) - Time dilation
2) Spaceship B will shrink in size (from the viewpoint of A) - Space contraction

When both of these happen in combination, the speed of a light-beam would appear the same from both ships.

Special Relativity as an equivalence between Space and Time:

In day to day life, we see the world four-dimensionally, three space dimensions, and a time dimension.  That is, we take any place to be our origin, and get an x, y, and z dimension and we take some time to be time 0, then, given any four dimensional vector, (x,y,z,t) we can say exactly what happened there.  However, we think of the space dimensions and the time dimensions as different.  On the other hand, Einstein’s Special Relativity implies that there is no difference between space and time in the following sense:

Just as in a two-dimensional coordinate system, a car that goes 100mi East has motion similar to that of a car that goes 100mi north, which has motion similar to a car that goes 60mi east and 80mi north, as they all traveled 100mi; Einstein argues that an object that travels X-space in Y-time is similar to an object that travels Y-space in X-time.  This has many interesting implications, the most famous of which states that an object nearing the speed of light nears a phase in which time does not move at all.  That is, if an object is travelling at the speed of light, time does not change from its perspective.  This yields the Twin paradox:

If two identical twins are born, and one goes on a trip at a speed close to that of light, c.  When the two meet again, the twin who took the trip would barely age, while the other twin would become old.  In effect, If A is travelling faster than B, then A is time travelling relative to B.

 

General Relativity:

 

In 1907, Einstein began an eight-year search on how to incorporate a relativistic theory of gravity into his special relativity theory of light, space, and time. In succeeding, Einstein described general relativity as follows. General relativity generalizes special relativity and Newton's law of universal gravitation into a single unifying theory of relativity.

            General relativity incorporates space, time and energy into a single fabric of space-time, on which the effects of gravity can be seen as curves and impressions. These curves are created by massive objects, and, in turn, dictate the straight-line motion of these objects, bending there paths of motion along the curves of space time, much like a marble would be bent by a massive object if both were on a trampoline. Paraphrasing the relativist John Archibald Wheeler, space-time tells matter how to move; matter tells space-time how to curve.

             General relativity as an explanation of gravity satisfies a more stringent general principle of relativity than Newtonian gravity at a large scale, mainly that the laws of physics are the same for all observers. This was a very important concept for Einstein in the development of first special relativity, and eventually general relativity. Einstein’s connection between the invariable connections of the laws of physics and the properties of light, time, and space was that the speed of light is a constant, non-varying value and thus a law of physics which cannot be alter if the laws of physics are to be accepted. As aforementioned, this has several wide reaching implications described primarily by special relativity, namely that time and distance is relativity to the frame of reference.

            Specific implications of general relative, as differing from classic models of physics in the universe include gravitational time dilation, gravitational lensing, the gravitational redshift of light, and the gravitational time delay.

            As general relativity combines space and time into a single Cartesian area, the effects of time dilation can be seen  with acceleration across space-time. A good example can be found in this video at 2:40.

http://www.youtube.com/watch?feature=iv&src_vid=G-R8LGy-OVs&v=xvZfx7iwq94&annotation_id=annotation_276544

 

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