Introduction to special relativity: Difference between revisions

Revision as of 06:59, 5 October 2013

Revision as of 23:28, 20 October 2013

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A [[frame of reference|reference frame]] is simply a selection of what constitutes a stationary object. Once the velocity of a certain object is arbitrarily defined to be zero, the velocity of everything else in the universe can be measured relative to that object.<ref group="Note">There exists a more technical but mathematically convenient description of reference frames. A reference frame may be considered to be an identification of points in space at different times. That is, it is the identification of space points at different times as being the same point. This concept, particularly useful in making the transition to relativistic spacetime, is described in the language of [[affine space]] by VI Arnold in ''Mathematical Methods in Classical Mechanics'', and in the language of [[fibre bundle]]s by [[Roger Penrose]] in ''[[The Road to Reality]]''.</ref>

One oft-used example is the difference in measurements of objects on a train as made by an observer on the train compared to those made by one standing on a nearby platform as it passes.

Consider the seats on the train car in which the passenger observer is sitting.

The distances between these objects and the passenger observer do not change. Therefore, this observer measures all of the seats to be at rest, since he is stationary from his own perspective.

The observer standing on the platform would see exactly the same objects but interpret them very differently. The distances between themself and the seats on the train car are changing, and so they conclude that they are moving forward, as is the whole train. Thus for one observer the seats are at rest, while for the other the seats are moving, and both are correct, since they are using different definitions of "at rest" and "moving". Each observer has a distinct "frame of reference" in which velocities are measured, ''the rest frame of the platform'' and ''the rest frame of the train''&nbsp;– or simply ''the platform frame'' and ''the train frame''.

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==Reference frames and Lorentz transformations: relativity revisited==

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Changes in reference frame, represented by velocity transformations in classical mechanics, are represented by rotations in Minkowski space. These rotations are called [[Lorentz transformation]]s. They are different from the Galilean transformations because of the unique form of the Minkowski metric. The Lorentz transformations are the relativistic equivalent of Galilean transformations. Laws of physics, in order to be relativistically correct, must stay the same under Lorentz transformations. The physical statement that they must be the same in all inertial reference frames remains unchanged, but the mathematical transformation between different reference frames changes. Newton's laws of motion are invariant under Galilean rather than Lorentz transformations, so they are immediately recognisable as non-relativistic laws and must be discarded in relativistic physics. The [[Schrödinger equation]] is also non-relativistic.

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Any object that has mass when at rest (in a given inertial frame of reference), equivalently has ''rest energy'' as can be calculated using Einstein's equation ''E''=''mc''². Rest energy, being a form of energy, is interconvertible with [[Forms of energy|other forms]] of energy. As with any energy transformation, the total amount of energy [[conservation of energy|does not increase or decrease]] in such a process. From this perspective, the amount of matter in the [[universe]] contributes to its total energy.

Similarly, the total of amount of energy of any system also manifests as an equivalent total amount of mass, not limited to the case of the relativistic mass of a moving body. For example, adding 25 [[kilowatt-hours]] (90 [[megajoule|megajoules]]s) of ''any'' form(s) of energy to an object increases its mass by 1 [[microgram]]. If you had a sensitive enough mass [[Weighing scale|balance or scale]], this mass increase could be measured. Our [[Sun]] (or a nuclear bomb) converts [[nuclear potential energy]] to other forms of energy; its total mass doesn't decrease due to that in itself because it still contains the same total energy in different forms, but its mass does decrease when the energy escapes out to its surroundings, largely as [[radiant energy]].

==Applications==

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*[http://www.phys.unsw.edu.au/einsteinlight Einstein Light] An [http://www.sciam.com/article.cfm?chanID=sa004&articleID=0005CFF9-524F-1340-924F83414B7F0000 award]-winning, non-technical introduction (film clips and demonstrations) supported by dozens of pages of further explanations and animations, at levels with or without mathematics.

*[http://www.einstein-online.info/en/elementary/index.html Einstein Online] Introduction to relativity theory, from the Max Planck Institute for Gravitational Physics.

*[http://www.relativitycalculator.com/explaining_relativity_for_laymen.shtml Explaining Relativity for The Laymen ]

===Special relativity explained (using simple or more advanced math)===