Difference between revisions of "Theory of relativity"

Revision as of 01:26, May 5, 2007

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-Relativity refers to two [[physics]] theories; general relativity (GR) and special relativity (SR), put foward by [[Albert Einstein]]. The Theory of Relativity is a geometrical theory of gravitation, while Special Relativity is a limiting case. Einstein formed two postulates around which the theory is based:
+If you're reading this you are absolutely retarded.
-# ''The [[speed of light]] is constant for all (inertial) observers, regardless of their velocities relative to each other.''
-# ''The laws of physics are obeyed in all reference frames.''
-The theory of relativity was first proposed based on mathematical theory developed by [[Henri Poincaré]] and [[Hendrik Lorentz]]. This theory differs from [[Isaac Newton]]'s theory of gravitation by disposing with the idea of a universal, mutually agreeable scale of time (i.e. a universal clock that all times can refer to) and space (i.e. a universal sheet of "graph paper", which location refers to).  At low speeds (relative to light-speed), the Einstein-Lorentzian relativity equations are equivalent to Newton's formulas.
-The famous equation attributed to Einstein, ''E=mc<sup>2</sup>'', describes the relationship between energy and the rest mass of a body.
-In general terms, relativity predicts that space-time can be curved by massive bodies, so that (for example) near a [[black hole]] the sum of the angles in a triangle is not exactly 180 degrees, time passes more rapidly away from a black hole than near it (for a distant observer) and other apparent violations of [[geometry]] and common sense.
-Relativity is important for massive or fast-moving bodies: at low mass and low speed, it can be accurately approximated by [[classical mechanics]] (such as [[Isaac Newton]]'s laws of motion). At the two extremes, modeling the behavior of electrons requires that relativistic effects be taken into account (the chemically significant phenomenon of [[electron spin]] arises from relativity), and the course light passing through a region containing many massive bodies such as galaxies will be distorted ([[classical mechanics]], in which light travels with infinite speed in straight lines, does not predict this). These are both experimentally confirmed ([[electron spin]] was known before relativity arose, and telescopic observations confirm that galactic clusters distort the paths of the light passing through them).
-General relativity successfully explains the seemingly anomalous precession of Mercury's perihelion.  While other explanations based in Newtonian gravity had been proposed, none were consistent with observation.
-British Historian Paul Johnson declares the turning point in 20th century to have been when fellow Briton Sir [[Arthur Eddington]], an esteemed English astronomer, ventured out on a boat off Africa in 1919 with a local Army unit to observe the bending of starlight around the sun during a total eclipse.   Upon his return to England declared that his observations proven the theory of relativity.  In fact recent analysis of Eddington's work revealed that he was biased in selecting his data, and that overall his data were inconclusive about the theory of relativity. The prediction was later confirmed by more rigorous experiments, such as those performed by the [[Hubble Space Telescope]] {{fact}}.  Lorentz has this to say on the discrepancies between the empirical eclipse data and Einstein's predictions.
-::''It indeed seems that the discrepancies may be ascribed to faults in observations, which supposition is supported by the fact that the observations at Prince's Island, which, it is true, did not turn out quite as well as those mentioned above, gave the result, of 1.64, somewhat lower than Einstein's figure.''<ref>http://ia331314.us.archive.org/2/items/theeinsteintheor11335gut/11335-h/11335-h.htm</ref>
-The prediction that light is bent by gravity is predicted both by Newtonian physics and relativity, but relativity predicts a larger deflection.
-==Special relativity==
-Special relativity is the limiting case of General relativity where all gravitational fields are weak. It is based on two postulates; one, that the laws of physics are identical to all [[inertial observers]], and two, that the [[speed of light]] ''in vacuo'' is a universal constant.
-===Time dilation===
-[[Image:Light cone.png|right|thumb|Light-cone diagram]]
-One important consequence of SR's postulates is that an observer in one reference frame will observe a clock in another frame to be "ticking" more slowly than in the observer's own frame. This can be proven mathematically using basic geometry.
-The length of an event <math>t</math>, as seen by a (relative) stationary observer observing an event is given by:
-<math> t = \frac{t_{0}} {\sqrt{1 - \frac{v^{2}}{c^{2}}}}</math>
-Where
-:<math>t_0</math> is the "proper time" or the length of the event in the observed frame of reference.
-:<math>v</math> is the relative velocity between the reference frames.
-:<math>c</math> is the speed of light (3x10<sup>8</sup> ms<sup>-1</sup>).
-Evidence for time dilation was discovered by studying [[muon decay]]. [[Muons]] are [[subatomic]] [[particles]] with a very short [[halflife]] (1.53 microseconds at rest) and a very fast speed (0.994c). By putting muon detectors at the top (D<sub>1</sub>) and bottom (D<sub>2</sub>) of a mountain with a separation of 1900m, scientists could measure accurately the proportion of muons reaching the second detector in comparison to the first. The proportion found was different to the proportion that was calculated without taking into account relativistic effects.
-Using the equation for exponential decay, they could use this proportion to calculate the time taken for the muons to decay, relative to the muon. Then, using the time dilation equation they could then work out the dilated time. The dilated time showed a good correlation with the time it took the muons to reach the second sensor, thereby proving the theory.
-The time taken for a muon to travel from D<sub>1</sub> to D<sub>2</sub> as measured by a stationary observer is:
-<math> t = \frac{s}{v} = \frac{1900}{0.994\times(3\times10^{8})} = 6.37\mu\textrm{s}  </math>
-The fraction of muons arriving at D<sub>2</sub> in comparison to D<sub>1</sub> was 0.732. (Given by <math> \frac{N}{N_0} = 0.732 </math>)
-Since (from the equation for exponential decay) <math> \frac{N}{N_{0}} =  e^{-\lambda t_{0}} </math> then
-<math> t_{0} = \frac {ln(0.732)}{ln (0.2)} \times 1.53\times 10^{-6} = 0.689\mu\textrm{s}</math>
-This gives the time for the proportion of decay to occur for an observer who is stationary, relative to the muon.
-Putting this into the time dilation equation gives:
-<math> t = \frac{t_{0}}{\sqrt{1 - \frac{v^{2}}{c^{2}}}} = \frac{0.689 \times{10^{-6}}}{\sqrt{1 - \frac{0.994^{2}}{1^{2}}}} = 6.3\times 10^{-6}\textrm{s}</math>
-This is in good agreement with the value calculated above, thereby providing evidence to support time dilation.
-===Length contraction===
-When two inertial reference frames move past each other in a straight line with constant relative velocity, an observer in one reference frame would observe a metre rule in the other frame to be shorter.
-The length, <math>l</math>, of an object as seen by a (relative) stationary observer is given by:
-<math> l = l_{0} \sqrt{1- \frac{v^{2}}{c^{2}}}</math>
-Where
-:<math>l_0</math> is the "proper length" or the length of the object in the observed frame of reference.
-:<math>v</math> is the relative velocity between the reference frames.
-:<math>c</math> is the speed of light (3x10<sup>8</sup> ms<sup>-1</sup>).
-===Mass increase===
-We also see that as a body moves with increasing velocity its [[mass]] also increases.
-The mass, <math>m</math>, of an object as detected by a (relative) stationary observer is given by:
-<math> m = \frac{m_{0}} {\sqrt{1 - \frac{v^{2}}{c^{2}}}}</math>
-Where
-:<math>m_0</math> is the "rest mass" or the mass of the object when it is at rest.
-:<math>v</math> is the relative velocity of the object.
-:<math>c</math> is the speed of light (3x10<sup>8</sup> ms<sup>-1</sup>).
-Since speed is relative, it follows that two observers in different inertial reference frames may disagree on the mass and kinetic energy of a body. Since all inertial reference frames are treated on an equal footing, it follows that mass and energy are interchangeable.
-==General Relativity==
-===Einstein field equations===
-The Einstein field equations is
-:<math> G_{uv} = 8\pi\, T_{uv} </math>
-where ''G<sub>uv</sub>'' is the [[Einstein curvature tensor]], and ''T<sub>uv</sub>'' is the [[stress-energy tensor]], ''G<sub>uv</sub>'' and ''T<sub>uv</sub>'' are both rank 2 symmetric tensors.  The Einstein field equations is a system of [[partial differential equations]] that relates the curvature of space to the mass occupying the space.
-==Evidence for Relativity==
-No particle accelerator built since the 1950s would work unless the mass increase predicted by special relativity not only occurred, but occurred to the precise degree predicted by the theory.{{fact}} In 1972, scientists flew extremely accurate clocks around the world in both directions on commercial airlines, and were directly able to observe the relativistic "twin paradox" the eastbound clock gained 273 ns and the westbound clock lost 59 ns, matching the predictions of general relativity to within experimental accuracy <ref>Hafele-Keating Experiment [http://www.answers.com/topic/hafele-keating-experiment]</ref> <ref>as described in [http://math.ucr.edu/home/baez/physics/Relativity/SR/experiments.html What is the experimental basis of Special Relativity?], a personal web page, which cites Haefele and Keating (1972), ''Science'' Vol. 177 pp 166-170 as its source</ref> <ref>Sullivan, Walter (1972), "Relativity Theory Awaits Affirmation",  September 23, 1972, p. 61. Note: Article refers to a different experiment, which Sullivan discusses, saying that if successful it would be "the second time within a year" that relativity had been confirmed, then proceeds to discuss Hafele[sic] and Keating's experiment as the first.</ref>
-Furthermore, relativity has been proven to be vital to make the [[Global Positioning System]] ([[GPS]]) function properly <ref>How Relativity is vital to GPS [http://www.astronomy.ohio-state.edu/~pogge/Ast162/Unit5/gps.html]</ref>.
-==Pending research==
-Today some physicists are working on a [[quantum theory of gravity]] (the "theory of everything"), such as [[string theory]] and [[loop quantum gravity]].  Critics increasingly point out that [[string theory]] and [[loop quantum gravity]] are largely untestable and unfalsifiable, and thus potentially unscientific under the principles of science advanced by [[Karl Popper]].
-==Government Support for Relativistic research==
-The Theory of Relativity enjoys a disproportionate share of federal funding of physics research today,<ref>The Democratic Congress insisted on the $250 million LIGO project despite substantial criticism by scientists that it was wasting scarce research dollars.  John Travis, "LIGO: a $ 250 million gamble; Laser Interferometer Gravitational-Wave Observatory; includes related article," ''Science'' p. 612 (Apr. 30, 1993).  "Adding to the acrimony is LIGO's $ 250 million price tag, which some hold responsible for NSF's recent funding woes."  ''Id.''</ref> much of it unsuccessful.  The $365 million dollar LIGO project, for example, has failed to detect the gravity waves predicted by relativity.<ref>http://www.npr.org/programs/atc/features/2002/sept/gravitywaves/index.html</ref>  However, more than twenty years of observing the [[pulsar]] pair PSR 1913+16 have shown its orbital period to be dropping at exactly the rate expected due to loss of orbital energy by gravitational radiation <ref>http://nobelprize.org/nobel_prizes/physics/laureates/1993/press.html</ref>, resulting in the 1993 Nobel Prize for physics being awarded to the discoverers of the pulsar pair, Joseph Taylor and Russell Hulse.
-There is a correlation between enthusiasm for the theory of relativity and political views, and there is an unmistakable effort to censor or ostracize criticism of relativity.<ref>Although the [[Examples of Bias in Wikipedia|liberally biased Wikipedia]] contains lengthy criticisms of the subjects of many entries, and even though publications like ''The Economist'' recognize the lack of scientific satisfaction in the theory (see, e.g., "Weighing the Universe," The Economist (Jan. 25, 2007)), Wikipedia's entry on [http://en.wikipedia.org/wiki/Theory_of_Relativity Theory of Relativity] omits one word of criticism.</ref>  Physicist [[Robert Dicke]] of Princeton University was a prominent critic<ref>http://www.time.com/time/magazine/article/0,9171,943324,00.html</ref> of the theory of relativity and that may have hurt him professionally,<ref>Despite being one of the most accomplished physicists in the 20th century, Dicke was never given a Nobel Prize.</ref> even though his theory "has enjoyed a renaissance in connection with theories of higher dimensional space-time."  The full quote:
-:"Initially a popular alternative to General Relativity, the Brans-Dicke theory lost favor as it became clear that omega must be very large-an artificial requirement in some views. Nevertheless, the theory has remained a paradigm for the introduction of scalar fields into gravitational theory, and as such has enjoyed a renaissance in connection with theories of higher dimensional space-time."<ref>http://nedwww.ipac.caltech.edu/level5/Glossary/Essay_bekenstein.html</ref>
-== References ==
-<references/>
-[[Category:Physics]]
-==External Links ==
-:[http://ia331314.us.archive.org/2/items/theeinsteintheor11335gut/11335-h/11335-h.htm The Einstein Theory of Relativity, by H.A. Lorentz.]

Difference between revisions of "Theory of relativity"

Revision as of 01:26, May 5, 2007

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