Relativity Science Calculator - Einstein's Gravitational Waves .
In the future you will receive a little piece of software to bring up Relativity Science Calculator directly from within this web pageRelativity Science Calculator


Minkowski pseudo-Euclidean spacetime

Einstein Gravitational Waves

"Of all the communities available to us there is not one I would want to devote myself to, except for the society of the true searchers, which has very few living members at any time ... " - Albert Einstein ( 1879 - 1955 )

[ source: Einstein letter to Max Born ( revealed 1971 ), as referenced in "Gravitation", by Misner, et al. ]

Minkowski pseudo-Euclidean spacetime

The Weak Gravity Field


Minkowski pseudo-Euclidean spacetimeSee: Riemann"s Flat ( inertial, non - accelerating ) Spacetime Metric See: Minkowski's Light Sphere in pseudo-Euclidean special relativitySee: Minkowski's Light Sphere in pseudo-Euclidean special relativity


We already know that the Riemann - Christoffel Curvature Tensor in a locally Minkowski, pseudo - Euclidean, coordinate system comprising a geodesic frame, reduces from

Minkowski pseudo-Euclidean spacetime


Minkowski pseudo-Euclidean spacetime

in the curved spacetime of general relativity.

That is,

Minkowski pseudo-Euclidean spacetime

reduces to

Minkowski pseudo-Euclidean spacetime

in a locally Minkowski, pseudo - Euclidean, coordinate system comprising a geodesic ( or Newton inertial ) frame.


Therefore, the Ricci Tensor in a weak gravitational field becomes

Minkowski pseudo-Euclidean spacetime

Final Derivation: The Einstein Gravitational Wave Equation

Minkowski pseudo-Euclidean spacetimeharmonic coordinate system in general relativityMinkowski pseudo-Euclidean spacetimethe geodesic equation

The D'Alembertian Operator

Minkowski pseudo-Euclidean spacetimeSean Carroll's "Lecture Notes on General Relativity"

Chinese scientists find evidence for speed of gravity

Minkowski pseudo-Euclidean spacetime
illustration only

Chinese scientists revealed Wednesday ( 2012-12-27 ) that they have found evidence supporting the hypothesis that gravity travels at the speed of light based on data gleaned from observing Earth tides.

Scientists have been trying to measure the speed of gravity for years through experiments and observations, but few have found valid methods.

By conducting six observations of total and annular solar eclipses, as well as Earth tides, a team headed by Tang Keyun, a researcher with the Institute of Geology and Geophysics under the Chinese Academy of Sciences (CAS), found that the Newtonian Earth tide formula includes a factor related to the propagation of gravity.

"Earth tide" refers to a small change in the Earth's surface caused by the gravity of the moon and sun.

Based on the data, the team, with the participation of the China Earthquake Administration and the University of the CAS, found that gravitational force released from the sun and gravitational force recorded at ground stations on Earth did not travel at the same speed, with the time difference exactly the same as the time it takes for light to travel from the sun to observation stations on Earth.

The scientists admitted that the observation stations are located near oceans, indicating that the influence of ocean tides might have been strong enough to interfere with the results.

Consequently, the team conducted separate observations of Earth tides from two stations in Tibet and Xinjiang, two inland regions that are far away from all four oceans, as well as took measures to filter out other potential disturbances.

By applying the new data to the propagation equation of gravity, the team found that the speed of gravity is about 0.93 to 1.05 times the speed of light with a relative error of about 5 percent, providing the first set of strong evidence showing that gravity travels at the speed of light.

Their findings have been published online in English by German science and technology publishing group Springer.

Printed articles in both Chinese and English will be carried in a January 2013 edition of the Chinese Science Bulletin, according to the CAS Institute of Geology and Geophysics.

Source: Xinhua News Agency:

1993 Nobel Prize Speed Read: Catching Gravity's Waves

Nobel Prize quotation:

For a second time, the Nobel Prize in Physics for 1993 was awarded to the discovery of a burnt - out star remnant known as a pulsar. Awarding the Prize to Russell Hulse and Joseph Taylor not only rewarded their discovery of two pulsars dancing around each other but also acknowledged their discovery of a space laboratory that could test one of Albert Einstein's most important theories.

According to Einstein's general theory of relativity of 1916, the Universe exists in three - dimensions plus time as a fourth dimension. This space - time, as it is commonly known, behaves much like a liquid, being distorted by the presence of massive bodies, such as stars, and forming ripples of gravitational radiation as these bodies move through the cosmos. Finding these predicted ripples in the fabric of space - time proved difficult as it required locating an object large enough and travelling fast enough through space to create gravitational waves that can reach Earth before fading away.

In the same year that Antony Hewish received the 1974 Nobel Prize in Physics for his role in the discovery of a pulsar - the collapsed and superdense corpse of a massive star, known as a neutron star, that is left behind when it dies in a supernova explosion - Joseph Taylor and his student Russell Hulse discovered a pair of pulsars that are close enough together to orbit around each other in space. Since this so - called 'binary pulsar' is moving fast and the two stars are close together, Einstein's theory predicted that they should generate significant amounts of gravitational radiation, which in turn steals energy from the two pulsars, making them spiral slowly towards each other. After four years of meticulous observations Taylor showed that Einstein's theory passed all tests: the two pulsars are not only spiralling towards each other, but they are doing so at almost exactly the rate predicted by the theory.

Hulse and Taylor's observations, although indirect, provided the strongest proof yet for gravitational radiation. Their findings have provided the impetus to develop a series of gravity - wave detectors, which aim to catch gravitational radiation from astronomical phenomena like black holes or two merging neutron stars through more direct means, as their passing waves wash over Earth.

Source: Nobel Prize Speed Read: "Catching Gravity's Waves"

Inflationary Gravitational Waves: First Definitive Proof of the Big Bang

"BICEP2 Collaboration Experiment - Part I: Detection of B - mode POLARIZTION AT DEGREE ANGULAR SCALES", published 17 March, 2014. Then, Minkowski pseudo-Euclidean spacetime "BICEP2 Collaboration Experiment and Three-Year Data Set - Part II", published 4 August, 2014. This is the first direct detection of rippling inflationary gravitational waves at a time 380,000 years after the Big Bang and therefore only 380,000 light-years distance from it. It is reported in journal Nature on March 17, 2014, by Dr. John Kovac, team leader of the BICEP2 ( for Background Imaging of Cosmic Extragalactic Polarization ) Collaboration utilizing the SPT ( South Pole telescope ) facility, Amundsen - Scott South Pole Station, by looking at the CMB ( cosmic microwave background ), the weak radiation afterglow of the Big Bang first discovered and confirmed in 1964 by Arno Penzias and Robert Wilson earning them both the 1978 Nobel Physics Prize. In fact, SPT is basically a giant superconducting thermometer! Theoretical physicist Alan Guth, Massachusetts Institute of Technology, first proposed his theory of "cosmic inflation" in 1979 while at Cornell University as a junior particle physicist who's quoted in journal Nature, "This is a totally new, independent piece of cosmological evidence that the inflationary picture fits together" and "definitely worthy of a Nobel Prize". See also: ; doi:10.1038/nature.2014.14885 in journal Nature. This discovery in cosmology physics furthermore confirms an integral nexus between Einstein's general relativity with the basic model of quantum physics. It further provides definitive empirical proof of the existence of the Big Bang itself which heretofore was only a theoretical singularity first derisively named by English astronomer Fred Hoyle on the BBC radio's 'Third Programme broadcast' on March 28, 1949.

Note: This experimental research project does not prove that Einstein's gravitational waves exist - that was first acknowledged in the Nobel Physics Prize of 1993 by Hulse - Taylor - however this experimental research project provides not only continuing evidence for gravity waves but more importantly, evidence from the time of the Big Bang of the nexus between General Relativity Cosmology and the subatomic realm of Quantum Physics by invoking the "Inflationary Theory" of Alan Guth, M.I.T. mathematical theoretical physicist.


  1. CMB ( Cosmic Microwave Background ) <==> miniscule thermal heat ( afterglow ) radiation energy from the initial Big Bang. It is also, therefore, a signature or fingerprint of the "energy - aftermath" caused by the Big Bang;

  2. Gravitational Waves <==> the compressions and expansions of a gravity ( induced ) energy field caused by, for example, binary pulsars in extremely fast orbital rotations about each other;

  3. CMB + Gravity Waves <==> the wave - like compressions and expansions of a rippling / undulating gravity energy field imprinted upon the CMB as a signature or fingerprint showing the fossilized cosmic history of Big Bang events such as primordial quantum wave - particles where it is here that the ultimate nexus between quantum relativistic physics and general relativity will be finally discovered;

  4. CMB + Inflationary Gravity Waves <==> the same as above except offering a fossilized cosmic history of the Big Bang close to the moment of its occurence;

  5. Space - Time + CMB + Gravity Waves <==> the space - time points are just buoy "way - points" of clocks designated along geodesic gravity lines of force in space as these clocks are slowed and speeded up by rippling / undulating gravity waves shown in the CMB signature fingerprints.

§ References:

  1. "Introduction to Tensor Calculus, Relativity and Cosmology", by D. F. Lawden, Emeritus Professor, University of Aston in Birmingham, U.K., Dover Publications, Inc.

  2. "General Relativity and Gravitational Waves", by J. ( Joseph ) Weber ( 1919 – 2000 ), Professor of Physics, University of Maryland, 2004 Dover Publications, Inc., originally published 1961 by Interscience Publishers ( New York ).

  3. Minkowski pseudo-Euclidean spacetime "General Relativity", by Dr. Valeria Ferrari, Leonardo Gualtieri ( Research Associate ), Dipartimento di Fisica, Sapienza Universita' di Roma. According to Dr. Ferrari, Professor of Theoretical Physics, whose specialty is the study of gravitational waves within the context of Einstein's General Relativity mathematics, "During my scientific career, I have developed several aspects of the theory of gravity that are related to gravitational waves". This paper is a considerably less turgidly dense mathematical presentation of general relativity and specifically 'gravitational waves' than otherwise available in the physics literature.

  4. "Gravitation and Inertia", by Ignazio Ciufolini and John Archibald Wheeler, Princeton Series in Physics, Chapter 3: Tests of Einstein Geometrodynamics, especially 'Section 3.5.1 - Pericenter Advance' for the Hulse and Taylor PSR 1913+16 famous binary pulsar observational experiment.

  5. Minkowski pseudo-Euclidean spacetime "The Discovery of The Binary Pulsar", Nobel Lecture, December 8, 1993, by Russell A. Hulse; and Minkowski pseudo-Euclidean spacetime "Binary Pulsars and Relativistic Gravity", Nobel Lecture, December 8, 1993, Joseph H. Taylor, Jr. Nobel Prize Speed Read: "Catching Gravity's Waves"

  6. relativistic photon rocketship "Photon rockets and gravitational radiation", by Thibault Damour, Institute des Hautes Etudes Scientifiques, and DARC, CNRS - Observatoire de Paris, November 24, 1994, mathematically researches that as a by-product of the outgoing photon exhaust efflux of the photon rocket, gravitational waves are genuinely radiated at some future infinity in complete conformity with general relativity theory based on post-Minkowskian ( i.e., post-special relativity ) spacetime theory.

  7. "Gravitation and Spacetime (Second Edition)", by Hans C. Ohanian and Remo Ruffini ( Nov 17, 1994 ), W.W. Norton & Company, Chapter 5: Gravitational Waves, especially Section 5.4 for Hulse and Taylor's PSR 1913+16 famous binary pulsar observational experiment.

  8. Minkowski pseudo-Euclidean spacetime "Observational evidences for the speed of the gravity based on the Earth tide", by Tang KeYun, HUA ChangCai, Wen Wu, CHI ShunLiang, YOU QinqYu & YU Dan, Chinese Science Bulletin, Theoretical Physics, October 16, 2012.

  9. Minkowski pseudo-Euclidean spacetime "Detecting high - frequency gravitational waves with optically levitated sensors", January 3, 2013, Asimina Arvanitaki, Stanford University, and Andrew A. Geraci, University of Nevada, this being one among the latest attempts to directly observe the existence of gravitational waves first predicted by Einstein's General Relativity.

  10. Minkowski pseudo-Euclidean spacetime "A Massive Pulsar in a Compact Relativistic Binary", Science Mag Online, April 26, 2013, Vol.: 340, Issue: 6131 [ DOI: 10.1126/science.1233232 ], authors: John Antoniadis, Paulo C. C. Freire, Norbert Wex, Thomas M. Tauris, Ryan S. Lynch, Marten H. van Kerkwijk, Michael Kramer, Cees Bassa, Vik S. Dhillon, Thomas Driebe, Jason W. T. Hessels, Victoria M. Kaspi, Vladislav I. Kondratiev, Norbert Langer, Thomas R. Marsh, Maura A. McLaughlin, Timothy T. Pennucci, Scott M. Ransom, Ingrid H. Stairs, Joeri van Leeuwen, Joris P. W. Verbiest, David G. Whelan. This article is otherwise known as "Einstein's famous gravity theory passes toughest test yet" using a naturally occurring cosmic laboratory some 7,000 light years from earth, of a tightly bound, close - binary orbital system comprised of a neutron pulsar PSR J0348+0432 and its companion white dwarf, whereby general relativity ( GR ) accurately describes the mutually inward orbital decay for this close - orbital binary system and hence completely accounts for any close - binary system energy loss which is then transferred into the emission production of space - time gravitational waves to be ultimately detected by ground - based gravitational wave detectors directed at PSR J0348+0432.

    In other words, in this paper optical and radio telescopes strongly confirm GR ( general relativity ) in observations of an extreme gravitational binary system comprised of a most massive neutron pulsar heretofore measured to date with a companion white dwarf, this overall system having twice the mass of the sun with designated nomenclature PSR J0348+0432. The emitted gravitational radiation is already in excellent agreement with Einstein's General Relativity Theory for gravitational waves.

  11. Minkowski pseudo-Euclidean spacetime "Gravitational - Wave Limits From Pulsar Timing Constrain Supermassive Black Hole Evolution", submitted October 17, 2013, authors: R. M. Shannon, V. Ravi, W. A. Coles, G. Hobbs, M. J. Keith, R. N. Manchester, J. S. B. Wyithe, M. Bailes, N. D. R. Bhat, S. Burke-Spolaor, J. Khoo, Y. Levin, S. Osłowski, J. M. Sarkissian, W. van Straten, J. P. W. Verbiest, J-B. Wang, in affiliation with the Parkes Pulsar Timing Array, Australia. They were using the regularity of extremely precised timed signals from millisecond pulsars acting as clocks in space received by the CSIRO Parkes Radio Telescope, to better understand the upper limit of weight gain in binary merging galaxies and their inherent center black holes by studying the limits of emitted gravitational - wave backgrounds ( GWBs ), as "manifested as a red - noise process in pulse arrival time measurements from pulsars".

  12. Minkowski pseudo-Euclidean spacetime "BICEP2 Collaboration Experiment - Part I: Detection of B - mode POLARIZTION AT DEGREE ANGULAR SCALES", published 17 March, 2014.

  13. Minkowski pseudo-Euclidean spacetime "BICEP2 Collaboration Experiment and Three-Year Data Set - Part II", published 4 August, 2014.

Minkowski pseudo-Euclidean spacetime

[ Mail this page to a friend ]

Powered by WebRing.

Minkowski pseudo-Euclidean spacetime Minkowski pseudo-Euclidean spacetimeMinkowski pseudo-Euclidean spacetime
Your ip address is:
This document was last modified on: (none)
Your browser is: CCBot/2.0 (

Minkowski pseudo-Euclidean spacetime

note: for a secure encrypted connection
type 'https' in the url address bar - i.e.,

html sitemap   |   visual sitemap  |  shopping cart sitemap  |  shopping cart