Essay:Rebuttal to Counterexamples to Relativity
This is intended as an article rebutting the points in the Counterexamples to Relativity article. That article's talk page has proven to be less than satisfactory for this purpose, because it gets archived, and much of its material has degenerated into personal disputes. We believe that the two sides of the issue are better handled in two articles—this one and Counterexamples to Relativity, rather than a talk page.
Unlike most essay pages, anyone is welcome to contribute. We ask that you abide by the usual guidelines—do not remove nonvandal, nonparody, nonlibelous material without discussing it first on the talk page, or explaining afterthefact for serious problems.
 Computer simulations based on the theory of relativity predict far more black holes than are observed.
 The first cited article says absolutely nothing about the number of black holes, modeled or observed. It is about a discrepancy between computer models predicting the masses of black holes at the centers of galaxies and the observed masses. The article suggests a heretoforeunmodeled mechanism whereby galaxy evolution would cause less mass to go into the black holes. The article in no way suggests that black holes don't exist.
 REPLY: Are you denying that the theory of relativity predicts far more black holes than are observed?
 The issue of computer simulations' prediction of the expected number of black holes is a matter of cosmology and galactic evolution, not relativity itself. Kepler's laws of motion would be true even if there happened to be no planets in the universe. Relativity makes no predictions about the number of black holes we should expect to find. (When Einstein formulated the theory, he expected that number to be zero.) The Einstein field equations simply show that such things are theoretically possible.
 REPLY: Are you denying that the theory of relativity predicts far more black holes than are observed?
 The second cited article, from National Geographic, November 6, 2014, is about whether a certain object speeding past Sagittarius A* is a star or merely a gas cloud, concluding that it is a star. No scientist doubts that the thing that this object is speeding past, Sagittarius A*, is a black hole. The assertion "it is doubtful whether black holes even exist" is totally unsupported by the cited article, or any other article that we know of.
 The first cited article says absolutely nothing about the number of black holes, modeled or observed. It is about a discrepancy between computer models predicting the masses of black holes at the centers of galaxies and the observed masses. The article suggests a heretoforeunmodeled mechanism whereby galaxy evolution would cause less mass to go into the black holes. The article in no way suggests that black holes don't exist.
 Quasars are disappearing, contrary to the theory of relativity.
 Relativity does not predict quasars; relativity was formulated in 1905, and quasars weren't discovered until the 1950s. The word "relativity" does not occur anywhere in the cited article.
 While quasars are associated with black holes, no serious scientist believes that black holes don't exist or that relativity is wrong.
 That astronomers have stopped looking for this phenomenon, after finding more than 10 examples of it, may or may not have been a wise decision regarding the allocation of telescope and satellite time.
 The orbital radius of the Moon's orbit is increasing, contrary to what Relativity predicts.
 This could be a counterexample to both GR and Newtonian gravity—in both, the radius is defined in terms of conserved quantities.
 The objection has been raised that this would still be a counterexample to Relativity.
 Yes, if it were actually true that the Moon's orbit is undergoing some kind of anomalous perturbation, it would indeed be a disproof of Relativity, Newtonian mechanics, and, in fact, all of physics since Galileo.
 Actually, the average radius of the Moon's orbit is in fact increasing. By 38mm a year. This was first predicted in the late 19th century and actually measured since at least the early 1970s and more accurately thereafter thanks to the mirrors left for that purpose by the Apollo astronauts. The reason for this is wellknown and simple enough to be explained on scienceoriented TV shows from time to time. To put it simply: the Moon pulls on the Earth, causing the tides and slowing down its rotation slightly, lengthening it's day by 2 milliseconds every 100 years. Reciprocally, the Earth pulls on the Moon and accelerates it slightly thus increasing the height of its orbit and energy is conserved. For a more complete explanation see.^{[1]} This behavior, predicted over 100 years ago, observed and measured, is in no way "anomalous" and relativity, general, special or otherwise doesn't really concern itself with tidal mechanics so on that point at least physics, Galilean, Newtonian and Einsteinian, are quite safe for now.
 Yes, if it were actually true that the Moon's orbit is undergoing some kind of anomalous perturbation, it would indeed be a disproof of Relativity, Newtonian mechanics, and, in fact, all of physics since Galileo.
 The objection has been raised that this would still be a counterexample to Relativity.
 This could be a counterexample to both GR and Newtonian gravity—in both, the radius is defined in terms of conserved quantities.
 The Pioneer anomaly.
 The "Pioneer anomaly" is the deviation in the motion of the Pioneer 10 and Pioneer 11 spacecraft from their predicted motion, at the distance of Saturn and beyond. It should be noted that the anomaly is about 1000 times greater than the difference between the classical Newtonian prediction and the prediction of relativity, so this is not a problem with relativity per se; it is more general than that.
 Calculating the force caused by heat (that is, miniscule amounts of infrared radiation) from the radioactive power source was one of the first effects that was examined. The anomaly arose when this and other known effects could not fully explain the deviation.
 The problem is believed to have been solved by taking into account the reflection of the radiation from the power source off of the back of the antenna dish.^{[2]} The solution is sometimes described as an application of "Phong shading", a technique of computer graphics that is now considered imprecise. But Phong shading itself is not what is important. The "ray tracing" computer graphics technique that underlies Phong shading was what inspired the scientists to take reflection into account.^{[3]}
The most detailed analysis to date, by some of the original investigators, explicitly looks at two methods of estimating thermal forces, then states "We find no statistically significant difference between the two estimates and conclude that once the thermal recoil force is properly accounted for, no anomalous acceleration remains."^{[4]}
 the solar flattening is ... too small to agree with that predicted from its surface rotation.
 This observation is interesting, but the predictions of oblateness come from analysis of fluid mechanics; relativity is not involved, and the cited paper makes no mention of relativity.
 We expect a very large rotating body to show oblateness according to wellknown principles involving centrifugal force. This is particularly easy to observe with Jupiter, though the other planets, including Earth, show it too. Scientists do not know why the Sun exhibits nearly zero oblateness, but relativity is not believed to be the cause.
 Now it happens that there is a connection between solar oblateness and the calculation of the precession of the perihelion of Mercury, and that involves General Relativity. When checking the observed precession against the effect predicted by Relativity, one needs to subtract the effect of solar oblateness, along with the other effects, such as equinoctial precession and the gravitational effects of other planets. The effect of solar oblateness is a mere .0254 arcseconds per century, insignificant in comparison with precession (about 5500) and other planets' gravity (about 550). The figure of .0254 was calculated based on what fluid dynamics predicted, and was subtracted in the figures quoted below in item #9. When that tiny effect is removed, the error bars still overlap that for the GR prediction.
 Quantum entanglement near the event horizon of a black hole ....
 It is well known that quantum gravity (that is, the "Theory of Everything") is an unsolved problem, and it is the subject of much discussion in the physics community. The whole topic of string theory, for example, revolves around this. Among the places where General Relativity and Quantum Mechanics collide most notoriously is within the Planck length of a black hole's event horizon. Among the issues involved is the notion of "quantum loss of information", that was the subject of a famous bet among Stephen Hawking, Kip Thorne, and John Preskill. (Hawking and Thorne lost.) Basically, physicists do not know just what happens within quantummechanical distances (the Planck length) of a black hole. But no one doubts the behavior of black holes at reasonable distances, or, for that matter, General Relativity at reasonable distances.
 The speed of light in a vacuum is slower than expected
 It is unfortunate that, whenever a sensationalheadlinehungry writer writes anything relating to the propagation of light, they are tempted to scream something along the lines of "Einstein proved wrong." Such sensationalist headlines can be seen in both the popular press and here at Conservapedia.
 But relativity never said anything about vacuum polarization.
 The factor "c" appearing in equations of relativity (E=mc^2, the Lorentz factor, etc.) is the calibration constant for space vs. time. While it was perceived as the "speed of light" back in 1905, that depended on the classical theory of light, from Faraday, Maxwell, et al., at that time. Under the classical theory, Maxwell's equations were considered to be exactly correct, and light was considered to travel at exactly the speed indicated by those equations, which speed is denoted "c". The speed "c" would be better described as "that speed that all observers, even those in relative motion, will consider to be the same." The experimental basis for relativity (MichelsonMorley experiment) was that light obeyed that property. That, plus the fact that "c" appears in Maxwell's equations in a way that makes it independent of an observer's state of motion, made it clear that "c" was in fact the speed of light. But that depended on the belief that Maxwell's equations were exactly correct. But that was before Quantum Mechanics and gauge interactions. Under Quantum Mechanics, the propagation of light is determined by the behavior of photons, not by Maxwell's field equations. Of course the two results are almost identical, as is required by the Correspondence Principle. But, under the modern "Standard Model" of Quantum Electrodynamics, photons can interact with the vacuum, due to "vacuum polarization", leading to extremely tiny higherorder corrections to the equations governing the behavior of photons. This can cause photons to travel at a speed slower than "c".
 Now the situation is made more complex by the fact that models of supernova behavior indicate that the light is emitted after the neutrinos, because the neutrinos are emitted at the instant of the core collapse, and the light must wait until the effect of the collapse reaches the surface. After taking that into account, the cited article says that the extra delay for supernova SN1987A was 4.7 hours. That discrepancy is only 53 parts per trillion, and hence can only be observed in light from very distant supernovas.
 Calculating the speed of the neutrinos is interesting, because the observation is that light traveled slower than the neutrinos, even though neutrinos have nonzero mass. Since neutrinos do not participate in the electromagnetic interaction, they are not subject to the same vacuum polarization as photons. Their retardation comes only from their mass and the normal equations of relativity.
 Taking the mass of an electron neutrino as 0.25 eV (using the usual E=mc^2 formula that all scientists use for this), a neutrino would have to have a kinetic energy of about 0.025 MeV to experience a retardation of 53 parts per trillion. Since the energy of astronomical neutrinos is generally believed to be in the range of 0.5 to 20 MeV (it's really hard to measure) the expected retardation of the neutrinos from SN1987A is much less than that of the light.
 It's interesting that the issue of whether neutrinos travel faster than light actually did come up in another round sensationalist headlinegrabbing articles, from an experiment at Gran Sasso, in the popular press and here at Conservapedia. The first headline was that neutrinos traveled faster than light, a claim retracted after a cable was fixed, but then reported here that someone (erroneously) had said they had traveled at exactly the same speed as light, which also violates relativity because neutrinos have nonzero mass. In any case, that discrepancy would have been several orders of magnitude too small to measure in the Gran Sasso experiment, and the discrepancy from vacuum polarization several orders of magnitude smaller still.
 Celestial signals defy Einstein.
 It shouldn't be surprising that, when Einstein died nearly 60 years ago, he didn't know everything that there is to know about spacetime. Newton didn't know everything there is to know about calculus (Hilbert spaces) or classical mechanics (Lissajous orbits), and Bohr and Schrödinger didn't know everything there is to know about Quantum mechanics (entanglement). What Einstein knew, at the time, about spacetime was how to give a precisely relativistically correct formula for how matter and energy (and momentum and stress) give curvature to spacetime, which in turn gives rise to gravity. These equations have been confirmed, with great accuracy, repeatedly.
 Einstein's equations are known to work for "ordinary" interactions at the planetary and galactic level, but don't work at the quantum level, and may not be fully correct at the deep cosmic level. The cited article says "Every object there is, from a planet orbiting the sun to a rocket coasting to the moon or a pencil dropped carelessly on the floor, follows its [spacetime's] imperceptible contours." This is a confirmation of what Einstein said. The article says that there may be more subtlety to spacetime than was previously known. Of course this has been hinted at for some time with recent developments in cosmology. "Breaking relativity" is an unfortunate choice of subtitle.
 Relativity breaks down at high energies.
 This is interesting. We look forward to seeing whether this plays out the same way that the supraluminal neutrinos did. Until then, note that the discrepancy, 33 picoradians, is such that, if you were to shine a laser beam at the Sun, with that amount of angular error, it would miss its target by about 5 meters. We hope the author will explain how he measured an angle that precisely.
 Subatomic particles have a speed observed to be faster than the speed of light, which contradicts a fundamental assumption of Relativity. The Italian lab that "shocked the scientific world" has announced more precise results, confirming their previous announcement.
 This is an interesting observation. The world's best scientific minds are looking into it. That relativity is incorrect is not being taken seriously as a possible explanation.
 Update: The problem seems to have been caused by a faulty cable connection between a computer and a GPS unit. When the connection was repaired, the travel time increased by 60 nanoseconds, which had been the amount of the anomaly.^{[6]}^{[7]} The claims of fasterthanlight neutrinos have now been refuted very thoroughly.^{[8]}^{[9]}
 The objection has been raised that a recent news report from the BBC ("now we are 100% sure that the speed of light is the speed of neutrinos") is also contradictory, since neutrinos have mass and are therefore forbidden by relativity to travel at exactly the speed of light. Since the neutrino energies were 17GeV, and the current estimate for the neutrino mass is about 0.25eV, the deviation from the speed of light would be about 1 part in 10^{22}. This means that the neutrinos would arrive at the detector about .26x10^{−24} seconds (.26 yoctoseconds) later than the speed of light itself. This is one quarter of a billionth of a femtosecond, or about .26x10^{−15} of a nanosecond. The accuracy of the GPS units and cesium clocks used in the measurement is greater than a nanosecond, so the discrepancy cannot possibly be detected. It is unfortunate that the claim "the speed of light is the speed of neutrinos" was taken so literally.
 A "counterrebuttal" has been made: The politicized rush to rehabilitate the Theory of Relativity was far from convincing, and the "resolution" was a clear statement that is flatly contrary to the Theory. Just what statement is being referred to as the "resolution" is not clear, but our best guess is that it is the statement by Sandro Centro, quoted by Jason Palmer in the cited BBC article. As noted above, that statement is in error by about 15 orders of magnitude less than the resolution of the measurement. None of the assertions of relativity denies that anyone could ever make a statement that is not precisely correct.
 Anomalies in the locations of spacecraft that have flown by Earth ("flybys").
 This may be another case of the Pioneer anomaly, or it may be something else. However, it is very unlikely that it shows that relativity is wrong and Newtonian mechanics is correct. Saying that, every time someone finds some phenomenon that is puzzling, that shows that relativity is wrong, is not a convincing way to do science. The cited paper is about unexpected behavior of some spacecraft as they use "gravity assists" in nearEarth flybys. The hypothesized causes involve errors in the mathematical models to calculate such effects as relativistic effects (the detailed calculation of them, not the question of whether they exist), tidal effects, Earth radiation pressure, or atmospheric drag. The paper suggests that most of those can be ruled out, though there could be roundoff and integration errors, or errors in the spherical harmonic representation of Earth's gravity field.
 Spiral galaxies confound Relativity, and unseen "dark matter" has been invented to try to retrofit observations to the theory.
 Correct me if I'm wrong, but wasn't it due to the acceleration of various parts of galaxies that accelerated funny that led to dark matter (based on simple Newtonian dynamics)?
 The acceleration in the expansion of the universe confounds Relativity, and unseen "dark energy" has been invented to try to retrofit observations to the theory.
 Relativity does not "forbid" or "permit" any particular expansion rate. The standard equations of relativity are silent on the issue of expansion, or dark matter, or dark energy. The equations were later "tweaked" with a "cosmological constant", to allow for a static universe, which was part of conventional wisdom at the time. The tweaking was abandoned when the universe was found to be expanding, much as the NewcombHall tweaking of the gravity equations was found to be wrong. The cited Livescience article is not about relativity; no sensible scientist denies relativity. In fact, neither the word "relativity" nor "Einstein" appears anywhere in the article.
 This is the dark energy/cosmological constant argument. The cosmological constant was added by Einstein after he discovered that his field equations () predicted that the universe was expanding, contradicting his firm philosophical belief in a static universe. So he inserted to the LHS so that it would predict a static universe. A few years later, Hubble showed the universe to be expanding, and Einstein called the cosmological constant the worst mistake of his career. So, it sort of had a bad reputation, and people didn't want to seriously consider it, until recent observations have shown the universe's expansion to be accelerating forced them to do so. It could have had a very different history. Einstein could have had that term in the EFE's from the start, and pointed out that it would determine if the universe's expansion was accelerating (or not expanding at all!) and it would take further observation to determine its value.
 Increasingly precise measurements of the advance of the perihelion of Mercury show a shift greater than predicted by Relativity, well beyond the margin of error.
 A footnote goes on to say that "In a complicated or contrived series of calculations that most physics majors cannot duplicate even after learning them, the theory of general relativity's fundamental formula, , was conformed to match Mercury's thenobserved precession of 5600.0 arcseconds per century. Subsequently, however, more sophisticated technology has measured a different value of this precession (5599.7 arcseconds per century, with a margin of error of only 0.01) ..."
 Considering only the anomalous precession, that is, the precession that remains after all known other factors (other planets and asteroids, solar oblateness) have been accounted for, general relativity predicts 42.98 ±0.04 arcseconds per century. Some observed values are:
 43.11 ± 0.21 (Shapiro et al., 1976)
 42.92 ± 0.20 (Anderson et al., 1987)
 42.94 ± 0.20 (Anderson et al., 1991)
 43.13 ± 0.14 (Anderson et al., 1992)
 Source: Pijpers 2008
 These error bars, and that of the relativity formula, all overlap.
 The formula for mechanics under general relativity is complicated, but it is not contrived or conformed. "Conformed" suggests that it was somehow adjusted or "tweaked" to match the 42.98 figure. The formula is
 To begin to explain the formula, Newton's law of gravity, combining F = ma and , is
 In Einstein's equation, is the "stressenergy tensor", and gives the density of the Sun, taking the place of . is the "Einstein curvature tensor", and says how spacetime curves to create an apparent gravitational acceleration.
 There is nothing to tweak to get a value of 42.98 arcseconds. 8 is 8. is . K is Newton's constant of gravitation in both formulas.

 The above discussion notwithstanding, more sophisticated technology has measured a precession of 5599.7 arcseconds per century, with a margin of error of only 0.01, which disproves the prediction of the Theory of Relativity. Notice how publication of data stopped two decades ago when the observations diverged from the theory.Andy Schlafly 14:50, 14 April 2012 (EDT)
 Measurements of planetary motion are now calculated relative to the "International Celestial Reference Frame" (ICFR), replacing the older, and much less accurate "equinoctial" frame. The older measurements got a value of about 5600 arcseconds/century for the precession of Mercury, nearly all of which (5025 arcseconds) was because of the rotation of the "equinoctial" frame. The ICFR frame removes that source of uncertainty, and, with the very accurate radar measurements conducted by NASA between 1987 and 1997,^{[10]} gets a value of 574.10±0.65 arcseconds observed, in good agreement with the predicted 574.64±0.69 value.
 The ICFR is described in this document, dated 2003.
 REPLY: The year 1997 was nearly 20 years ago, and the observed data based on increasingly sophisticated technology was diverging from relativity's predictions even then. Recent data on this is not published because it would further disprove relativity and embarrass relativists who cling to the theory.

 The cited JurgensRojasSladeStandishChandler paper was published in April 1998, so it should come as no surprise that their data came to an end in 1997. They probably decided that, after collecting data for 10 years, it was time to publish. This is common in the scientific community. Galileo's experiment involving cannonballs and the Leaning Tower of Pisa is no longer being conducted. The SternGerlach experiment (just to pick one random example) was conducted only a small number of times before being published. People don't continue to conduct it to see whether spin quantization of Silver atoms still occurs.

 More recent Mercury data, particularly from the MESSENGER space probe, have provided positional data vastly better than anything Leverrier could have dreamed of. (In fact, Because of the many interplanetary spacecraft of the last few decades, we now have a huge amount of incredibly accurate data on a large number of bodies in the Solar System.) Perhaps Andy believes that the scientific community has been remiss in not continuing to analyze these Mercury data to the present day, presumably looking for evidence of whether relativity is true or false.

 Perhaps Andy could provide his own ideas about why, other than relativity, the precession occurs. This would not just be a matter of quibbling over 42.98 and 42.99, but of explaining the discrepancy between 42.99 and zero. This point was brought up on the Community Portal in December, with no reply forthcoming.

 Of course, even absent an alternative theory, showing a discrepancy between observation and theory would be interesting.

 Now a possible approach, if one believes that the data are inconsistent with relativity, would be to bring the subject up in the many internet forums devoted to physics. One might be able to find out what further analyses are being done, suggest new analyses, or find out how to get the data to make one's own analysis.

 Getting to the specific points of the note above, we are not aware of any evidence that the data were diverging from the theory back in 1997; perhaps Andy could provide supporting data. We see no evidence that the data exist but have not been published, and we see no evidence that any such lack of publication arises because it would embarrass anyone. Seeing discussion of these points in an internet physics forum might help clear these matters up.

 It's one thing to speculate on science; it's quite another to speculate on the motives of scientists, particularly the idea that scientists are embarrassed by their knowledge that relativity is wrong, and that they are covering up this embarrassment as part of some political agenda.
 REPLY: The relativists' silence in the journals about increasingly precise measurements of the advance of the perihelion of Mercury is akin to the famous story of the dog that didn't bark, which is itself compelling proof.
 You can't just invoke the Sherlock Holmes Silver Blaze story to support any claim you wish to make. In that story, Holmes knew that the guilty person had to have been in a certain house at a certain time. The dog would have barked if that person had been a stranger, because dogs bark at strangers. Therefore, the villain was in his own house. There was a specific and credible chain of logic from the nonbarking dog to the identification of the guilty party.
 REPLY: The relativists' silence in the journals about increasingly precise measurements of the advance of the perihelion of Mercury is akin to the famous story of the dog that didn't bark, which is itself compelling proof.
 It's one thing to speculate on science; it's quite another to speculate on the motives of scientists, particularly the idea that scientists are embarrassed by their knowledge that relativity is wrong, and that they are covering up this embarrassment as part of some political agenda.

 In the perihelion case, there is abundant orbital data (undoubtedly gigabytes of it) for the various planets and moons. Some of it was in the Jurgens et al paper noted above, and other data was analyzed in the Pijpers paper. That paper, by the way, says "The value of the gravitational quadrupole moment (28) when combined with planetary ranging data for the precession of the orbit of Mercury yields a value [...] which is consistent with GR ..."

 There is actually a very simple explanation for the scientific community's silence on this matter, a deduction of which Mr. Holmes would approve: The reason that no one is publishing data or analyses that claim to refute relativity is that such claim would be false, and that the existing analyses, using exquisitely accurate spacecraft data, are correct.
 REPLY: The supposed precession of Mercury is based on nonrepeatable observations as well as observations made by individuals with vested interests that the theories of relativity remain true. The error bars of various predictions could have been shifted by backfiguring to what would move them the closest in the future to the error range supposed to accompany the theoretical values. The foolishness around Global Warming theories show us that such a step is not only possible, but probable due to the observed vanity of scientists as well as to the falsification of the 1919 measurements made in hopes of rectifying the absence of a concrete example of the theories nearly two decades after their first proposal by Henri Poincaré.

 Regarding which, even the authorship of the theories of relativity is an example of the misrepresentations used to promote it to fuel the selfaggrandizement of physicists and their profit motive, to be attained by increasing the esteem of the physics profession on the questionable basis of making academic noise to attract research dollars by using the theories as their tympana.
 I know that the author of the above objection is very careful and literate with the words he uses, so I'm baffled by a few things, such as his use of "supposed precession". This seems to indicate that he thinks this is fictional, and that the precession is actually zero. If so, he would seem to be trying to outdo the person who is perhaps the world's foremost relativity denier, Andy Schlafly. Andy gets into arguments over things like whether the precession is 42.98 or 42.99, but he does not claim that it is zero. In any case, celestial mechanics calculations are now so precise (as in the gravityassist manipulations of the Cassini and Messenger spacecraft) that the positions of bodies in the solar system are now known to vastly more accuracy than the 18^{th} century astronomers could make.
 ... "nonrepeatable observations". Perhaps he means that the actual, original observations, dating back to 1700 or so, haven't been made since. This is true, especially since Leverrier is long dead. And we can no longer conduct the actual MichelsonMorley experiment, though it has been repeated many times. And we can't go back and observe the actual Chicxulub asteroid strike.
 The claim that the people (Urbain Leverrier and others) were "individuals with vested interests that the theories of relativity remain true" seems rather farfetched. He died long before relativity was formulated.
 ... "The error bars of various predictions could have been shifted". Yes, it is possible to fudge experimental data, sometimes sufficiently to change a result. This has been done many times, in many fields. I suppose people could manipulate the precession data to make relativity look good, or to make relativity look bad. But modern data are so accurate that no one even needs to think about doing that.
 ... "such a step [fudging] is not only possible, but probable due to the observed vanity of scientists". That's a lot of scientists pursuing their vanity. All in some conspiracy to promote relativity?
 ... "falsification of the 1919 measurements". It is well known that Eddington's report on the eclipse involved data selection ("fudging") that wouldn't be acceptable today. And that he had a vested interest in promoting relativity. Fortunately, we have enormous amounts of vastly more accurate data on the bending of light. And the conspiracy to fake all this would have to be gigantic. Or do you actually believe that everyone who accepts relativity is part of a giant conspiracy?
 ... "rectifying the absence of a concrete example". How about "finding a concrete example", the way scientists routinely do?
 ... "promote it to fuel the selfaggrandizement of physicists and their profit motive". Yes, these people have jobs that pay money. Sean Hannity's salary last year was $36 million, for example.
 ... "making academic noise". I actually enjoy reading those articles. But I'm not involved in making decisions about where to spend research money.
 SamHB (talk)
 Regarding which, even the authorship of the theories of relativity is an example of the misrepresentations used to promote it to fuel the selfaggrandizement of physicists and their profit motive, to be attained by increasing the esteem of the physics profession on the questionable basis of making academic noise to attract research dollars by using the theories as their tympana.
 Despite wasting millions of taxpayer dollars searching for gravity waves predicted by the theory, none has ever been found. Sound like global warming?
 True, the direct searches for gravitational waves had not yet yielded any clear results at the time that item was written (September 2012), though indirect observations had been made (the Hulse/Taylor observations.) Before people dismiss indirect observations, recall that no one has ever seen an electron.
 The Earthbased LIGO detectors had, at that time, not detected any unambiguous gravitational wave signatures from such events as a blackhole merger. It was barely sensitive enough to find such things in the Milky Way or very nearby galaxies. It was upgraded in a plan that completed in 2014. It was hoped that, after the upgrade, it would be able to see these events clearly and unambiguously.
 The spacebased LISA detectors have not been built yet, and the original proposal has been scrapped because of budgetary problems. A new version, called "eLISA" has been proposed, and should be sensitive to events as far away as redshift 15.
 Whether these experiments are a good use of money is another question, one that has no bearing on whether relativity is correct.
 The objection has been raised that the experiments should not have been funded if scientists were going to ignore negative results.
 The results are only partly negative. The scientists knew all along that a certain amount of luck would be involved in finding a sufficiently strong signal within the time frame of the experiment. The failure so far does not mean that blackhole mergers do not emit gravitational waves; just that they haven't been lucky enough to find them. They will continue to search.
 The objection has been raised that the experiments should not have been funded if scientists were going to ignore negative results.
 Update: Another, much more commonplace observation of gravitational wave emission has been reported.^{[11]} The article suggests that, since it shows detectable gravitational waves are more common than previously thought, there is optimism that the eLISA detector, when completed, might find one source per week.
 Update 2: Gravitational waves have been detected directly through LIGO: the Laser Interferometer GravitationalWave Observatory.

 First detection on 14 September 2015. See LIGO Scientific Collaboration and Virgo Collaboration, "Observation of Gravitational Waves from a Binary Black Hole Merger," Physical Review Letters, 116, 061102 – published 11 February 2016.

 Second detection on 26 December 2015 (the "boxing day event"). See LIGO Scientific Collaboration and Virgo Collaboration, "GW151226: Observation of Gravitational Waves from a 22SolarMass Binary Black Hole Coalescence," Physical Review Letters, 116, 241103 – published 15 June 2016.

 Third detection on 4 January 2017. See LIGO Scientific and Virgo Collaboration, "GW170104: Observation of a 50SolarMass Binary Black Hole Coalescence at Redshift 0.2," Physical Review Letters, 118, 221101 – published 1 June 2017.
 So, in this respect, gravitational waves ARE like global warming: both are true, verified, factual phenomena, which exist whether or not any particular person wants them to exist. As John Adams pointed out in 1770, "Facts are stubborn things; and whatever may be our wishes, our inclinations, or the dictates of our passions, they cannot alter the state of facts."
 The discontinuity in momentum as velocity approaches "c" for infinitesimal mass, compared to the momentum of light.
 The formulas for velocity, momentum, and mass can in fact be written in such a way that they appear to have discontinuities, just as the tangent function has discontinuities while the underlying sine and cosine functions do not. But they can also be written in a form that does not show discontinuities.
 All particles, with or without mass, can have any value of momentum. The formula for the velocity of a particle, in terms of its mass and momentum, is
 For a particle with mass, this means that momentum of zero gives a speed of zero, and, as the momentum approaches infinity, the speed approaches c.
 For a massless particle, the speed is always c.
 Furthermore, this discontinuity in momentum does exist in Newtonian physics with the formula . If we let v approach c while m approaches 0 we get , while light has a nonzero momentum.
 observations don't match predictions and cosmic causality.
 The fact that "observations don't match predictions" has shown up many times in the history of science. That is, the accepted wisdom of the day was found to be false, leading to improved theories:
 There were once assumed, by Aristotle and many others, to be four elements: earth, air, fire, and water. Subsequent experimental investigation, by numerous people, replaced that theory.
 The ancient notion of gravity, that objects fall at a speed proportional to their mass (often ascribed, perhaps imprecisely, to Aristotle), was found to be contrary to experimental evidence, and was replaced by Galilean/Newtonian mechanics.
 The geocentrism of Ptolemy lasted a long time until it was found to be contrary to experimental evidence, and was replaced by the Heliocentric theory of Copernicus, Galileo, and Newton.
 The "phlogiston theory" of combustion was accepted until it proved to be contrary to experimental evidence, and was replaced by the modern oxidation theory by Antoine Lavoisier.
 The "caloric theory" supposed that heat was a material substance called "caloric", and that that substance was conserved. It took a long time for Joule and others to develop the modern "kinetic theory" as a replacement.
 The current "counterexample" is about the "horizon problem", a problem of cosmology which has been known for a few decades. Under the kind of expansion of the universe that nonquantummechanics would require, there are places in the universe that are not causally connected and yet have nearly the same temperature. The classical expansion of the universe would have magnified early nonuniformities by about 50 orders of magnitude, an impossible situation. The currently accepted theory dealing with this problem is "inflation". Not all scientists accept this, but most do; other explanations are more exotic than most scientists are willing to accept.
 An interesting thing about inflation is that it was formulated to solve a different problem—the dominance of matter over antimatter. It was found to address the flatness problem as well. When a theory explains phenomena other than what it was intended for, that of course lends it additional credence.
 Whether cosmic inflation is implausible is not for us to say. The existence of subatomic particles was once considered implausible.
 The cited National Geographic article was in fact not about the problem of temperature uniformity, but about various hypotheses, much less widely accepted than inflation, about alternate universes, and whether black hole singularities might connect them. The issue is not about the existence of black holes, but about the connectedness of their singularities. This is really fascinating stuff. The book The Hidden Reality, by Brian Greene, is a fascinating account of these issues. We highly recommend it.
 The fact that "observations don't match predictions" has shown up many times in the history of science. That is, the accepted wisdom of the day was found to be false, leading to improved theories:
 The logical problem of a force which is applied at a right angle to the velocity of a relativistic mass  does this act on the rest mass or the relativistic mass?
 The simple answer is, unequivocally, that it acts on the 'relativistic' mass. The question seems to relate to a simple misunderstanding of Special Relativity. Einstein's theories lead to the conclusion that observers in different inertial frames of reference (i.e. observers with differing, but constant velocities relative to the thing being observed) will observe different inertial masses in the body being observed. However, there is no variance in the body's mass with regard to the direction of the force. Thus to a given observer, a force in any direction will operate on the same mass. However, to a different observer, this mass may be different, although still the constant with regard to the direction of the force.
 The observed lack of curvature in overall space.
 Spacetime has very definite curvature near any massive object—this is what makes gravity work. The global curvature of spacetime is an altogether different issue. Whether the average global curvature is zero has consequences for cosmological theories, but it has essentially no effect on the curvature that keeps the Earth in its orbit. If it did have an effect, the issue would have been settled long ago.
 The universe shortly after its creation, when quantum effects dominated and contradicted Relativity.
 We're still working on a quantum theory of gravity; this isn't so much a counterexample as saying that (classical) GR isn't valid in that domain.
 The actionatadistance of quantum entanglement.
 Special Relativity only forbids the transmission of matter, energy or information at a speed faster than light. There are plenty of other things that can move faster than light. Consider a laser on Earth which is rotating on a pivot, whose light shines onto the hull of a satellite 200,000 km away (2e8 metres). If the laser rotates at a sedentary one revolution ever four seconds, the speed of the laser beam's tip crossing the satellite's hull is 3.14e8 metres per second  faster than the speed of light. However, this is not a transfer of information. Any information is travelling from Earth to the satellite, obeying the universal speed limit. Similarly, the only information that can be transmitted by the quantum entanglement of two particles is from the originator of the particles to the two observers, not from one observer to another. Faster than light transmission of information using quantum entanglement has never been observed, nor has even conceived how such a mechanism might work.^{[12]}
 The actionatadistance by Jesus, described in John 4:4654, Matthew 15:28, and Matthew 27:51.
 As an argument against relativity, there are two reasons that this is invalid (beyond simply questioning the evidential validity of the Bible):
 a) These passages clearly refer to a miracle. A miracle, being an act of God, is not subject to the laws of physics.
 b) It is highly debatable as to whether the verses do describe actionatadistance in the sense of an action whose influence travels instantaneously (and therefore faster than the speed of light). This itself may be argued from two viewpoints:
 i) When reading these passages, as with consideration of many apparent relativistic anomalies, the true picture of causality must be considered. In each case there are two apparent events. Event A  Jesus does something (says 'thy son liveth', says 'be it unto thee even as thou wilt', or Christ's spirit leaving His body). Event B  the apparent result (the son lives, her daughter is made whole, or the earth quakes). However, it is not the case in any of these examples that A causes B. Both A and B are caused by a third event. In the first two cases it is Christ's thought that causes the miracle and that causes His lips to announce the miracle. This thought would have occurred fractions of a second before either event, and is the noninstantaneous cause of both. In the last case it is Christ's death that is the precursor and cause of both events.
 ii) It must be considered that at the time when the Gospels were written, neither their authors nor their intended readers were aware of any concept of the speed of light and were unable to measure the billionths of a second difference between the events being considered here. Thus just as in modern parlance the phrase 'at the same moment' has a tolerance of milliseconds (unless specifically couched to mean otherwise) so do the various terms used by the Evangelists. They would never have considered it an important issue, and would therefore not have worried about the degree of precision.
 Miracles do not violate logic, and the Theory of Relativity asserts that these actionatadistance miracles described in the Gospels are impossible. No plausible medium for these miracles, even if they were noninstantaneous actionatadistance, has been proposed.
 Scientists' choosing not to try to explain "plausible media" for things described in the Bible is not evidence that Relativity is wrong.
 Miracles do not violate logic, and the Theory of Relativity asserts that these actionatadistance miracles described in the Gospels are impossible. No plausible medium for these miracles, even if they were noninstantaneous actionatadistance, has been proposed.
 As an argument against relativity, there are two reasons that this is invalid (beyond simply questioning the evidential validity of the Bible):
 The failure to discover gravitons, despite wasting hundreds of millions in taxpayer money in searching.
 Gravitons are a prediction of Quantum mechanics, not of relativity, although the concept is an extension of the relativistic idea that forces take a finite time to be transmitted over a distance.
 No one expects to observe gravitons. Calculations show that it is wellnigh impossible with any conceivable detector that we could build. No one is designing, funding, or building any apparatus to search for gravitons.
 Now it happens that theoretical physicists discuss and speculate on the existence and nature of such things as gravitons as part of their theoretical work. Some of these discussions take place among scientists who receive their salaries from various government agencies that are funded by taxpayers. Whether all of the things that scientists think about, talk about, and write about constitute a good use of money is not for us to say.
 Newly observed data reveal that the finestructure constant, α (alpha), actually varies throughout the universe, demonstrating that all inertial frames of reference do not experience identical laws of physics as claimed by Relativity
 Whilst this observation is unconfirmed, if true it would still not invalidate relativity. Many things may vary with position in space, and relativity does not deny this. There is no suggestion that the finestructure constant is different at the same point in space for observers in different (inertial or noninertial) frames, as the 'counterexample' implies.
 The double star "W13" weighs "40 times as much as the sun—more than enough to form a black hole. So why is it not a black hole? The only explanation [a leading scientist] can think of ... does not make astrophysical sense."
 When physicists encounter something puzzling, their first reaction is usually not to assume that it shows that relativity is wrong. In fact the cited article never mentions relativity at all. It is about "magnetars", a type of neutron star about which very little is known, other than their extremely strong magnetic fields.
 Many scientific discoveries have arisen from observations that were puzzling at first. Edwin Hubble's observations of galactic redshift led to the realization that the universe is expanding isotropically. The observations by Jocelyn Bell and Antony Hewish, of periodic pulsation in the radio emissions of a star, were so puzzling at first that they seemed to suggest transmissions from intelligent extraterrestrials. They had actually discovered pulsars. When Carl Anderson saw unexplained particle tracks in a cloud chamber, he had discovered antiparticles.
 None of these people assumed that the explanation for these observations was that relativity was wrong. They were all astrophysicists and were quite familiar with relativity. In fact, Anderson's antiparticles had been predicted by the Dirac equation, a synthesis of special relativity and the Schrödinger equation of quantum mechanics, from a few years earlier.
 The inability of the theory to lead to other insights, contrary to every verified theory of physics.
 It is utterly baffling how anyone could make such an assertion. The insights from relativity are multitudinous. Relativity forms the basis for astronomy, cosmology, electrodynamics, and many other fields. The interconnection between the electric and magnetic forces is now seen to be a straightforward consequence of relativity. Relativity combined with quantum mechanics are the basis of all of contemporary physics.
 The Dirac equation, which gives rise to antiparticles and the theory of spinors, was an early example of introducing relativity into the Schrödinger equation.
 More generally, special relativity was combined with quantum theory to produce quantum field theory (QFT). An example of a QFT is quantum electrodynamics, the most precise theory in physics. Furthermore, string theory is Lorentz invariant and produces general relativity in the low energy limit.
 The change in mass over time of standard kilograms preserved under ideal conditions.
 We are baffled that anyone would connect this problem with relativity. The nonrelativity principle of conservation of mass has been known, in general, for hundreds of years, going back to the time of the alchemists, and has been a fundamental and accurate principle since the 19th century. The principle of conservation of energy has also been a fundamental and accurate principle since the 19th century. Relativity simply generalizes this to a principle of both together, with even greater precision. So, in principle, it is recognized that the mass of the standard kilogram could change if an energy transfer took place. But no combustion, corrosion, or nuclear decay is suspected of having taken place. In any case, the amount of energy that would have to have been released is 1.25 megawatthours, which would certainly have been noticed.
 Relativity does not promise uniformity of the universe any more strongly than classical physics did. The apparent change in mass of the standard kilogram is simply a mystery.
 The uniformity in temperature throughout the universe.
 The cited article is fascinating, and is about a fascinating aspect of contemporary physics. Like item 23, it would have been useful to say what the article is about.
 The cited article is about speculation that the constant "alpha" (see item 17 above) may not be constant. It might have decreased, by 45 parts per billion, as recently (in cosmic time) as two billion years ago, based on data from the Oklo "natural fission reactor". Other measurements have been made of alpha at earlier times, such as measurement of light from distant quasars. These measurements suggest that alpha has increased by a few parts per 10^{5} in 12 billion years.
 There is plenty of literature on theories about change in alpha, and some of it indicates that this may be due to change in the speed of light. Specifically, the Oklo data may suggest that the speed of light may have been increasing slightly. (This is the opposite of the direction of change claimed by fundamentalists, but is much smaller in any case.)
 Speculation on a different speed of light in the past may relate to theories of "cosmic inflation", which touches on the question of why the Cosmic Background Radiation is so nearly isotropic, which indicates a nearuniformity of temperature, which requires inflation or some equivalent mechanism.
 None of the scientists working in this area seem to doubt the fundamental correctness of relativity.
 "According to Einstein's view on the universe, spacetime should be smooth and continuous" but observations instead show "inexplicable static" greater than "all artificial sources of" possible background noise.
 The cited article is fascinating, and is about a fascinating aspect of contemporary physics. Like item 23, it would have been useful to say what the article is about.
 The cited article is about a very recent and exciting development in fundamental theoretical physics, generally called the "holographic principle". This proposes that our perceived 3dimensional space actually arises from a "hologram" on a 2dimensional space. Much has been written about this recently, including the bestselling book The Hidden Reality by Brian Greene. This hologram manifests itself in the "foamlike" ripples of spacetime, at the scale of the Planck length, which is so small that there seemed to be no way to detect it directly.
 But it seems that some "inexplicable static" in the results of another unrelated experiment, searching for gravitational waves, may be the first hints of the holographic nature of space. If so, this is a lucky and serendipitous result.
 Serendipitous scientific discoveries have been made many times, as when Henri Becquerel put a photographic plate in a dark drawer because the weather was cloudy, and thereby discovered radioactivity.
 That the "foamlike" nature of space at short distances is contrary to the continuous nature presumed by classical mechanics and relativity has been known for some time. This is the problem that quantum gravity seeks to solve.
 "The snag is that in quantum mechanics, time retains its Newtonian aloofness, providing the stage against which matter dances but never being affected by its presence. These two [QM and Relativity] conceptions of time don't gel."
 Quoting things without explaining the context is often a bad idea, and the indicated item is a good example of this. It gives no hint of what the article from which the quote was taken is about. The article is about one scientist's contribution to the problem of unifying relativity and quantum mechanics. The scientist, Petr HoYava of Berkeley, has come up with an approach that he says eliminates the infinities that have plagued other unification attempts.
 The two quoted sentences are HoYava's statement of the problem. So it comes as no surprise that he says that there is a conflict between relativity and quantum mechanics. The very next paragraph begins:
 The solution, HoYava says, is to snip threads that bind time to space at very high energies .... At low energies, general relativity emerges from this underlying framework ..."
 It is well known that, just as classical mechanics emerges from quantum mechanics at nonmicroscopic scales, and classical mechanics emerges from relativity at low speeds, both relativity and quantum mechanics should emerge from the Grand Unified Theory (whatever that turns out to be) at the appropriate scales.
 The theory predicts wormholes just as it predicts black holes, but wormholes violate causality and permit absurd time travel.
 The topology of wormholes is an interesting topic, widely discussed among theoretical physicists and mathematicians. There is much speculation about what they would be like (if they could exist at all under quantum gravity), and what kind of "cosmic censorship" or "chronology protection" theorems might make practical time travel impossible. The nature of these theorems seems to be intertwined with theories of quantum gravity and "grand unification", so the exact form of the "cosmic censorship", if it exists, can't be known until quantum mechanics and relativistic geometry are unified. It is an exciting field of research. No one believes that the "cosmic censorship" will take the form of relativity not being a true nonquantum approximation to reality.
 The theory predicts natural formation of highly ordered (and thus low entropy) black holes despite the increase in entropy required by the Second Law of Thermodynamics.
 Since the 70's much work has been done on the subject of black hole thermodynamics,^{[13]}^{[14]} most notably by the Lucasian Professorship of Mathematics at Cambridge Stephen Hawking. When quantum field theory is added to the analysis of black holes it is found that they do not possess "low entropy" (quite the opposite, in fact) and are consistent with the laws of thermodynamics.^{[15]} The Counterexamples to Relativity article has labelled this work in a footnote as "[c]ontrived explanations", with no explanation for this characterization given.
 Data from the PSR B1913+16 increasingly diverge from predictions of the General Theory of Relativity such that, despite a Nobel Prize in Physics being awarded for early work on this pulsar, no data at all have been released about it for over five years.
 Please read the cited paper carefully. It is a survey of their observations over a 30year period. They point out that their data matches general relativity to within 0.2 percent, and is now down in the "noise" of other effects, such as lack of accurate knowledge of just how far away the pulsars are, and lack of accurate knowledge of galactic constants. As they say in the abstract, "tighter bounds will be difficult to obtain." The paper, written in 2004, also notes that, because the pulsar beams are slowly tilting out of the line of sight to Earth, "A core component [of the emission] is quite prominent in the data taken in 198081, but it faded very significantly between 1980 and 1998 and was nearly gone by 2003."
 That is why they are not releasing further data. 30 years is a fairly long time to watch a pair of pulsars. They're not doing the experiment any more—it did its job, and it's finished. No one drops cannonballs off the Leaning Tower of Pisa any more either.
 The data are not diverging from the predictions.
 The lack of useful devices developed based on any insights provided by the theory; no lives have been saved or helped, and the theory has not led to other useful theories and may have interfered with scientific progress. This stands in stark contrast with every verified theory of science.
 The Global Positioning System (GPS) uses general relativity to achieve greater accuracy.^{[16]}
 In fact, relativity is what makes the magnetic force necessary. The magnetic force is used in, among other things, electric motors and generators.
 Even if it were the case that no practical applications have come from relativity, that is irrelevant. The validity of a theory is not based on the creation of useful devices. It is based on its ability to accurately predict the results of an experiment. Relativity "has held up under extensive experimental scrutiny".^{[17]}
 If scientific theories were judged by their application in useful devices, the following Nobelworthy theories would be rejected:
 cosmic inflation
 parity violation in the weak force
 the "standard model", with strange/charm/top/bottom/mu/tau
 the Chandrasekhar limit for white dwarf stars
 Relativity requires different values for the inertia of a moving object: in its direction of motion, and perpendicular to that direction. This contradicts the logical principle that the laws of physics are the same in all directions.
 The rules for calculating inertia and other questions of mechanics are well known. The inertia, that is, the way that a force affects an object's momentum, is well known. Hundreds of physics textbooks discuss this in great detail, in terms of the Lorentz transform and the concepts of the force and momentum 4vectors. The "inertia" comes from what is now called the mass, which used to be called the "rest mass". Archaic treatments formulated this in terms of the "relativistic mass", which was different. The mass is a scalar, and has no direction. The formulas for calculating the motion in terms of forces, in the direction of motion or transverse to it, are well known.
 Relativity requires that anything traveling at the speed of light must have mass zero, so it must have momentum zero. But the laws of electrodynamics require that light have nonzero momentum.
 This seems to be another basic misunderstanding of relativity, from someone who gave up halfway through the textbook. Newtonian momentum (p = mv) does certainly indicate that a body with zero mass (m) must have zero momentum whatever its velocity (v). However, the relativistic equation for momentum is:
 where m_{0} is the rest mass of the object and ? is the Lorentz factor, given by
 where c is the speed of light.
 For the case of a photon, where rest mass is zero and v is equal to c, this gives p as zero divided by zero  an undetermined value.
 However, with the substitution of the famous E=mc^{2}, where E is the energy of the body, the momentum equation can be rearranged to:
 With a photon of zero rest mass, this gives:
 Finally, substituting Planck's Equation for the energy of a photon where h is Planck's Constant and f is the frequency of the photon, we get the familiar (and experimentally demonstrated) value for a photon's momentum of:
 where is the photon's wavelength.^{[18]}
 This seems to be another basic misunderstanding of relativity, from someone who gave up halfway through the textbook. Newtonian momentum (p = mv) does certainly indicate that a body with zero mass (m) must have zero momentum whatever its velocity (v). However, the relativistic equation for momentum is:
 Unlike most welltested fundamental physical theories, the theory of relativity violates conditions of a conservative field. Path independence, for example, is lacking under the theory of relativity, as in the "twin paradox" whereby the age of each twin under the theory is dependent on the path he traveled.
 There are no "conditions of a conservative field". A conservative field is one that has a curl of zero. Perhaps what was meant was that the gravitational field around the Sun, under Newtonian mechanics, is conservative. This is true because it is the gradient of an inversesquare scalar field, and all gradients have a curl of zero. Under relativity, the curl is also zero, due to the Bianchi identity and the symmetries of Riemann's tensor. See the extensive discussion here.
 The reference to the twin paradox suggests that the author thought that the passage of time is some kind of scalar field that should be obtainable as the path integral of a conservative vector field. It is not. Passage of time is a property of one's path through spacetime, and is similar to path length. (In fact, under the Lorentz/Minkowski metric, it is exactly path length.) Just as two paths from point A to point B on a sheet of paper can have different lengths, the paths of the twins can have different lengths, and hence different elapsed local times.
 The Ehrenfest Paradox: Consider a spinning hoop, where the tangential velocity is near the speed of light. In this case, the circumference (2πR) is lengthcontracted. However, since R is always perpendicular to the motion, it is not contracted. This leads to an apparent paradox: does the radius of the accelerating hoop equal R, or is it less than R?
 The "Ehrenfest paradox" is not an actual paradox. Noninertial relativistic motion of solid bodies is quite complicated, involving such concepts as "Born rigidity", "Langevin observers", the "LangevinLandauLifschitz metric", and "quotient manifolds". In general, the subject is complicated, and has provided physicists with much food for thought. But it does not disprove relativity.
 Based on Relativity, Einstein predicted in 1905 that clocks at the Earth's equator would be slower than clocks at the North Pole, due to different velocities; in fact, all clocks at sea level measure time at the same rate, and Relativists made new assumptions about the Earth's shape to justify this contradiction of the theory; they also make the implausible claim that relativistic effects from gravitation precisely offset the effects from differences in velocity.
 The claims of that item are preposterous. Read the cited paper (or its abstract) carefully. Einstein's statement that clocks would run slower at the equator, due to time dilation, was correct according to special relativity alone. What Einstein didn't realize, because he wouldn't discover general relativity for another 10 years, was that the gravitational time shift would offset that.
 A "geoid" (the shape discussed in the paper) is a theoretical shape used in mathematical physics, that is in equilibrium between the effects of centrifugal force (from rotation) and gravity. It is essentially an oblate spheroid. It can be thought of as the shape a rotating planet would take if it were completely fluid. Or it could be thought of as the shape of "global sea level". Jupiter, because of its rapid rotation, has a very pronounced flattening at the poles. Since Jupiter is not solid, its shape is a geoid. The Earth is very nearly a geoid, of course. But not exactly, because of gravitational nonuniformities, and things like mountains, that can exist because of the Earth's rigidity. No one "made new assumptions about the Earth's shape" to justify anything. The assumption that the Earth's shape is a geoid is a theoretical assumption due to the approximately fluid nature of the Earth. But no one claims that the Earth's shape is anything other than what it is observed and measured to be.
 What the paper is about is the fact that the effects of rotational speed and gravitational time dilation happen to cancel each other on an ideal geoid. So all clocks at "sea level" on an ideal geoidshaped planet run at the same speed. Whether this result is implausible is not for us to say.
 The cited paper does not refute relativity.
 The Twin Paradox: Consider twins who are separated with one traveling at a very high speed such that his "clock" (age) slows down, so that when he returns he has a younger age than the twin; this violates Relativity because both twins should expect the other to be younger, if motion is relative. Einstein himself admitted that this contradicts Relativity.
 The physics and mathematics underlying the "twin paradox" are well known. That one of the twins will have had to undergo different accelerations from the other before returning to the same point is what enables them to perceive different passage of time. This does not contradict relativity, and Einstein never said that it does. His explanation in terms of different acceleration is correct.
 The comment about extending the length of the trip so that the acceleration would be de minimis is wrong. It seems to suggest that the acceleration could be reduced until it is negligible. It can be reduced by lengthening the trip, but it is not negligible. The Lorentz transform, and the equations of motion, are mathematically exact. The integral of a very small function over a long period is still significant. If the twins followed different paths in spacetime, which they must in order to measure different elapsed proper time, they must have undergone different accelerations, however small those differences may have been.
 Of course, if they never come back to the same point, they could both undergo zero acceleration.
 Based on Relativity, Einstein claimed in 1909 that the aether does not exist, but in order to make subatomic physics work right, theorists had to introduce the aetherlike concept of the Higgs field, which fills all of space and breaks symmetries.
 Quantum field theory abounds with fields. The Higgs particle has a Higgs field. It has nothing to do with the "luminiferous aether".
 Minkowski space is predicated on the idea of fourdimensional vectors of which one component is time. However, one of the properties of a vector space is that every vector have an inverse. Time cannot be a vector because it has no inverse.
 Time isn't a vector. It is a component of the vector space known as "spacetime". Vectors have negatives; the word "inverse" is not typically used here. While there are thermodynamic and other reasons for not allowing time to go backwards in the real world, the mathematics of spacetime allow vectors with any components, even negative ones. Mathematicians define a 4dimensional vector space as having two operators: addition and scalar multiplication. There is also the identity vector (0,0,0,0). So, to the extent that one asks what vector can be added to (0,0,0,t) to produce (0,0,0,0), the answer is (0,0,0,t), but that has nothing to do with relativity.
 In Genesis 1:68, we are told that one of God's first creations was a firmament in the heavens. This likely refers to the creation of the luminiferous aether.
 That a Bible verse "likely" refers to a scientific phenomenon does not make good science. The objection appears to be claiming that the Bible contradicts the MichelsonMorley experiment, so the latter must be wrong. The MichelsonMorley experiment is very well known, has been repeated countless times, and is incontrovertible. To suggest that the Bible verse in Genesis contradicts such an incontrovertible phenomenon does a disservice to both the Bible and to science.
 It is impossible to perform an experiment to determine whether Einstein's theory of relativity is correct, or the older Lorentz aether theory is correct. Believing one over the other is a matter of faith.
 Modern formulations of the Lorentz aether theory may very well make it completely equivalent to relativity, both special and general. But that doesn't make relativity wrong; it just means that another theory is just as correct. The universal preference of the scientific community for relativity over the Lorentz theory is probably not based on religious faith, but on simplicity, as expressed in Occam's razor. The Lorentz theory postulates an aether that no experiment can possibly determine the properties of, while relativity postulates no aether.
 Despite a century of wasting billions of dollars in work on the theory, "No one knows how to solve completely the equations of general relativity that describe gravity; they are simply beyond current understanding."
 They are not "beyond understanding". They are simply beyond closedform solution. Cosmologists work with approximate solutions, calculated by extensive computer calculations, all the time. A wellknown example of this is the simulation of galaxy dynamics. Particle physicists do this also, in, for example, quantum chromodynamics (QCD) calculations. It is fortunate that the equations of Keplerian/Newtonian planetary motion were solvable by the mathematical methods of the 17th century—a closedform solution to a secondorder differential equation. Modern physics problems are much harder. But, with modern computers, we can solve the equations of gravity to enormous precision.
 Experiments in electromagnetic induction contradict Relativity: "Einstein's Relativity ... can not explain the experiment in graph 2, in which moving magnetic field has not produced electric field."
 The first cited reference, from which the quote was taken, is a totally crackpot web page, from a web site that seems to specialize in hosting crackpot papers. The writing is utterly illiterate and incoherent, as in this sentence: "According to Faraday's Law it can be explained as that, duo to the magnetic flux in conductor line changing, firstly induced electromotive force dU coming from the linewinded conductor to bring out voltage, then based on differential form of Ohm's Law, the physical natural would be regarded as 'voltage before electric current' "
 Relativity breaks down if a solenoid is traveling at or near the speed of light.
 The equations of electrodynamics (Maxwell's equations), and their connection with relativity, are well known. Hundreds of electrodynamics textbooks cover this subject. The equations are correct at all realizable speeds, even relativistic (near the speed of light) speeds. (Maxwell's equations are said to be the only equations from classical physics that did not need to be modified for relativity.) The equations correctly describe the behavior of magnets (this is presumably what was meant by "solenoids"), charges, and electric and magnetic fields, even at speeds near the speed of light. Of course the equations don't work at the speed of light. The cited article never discussed speeds near the speed of light, only at the speed of light. The questioner was rightly taken to task for his physically unrealizable assumption.
 The Pauli Exclusion Principle states that no two electrons...
 This is wrong on many levels. If there were exactly as many quantummechanical states (eigenfunctions) as there are particles, then, indeed, a fermion particle could only go to another state if the particle already in that state moved. But there are many more available states than there are particles.
 The cited article was a lecture by Brian Cox, a "popularizer" of physics, and the comments on the web page take him to task over a great many points, including a confusion between "quantum states" and "energy states", and what quantummechanical interconnectedness really means. People would be well advised to read those comments, as well as the analysis by Sean Carroll here, which points out the many flaws in Brian Cox's reasoning.
 In any case, this is about quantum mechanics, not relativity.
 The recent findings of gravitational waves are actually just dust.
 This is about the observations by the "BICEP2" telescope early in 2014. The claim was that analysis of the polarization of the Cosmic microwave background (CMB) would show that the CMB had been influenced by gravitational waves in the first fraction of a second after the big bang. That is, if noise from interstellar dust grains didn't confound the measurements. It is now believed that the dust grain noise is too high to make this a reliable measurement.
 Please read the cited article. It indicates that, based on observations by the Planck satellite, it should be possible to make a cleaner observation. The balloonborne "Spider" telescope is slated to be launched later this year, and it might be successful.
 Taking the failure of the BICEP2 observations as a counterexample to relativity is like saying "I thought of a new and clever proof of the existence of God last week, but unfortunately there was a flaw in my logic, so therefore God doesn't exist."
 In any case, another indirect observation of gravitational waves has already been made, in the HulseTaylor observations of binary pulsar PSR B1913 16 in the 1990s.
 The theory of relativity ... implausible assumptions, including an invariant speed of light, denial of action at a distance, denial of basic, wellproven principles of quantum mechanics, and insistence that all places in the universe be equivalent to each other.
 The invariant speed of light is an observation from the MichelsonMorley experiment. They did not take a position on whether it was "implausible"; they just reported their observations, and the scientific community accepts this, implausible or not. One can't say that something didn't happen because one finds it implausible.
 All of the scientists working on the wellproven principles of quantum mechanics, all of them, accept relativity. Relativity is built into those principles, such as Quantum Field Theory, Quantum Electrodynamics, and Quantum Chromodynamics. These theories just don't work without relativity, and no one tries to take relativity out of them.
 We don't quite know what "all places in the universe [are] equivalent to each other" means. No one asserts this in any literal way. Perhaps it is a reference to the laws of physics being the same everywhere, or there being no "origin" of space. Those principles come out of Galilean mechanics, hundreds of years before relativity.
 The theory of relativity has discontinuities whereby the limit of a physical quantity ...
 The formulas connecting momentum, velocity, and mass, are well known, and can be found in any high school or college level textbook on the subject.
 It is a wellknown fact that, by tweaking the order in which various quantities are held constant are allowed to change, one can get different results. For example, this phenomenon is the essence of the difference between "pointwise continuity" and "uniform continuity" in mathematical analysis, and is the reason why various forms of convergence (pointwise, uniform, and convergence in measure under various norms) in Lebesgue spaces is complicated.
 The formula connecting mass, speed, and momentum is, in all cases without exception:
 While this formula is not a very useful way of expressing it for practical use, and there are many other equivalent expressions that one will see in the literature and here at Conservapdia, it has the advantage that there are no fractions and no square roots.
 If one specializes that formula in certain ways, one can get asymptotes and other situations in which a limit of finite quantities is infinity, or other discontinuous phenomena occur. This is all covered in elementary calculus courses. In the example on the other page, the quantity of interest is the limit of p as m approaches 0 and v approaches c. This is a limit across a 2dimensional space, which is a prime example of how one can get different results depending on how the two variables are made to approach their limit. The version of the formula in this case is:
 Note that, expressed in this form, the numerator goes to zero because m goes to zero, and the denominator goes to zero because v goes to c. This sort of thing is a dead giveaway that some mathematical trickery is going to be invoked.
 Discontinuities in General Relativity are wellrecognized.
 The fact that one has found a scholarly paper with the words "discontinuity" and "relativity" in the title does not make relativity false. It is extremely unlikely that the author of that paper considered relativity to be false; he would surely have used a different title if that were the case.
 While only a quick abstract of the paper is given, it appears that the paper is about discontinuities in the stressenergy tensor. That is completely permissible, and General Relativity can deal with that.
Unless someone can come up with a sensible example, we will not be posting further rebuttals. The recent ones have been hideously pointless, and not worth replying to. Many of them have cited articles that have nothing to do with relativity. For example, tides do not disprove relativity. It's possible that, because of the rather famous nature of the "counterexamples" page (it is cited around the world, and has nearly 2 million web views), people are simply putting in parody, or trolling, or humor, or whatever, in an attempt to see their work on a worldfamous page.
See also
 Theory of relativity
 General Theory of Relativity
 Special Theory of Relativity
 Counterexamples to Relativity
 E=mc²
 Logical Flaws in E=mc²
 Essay:Rebuttal to Logical Flaws in E=mc²
References
 ↑ http://curious.astro.cornell.edu/question.php?number=124
 ↑ http://www.technologyreview.com/blog/arxiv/26589/
 ↑ https://en.wikipedia.org/wiki/Pioneer_anomaly
 ↑ Turyshev, Slava G.; Toth, Viktor T.; Kinsella, Gary; Lee, SiuChun; Lok, Shing M.; Ellis, Jordan (2012). "Support for the Thermal Origin of the Pioneer Anomaly". Physical Review Letters 108 (24): 241101. doi:10.1103/PhysRevLett.108.241101. PMID 23004253. Bibcode: 2012PhRvL.108x1101T.
 ↑ Isaacson, Walter (2008). Einstein: His Life and Universe (New York: Simon and Schuster), p. 390. Retrieved from GoogleBooks archive on February 19, 2015.
 ↑ http://www.cbc.ca/news/world/story/2012/02/22/technologyfasterthanlightneutrinos.html
 ↑ https://www.foxnews.com/scitech/2012/02/22/loosewireledtostunningfasterthanlightparticlefinding/?intcmp=features
 ↑ http://news.sciencemag.org/scienceinsider/2012/02/breakingnewserrorundoesfaster.html
 ↑ http://news.sciencemag.org/scienceinsider/2012/06/onceagainphysicistsdebunk.html
 ↑ http://trsnew.jpl.nasa.gov/dspace/bitstream/2014/19295/1/980601.pdf
 ↑ https://www.bbc.co.uk/news/scienceenvironment19408363 BBC article
 ↑ https://web.archive.org/web/20150117231730/http://curious.astro.cornell.edu/question.php?number=612
 ↑ http://adsabs.harvard.edu/abs/1973CMaPh..31..161B
 ↑ https://arxiv.org/pdf/grqc/9307035v1.pdf
 ↑ http://adsabs.harvard.edu/abs/1973PhRvD...7.2333B
 ↑ http://www.astronomy.ohiostate.edu/~pogge/Ast162/Unit5/gps.html
 ↑ http://relativity.livingreviews.org/Articles/lrr20063/
 ↑ http://hyperphysics.phyastr.gsu.edu/hbase/relativ/relmom.html