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 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.
 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 gravityin 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 1970's 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 behavoiur, 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, Galillean, 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 gravityin 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.
 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.
 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 ^{[3]} ^{[4]}. The claims of fasterthanlight neutrinos have now been refuted very thoroughly^{[5]}^{[6]}.
 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.
 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^{[7]}, 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.
 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 have not yet yielded any clear results, though indirect observations have been made (the Hulse/Taylor observations.) Before people dismiss indirect observations, recall that no one has ever seen an electron.
 The Earthbased LIGO detectors have, so far, not detected any unambiguous gravitational wave signatures from such events as a blackhole merger. It is barely sensitive enough to find such things in the Milky Way or very nearby galaxies. It is being upgraded in a plan that should complete in 2014. It is hoped that, after the upgrade, it will 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 neen reported^{[8]}. 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.
 This has nothing to do with global warming.
 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.
 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 200,000Km 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.^{[9]}
 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.
 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 Theory, 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 noninertial frame, 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 relatitivity 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 19^{th} century. The principle of conservation of energy has also been a fundamental and accurate principle since the 19^{th} 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^{[10]}^{[11]}, 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^{[12]}. 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 30 year 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^{[13]}.
 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" ^{[14]}.
 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.^{[15]}
 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 dicussed 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 realtivity.
 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.
 General Relativity predicts how the gravitational fields of the Sun and Moon generate ocean tides. However, in the summer of 2009, tides along the East Coast of the United States were higher than expected.
 This one is utterly absurd. The calculation of the gravity of the Sun and Moon in producing tides has been known for hundreds of years, explained by Newtonian gravity. The effect of relativity on this is microscopic.
 The cited article is about the many things affecting the gross behavior of tides. Keep in mind that the factors affecting the tides involve a lot of hardtopreciselyquantify things such as wind and ocean currents, and the melting of glaciers. As an example of how imprecise things are, the Atlantic and Pacific Oceans differ in mean height by about 8 inches at the Panama Canal, and the tides are about 20 feet on the Pacific side and 1 foot on the Atlantic side. As another example, tides in the Bay of Fundy are as high as 53 feet. Tides are not a simple calculation from Newtonian or Einsteinian mechanics. The difference between Newtonian gravitation and Einsteinian gravitation is utterly insignificant in comparison to these gross effects.
 The supermassive black hole within the Andromeda galaxy puzzled researchers by increasing in brightness by a factor of 100 in 2006.
 This item is about unexpected behavior of the supermassive black holes at the centers of many galaxies. Black holes are a prediction of relativity. The fact that people are still learning new things about them is hardly surprising.
 The cited article never mentions relativity or the possibility that relativity is wrong. In fact, the entire discussion is in the context of black holes. The second study was about a black hole at the center of a galaxy apparently wandering out of place. The hypothesis is that a merger of two galaxies was involved, and "the theoretical prediction is that when two black holes merge, the newly combined black hole receives a 'kick' due to the emission of gravitational waves ..." Gravitational waves are, of course, a specific prediction of general relativity.
 Scientists are unable to explain a June 2012 cluster of earthquakes in Ireland.
 This one is even more absurd than the one above about tides. We cannot fathom why anyone would think earthquakes are a counterexample to relativity.
 Apparently, the equations of General Relativity do not apply to the motions of extrasolar planets.
 This refers to a recently discovered planetary system in which another star is closer than had previously been seen in such a system. Systems involving two stars and a planet constitute the "three body problem", which has never been solved analytically. But if only one of the objects is massive, such as the Sun, the system can be stable for all practical purposes, which is why the solar system is effectively stable even though it is a manybody problem. But two stars make the system much more problematical. In the past, such systems have had the other star far enough away that it has essentially no effect. The Gamma Cephei system is different, and scientists are eager to analyze it in detail. They are frustrated in this by the extremely scant data about the planet's orbit, since that information has to be gleaned from tiny spectroscopic shifts (in only one dimension!) of the two stars.
 The effect of Relativity on this is, of course, the precession of the "perihelion" due to the effects of General Relativity. From the information that has been gathered, the precession should be about 1.14 arcseconds per Earth century, or about 1/37^{th} that of Mercury. The precession of Mercury was established with accurate visual observations. Measuring something 1/37^{th} as large, from the Doppler shift in spectroscopic measurements, is utterly beyond current technology. Other than that, there is no reason to consider relativity. Classical mechanics will do just fine.
 General Relativity fails to predict the Allais Effect.
 A quick Google search will show that there is no "concerted effort to suppress knowledge about the phenomenon". Tom van Flandern (no darling of those who accept relativity; he has been cited at Conservapedia in the "Lack of evidence for Relativity" section) explains the phenomenon in his 2003 paper Allais gravity and pendulum effects during solar eclipses explained: "Here we show that an unusual phenomenon that occurs only during solar eclipses, rapid air mass movement for the bulk of the atmosphere above normal cloud levels, appears to be a sufficient explanation for both the magnitude and behavior of the anomaly previously reported in these pages."
 The fact that "attempts to duplicate the result have been reported as failures" is certainly consistent with an effort to suppress knowledge, but it's also consistent with the effect not existing.
 Scientists at the Collider Detector at Fermilab collided protons and antiprotons ....
 Actually, the energy released in a collision should equal the initial kinetic energy of the colliding particles plus their rest mass energy, minus the rest mass energy of the resultant particles. There is no suggestion that this wasn't the case in the cited experiment.
 The title of the cited article is "Has new physics been found at the ageing Tevatron?" It is about the discovery of more muons than predicted, as well as some muons that appear to have originated from outside of the "pipe" area of the Tevatron. There was no suggestion at all that relativity was violated. The article was simply about a new discovery. Relativity never made the claim that no new physics would ever again be discovered.
 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.
 See this link:^{[16]} for a readable explanation of the problems that arise at the scales at which relativity and QM collide.
 For an overview of the "AMPS" theory and the "firewall" controversy, see this link:^{[17]}.
 Extremely interested readers might also be interested in this paper:^{[18]}.
 In none of these papers does anyone express the slightest doubt that the standard formulation of General Relativity, or the standard formulation of Quantum Mechanics, is correct. Because of things like perihelion precession, the Shapiro effect, the observed behavior of stars near black holes, and radiation from their accretion disks, there is absolutely no doubt that General Relativity is correct for matter in the large, including phenomena near black holes but not so close that quantum gravity comes into play.
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. Tides, and earthquakes, 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.
References
 ↑ http://curious.astro.cornell.edu/question.php?number=124
 ↑ http://www.technologyreview.com/blog/arxiv/26589/
 ↑ http://www.cbc.ca/news/world/story/2012/02/22/technologyfasterthanlightneutrinos.html
 ↑ http://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
 ↑ [1]
 ↑ http://www.bbc.co.uk/news/scienceenvironment19408363 BBC article
 ↑ http://curious.astro.cornell.edu/question.php?number=612
 ↑ http://adsabs.harvard.edu/abs/1973CMaPh..31..161B
 ↑ http://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
 ↑ http://www.physlink.com/education/askexperts/ae635.cfm
 ↑ http://quantumfrontiers.com/2012/12/03/isaliceburningtheblackholefirewallcontroversy/
 ↑ http://arxiv.org/pdf/hepth/9209055v1.pdf