Income distribution

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Income_distribution 

In economics, income distribution covers how a country's total GDP is distributed amongst its population. Economic theory and economic policy have long seen income and its distribution as a central concern. Classical economists such as Adam Smith (1723–1790), Thomas Malthus (1766–1834), and David Ricardo (1772–1823) concentrated their attention on factor income-distribution, that is, the distribution of income between the primary factors of production (land, labour and capital). Modern economists have also addressed issues of income distribution, but have focused more on the distribution of income across individuals and households. Important theoretical and policy concerns include the balance between income inequality and economic growth, and their often inverse relationship.

The Lorenz curve can represent the distribution of income within a society. The Lorenz curve is closely associated with measures of income inequality, such as the Gini coefficient.

Measurement

Main article: Income inequality metrics

The concept of inequality is distinct from that of poverty and fairness. Income inequality metrics (or income distribution metrics) are used by social scientists to measure the distribution of income, and economic inequality among the participants in a particular economy, such as that of a specific country or of the world in general. While different theories may try to explain how income inequality comes about, income inequality metrics simply provide a system of measurement used to determine the dispersion of incomes.

Limitations

There exist some problems and limitations in the measurement of inequality as there is a large gap between the national accounts (which focus on macroeconomic totals) and inequality studies (which focus on distribution).

The lack of a comprehensive measure about how the pretax income differs from the post-tax income makes hard to assess how government redistribution effects inequality.

There is not a clear view on how long-run trends in income concentration are shaped by the major changes in woman's labour force participation.

Causes of income inequality

Main article: Economic inequality

Causes of income inequality and of levels of equality/inequality include: labor economics, tax policies, other economic policies, labor union policies, Federal Reserve monetary policies & fiscal policies, the market for labor, abilities of individual workers, technology and automation, education, globalization, gender bias, racism, and culture.

How to improve income inequality

Taxes

The progressive income tax takes a larger part of high incomes and a smaller percentage of low incomes. So that the poor pay less on taxes and keep larger percentage of their income, whereas the rich otherwise. It can be justified by the fact, that 100 dollars for the rich person mean less (almost nothing) than for the poor one (it can be the whole amount of income tax). The government uses the tax revenue also for the necessary and beneficial activities for the society. Let's say that everybody in society would have the same benefit from this activity, but the rich pay more for it, so this tax reduces the inequality twice.

In-kind transfers

If a cash is given to a poor person, he or she may not make "the best" choice in case, what to buy for this extra money. Then, there is the solution in form of the food stamps or directly the food as an in-kind transfer to the poorest.

Housing subsidies

The rent and upkeep of housing form a large portion of spending in the lower income families. Housing subsidies were designed to help the poor obtaining adequate housing.

Welfare and Unemployment benefits

This provides actual money to the people with very low or no income and gives them an absolute freedom in decision-making how to use this benefit. That is fine only if we assume that they are rational and make decisions in their best interest. However, the unemployment benefits do not motivate unemployed people to find the job, because they have no obligations and get money for nothing.

Distribution measurement internationally

Main article: List of countries by income inequality

Using Gini coefficients, several organizations, such as the United Nations (UN) and the US Central Intelligence Agency (CIA), have measured income inequality by country. The Gini index is also widely used within the World Bank. It is an accurate and reliable index for measuring income distribution on a country by country level. The Gini index measurements go from 0 to 1 for 1 being perfect inequality and 0 being perfect equality. The world Gini index is measured at 0.52 as of 2016.

2018 World gini Index

The World Inequality Lab at the Paris School of Economics published in December 2017 the World Inequality Report 2018 that provides estimates of global income and wealth inequality.

Trends

Idealized hypothetical Kuznets curve

Standard economic theory stipulates that inequality tends to increase over time as a country develops, and to decrease as a certain average income is attained. This theory is commonly known as the Kuznets curve after Simon Kuznets. However, many prominent economists disagree with the need for inequality to increase as a country develops. Further, empirical data on the proclaimed subsequent decrease of inequality is conflicting.

There are two ways of looking at income inequality, within country inequality (intra-country inequality) – which is inequality within a nation; or between country inequality (inter-country inequality) which is inequality between countries.

According to intra-country inequality at least in the OECD countries, a May 2011 report by OECD stated that the gap between rich and poor within OECD countries (most of which are "high income" economies) "has reached its highest level for over 30 years, and governments must act quickly to tackle inequality".

Furthermore, increased inter-country income inequality over a long period is conclusive, with the Gini coefficient (using PPP exchange rate, unweighted by population) more than doubling between 1820 and the 1980s from .20 to .52 (Nolan 2009:63). However, scholars disagree about whether inter-country income inequality has increased (Milanovic 2011), remained relatively stable (Bourguignon and Morrison 2002), or decreased (Sala-i-Martin, 2002) since 1980. What Milanovic (2005)  calls the “mother of all inequality disputes” emphasizes this debate by using the same data on Gini coefficient from 1950–2000 and showing that when countries’ GDP per capita incomes are unweighted by population income inequality increases, but when they are weighted inequality decreases. This has much to do with the recent average income rise in China and to some extent India, who represent almost two-fifths of the world. Notwithstanding, inter-country inequality is significant, for instance as a group the bottom 5% of US income distribution receives more income than over 68 percent of the world, and of the 60 million people that make up the top 1% of income distribution, 50 million of them are citizens of Western Europe, North America or Oceania (Milanovic 2011:116,156).

In a TED presentation shown here, Hans Rosling presented the distribution and change in income distribution of various nations over the course of a few decades along with other factors such as child survival and fertility rate.

As of 2018, Albania has the smallest gap in wealth distribution with Zimbabwe having the largest gap in wealth distribution.

Income distribution in different countries

Thailand

• Thailand has been ranked the world's third most unequal nation after Russia and India, with a widening gap between rich and poor according to Oxfam in 2016. A study by Thammasat University economist Duangmanee Laovakul in 2013 showed that the country's top 20 land owners owned 80 percent of the nation's land. The bottom 20 owned only 0.3 percent. Among those having bank deposits, 0.1 percent of bank accounts held 49 per cent of total bank deposits. As of 2019, Thai per capita income is US$8,000 a year. The government aims to raise it to US$15,000 (498,771 baht) per year, driven by average GDP growth of five to six percent. Under the 20-year national plan stretching out to 2036, the government intends to narrow the income disparity gap to 15 times, down from 20 times in 2018.

Income distribution in the United States

Main article: Household income in the United States

Further information: Income inequality in the United States

2011: In the United States, income has become distributed more unequally over the past 30 years, with those in the top quintile (20 percent) earning more than the bottom 80 percent combined.

2019: The wealthiest 10 % of American households control nearly 75 % of household net worth.

• Post-tax Gini coefficient: 0.39.
• Unemployment rate: 4.4 %.
• GDP per capita: $53 632.
• Poverty rate: 17.8 %.

Low unemployment rate and high GDP are signs of the health of the U.S. economy. But there is almost 18 % of people living below the poverty line and the Gini coefficient is quite high. That ranks the United States 9th income inequal in the world.

Income distribution in the United Kingdom

Inequality in the UK has been very high in the past, and did not change much until the onset of industrialization. Incomes used to be remarkably concentrated pre-industrial evolution: up to 40% of total income went into the pockets of the richest 5%. In the more recent years income distribution is still an issue. The UK experienced a large increase in inequality during the 1980s—the incomes of the highest deciles increase while everyone else was stagnant. Uneven growth in the years leading up to 1991 meant further increases in inequality. Throughout the 1990s and 2000s, more even growth across the distribution meant little changes in inequality, with rising incomes for everybody. In sight of Brexit, there is more predicted income distribution discrepancies between wages.

2019: The United Kingdom was doing a lot to reduce one of the widest gap between rich and poor citizens, what has led to getting on the 13th place in the ranking of income inequality in the world.

• Post-tax Gini coefficient: 0.35.
• Unemployment rate: 4.3 %.
• GDP per capita: $39 425.
• Poverty rate: 11.1 %.

Russia

• Post-tax Gini coefficient: 0.38.
• Unemployment rate: 5.2 %.
• GDP per capita: $24 417.
• Poverty rate: NA.

Occupying the 11th place in the ranking of income inequality in the world. USA TODAY stated: "Russia has a Corruption Perceptions Index score of 28 – tied for the worst among OECD member states and affiliates and one of the lowest in the world. " The cause of the income gap are the close connections of Russian oligarchs and the government, thanks to theese relationships oligarchs get lucrative business deals and earn more and more money.

South Africa

• Post-tax Gini coefficient: 0.62.
• Unemployment rate: 27.3 %.
• GDP per capita: $12 287.
• Poverty rate: 26.6 %.

The highest income inequality is in the South Africa, based on 2019 data. It is due to the recent policy of apartheid. There were huge differences between white and the other people, not only in wages, but also in the place they can enter and so on.

Other

High income inequality appears in China, India, Costa Rica, Brazil, Mexico, Chile, Turkey, Lithuania, South Korea, New Zealand and Latvia too.

Development of income distribution as a stochastic process

It is very difficult to create a realistic and not very complicated theoretical model, because the forces determining the distribution of income (DoI) are so varied and complex and they continuously interact and fluctuate.

In this model let assume that the income scale is divided into an enumerable infinity of income ranges, which have uniform proportionate distribution. The development through time of the DoI between ranges we shall regard to be the stochastic process. The income of any person in one year may depend on the income in the previous year and on a chance of progress. Assuming that to every "dying" income receiver, there is an heir to his or her income in the following year, and vice versa. This implies that the number of incomes is constant through time. (It is not difficult to allow more or less than one heir to each dying individual, but it will lose the simplicity.)

Under these assumptions any historical development of the DoI can be described by the following vectors and matrices.

• ${\displaystyle X_{r}(0)}$ ... number of the income receivers in range r = 1, 2, ... in the initial year ${\displaystyle Y_{0}}$
• ${\displaystyle p'_{rs}(t)}$ ... matrix, that contains proportions of the occupants of r-th range in the year ${\displaystyle Y_{t}}$ shifted to the s-th range in the following year ${\displaystyle Y_{t+1}}$

The vector of the DoI can be expressed as

${\displaystyle X_{s}(t+1)=\sum _{r=0}^{\infty }X_{r}(t)p'_{rs}(t).}$

The elements of proportion matrices can be estimated from historical data.

Luminiferous aether

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Luminiferous_aether 

 

The luminiferous aether: it was hypothesised that the Earth moves through a "medium" of aether that carries light

Luminiferous aether or ether ("luminiferous", meaning "light-bearing") was the postulated medium for the propagation of light. It was invoked to explain the ability of the apparently wave-based light to propagate through empty space (a vacuum), something that waves should not be able to do. The assumption of a spatial plenum of luminiferous aether, rather than a spatial vacuum, provided the theoretical medium that was required by wave theories of light.

The aether hypothesis was the topic of considerable debate throughout its history, as it required the existence of an invisible and infinite material with no interaction with physical objects. As the nature of light was explored, especially in the 19th century, the physical qualities required of an aether became increasingly contradictory. By the late 1800s, the existence of the aether was being questioned, although there was no physical theory to replace it.

The negative outcome of the Michelson–Morley experiment (1887) suggested that the aether did not exist, a finding that was confirmed in subsequent experiments through the 1920s. This led to considerable theoretical work to explain the propagation of light without an aether. A major breakthrough was the theory of relativity, which could explain why the experiment failed to see aether, but was more broadly interpreted to suggest that it was not needed. The Michelson-Morley experiment, along with the blackbody radiator and photoelectric effect, was a key experiment in the development of modern physics, which includes both relativity and quantum theory, the latter of which explains the particle-like nature of light.

The history of light and aether

See also: Timeline of luminiferous aether

Particles vs. waves

Main article: Wave–particle duality

In the 17th century, Robert Boyle was a proponent of an aether hypothesis. According to Boyle, the aether consists of subtle particles, one sort of which explains the absence of vacuum and the mechanical interactions between bodies, and the other sort of which explains phenomena such as magnetism (and possibly gravity) that are, otherwise, inexplicable on the basis of purely mechanical interactions of macroscopic bodies, "though in the ether of the ancients there was nothing taken notice of but a diffused and very subtle substance; yet we are at present content to allow that there is always in the air a swarm of steams moving in a determinate course between the north pole and the south".

Christiaan Huygens's Treatise on Light (1690) hypothesized that light is a wave propagating through an aether. He and Isaac Newton could only envision light waves as being longitudinal, propagating like sound and other mechanical waves in fluids. However, longitudinal waves necessarily have only one form for a given propagation direction, rather than two polarizations like a transverse wave. Thus, longitudinal waves can not explain birefringence, in which two polarizations of light are refracted differently by a crystal. In addition, Newton rejected light as waves in a medium because such a medium would have to extend everywhere in space, and would thereby "disturb and retard the Motions of those great Bodies" (the planets and comets) and thus "as it [light's medium] is of no use, and hinders the Operation of Nature, and makes her languish, so there is no evidence for its Existence, and therefore it ought to be rejected".

Isaac Newton contended that light is made up of numerous small particles. This can explain such features as light's ability to travel in straight lines and reflect off surfaces. Newton imagined light particles as non-spherical "corpuscles", with different "sides" that give rise to birefringence. But the particle theory of light can not satisfactorily explain refraction and diffraction. To explain refraction, Newton's Third Book of Opticks (1st ed. 1704, 4th ed. 1730) postulated an "aethereal medium" transmitting vibrations faster than light, by which light, when overtaken, is put into "Fits of easy Reflexion and easy Transmission", which caused refraction and diffraction. Newton believed that these vibrations were related to heat radiation:

Is not the Heat of the warm Room convey'd through the vacuum by the Vibrations of a much subtiler Medium than Air, which after the Air was drawn out remained in the Vacuum? And is not this Medium the same with that Medium by which Light is refracted and reflected, and by whose Vibrations Light communicates Heat to Bodies, and is put into Fits of easy Reflexion and easy Transmission?

In contrast to the modern understanding that heat radiation and light are both electromagnetic radiation, Newton viewed heat and light as two different phenomena. He believed heat vibrations to be excited "when a Ray of Light falls upon the Surface of any pellucid Body". He wrote, "I do not know what this Aether is", but that if it consists of particles then they must be

exceedingly smaller than those of Air, or even than those of Light: The exceeding smallness of its Particles may contribute to the greatness of the force by which those Particles may recede from one another, and thereby make that Medium exceedingly more rare and elastic than Air, and by consequence exceedingly less able to resist the motions of Projectiles, and exceedingly more able to press upon gross Bodies, by endeavoring to expand itself.

Bradley suggests particles

In 1720, James Bradley carried out a series of experiments attempting to measure stellar parallax by taking measurements of stars at different times of the year. As the Earth moves around the sun, the apparent angle to a given distant spot changes. By measuring those angles the distance to the star can be calculated based on the known orbital circumference of the Earth around the sun. He failed to detect any parallax, thereby placing a lower limit on the distance to stars.

During these experiments, Bradley also discovered a related effect; the apparent positions of the stars did change over the year, but not as expected. Instead of the apparent angle being maximized when the Earth was at either end of its orbit with respect to the star, the angle was maximized when the Earth was at its fastest sideways velocity with respect to the star. This effect is now known as stellar aberration.

Bradley explained this effect in the context of Newton's corpuscular theory of light, by showing that the aberration angle was given by simple vector addition of the Earth's orbital velocity and the velocity of the corpuscles of light, just as vertically falling raindrops strike a moving object at an angle. Knowing the Earth's velocity and the aberration angle, this enabled him to estimate the speed of light.

Explaining stellar aberration in the context of an aether-based theory of light was regarded as more problematic. As the aberration relied on relative velocities, and the measured velocity was dependent on the motion of the Earth, the aether had to be remaining stationary with respect to the star as the Earth moved through it. This meant that the Earth could travel through the aether, a physical medium, with no apparent effect – precisely the problem that led Newton to reject a wave model in the first place.

Wave-theory triumphs

A century later, Thomas Young and Augustin-Jean Fresnel revived the wave theory of light when they pointed out that light could be a transverse wave rather than a longitudinal wave; the polarization of a transverse wave (like Newton's "sides" of light) could explain birefringence, and in the wake of a series of experiments on diffraction the particle model of Newton was finally abandoned. Physicists assumed, moreover, that, like mechanical waves, light waves required a medium for propagation, and thus required Huygens's idea of an aether "gas" permeating all space.

However, a transverse wave apparently required the propagating medium to behave as a solid, as opposed to a fluid. The idea of a solid that did not interact with other matter seemed a bit odd, and Augustin-Louis Cauchy suggested that perhaps there was some sort of "dragging", or "entrainment", but this made the aberration measurements difficult to understand. He also suggested that the absence of longitudinal waves suggested that the aether had negative compressibility. George Green pointed out that such a fluid would be unstable. George Gabriel Stokes became a champion of the entrainment interpretation, developing a model in which the aether might be (by analogy with pine pitch) rigid at very high frequencies and fluid at lower speeds. Thus the Earth could move through it fairly freely, but it would be rigid enough to support light.

Electromagnetism

In 1856, Wilhelm Eduard Weber and Rudolf Kohlrausch measured the numerical value of the ratio of the electrostatic unit of charge to the electromagnetic unit of charge. They found that the ratio equals the product of the speed of light and the square root of two. The following year, Gustav Kirchhoff wrote a paper in which he showed that the speed of a signal along an electric wire was equal to the speed of light. These are the first recorded historical links between the speed of light and electromagnetic phenomena.

James Clerk Maxwell began working on Michael Faraday's lines of force. In his 1861 paper On Physical Lines of Force he modelled these magnetic lines of force using a sea of molecular vortices that he considered to be partly made of aether and partly made of ordinary matter. He derived expressions for the dielectric constant and the magnetic permeability in terms of the transverse elasticity and the density of this elastic medium. He then equated the ratio of the dielectric constant to the magnetic permeability with a suitably adapted version of Weber and Kohlrausch's result of 1856, and he substituted this result into Newton's equation for the speed of sound. On obtaining a value that was close to the speed of light as measured by Hippolyte Fizeau, Maxwell concluded that light consists in undulations of the same medium that is the cause of electric and magnetic phenomena.

Maxwell had, however, expressed some uncertainties surrounding the precise nature of his molecular vortices and so he began to embark on a purely dynamical approach to the problem. He wrote another paper in 1864, entitled "A Dynamical Theory of the Electromagnetic Field", in which the details of the luminiferous medium were less explicit. Although Maxwell did not explicitly mention the sea of molecular vortices, his derivation of Ampère's circuital law was carried over from the 1861 paper and he used a dynamical approach involving rotational motion within the electromagnetic field which he likened to the action of flywheels. Using this approach to justify the electromotive force equation (the precursor of the Lorentz force equation), he derived a wave equation from a set of eight equations which appeared in the paper and which included the electromotive force equation and Ampère's circuital law. Maxwell once again used the experimental results of Weber and Kohlrausch to show that this wave equation represented an electromagnetic wave that propagates at the speed of light, hence supporting the view that light is a form of electromagnetic radiation.

The apparent need for a propagation medium for such Hertzian waves can be seen by the fact that they consist of orthogonal electric (E) and magnetic (B or H) waves. The E waves consist of undulating dipolar electric fields, and all such dipoles appeared to require separated and opposite electric charges. Electric charge is an inextricable property of matter, so it appeared that some form of matter was required to provide the alternating current that would seem to have to exist at any point along the propagation path of the wave. Propagation of waves in a true vacuum would imply the existence of electric fields without associated electric charge, or of electric charge without associated matter. Albeit compatible with Maxwell's equations, electromagnetic induction of electric fields could not be demonstrated in vacuum, because all methods of detecting electric fields required electrically charged matter.

In addition, Maxwell's equations required that all electromagnetic waves in vacuum propagate at a fixed speed, c. As this can only occur in one reference frame in Newtonian physics (see Galilean relativity), the aether was hypothesized as the absolute and unique frame of reference in which Maxwell's equations hold. That is, the aether must be "still" universally, otherwise c would vary along with any variations that might occur in its supportive medium. Maxwell himself proposed several mechanical models of aether based on wheels and gears, and George Francis FitzGerald even constructed a working model of one of them. These models had to agree with the fact that the electromagnetic waves are transverse but never longitudinal.

Problems

By this point the mechanical qualities of the aether had become more and more magical: it had to be a fluid in order to fill space, but one that was millions of times more rigid than steel in order to support the high frequencies of light waves. It also had to be massless and without viscosity, otherwise it would visibly affect the orbits of planets. Additionally it appeared it had to be completely transparent, non-dispersive, incompressible, and continuous at a very small scale. Maxwell wrote in Encyclopædia Britannica:

Aethers were invented for the planets to swim in, to constitute electric atmospheres and magnetic effluvia, to convey sensations from one part of our bodies to another, and so on, until all space had been filled three or four times over with aethers. ... The only aether which has survived is that which was invented by Huygens to explain the propagation of light.

Contemporary scientists were aware of the problems, but aether theory was so entrenched in physical law by this point that it was simply assumed to exist. In 1908 Oliver Lodge gave a speech on behalf of Lord Rayleigh to the Royal Institution on this topic, in which he outlined its physical properties, and then attempted to offer reasons why they were not impossible. Nevertheless, he was also aware of the criticisms, and quoted Lord Salisbury as saying that "aether is little more than a nominative case of the verb to undulate". Others criticized it as an "English invention", although Rayleigh jokingly stated it was actually an invention of the Royal Institution.

By the early 20th century, aether theory was in trouble. A series of increasingly complex experiments had been carried out in the late 19th century to try to detect the motion of the Earth through the aether, and had failed to do so. A range of proposed aether-dragging theories could explain the null result but these were more complex, and tended to use arbitrary-looking coefficients and physical assumptions. Lorentz and FitzGerald offered within the framework of Lorentz ether theory a more elegant solution to how the motion of an absolute aether could be undetectable (length contraction), but if their equations were correct, the new special theory of relativity (1905) could generate the same mathematics without referring to an aether at all. Aether fell to Occam's Razor.

Relative motion between the Earth and aether

Aether drag

Main article: Aether drag hypothesis

The two most important models, which were aimed to describe the relative motion of the Earth and aether, were Augustin-Jean Fresnel's (1818) model of the (nearly) stationary aether including a partial aether drag determined by Fresnel's dragging coefficient, and George Gabriel Stokes' (1844) model of complete aether drag. The latter theory was not considered as correct, since it was not compatible with the aberration of light, and the auxiliary hypotheses developed to explain this problem were not convincing. Also, subsequent experiments as the Sagnac effect (1913) also showed that this model is untenable. However, the most important experiment supporting Fresnel's theory was Fizeau's 1851 experimental confirmation of Fresnel's 1818 prediction that a medium with refractive index n moving with a velocity v would increase the speed of light travelling through the medium in the same direction as v from c/n to:

${\displaystyle {\frac {c}{n}}+\left(1-{\frac {1}{n^{2}}}\right)v.}$

That is, movement adds only a fraction of the medium's velocity to the light (predicted by Fresnel in order to make Snell's law work in all frames of reference, consistent with stellar aberration). This was initially interpreted to mean that the medium drags the aether along, with a portion of the medium's velocity, but that understanding became very problematic after Wilhelm Veltmann demonstrated that the index n in Fresnel's formula depended upon the wavelength of light, so that the aether could not be moving at a wavelength-independent speed. This implied that there must be a separate aether for each of the infinitely many frequencies.

Negative aether-drift experiments

The key difficulty with Fresnel's aether hypothesis arose from the juxtaposition of the two well-established theories of Newtonian dynamics and Maxwell's electromagnetism. Under a Galilean transformation the equations of Newtonian dynamics are invariant, whereas those of electromagnetism are not. Basically this means that while physics should remain the same in non-accelerated experiments, light would not follow the same rules because it is travelling in the universal "aether frame". Some effect caused by this difference should be detectable.

A simple example concerns the model on which aether was originally built: sound. The speed of propagation for mechanical waves, the speed of sound, is defined by the mechanical properties of the medium. Sound travels 4.3 times faster in water than in air. This explains why a person hearing an explosion underwater and quickly surfacing can hear it again as the slower travelling sound arrives through the air. Similarly, a traveller on an airliner can still carry on a conversation with another traveller because the sound of words is travelling along with the air inside the aircraft. This effect is basic to all Newtonian dynamics, which says that everything from sound to the trajectory of a thrown baseball should all remain the same in the aircraft flying (at least at a constant speed) as if still sitting on the ground. This is the basis of the Galilean transformation, and the concept of frame of reference.

But the same was not supposed to be true for light, since Maxwell's mathematics demanded a single universal speed for the propagation of light, based, not on local conditions, but on two measured properties, the permittivity and permeability of free space, that were assumed to be the same throughout the universe. If these numbers did change, there should be noticeable effects in the sky; stars in different directions would have different colours, for instance.

Thus at any point there should be one special coordinate system, "at rest relative to the aether". Maxwell noted in the late 1870s that detecting motion relative to this aether should be easy enough—light travelling along with the motion of the Earth would have a different speed than light travelling backward, as they would both be moving against the unmoving aether. Even if the aether had an overall universal flow, changes in position during the day/night cycle, or over the span of seasons, should allow the drift to be detected.

First order experiments

Although the aether is almost stationary according to Fresnel, his theory predicts a positive outcome of aether drift experiments only to second order in ${\displaystyle v/c}$, because Fresnel's dragging coefficient would cause a negative outcome of all optical experiments capable of measuring effects to first order in ${\displaystyle v/c}$. This was confirmed by the following first-order experiments, which all gave negative results. The following list is based on the description of Wilhelm Wien (1898), with changes and additional experiments according to the descriptions of Edmund Taylor Whittaker (1910) and Jakob Laub (1910):

• The experiment of François Arago (1810), to confirm whether refraction, and thus the aberration of light, is influenced by Earth's motion. Similar experiments were conducted by George Biddell Airy (1871) by means of a telescope filled with water, and Éleuthère Mascart (1872).
• The experiment of Fizeau (1860), to find whether the rotation of the polarization plane through glass columns is changed by Earth's motion. He obtained a positive result, but Lorentz could show that the results have been contradictory. DeWitt Bristol Brace (1905) and Strasser (1907) repeated the experiment with improved accuracy, and obtained negative results.
• The experiment of Martin Hoek (1868). This experiment is a more precise variation of the Fizeau experiment (1851). Two light rays were sent in opposite directions – one of them traverses a path filled with resting water, the other one follows a path through air. In agreement with Fresnel's dragging coefficient, he obtained a negative result.
• The experiment of Wilhelm Klinkerfues (1870) investigated whether an influence of Earth's motion on the absorption line of sodium exists. He obtained a positive result, but this was shown to be an experimental error, because a repetition of the experiment by Haga (1901) gave a negative result.
• The experiment of Ketteler (1872), in which two rays of an interferometer were sent in opposite directions through two mutually inclined tubes filled with water. No change of the interference fringes occurred. Later, Mascart (1872) showed that the interference fringes of polarized light in calcite remained uninfluenced as well.
• The experiment of Éleuthère Mascart (1872) to find a change of rotation of the polarization plane in quartz. No change of rotation was found when the light rays had the direction of Earth's motion and then the opposite direction. Lord Rayleigh conducted similar experiments with improved accuracy, and obtained a negative result as well.

Besides those optical experiments, also electrodynamic first-order experiments were conducted, which should have led to positive results according to Fresnel. However, Hendrik Antoon Lorentz (1895) modified Fresnel's theory and showed that those experiments can be explained by a stationary aether as well:

• The experiment of Wilhelm Röntgen (1888), to find whether a charged condenser produces magnetic forces due to Earth's motion.
• The experiment of Theodor des Coudres (1889), to find whether the inductive effect of two wire rolls upon a third one is influenced by the direction of Earth's motion. Lorentz showed that this effect is cancelled to first order by the electrostatic charge (produced by Earth's motion) upon the conductors.
• The experiment of Königsberger (1905). The plates of a condenser are located in the field of a strong electromagnet. Due to Earth's motion, the plates should have become charged. No such effect was observed.
• The experiment of Frederick Thomas Trouton (1902). A condenser was brought parallel to Earth's motion, and it was assumed that momentum is produced when the condenser is charged. The negative result can be explained by Lorentz's theory, according to which the electromagnetic momentum compensates the momentum due to Earth's motion. Lorentz could also show, that the sensitivity of the apparatus was much too low to observe such an effect.

Second order experiments

The Michelson–Morley experiment compared the time for light to reflect from mirrors in two orthogonal directions.

While the first-order experiments could be explained by a modified stationary aether, more precise second-order experiments were expected to give positive results, however, no such results could be found.

The famous Michelson–Morley experiment compared the source light with itself after being sent in different directions, looking for changes in phase in a manner that could be measured with extremely high accuracy. In this experiment, their goal was to determine the velocity of the Earth through the aether. The publication of their result in 1887, the null result, was the first clear demonstration that something was seriously wrong with the aether hypothesis (Michelson's first experiment in 1881 was not entirely conclusive). In this case the MM experiment yielded a shift of the fringing pattern of about 0.01 of a fringe, corresponding to a small velocity. However, it was incompatible with the expected aether wind effect due to the Earth's (seasonally varying) velocity which would have required a shift of 0.4 of a fringe, and the error was small enough that the value may have indeed been zero. Therefore, the null hypothesis, the hypothesis that there was no aether wind, could not be rejected. More modern experiments have since reduced the possible value to a number very close to zero, about 10⁻¹⁷.

It is obvious from what has gone before that it would be hopeless to attempt to solve the question of the motion of the solar system by observations of optical phenomena at the surface of the earth.

— A. Michelson and E. Morley. "On the Relative Motion of the Earth and the Luminiferous Æther". Philosophical Magazine S. 5. Vol. 24. No. 151. December 1887.

A series of experiments using similar but increasingly sophisticated apparatuses all returned the null result as well. Conceptually different experiments that also attempted to detect the motion of the aether were the Trouton–Noble experiment (1903), whose objective was to detect torsion effects caused by electrostatic fields, and the experiments of Rayleigh and Brace (1902, 1904), to detect double refraction in various media. However, all of them obtained a null result, like Michelson–Morley (MM) previously did.

These "aether-wind" experiments led to a flurry of efforts to "save" aether by assigning to it ever more complex properties, while only few scientists, like Emil Cohn or Alfred Bucherer, considered the possibility of the abandonment of the aether hypothesis. Of particular interest was the possibility of "aether entrainment" or "aether drag", which would lower the magnitude of the measurement, perhaps enough to explain the results of the Michelson-Morley experiment. However, as noted earlier, aether dragging already had problems of its own, notably aberration. In addition, the interference experiments of Lodge (1893, 1897) and Ludwig Zehnder (1895), aimed to show whether the aether is dragged by various, rotating masses, showed no aether drag. A more precise measurement was made in the Hammar experiment (1935), which ran a complete MM experiment with one of the "legs" placed between two massive lead blocks. If the aether was dragged by mass then this experiment would have been able to detect the drag caused by the lead, but again the null result was achieved. The theory was again modified, this time to suggest that the entrainment only worked for very large masses or those masses with large magnetic fields. This too was shown to be incorrect by the Michelson–Gale–Pearson experiment, which detected the Sagnac effect due to Earth's rotation (see Aether drag hypothesis).

Another, completely different attempt to save "absolute" aether was made in the Lorentz–FitzGerald contraction hypothesis, which posited that everything was affected by travel through the aether. In this theory the reason the Michelson–Morley experiment "failed" was that the apparatus contracted in length in the direction of travel. That is, the light was being affected in the "natural" manner by its travel through the aether as predicted, but so was the apparatus itself, cancelling out any difference when measured. FitzGerald had inferred this hypothesis from a paper by Oliver Heaviside. Without referral to an aether, this physical interpretation of relativistic effects was shared by Kennedy and Thorndike in 1932 as they concluded that the interferometer's arm contracts and also the frequency of its light source "very nearly" varies in the way required by relativity.

Similarly the Sagnac effect, observed by G. Sagnac in 1913, was immediately seen to be fully consistent with special relativity. In fact, the Michelson-Gale-Pearson experiment in 1925 was proposed specifically as a test to confirm the relativity theory, although it was also recognized that such tests, which merely measure absolute rotation, are also consistent with non-relativistic theories.

During the 1920s, the experiments pioneered by Michelson were repeated by Dayton Miller, who publicly proclaimed positive results on several occasions, although they were not large enough to be consistent with any known aether theory. However, other researchers were unable to duplicate Miller's claimed results. Over the years the experimental accuracy of such measurements has been raised by many orders of magnitude, and no trace of any violations of Lorentz invariance has been seen. (A later re-analysis of Miller's results concluded that he had underestimated the variations due to temperature.)

Since the Miller experiment and its unclear results there have been many more experimental attempts to detect the aether. Many experimenters have claimed positive results. These results have not gained much attention from mainstream science, since they contradict a large quantity of high-precision measurements, all the results of which were consistent with special relativity.

Lorentz aether theory

Main article: Lorentz ether theory

Between 1892 and 1904, Hendrik Lorentz developed an electron-aether theory, in which he introduced a strict separation between matter (electrons) and aether. In his model the aether is completely motionless, and won't be set in motion in the neighborhood of ponderable matter. Contrary to earlier electron models, the electromagnetic field of the aether appears as a mediator between the electrons, and changes in this field cannot propagate faster than the speed of light. A fundamental concept of Lorentz's theory in 1895 was the "theorem of corresponding states" for terms of order v/c. This theorem states that an observer moving relative to the aether makes the same observations as a resting observer, after a suitable change of variables. Lorentz noticed that it was necessary to change the space-time variables when changing frames and introduced concepts like physical length contraction (1892) to explain the Michelson–Morley experiment, and the mathematical concept of local time (1895) to explain the aberration of light and the Fizeau experiment. This resulted in the formulation of the so-called Lorentz transformation by Joseph Larmor (1897, 1900) and Lorentz (1899, 1904), whereby (it was noted by Larmor) the complete formulation of local time is accompanied by some sort of time dilation of electrons moving in the aether. As Lorentz later noted (1921, 1928), he considered the time indicated by clocks resting in the aether as "true" time, while local time was seen by him as a heuristic working hypothesis and a mathematical artifice. Therefore, Lorentz's theorem is seen by modern authors as being a mathematical transformation from a "real" system resting in the aether into a "fictitious" system in motion.

The work of Lorentz was mathematically perfected by Henri Poincaré, who formulated on many occasions the Principle of Relativity and tried to harmonize it with electrodynamics. He declared simultaneity only a convenient convention which depends on the speed of light, whereby the constancy of the speed of light would be a useful postulate for making the laws of nature as simple as possible. In 1900 and 1904 he physically interpreted Lorentz's local time as the result of clock synchronization by light signals. In June and July 1905 he declared the relativity principle a general law of nature, including gravitation. He corrected some mistakes of Lorentz and proved the Lorentz covariance of the electromagnetic equations. However, he used the notion of an aether as a perfectly undetectable medium and distinguished between apparent and real time, so most historians of science argue that he failed to invent special relativity.

End of aether

Special relativity

Aether theory was dealt another blow when the Galilean transformation and Newtonian dynamics were both modified by Albert Einstein's special theory of relativity, giving the mathematics of Lorentzian electrodynamics a new, "non-aether" context. Unlike most major shifts in scientific thought, special relativity was adopted by the scientific community remarkably quickly, consistent with Einstein's later comment that the laws of physics described by the Special Theory were "ripe for discovery" in 1905. Max Planck's early advocacy of the special theory, along with the elegant formulation given to it by Hermann Minkowski, contributed much to the rapid acceptance of special relativity among working scientists.

Einstein based his theory on Lorentz's earlier work. Instead of suggesting that the mechanical properties of objects changed with their constant-velocity motion through an undetectable aether, Einstein proposed to deduce the characteristics that any successful theory must possess in order to be consistent with the most basic and firmly established principles, independent of the existence of a hypothetical aether. He found that the Lorentz transformation must transcend its connection with Maxwell's equations, and must represent the fundamental relations between the space and time coordinates of inertial frames of reference. In this way he demonstrated that the laws of physics remained invariant as they had with the Galilean transformation, but that light was now invariant as well.

With the development of the special theory of relativity, the need to account for a single universal frame of reference had disappeared – and acceptance of the 19th-century theory of a luminiferous aether disappeared with it. For Einstein, the Lorentz transformation implied a conceptual change: that the concept of position in space or time was not absolute, but could differ depending on the observer's location and velocity.

Moreover, in another paper published the same month in 1905, Einstein made several observations on a then-thorny problem, the photoelectric effect. In this work he demonstrated that light can be considered as particles that have a "wave-like nature". Particles obviously do not need a medium to travel, and thus, neither did light. This was the first step that would lead to the full development of quantum mechanics, in which the wave-like nature and the particle-like nature of light are both considered as valid descriptions of light. A summary of Einstein's thinking about the aether hypothesis, relativity and light quanta may be found in his 1909 (originally German) lecture "The Development of Our Views on the Composition and Essence of Radiation".

Lorentz on his side continued to use the aether hypothesis. In his lectures of around 1911, he pointed out that what "the theory of relativity has to say ... can be carried out independently of what one thinks of the aether and the time". He commented that "whether there is an aether or not, electromagnetic fields certainly exist, and so also does the energy of the electrical oscillations" so that, "if we do not like the name of 'aether', we must use another word as a peg to hang all these things upon". He concluded that "one cannot deny the bearer of these concepts a certain substantiality".

Other models

Main article: Aether theories

In later years there have been a few individuals who advocated a neo-Lorentzian approach to physics, which is Lorentzian in the sense of positing an absolute true state of rest that is undetectable and which plays no role in the predictions of the theory. (No violations of Lorentz covariance have ever been detected, despite strenuous efforts.) Hence these theories resemble the 19th century aether theories in name only. For example, the founder of quantum field theory, Paul Dirac, stated in 1951 in an article in Nature, titled "Is there an Aether?" that "we are rather forced to have an aether". However, Dirac never formulated a complete theory, and so his speculations found no acceptance by the scientific community.

Einstein's views on the aether

When Einstein was still a student in the Zurich Polytechnic in 1900, he was very interested in the idea of aether. His initial proposal of research thesis was to do an experiment to measure how fast the Earth was moving through the aether. "The velocity of a wave is proportional to the square root of the elastic forces which cause [its] propagation, and inversely proportional to the mass of the aether moved by these forces."

In 1916, after Einstein completed his foundational work on general relativity, Lorentz wrote a letter to him in which he speculated that within general relativity the aether was re-introduced. In his response Einstein wrote that one can actually speak about a "new aether", but one may not speak of motion in relation to that aether. This was further elaborated by Einstein in some semi-popular articles (1918, 1920, 1924, 1930).

In 1918 Einstein publicly alluded to that new definition for the first time. Then, in the early 1920s, in a lecture which he was invited to give at Lorentz's university in Leiden, Einstein sought to reconcile the theory of relativity with Lorentzian aether. In this lecture Einstein stressed that special relativity took away the last mechanical property of the aether: immobility. However, he continued that special relativity does not necessarily rule out the aether, because the latter can be used to give physical reality to acceleration and rotation. This concept was fully elaborated within general relativity, in which physical properties (which are partially determined by matter) are attributed to space, but no substance or state of motion can be attributed to that "aether" (by which he meant curved space-time).

In another paper of 1924, named "Concerning the Aether", Einstein argued that Newton's absolute space, in which acceleration is absolute, is the "Aether of Mechanics". And within the electromagnetic theory of Maxwell and Lorentz one can speak of the "Aether of Electrodynamics", in which the aether possesses an absolute state of motion. As regards special relativity, also in this theory acceleration is absolute as in Newton's mechanics. However, the difference from the electromagnetic aether of Maxwell and Lorentz lies in the fact that "because it was no longer possible to speak, in any absolute sense, of simultaneous states at different locations in the aether, the aether became, as it were, four-dimensional since there was no objective way of ordering its states by time alone". Now the "aether of special relativity" is still "absolute", because matter is affected by the properties of the aether, but the aether is not affected by the presence of matter. This asymmetry was solved within general relativity. Einstein explained that the "aether of general relativity" is not absolute, because matter is influenced by the aether, just as matter influences the structure of the aether.

The only similarity of this relativistic aether concept with the classical aether models lies in the presence of physical properties in space, which can be identified through geodesics. As historians such as John Stachel argue, Einstein's views on the "new aether" are not in conflict with his abandonment of the aether in 1905. As Einstein himself pointed out, no "substance" and no state of motion can be attributed to that new aether. Einstein's use of the word "aether" found little support in the scientific community, and played no role in the continuing development of modern physics.

Criticism of the theory of relativity

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Criticism_of_the_theory_of_relativity 

Criticism of the theory of relativity of Albert Einstein was mainly expressed in the early years after its publication in the early twentieth century, on scientific, pseudoscientific, philosophical, or ideological bases. Though some of these criticisms had the support of reputable scientists, Einstein's theory of relativity is now accepted by the scientific community.

Reasons for criticism of the theory of relativity have included alternative theories, rejection of the abstract-mathematical method, and alleged errors of the theory. According to some authors, antisemitic objections to Einstein's Jewish heritage also occasionally played a role in these objections. There are still some critics of relativity today, but their opinions are not shared by the majority in the scientific community.

Special relativity

Relativity principle versus electromagnetic worldview

Around the end of the 19th century, the view was widespread that all forces in nature are of electromagnetic origin (the "electromagnetic worldview"), especially in the works of Joseph Larmor (1897) and Wilhelm Wien (1900). This was apparently confirmed by the experiments of Walter Kaufmann (1901–1903), who measured an increase of the mass of a body with velocity which was consistent with the hypothesis that the mass was generated by its electromagnetic field. Max Abraham (1902) subsequently sketched a theoretical explanation of Kaufmann's result in which the electron was considered as rigid and spherical. However, it was found that this model was incompatible with the results of many experiments (including the Michelson–Morley experiment, the Experiments of Rayleigh and Brace, and the Trouton–Noble experiment), according to which no motion of an observer with respect to the luminiferous aether ("aether drift") had been observed despite numerous attempts to do so. Henri Poincaré (1902) conjectured that this failure arose from a general law of nature, which he called "the principle of relativity". Hendrik Antoon Lorentz (1904) created a detailed theory of electrodynamics (Lorentz ether theory) that was premised on the existence of an immobile aether and employed a set of space and time coordinate transformations that Poincaré called the Lorentz transformations, including the effects of length contraction and local time. However, Lorentz's theory only partially satisfied the relativity principle, because his transformation formulas for velocity and charge density were incorrect. This was corrected by Poincaré (1905) who obtained full Lorentz covariance of the electrodynamic equations.

Criticizing Lorentz's 1904 theory, Abraham (1904) held that the Lorentz contraction of electrons requires a non-electromagnetic force to ensure the electron's stability. This was unacceptable to him as a proponent of the electromagnetic worldview. He continued that as long as a consistent explanation is missing as to how those forces and potentials act together on the electron, Lorentz's system of hypotheses is incomplete and doesn't satisfy the relativity principle. Poincaré (1905) removed this objection by showing that the non-electromagnetic potential ("Poincaré stress") holding the electron together can be formulated in a Lorentz covariant way, and showed that in principle it is possible to create a Lorentz covariant model for gravitation which he considered non-electromagnetic in nature as well. Thus the consistency of Lorentz's theory was proven, but the electromagnetic worldview had to be given up. Eventually, Albert Einstein published in September 1905 what is now called special relativity, which was based on a radical new application of the relativity principle in connection with the constancy of the speed of light. In special relativity, the space and time coordinates depend on the inertial observer's frame of reference, and the luminiferous aether plays no role in the physics. Although this theory was founded on a very different kinematical model, it was experimentally indistinguishable from the aether theory of Lorentz and Poincaré, since both theories satisfy the relativity principle of Poincaré and Einstein, and both employ the Lorentz transformations. After Minkowski's introduction in 1908 of the geometric spacetime model for Einstein's version of relativity, most physicists eventually decided in favor of the Einstein-Minkowski version of relativity with its radical new views of space and time, in which there was no useful role for the aether.

Claimed experimental refutations

Kaufmann–Bucherer–Neumann experiments: To conclusively decide between the theories of Abraham and Lorentz, Kaufmann repeated his experiments in 1905 with improved accuracy. However, in the meantime the theoretical situation had changed. Alfred Bucherer and Paul Langevin (1904) developed another model, in which the electron is contracted in the line of motion, and dilated in the transverse direction, so that the volume remains constant. While Kaufmann was still evaluating his experiments, Einstein published his theory of special relativity. Eventually, Kaufmann published his results in December 1905 and argued that they are in agreement with Abraham's theory and require rejection of the "basic assumption of Lorentz and Einstein" (the relativity principle). Lorentz reacted with the phrase "I am at the end of my Latin", while Einstein did not mention those experiments before 1908. Yet, others started to criticize the experiments. Max Planck (1906) alluded to inconsistencies in the theoretical interpretation of the data, and Adolf Bestelmeyer (1906) introduced new techniques, which (especially in the area of low velocities) gave different results and which cast doubts on Kaufmann's methods. Therefore, Bucherer (1908) conducted new experiments and arrived at the conclusion that they confirm the mass formula of relativity and thus the "relativity principle of Lorentz and Einstein". Yet Bucherer's experiments were criticized by Bestelmeyer leading to a sharp dispute between the two experimentalists. On the other hand, additional experiments of Hupka (1910), Neumann (1914) and others seemed to confirm Bucherer's result. The doubts lasted until 1940, when in similar experiments Abraham's theory was conclusively disproved. (It must be remarked that besides those experiments, the relativistic mass formula had already been confirmed by 1917 in the course of investigations on the theory of spectra. In modern particle accelerators, the relativistic mass formula is routinely confirmed.)

In 1902–1906, Dayton Miller repeated the Michelson–Morley experiment together with Edward W. Morley. They confirmed the null result of the initial experiment. However, in 1921–1926, Miller conducted new experiments which apparently gave positive results. Those experiments initially attracted some attention in the media and in the scientific community but have been considered refuted for the following reasons:  Einstein, Max Born, and Robert S. Shankland pointed out that Miller had not appropriately considered the influence of temperature. A modern analysis by Roberts shows that Miller's experiment gives a null result, when the technical shortcomings of the apparatus and the error bars are properly considered. Additionally, Miller's result is in disagreement with all other experiments, which were conducted before and after. For example, Georg Joos (1930) used an apparatus of similar dimensions to Miller's, but he obtained null results. In recent experiments of Michelson–Morley type where the coherence length is increased considerably by using lasers and masers the results are still negative.

In the 2011 Faster-than-light neutrino anomaly, the OPERA collaboration published results which appeared to show that the speed of neutrinos is slightly faster than the speed of light. However, sources of errors were found and confirmed in 2012 by the OPERA collaboration, which fully explained the initial results. In their final publication, a neutrino speed consistent with the speed of light was stated. Also subsequent experiments found agreement with the speed of light, see measurements of neutrino speed.

Acceleration in special relativity

It was also claimed that special relativity cannot handle acceleration, which would lead to contradictions in some situations. However, this assessment is not correct, since acceleration actually can be described in the framework of special relativity (see Acceleration (special relativity), Proper reference frame (flat spacetime), Hyperbolic motion, Rindler coordinates, Born coordinates). Paradoxes relying on insufficient understanding of these facts were discovered in the early years of relativity. For example, Max Born (1909) tried to combine the concept of rigid bodies with special relativity. That this model was insufficient was shown by Paul Ehrenfest (1909), who demonstrated that a rotating rigid body would, according to Born's definition, undergo a contraction of the circumference without contraction of the radius, which is impossible (Ehrenfest paradox). Max von Laue (1911) showed that rigid bodies cannot exist in special relativity, since the propagation of signals cannot exceed the speed of light, so an accelerating and rotating body will undergo deformations.

Paul Langevin and von Laue showed that the twin paradox can be completely resolved by consideration of acceleration in special relativity. If two twins move away from each other, and one of them is accelerating and coming back to the other, then the accelerated twin is younger than the other one, since he was located in at least two inertial frames of reference, and therefore his assessment of which events are simultaneous changed during the acceleration. For the other twin nothing changes since he remained in a single frame. Another example is the Sagnac effect. Two signals were sent in opposite directions around a rotating platform. After their arrival a displacement of the interference fringes occurs. Sagnac himself believed that he had proved the existence of the aether. However, special relativity can easily explain this effect. When viewed from an inertial frame of reference, it is a simple consequence of the independence of the speed of light from the speed of the source, since the receiver runs away from one beam, while it approaches the other beam. When viewed from a rotating frame, the assessment of simultaneity changes during the rotation, and consequently the speed of light is not constant in accelerated frames.

As was shown by Einstein, the only form of accelerated motion that cannot be non-locally described is the one due to gravitation. Einstein was also unsatisfied with the fact that inertial frames are preferred over accelerated frames. Thus over the course of several years (1908–1915), Einstein developed general relativity. This theory includes the replacement of Euclidean geometry by non-Euclidean geometry, and the resultant curvature of the path of light led Einstein (1912) to the conclusion that (like in extended accelerated frames) the speed of light is not constant in extended gravitational fields. Therefore, Abraham (1912) argued that Einstein had given special relativity a coup de grâce. Einstein responded that within its area of application (in areas where gravitational influences can be neglected) special relativity is still applicable with high precision, so one cannot speak of a coup de grâce at all.

Superluminal speeds

In special relativity, the transfer of signals at superluminal speeds is impossible, since this would violate the Poincaré-Einstein synchronization, and the causality principle. Following an old argument by Pierre-Simon Laplace, Poincaré (1904) alluded to the fact that Newton's law of universal gravitation is founded on an infinitely great speed of gravity. So the clock-synchronization by light signals could in principle be replaced by a clock-synchronization by instantaneous gravitational signals. In 1905, Poincaré himself solved this problem by showing that in a relativistic theory of gravity the speed of gravity is equal to the speed of light. Although much more complicated, this is also the case in Einstein's theory of general relativity.

Another apparent contradiction lies in the fact that the group velocity in anomalously dispersive media is higher than the speed of light. This was investigated by Arnold Sommerfeld (1907, 1914) and Léon Brillouin (1914). They came to the conclusion that in such cases the signal velocity is not equal to the group velocity, but to the front velocity which is never faster than the speed of light. Similarly, it is also argued that the apparent superluminal effects discovered by Günter Nimtz can be explained by a thorough consideration of the velocities involved.

Also quantum entanglement (denoted by Einstein as "spooky action at a distance"), according to which the quantum state of one entangled particle cannot be fully described without describing the other particle, does not imply superluminal transmission of information (see quantum teleportation), and it is therefore in conformity with special relativity.

Paradoxes

Insufficient knowledge of the basics of special relativity, especially the application of the Lorentz transformation in connection with length contraction and time dilation, led and still leads to the construction of various apparent paradoxes. Both the twin paradox and the Ehrenfest paradox and their explanation were already mentioned above. Besides the twin paradox, also the reciprocity of time dilation (i.e. every inertially moving observer considers the clock of the other one as being dilated) was heavily criticized by Herbert Dingle and others. For example, Dingle wrote a series of letters to Nature at the end of the 1950s. However, the self-consistency of the reciprocity of time dilation had already been demonstrated long before in an illustrative way by Lorentz (in his lectures from 1910, published 1931) and many others—they alluded to the fact that it is only necessary to carefully consider the relevant measurement rules and the relativity of simultaneity. Other known paradoxes are the Ladder paradox and Bell's spaceship paradox, which also can simply be solved by consideration of the relativity of simultaneity.

Aether and absolute space

Many physicists (like Hendrik Lorentz, Oliver Lodge, Albert Abraham Michelson, Edmund Taylor Whittaker, Harry Bateman, Ebenezer Cunningham, Charles Émile Picard, Paul Painlevé) were uncomfortable with the rejection of the aether, and preferred to interpret the Lorentz transformation based on the existence of a preferred frame of reference, as in the aether-based theories of Lorentz, Larmor, and Poincaré. However, the idea of an aether hidden from any observation was not supported by the mainstream scientific community, therefore the aether theory of Lorentz and Poincaré was superseded by Einstein's special relativity which was subsequently formulated in the framework of four-dimensional spacetime by Minkowski.

Others such as Herbert E. Ives argued that it might be possible to experimentally determine the motion of such an aether, but it was never found despite numerous experimental tests of Lorentz invariance (see tests of special relativity).

Also attempts to introduce some sort of relativistic aether (consistent with relativity) into modern physics such as by Einstein on the basis of general relativity (1920), or by Paul Dirac in relation to quantum mechanics (1951), were not supported by the scientific community (see Luminiferous aether#End of aether?).

In his Nobel lecture, George F. Smoot (2006) described his own experiments on the Cosmic microwave background radiation anisotropy as "New Aether drift experiments". Smoot explained that "one problem to overcome was the strong prejudice of good scientists who learned the lesson of the Michelson and Morley experiment and Special Relativity that there were no preferred frames of reference." He continued that "there was an education job to convince them that this did not violate Special Relativity but did find a frame in which the expansion of the universe looked particularly simple."

Alternative theories

The theory of complete aether drag, as proposed by George Gabriel Stokes (1844), was used by some critics as Ludwig Silberstein (1920) or Philipp Lenard (1920) as a counter-model of relativity. In this theory, the aether was completely dragged within and in the vicinity of matter, and it was believed that various phenomena, such as the absence of aether drift, could be explained in an "illustrative" way by this model. However, such theories are subject to great difficulties. Especially the aberration of light contradicted the theory, and all auxiliary hypotheses, which were invented to rescue it, are self-contradictory, extremely implausible, or in contradiction to other experiments like the Michelson–Gale–Pearson experiment. In summary, a sound mathematical and physical model of complete aether drag was never invented, consequently this theory was no serious alternative to relativity.

Another alternative was the so-called emission theory of light. As in special relativity the aether concept is discarded, yet the main difference from relativity lies in the fact that the velocity of the light source is added to that of light in accordance with the Galilean transformation. As the hypothesis of complete aether drag, it can explain the negative outcome of all aether drift experiments. Yet, there are various experiments that contradict this theory. For example, the Sagnac effect is based on the independence of light speed from the source velocity, and the image of Double stars should be scrambled according to this model—which was not observed. Also in modern experiments in particle accelerators no such velocity dependence could be observed. These results are further confirmed by the De Sitter double star experiment (1913), conclusively repeated in the X-ray spectrum by K. Brecher in 1977; and the terrestrial experiment by Alväger, et al. (1963);, which all show that the speed of light is independent of the motion of the source within the limits of experimental accuracy.

Principle of the constancy of the speed of light

Some consider the principle of the constancy of the velocity of light insufficiently substantiated. However, as already shown by Robert Daniel Carmichael (1910) and others, the constancy of the speed of light can be interpreted as a natural consequence of two experimentally demonstrated facts:

1. The velocity of light is independent of the velocity of the source, as demonstrated by De Sitter double star experiment, Sagnac effect, and many others (see emission theory).
2. The velocity of light is independent of the direction of velocity of the observer, as demonstrated by Michelson–Morley experiment, Kennedy–Thorndike experiment, and many others (see luminiferous aether).

Note that measurements regarding the speed of light are actually measurements of the two-way speed of light, since the one-way speed of light depends on which convention is chosen to synchronize the clocks.

General relativity

General covariance

Einstein emphasized the importance of general covariance for the development of general relativity, and took the position that the general covariance of his 1915 theory of gravity ensured implementation of a generalized relativity principle. This view was challenged by Erich Kretschmann (1917), who argued that every theory of space and time (even including Newtonian dynamics) can be formulated in a covariant way, if additional parameters are included, and thus general covariance of a theory would in itself be insufficient to implement a generalized relativity principle. Although Einstein (1918) agreed with that argument, he also countered that Newtonian mechanics in general covariant form would be too complicated for practical uses. Although it is now understood that Einstein's response to Kretschmann was mistaken (subsequent papers showed that such a theory would still be usable), another argument can be made in favor of general covariance: it is a natural way to express the equivalence principle, i.e., the equivalence in the description of a free-falling observer and an observer at rest, and thus it is more convenient to use general covariance together with general relativity, rather than with Newtonian mechanics. Connected with this, also the question of absolute motion was dealt with. Einstein argued that the general covariance of his theory of gravity supports Mach's principle, which would eliminate any "absolute motion" within general relativity. However, as pointed out by Willem de Sitter in 1916, Mach's principle is not completely fulfilled in general relativity because there exist matter-free solutions of the field equations. This means that the "inertio-gravitational field", which describes both gravity and inertia, can exist in the absence of gravitating matter. However, as pointed out by Einstein, there is one fundamental difference between this concept and absolute space of Newton: the inertio-gravitational field of general relativity is determined by matter, thus it is not absolute.

Bad Nauheim Debate

In the "Bad Nauheim Debate" (1920) between Einstein and (among others) Philipp Lenard, the latter stated the following objections: He criticized the lack of "illustrativeness" of Einstein's version of relativity, a condition that he suggested could only be met by an aether theory. Einstein responded that for physicists the content of "illustrativeness" or "common sense" had changed in time, so it could no longer be used as a criterion for the validity of a physical theory. Lenard also argued that with his relativistic theory of gravity Einstein had tacitly reintroduced the aether under the name "space". While this charge was rejected (among others) by Hermann Weyl, in an inaugural address given at the University of Leiden in 1920, shortly after the Bad Nauheim debates, Einstein himself acknowledged that according to his general theory of relativity, so-called "empty space" possesses physical properties that influence matter and vice versa. Lenard also argued that Einstein's general theory of relativity admits the existence of superluminal velocities, in contradiction to the principles of special relativity; for example, in a rotating coordinate system in which the Earth is at rest, the distant points of the whole universe are rotating around Earth with superluminal velocities. However, as Weyl pointed out, it is incorrect to handle a rotating extended system as a rigid body (neither in special nor in general relativity)—so the signal velocity of an object never exceeds the speed of light. Another criticism that was raised by both Lenard and Gustav Mie concerned the existence of "fictitious" gravitational fields in accelerating frames, which according to Einstein's Equivalence Principle are no less physically real than those produced by material sources. Lenard and Mie argued that physical forces can only be produced by real material sources, while the gravitational field that Einstein supposed to exist in an accelerating frame of reference has no concrete physical meaning. Einstein responded that, based on Mach's principle, one can think of these gravitational fields as induced by the distant masses. In this respect the criticism of Lenard and Mie has been vindicated, since according to the modern consensus, in agreement with Einstein's own mature views, Mach's principle as originally conceived by Einstein is not actually supported by general relativity, as already mentioned above.

Silberstein–Einstein controversy

Ludwik Silberstein, who initially was a supporter of the special theory, objected at different occasions against general relativity. In 1920 he argued that the deflection of light by the sun, as observed by Arthur Eddington et al. (1919), is not necessarily a confirmation of general relativity, but may also be explained by the Stokes-Planck theory of complete aether drag. However, such models are in contradiction with the aberration of light and other experiments (see "Alternative theories"). In 1935, Silberstein claimed to have found a contradiction in the Two-body problem in general relativity. The claim was refuted by Einstein and Rosen (1935).

Philosophical criticism

The consequences of relativity, such as the change of ordinary concepts of space and time, as well as the introduction of non-Euclidean geometry in general relativity, were criticized by some philosophers of different philosophical schools. Many philosophical critics had insufficient knowledge of the mathematical and formal basis of relativity, which led to the criticisms often missing the heart of the matter. For example, relativity was misinterpreted as some form of relativism. However, this is misleading as it was emphasized by Einstein or Planck. On one hand it's true that space and time became relative, and the inertial frames of reference are handled on equal footing. On the other hand, the theory makes natural laws invariant—examples are the constancy of the speed of light, or the covariance of Maxwell's equations. Consequently, Felix Klein (1910) called it the "invariant theory of the Lorentz group" instead of relativity theory, and Einstein (who reportedly used expressions like "absolute theory") sympathized with this expression as well.

Critical responses to relativity were also expressed by proponents of neo-Kantianism (Paul Natorp, Bruno Bauch etc.), and phenomenology (Oskar Becker, Moritz Geiger etc.). While some of them only rejected the philosophical consequences, others rejected also the physical consequences of the theory. Einstein was criticized for violating Immanuel Kant's categoric scheme, i.e., it was claimed that space-time curvature caused by matter and energy is impossible, since matter and energy already require the concepts of space and time. Also the three-dimensionality of space, Euclidean geometry, and the existence of absolute simultaneity were claimed to be necessary for the understanding of the world; none of them can possibly be altered by empirical findings. By moving all those concepts into a metaphysical area, any form of criticism of Kantianism would be prevented. Other pseudo-Kantians like Ernst Cassirer or Hans Reichenbach (1920), tried to modify Kant's philosophy. Subsequently, Reichenbach rejected Kantianism at all and became a proponent of logical positivism.

Based on Henri Poincaré's conventionalism, philosophers such as Pierre Duhem (1914) and Hugo Dingler (1920) argued that the classical concepts of space, time, and geometry were, and will always be, the most convenient expressions in natural science, therefore the concepts of relativity cannot be correct. This was criticized by proponents of logical positivism such as Moritz Schlick, Rudolf Carnap, and Reichenbach. They argued that Poincaré's conventionalism could be modified to bring it into accord with relativity. Although it is true that the basic assumptions of Newtonian mechanics are simpler, it can only be brought into accord with modern experiments by inventing auxiliary hypotheses. On the other hand, relativity doesn't need such hypotheses, thus from a conceptual viewpoint, relativity is in fact simpler than Newtonian mechanics.

Some proponents of Philosophy of Life, Vitalism, Critical realism (in German speaking countries) argued that there is a fundamental difference between physical, biological and psychological phenomena. For example, Henri Bergson (1921), who otherwise was a proponent of special relativity, argued that time dilation cannot be applied to biological organisms, therefore he denied the relativistic solution of the twin paradox. However, those claims were rejected by Paul Langevin, André Metz and others. Biological organisms consist of physical processes, so there is no reason to assume that they are not subject to relativistic effects like time dilation.^{[A 38][B 37][C 21]}

Based on the philosophy of Fictionalism, the philosopher Oskar Kraus (1921) and others claimed that the foundations of relativity were only fictitious and even self-contradictory. Examples were the constancy of the speed of light, time dilation, length contraction. These effects appear to be mathematically consistent as a whole, but in reality they allegedly are not true. Yet, this view was immediately rejected. The foundations of relativity (such as the equivalence principle or the relativity principle) are not fictitious, but based on experimental results. Also, effects like constancy of the speed of light and relativity of simultaneity are not contradictory, but complementary to one another.

In the Soviet Union (mostly in the 1920s), philosophical criticism was expressed on the basis of dialectic materialism. The theory of relativity was rejected as anti-materialistic and speculative, and a mechanistic worldview based on "common sense" was required as an alternative. Similar criticisms also occurred in the People's Republic of China during the Cultural Revolution. (On the other hand, other philosophers considered relativity as being compatible with Marxism.)

Relativity hype and popular criticism

Although Planck already in 1909 compared the changes brought about by relativity with the Copernican Revolution, and although special relativity was accepted by most of the theoretical physicists and mathematicians by 1911, it was not before publication of the experimental results of the eclipse expeditions (1919) by a group around Arthur Stanley Eddington that relativity was noticed by the public. Following Eddington's publication of the eclipse results, Einstein was glowingly praised in the mass media, and was compared to Nikolaus Copernicus, Johannes Kepler and Isaac Newton, which caused a popular "relativity hype" ("Relativitätsrummel", as it was called by Sommerfeld, Einstein, and others). This triggered a counter-reaction of some scientists and scientific laymen who could not accept the concepts of modern physics, including relativity theory and quantum mechanics. The ensuing public controversy regarding the scientific status of Einstein's theory of gravity, which was unprecedented, was partly carried out in the press. Some of the criticism was not only directed to relativity, but personally at Einstein as well, who some of his critics accused of being behind the promotional campaign in the German press. 

Academic and non-academic criticism

Some academic scientists, especially experimental physicists such as the Nobel laureates Philipp Lenard and Johannes Stark, as well as Ernst Gehrcke, Stjepan Mohorovičić, Rudolf Tomaschek and others criticized the increasing abstraction and mathematization of modern physics, especially in the form of relativity theory, and later quantum mechanics. It was seen as a tendency to abstract theory building, connected with the loss of intuitive "common sense". In fact, relativity was the first theory, in which the inadequacy of the "illustrative" classical physics was thought to have been demonstrated. Some of Einstein's critics ignored these developments and tried to revitalize older theories, such as aether drag models or emission theories (see "Alternative Theories"). However, those qualitative models were never sufficiently advanced to compete with the success of the precise experimental predictions and explanatory powers of the modern theories. Additionally, there was also a great rivalry between experimental and theoretical physicists, as regards the professorial activities and the occupation of chairs at German universities. The opinions clashed at the "Bad Nauheim debates" in 1920 between Einstein and (among others) Lenard, which attracted much public attention.

In addition, there were many critics (with or without physical training) whose ideas were far outside the scientific mainstream. These critics were mostly people who had developed their ideas long before the publication of Einstein's version of relativity, and they tried to resolve in a straightforward manner some or all of the enigmas of the world. Therefore, Wazeck (who studied some German examples) gave to these "free researchers" the name "world riddle solver" ("Welträtsellöser", such as Arvid Reuterdahl, Hermann Fricke or Johann Heinrich Ziegler). Their views had quite different roots in monism, Lebensreform, or occultism. Their views were typically characterized by the fact that they practically rejected the entire terminology and the (primarily mathematical) methods of modern science. Their works were published by private publishers, or in popular and non-specialist journals. It was significant for many "free researchers" (especially the monists) to explain all phenomena by intuitive and illustrative mechanical (or electrical) models, which also found its expression in their defense of the aether. For this reason they objected to the abstractness and inscrutability of the relativity theory, which was considered a pure calculation method that cannot reveal the true reasons underlying the phenomena. The "free researchers" often used Mechanical explanations of gravitation, in which gravity is caused by some sort of "aether pressure" or "mass pressure from a distance". Such models were regarded as an illustrative alternative to the abstract mathematical theories of gravitation of both Newton and Einstein. The enormous self-confidence of the "free researchers" is noteworthy, since they not only believed themselves to have solved the great riddles of the world, but many also seemed to expect that they would rapidly convince the scientific community.

Since Einstein rarely defended himself against these attacks, this task was undertaken by other relativity theoreticians, who (according to Hentschel) formed some sort of "defensive belt" around Einstein. Some representatives were Max von Laue, Max Born, etc. and on popular-scientific and philosophical level Hans Reichenbach, André Metz etc., who led many discussions with critics in semi-popular journals and newspapers. However, most of these discussions failed from the start. Physicists like Gehrcke, some philosophers, and the "free researchers" were so obsessed with their own ideas and prejudices that they were unable to grasp the basics of relativity; consequently, the participants of the discussions were talking past each other. In fact, the theory that was criticized by them was not relativity at all, but rather a caricature of it. The "free researchers" were mostly ignored by the scientific community, but also, in time, respected physicists such as Lenard and Gehrcke found themselves in a position outside the scientific community. However, the critics didn't believe that this was due to their incorrect theories, but rather due to a conspiracy of the relativistic physicists (and in the 1920s and 1930s of the Jews as well), which allegedly tried to put down the critics, and to preserve and improve their own positions within the academic world. For example, Gehrcke (1920/24) held that the propagation of relativity is a product of some sort of mass suggestion. Therefore, he instructed a media monitoring service to collect over 5000 newspaper clippings which were related to relativity, and published his findings in a book. However, Gehrcke's claims were rejected, because the simple existence of the "relativity hype" says nothing about the validity of the theory, and thus it cannot be used for or against relativity.

Afterward, some critics tried to improve their positions by the formation of alliances. One of them was the "Academy of Nations", which was founded in 1921 in the US by Robert T. Browne and Arvid Reuterdahl. Other members were Thomas Jefferson Jackson See and as well as Gehrcke and Mohorovičić in Germany. It is unknown whether other American critics such as Charles Lane Poor, Charles Francis Brush, Dayton Miller were also members. The alliance disappeared as early as the mid-1920s in Germany and by 1930 in the USA.

Chauvinism and antisemitism

Main article: Deutsche Physik

Shortly before and during World War I, there appeared some nationalistically motivated criticisms of relativity and modern physics. For example, Pierre Duhem regarded relativity as the product of the "too formal and abstract" German spirit, which was in conflict with the "common sense". Similarly, popular criticism in the Soviet Union and China, which partly was politically organized, rejected the theory not because of factual objections, but as ideologically motivated as the product of western decadence.

So in those countries, the Germans or the Western civilization were the enemies. However, in Germany the Jewish ancestry of some leading relativity proponents such as Einstein and Minkowski made them targets of racially minded critics, although many of Einstein's German critics did not show evidence of such motives. The engineer Paul Weyland, a known nationalistic agitator, arranged the first public meeting against relativity in Berlin in 1919. While Lenard and Stark were also known for their nationalistic opinions, they declined to participate in Weyland's rallies, and Weyland's campaign eventually fizzled out due to a lack of prominent speakers. Lenard and others instead responded to Einstein's challenge to his professional critics to debate his theories at the scientific conference held annually at Bad Nauheim. While Einstein's critics, assuming without any real justification that Einstein was behind the activities of the German press in promoting the triumph of relativity, generally avoided antisemitic attacks in their earlier publications, it later became clear to many observers that antisemitism did play a significant role in some of the attacks.

Reacting to this underlying mood, Einstein himself openly speculated in a newspaper article that in addition to insufficient knowledge of theoretical physics, antisemitism at least partly motivated their criticisms. Some critics, including Weyland, reacted angrily and claimed that such accusations of antisemitism were only made to force the critics into silence. However, subsequently Weyland, Lenard, Stark and others clearly showed their antisemitic biases by beginning to combine their criticisms with racism. For example, Theodor Fritsch emphasized the alleged negative consequences of the "Jewish spirit" within relativity physics, and the far right-press continued this propaganda unhindered. After the murder of Walther Rathenau (1922) and murder threats against Einstein, he left Berlin for some time. Gehrcke's book on "The mass suggestion of relativity theory" (1924) was not antisemitic itself, but it was praised by the far-right press as describing an alleged typical Jewish behavior, which was also imputed to Einstein personally. Philipp Lenard in 1922 spoke about the "foreign spirit" as the foundation of relativity, and afterward he joined the Nazi party in 1924; Johannes Stark did the same in 1930. Both were proponents of the so-called German Physics, which only accepted scientific knowledge based on experiments, and only if accessible to the senses. According to Lenard (1936), this is the "Aryan physics or physics by man of Nordic kind" as opposed to the alleged formal-dogmatic "Jewish physics". Additional antisemitic critics can be found in the writings of Wilhelm Müller, Bruno Thüring and others. For example, Müller erroneously claimed that relativity was a purely "Jewish affair" and it would correspond to the "Jewish essence" etc., while Thüring made comparisons between the Talmud and relativity.

Accusations of plagiarism and priority discussions

Some of Einstein's critics, like Lenard, Gehrcke and Reuterdahl, accused him of plagiarism, and questioned his priority claims to the authorship of relativity theory. The thrust of such allegations was to promote more traditional alternatives to Einstein's abstract hypothetico-deductive approach to physics, while Einstein himself was to be personally discredited. It was argued by Einstein's supporters that such personal accusations were unwarranted, since the physical content and the applicability of former theories were quite different from Einstein's theory of relativity. However, others argued that between them Poincaré and Lorentz had earlier published several of the core elements of Einstein's 1905 relativity paper, including a generalized relativity principle that was intended by Poincaré to apply to all physics. Some examples:

• Johann Georg von Soldner (1801) was credited for his calculation of the deflection of light in the vicinity of celestial bodies, long before Einstein's prediction which was based on general relativity. However, Soldner's derivation has nothing to do with Einstein's, since it was fully based on Newton's theory, and only gave half of the value as predicted by general relativity.
• Paul Gerber (1898) published a formula for the perihelion advance of Mercury, which was formally identical to an approximate solution given by Einstein. However, since Einstein's formula was only an approximation, the solutions are not identical. In addition, Gerber's derivation has no connection with General relativity and was even regarded as meaningless.
• Woldemar Voigt (1887) derived a transformation, which is very similar to the Lorentz transformation. As Voigt himself acknowledged, his theory was not based on electromagnetic theory, but on an elastic aether model. His transformation also violates the relativity principle.
• Friedrich Hasenöhrl (1904) applied the concept of electromagnetic mass and momentum (which were known long before) to cavity radiation and thermal radiation. Yet, the applicability of Einstein's Mass–energy equivalence goes much further, since it is derived from the relativity principle and applies to all forms of energy.
• Menyhért Palágyi (1901) developed a philosophical "space-time" model in which time plays the role of an imaginary fourth dimension. Palágyi's model was only a reformulation of Newtonian physics, and had no connection to electromagnetic theory, the relativity principle, or to the constancy of the speed of light.

Some contemporary historians of science have revived the question as to whether Einstein was possibly influenced by the ideas of Poincaré, who first stated the relativity principle and applied it to electrodynamics, developing interpretations and modifications of Lorentz's electron theory that appear to have anticipated what is now called special relativity.  Another discussion concerns a possible mutual influence between Einstein and David Hilbert as regards completing the field equations of general relativity (see Relativity priority dispute).

A Hundred Authors Against Einstein

A collection of various criticisms can be found in the book Hundert Autoren gegen Einstein (A Hundred Authors Against Einstein), published in 1931. It contains very short texts from 28 authors, and excerpts from the publications of another 19 authors. The rest consists of a list that also includes people who only for some time were opposed to relativity. From among Einstein's concepts the most targeted one is space-time followed by the speed of light as a constant and the relativity of simultaneity, with other concepts following. Besides philosophic objections (mostly based on Kantianism), also some alleged elementary failures of the theory were included; however, as some commented, those failures were due to the authors' misunderstanding of relativity. For example, Hans Reichenbach wrote a report in the entertainment section of a newspaper, describing the book as “a magnificent collection of naive mistakes” and as “unintended droll literature.” Albert von Brunn interpreted the book as a pamphlet "of such deplorable impotence as occurring elsewhere only in politics" and "a fallback into the 16th and 17th centuries" and concluded “it can only be hoped that German science will not again be embarrassed by such sad scribblings”, and Einstein said, in response to the book, that if he were wrong, then one author would have been enough.

According to Goenner, the contributions to the book are a mixture of mathematical–physical incompetence, hubris, and the feelings of the critics of being suppressed by contemporary physicists advocating the new theory. The compilation of the authors show, Goenner continues, that this was not a reaction within the physics community—only one physicist (Karl Strehl) and three mathematicians (Jean-Marie Le Roux, Emanuel Lasker and Hjalmar Mellin) were present—but a reaction of an inadequately educated academic citizenship, which didn't know what to do with relativity. As regards the average age of the authors: 57% were substantially older than Einstein, one third was around the same age, and only two persons were substantially younger. Two authors (Reuterdahl, von Mitis) were antisemitic and four others were possibly connected to the Nazi movement. On the other hand, no antisemitic expression can be found in the book, and it also included contributions of some authors of Jewish ancestry (Salomo Friedländer, Ludwig Goldschmidt, Hans Israel, Emanuel Lasker, Oskar Kraus, Menyhért Palágyi).

Status of criticism

See also: Tests of special relativity and Tests of general relativity

The theory of relativity is considered to be self-consistent, is consistent with many experimental results, and serves as the basis of many successful theories like quantum electrodynamics. Therefore, fundamental criticism (like that of Herbert Dingle, Louis Essen, Petr Beckmann, Maurice Allais and Tom van Flandern) has not been taken seriously by the scientific community, and due to the lack of quality of many critical publications (found in the process of peer review) they were rarely accepted for publication in reputable scientific journals. Just as in the 1920s, most critical works are published in small publication houses, alternative journals (like "Apeiron" or "Galilean Electrodynamics"), or private websites. Consequently, where criticism of relativity has been dealt with by the scientific community, it has mostly been in historical studies.

However, this does not mean that there is no further development in modern physics. The progress of technology over time has led to extremely precise ways of testing the predictions of relativity, and so far it has successfully passed all tests (such as in particle accelerators to test special relativity, and by astronomical observations to test general relativity). In addition, in the theoretical field there is continuing research intended to unite general relativity and quantum theory, between which a fundamental incompatibility still remains. The most promising models are string theory and loop quantum gravity. Some variations of those models also predict violations of Lorentz invariance on a very small scale.