According to the special theory of relativity, the aberration looks as a transform of the celestial sphere due to different frames of reference and is virtually a special case of velocity addition, namely one of the light beam and frames ' relative velocity v. The formula from relativistic aberration can be simplified to

A priori, it is not clear whether the new local frames in free fall coincide with the reference frames in which the laws of special relativity hold — that theory is based on the propagation of light, and thus on electromagnetism, which could have a different set of preferred frames.

There are alternatives to general relativity built upon the same premises, which include additional rules and / or constraints, leading to different field equations.

In 1908 he published the first of several papers on relativity, in which he derived the mass-energy relationship in a different way from Albert Einstein's derivation .< ref >

In physics, the Lorentz transformation or Lorentz-Fitzgerald transformation describes how, according to the theory of special relativity, different measurements of space and time by two observers can be converted into the measurements observed in either frame of reference.

To a certain extent, general relativity can be seen to be a relational theory, in which the only physically relevant information is the relationship between different events in space-time.

Time has a different meaning in quantum mechanics and general relativity and hence there are subtle issues to resolve when trying to formulate a theory which combines the two.

The concept of linguistic relativity describes different formulations of the principle that cognitive processes such as thought and experience may be influenced by the categories and patterns of the language that a person speaks.

He argued that when Whorf was describing in English how a Hopi speaker's view of time was different, he was in fact translating the Hopi concept into English and therefore disproving the existence of linguistic relativity.

Since neither Sapir nor Whorf had ever stated an actual hypothesis, Brown and Lenneberg formulated one based on a condensation of the different expressions of the notion of linguistic relativity in their works.

The fact that what had been believed to be random differences between color naming in different languages could be shown to follow universal patterns was seen as a powerful argument against linguistic relativity.

Levinson presented research results documenting rather significant linguistic relativity effects in the linguistic conceptualization of spatial categories between different languages.

The gold standard of psycholinguistic studies on linguistic relativity is now finding cognitive differences in speakers of different language when no language is involved in an experimental task ( thus rendering inapplicable Pinker's claim that linguistic relativity is absurd because it is " circular ").

Following Einstein's original presentation of special relativity in 1905, many different sets of postulates have been proposed in various alternative derivations.

Earlier attempts at reconciliation of Christianity with Newtonian mechanics appear quite different from later attempts at reconciliation with the newer scientific ideas of evolution or relativity.

Observers in different locations, that are in relative motion or at different altitudes, can disagree about the rates of each other's clocks, owing to effects described by the theory of relativity.

The problem can be understood in terms of the relativity of simultaneity in special relativity, which says that different inertial reference frames will disagree on whether two events at different locations happened " at the same time " or not, and they can also disagree on the order of the two events ( technically, these disagreements occur when spacetime interval between the events is ' space-like ', meaning that neither event lies in the future light cone of the other ).

According to special relativity, one can change a spatial and time separation ( L < sub > 1 </ sub >, Δt < sub > 1 </ sub >) into another ( L < sub > 2 </ sub >, Δt < sub > 2 </ sub >) by changing one's reference frame, as long as the change maintains the spacetime interval s. Such a change in reference frame corresponds to changing one's motion ; in a moving frame, lengths and times are different from their counterparts in a stationary reference frame.

Schwarzschild wormholes and Schwarzschild black holes are different, mathematical solutions of general relativity and Einstein – Cartan – Sciama – Kibble theory of gravity.

Albert Einstein, in his paper of 1905 that established relativity, showed that both the electric and magnetic fields are part of the same phenomena viewed from different reference frames.

Furthermore, it was subject to relativity and thus was not constant for all observers, therefore, in 2012, the IAU redefined it again to just simply be.

It thus satisfies a more stringent general principle of relativity, namely that the laws of physics are the same for all observers.

Since relativity postulates that the speed of light is the same for all observers, the Lorentz transformation must preserve the spacetime interval between any two events in Minkowski space.

Special relativity incorporates the principle that the speed of light is the same for all inertial observers regardless of the state of motion of the source.

This theory has a wide range of consequences which have been experimentally verified, including counter-intuitive ones such as length contraction, time dilation and relativity of simultaneity, contradicting the classical notion that the duration of the time interval between two events is equal for all observers.

# The laws of physics are the same for all observers in uniform motion relative to one another ( principle of relativity ).

Special relativity does not claim that all observers are equivalent, only that all observers at rest in inertial reference frames are equivalent.

The starting point for general relativity is the equivalence principle, which equates free fall with inertial motion, and describes free-falling inertial objects as being accelerated relative to non-inertial observers on the ground.

The essential idea behind relational quantum mechanics, following the precedent of special relativity, is that different observers may give different accounts of the same series of events: for example, to one observer at a given point in time, a system may be in a single, " collapsed " eigenstate, while to another observer at the same time, it may be in a superposition of two or more states.

Special relativity suggests that the concept of simultaneity is not universal: according to the relativity of simultaneity, observers in different frames of reference can have different perceptions of whether a given pair of events happened at the same time or at different times, with there being no physical basis for preferring one frame's judgments over another's ( though in a case where one event A happens in the past light cone of another event B, all frames will agree that A happened in the past of B ).

It is important to the definition of both comoving distance and proper distance in the cosmological sense ( as opposed to proper length in special relativity ) that all observers have the same cosmological age.

Even light itself does not have a " velocity " of c in this sense ; the total velocity of any object can be expressed as the sum where is the recession velocity due to the expansion of the universe ( the velocity given by Hubble's law ) and is the " peculiar velocity " measured by local observers ( with and, the dots indicating a first derivative ), so for light is equal to c (- c if the light is emitted towards our position at the origin and + c if emitted away from us ) but the total velocity is generally different than c .( Davis and Lineweaver 2003, p. 19 ) Even in special relativity the coordinate speed of light is only guaranteed to be c in an inertial frame, in a non-inertial frame the coordinate speed may be different than c ; in general relativity no coordinate system on a large region of curved spacetime is " inertial ", but in the local neighborhood of any point in curved spacetime we can define a " local inertial frame " and the local speed of light will be c in this frame, with massive objects such as stars and galaxies always having a local speed smaller than c. The cosmological definitions used to define the velocities of distant objects are coordinate-dependent-there is no general coordinate-independent definition of velocity between distant objects in general relativity ( Baez and Bunn, 2006 ).

If special relativity is to hold up exactly to this scale, different observers would observe quantum gravity effects at different scales, due to the Lorentz-FitzGerald contraction, in contradiction to the principle that all inertial observers should be able to describe phenomena by the same physical laws.

# The principle of relativity holds, i. e. equivalence of all inertial observers.

In general relativity, negative mass is generalized to refer to any region of space in which for some observers the mass density is measured to be negative.

* Frame fields in general relativity ( Lemaître observers in the Schwarzschild vacuum )

In the " membrane paradigm ", the black hole is described as it should be seen by an array of these stationary, suspended noninertial observers, and since their shared coordinate system ends at the event horizon ( because an observer cannot legally hover at or below the event horizon under general relativity ), this conventional-looking radiation is described as being emitted by an arbitrarily-thin shell of " hot " material at or just above the event horizon, where this coordinate system fails.

Wigner postulated that for the transition probability between states to be the same to all observers related by a transformation of special relativity.

In the following examples, certain influences may appear to travel faster than light, but they do not convey energy or information faster than light, so they do not violate special relativity.

Let M be a ( pseudo -) Riemannian manifold, which may be taken as the spacetime of general relativity.

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 ".

The resolution of these points may come from a better understanding of general relativity.

It generalizes Galileo's principle of relativity — that all uniform motion is relative, and that there is no absolute and well-defined state of rest ( no privileged reference frames )— from mechanics to all the laws of physics, including both the laws of mechanics and of electrodynamics, whatever they may be.

The concept of geodesics becomes critical in general relativity, since geodesic motion may be thought of as " pure motion " ( inertial motion ) in spacetime, that is, free from any external influences.

It is thought that it may not be possible to convert a wormhole into a time machine in this manner ; the predictions are made in the context of general relativity, but general relativity does not include quantum effects.

In a theory like general relativity, which presumes a single space-time continuum, the paradox may be blocked.

This may explain the widespread misconception that this spacetime is a solution of the field equation of general relativity.

Thus the conquest of actual infinity may be considered an expansion of our scientific horizon no less revolutionary than the Copernican system or than the theory of relativity, or even of quantum and nuclear physics.

Everything is compatible with relativity now, but we see immediately that the expression for the density is no longer positive definite-the initial values of both ψ and ∂< sub > t </ sub > ψ may be freely chosen, and the density may thus become negative, something that is impossible for a legitimate probability density.

Some theories, most notably special and general relativity, suggest that suitable geometries of spacetime, or certain types of motion in space, may allow time travel into the past and future.

The principle that the mass of a system of particles must be equal to the sum of their rest masses, even though true in classical physics, may be false in special relativity.

The principle of matter conservation may be considered as an approximate physical law that is true only in the classical sense, without consideration of special relativity and quantum mechanics.

In contrast to classical physics, modern physics is a slightly looser term which may refer to just quantum physics or to 20th and 21st century physics in general and so always includes quantum theory and may include relativity.