Postulates
In his autobiographical notes published in November 1949 Einstein described how he had arrived at the two fundamental postulates on which he based the special theory of relativity. After describing in detail the state of both mechanics and electrodynamics at the beginning of the 20th century, he wrote:[9]
Reflections of this type made it clear to me as long ago as shortly after 1900, i.e., shortly after Planck's trailblazing work, that neither mechanics nor electrodynamics could (except in limiting cases) claim exact validity. Gradually I despaired of the possibility of discovering the true laws by means of constructive efforts based on known facts. The longer and the more desperately I tried, the more I came to the conviction that only the discovery of a universal formal principle could lead us to assured results... How, then, could such a universal principle be found?
– Albert Einstein: Autobiographical Notes
He discerned two fundamental propositions that seemed to be the most assured, regardless of the exact validity of the (then) known laws of either mechanics or electrodynamics. These propositions were:(1) the constancy of the speed of light, and (2) the independence of physical laws (especially the constancy of the speed of light) from the choice of inertial system. In his initial presentation of special relativity in 1905 he expressed these postulates as:[1]
- The Principle of Relativity – The laws by which the states of physical systems undergo change are not affected, whether these changes of state be referred to the one or the other of two systems in uniform translatory motion relative to each other.[1]
- The Principle of Invariant Light Speed – Light in vacuum propagates with the speed c (a fixed constant) in terms of any system of inertial coordinates, regardless of the state of motion of the light source.[1]
It should be noted that the derivation of special relativity depends not only on these two explicit postulates, but also on several tacit assumptions (which are made in almost all theories of physics), including the isotropy Isotropy is uniformity in all directions. Precise definitions depend on the subject area. The word is made up from Greek iso and tropos (direction). Exceptions, or inequalities, are frequently indicated by the prefix an, hence anisotropy. Anisotropy is also used to describe situations where properties vary systematically, dependent on direction and homogeneity In physics, homogeneous mixtures are mixtures that have definite and consistent chemical composition and physical properties. Particles are uniformly spread. For example, any amount of a given mixture has the same composition and properties. Examples are solutions and some alloys . A homogeneous mixture is a uniform mixture consisting of only one of space and the independence of measuring rods and clocks from their past history.[10]
Following Einstein's original presentation of special relativity in 1905, many different sets of postulates have been proposed in various alternative derivations.[11] However, the most common set of postulates remains those employed by Einstein in his original paper. A more mathematical statement of the Principle of Relativity made later by Einstein, which introduces the concept of simplicity not mentioned above is:[12]
Special principle of relativity: If a system of coordinates K is chosen so that, in relation to it, physical laws hold good in their simplest form, the same laws hold good in relation to any other system of coordinates K' moving in uniform translation relatively to K.
– Albert Einstein: The foundation of the general theory of relativity, Section A, §1
The two postulates of special relativity imply the applicability to physical laws of the Poincaré group In physics and mathematics, the Poincaré group, named after Henri Poincaré, is the group of isometries of Minkowski spacetime. It is a 10-dimensional noncompact Lie group. The abelian group of translations is a normal subgroup while the Lorentz group is a subgroup, the stabilizer of a point. That is, the full Poincaré group is the affine group of symmetry transformations, of which the Lorentz transformations In physics, the Lorentz transformation describes how, according to the theory of special relativity, two observers' varying measurements of space and time can be converted into each other's frame of reference. It reflects the surprising fact that observers moving at different velocities report different distances, passage of time, and in some are a subset, thereby providing a mathematical framework for special relativity. Many of Einstein's papers present derivations of the Lorentz transformation based upon these two principles.[13]
Einstein consistently based the derivation of Lorentz invariance (the essential core of special relativity) on just the two basic principles of relativity and light-speed invariance. He wrote:[9]
The insight fundamental for the special theory of relativity is this: The assumptions relativity and light speed invariance are compatible if relations of a new type ("Lorentz transformation") are postulated for the conversion of coordinates and times of events... The universal principle of the special theory of relativity is contained in the postulate: The laws of physics are invariant with respect to Lorentz transformations (for the transition from one inertial system to any other arbitrarily chosen inertial system). This is a restricting principle for natural laws...
– Albert Einstein: Autobiographical Notes
Thus many modern treatments of special relativity base it on the single postulate of universal Lorentz covariance, or, equivalently, on the single postulate of Minkowski spacetime In physics and mathematics, Minkowski space is the mathematical setting in which Einstein's theory of special relativity is most conveniently formulated. In this setting the three ordinary dimensions of space are combined with a single dimension of time to form a four-dimensional manifold for representing a spacetime. Minkowski space is named.[14][15]
From the principle of relativity alone without assuming the constancy of the speed of light, i.e. using the isotropy of space and the symmetry implied by the principle of special relativity, one can show that the space-time transformations between inertial frames are either Euclidean, Galilean, or Lorentzian. In the Lorentzian case, one can then obtain relativistic interval conservation and a certain finite limiting speed. Experiments suggest that this speed is the speed of light in vacuum. [16][17]
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