Next: Invariance of Transverse Lengths Up: Theoretical Basis of Special Previous: Theoretical Basis of Special
In 1905, Albert Einstein reconciled all of the aforementioned results within a new theoretical framework known as special relativity. The two postulates of this framework are:
Postulate 1 is motivated by the observation that Newton's laws of motion take equivalent forms in all inertial reference frames. (See Section 1.5.4.) One corollary of this observation is that no identical experiment in Newtonian dynamics, preformed in various different inertial frames, can provided a way to distinguish one frame from another. Einstein simply generalized this equivalence principle by assuming that it applies to all laws of physics. Thus, according to Einstein, all laws of physics take equivalent forms in all inertial reference frames, implying that no identical experiment, of any kind, performed in various different inertial frames, can provided a way to distinguish one frame from another. Incidentally, the nomenclature `relativity' derives from the fact that it is impossible to determine that any given inertial frame constitutes an absolute standard of rest; in this respect, all motion is relative.
Postulate 2 follows from Einstein's rejection of the idea of an aether. Einstein assumed that an electromagnetic wave is a self-perpetuating disturbance of electric and magnetic fields that is capable of propagating through a vacuum without the need for a medium. Suppose that we measure the speed of light in vacuum in various different inertial reference frames. If the results of these identical experiments give different speeds then we have found a way of distinguishing the various reference frames from one another. In fact, we could provide a distinct label for each reference frame in terms of its associated speed of light in vacuum. However, this state of affairs is forbidden by Einstein's first postulate. Hence, the speed of light in vacuum must be the same in all of the reference frames.
The speed of light cannot depend on the motion of the source, because, if it did, then we could place a stationary source in each possible inertial reference frame, and then distinguish different frames from one another on the basis of the different speeds of the light emitted by these sources, and measured by a stationary receiver in a particular reference frame. However, this state of affairs is forbidden by Einstein's first postulate. Furthermore, the speed of light cannot depend on the motion of the receiver, because, if it did, then we could place a stationary source in a particular inertial reference frame, and then distinguish different inertial frames from one another on the basis of the different speeds of the light emitted by this source, and measured by stationary receivers in the latter frames.
Incidentally, if light waves propagate through a vacuum with the same speed in all directions in one inertial reference frame then they must do so in all inertial reference frames, otherwise we could distinguish the former reference frame from the others, which is contrary to Einstein's first postulate. However, Maxwell's equations predict that light waves propagate with the same speed in all directions in the (presumably inertial) frame of reference in which they are formulated. (See Section 2.4.4.) Hence, a more precise version of Einstein's second postulate is that light waves propagate with an invariant speed in all directions in all inertial frames of reference, irrespective of the motion of the source or the receiver.
Let us consider whether Einstein's first postulate also demands that the speed of sound is the same in all inertial reference frames. Suppose that we measure the speed of sound, in the same gas, in various different inertial reference frames. In general, the measured speed will be different in different reference frames. [See Equation (3.2).] However, this does not violate Einstein's first postulate, because we are not performing the same experiment in the various different reference frames, because each reference frame has a different velocity with respect to the rest frame of the gas. The essential difference between light waves and sound waves is that, because the medium (i.e., aether) with respect to which light waves in a vacuum propagate does not exist, this non-existent medium does not have an identifiable rest frame, whereas the gas through which sound waves propagate always has an identifiable rest frame.
Incidentally, because the Michelson-Morley and Kennedy-Thorndike experiments are, in effect, trying to measure the difference between the speeds of light in vacuum in two different inertial frames, Einstein's second postulate guarantees that they should both give null results.