theory of special relativity

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) it can be shown that the spacetime transformations between inertial frames are either Euclidean, Galilean, or Lorentzian. 4‑4a. ", "Measuring Speed of Light: Why? Even before the Michelson–Morley experiment, Fizeau's experimental results were among a number of observations that created a critical situation in explaining the optics of moving bodies.

Units in the primed axes have a different scale from units in the unprimed axes. This equation not only describe the intrinsic angular momentum of the electrons called spin, it also led to the prediction of the antiparticle of the electron (the positron),[p 24][p 25] and fine structure could only be fully explained with special relativity. Special relativity predicts otherwise. )[note 3] and temporal separation between two events ( The notation makes it clear the equations are manifestly covariant under the Poincaré group, thus bypassing the tedious calculations to check this fact. when {\displaystyle t} where Special relativity revealed that the speed of light is a limit that can be approached but not reached by any material object. The equations that relate measurements made in different frames are called transformation equations. Be on the lookout for your Britannica newsletter to get trusted stories delivered right to your inbox. t The measured shape of an object is a hypothetical snapshot of all of the object's points as they exist at a single moment in time. .

γ d Drawing a Minkowski spacetime diagram to illustrate a Lorentz transformation.

[p 22][note 10]. The theory of special relativity was developed by Albert Einstein in 1905, and it forms part of the basis of modern physics. (For a more-detailed treatment of special relativity, see relativity: Special relativity.).

{\displaystyle ct'} 2

The results of various experiments, including the Michelson–Morley experiment in 1887 (subsequently verified with more accurate and innovative experiments), led to the theory of special relativity, by showing that the aether did not exist. Differentiating the above equation by τ produces: So in special relativity, the acceleration four-vector and the velocity four-vector are orthogonal.

[29]:169–174, Thomas rotation provides the resolution to the well-known "meter stick and hole paradox". The transverse Doppler effect is one of the main novel predictions of the special theory of relativity.

from 0 to 3, and The The transformation can apply to the y- or z-axis, or indeed in any direction parallel to the motion (which are warped by the γ factor) and perpendicular; see the article Lorentz transformation for details. Conservation of energy implies that, in any reaction, a decrease of the sum of the masses of particles must be accompanied by an increase in kinetic energies of the particles after the reaction. Nevertheless, relativistic Doppler shift for the longitudinal case, with source and receiver moving directly towards or away from each other, can be derived as if it were the classical phenomenon, but modified by the addition of a time dilation term, and that is the treatment described here. in the primed coordinate system transform to

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