Velocities of the same body in two frames of reference (see text).

Applications of relativistic principles

Particle accelerators

Modern particle accelerators raise particles to speeds very near that of light. At these energies and speeds the differences in behaviour predicted by classical physics and by the special theory of relativity are huge; the machines must be designed in accordance with relativistic principles, or they will not operate.

Electron synchrotrons operate at energies of several thousand million electron volts, which means that the relativistic mass of an electron orbiting at maximum energy is roughly 10,000 times its rest mass. Accordingly, the magnetic field required to maintain the electrons in orbit is 10,000 times as powerful as it would have to be if nonrelativistic physics held, at the same speed. On the other hand, at that given energy the speed of the electrons is in fact very nearly equal to the speed of light, the difference amounting to no more than one part in 100,000,000 (108). At the same energy, but by nonrelativistic mechanics, the speed of the electrons would be about 100 times the speed of light. This difference has a very practical consequence: in those particle accelerators designed for highly relativistic energies, the synchrotrons, particles are injected into a circular orbit already near the speed of light, and their velocities change only slightly as their energies are brought up to the highest design value. If the orbit diameter is kept nearly constant, particles at all energies will circulate at the same frequency, and only the magnetic field that keeps them in orbit needs to be increased to keep pace with the increasing mass. The accelerating voltage is applied at the constant frequency required so that the particles will always be accelerated forward.

Relativistic particle physics

The physics of subatomic particles depends on the principles of the special theory of relativity. These principles have their most direct application when particles are created, annihilated, or converted into different particles. In most particle transformations, large amounts of energy are involved; the total (rest) masses of the particles involved in the transformations will change, and this change will be related to the amounts of energy expended or gained by the rule that the change in mass (Dm0) is balanced by a corresponding change in energy (DE), divided by the square of the speed of light (c2): Dm0 = -c-2DE. This rule has been confirmed universally and, by now, is being taken for granted.

The units, or quanta, of electromagnetic energy, called photons, have long been regarded as a species of particle in which are combined the properties of zero rest mass with nonvanishing relativistic mass, because they travel at the speed of light. The relativistic mass equals its total energy E divided by c2. The energy of a photon also is equal to the product of its frequency n and Planck's constant h. The relativistic mass of a photon can be checked experimentally if the photon is absorbed or deflected in its interactions with particles, when the change in its linear momentum (product of velocity and relativistic mass) results in a recoil by the other particles. If a high-frequency photon, a gamma photon, collides with a free electron, the result is called the Compton effect, which involves both an observable recoil on the part of the electron and an altered frequency of the deflected photon. Again, relativity is confirmed by experiment.

It has been conjectured that gravitational waves, also, are composed of zero-rest-mass quanta travelling at the speed of light (gravitons). As the quantum theory of the gravitational field has not been definitely established and as the detection of individual gravitons may remain beyond experimental capabilities for years to come, the existence of gravitons cannot be considered assured.

There is another species of zero-rest-mass particles, produced in radioactive decay involving the ejection of electrons or positrons from atomic nuclei (so-called beta decay). These particles, known as neutrinos, have no electric charge and travel at the speed of light. Several distinct species of neutrinos are now known, each produced in a different kind of beta decay. Neutrinos interact with other particles extremely weakly. As a result, they can traverse large amounts of matter with little chance of being deflected or absorbed. Though their existence has been confirmed beyond a doubt, their detection and detailed examination remain challenging problems.

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Contents:

Introduction
    The special theory of relativity
       Historical background
       Relativity of space and time
       Consequences
          The limiting character of the speed of light
          Variable mass
          Invariant intervals
          The "twin paradox"
          Four-dimensional space-time
    The general theory of relativity
       Physical origins
       The principle of equivalence
       Curved space-time
          The principles
          The mathematical expression
       Confirmation of the theory
          Advance of Mercury's perihelion
          Gravitational redshift
          Optical effects of gravitation
          Gravitational waves
          Future astrophysical tests
       Conceptual implications of general relativity
       Schwarzschild's solution of the field equations
    Applications of relativistic principles
       Particle accelerators
       Relativistic particle physics
       Relativistic cosmology
    Modifications of general relativity
    Bibliography