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Albert Einstein's theory of relativity Formula and Explained | Gurugrah


Theory of Relativity –

The theory of relativity usually includes two interrelated ideas by Albert Einstein. Special relativity and general relativity were proposed and published in 1905 and 1915, respectively. Special relativity applies to all physical phenomena in the absence of gravity. General relativity explains the law of gravitation and its relation to other forces of nature. It applies to the cosmological and astrophysical fields, including astronomy.

The theory transformed theoretical physics and astronomy during the 20th century, largely replacing the 200-year-old theory of mechanics created by Isaac Newton. It introduced concepts including 4-dimensional spacetime as a unified entity of space and time, simultaneous relativity, kinematic and gravitational time dilation, and length contraction.

In the field of physics, relativity improved the science of elementary particles and their fundamental interactions, ushering in the atomic age. Along with relativity, cosmology and astrophysics predicted extraordinary astronomical phenomena such as neutron stars, black holes, and gravitational waves.

Development and Acceptance –

Albert Einstein published his theory of special relativity in 1905, which Albert A. It is based on a number of theoretical results and empirical findings obtained by Michelson, Hendrik Lorentz, Henri Poincaré and others. Max Planck, Hermann Minkowski and others did subsequent work.

Einstein developed general relativity between 1907 and 1915, with contributions from many others after 1915. The final version of General Relativity was published in 1916.

The term “theory of relativity” was based on the expression “relativistic theory” (German) used by Planck in 1906, which emphasized how the theory used the principle of relativity. In the discussion section of the same paper, Alfred Bücherer used the expression “theory of relativity” (German: ) for the first time.

By the 1920s, the physics community understood and accepted special relativity. It rapidly became an important and necessary tool for theorists and experimentalists in the new fields of nuclear physics, nuclear physics and quantum mechanics.

Special Relativity -

Special relativity is a theory of the structure of space-time. It was introduced in Einstein’s 1905 paper “On the Electrodynamics of Moving Bodies” (for contributions from many other physicists and mathematicians, see History of special relativity). Special relativity is based on two postulates that are contradictory in classical mechanics.

1. The laws of physics are the same for all observers relative to each other in any inertial frame of reference (principle of relativity).

2. The speed of light in a vacuum is the same for all observers, regardless of their relative speed or the speed of the light source.

The resulting theory withstands experiments better than classical mechanics. For example, postulate 2 explains the results of the Michelson–Morley experiment. Furthermore, the theory has several surprising and counterproductive consequences. Some of these are-

1. Relativity of simultaneity: Two events, simultaneous for one observer, cannot be simultaneous for another observer if the observers are in relative motion.

2. Time dilation: moving clocks are measured to tick more slowly than an observer’s “stationary” clock.

3. Length contraction: objects are measured to shorten in the direction in which they are moving with respect to the observer.

4. The maximum speed is finite: No physical object, message or field line can travel faster than the speed of light in a vacuum.

• The effect of gravity can only travel through space at the speed of light, not faster or instantaneously.

• Mass-energy equivalence: E = mc 2, energy and mass are equivalent and mutable.

• Relativistic mass, an idea used by some researchers.

The defining feature of special relativity is the replacement of the Galilean transformations of classical mechanics by the Lorentz transformations. (See Maxwell’s equations of electromagnetism.)

Modern Applications –

Far from being of merely theoretical interest, relativistic effects are significant practical engineering concerns. Satellite-based measurements need to take relativistic effects into account, as each satellite is in motion relative to an Earth-bound user and thus in a different frame of reference under the theory of relativity.

Global positioning systems such as GPS, GLONASS and Galileo must account for all relativistic effects such as the consequences of Earth’s gravitational field in order to work with accuracy. This is also the case in the high-precision measurement of time. Instruments ranging from electron microscopes to particle accelerators would not work if relativistic ideas were discarded.

Asymptotic Isomerism –

The space-time isomorphism group for special relativity is the Poincare group, which is a ten-dimensional group of three Lorentz boosts, three rotations, and four space-time translations. It is logical to ask what symmetries might apply in general relativity.

A facile case may be to consider the symmetry of spacetime as observed by observers far away from all sources of the gravitational field. The naïve expectation for an asymptotically flat spacetime symmetry can be to extend and reproduce the symmetry of the flat spacetime of special relativity, ie. Poincaré Group.

In 1962, Hermann Bondi, MG van der Burgh, AW Metzner and Rainer K. Sachs addressed this asymptotic symmetry problem to investigate the flow of energy at infinity due to the propagation of gravitational waves. His first step was to decide on some physically sensible boundary conditions, which characterize the gravitational field at light-like infinity, to state that this means that a metric is asymptotically flat, There are no a priori assumptions about the nature of the asymptotic isomorphism group – not even the assumption that such a group exists.

Then after designing what they considered to be the most sensible boundary conditions, they investigated the nature of the resulting asymptotic symmetry transformations, which leave invariant the form of suitable boundary conditions for asymptotically flat gravitational fields. What they found was that the asymptotic symmetry transformations actually form a group and that the structure of this group does not depend on the particular gravitational field that is present. This means that, as expected, the kinematics of space-time can be decoupled from the dynamics of the gravitational field, at least at spatial infinity.

A startling surprise In 1962 was his discovery of the asymptotic isomorphism group of a rich infinite-dimensional group (the so-called BMS group) instead of the finite-dimensional Poincare group, which is a subgroup of the BMS group. Not only are Lorentz transformations asymptotic symmetry transformations, there are additional transformations, Which are not Lorentz transformations, but asymptotic symmetry transformations. In fact, they found an additional infinity of transformation generators known as translations. This implies the conclusion that general relativity does not reduce to special relativity in the case of weak fields at long distances.


By Chanchal Sailani | December 19, 2022, | Editor at Gurugrah_Blogs.



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