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In the Einstein – Cartan theory, however, the minimal coupling between torsion and Dirac spinors generates a repulsive spin – spin interaction which is significant in fermionic matter at extremely high densities.
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Einstein and –
* 1939 – Albert Einstein and Leó Szilárd write a letter to Franklin D. Roosevelt, urging him to begin the Manhattan Project to develop a nuclear weapon.
Left: just before the appearance of a Bose – Einstein condensate.
A Bose – Einstein condensate ( BEC ) is a state of matter of a dilute gas of weakly interacting bosons confined in an external potential and cooled to temperatures very near to absolute zero.
This state of matter was first predicted by Satyendra Nath Bose and Albert Einstein in 1924 – 25.
A record cold temperature of 450 ± 80 pK in a Bose – Einstein condensate ( BEC ) of sodium atoms was achieved in 2003 by researchers at MIT.
It can also be found in Fermi – Dirac statistics ( for particles of half-integer spin ) and Bose – Einstein statistics ( for particles of integer spin ).
At very low temperatures in the vicinity of absolute zero, matter exhibits many unusual properties, including superconductivity, superfluidity, and Bose – Einstein condensation.
Note that the above formula is only applicable to classical ideal gases and not Bose – Einstein or Fermi gases.
His half-brother was Charles Einstein ( 1926 – 2007 ), a writer for such television programs as Playhouse 90 and Lou Grant.
In the classical limit, i. e. at large values of or at small density of states — when wave functions of particles practically do not overlap — both the Bose – Einstein or Fermi – Dirac distribution become the Boltzmann distribution.
Velocity-distribution data of a gas of rubidium atoms, confirming the discovery of a new phase of matter, the Bose – Einstein condensate.
Left: just before the appearance of a Bose – Einstein condensate.
A Bose – Einstein condensate ( BEC ) is a state of matter of a dilute gas of bosons cooled to temperatures very near absolute zero ( or ).
This state of matter was first predicted by Satyendra Nath Bose and Albert Einstein in 1924 – 25.
The result of the efforts of Bose and Einstein is the concept of a Bose gas, governed by Bose – Einstein statistics, which describes the statistical distribution of identical particles with integer spin, now known as bosons.
EPR ( Einstein – Podolsky – Rosen ) paradox
* Bohr – Einstein debates
* Penrose, Roger: " Singularities and time-asymmetry ", Chapter 12 in General Relativity: An Einstein Centenary Survey ( Hawking and Israel, editors ), ( 1979 ), see especially section 12. 3. 2, pp. 617 – 629 ( ISBN 0-521-22285-0 )
Nearly simultaneously David Hilbert published " The Foundations of Physics ", an axiomatic derivation of the field equations ( see Einstein – Hilbert action ).
* Einstein – Hilbert action
* Einstein – Hilbert equations
Einstein and Cartan
Examples are Brans – Dicke theory, teleparallelism, and Einstein – Cartan theory.
Schwarzschild wormholes and Schwarzschild black holes are different, mathematical solutions of general relativity and Einstein – Cartan – Sciama – Kibble theory of gravity.
In the Einstein – Cartan – Sciama – Kibble theory of gravity, however, it forms a regular Einstein – Rosen bridge.
In some alternative theories like Einstein – Cartan theory, the stress – energy tensor may not be perfectly symmetric because of a nonzero spin tensor, which geometrically corresponds to a nonzero torsion tensor.
* Riemann – Cartan geometry in Einstein – Cartan theory ( motivation )
The Einstein – Cartan – Sciama – Kibble theory of gravity extends general relativity by removing a constraint of the symmetry of the affine connection and regarding its antisymmetric part, the torsion tensor, as a dynamical variable.
* Einstein – Cartan theory
They have many applications in geometry and physics: see the method of moving frames, Cartan connection applications and Einstein – Cartan theory for some examples.
In theoretical physics, the Einstein – Cartan theory, also known as the Einstein – Cartan – Sciama – Kibble theory or the Cartan – Sciama – Kibble theory is a classical theory of gravitation similar to general relativity but relaxing the assumption that the metric be torsion-free.
Einstein – Cartan theory has been historically overshadowed by its torsion-free counterpart and other alternatives like Brans – Dicke theory because torsion seemed to add little predictive benefit at the expense of the tractability of its equations.
Since Einstein – Cartan theory is purely classical, it also does not fully address the issue of quantum gravity.
Interest in Einstein – Cartan theory has been renewed in recent years, however, as theorists try to incorporate torsion into novel quantum theories or as they explore its cosmological implications.
( We denote the stress-energy tensor by because the customary symbol in general relativity is used in Einstein – Cartan theory to denote affine torsion.
Although spin-orbit coupling is a relatively minor phenomenon in gravitational physics, Einstein – Cartan theory is quite important because
Einstein – Cartan theory can thus be viewed as the minimal ω-consistent extension of general relativity.
A mathematical proof has been published that general relativity plus a fluid of many tiny rotating black holes generate affine torsion that enters the field equations exactly as in the equations of Einstein – Cartan theory ( Petti, 1986 ).
Einstein and theory
In 1915, Albert Einstein developed his theory of general relativity, having earlier shown that gravity does influence light's motion.
In 1916, Albert Einstein published his theory of general relativity, which provided a unified description of gravity as a geometric property of space and time.
At the time, Einstein believed in a static universe, but found that his original formulation of the theory did not permit it.
Albert Einstein, in 1922, said regarding contemporary theories of superconductivity that “ with our far-reaching ignorance of the quantum mechanics of composite systems we are very far from being able to compose a theory out of these vague ideas ”
By 1907 Einstein had framed the fundamentals of the theory of gravity, but then struggled for nearly 8 years with a confounding problem of putting the theory into final form.
Hilbert fully credited Einstein as the originator of the theory, and no public priority dispute concerning the field equations ever arose between the two men during their lives.
In 1905, Einstein explained this puzzle by resurrecting the particle theory of light to explain the observed effect.
After important contributions of Hendrik Lorentz and Henri Poincaré, in 1905, Albert Einstein solved the problem with the introduction of special relativity, which replaces classical kinematics with a new theory of kinematics that is compatible with classical electromagnetism.
Einstein struggled to the end of his life for a theory that could better comply with his idea of causality, protesting against the view that there exists no objective physical reality other than that which is revealed through measurement interpreted in terms of quantum mechanical formalism.
In the EPR paper ( 1935 ) the authors realised that quantum mechanics was inconsistent with their assumptions, but Einstein nevertheless thought that quantum mechanics might simply be augmented by hidden variables ( i. e. variables which were, at that point, still obscure to him ), without any other change, to achieve an acceptable theory.
After constructing the full theory of general relativity in 1916, Einstein solved for the space-space components in a post-Newtonian approximation, and calculated the correct amount of light deflection – double the Newtonian value.
General relativity, or the general theory of relativity, is the geometric theory of gravitation published by Albert Einstein in 1916 and the current description of gravitation in modern physics.
Soon after publishing the special theory of relativity in 1905, Einstein started thinking about how to incorporate gravity into his new relativistic framework.
Einstein used approximation methods in working out initial predictions of the theory.
In 1917, Einstein applied his theory to the universe as a whole, initiating the field of relativistic cosmology.
Einstein himself had shown in 1915 how his theory explained the anomalous perihelion advance of the planet Mercury without any arbitrary parameters (" fudge factors ").
* 1905: Albert Einstein publishes his theory of special relativity and E = mc < sup > 2 </ sup >.
Einstein ’ s general theory modifies the distinction between nominally " inertial " and " noninertial " effects by replacing special relativity's " flat " Euclidean geometry with a curved metric.
The space M × C is compactified over the compact set C, and after Kaluza-Klein decomposition we have an effective field theory over M. A splitting of five-dimensional spacetime into the Einstein equations and Maxwell equations in four dimensions was first discovered by Gunnar Nordström in 1914, in the context of his theory of gravity, but subsequently forgotten.
Einstein based his theory on Lorentz's earlier work.
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