He found that the Lorentz transformation must transcend its connection with Maxwell's equations, and must represent the fundamental relations between the space and time coordinates of inertial frames of reference.

via Maxwell's relations.

Maxwell's relations are a set of equations in thermodynamics which are derivable from the definitions of the thermodynamic potentials.

In the philosophy of thermal and statistical physics, Maxwell's demon is a thought experiment created by the physicist James Clerk Maxwell to " show that the Second Law of Thermodynamics has only a statistical certainty ".

" Elsa Maxwell's column and radio show in 1946 referred to Kaner as " the breath of home to unknown thousands of our young men when they were lonely.

" This statement was surrounded in Maxwell's text by several others like it that show that it was no slip of the pen.

Similarly, Maxwell's equations show a differing behavior for the magnetic fields produced by electric currents, versus magnetic fields produced by changing electric fields.

Sharing the bill with Thurston Moore and Half Japanese, Tadpoles gave their final performance in February 2000 at a sold-out show at Maxwell's in Hoboken, which was the first time they ever played their legendary hometown club.

Thornlea's Drama Department conducted a weekly show called Maxwell's House that the OAC students put together in 2001-2002 as their collective graduating project.

Although the tour officially concluded with a performance at Johnny Brenda's in Philadelphia, the following week the band played an extra show at Maxwell's in Hoboken, NJ, opening for Yo la Tengo at one of the group's annual Hannukah concerts.

After joining IBM Research in 1972, he built on the work of IBM's Rolf Landauer to show that general-purpose computation can be performed by a logically and thermodynamically reversible apparatus ; and in 1982 he proposed a re-interpretation of Maxwell's demon, attributing its inability to break the second law to the thermodynamic cost of destroying, rather than acquiring, information.

Moreover, various phenomena occur in the world even though Maxwell's equations predicts them to be impossible, such as " nonclassical light " and quantum entanglement of electromagnetic fields ( see quantum optics ).

The speed of light and other EMR predicted by Maxwell's equations did not appear unless the equations were modified in a way first suggested by FitzGerald and Lorentz ( see history of special relativity ), or else otherwise it would depend on the speed of observer relative to the " medium " ( called luminiferous aether ) which supposedly " carried " the electromagnetic wave ( in a manner analogous to the way air carries sound waves ).

It is often useful to write Maxwell's equations in other forms ; these representations are still formally termed " Maxwell's equations ".

) The other two equations describe how the fields ' circulate ' around their respective sources ; the magnetic field ' circulates ' around electric currents and time varying electric field in Ampère's law with Maxwell's correction, while the electric field ' circulates ' around time varying magnetic fields in Faraday's law.

It also accounted for anomalous observations, including the properties of black body radiation, that other physicists, most notably Max Planck, had sought to explain using semiclassical models, in which light is still described by Maxwell's equations, but the material objects that emit and absorb light, do so in amounts of energy that are quantized ( i. e., they change energy only by certain particular discrete amounts and cannot change energy in any arbitrary way ).

From 1882 to 1889, Gibbs wrote five papers on physical optics, in which he investigated birefringence and other optical phenomena and defended Maxwell's electromagnetic theory of light against the mechanical theories of Kelvin and others.

Though Gibbs's research on physical optics is less well known today than his other work, it made a significant contribution to classical electromagnetism by applying Maxwell's equations to the theory of optical processes such as birefringence, dispersion, and optical activity.

Normally wave equations in physics can be derived from other physical laws-the wave equation for mechanical vibrations on strings and in matter can be derived from Newton's laws-where the analogue wavefunction is the displacement of matter, and electromagnetic waves from Maxwell's equations, where the wavefunctions are electric and magnetic fields.

It is one of the four Maxwell's equations which form the basis of classical electrodynamics, the other three being Gauss's law for magnetism, Faraday's law of induction, and Ampère's law with Maxwell's correction.

Maxwell's equations of electromagnetism relate the electric and magnetic fields to each other and to the motions of electric charges.

In all other cases the law is incorrect unless Maxwell's correction is included ( see below ).

On the other hand, the assertion of special relativity that Maxwell's equations are invariant for all frames of reference moving at constant velocities would predict no torque ( a null result ).

Using the above definition of the potentials and applying it to the other two Maxwell's equations ( the ones that are not automatically satisfied ) results in a complicated differential equation that can be simplified using the Lorenz gauge where A is chosen to satisfy:

The problems and solutions were originally published anonymously, but the solution of this problem ( and one other ) were included in Niven's The Scientific Papers of James Clerk Maxwell, which was published eleven years after Maxwell's death.

The architect's father entered Maxwell's coffee business and later developed other business interests of his own in Brazil.

: A profound formal difference exists between the theoretical concepts that physicists have formed about gases and other ponderable bodies, and Maxwell's theory of electromagnetic processes in so-called empty space.

Although the Sun and other stars radiate equally in all directions, their radiation pattern does not violate Maxwell's equations, because radiation from a star is incoherent.

The lyrics notably contain some quick direct allusions to other soul music ballads, mainly Maxwell's " Fortunate ", and Prince's " Adore ".

In order to establish the numerical value of ε < sub > 0 </ sub >, one makes use of the fact that if one uses the rationalized forms of Coulomb's law and Ampère's force law ( and other ideas ) to develop Maxwell's equations, then the relationship stated above is found to exist between ε < sub > 0 </ sub >, μ < sub > 0 </ sub > and c < sub > 0 </ sub >.

This can also be expressed in terms of vector field quantities by taking the divergence of Ampère's law with Maxwell's correction and combining with Gauss's law, yielding:

In the absence of free electric currents and time-dependent effects, Maxwell's equations describing the magnetic quantities reduce to

Still, Thomson's model ( along with a similar Saturnian ring model for atomic electrons, also put forward in 1904 by Nagaoka after James Clerk Maxwell's model of Saturn's rings ), were earlier harbingers of the later and more successful solar-system-like Bohr model of the atom.

Maxwell's correction to Ampère's law is particularly important: it shows that not only does a changing magnetic field induce an electric field, but also a changing electric field induces a magnetic field.

Maxwell's equations posit that there is electric charge, but not magnetic charge ( also called magnetic monopoles ), in the universe.

The motivation behind this approach began with the Kaluza-Klein theory in which it was noted that applying general relativity to a five dimensional universe ( with the usual four dimensions plus one small curled-up dimension ) yields the equivalent of the usual general relativity in four dimensions together with Maxwell's equations ( electromagnetism, also in four dimensions ).

Gibbs also stressed that the absence of a longitudinal electromagnetic wave, which is needed to account for the observed properties of light, is automatically guaranteed by Maxwell's equations ( by virtue of what is now called their " gauge invariance "), whereas in mechanical theories of light, such as Lord Kelvin's, it must be imposed as an ad hoc condition on the properties of the aether.

Edward also appears in Robin Maxwell's To The Tower Born: A Novel of the Lost Princes a story of what might have happened to the princes while they were in the tower.

* The second law of thermodynamics, Maxwell's demon and the arrow of time ( also Loschmidt's paradox ).

This equation also is a direct consequence of the linearity of Maxwell's equations.

These equations also describe radio waves, discovered by David Edward Hughes in 1879, around the time of James Clerk Maxwell's death.

Fully symmetric Maxwell's equations can also be written if one allows for the possibility of " magnetic charges " analogous to electric charges.

Starting with Gauss ' law for electricity ( also one of Maxwell's equations ) in differential form, we have:

Treating free charges separately from bound charges, Ampère's equation including Maxwell's correction in terms of the H-field is ( the H-field is used because it includes the magnetization currents, so J < sub > M </ sub > does not appear explicitly, see H-field and also Note ):

* In the 2005 video game From Russia with Love, Moneypenny appears with Lois Maxwell's likeness in the same film, and a voice by Karly Rothenberg ( who also voices Rosa Klebb in the game ).

She also features in Robin Maxwell's The Secret Diary of Anne Boleyn, Suzannah Dunn's The Queen of Subtleties and briefly in Margaret George's The Autobiography of Henry VIII.

The basic reason an EM field changes in character with distance from its source, is that Maxwell's equations prescribe different behaviors for each of the two source-terms of electric fields and also the two source-terms for magnetic fields.

The magnetic Aharonov – Bohm effect is also closely related to Dirac's argument that the existence of a magnetic monopole can be accommodated by the existing magnetic source-free Maxwell's equations if both electric and magnetic charges are quantized.

He voiced Pongo the Dalmatian in Disney's animated One Hundred and One Dalmatians ( 1961 ), and also guest-starred on Marilyn Maxwell's short-lived ABC series Bus Stop ( also 1961 ).

If the potential is a solution to Maxwell's equations then, after this gauge transformation, the new potential is also a solution to Maxwell's equations and no experiment can distinguish between these two solutions.

Maxwell's equations can also be expressed in a generally covariant form, which is as invariant under general coordinate transformation as Einstein's field equation.

also gave a careful analysis, including an application of Maxwell's law of the particle velocities in a gas.

The plane wave spectrum arises naturally as the eigenfunction or " natural mode " solution to the homogeneous electromagnetic wave equation in rectangular coordinates ( see also Electromagnetic radiation, which derives the wave equation from Maxwell's equations in source-free media, or Scott ).