Knowra Electromagnetic field tensor Electromagnetic field tensor The electromagnetic field tensor is an antisymmetric rank-two spacetime tensor that combines electric and magnetic fields. Its components transform together under Lorentz transformations, expressing their relativistic unity.
Special relativity : The theory that describes space, time, and physical laws for observers in inertial motion. Its Lorentz transformations mix the tensor’s electric and magnetic components.
Electric field : A vector field describing the electric force per unit charge at each point in space and time. Its three components occupy the time-space entries of the tensor.
James Clerk Maxwell : A Scottish physicist whose equations unified electricity, magnetism, and light. His field equations supplied the electromagnetic theory later written in tensor form.
Electromagnetic stress-energy tensor : A tensor describing the energy density, momentum density, and stresses carried by electromagnetic fields. It is built from the field tensor and quantifies the field’s energy and momentum.
Electric and magnetic fields : The separate three-dimensional vector fields used to describe electric and magnetic effects. Unlike the tensor, this split depends on an observer’s choice of reference frame.
Lorentz transformation : A linear transformation relating spacetime coordinates measured by inertial observers in relative motion. It specifies how the electromagnetic field tensor changes between inertial frames.
Magnetic field : A vector field describing the magnetic force on moving charges and magnetic dipoles. Its three components occupy the space-space entries of the tensor.
Hendrik Lorentz : A Dutch physicist who developed transformations relating measurements in moving reference frames. His transformations expose how electric and magnetic fields mix between inertial frames.
Differential forms : A mathematical language for antisymmetric quantities integrated over curves, surfaces, and higher-dimensional spaces. In this language, electromagnetic fields and Maxwell’s equations take especially concise forms.
Electromagnetic four-potential : A four-vector potential from which the electromagnetic field tensor can be derived. The potential generates the field tensor but changes under gauge transformations that leave the field unchanged.
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