Editing Radiation pressure (section)

=== Compression in a uniform radiation field ===

In general, the pressure of electromagnetic waves can be obtained from the [[Electromagnetic stress–energy tensor#Algebraic properties|vanishing of the trace of the electromagnetic stress tensor]]: since this trace [[Stress–energy tensor#Stress–energy of a fluid in equilibrium|equals 3''P'' − ''u'']], we get
<math display="block">P = \frac{u}{3},</math>
where {{math|''u''}} is the radiation energy per unit volume.

This can also be shown in the specific case of the pressure exerted on surfaces of a body in [[thermal equilibrium]] with its surroundings, at a temperature {{math|''T''}}: the body will be surrounded by a uniform radiation field described by the [[Planck law|Planck black-body radiation law]] and will experience a compressive pressure due to that impinging radiation, its reflection, and its own black-body emission. From that it can be shown that the resulting pressure is equal to one third of the total [[radiant energy]] per unit volume in the surrounding space.<ref>{{cite book | author = Shankar R. | title = Principles of Quantum Mechanics | edition = 2nd | url = https://www.fisica.net/mecanica-quantica/Shankar%20-%20Principles%20of%20quantum%20mechanics.pdf }}</ref><ref>{{cite book | last1 = Carroll | first1 = Bradley W | author2 = Dale A. Ostlie | title = An Introduction to Modern Astrophysics | edition = 2nd}}</ref><ref>{{cite book | last = Jackson | first = John David | year = 1999 | title = Classical Electrodynamics}}</ref><ref>Kardar, Mehran. "Statistical Physics of Particles".</ref>

By using [[Stefan–Boltzmann law]], this can be expressed as
<math display="block">P_\text{compress} = \frac{u}{3} = \frac{4\sigma}{3c} T^4,</math>
where <math>\sigma</math> is the [[Stefan–Boltzmann constant]].