Physicists use a 350-year-old theorem to reveal new properties of light waves
phys.org
phys.org
> The work, led by Xiaofeng Qian, assistant professor of physics at Stevens and reported in the August 17 online issue of Physical Review Research, also proves for the first time that a light wave's degree of non-quantum entanglement exists in a direct and complementary relationship with its degree of polarization. As one rises, the other falls, enabling the level of entanglement to be inferred directly from the level of polarization, and vice versa. This means that hard-to-measure optical properties such as amplitudes, phases and correlations—perhaps even these of quantum wave systems—can be deduced from something a lot easier to measure: light intensity.
> [..] Qian's team interpreted the intensity of a light as the equivalent of a physical object's mass, then mapped those measurements onto a coordinate system that could be interpreted using Huygens' mechanical theorem. "Essentially, we found a way to translate an optical system so we could visualize it as a mechanical system, then describe it using well-established physical equations," explained Qian.
> Once the team visualized a light wave as part of a mechanical system, new connections between the wave's properties immediately became apparent—including the fact that entanglement and polarization stood in a clear relationship with one another.
Photons cannot have mass in GR General Relativity because E=mc^2?
How do solar sails achieve thrust from photons and solar pressure if they are massless?
https://en.wikipedia.org/wiki/Radiation_pressure
"""Johannes Kepler put forward the concept of radiation pressure in 1619 to explain the observation that a tail of a comet always points away from the Sun.[9]
The assertion that light, as electromagnetic radiation, has the property of momentum and thus exerts a pressure upon any surface that is exposed to it was published by James Clerk Maxwell in 1862, and proven experimentally by Russian physicist Pyotr Lebedev in 1900[10] and by Ernest Fox Nichols and Gordon Ferrie Hull in 1901."""
E=mc^2
E=(m)(c^2)
E=(0)(c^2)
E=0
(Are photons "at relative rest" in Lagrangian points, accretion discs, superfluids, 0 Kelvin, and/or when created from just n-body gravity, etc?)
Energy-Momentum relation: https://en.wikipedia.org/wiki/Energy%E2%80%93momentum_relati... :
> [Energy-Momentum relation] is the extension of mass–energy equivalence for bodies or systems with non-zero momentum. It can be written as the following equation:
E^2 = (p^2)(c^2)+(m^2)(c^4)
E^2 = ppcc+(0)(c^4)
E = sqrt(ppcc)
E = sqrt((p^2)(c^2))
Anyways, further from "Energy-Momentum relation":
> The Dirac sea model, which was used to predict the existence of antimatter, is closely related to the energy–momentum relation
From "Dirac Sea" https://en.wikipedia.org/wiki/Dirac_sea :
> The Dirac sea interpretation and the modern QFT interpretation are related by what may be thought of as a very simple Bogoliubov transformation, an identification between the creation and annihilation operators of two different free field theories.
> [...] Dirac sea theory has been displaced by quantum field theory, though they are mathematically compatible
SQG Superfluid Quantum Gravity says there needn't be antimatter; there is pressure and there are phases of matter in a varyingly Superfluidic cosmos. The Dirac wikipedia article also mentions SQG.
And further from "Energy-Momentum relation":
> The quantities E, p, E′, p′ are all related by a Lorentz transformation. The relation allows one to sidestep Lorentz transformations when determining only the magnitudes of the energy and momenta by equating the relations in the different frames
Not just rarely; photons are never at rest, period. In circumstances where one might intuitively think they might change speed, instead they change frequency.
That includes that they do not change speed in materials with a different index of refraction than a vacuum, but in that case, they do seem to, so as a shorthand it's often said that the speed of light in e.g. glass is slower than in a vacuum, but that's really just a shorthand -- so that's a can of worms.
Anyway your second equation is the full version of your much more famous first equation precisely because we need the extra term for photons (or any other massless things).
Horologium Oscillatorium by Huygens: https://en.wikipedia.org/wiki/Horologium_Oscillatorium
Parallel axis theorem: https://en.wikipedia.org/wiki/Parallel_axis_theorem :
> The parallel axis theorem, also known as Huygens–Steiner theorem, or just as Steiner's theorem,[1] named after Christiaan Huygens and Jakob Steiner, can be used to determine the moment of inertia or the second moment of area of a rigid body about any axis, given the body's moment of inertia about a parallel axis through the object's center of gravity and the perpendicular distance between the axes
...
Harmonic oscillator: https://en.wikipedia.org/wiki/Harmonic_oscillator
Quantum Harmonic Oscillator: https://en.wikipedia.org/wiki/Quantum_harmonic_oscillator
Pendulum (mechanics) https://en.wikipedia.org/wiki/Pendulum_(mechanics)