Recent content by Sagittarius A-Star

In Geometric Algebra, the Hodge * operation is replaced by an algebraic operation, a multiplication with the unit pseudo-scalar ##I## (=##\gamma_0\gamma_1\gamma_2\gamma_3## = geometric product of all basis vectors). The dual of the EM-field bivector ##F## is ##G=FI##. An xt-component becomes...

This can be found in chapter 38 of the book "Introduction to Special Relativity, 2nd Edition" by Wolfgang Rindler: https://www.amazon.com/-/he/Introduction-Special-Relativity-Science-Publications/dp/0198539525?tag=pfamazon01-20 A shortened version of chapter 38 can be found under this link.

Addition: Geometric Algebra can also be applied to curved spacetime. I did not yet have a closer look to this. Source: https://davidhestenes.net/geocalc/pdf/Curv_cal.pdf

What also may help for understanding the EM field is to use Geometric Algebra, applied to 4D-spacetime. The wedge product ##\wedge## (=outer product) of two vectors is a bivector. The components of a 4-vector are projections on the four axes of the coordinate system (x, y, z, t). The...

With ##\gamma=1/\sqrt{1-\omega^2r^2/c^2}## ##dA = \gamma r dr d\phi## The proper area is ##A(R)= 2\pi \int_0^R \gamma r \, dr= {2 \pi c^2 \over \omega^2}(1-\sqrt{1-\omega^2R^2/c^2})## Calculation (using a substitution)...

The circumference will be measured in the non-Euclidean geometry of the rotating disk as ##U=\gamma 2\pi R## with ##\gamma=1/\sqrt{1-\omega^2R^2/c^2}##. Source: https://en.wikipedia.org/wiki/Ehrenfest_paradox#Einstein_and_general_relativity

I think for clarificaion one should distinguish between one-way- and two-way speeds. For applying the LT for a segment of the rim of the disk, one defines (not assumes) that the one-way speed of light is isotropic for synchronizing clocks, fixed to the rim of the disk. For "measuring" a...

Regarding "But here the static rulers in O_r should be twice as long": This is only true, if you apply the standard Lorentz transformation. You can do this only if you define, that the one-way speed of light with reference to O_r is the same clockwise and counterclockwise. But you can do this...

According to Wolfgang Rindler, the EP cannot be applied to the "paradox" of an accerated charge, because it's field is not local. An electric charge at rest on the surface of the earth does not radiate by energy conservation. A charge, fixed inside an orbiting satellite, does radiate. Source...

Maybe this helps: https://www.wolframphysics.org/technical-introduction/potential-relation-to-physics/time-and-spacetime/ via: https://www.wolframphysics.org/technical-introduction/

For example: If you send a light pulse from Earth to Alpha Centauri, then the spacetime-interval between the emition-event on Earth and the absorbtion-event on Alpha Centauri is zero. But a spacetime-interval along a worldline is called "proper time" only for time-like worldlines, not for...

For example: The distance from Earth to Alpha Centauri is 4.367 LY. If you travel with 99.99999999 % light speed (relative to Earth) to there, then the distance is length-contrated in your rest-frame by a factor of ##1/70710.7##. Calculation of gamma-factor...

Maybe that helps: Source: https://en.wikipedia.org/wiki/CPT_symmetry#Derivation_of_the_CPT_theorem

In classical physics, the only "asymmetric" law, which contains an arrow of time, is the the second law of thermodynamics.

I have the suspicion, that the following physics videos are also AI fake: https://www.youtube.com/@TheUniverseAccordingtoSusskind https://www.youtube.com/@PhysicswithFeynman-1