Did you know antennas work by warping space-time? I have been an EE for 30 years and did not know that. For a great introduction to a fascinating subject Google "Radiation, Antennas and Einstein". You don't need to plow through the math to get the gist of it and the author is a nice guy who responds to email queries. And "Take her up to warp 5 Scotty!"

 

I found this, actually quite interesting

https://esp.mit.edu/download/cebc1f39-b1c2-4214-a2f9-632c7f4100cf/S14332_radiation_splash.pdf

 

Another interesting thing about Einsten's theory is that a magnetic field can be viewed as the result of the Relativistic movement of the electron electric field..

 

Another interesting thing about Einsten's theory is that a magnetic field can be viewed as the result of the Relativistic movement of the electron electric field..

I'll always remember how, in the last couple weeks of Physics II (Intro to E&M), after spending weeks working with magnetic fields and solving all kinds of problems, the instructor came in and said, "Okay, today I'm going to prove to you that there's no such thing as a magnetic field." And then proceeded to do it.

 

Consider spacetime within a reasonable scope:




As we zoom in the curvature becomes less and more until we can no longer detect curve.




A highly distorted image can cause a loss of perspective. It is necessary to maintain an appropriate framework.


Spacetime mathematically derived from a composite of geometric theorems, differential geometry, but the language we write them in
is tensor calculus. All of these geometric objects exist within a manifold and are related by rules, relationships, and transformation laws.

Along with these geometric objects is the manifold. The manifolds are fixed and enclose the geometric objects,
with few exceptions the shape tends to be conservative. There are no shortages of 3D Cad but this video is intended to show manifolds.
https://www.youtube.com/shorts/9kBlAdS0ROs?feature=share

If the manifold is held fixed and only the coordinates move, the truths we observe must remain the same.
Because we are moving in space the observer might encounter some distortion. The motion through space changes what “local” means.
This mathematical kaleidoscope has been useful in problem solving by reorganizing data, it is not easy to get past the unfamiliar logic.



What are some of the achievements:

General Relativity - gravity as curvature
Quantum Mechanics - Hilbert space geometry
Gauge Theory - forces as connections on bundles
Special Relativity - spacetime as Minkowski geometry
Topology - new phases of matter
String Theory - complex geometry & dualities
Chaos Theory - Symplectic geometry of motion
Geometric Algebra - unified transformations
Category Theory - geometry of relationships

 

I strongly recommend that to learn about Einstein, read Einstein. So few people I discuss relativity with have ever read even one of Einstein's own books, they only read other writers' books about Einstein or his work! read the man himself, don't listen to others, e.g.



You can see the way he expressed his thoughts and reasoning at the time, rather than the historically sanitized approach taken by modern writers.