There's a fundamental connection between symmetry and conservation laws in physics, which holds true in both classical and quantum mechanics.

General Relativity is based on two foundational pillars: general covariance, meaning physical laws don't depend on coordinate choices, and the principle of equivalence, which states that gravity is the same as local acceleration.

Maxwell's equations are conformally invariant, meaning they depend on the space-time structure independent of scaling.

In flat spacetime, energy-momentum conservation is straightforward, but in General Relativity, it becomes complex due to the need for a covariant derivative and additional machinery.

If spacetime has symmetries, such as a timelike Killing field, it allows for the definition of genuinely conserved, coordinate-independent energy.

The physical world is constrained by the laws of physics, while imagination is unconstrained, allowing for limitless creativity.

I don't think we're in a straightforward simulation, but I do believe that underlying physics is rooted in information theory.

Physics is a victim of its own success; general relativity and quantum mechanics are so effective that they cover 99.9% of observations, making it hard to find deviations to combine them.

Defining energy in general relativity is complex; pseudotensors can provide conservation but break covariance, while covariant definitions work under symmetry but fail in general spacetimes, hinting at a deeper structure yet to be universally interpreted.