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

Einstein introduced the pseudotensor to represent the energy of the gravitational field, but it depends on chosen coordinates, which contradicts the principle of general covariance.

The laws of physics are translation invariant, meaning if I move 10 steps to the left, I experience the same laws of physics as if I was here, which corresponds to the conservation of momentum.

The splitting of positive and negative frequency components in quantum field theory is not conformally invariant, which presents a conceptual impasse.

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.

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

Conformal geometric algebra, which extends to five-dimensional space, allows for the representation of points, lines, planes, and spheres as algebraic objects, simplifying many geometric operations.

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.

Definitions of energy, such as mass in motion or the capacity to change, don't hold up in dynamically curved spacetime.