Math Makes Theoretical Physics a Little Less Scary. Or Maybe Not!

Physics equations, the least simple simple things in all of science.

I don’t have a justifiable reason for subjecting you to this, reader, but here we go anyway. If you share my love for STEM, this __ minute read should be a bit more bearable.

If you’ve ever studied advanced physics before, or just been interested in the science that weaves the fabric of the observable universe together, you’ve probably seen or heard of the term general relativity. It quantifies a relationship between spacetime and everything in it to establish the law of an expanding universe and gravity as a resultant force of the spacetime curvature. So, in 4-D, gravity is just a geometric property!

If you’re someone who likes math, the governing equation of GR isn’t so threatening. It’s explaining that when a massive object interacts with spacetime, it causes distortions in it that results in a geodesic curve defined by s, the scalar parameter of motion, and Γ, 𝛼, and β, which are affine connection coefficients — an object which, when projected on a smooth manifold, forms a Euclidean connection between two tangent spaces, which enables us to visualize spacetime via mathematical objects, making physics a lot easier to understand.

(Left) Einstein’s relativity equation; (Right) the minimally-expanded geodesic equation.

Overall, our G.O.A.T. Einstein did a great job of making his landmark equation seem as simple as possible…or did he?

The original governing equation I showed you before was actually pretty paraphrased. That elegant simplification of the field equation makes use of the Ricci tensor (R) and energy-momentum tensor (T). Think of math as a language. There are many ways of explaining or saying the same thing in different ways, each with nuances and lengths specific to them. I could say, ‘a period of 10 years’ or I could say ‘a decade’. Both statements are effectively equivalent, but they have slight semantic and rhythmic variations that may affect the interpretation of time passed (10 years).

Math is the exact same way. We can use equivalent variables to shorten equations for research…