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.
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 papers or number crunching, but ultimately, they come out of longer, painstakingly letter-heavy, and confusing equations. Expanding the equation in terms of the metric tensor g, this is what it actually looks like:
But wait, there’s more!
I’m still simplifying here. I’ve used the Einstein summation convention, so aᵢbᵢ = 𝛴ᵢaᵢbᵢ so I don’t have to explicitly render each sum, ∂^{μ} = ∂/(∂x_{μ}), where x_{μ} is the μᵗʰ coordinate in the system. The energy-momentum tensor also remained simplified.
The moral of the story is that you should enjoy the complexity of science and try to understand it. As someone who’s primarily interested in biology and math, learning how I could use mathematical syntax to describe the natural or organic phenomena and innovations that fascinate me. For example, if I wanted to understand the sum total of the energy — except for the nuclear components — present in benzene, everyone’s favorite hallmark aromatic compound, I could use the Hamiltonian Born Approximation to describe it:
Keep in mind, this is for a simple compound, not even a protein or the like! And yes, this too took me a long time to write 😭
But, after we are aware that this Hamiltonian can be calculated, the utility of writing out the sequence of subtracted energy values quickly decreases, and we realize that we can just use a summation:
Much cleaner!
All this to say that math is not only very interesting, but it also makes the rest of science interpretable. As E. F. Schumacher once said, “any intelligent fool can make things bigger and more complex… It takes a touch of genius — and a lot of courage to move in the opposite direction.”
The genius he talks about requires you to understand the fundamentals first. Once we do that, we start to realize that it’s better to say ‘a decade’ than ‘a period of 10 years’.
So, if you thought A.P. Physics C was scary (don’t worry, it wasn’t my easiest class, either), thank your lucky stars that you don’t have to parse through Einstein’s work just yet!
About the Author
Hi, my name is Okezue. I’m an aspiring engineer/scientist, a young researcher and entrepreneur, and high school student. To keep up with me, follow me on Instagram or Twitter (or my medium page).
To learn more about my work, visit my LinkedIn, Google profile, or website. See you in the next article! 👋🏾
