Favorite Physics Equations

Here are some of my favorite equations (no particular order).

1) The Drake Equation $$ N = R_* · f_p · n_e · f_1 · f_i · f_c · L$$

What it is/why I love it: Theoretically computes the number of civilizations (with which communication might be possible) in our galaxy. Doesn't have much practical use but always gets me wondering.


2) Newton's Second Law $$F = m · a$$

What it is/why I love it: Calculates net force on an object. When I studied physics, my professors would relate everything back to this equation. No matter how complicated, it seemed like every equation could be related in some way to this simple equation. Also, if you know the mass and the acceleration vector of something, in a way, you literally know everything about it.


3) Heisenberg Uncertainty Principle $$\Delta x · \Delta p \ge \frac{h}{4 · \pi}$$

What it is/why I love it: This equation literally has people questioning life itself. Some people refuse to believe in this because it means that there is always an inherent uncertainty surrounding specific particles. Their position and momentum can not both be known exactly. Ever.


4) Second Law of Thermodynamics $$\Delta S \ge 0 $$

What it is/why I love it: This equation means (net) entropy, "chaos" if you will, always increases in the universe. Awesome...


5) Definition of complex numbers $$ i^2 = -1 $$

What it is/why I love it: Opens up an entire new area of mathematics necessary in fields like quantum mechanics.


6) Shapley Value $$\phi _i (v) = \sum_{S \subseteq (N \setminus \{i\})} \frac{\lvert S \rvert ! · (n - \lvert S \rvert - 1)!}{n!} · (v(S \cup \{i\}) - v(S)))$$

What it is/why I love it: Game theory, in a sense the study of decision making, has two sub-fields: cooperative (participants are working towards a common goal) and non-cooperative (participants are competing for something). The Shapley value, calculated in cooperative decision making, produces the theoretically ideal value for the payoff for each player in the coalition of participants. It produces the fairest distributions of amassed assets AKA the best communal outcome. I am very interested in the science of decision making (see this article of mine), so I love the fact that there is a beautiful, thorough equation that can be used to make a theoretically-irrefutable best decision.


Honorable mentions