Orcun YILDIZ’s Reviews > The Biggest Ideas in the Universe: Space, Time, and Motion > Status Update

Newton’s theory doesn’t explain why the mass that is the source of the gravity is the same as that governs inertia and motion.

Riemann’s curvature tensor: take two vectors to make a closed loop, move the third vector in this loop, then the difference between the original third vector and the resulting vector becomes the fourth vector which tells you if that space is curved or not: remember euclidian geometry assumes parallel lines along right angles while you can have converging or diverging lines along spheres or hyperbolic

Twin paradox: 1 to 7 years, you experience less time if you don’t follow a straight path, Alice and Bob, close to speed of light.

Newtonian mechanics: give me positions and velocities and evolve them through time using Newton’s laws
Lagrangian mechanics: the principle of least action, given initial and final conditions, system will take the least action
Hamiltonian mechanics: elevate momentum to concept of its own, independent of velocity. Equation of motion when trajectory obeys this then momentum equals mass times velocity but not always.

- One of Kepler laws: the orbit of a planet sweeps out equal areas in equal times, thus they move quicker when they are closer to sun.
- spherical-cow philosophy: start simple and get an answer then add the complications later.
- Aristotles naive thinking that objects naturally stay at rest and there should be some “divine” force that moves them.