Let's Learn Physics: The Gravity of Hamiltonian Mechanics @zapphysics

Uploaded August 2021 | Updated September 2026, 12 hours ago

Last time, we went through a bunch of formalism to find a new way of doing classical mechanics which did not rely on our specific choice of coordinates, namely Hamiltonian mechanics. Now, we will see just how useful this formalism can be in simplifying physics problems!

Lets Learn Physics: The Gravity of Hamiltonian Mechanics

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$What does 1+2+3+... REALLY equal and what does it have to do with particle physics? The sum of natural numbers, 1+2+3+..., is a fairly regularly cited sum to show off the strange nature of mathematics. This is mainly due to the fact that it can (seemingly) easily be shown to be equal to -1/12. Thats right. Not only is the result finite, it is also a fraction as well as negative! This seems completely crazy and thats because there is an important factor of infinity that is hidden from view when proving this in the usual ways. So lets find out what this sum is equal to while still retaining this mysterious hidden infinity. The way of doing this is through what is known as regularization of the series (which is secretly done is the normal way of evaluating this sum as well). This parallels nicely to a technique in physics known as renormalization, where we take infinities that show up like this and hide them in other places, like the masses and charges of particles. This allows us to have finite physics, but we lose the ability to predict these quantities. ► Music Credit: Dj Quads Track Name: Its Near Music By: Dj Quads @ https://soundcloud.com/aka-dj-quads Original upload HERE - https://www.youtube.com/watch?v=UI79n3E1U_g Follow me on Twitter: https://twitter.com/ZapPhysics$

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