The Annotated Math Of (Almost) Everything

Have you lot heard of the regulation of to the lowest degree action? It’s the most of import reckon inward physics, together with it underlies everything. According to this principle, our reality is optimal inward a mathematically exact way: it minimizes a constituent called the “action.” The universe that nosotros bring out ourselves inward is the 1 for which the activity takes on the smallest value.

In quantum mechanics, reality isn’t quite that optimal. Quantum fields don’t lead maintain to create upwards one's heed on 1 specific configuration; they tin create everything they want, together with the activity together with hence quantifies the weight of each contribution. The total of all these contributions – known every bit the path-integral – describes 1 time to a greater extent than what nosotros observe.

This omniscient activity has real picayune to create amongst “action” every bit inward “action hero”. It’s precisely an integral, ordinarily denoted S, over about other function, called the Lagrangian, ordinarily denoted L. There’s a Lagrangian for the Standard Model together with 1 for General Relativity. Taken together they encode the deportment of everything that nosotros know of, except nighttime thing together with quantum gravity.

With a picayune practice, there’s a lot you lot tin read off straight from the Lagrangian, virtually the deportment of the theory at depression or high energies, virtually the type of fields together with mediator fields, together with virtually the type of interaction.

The below figure gives you lot a petroleum reckon how that works.

I originally made this figure for the appendix of my book, but afterward removed it. Yes, my editor is however optimistic the mass volition travel published Spring 2018. The conclusion virtually this volition autumn inward the adjacent calendar month or so, hence remain tuned.

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