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All the fundamental laws of physics can be written in terms of an action principle. This includes electromagnetism, general relativity, the standard model of particle physics, and attempts to go beyond the known laws of physics such as string theory. For example, (nearly) everything we know about the universe is captured in a Lagrangian where the terms carry the contributions of Einstein, Maxwell (or Yang and Mills) and Dirac respectively, and describe gravity, the forces of nature (electromagnetism and the nuclear forces) and the dynamics of particles like electrons and quarks.

Source: David Tong

Me: I am a second year undergrad and have a nice familiarity with the -1/4 F_ij F_ij term (electromagnetism) and how it results to the Maxwell's Equations, but am still curious to know how it seems like there is always a Lagrangian. Apart from one obvious advantage that the Euler Lagrange equations hold in any coordinate system and the Lagrangian holds the key to the symmetries of the system.

Qmechanic
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Gravity_CK
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1 Answers1

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Why does it seem like there is always a Lagrangian?

Typically we study forces of nature using differential equations, and these differential equations can typically be re-written in terms of other formalisms such as Lagrangian or Hamiltonian formulations.

In many cases (not all), we are able to understand the forces of nature using a Lagrangian formulation. This is probably "why [] it seem[s] like there is always a Lagrangian."

There is likely no other really satisfying answer appropriate to this forum--this forum is focused on main stream physics, not philosophy--or perhaps any forum.

All the fundamental laws of physics can be written in terms of an action principle.

Not necessarily.

In fact, even all the forces we know of are not immediately susceptible to the usual Lagrangian way. For example: Quantum gravity. We have yet to make sense of such a theory in the usual sense.

hft
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