7 votes
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How would someone discover the Einstein-Hilbert Action?

I don't know the history of how the Einstein-Hilbert action was discovered originally, but from a modern point of view it can be justified in several ways. First, if you want to represent gravity as ...
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3 votes

Derivation of gravitational dynamics using Lagrangian?

It is important to mention that in this model the point particle masses $m_i$ serve as sources $$ \rho({\bf x},t)=\sum_i m_i \delta^3({\bf x}-{\bf x}_i(t)) $$ for the gravitational potential field $\...
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2 votes

Derivation of gravitational dynamics using Lagrangian?

The first Lagrangian is the Lagrangian for the motion of a point particle in a Newtonian gravitational potential (or field), whereas the second is the Lagrangian for the gravitational potential (or ...
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2 votes

Gravity = Yang-Mills squared? What is the Lagrangian?

The statement $$ \text{(super) gravity} = [\text{(super) Yang-Mills]}^2 $$ is the punch line of the Bern-Carrasco-Johansson (BCJ) colour-kinematic duality conjecture that the perturbative on-shell ...
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2 votes
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Derivation of gravitational dynamics using Lagrangian?

First, is it essential to use two different Lagrangians? What is the physical basis and meaning of having two Lagrangians? Is it a rigorous approach? No, it is not essential to use two different ...
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1 vote
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What $\mu$ represents in Gryzinski's free fall atomic model equation?

It almost certainly represents the magnetic dipole moment of the electron — this is standard notation and (as noted in the wiki article) the last term is meant to account for interactions between the ...
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1 vote

How to know if the vibration system requires one degree of freedom or two? and how to pick the right coordinate to describe the movement?

There is no trick. If you take the linkage AC out the disk can rotate $~\theta~$ and move towards $~x~$ ,independent of the rotation $~\varphi~$ . The kinematic equation form the „linkage“ is $$x=\...
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