My attempt was to first rewrite ##S_M## slightly to make it more clear where ##g_{\mu\nu}## appears
$$S_M = \int d^4x \sqrt{-g} (g^{\mu\nu} \nabla_\mu\phi\nabla_\nu\phi-\frac{1}{2}m^2\phi^2).$$
Now we can apply the variation:
$$\begin{align*}
\delta S_M
&= \int d^4x (\delta\sqrt{-g})...
Hello all,
I understand the formation of the Lagrangian is: Kinetic Energy minus the potential energy.
(I realize one cannot prove this: it is a "principle" and it provides a verifiable equation of motion.
Moving on...
One inserts the Lagrangian into the form of the "Action" and minimizes it...
Although I've read many papers that propose a relation between action and entropy, I've been told that there is no generally accepted relation in physics.
But how/why are these concepts unrelated?
What about nobel laureate Frank Wilczek? He proposes that entropy and action are closely related...
The action for a relativistic point particle is baffling simple, yet I don't really understand why it is written as,
$$S = -m\int ds $$
I know it's right because we get the right equations of motion from it, but can one understand it in a more intuitive way?
Hello, When we applying the principle of least action, we require ##\delta S=0##, which corresponding to the action S being an extremum. I am just wondering why do we say that the action is a minimum instead of a maximum for a physical path? Can I use the path integral to explain this problem...
Einstein's field equations (EFEs) describe the pointwise relation between the geometry of the spacetime and possible sources described by an energy-momentum tensor ##T^{ab}##. As well known, such equations can be derived from a variational principle applied to the following action: $$S=\int\...
Book: Landau Lifshitz, The Classical Theorey of Fields, chapter 11, section 95.
I have gone through the derivation of Einstein field equations but not without holes to fill and fix in my understanding. Lets start with the action for the grtavitational field ##S_g## which after some explanation...
Is the motivation for the action principle purely from empirical evidence, or theoretical arguments, or a mixture of the two? As I understand it, there was some empirical evidence from Fermat's observations in optics, i.e. that light follows the path of least time, notions of virtual work and...
Dear PF Forum,
I have a problem with calculating energy which I should have learnt long ago in my high school time.
If I push (accelerate) a 1 kg object 1 meter/sec2 for 10 seconds, I spend energy like this.
Distance = 1/2 at2. So I would have pushed this object for 50 metres. So I'm using...
Hi guys,
I have a very basic question about the WZ model. I want to show that it is invariant under SUSY transformations.
The action is \int{d^4 x} \partial^\mu \phi* \partial_\mu \phi +i\psi^† \bar{\sigma}^\mu \partial_\mu \psi
The SUSY transformations are \delta\phi = \epsilon \psi ...
My grandson asked me this question:
If in fact,as Newton said,all actions are accompanied by an equal and opposite reaction, then there can be no single actions in the universe;all actions must therefor be part of a reaction between two opposite and equal actions,which are in fact also...
Dear all,
If we consider the lagrangian to have both geometric parts (Ricci scalar) and also a field, the action would take the form below:
\begin{equation}
S=\frac{1}{2\kappa}\int{\sqrt{-g} (\ R + \frac{1}{2} g^{\mu\nu} \partial_\mu \phi \partial_\nu \phi -V(\phi)\ )}
\end{equation}
which are...
Hello,
I've noticed that Planck's constant h and the action of a particle S both share the units of Joule-second. I was wondering if there were a connection between the two, but my Modern Physics textbook (Harris) doesn't say anything about it. Wikipedia's definition of Planck's constant says...
Hi guys,
I'm doing a project at the moment revolving around capillary action and surface tension. Today I conducted an experiment to observe capillary action in a capillary tube and paper towel at different temperatures of water. I don't understand why I've got the following results:
As you...
Hello Physics Forums!
Supposing that we have an action that says:
$$L=\frac{1}{2}R-g_{C\bar{D}}\partial_{\mu}z^C\partial^{\mu}\bar{z}^D+\frac{1}{4} + \frac{1}{4}ImM_{IJ}F^I_{\mu\nu}\cdot F^{J\mu\nu} +\frac{1}{4}ReM_{IJ}F^I_{\mu\nu}\cdot \tilde{F}^{J\mu\nu}$$
where...
This is with regards to the principle of least action.
I understand that an action is a functional (a function where functions have values assigned to them, I believe?)
When trying to figure this out, I understood minimising as finding the true path of the principle of least action. But that...
Homework Statement
i want to find the variation of this action with respect to ## g^{\mu\nu}## , where ##N_\mu(x^\nu)## is unit time like four velocity and ##\phi## is scalar field.
##I_{total}=I_{BD}+I_{N}##
##
I_{BD}=\frac{1}{16\pi}\int dx^4\sqrt{g}\left\{\phi...
So I tried googling it but unfortunately i haven't found anything, so I though i'll take my quarries here.
I would like to know, how scientists have tried to explain how quantum entanglement works.
Thanks for the answers. :)
hi,
please if somebody could explain why anybody would consider the "action" and is there any proof that the minimal action actually gives the correct route of a problem?