1. M

    Calculating Energy-Momentum Tensor in GR

    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})...
  2. T

    A Lagrangian to the Euler-Lagrange equation

    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...
  3. S

    I Why are action and entropy unrelated?

    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...
  4. H

    A Action for a relativistic free particle

    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?
  5. BookWei

    I The Principle of Least Action

    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...
  6. Gio83

    A Derive the Bianchi identities from a variational principle?

    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\...
  7. Mr-R

    A Landau Lifshitz Gravitational field equation

    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...
  8. F

    I What is the motivation for principle of stationary action

    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...
  9. Stephanus

    B Pushing wall

    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...
  10. F

    A Invariance of Wess Zumino Action under SUSY

    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 ...
  11. D

    B All actions are reactions

    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...
  12. S

    Lagrangian and dimension

    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...
  13. M

    Connection between Planck's Constant and Action?

    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...
  14. S

    Capillary action at different temperatures

    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...
  15. E

    Equation of motion from the action

    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...
  16. Clueless

    What does it mean to "minimise" an action ?

    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...
  17. T

    Varying the action with respect to metric

    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...
  18. P

    Attempts to explain quantum entaglement

    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. :)
  19. adoion

    Principle of least action?

    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?