Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Invariants (sorry i didn't know where to put it)

  1. Oct 8, 2006 #1
    That's the question, if we can interpretate mathematically using some kind of "invariant" theory for this situation:

    - Using Newton's second Law for gravity then we find that:

    [tex] \ddot r = -GM/r [/tex] (1)

    M is the mass of the earth, and m is the mass of the particle, amazingly using the equation (1) above [tex] r(t) \rightarrow r(m,t) = r(t) [/tex] , then the trajectories of the system of a particle under the gravity is invariant under mass change of the particle (if we make [tex] m' = m + \delta m [/tex] as an infinitesimal mass change of the particle the trajectories r(t) are the same)

    - Using the metric in GR we also find that the metric:

    [tex] g_{ab}=N(t)dt^{2} - \sum_{i,j}H_{ij}dx^{i}dx^{j} [/tex]

    where i,j=x,y,z

    then the solutions of the metric are invariant under infinitesimal changes of the function [tex] N(t)+ \delta N(t) [/tex]

    -And the last example, if we define the "charge" by:

    [tex] Q=e|\Phi|^{2} [/tex] you can check that charge is invariant under


    transformation of the Quantum wave function of the form [tex] \Phi\rightarrow e^{ia(x)}\Phi [/tex]

    My question involving math is if we can define some "conserved" quantities or properties of the system from these "peculiar" invariance of the system under m (mass of the particle) N(t) (any function of t) or invariance under "phase" transformation, hopes the problem seems clear.
     
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you help with the solution or looking for help too?
Draft saved Draft deleted



Similar Discussions: Invariants (sorry i didn't know where to put it)
  1. Primes (sorry) (Replies: 2)

Loading...