- #386
sweetser
Gold Member
- 360
- 0
Hello Lut:
I appreciate the importance of having an explicit way to show that energy is conserved. One reason I am not worried that we will eventually find it is that there is no "t" in the Lagrangian, so one can vary t without changing the action. A symmetry like that means that there is a conserved quantity, and it turns out to be energy.
There is no t in the action of GR either. Energy is conserved in GR, but it is not localized, one needing a volume of spacetime before one can say energy is conserved. The nonlocalization happens because one varies the metric field.
> Regarding the the current business. You can split the 4 degrees of freedom into 2 orthogonal vectors but you have an electrical and a matter current to describe, and only 2 df each. Or do I misunderstand ?
That sounds right. Both the graviton and photon travel at the speed of light, and thus only need 2 degrees of freedom each to describe a mediating particle where like attract (gravity) and like repel (EM).
doug
I appreciate the importance of having an explicit way to show that energy is conserved. One reason I am not worried that we will eventually find it is that there is no "t" in the Lagrangian, so one can vary t without changing the action. A symmetry like that means that there is a conserved quantity, and it turns out to be energy.
There is no t in the action of GR either. Energy is conserved in GR, but it is not localized, one needing a volume of spacetime before one can say energy is conserved. The nonlocalization happens because one varies the metric field.
> Regarding the the current business. You can split the 4 degrees of freedom into 2 orthogonal vectors but you have an electrical and a matter current to describe, and only 2 df each. Or do I misunderstand ?
That sounds right. Both the graviton and photon travel at the speed of light, and thus only need 2 degrees of freedom each to describe a mediating particle where like attract (gravity) and like repel (EM).
doug