Euler-Lagrange spacetime formulation

[AntonioLao]

Analogous to fluid mechanics, the quantization of spacetime is said to be described by using the Eulerian and Lagrangian formalism.

Eulerian description is done by independent variables of space and time, while Lagrangian is done by independent variable of time only. The position in space becomes the dependent variable for the Lagrangian formalism and the velocity becomes the dependent variable for the Eulerian formalism.

But in the quantum formalism, the product of position and velocity taking unit of mass is greater or equal Planck's constant of action or angular momentum.

[Guille]

Is there a formalism that takes velocity and time as independent varaibles and acceleration as the dependent one? Is there a hamiltonian formalism?

The acceleration would be very impotant in studying the nature of space-time. What formula do we use to calculate a particle's acceleration? Is it jsut as the one of normal bodies (s/(t1-t2)=a)?

[AntonioLao]

For conservative systems, the Hamiltonian is derived from the Lagrangian.

[Guille]

For conservative systems, the Hamiltonian is derived from the Lagrangian.

Yes, actually the hamiltonian mechanics is based on appying lagrangiags to lagrangians. Is there a similar for hamiltonians, application of hamiltionians to hamiltonians? If it's not yet developed it might be something improtant to look at.

[AntonioLao]

application of hamiltionians to hamiltonians?

Hamiltonian systems are time independent. Once time independence is achieved is there a second time independence like both directions of time independence?

[Guille]

Hamiltonian systems are time independent. Once time independence is achieved is there a second time independence like both directions of time independence?

well, there could be a time independence of time's time. Obviouslly, there is a time to time, that is, change to change. So if a system is independent of change, some could also be independent aswell of change's change. It may seem that all time independent systems are neccesarilly time's time independent, but no, for even if there is no change, there coul dbe change for the change (as the system is itself not isolated).

[AntonioLao]

If you can solve the puzzle of time-time-time-time---> independence then you also solve the CPT theorem.

[Guille]

If you can solve the puzzle of time-time-time-time---> independence then you also solve the CPT theorem.

There is only a time to time, but there is no further time to that. Wats exactly time independence to do with the CPT theorem?

[AntonioLao]

Wats exactly time independence to do with the CPT theorem?

The 'T' in CPT theorem stands for time reversal. That is to say all directions of time are equivalent.