- #1
Quantum Immortal
- 35
- 1
I never seen any intuitive interpretation of the LHS of the equations.
I realize the question is a tall order.
But i think something can be extracted.
-----------------------------------
*Is this statement correct?
The true information content of GR is :
1)The non covariant law of Newton reinterpreted as a curvature theory. A GR-like simple noncovariant model of gravity. Valid for slow speeds and weak field
2) SR in curved space time.
Lets put it differently
lets split the metric
g = η + X
now, interpret it, that we have the field X inside flat space (η minkosky metric = flat space)
Its not a crack pot theory, its just a stricked mathematical identity.
Its an equivalent reformulation, absolutely nothing changes.
Its easier to visualize stuff in flat space. Rather then curvature in 4D space time...
In the end of the day, saying that gravity is the curvature of space time, is just a philosophical statement. Here's a perfect bijection, between curved space GR, and "flat space GR".
Again, its just a reformulation of GR, just for pedagogical reasons. I'm with in the rules of the Forum.
With this small reinterpretation of the GR... I'll call it "Flat GR" (FGR)
*Is this statement correct?
The true information content of FGR is
1)Newton's law
2)SR
------------------------------------
*If yes. Can you explain, how this happen in the derivation of the GR equations??
--------------------------------
It is meant here by true information content. The analogy with How Electromagnetism is derived from conlombs law and SR. This is done by considering a reference frame, were Comlombs law is correct, then change reference frame. Because coulombs law, is not covariant, it will get messed up. The new messed up comlomb law, is added to the normal comlombs law as a system of equations, and a new source element is define for it. Now the system of equations are covariant.
You apply the same logic on Newton with SR
*If you have, just one of the 10 equations, the 00 equation. You can derive the other 9 from the first, with just certain Lorentz transformations and differentiation. Right?
------------------------------------
About non linearity: It is meant, that since SR equates energy and mass, and Newton law is about the attraction of masses, it follows, that the gravitational field acts on it self also. Making it nonlinear.
About the stress energy tensor: The Raw electric charge, by it self, has the only propety, that it can't be created or destroyed, you just need to keep the total charge constant. The propertis of mass however, is basically all of mechanics, that the source is the stress energy tensor, simply says, that mass follows the laws of mechanics.
The elements of the stress energy tensor are energy, momentum, force and tork.
The continuity equation of the stress energy tensor, is just all of mechanics...
This is why we need to use that as the source. Its not just random
--------------------------
*About FGR:
Are they some interpretations, about what the elements of X stand for? (potentials?? gravitomagnetism? torsions ?)
Interpretations, about what the equations of X represent?
In general reinterpret some stuff of FGR
We need to travel along a closed curve, in order to detect curvature. That resembles a loop current in a magnetic field.
What about the flat Riemann and ricci tensors?
I realize the question is a tall order.
But i think something can be extracted.
-----------------------------------
*Is this statement correct?
The true information content of GR is :
1)The non covariant law of Newton reinterpreted as a curvature theory. A GR-like simple noncovariant model of gravity. Valid for slow speeds and weak field
2) SR in curved space time.
Lets put it differently
lets split the metric
g = η + X
now, interpret it, that we have the field X inside flat space (η minkosky metric = flat space)
Its not a crack pot theory, its just a stricked mathematical identity.
Its an equivalent reformulation, absolutely nothing changes.
Its easier to visualize stuff in flat space. Rather then curvature in 4D space time...
In the end of the day, saying that gravity is the curvature of space time, is just a philosophical statement. Here's a perfect bijection, between curved space GR, and "flat space GR".
Again, its just a reformulation of GR, just for pedagogical reasons. I'm with in the rules of the Forum.
With this small reinterpretation of the GR... I'll call it "Flat GR" (FGR)
*Is this statement correct?
The true information content of FGR is
1)Newton's law
2)SR
------------------------------------
*If yes. Can you explain, how this happen in the derivation of the GR equations??
--------------------------------
It is meant here by true information content. The analogy with How Electromagnetism is derived from conlombs law and SR. This is done by considering a reference frame, were Comlombs law is correct, then change reference frame. Because coulombs law, is not covariant, it will get messed up. The new messed up comlomb law, is added to the normal comlombs law as a system of equations, and a new source element is define for it. Now the system of equations are covariant.
You apply the same logic on Newton with SR
*If you have, just one of the 10 equations, the 00 equation. You can derive the other 9 from the first, with just certain Lorentz transformations and differentiation. Right?
------------------------------------
About non linearity: It is meant, that since SR equates energy and mass, and Newton law is about the attraction of masses, it follows, that the gravitational field acts on it self also. Making it nonlinear.
About the stress energy tensor: The Raw electric charge, by it self, has the only propety, that it can't be created or destroyed, you just need to keep the total charge constant. The propertis of mass however, is basically all of mechanics, that the source is the stress energy tensor, simply says, that mass follows the laws of mechanics.
The elements of the stress energy tensor are energy, momentum, force and tork.
The continuity equation of the stress energy tensor, is just all of mechanics...
This is why we need to use that as the source. Its not just random
--------------------------
*About FGR:
Are they some interpretations, about what the elements of X stand for? (potentials?? gravitomagnetism? torsions ?)
Interpretations, about what the equations of X represent?
In general reinterpret some stuff of FGR
We need to travel along a closed curve, in order to detect curvature. That resembles a loop current in a magnetic field.
What about the flat Riemann and ricci tensors?