On Wednesday, September 4, 2019 at 2:37:07 PM UTC-6, Lawrence Crowell wrote:
>
> On Wednesday, September 4, 2019 at 1:48:15 PM UTC-5, Alan Grayson wrote:
>>
>>
>>
>> On Wednesday, September 4, 2019 at 4:08:58 AM UTC-6, Lawrence Crowell
>> wrote:
>>>
>>> You also have to include the total gravitational energy or T^{ab} due
>>> to local sources and Λg^{ab}.
>>>
>>> The ADM Hamiltonian constraint is NH = 0 where this Hamiltonian is
>>> determined by the traceless transverse part of the extrinsic curvature or
>>> Gauss fundamental form. For a general spacetime manifold there is no way to
>>> define mass-energy and for most Petrov types the mass-energy is simply no
>>> defined. Think of a spherical space with matter throughout. There is no way
>>> to construct a Gaussian surface with which to integrate a total mass or
>>> energy. Also if that putative surface is embedded in mass-energy then that
>>> surface is subject to diffeomorphisms of local curvature. Energy is then
>>> not localizable, and in general things that we want invariant are so
>>> independent of such diffeomorphisms.
>>>
>>> LC
>>>
>>
>> The energy of the gravitational field is positive for each particle of
>> average mass. But how does one calculate the negative potential energy for
>> each average mass particle? I can calculate the potential energy of a test
>> particle at some location IN a field, but how can I calculate the total
>> negative potential energy OF the field (for a particle of average mass)? AG
>>
>
> V = -GMm/r
>
Sure. That's the formula for a particle of mass m at distance r from the
center of mass, for mass M. How can you equate that (when integrated from r
to infinity) as the potential energy of the FIELD? AG
>
> Read the following where by using H = 0, zero energy and just Newtoin's
> laws it is easy to derive the FLRW equations for k = 0 or a flat spatial
> surface.
>
> LC
>
>
> https://physics.stackexchange.com/questions/257476/how-did-the-universe-shift-from-dark-matter-dominated-to-dark-energy-dominate/257542#257542
>
>
>
>
>>
>>>
>>> On Tuesday, September 3, 2019 at 10:00:55 PM UTC-5, Alan Grayson wrote:
>>>>
>>>> Just sum over the estimated total of 10^80 particles, using mc^2 by
>>>> first estimating the average mass of those particles for the rest energy,
>>>> adding their average potential gravitational energy and their average
>>>> kinetic energy. Why not? AG
>>>>
>>>
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