On Thursday, September 5, 2019 at 1:32:24 AM UTC-6, Alan Grayson wrote:
>
>
>
> 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
>
I'm not the brightest bulb in the room, particularly when it comes to
physics, but ISTM you're adding apples and oranges when adding the negative
potential energy of a TEST PARTICLE *IN* a gravitational field, with mass
m, to the positive energy equivalent of the mass creating the field, M. 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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