On Saturday, September 7, 2019 at 2:05:11 PM UTC-6, Lawrence Crowell wrote:
>
> On Friday, September 6, 2019 at 10:31:32 PM UTC-5, 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
>>>
>>> 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
>>>
>>
>> But if the spatial surface is flat, there is no gravity. So how can this
>> be an argument for claiming the total estimated of a universe with gravity
>> is zero? AG
>>
>
> Not so, for it is embedded in spacetime and there is an extrinsic
> curvature. You have to research some of this, such as reading Misner,
> Throne & Wheeler *Gravitation* Ch 21.
>
> LC
>
Thanks. I have that book handly and will study your reference. However, on
the other issue I raised, I think I am on firm ground that there is no
general definition for the potential energy *OF* a gravitational field;
rather just the potential energy of a test particle -- in which case
there's something awry wih your additional of gravitation potential energy
with rest and kinetic energy. AG
>
>
>>
>>>
>>> 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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