On Sunday, September 8, 2019 at 1:28:36 PM UTC-6, Lawrence Crowell wrote:
>
>
>
> On Sunday, September 8, 2019 at 12:47:28 AM UTC-5, Alan Grayson wrote:
>>
>>
>>
>> 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
>>
>
> The definition of energy as some constant of dynamics is difficult in
> general relativity.
>
> LC
>
Since Newtonian gravity doesn't define (negative) potential energy for a
gravitational *field*, and GR doesn't even define (negative) potential
energy, do you concede there's no basis for the conclusion that the net
estimated energy of the universe is exactly zero? There seems to be nothing
negative to add to the positive energies to get zero. 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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