On Sunday, September 8, 2019 at 9:02:15 PM UTC-5, Alan Grayson wrote:
>
>
>
> 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
>
As I keep saying, you have to use sum E = 0 that comes from ADM relativity
or the Tolman result within the framework of general relativity.
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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