On Monday, September 9, 2019 at 4:44:51 AM UTC-6, Lawrence Crowell wrote:
>
> 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
>
A = RA = RIchard Arnowitt. I met him when I was doing my MS in physics at
Northeastern University. Never took a course with the guy, but I noticed he
had an awful nervous habit of chewing his nails to their cuticles.
Literally! Really! I guess his theory didn't bring him any peace. In any
event, CMIIAW, but it seems that ADM is a special case where one ASSUMES E
= 0. Bruce didn't seem impressed. Otherwise he wouldn't have categorically
denied that E = 0 for the total universe. It would be useful if he would
comment here. Probably too much to expect. 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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