How to estimate the total energy of the visible universe

[Alan Grayson]

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

[Lawrence Crowell]

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

[John Clark]

On Tue, Sep 3, 2019 at 11:01 PM Alan Grayson <agrays...@gmail.com> 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

What about the energy in light, it's being redshifted by the expanding universe and thus becoming weaker, where did all that energy go? I would maintain the energy went nowhere it was just destroyed.  When looked at at the scale of the entire universe why would anyone even expect energy to be conserved? Noether's Theorem says if there is time-translation invariance, that is to say if things generally look about the same from one time period to another, then matter-energy is conserved, but in our expanding accelerating universe things don't look the same. So it might be better to say that in general relativity spacetime can create energy, as it does when it accelerates the expansion of the universe, or destroy energy, as it does when it redshifts photons in a expanding universe). So energy simply isn’t conserved globally at the level of the entire cosmos, although it is locally at least approximately.

John K Clark

[Lawrence Crowell]

I would argue it goes into the gravity field. The expansion of space stretches the wavelength of photons and the loss of energy in the photon is taken up by gravitation in the form of  Λg_{ab} for Λ the cosmological constant. 

The lack of Killing vectors in a type O spacetime of a cosmology, which also happens with type N and III, just means there is no Noether principle of symmetry associated with time translation. That is what conserves energy. This does have some odd prospects, such as for k = 1 spacetime with positive spatial curvature, where space is a sphere, then the expansion of that space means for a constant vacuum energy density that vacuum energy is being generated out of nothing. For k = 0 the spatial surface is flat and infinite and while expanding the vacuum energy adjusts by a multiplier of "infinity," which is not observable. In fact either way a local observer is bounded by the cosmological horizon and that will bound observations to a finite vacuum energy. 

LC

[Alan Grayson]

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

[Alan Grayson]

It's claimed the energy is undefined in GR. Regardless, what I am trying to do is estimate what the total energy is, not whether it's conserved for an expanding or contracting universe. AG 

[Lawrence Crowell]

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

https://physics.stackexchange.com/questions/257476/how-did-the-universe-shift-from-dark-matter-dominated-to-dark-energy-dominate/257542#257542

[John Clark]

On Wed, Sep 4, 2019 at 2:52 PM Alan Grayson <agrays...@gmail.com> wrote:

> It's claimed the energy is undefined in GR. Regardless, what I am trying to do is estimate what the total energy is, not whether it's conserved for an expanding or contracting universe. AG 

You want to know the total energy of the universe during what time period? According to General Relativity the acceleration of the universe is caused by Dark Energy that is inherent in empty space, it works out to be about 10^-10 joules per cubic meter. But that acceleration means more cubic meters are constantly being created so, assuming General Relativity is 100% correct, the total energy in the universe will keep increasing forever.

John K Clark

[Alan Grayson]

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 

[Alan Grayson]

I told you; I just want to estimate the total energy of the observable universe, at any time t. I am not dealing with any conservation law, although I grant you raise an interesting issue. Moreover, I think the photons can be considered among the 10^80 particles, but clearly those photons have energy h * f, and I assume we can assign some average frequency to estimate the total contribution from those photons. AG

[Alan Grayson]

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

[Alan Grayson]

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 

[Alan Grayson]

It isn't clear, in a particle model for photons, why the reddening due to cosmic expansion is objectively the result of energy loss. In the case of reddening due to relative motion, Doppler effect, perhaps it's not an objective effect, but just from some reference frame or pov. AG 

[Lawrence Crowell]

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

[Alan Grayson]

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  

[Lawrence Crowell]

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

[Alan Grayson]

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

[Lawrence Crowell]

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

[Alan Grayson]

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 

[Alan Grayson]

On Tuesday, September 3, 2019 at 9:00:55 PM UTC-6, 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

I recall that Bruce had an interesting comment why the total energy of the universe is not zero. But I can't find it. Where is it? TIA, AG