Total energy of the universe

[Alan Grayson]

If it's not conserved, as seems implied by the red shift due to expansion, where does it go? TIA, AG

[Bruce Kellett]

On Fri, May 8, 2020 at 6:00 PM Alan Grayson <agrays...@gmail.com> wrote:

If it's not conserved, as seems implied by the red shift due to expansion, where does it go? TIA, AG

Silly question. If it is not conserved, it does't have to go anywhere -- it just vanishes.

Bruce

[Alan Grayson]

When an expanding gas cools, doesn't the energy go into work done to cause the expansion? Is it your opinion then, that something cannot come from nothing, but something can become nothing? AG

[Bruce Kellett]

That's what non-conservation means -- something can come from nothing and go to nothing.

Bruce

[Alan Grayson]

If you believe in what's called "evidence", and extrapolating from it to create a hypothetical physical theory, can you give a single example of something coming from nothing? AG 

[Bruce Kellett]

Two examples. The universe; Dark energy.

Bruce

[Alan Grayson]

We have no clue how the universe began, or even IF it began; and we have zero understanding of dark energy, other than it probably exists and gravitationally interacts with ordinary matter. Where's the rigor? AG 

[Alan Grayson]

In my reply above, I was really referring to dark matter. However, the same argument (wrt origin) can be said of dark energy (except that it seems to have the opposite sign (repulsive) of the gravity we're familiar with). More important though for this discussion, is that its origin is completely unknown, as is the case for ordinary matter and dark matter. We just can't assert they arose from nothing. So what would non-conservation of energy mean? Maybe, the apparent loss of energy as the universe expands, causes it to expand. IOW, not a real loss but a lower energy density spread over larger volumes of space, keeping the total energy unchanged. AG 

[ronaldheld]

If you attempt to Sum up all of the components, how close to 0 do you get?

    Ronald

[smit joshi]

Just a laymen curiosity

Alan Gray by your thought that "When an expanding gas cools, doesn't the energy go into work done to cause the expansion". Let us assume that the energy loss of red shift fuels the expansion of our universe. We know that E=hc/(lamda) and derivative of energy w.r.t wavelength is -hc/(lamda)^2 so as wavelength increase the loss in energy decreases so the rate of expansion should decelerate rather than accelerating.

So I think we cannot compare this two observations.

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[Lawrence Crowell]

There is no global meaning to energy conservation. There is the Hamiltonian constraint Nℌ = 0, which just says that for a local region where the lapse function can be parallel translated to the energy is zero. This is for Petrov type O solutions 

Nℌ = 0 = ½(da/dt)^2 - 4πGρa^2/3c^3 - k

Which leads to the FLRW constraint

(a’/a)^2 = 8πGρ/3c^3 – k/a^2 a’ = da/dt

Where the Hubble parameter H = 70km/s-Mpc  is (a’/a)^2 = H^2. This means that in a local region we have energy conservation FAPP. The difficulty is this is not a property of the symmetries of the system so we have no way to extend this globally.

What this ultimately means is that all physics is local. It does not mean we have mass-energy locally vanishing. The apparent increase in the kinetic energy due to expansion is well enough compensated for by a decease in gravitational potential energy. There is nothing mysterious going on here. All this means is there is a limitation or horizon to our ability to know if there are global symmetries to the universe. As such there is no meaning to conservation principles.

LC

On Friday, May 8, 2020 at 3:00:18 AM UTC-5, Alan Grayson wrote:

[Alan Grayson]

On Friday, May 8, 2020 at 12:43:55 PM UTC-6, ronaldheld wrote:

If you attempt to Sum up all of the components, how close to 0 do you get?

    Ronald

I didn't try to do that. And I am not asserting the total energy of the observable universe is zero. AG 

[Alan Grayson]

On Friday, May 8, 2020 at 1:45:15 PM UTC-6, smit joshi wrote:

Just a laymen curiosity

Alan Gray by your thought that "When an expanding gas cools, doesn't the energy go into work done to cause the expansion". Let us assume that the energy loss of red shift fuels the expansion of our universe. We know that E=hc/(lamda) and derivative of energy w.r.t wavelength is -hc/(lamda)^2 so as wavelength increase the loss in energy decreases so the rate of expansion should decelerate rather than accelerating.

So I think we cannot compare this two observations.

The expansion is probably not caused solely by loss of energy by photons as I hypothesized. It could also be caused by dark energy, which we know virtually nothing about, and is more or less a placeholder to explain repulsive gravity. AG

On Fri, May 8, 2020 at 6:35 PM Alan Grayson <agrays...@gmail.com> wrote:

On Friday, May 8, 2020 at 5:33:53 AM UTC-6, Bruce wrote:

On Fri, May 8, 2020 at 9:02 PM Alan Grayson <agrays...@gmail.com> wrote:

On Friday, May 8, 2020 at 4:24:36 AM UTC-6, Bruce wrote:

On Fri, May 8, 2020 at 7:11 PM Alan Grayson <agrays...@gmail.com> wrote:

On Friday, May 8, 2020 at 2:56:50 AM UTC-6, Bruce wrote:

On Fri, May 8, 2020 at 6:00 PM Alan Grayson <agrays...@gmail.com> wrote:

If it's not conserved, as seems implied by the red shift due to expansion, where does it go? TIA, AG

Silly question. If it is not conserved, it does't have to go anywhere -- it just vanishes.

Bruce

When an expanding gas cools, doesn't the energy go into work done to cause the expansion? Is it your opinion then, that something cannot come from nothing, but something can become nothing? AG

That's what non-conservation means -- something can come from nothing and go to nothing.

Bruce

If you believe in what's called "evidence", and extrapolating from it to create a hypothetical physical theory, can you give a single example of something coming from nothing? AG 

Two examples. The universe; Dark energy.

Bruce

We have no clue how the universe began, or even IF it began; and we have zero understanding of dark energy, other than it probably exists and gravitationally interacts with ordinary matter. Where's the rigor? AG 

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[Alan Grayson]

On Friday, May 8, 2020 at 4:50:55 PM UTC-6, Lawrence Crowell wrote:

There is no global meaning to energy conservation. There is the Hamiltonian constraint Nℌ = 0, which just says that for a local region where the lapse function can be parallel translated to the energy is zero. This is for Petrov type O solutions 

Nℌ = 0 = ½(da/dt)^2 - 4πGρa^2/3c^3 - k

Which leads to the FLRW constraint

(a’/a)^2 = 8πGρ/3c^3 – k/a^2 a’ = da/dt

Where the Hubble parameter H = 70km/s-Mpc  is (a’/a)^2 = H^2. This means that in a local region we have energy conservation FAPP. The difficulty is this is not a property of the symmetries of the system so we have no way to extend this globally.

What this ultimately means is that all physics is local. It does not mean we have mass-energy locally vanishing. The apparent increase in the kinetic energy due to expansion is well enough compensated for by a decease in gravitational potential energy.

This is the claim, but I haven't seen any proof of it. Do you have one? Take a planet. Can you show that Mc^2, where M is the planet's mass, is equal to its negative gravitational potential energy? AG

 

There is nothing mysterious going on here. All this means is there is a limitation or horizon to our ability to know if there are global symmetries to the universe. As such there is no meaning to conservation principles.

We can estimate the volume of the observable universe and its average mass-energy density. So it seems we can estimate its total energy. Does that energy remain constant or not as the universe expands? This seems like a reasonable question to ask. AG 

[Alan Grayson]

Another hypothetical possibility is that the energy lost by photons, and observed by the cosmological red shift, is gained by the Cosmological Constant.  AG

[Alan Grayson]

On Friday, May 8, 2020 at 8:28:02 PM UTC-6, Alan Grayson wrote:

On Friday, May 8, 2020 at 4:50:55 PM UTC-6, Lawrence Crowell wrote:

There is no global meaning to energy conservation. There is the Hamiltonian constraint Nℌ = 0, which just says that for a local region where the lapse function can be parallel translated to the energy is zero. This is for Petrov type O solutions 

Nℌ = 0 = ½(da/dt)^2 - 4πGρa^2/3c^3 - k

Which leads to the FLRW constraint

(a’/a)^2 = 8πGρ/3c^3 – k/a^2 a’ = da/dt

Where the Hubble parameter H = 70km/s-Mpc  is (a’/a)^2 = H^2. This means that in a local region we have energy conservation FAPP. The difficulty is this is not a property of the symmetries of the system so we have no way to extend this globally.

What this ultimately means is that all physics is local. It does not mean we have mass-energy locally vanishing. The apparent increase in the kinetic energy due to expansion is well enough compensated for by a decease in gravitational potential energy.

This is the claim, but I haven't seen any proof of it. Do you have one? Take a planet. Can you show that Mc^2, where M is the planet's mass, is equal to its negative gravitational potential energy? AG

Apriori, the claim seems unreasonable -- because the mass-energy equivalent of a material body like a planet is huge, but the negative gravitational energy seems small by comparison --goes as -1/r. AG

[Lawrence Crowell]

On Friday, May 8, 2020 at 9:28:02 PM UTC-5, Alan Grayson wrote:

On Friday, May 8, 2020 at 4:50:55 PM UTC-6, Lawrence Crowell wrote:

There is no global meaning to energy conservation. There is the Hamiltonian constraint Nℌ = 0, which just says that for a local region where the lapse function can be parallel translated to the energy is zero. This is for Petrov type O solutions 

Nℌ = 0 = ½(da/dt)^2 - 4πGρa^2/3c^3 - k

Which leads to the FLRW constraint

(a’/a)^2 = 8πGρ/3c^3 – k/a^2 a’ = da/dt

Where the Hubble parameter H = 70km/s-Mpc  is (a’/a)^2 = H^2. This means that in a local region we have energy conservation FAPP. The difficulty is this is not a property of the symmetries of the system so we have no way to extend this globally.

What this ultimately means is that all physics is local. It does not mean we have mass-energy locally vanishing. The apparent increase in the kinetic energy due to expansion is well enough compensated for by a decease in gravitational potential energy.

This is the claim, but I haven't seen any proof of it. Do you have one? Take a planet. Can you show that Mc^2, where M is the planet's mass, is equal to its negative gravitational potential energy? AG

The Hamiltonian constraint above and the FLRW equation are all you need. It is right there.

 

 

There is nothing mysterious going on here. All this means is there is a limitation or horizon to our ability to know if there are global symmetries to the universe. As such there is no meaning to conservation principles.

We can estimate the volume of the observable universe and its average mass-energy density. So it seems we can estimate its total energy. Does that energy remain constant or not as the universe expands? This seems like a reasonable question to ask. AG 

Consider a quantum gravitational wave, say at or near the Planck scale, in the earliest phase of the universe. For that now redshifted or expanded to the scale of the CMB this means such data, from the near Planck time of the earliest universe, is around 2 trillion light years away. I have indicated numerous times how this comes about, This is as far as we can say anything about the physics of cosmology. Beyond that scale we are faced with a  fundamental horizon of unobservability. As a result all we can say is that for any local system energy is conserved, but this conservation law is not due to any global symmetry. The Hamiltonian constraint is a manifestation of a local gauge-like principle of general relativity, and it has no global content. On a global level we cab' say anything; it is unknowable.

Quantum mechanics is curiously similar. We have nonlocality of a wave, but we can only infer some things from that by local measurements that localizes waves or fields. We are not able to ever perform a perfect observation of a global wave. There is an epistemic horizon in QM that I think is dual or complementary to that of spacetime or general relativity.

LC

[Alan Grayson]

On Saturday, May 9, 2020 at 4:58:20 AM UTC-6, Lawrence Crowell wrote:

On Friday, May 8, 2020 at 9:28:02 PM UTC-5, Alan Grayson wrote:

On Friday, May 8, 2020 at 4:50:55 PM UTC-6, Lawrence Crowell wrote:

There is no global meaning to energy conservation. There is the Hamiltonian constraint Nℌ = 0, which just says that for a local region where the lapse function can be parallel translated to the energy is zero. This is for Petrov type O solutions 

Nℌ = 0 = ½(da/dt)^2 - 4πGρa^2/3c^3 - k

Which leads to the FLRW constraint

(a’/a)^2 = 8πGρ/3c^3 – k/a^2 a’ = da/dt

Where the Hubble parameter H = 70km/s-Mpc  is (a’/a)^2 = H^2. This means that in a local region we have energy conservation FAPP. The difficulty is this is not a property of the symmetries of the system so we have no way to extend this globally.

What this ultimately means is that all physics is local. It does not mean we have mass-energy locally vanishing. The apparent increase in the kinetic energy due to expansion is well enough compensated for by a decease in gravitational potential energy.

This is the claim, but I haven't seen any proof of it. Do you have one? Take a planet. Can you show that Mc^2, where M is the planet's mass, is equal to its negative gravitational potential energy? AG

The Hamiltonian constraint above and the FLRW equation are all you need. It is right there.

If it's so obvious, there'd be no dispute about this. But there definitely is! Bruce, e.g. Can you cite a paper where it's explicitly proven? TIA, AG 

 

 

There is nothing mysterious going on here. All this means is there is a limitation or horizon to our ability to know if there are global symmetries to the universe.

There are surely limitations on our observational abilities, but why is a symmetry necessary? Nature seems pretty asymmetric; e.g., imbalance of matter and anti-matter. AG 

[Lawrence Crowell]

On Saturday, May 9, 2020 at 6:22:44 AM UTC-5, Alan Grayson wrote:

On Saturday, May 9, 2020 at 4:58:20 AM UTC-6, Lawrence Crowell wrote:

On Friday, May 8, 2020 at 9:28:02 PM UTC-5, Alan Grayson wrote:

On Friday, May 8, 2020 at 4:50:55 PM UTC-6, Lawrence Crowell wrote:

There is no global meaning to energy conservation. There is the Hamiltonian constraint Nℌ = 0, which just says that for a local region where the lapse function can be parallel translated to the energy is zero. This is for Petrov type O solutions 

Nℌ = 0 = ½(da/dt)^2 - 4πGρa^2/3c^3 - k

Which leads to the FLRW constraint

(a’/a)^2 = 8πGρ/3c^3 – k/a^2 a’ = da/dt

Where the Hubble parameter H = 70km/s-Mpc  is (a’/a)^2 = H^2. This means that in a local region we have energy conservation FAPP. The difficulty is this is not a property of the symmetries of the system so we have no way to extend this globally.

What this ultimately means is that all physics is local. It does not mean we have mass-energy locally vanishing. The apparent increase in the kinetic energy due to expansion is well enough compensated for by a decease in gravitational potential energy.

This is the claim, but I haven't seen any proof of it. Do you have one? Take a planet. Can you show that Mc^2, where M is the planet's mass, is equal to its negative gravitational potential energy? AG

The Hamiltonian constraint above and the FLRW equation are all you need. It is right there.

If it's so obvious, there'd be no dispute about this. But there definitely is! Bruce, e.g. Can you cite a paper where it's explicitly proven? TIA, AG 

Tolman computed some of this early on, His old book Relativity, Thermodynamics, and Cosmology. Oxford: Clarendon Press. 1934 is a source. There is nothing about physical cosmology that says we will witness some horrendous violation of energy conservation locally. It does tell us that since GR is a local principle, based on local translations of vectors etc, there is then no general symmetry rule for energy conservation.

 

There is nothing mysterious going on here. All this means is there is a limitation or horizon to our ability to know if there are global symmetries to the universe.

There are surely limitations on our observational abilities, but why is a symmetry necessary? Nature seems pretty asymmetric; e.g., imbalance of matter and anti-matter. AG 

That has nothing in particular to do with this.

LC

[Alan Grayson]

On Saturday, May 9, 2020 at 5:49:07 AM UTC-6, Lawrence Crowell wrote:

On Saturday, May 9, 2020 at 6:22:44 AM UTC-5, Alan Grayson wrote:

On Saturday, May 9, 2020 at 4:58:20 AM UTC-6, Lawrence Crowell wrote:

On Friday, May 8, 2020 at 9:28:02 PM UTC-5, Alan Grayson wrote:

On Friday, May 8, 2020 at 4:50:55 PM UTC-6, Lawrence Crowell wrote:

There is no global meaning to energy conservation. There is the Hamiltonian constraint Nℌ = 0, which just says that for a local region where the lapse function can be parallel translated to the energy is zero. This is for Petrov type O solutions 

Nℌ = 0 = ½(da/dt)^2 - 4πGρa^2/3c^3 - k

Which leads to the FLRW constraint

(a’/a)^2 = 8πGρ/3c^3 – k/a^2 a’ = da/dt

Where the Hubble parameter H = 70km/s-Mpc  is (a’/a)^2 = H^2. This means that in a local region we have energy conservation FAPP. The difficulty is this is not a property of the symmetries of the system so we have no way to extend this globally.

What this ultimately means is that all physics is local. It does not mean we have mass-energy locally vanishing. The apparent increase in the kinetic energy due to expansion is well enough compensated for by a decease in gravitational potential energy.

This is the claim, but I haven't seen any proof of it. Do you have one? Take a planet. Can you show that Mc^2, where M is the planet's mass, is equal to its negative gravitational potential energy? AG

Sorry; I may have been confused about what you were claiming. I thought you claimed the total energy of the cosmos is zero, in which case the role of rest energy cannot be ignored. But apparently you just meant that kinetic energy and gravitational potential energy sum to zero, which is apriori plausible. AG 

The Hamiltonian constraint above and the FLRW equation are all you need. It is right there.

If it's so obvious, there'd be no dispute about this. But there definitely is! Bruce, e.g. Can you cite a paper where it's explicitly proven? TIA, AG 

Tolman computed some of this early on, His old book Relativity, Thermodynamics, and Cosmology. Oxford: Clarendon Press. 1934 is a source. There is nothing about physical cosmology that says we will witness some horrendous violation of energy conservation locally. It does tell us that since GR is a local principle, based on local translations of vectors etc, there is then no general symmetry rule for energy conservation.

 

There is nothing mysterious going on here. All this means is there is a limitation or horizon to our ability to know if there are global symmetries to the universe.

There are surely limitations on our observational abilities, but why is a symmetry necessary? Nature seems pretty asymmetric; e.g., imbalance of matter and anti-matter. AG 

That has nothing in particular to do with this.

You're probably right. I was just inquiring why symmetry principles are so important. AG 

[Lawrence Crowell]

On Saturday, May 9, 2020 at 7:00:20 AM UTC-5, Alan Grayson wrote:

On Saturday, May 9, 2020 at 5:49:07 AM UTC-6, Lawrence Crowell wrote:

On Saturday, May 9, 2020 at 6:22:44 AM UTC-5, Alan Grayson wrote:

On Saturday, May 9, 2020 at 4:58:20 AM UTC-6, Lawrence Crowell wrote:

On Friday, May 8, 2020 at 9:28:02 PM UTC-5, Alan Grayson wrote:

On Friday, May 8, 2020 at 4:50:55 PM UTC-6, Lawrence Crowell wrote:

There is no global meaning to energy conservation. There is the Hamiltonian constraint Nℌ = 0, which just says that for a local region where the lapse function can be parallel translated to the energy is zero. This is for Petrov type O solutions 

Nℌ = 0 = ½(da/dt)^2 - 4πGρa^2/3c^3 - k

Which leads to the FLRW constraint

(a’/a)^2 = 8πGρ/3c^3 – k/a^2 a’ = da/dt

Where the Hubble parameter H = 70km/s-Mpc  is (a’/a)^2 = H^2. This means that in a local region we have energy conservation FAPP. The difficulty is this is not a property of the symmetries of the system so we have no way to extend this globally.

What this ultimately means is that all physics is local. It does not mean we have mass-energy locally vanishing. The apparent increase in the kinetic energy due to expansion is well enough compensated for by a decease in gravitational potential energy.

This is the claim, but I haven't seen any proof of it. Do you have one? Take a planet. Can you show that Mc^2, where M is the planet's mass, is equal to its negative gravitational potential energy? AG

Sorry; I may have been confused about what you were claiming. I thought you claimed the total energy of the cosmos is zero, in which case the role of rest energy cannot be ignored. But apparently you just meant that kinetic energy and gravitational potential energy sum to zero, which is apriori plausible. AG 

The condition Nℌ = 0, for ℌ = ½√(g)[Tr(K^2) - (TrK)^2] - R^(3), means the normal vector or lapse N, with dN = Kdx for K the extrinsic curvature, can be parallel translated to define an extrinsic curvature so that mass-energy is localized. An addition requirement is needed. A manifold with an even or homogeneous distribution of particles is such that a Gaussian surface can’t be found that defines mass-energy on the manifold. This is whether the manifold is open as in ℝ^3 or the sphere S^3. The above Hamiltonian has as its first part is the kinetic energy ½a’^2, a’ = da/dt with a the scale factor and the potential energy part is ℝ^3, or the Ricci scalar curvature of the spatial manifold. 

LC 
 

[John Clark]

On Fri, May 8, 2020 at 7:33 AM Bruce Kellett <bhkel...@gmail.com> wrote:

 

>> If you believe in what's called "evidence", and extrapolating from it to create a hypothetical physical theory, can you give a single example of something coming from nothing? AG 

> Two examples. The universe; Dark energy.

Alan Grayson kindly provides us with another example, words, they are not conserved, no matter how many he expells he never runs out of words and most of them pop into existence for no reason whatsoever.

John K Clark

 

[Alan Grayson]

It's obviously an open question whether the universe and dark energy (and everything else) came from nothing or something preexisting and possibly eternal; obvious to those who can think clearly. That's why I was surprised that Bruce would make such a claim, since he's about the clearest thinker on these matters that I've the good fortune to have met (online) -- just as it's obvious that the UP is a statistical statement, since uncertainty is a synonym for standard deviation, the definition of which can be easily found online or in any text on statistics. BTW, have you found the flaw in the "proof" I found online and posted, of the time-energy form of the UP? AG

 

[Alan Grayson]

Clark imbecile; have you looked up standard deviation? Same as uncertainty. So much for your denial that the UP has nothing to do with ensembles! AG