General Relativity and Noether's theorem

[John Clark]

On Sat, May 9, 2020 at 7:49 AM Lawrence Crowell <goldenfield...@gmail.com> wrote:

> since GR is a local principle, based on local translations of vectors etc, there is then no general symmetry rule for energy conservation.

General Relativity and Noether's theorem were both found in 1916, and so physicists knew that there was not a law of conservation of energy, so they must have known the distant past and distant future must be very different from how things are now. So why didn't they know in 1916 that something like the Big Bang must be true and something like the Steady State Theory must be wrong? But the Steady State Theory didn't die till the 1960's.

John K Clark

[Lawrence Crowell]

The bias was the universe "always existed." or is eternal. The idea the universe could have emerged at some finite time in the past sounded simply theological.  It was why Einstein introduced the cosmological constant, for without that the universe would in a finite time implode by gravitation. Interestingly a larger cosmological constant is invoked now to model an accelerated expansion of the universe. Hubble found the cosmic redshift and Einstein declared this his greatest blunder. The metric for a cosmology by Friedman, Lemaitre, Robertson and Walker was developed into the 1930. This with the de Sitter metric predicted expansion of the universe. Then came WWII, which shifted the focus of physics and cosmology did not come back until the late 40s. Hoyle, Bondi and Gold in the 1950s expressed their dislike of a finite past to the universe, and they proposed a continuous generation of matter. They argued this was no worse than a one time generation of everything. Tolman argued that in fact with the FLRW nothing in total could be said or measured in any way to have been created in the big bang. Things hung in the balance until Penzias and Wilson found a cosmic microwave background. This clinched the big bang with a hot thermal past. 

It is interesting in a way that a sort of anti-theism worked against the big bang. It was considered in conflict with material dialectic in the USSR and in China after 1949 was strictly forbidden to be taught or studied. The big bang was taken up by various religions or churches. Lemaitre as a priest lobbied against the Catholic Church taking this up as some theology of divine creation. He argued this was evidence of some form of "radioactive decay," and so not necessarily theological. In recent times with the big bang now being better understood as a manifestation of inflation, curiously a vacuum transition similar to the decay that Lemaitre foresaw, religious communities have come increasingly against big bang. A part of that is this does not conform to biblical literal creation. 

LC

[Alan Grayson]

On Saturday, May 9, 2020 at 3:49:57 PM UTC-6, Lawrence Crowell wrote:

On Saturday, May 9, 2020 at 12:25:41 PM UTC-5, John Clark wrote:

On Sat, May 9, 2020 at 7:49 AM Lawrence Crowell <goldenfield...@gmail.com> wrote:

> since GR is a local principle, based on local translations of vectors etc, there is then no general symmetry rule for energy conservation.

General Relativity and Noether's theorem were both found in 1916, and so physicists knew that there was not a law of conservation of energy, so they must have known the distant past and distant future must be very different from how things are now. So why didn't they know in 1916 that something like the Big Bang must be true and something like the Steady State Theory must be wrong? But the Steady State Theory didn't die till the 1960's.

John K Clark

The bias was the universe "always existed." or is eternal. The idea the universe could have emerged at some finite time in the past sounded simply theological.  It was why Einstein introduced the cosmological constant, for without that the universe would in a finite time implode by gravitation. Interestingly a larger cosmological constant is invoked now to model an accelerated expansion of the universe. Hubble found the cosmic redshift and Einstein declared this his greatest blunder. The metric for a cosmology by Friedman, Lemaitre, Robertson and Walker was developed into the 1930. This with the de Sitter metric predicted expansion of the universe. Then came WWII, which shifted the focus of physics and cosmology did not come back until the late 40s. Hoyle, Bondi and Gold in the 1950s expressed their dislike of a finite past to the universe, and they proposed a continuous generation of matter. They argued this was no worse than a one time generation of everything. Tolman argued that in fact with the FLRW nothing in total could be said or measured in any way to have been created in the big bang. Things hung in the balance until Penzias and Wilson found a cosmic microwave background. This clinched the big bang with a hot thermal past. 

I think we should keep in mind that we have absolutely no knowledge of what happened when the universe "began", or even IF it began! All we know is that it was incredibly dense and hot, a few Planck intervals AFTER a presumed beginning.  Now, assuming energy is not conserved, it's still a reasonable question about where the lost energy goes, as the reddening proceeds. Could it go into changing the cosmological constant? AG

[Lawrence Crowell]

On Saturday, May 9, 2020 at 9:31:50 PM UTC-5, Alan Grayson wrote:

On Saturday, May 9, 2020 at 3:49:57 PM UTC-6, Lawrence Crowell wrote:

On Saturday, May 9, 2020 at 12:25:41 PM UTC-5, John Clark wrote:

On Sat, May 9, 2020 at 7:49 AM Lawrence Crowell <goldenfield...@gmail.com> wrote:

> since GR is a local principle, based on local translations of vectors etc, there is then no general symmetry rule for energy conservation.

General Relativity and Noether's theorem were both found in 1916, and so physicists knew that there was not a law of conservation of energy, so they must have known the distant past and distant future must be very different from how things are now. So why didn't they know in 1916 that something like the Big Bang must be true and something like the Steady State Theory must be wrong? But the Steady State Theory didn't die till the 1960's.

John K Clark

The bias was the universe "always existed." or is eternal. The idea the universe could have emerged at some finite time in the past sounded simply theological.  It was why Einstein introduced the cosmological constant, for without that the universe would in a finite time implode by gravitation. Interestingly a larger cosmological constant is invoked now to model an accelerated expansion of the universe. Hubble found the cosmic redshift and Einstein declared this his greatest blunder. The metric for a cosmology by Friedman, Lemaitre, Robertson and Walker was developed into the 1930. This with the de Sitter metric predicted expansion of the universe. Then came WWII, which shifted the focus of physics and cosmology did not come back until the late 40s. Hoyle, Bondi and Gold in the 1950s expressed their dislike of a finite past to the universe, and they proposed a continuous generation of matter. They argued this was no worse than a one time generation of everything. Tolman argued that in fact with the FLRW nothing in total could be said or measured in any way to have been created in the big bang. Things hung in the balance until Penzias and Wilson found a cosmic microwave background. This clinched the big bang with a hot thermal past. 

I think we should keep in mind that we have absolutely no knowledge of what happened when the universe "began", or even IF it began! All we know is that it was incredibly dense and hot, a few Planck intervals AFTER a presumed beginning.  Now, assuming energy is not conserved, it's still a reasonable question about where the lost energy goes, as the reddening proceeds. Could it go into changing the cosmological constant? AG

Rewinding the clock so the observable universe is more dense and hotter does press things into an extremely hot dense situation in the finite past. This situation into the past is generated by inflation. Inflation was an enormous expansion that ended by a vacuum transition that generated particles and fields. There is reasonable observational support for this. This then leads to eternal inflation, where the vacuum bubble that results from a quantum transition has a finite causal extent. This vacuum transition is illustrated in the diagram below. This means there is an inflationary spacetime, with a huge cosmological constant on a false vacuum that has local instabilities with Coleman-DeLuccia bubbles that result. 

This is however not the end of the story. The Coleman-DeLuccia bubbles are the origin of our local observable universe, but the inflationary spacetime has also a finite duration into the past. This was shown by Vilenkin and it points to an earlier more fundamental "umbilicus" of probably a quantum nature. The past incompleteness of inflation can be seen fairly easily, The line element or metric

ds^2 = dt^2 - a(t)dΣ^2

for dΣ^2 the line element of space gives the FLRW Hamitonian constraint

ℌ = 0 = (å/a)^2 – H^2 - k

for H = 8πGρ/3c^2 = Λ/3 the Hubble parameter. This can be written as the integral

∫da/a = ∫Hdt,

with k = 0 and this can be integrated. The difficult with assuming this can be extended to an arbitrary time into the past is that the left-hand side is ln(a), that diverges for a → 0 and this corresponds to t → -∞ in a fairly nasty way. The Hubble parameter H is 1/√Area and time is a parameter such that (Ht) → entropy and with the Bekenstein bound S_ent = A/4ℓ^2 and this Planck length ℓ is a regularization cut off. This means the time as an endpoint.

Another way to see this is that Hdt defines the motion of particles, or galaxies on a large scale, and this motion is parameterized by proper time. Momentum of a particle is given by p^2 = g_{ab}P^aP^b with P = dU/ds. This gives the energy E = √{p^2 + m^2} and so

∫Hdt = ∫mda/[√{(m^2 + p^2)}a] = ln[(E + m)/p] = ½ln[(γ + 1)/(γ – 1)] 

which diverges in the past or where the Lorentz gamma factors approach unity. This tells us that the time → -∞ where say the relative velocity between two particles would be zero is a divergence. This in effect corrected with the regularization above as seen in the Planck length ℓ.

We may still in one sense have time extended t → -∞, in de Sitter spacetime with a ~ cosh(t√(Λ/3)) where the bottleneck is the Planck scale. In this setting we still have a block on classical extension to the infinite past, but where there is some condition with quantum gravitation.

The pocket world we observe emerged from this inflationary manifold. It is either some Swiss cheese hole in the space, or maybe a spatial manifold that popped off this dS manifold. The result of Vilenkin tells us this inflationary manifold, at least as can be described with classical or semi-classical physics has a finite time into the past, where through this bottle neck is a quantum gravitational description.

LC

[John Clark]

On Sat, May 9, 2020 at 10:31 PM Alan Grayson <agrays...@gmail.com> wrote:

> Now, assuming energy is not conserved, it's still a reasonable question about where the lost energy goes,

No, that is NOT a reasonable question, that is not even close to being a reasonable question! If the lost energy actually went somewhere then the energy has been conserved because that's what "conserved" means. And if the lost energy went nowhere then the energy has not been conserved because that's what "not conserved" means.

John K Clark

 

[Alan Grayson]

Try to look beneath the surface of things. Of course, if I ask the question, it implies conservation of energy. I think the question is reasonable, which calls into question what the math allegedly implies. BTW, do you plan to deal with my question related to the UP, or are you content to live in ignorance? AG 

 

[Bruno Marchal]

On 9 May 2020, at 23:49, Lawrence Crowell <goldenfield...@gmail.com> wrote:

On Saturday, May 9, 2020 at 12:25:41 PM UTC-5, John Clark wrote:

On Sat, May 9, 2020 at 7:49 AM Lawrence Crowell <goldenfield...@gmail.com> wrote:

> since GR is a local principle, based on local translations of vectors etc, there is then no general symmetry rule for energy conservation.

General Relativity and Noether's theorem were both found in 1916, and so physicists knew that there was not a law of conservation of energy, so they must have known the distant past and distant future must be very different from how things are now. So why didn't they know in 1916 that something like the Big Bang must be true and something like the Steady State Theory must be wrong? But the Steady State Theory didn't die till the 1960's.

John K Clark

The bias was the universe "always existed." or is eternal. The idea the universe could have emerged at some finite time in the past sounded simply theological. 

Yet, as I discovered recently, when the theologian and astrophysicist Lemaitre proposed his “Big Bang theory” (which he called the "primitive atome theory”, he was asked if he considered this as a confirmation of the Bible, and, like a serious theologian, he insisted that those have nothing in common; Physics just does not address the theological question at all, and the metaphor in the bible is about a very different subject of matter. He was better than his friend Einstein on this. This is rather remarkable, and unfortunately, not well known by most christians, who did consider that the big-bang was a confirmation of the statement that the physical universe has a finite origin in time.

It was why Einstein introduced the cosmological constant, for without that the universe would in a finite time implode by gravitation. Interestingly a larger cosmological constant is invoked now to model an accelerated expansion of the universe. Hubble found the cosmic redshift and Einstein declared this his greatest blunder. The metric for a cosmology by Friedman, Lemaitre, Robertson and Walker was developed into the 1930. This with the de Sitter metric predicted expansion of the universe. Then came WWII, which shifted the focus of physics and cosmology did not come back until the late 40s. Hoyle, Bondi and Gold in the 1950s expressed their dislike of a finite past to the universe, and they proposed a continuous generation of matter. They argued this was no worse than a one time generation of everything. Tolman argued that in fact with the FLRW nothing in total could be said or measured in any way to have been created in the big bang. Things hung in the balance until Penzias and Wilson found a cosmic microwave background. This clinched the big bang with a hot thermal past. 

It is interesting in a way that a sort of anti-theism worked against the big bang.

That is interesting to notice too.

It was considered in conflict with material dialectic in the USSR and in China after 1949 was strictly forbidden to be taught or studied. The big bang was taken up by various religions or churches. Lemaitre as a priest lobbied against the Catholic Church taking this up as some theology of divine creation. He argued this was evidence of some form of "radioactive decay," and so not necessarily theological.

OK. (As I say above, he insisted to not confuse theology and physics, at that occasion, also).

In recent times with the big bang now being better understood as a manifestation of inflation, curiously a vacuum transition similar to the decay that Lemaitre foresaw, religious communities have come increasingly against big bang. A part of that is this does not conform to biblical literal creation. 

OK.

Bruno

LC

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[John Clark]

On Sun, May 10, 2020 at 7:42 AM Alan Grayson <agrays...@gmail.com> wrote:

> Of course, if I ask the question, it implies conservation of energy. 

Then why do you imply conservation of energy when we specifically said energy is not conserved? Nobody thinks Entropy is conserved so it would be silly to ask where it came from, and the same would be true for energy if it is also not conserved. The second law of thermodynamics can be derived by logic alone but the first law can not be, conserved energy is not more logical or more mathematical than non-conservation, the only reason we ever thought energy was conserved was that it seemed to be conserved in most of our experiments, but now we have seen a few examples, such as the cosmological redshift, where energy is not conserved. When new information is found our thinking must change, that's science.

 > do you plan to deal with my question related to the UP, 

I saw no question related to the UP, I just saw a string of unrelated words with a question mark at the end.

John K Clark

[Alan Grayson]

Are you dumb, or just playing dumb? The question was repeatedly posed on another thread! AG 

[Alan Grayson]

On Sunday, May 10, 2020 at 6:56:35 AM UTC-6, John Clark wrote:

On Sun, May 10, 2020 at 7:42 AM Alan Grayson <agrays...@gmail.com> wrote:

> Of course, if I ask the question, it implies conservation of energy. 

Then why do you imply conservation of energy when we specifically said energy is not conserved? Nobody thinks Entropy is conserved so it would be silly to ask where it came from, and the same would be true for energy if it is also not conserved. The second law of thermodynamics can be derived by logic alone but the first law can not be, conserved energy is not more logical or more mathematical than non-conservation, the only reason we ever thought energy was conserved was that it seemed to be conserved in most of our experiments, but now we have seen a few examples, such as the cosmological redshift, where energy is not conserved. When new information is found our thinking must change, that's science.

No point arguing with a dummy. All our experience indicates that energy is conserved, but those who know how the BB occurred argue otherwise. How many people are in that group? AG 

 > do you plan to deal with my question related to the UP, 

I saw no question related to the UP, I just saw a string of unrelated words with a question mark at the end.

 

Are you dumb, or just playing dumb? The question was repeatedly posed on another thread! AG 

 

John K Clark

[John Clark]

On Sun, May 10, 2020 at 10:30 AM Alan Grayson <agrays...@gmail.com> wrote:

> All our experience indicates that energy is conserved,

Your knowledge is 91 years out of date, all our experience does NOT indicate energy is conserved. Edwin Hubble discovered the cosmological redshift in 1929.

John K Clark

[Alan Grayson]

That's just an interpretation, YOUR interpretation, and probably NOT Hubble's. Haven't you heard? Energy has mass equivalence, so one can ask how the energy/mass "vanished". AG

[John Clark]

On Sun, May 10, 2020 at 10:46 AM Alan Grayson <agrays...@gmail.com> wrote:

 > Haven't you heard? Energy has mass equivalence, so one can ask how the energy/mass "vanished". AG

And the answer you imbecile is that on the cosmological scale energy/mass is NOT conserved, so just like everything else that is NOT conserved just vanishing is just fine. And if you don't like that answer it's because the question "where does something that is not conserved go?" is as dumb as dogshit.

John K Clark

[smitra]

On 10-05-2020 16:46, Alan Grayson wrote:
> On Sunday, May 10, 2020 at 8:40:29 AM UTC-6, John Clark wrote:
>
>> On Sun, May 10, 2020 at 10:30 AM Alan Grayson <agrays...@gmail.com>
>> wrote:
>>

>>>> ___All our experience indicates that energy is conserved,_

>>
>> Your knowledge is 91 years out of date, all our experience does NOT
>> indicate energy is conserved. Edwin Hubble discovered the
>> cosmological redshift in 1929.
>>
>> John K Clark
>
> That's just an interpretation, YOUR interpretation, and probably NOT
> Hubble's. Haven't you heard? Energy has mass equivalence, so one can
> ask how the energy/mass "vanished". AG
>

What matters is if the relevant laws of physics, in this case GR, are
consistent. Energy is a quantity that's defined in such a way that it is
going to be conserved. Energy cannot be directly measured. What you
measure in an experiment is always going to be the way your measurement
apparatus is going to interact with the measured system. The way that
happens is described by the laws of physics. Whether or not there exists
a conserved energy does not matter here. If some quantity that you can
call "energy" is or is not conserved, then you may verify that.

Saibal

[Alan Grayson]

Considering the velocity induced Doppler shift. Is the energy of the horn increased when the train is coming toward you, and reduced when it recedes, or is it just an apparent effect? Maybe the cosmological red shift is just an apparent effect, having nothing to do with violation of conservation of energy, Also, tell me how the BB occurred? A genius like you should surely know. But then again, since you haven't a clue about the UP, I suppose I am asking too much. AG  

[Lawrence Crowell]

One way of thinking about it is that quantum field theory is based on the idea that quantum fields can be localized down to a point, and in principle to every point on a spatial manifold. Quantum gravitation on the other hand with the holographic principle and the Planck scale requires a Hilbert space that is finite, or at least the states relevant to physics are a finite number. However, if you think about it the if QFT is restricted to a finite gridding it means there is some fundamental length to special relativity, but that transforms by based Lorentz group transformations. So if those lengths are fundamental then Lorentz symmetry is violated on a small scale. That creates a whole lot of trouble. However, there is maybe a way out of this. There are vacuum modes in a transPlanckian domain that are not entangled with anything. These are though stretched to larger wavelengths by the expansion of the universe, where upon they become entangled. This would be one way that vacuum energy remains constant though the universe keeps expanding to generate more spatial volume. Then in effect by pulling transPlanckian modes out of the doldrums of being maximally mixed states into the subPlanckian domain where they become entangled with the rest of the vacuum. By this vacuum energy is continually being pumped into the universe. These modes  as transPlanckian modes are not interacting with anything, so they contribute nothing, once out of this doldrum they contribute vacuum energy.

We, the frogish hapless local observers we are, may never know whether energy is really being created. If the universe is a spatially finite sphere the spherical curvature may be far larger than the square of the horizon length. We may never know it if is a sphere or it if is a flat spacetime or maybe even an octahedron in a hyperbolic tessellation. As local observers we may never be able to observe a violation of mass-energy conservation, even if the universe is a spatial sphere and there is indeed a violation of energy conservation by the generation of ever more vacuum.

LC

 

[Alan Grayson]

In your opinion is it plausible that the cosmological red-shift is an illusion in the sense that no energy is actually being lost. We speak of expanding space "stretching" photons, but that's never been observed. It's just a convenient story, perhaps without substance. Maybe the reddening is just the result of the relative velocities of distant galaxies wrt the Earth, no different than a train which is approaching and receding an observer, changes the incoming observed frequency of the train's horn. AG 

 

[Alan Grayson]

Another possibility is that the cosmological red-shift represents a real loss of energy, but is compensated for by the energy gain of vacuum energy from the added (expanded) space. In this case total energy might be conserved, but still doesn't explain where the lost red-shift energy went. AG 

 

[Alan Grayson]

Thinking further about this, I prefer my original hypothesis above, that the cosmological red-shift doesn't imply real loss of energy. It's just an apparent effect due to relative motion, the usual Doppler shift. AG

 

[Bruce Kellett]

On Mon, May 11, 2020 at 4:24 PM Alan Grayson <agrays...@gmail.com> wrote:

Thinking further about this, I prefer my original hypothesis above, that the cosmological red-shift doesn't imply real loss of energy. It's just an apparent effect due to relative motion, the usual Doppler shift. AG

The cosmologist Ted Bunn has a theory something like this: it involves selecting a particular way of parallel transporting the light from the distant galaxies to us so that the red shift can be interpreted as a Doppler shift. I have no references, but I think he has a web site or blog where he discusses this. It is not a popular theory.

Bruce

[Alan Grayson]

Thanks. I'll check it out. The alternative involves "stretching" of photons due to spatial expansion. How the heck would that happen? AG 

[Lawrence Crowell]

Classically the redshift of photons and the loss of energy is made up for by the drop in gravitational potential energy. Photons are stretched out with the expansion of space. We though have no symmetry principle that dictates a global conservation of energy. Also with the gravitational potential defined by a cosmological constant, a potential defined as Φ = 8π(Gρ/3c^2)a^{-2} for 8πGρ/3c^2 the cosmological constant, the cosmological constant in a quantum mechanical setting has some strange implications.

LC

[Alan Grayson]

For a single photon which is reddening, the gravitational potential energy of what exactly is being reduced? How are photons "stretched" -- by the man behind the curtain? AG

[Alan Grayson]

On Monday, May 11, 2020 at 12:42:03 AM UTC-6, Bruce wrote:

He works at the Lawrence Livermore Laboratory, but I can't find any web site or blog. AG 

[Alan Grayson]

On Monday, May 11, 2020 at 12:42:03 AM UTC-6, Bruce wrote:

Maybe you can offer an opinion; is there anything in the data that indicates the so-called cosmological redshift is not simply Doppler shift due to recession? TIA, AG 

[Alan Grayson]

Ted Bunn does have a blog. Here it is:   https://blog.richmond.edu/physicsbunn/about/  AG

[Bruce Kellett]

A quick search for "red shift" on his blog leads to the paper: arxiv:0808.1081v2

Bruce