[Kryptid]

If we look at our entire Universe, and with the exception of gravity force - than NO NEW ENERGY OR MASS could be created.

If gravity can create energy, then that would make it violate conservation of energy.

It sets their Kinetic/potential energy for free.

That violates conservation of energy.

its Kinetic/potential energy is contributed for free by the gravity force.

That violates conservation of energy.

That free gravity force adds the Kinetic energy + potential energy to the new created particles in the system without consuming it from any other source in the system.

That violates conservation of energy.

[Bored chemist]

That is correct to all kinds of mater/energies/forces... except ONE - Gravity force.

No
while it's generally ignored because it's small, if gravitational force can act on a body then it's not isolated.

So, for example, the Earth isn't an isolated system because (among other things) it is acted on by the Moon's gravity.

[Bored chemist]

Again - Gravity force is based on the mass in that isolated system, but it doesn't consume any mass or energy from that system.

Again; this is just the same as a spring.

[Dave Lev (OP)]

Quote from: Dave Lev on Yesterday at 07:22:05
If we look at our entire Universe, and with the exception of gravity force - than NO NEW ENERGY OR MASS could be created.

If gravity can create energy, then that would make it violate conservation of energy.

In the article it is stated:
https://en.wikipedia.org/wiki/Conservation_of_mass
"energy can neither be created nor destroyed; rather, it can only be transformed or transferred from one form to another."
So, they clearly claim about energy transformation.
Let's use the magnetic energy as an example
This energy is based on transformation. However, let's assume that the magnetic force/field is also free as the gravity force and try to understand the impact of that.
So, let's assume that the magnetic field is only affected by the mass of a BH and not by its rotation/spin velocity/energy.
Do you agree that if that was the case, than this free magnetic field could add new energy to our Universe?
If so, why are you so sure that free gravity force can't add new force/energy?

Now, let's assume that we all agree that there is no way to add extra energy to the mass that is located in that isolated system. Not by magnetic field and not by gravity force. Actually, I'm not asking to add new energy to the current mass in the isolated system/universe.
I only claim for added energy to the new created particales.
In this case, we must focus on other version of this law that is called:
https://en.wikipedia.org/wiki/Conservation_of_mass
"The law of conservation of mass or principle of mass conservation states that for any system closed to all transfers of matter and energy, the mass of the system must remain constant over time, as the system's mass cannot change, so quantity can neither be added nor be removed. Therefore, the quantity of mass is conserved over time."
So, they discuss about: "the quantity of mass is conserved over time"
However, we discuss on new created particles.
Those new particles are added as new mass to the system, therefore, we might get a twist in the story.
In that article it is also stated:
"For systems where large gravitational fields are involved, general relativity has to be taken into account, where mass-energy conservation becomes a more complex concept, subject to different definitions, and neither mass nor energy is as strictly and simply conserved as is the case in special relativity."
We discuss about SMBH with very high gravitational field. So it meets the definition of: "systems where large gravitational fields are involved"
So, what is the real meaning of: "mass-energy conservation becomes a more complex concept, subject to different definitions, and neither mass nor energy is as strictly and simply conserved as is the case in special relativity.?
Do you agree that technically, the new created particle around a SMBH which had been created under very high gravity field (and only for those new created particles) might be subject to different definitions?
Could it be that the real meaning of: "neither mass nor energy is as strictly and simply conserved" is - extra energy due to the involvement of large gravitational fields?

[Bored chemist]

Could it be that the real meaning of: "neither mass nor energy is as strictly and simply conserved" is - extra energy due to the involvement of large gravitational fields?

No.


It "neither mass nor energy is strictly and simply conserved" means that you can interconvert them, so either can change, but the overall total is conserved.

[Kryptid]

Do you agree that if that was the case, than this free magnetic field could add new energy to our Universe?

No.

If so, why are you so sure that free gravity force can't add new force/energy?

Because, as you quoted here:

In the article it is stated:
https://en.wikipedia.org/wiki/Conservation_of_mass
"energy can neither be created nor destroyed

I bolded the important bit. It's the part that you keep ignoring.

Those new particles are added as new mass to the system, therefore, we might get a twist in the story.

No, no we don't. There is no "twist in the story".

Do you agree that technically, the new created particle around a SMBH which had been created under very high gravity field (and only for those new created particles) might be subject to different definitions?
Could it be that the real meaning of: "neither mass nor energy is as strictly and simply conserved" is - extra energy due to the involvement of large gravitational fields?

No. I think what they are talking about is the fact that a reference frame in a gravitational field is different than a non-accelerating frame in empty space. As such, the total amount of mass-energy in the system can look different to different observers (but the total amount of mass-energy in an inertial reference frame is constant). To a distant observer, the total amount of mass-energy of the black hole and any particles that it produces will be constant. It won't increase over time.

There is only one case I know of where conservation of energy is possibly/probably violated: the expansion of the Universe. As the Universe expands, photons of light travelling through it are redshifted, reducing their energy. That energy isn't transmitted to anything else, it's simply gone. Likewise, the gravitational potential energy between distant galaxies is increasing over time because the expansion is driving them further apart (against gravity). Then there is dark energy, which seems to have a constant density per unit of space, yet more space is being created over time. Therefore, the total amount of dark energy in the Universe increases over time.

This is allowed by modern physics because of the assumptions of Noether's theorem. Conservation of energy, as derived by Noether's theorem, is based on the assumption that the space where the conservation laws hold is static. Since space is expanding, it is no longer static and thus energy can be created or destroyed due to that expansion. In a universe where space does not expand or contract, conservation of mass/energy holds absolutely.

Since your model assumes that space does not expand or contract, then it is forced to obey conservation of mass/energy. Your black hole, therefore, cannot create mass/energy. It is stuck with what it already has.

[Dave Lev (OP)]

Quote from: Dave Lev on Yesterday at 20:56:33
Could it be that the real meaning of: "neither mass nor energy is as strictly and simply conserved" is - extra energy due to the involvement of large gravitational fields?

No.
It "neither mass nor energy is strictly and simply conserved" means that you can interconvert them, so either can change, but the overall total is conserved.

I disagree as they didn't claim for the total energy/mass.

Quote from: Dave Lev on Yesterday at 20:56:33
Do you agree that technically, the new created particle around a SMBH which had been created under very high gravity field (and only for those new created particles) might be subject to different definitions?
Could it be that the real meaning of: "neither mass nor energy is as strictly and simply conserved" is - extra energy due to the involvement of large gravitational fields?

No. I think what they are talking about is the fact that a reference frame in a gravitational field is different than a non-accelerating frame in empty space. As such, the total amount of mass-energy in the system can look different to different observers (but the total amount of mass-energy in an inertial reference frame is constant). To a distant observer, the total amount of mass-energy of the black hole and any particles that it produces will be constant. It won't increase over time.

Sorry, I think differently.
They don't claim for "different observers", or for "reference frame in a gravitational field is different than a non-accelerating frame in empty space".
Just to remind you that this is not relativity law.
Therefore, I disagree with your following explanation: 'the total amount of mass-energy in the system can look different to different observers (but the total amount of mass-energy in an inertial reference frame is constant)."
They clearly claim that: "where mass-energy conservation becomes a more complex concept, subject to different definitions, and neither mass nor energy is as strictly and simply conserved as is the case in special relativity"
So, they highlight the "different definitions" and not the "different observers" as you claim.
What do you understand from: "neither mass nor energy is as strictly and simply conserved as is the case in special relativity?
How could it be that you have decided to ignore that open gate for new energy in new created mass/particles?
Would you kindly reconsider your answer?

There is only one case I know of where conservation of energy is possibly/probably violated: the expansion of the Universe. As the Universe expands, photons of light travelling through it are redshifted, reducing their energy. That energy isn't transmitted to anything else, it's simply gone. Likewise, the gravitational potential energy between distant galaxies is increasing over time because the expansion is driving them further apart (against gravity). Then there is dark energy, which seems to have a constant density per unit of space, yet more space is being created over time. Therefore, the total amount of dark energy in the Universe increases over time.

In one hand you claim that "energy can neither be created nor destroyed" and :

There is no "twist in the story".

While on the other hand you open widely the door for the creation of new dark energy which is vital for the BBT.
You claim that it is due to the expansion. However in those articles they don't even mention the expansion or Redshift.
Same issue with that imagination that is called: "Noether's theorem"

This is allowed by modern physics because of the assumptions of Noether's theorem. Conservation of energy, as derived by Noether's theorem, is based on the assumption that the space where the conservation laws hold is static. Since space is expanding, it is no longer static and thus energy can be created or destroyed due to that expansion. In a universe where space does not expand or contract, conservation of mass/energy holds absolutely.

If Noether's theorem or the expansion idea were correct, why our scientists didn't add them in those articles as a valid way to twist the conservation of mass/energy?
So, with all my appreciation to your deep knowledge in science, if you claim that there is no twist in the story, then don't you think that there is no twist also for the BBT stoy?
However, if you think that there is away to twist the conservation of mass/energy, why do you hold that twist only to the theory that you believe in it?
Don't you agree that there must be one law to all the theories?
How could it be that you hold the flag of "energy can neither be created nor destroyed" in order to destroy any theory, while in the same token you twist it for that BBT?
Actually, you clearly claim that the expansion works against gravity:

the gravitational potential energy between distant galaxies is increasing over time because the expansion is driving them further apart (against gravity).

While in the article about the conservation of mass they clearly open the door for a twist due to large gravitational fields:
https://en.wikipedia.org/wiki/Conservation_of_mass
"For systems where large gravitational fields are involved, general relativity has to be taken into account, where mass-energy conservation becomes a more complex concept, subject to different definitions, and neither mass nor energy is as strictly and simply conserved as is the case in special relativity."
So, if you reject that idea, how can you claim that while the expansion works against the gravity suddenly you can twist this law?
Our  scientists that have set those two articles about Conservation_of_Energy/mass didn't consider the BBT or theory D.
You claim that there is no way to twist it.
Therefore, if you wish to kick out any unwanted theory, you also need to kick out the BBT.
It reminds me our discussion about relativity.
Also there it was stated that ONLY the BBT can overcome the relativity law.
I hope that by now we all agree that if there is a twist in the relativity law for the BBT, that twist should be valid to other theory.
In the same token - If there is a twist in the Conservation_of_Energy/mas law for the BBT, that twist should be valid to any other theory including theory D, and especially while this theory fully meets the criteria "For systems where large gravitational fields are involved..." while you confirm that the expansion in the BBT works against the gravity force!!!
So, if there is a way to twist Conservation_of_Energy/mass then theory D can do it much better than the BBT.

Since your model assumes that space does not expand or contract, then it is forced to obey conservation of mass/energy. Your black hole, therefore, cannot create mass/energy. It is stuck with what it already has.

In those articles there is no single word about space expansion. So, why are you so sure that only the space expansion can twist the law while there is no backup for this assumption in those articles?
Conclusion -
If you still believe that ONLY the BBT can overcome that law, than it is your obligation to show in those specific laws how you can twist them.
Please show the gate for new added dark energy due to expansion ONLY in those two Conservation_of_mass/energy articales

Quote from: Dave Lev on Yesterday at 20:56:33
Do you agree that if that was the case, than this free magnetic field could add new energy to our Universe?

No.

How could it be?
Do you agree the energy in mass of new created particles is coming from the magnetic field?
If it was free, than why can't we assume that the added mass was also was for free?
However, I can understand that in this case it would blow out the Conservation_of_mass/energy, but this was just an hypothetical idea.

[Kryptid]

So, they highlight the "different definitions" and not the "different observers" as you claim.

They don't say what those "different definitions" are, now do they?

How could it be that you have decided to ignore that open gate for new energy in new created mass/particles?

I haven't. There is no "open gate".

However in those articles they don't even mention the expansion or Redshift.

Wikipedia is not exhaustive.

Same issue with that imagination that is called: "Noether's theorem"

Noether's theorem isn't imagination. It has been proven. When its base assumption holds, it does too. That's what a theorem is. By calling Noether's theorem "imagination", you might as well be calling Pythagoras' theorem imagination.

If Noether's theorem or the expansion idea were correct, why our scientists didn't add them in those articles as a valid way to twist the conservation of mass/energy?

Wikipedia isn't necessarily written by scientists.

Don't you agree that there must be one law to all the theories?

Yes, which is why energy conservation can't be violated in a static, non-expanding universe (i.e. the one your propose).

In those articles there is no single word about space expansion. So, why are you so sure that only the space expansion can twist the law while there is no backup for this assumption in those articles?

It's Wikipedia. You can't expect it to know everything.

Do you agree the energy in mass of new created particles is coming from the magnetic field?

No.

If it was free, than why can't we assume that the added mass was also was for free?

It isn't.

[Bored chemist]

If Noether's theorem or the expansion idea were correct, why our scientists didn't add them in those articles as a valid way to twist the conservation of mass/energy?

That's a silly question.
The answer is  "because scientists are not in the business of "twisting" things.

But it's even more stupid than that, because scientists do add Noether's theorem to posts and articles..

https://www.thenakedscientists.com/forum/index.php?topic=65377.msg477790#msg477790
https://www.thenakedscientists.com/forum/index.php?topic=71752.msg526975#msg526975
https://www.thenakedscientists.com/forum/index.php?topic=72032.msg529808#msg529808
https://www.thenakedscientists.com/forum/index.php?topic=79170.msg601184#msg601184

and so on.

[Dave Lev (OP)]

It's Wikipedia. You can't expect it to know everything.

How could you misestimate the knowledge of those scientists from Wikipedia?
If you claim that they don't know about the subject that they write then why we use their articles to prove that there is no way to add extra energy or mass?
Actually, you can claim that any scientist doesn't know everything. However, if they focus on a subject, don't you agree that they must have wide knowledge in this subject?
So on which kind of science/scientists do you wish to base our discussion?
As you might understand, I have full trust in those scientists from Wikipedia (especially, as they don't position the BBT or any other theory in front of their eyes.)

So, let's focus again in the following key statement:
https://en.wikipedia.org/wiki/Conservation_of_mass
"For systems where large gravitational fields are involved, general relativity has to be taken into account, where mass-energy conservation becomes a more complex concept, subject to different definitions, and neither mass nor energy is as strictly and simply conserved as is the case in special relativity."

Would you kindly advice if you agree with my understanding:

Quote from: Dave Lev on Yesterday at 20:56:33
Could it be that the real meaning of: "neither mass nor energy is as strictly and simply conserved" is - extra energy due to the involvement of large gravitational fields?

No.
It "neither mass nor energy is strictly and simply conserved" means that you can interconvert them, so either can change, but the overall total is conserved.

I disagree as they didn't claim for the total energy/mass.

I wonder why BC claims that:
"neither mass nor energy is strictly and simply conserved" means that you can interconvert them, so either can change, but the overall total is conserved.
Where do we see in this statement that the overall total of mass/energy is conserved?
I have tried to translate it and the simple meaning is: "Not mass or energy is kept conserved".
Please advice if you agree with me or with BC.

[Kryptid]

How could you misestimate the knowledge of those scientists from Wikipedia?

(1) Wikipedia is not a scientific website. Anyone can edit it. Most of the writers of those articles are probably not scientists.
(2) Funny how you are promoting the scientific knowledge on Wikipedia here, yet you dismiss that very same scientific knowledge when it talks about the expansion of the Universe.

If you claim that they don't know about the subject that they write then why we use their articles to prove that there is no way to add extra energy or mass?

You can know something about a subject without knowing everything about it.

Actually, you can claim that any scientist doesn't know everything. However, if they focus on a subject, don't you agree that they must have wide knowledge in this subject?

Having wide knowledge of a subject is not the same as knowing absolutely everything about a subject.

So on which kind of science/scientists do you wish to base our discussion?

That which is based on evidence.

Would you kindly advice if you agree with my understanding:

There is very little about your understanding of anything that I agree with.

[Bored chemist]

I wonder why BC claims that:
"neither mass nor energy is strictly and simply conserved" means that you can interconvert them, so either can change, but the overall total is conserved.

Because "you can interconvert them, so either can change, but the overall total is conserved."
Is true.
I can't rule out the idea that they meant something else entirely, but it's likely that they didn't go to the trouble of writing something that's actually wrong.

[Dave Lev (OP)]

Quote from: Dave Lev on Yesterday at 05:57:15
How could you misestimate the knowledge of those scientists from Wikipedia?

(1) Wikipedia is not a scientific website. Anyone can edit it. Most of the writers of those articles are probably not scientists.
(2) Funny how you are promoting the scientific knowledge on Wikipedia here, yet you dismiss that very same scientific knowledge when it talks about the expansion of the Universe.

I read your answer and I still do not believe that you claim that those scientists that wrote that article have no real knowledge in that subject.
However, it is clear to me why you do claim that they have so poor knowledge in this subject:

You can know something about a subject without knowing everything about it.

Quote from: Dave Lev on Yesterday at 05:57:15
Actually, you can claim that any scientist doesn't know everything. However, if they focus on a subject, don't you agree that they must have wide knowledge in this subject?

Having wide knowledge of a subject is not the same as knowing absolutely everything about a subject.

Can I assume that you do understand that the real meaning in English for: "neither mass nor energy is strictly and simply conserved" is: "Not mass or energy is kept conserved"?
Hence, as you can't claim that my understanding in English is incorrect, than you claim that those scientists that wrote that article has no real knowledge in this subject.
In the same token, as I do not accept the estimation that: "the overall total mass/energy is conserved" forever and ever...
Then you also claim that:

There is very little about your understanding of anything that I agree with.

So would you kindly just advice if at least my understanding in English is correct.
Do you agree that "neither mass nor energy is strictly and simply conserved" means: "Not mass or energy is kept conserved".
Therefore, the real meaning of:
"For systems where large gravitational fields are involved, general relativity has to be taken into account, where mass-energy conservation becomes a more complex concept, subject to different definitions, and neither mass nor energy is as strictly and simply conserved as is the case in special relativity."
MUST BE:
"For systems with large gravitational fields (as BH or SMBH), general relativity has to be taken into account, where mass-energy conservation becomes a more complex concept, subject to different definitions, and Not mass or energy is kept conserved as is the case in special relativity."

[Dave Lev (OP)]

But it's even more stupid than that, because scientists do add Noether's theorem to posts and articles..
https://www.thenakedscientists.com/forum/index.php?topic=65377.msg477790#msg477790

Thanks for the article:
https://gravityandlevity.wordpress.com/2011/01/20/problems-you-can-solve-just-by-looking-at-them-the-meaning-of-noethers-theorem/
It is stated clearly that Noether’s Theorem deals with conserved quantity.
"Noether’s Theorem guarantees that for each of these symmetries there is a conserved quantity."
"Noether’s Theorem also allows you to identify less obvious conserved quantities.  For example, imagine that the force-emitting object is a cylinder with a helical coil wrapped around it"
"Noether’s Theorem therefore guarantees that a particular combination of linear momentum and angular momentum will be conserved forever."
However, at the end they claim:
"Probably the most profound insight of Noether’s Theorem comes from its view of the principle of energy conservation itself.  Energy conservation appears naturally from Noether’s Theorem when you assume that the environment is symmetric with respect to translations in time.  That is, saying that energy is conserved is equivalent to saying that the laws of physics are unchanging in time."
So, it is all about conserved quantity and an idea about conserved energy if the environment is symmetric.
Hence, why do you think that this law could help you to get the extra dark energy that you need for the expansion in space?
How do you see a change in the energy due to that Theorem?
If there is a change, why it is an added extra energy and not added extra mass?
Why suddenly when it comes to the BBT, the law of conservation of energy/mass doesn't work as it should?

Because "you can interconvert them, so either can change, but the overall total is conserved."
Is true.

If it is added energy, Why not normal energy, normal mass or the energy for dark mater?
Why are you so sure that this Noether’s Theorem that only focus on conserved quantity - (or REAL MATER), can give you the requested dark energy (and only dark energy) for free due to the expansion in space?
If it is ONLY dark energy how could it be that it fully meets the quantity that is vital for the BBT, no more no less?
Can you please prove it?

[Bored chemist]

Hence, why do you think that this law could help you to get the extra dark energy that you need for the expansion in space?

I don't.

How do you see a change in the energy due to that Theorem?

I don't.



There's been a lot of focus on the meaning of ""neither mass nor energy is strictly and simply conserved" "
It's a quote from wiki, it's not holy scripture.
If we don't know what they meant (and we don't) the best thing to do is ignore it.

Why suddenly when it comes to the BBT, the law of conservation of energy/mass doesn't work as it should?

One of very few things we do know about the BB is that it changed the laws of physics.

However, there's a difference between they changed once 14 billion years ago and your contention which is that they are continuing to change all the time.

[Kryptid]

I read your answer and I still do not believe that you claim that those scientists that wrote that article have no real knowledge in that subject.

There you go again. Do you have any evidence that the article was written by scientists?

However, it is clear to me why you do claim that they have so poor knowledge in this subject:

I never said they have "poor knowledge" on the subject.

Can I assume that you do understand that the real meaning in English for: "neither mass nor energy is strictly and simply conserved" is: "Not mass or energy is kept conserved"?

No.

[Malamute Lover]

“For systems where large gravitational fields are involved, general relativity has to be taken into account, where mass-energy conservation becomes a more complex concept, subject to different definitions, and neither mass nor energy is as strictly and simply conserved as is the case in special relativity.”

The key to understanding the Wiki article statement Is that the article is about Conservation of Mass.  Mass-Energy conservation is not being discussed. Within the mathematical models of each of the several non-relativistic theoretical systems discussed, mass is strictly conserved. In actuality, all energy production in chemistry and the like results in the loss of some mass but this loss is essentially unmeasurable. c^2 is a really really big number so tiny amounts of m can yield a whole lot of E. There is conservation of mass-energy but in just about all real-world settings, the loss of mass can be ignored, being far too small to matter in calculations.

Special Relativity gets a little odd in that there is rest mass and there is relativistic mass, which also includes the mass equivalent of the energy of the system.  Not going there today.

But the real problem in understanding appears to be about how General Relativity fits into the picture. Mass by itself is not conserved in GR and neither is energy by itself. Claims are made that even mass-energy or even just plain energy is not conserved but I do not think that is the case.

The Cosmic Microwave Background (CMB) is often given as an example. The energy of a photon is related to its frequency. When the universe was denser, the CMB photons had a higher frequency. The number of photons has not changed but the frequency is lower today. Each photon has less energy. Where did the energy go?

The reduction in frequency is due to space having expanded. The gravitational field of the universe is weaker now because the mass is spread further apart. Recall that a gravitational field contains negative energy. It ‘pulls’ rather than ‘pushes’. The positive energy lost by the photons due to the expansion of space exactly matches the negative energy lost by the gravitational field from having the photons further apart, resulting in a weaker gravitational field. Both have moved closer to zero by the same amount. Energy is conserved.

[Dave Lev (OP)]

Quote from: Dave Lev on Today at 10:11:04
Can I assume that you do understand that the real meaning in English for: "neither mass nor energy is strictly and simply conserved" is: "Not mass or energy is kept conserved"?

No.

Sorry, I disagree.
Let's use the help from cambridge:
https://dictionary.cambridge.org/spellcheck/english/?q=%22neither+mass+nor+energy+is+strictly+and+simply+conserved%22
neither  - not either of two things
strictly - completely or entirely:
simply - completely or as much as possible
Hence, the meaning is:
"Not mass and not Energy is completely or entirely or as much as possible conserved"
If you have better translation that contradicts my understanding, than please offer it.
So, the meaning of that message in English is very clear to me.

There's been a lot of focus on the meaning of ""neither mass nor energy is strictly and simply conserved" "
It's a quote from wiki, it's not holy scripture.
If we don't know what they meant (and we don't) the best thing to do is ignore it.

Sorry again. I disagree.
It is quite easy to understand the simple meaning that message:

"For systems with large gravitational fields (as BH or SMBH), general relativity has to be taken into account, where mass-energy conservation becomes a more complex concept, subject to different definitions, and Not mass or energy is kept conserved as is the case in special relativity."

So the meaning is clear, but you don't like that meaning. This is also very clear.

But the real problem in understanding appears to be about how General Relativity fits into the picture. Mass by itself is not conserved in GR and neither is energy by itself. Claims are made that even mass-energy or even just plain energy is not conserved but I do not think that is the case.

Thanks for joining the discussion.
So, based on your answer: "Claims are made that even mass-energy or even just plain energy is not conserved" means that you fully agree that my English understanding is correct.
However, you think that this statement is incorrect: "but I do not think that is the case"
As long as we all agree with the meaning in English, than this is al least good start.

The key to understanding the Wiki article statement Is that the article is about Conservation of Mass.  Mass-Energy conservation is not being discussed. Within the mathematical models of each of the several non-relativistic theoretical systems discussed, mass is strictly conserved. In actuality, all energy production in chemistry and the like results in the loss of some mass but this loss is essentially unmeasurable. c^2 is a really really big number so tiny amounts of m can yield a whole lot of E. There is conservation of mass-energy but in just about all real-world settings, the loss of mass can be ignored, being far too small to matter in calculations.

Yes, I fully agree with your explanation.
However, in this case you focus on mass loss: " In actuality, all energy production in chemistry and the like results in the loss of some mass but this loss is essentially unmeasurable."
So, I can fully agree that there is full conservation of energy/mass in any given isolated system.
However, it gets more complicated under new created particles.
Those new created particles could be created ONLY under very high gravity force/field near the photon zone around a massive object as BH or SMBH.
The idea is that those new created particles (ordinary particles) are created from a virtual particles.
https://en.wikipedia.org/wiki/Virtual_particle
"Virtual particles do not necessarily carry the same mass as the corresponding real particle, although they always conserve energy and momentum. The longer the virtual particle exists, the closer its characteristics come to those of ordinary particles."
So, it is also stated that there is always a" conserve energy and momentum" between the virtual particle to ordinary particle. Therefore, if the virtual particle is orbiting at the speed of light due to the ultra high gravity force of the SMBH, then also the new created ordinary particle should carry the same momentum and orbit at the same speed of light (due to the gravity force)
So, while the ordinary particle gets its mass energy (E=Mc^2) from the isolated system, it also gets its momentum/velocity from the virtual particle. That velocity represents its kinetic energy and it is based on the idea of "conserve energy and momentum" between virtual to ordinary particles.

Therefore, in the process of creating new particle we get extra kinetic energy.
We also need to add the extra potential energy. The virtual particle already orbits near the photon zone. So, as it converts to ordinary particle it gets also a potential energy for free. All of that due to gravity force.
Without gravity force, there will be no virtual particles and of course no ordinary particles.
So, the momentum that the gravity force gives for free to the virtual particle is transformed to the ordinary particle.
Therefore, do you agree that new (Kinetic + Potential) energy is added to the system by the new created ordinary particles?

Quote from: Dave Lev on Today at 10:42:31
Why suddenly when it comes to the BBT, the law of conservation of energy/mass doesn't work as it should?

One of very few things we do know about the BB is that it changed the laws of physics.

Sorry
Nothing could change the law of physics. Not the BBT and not any other theory.
If you need to change the law of physics in order to hold the BBT, than it is better to you to set the BBT in the garbage!!!
I clearly claim that Theory D doesn't violate any law of physics, while you clearly claim that the BBT violets the law of physics.
Therefore, don't you agree that we should consider replacing the BBT by more advanced  theory?

[Bored chemist]

It is quite easy to understand the simple meaning that message:

Plainly not true, or there wouldn't be a discussion about it.

I clearly claim that Theory D doesn't violate any law of physics, while you clearly claim that the BBT violets the law of physics.

It is true that you clearly claim that.
That is not the same as saying that it is clear that the statement is true.

[Malamute Lover]

But the real problem in understanding appears to be about how General Relativity fits into the picture. Mass by itself is not conserved in GR and neither is energy by itself. Claims are made that even mass-energy or even just plain energy is not conserved but I do not think that is the case.

Thanks for joining the discussion.
So, based on your answer: "Claims are made that even mass-energy or even just plain energy is not conserved" means that you fully agree that my English understanding is correct.
However, you think that this statement is incorrect: "but I do not think that is the case"
As long as we all agree with the meaning in English, then this is at least good start.

I explained why I did not think the claim often made about General Relativity not conserving energy in the CMB is incorrect. Are you disagreeing with my explanation? I am confused. By leaving GR out of my statement, are you implying that I am saying something more universal?

The key to understanding the Wiki article statement Is that the article is about Conservation of Mass.  Mass-Energy conservation is not being discussed. Within the mathematical models of each of the several non-relativistic theoretical systems discussed, mass is strictly conserved. In actuality, all energy production in chemistry and the like results in the loss of some mass but this loss is essentially unmeasurable. c^2 is a really really big number so tiny amounts of m can yield a whole lot of E. There is conservation of mass-energy but in just about all real-world settings, the loss of mass can be ignored, being far too small to matter in calculations.

Yes, I fully agree with your explanation.
However, in this case you focus on mass loss: " In actuality, all energy production in chemistry and the like results in the loss of some mass but this loss is essentially unmeasurable."
So, I can fully agree that there is full conservation of energy/mass in any given isolated system.
However, it gets more complicated under new created particles.
Those new created particles could be created ONLY under very high gravity force/field near the photon zone around a massive object as BH or SMBH.
The idea is that those new created particles (ordinary particles) are created from a virtual particles.
https://en.wikipedia.org/wiki/Virtual_particle
"Virtual particles do not necessarily carry the same mass as the corresponding real particle, although they always conserve energy and momentum. The longer the virtual particle exists, the closer its characteristics come to those of ordinary particles."
So, it is also stated that there is always a" conserve energy and momentum" between the virtual particle to ordinary particle. Therefore, if the virtual particle is orbiting at the speed of light due to the ultra high gravity force of the SMBH, then also the new created ordinary particle should carry the same momentum and orbit at the same speed of light (due to the gravity force)
So, while the ordinary particle gets its mass energy (E=Mc^2) from the isolated system, it also gets its momentum/velocity from the virtual particle. That velocity represents its kinetic energy and it is based on the idea of "conserve energy and momentum" between virtual to ordinary particles.

Therefore, in the process of creating new particle we get extra kinetic energy.
We also need to add the extra potential energy. The virtual particle already orbits near the photon zone. So, as it converts to ordinary particle it gets also a potential energy for free. All of that due to gravity force.
Without gravity force, there will be no virtual particles and of course no ordinary particles.
So, the momentum that the gravity force gives for free to the virtual particle is transformed to the ordinary particle.
Therefore, do you agree that new (Kinetic + Potential) energy is added to the system by the new created ordinary particles?

I do not agree. The mechanism of Hawking-Bekenstein (1) radiation implicitly assumes that the two virtual particles have opposite mass-energy signs, totaling zero. This is why virtual particles do not fall on the mass shell, which is the double-sided hyperboloid that represents solutions to the energy momentum relation. Pictures of this usually show two things like turtle shells but it should be understood that like 2D hyperbolas they extend without limit.  In this view, virtual particles have both positive and negative mass-energy and how much of what shows up where depends on circumstances. So in general virtual particles do not fall on the mass shell except perhaps at the zero point.

The idea of Hawking-Bekenstein radiation is that virtual particle pairs created near the event horizon might be pulled apart by the strong gravity. The negative mass-energy particle would be absorbed into the black hole which would then contain less mass-energy. The positive energy would be free to escape, with its now real mass-energy being balanced by the loss of mass-energy of the black hole. No violation of mass-energy conservation.

I have never successfully plowed through the necessary tensor transformations involved but I do have some issues. Why is it that only the negative mass-energy particle gets absorbed? Seems that half the time, it should be the positive mass-energy particle that gets absorbed, increasing the mass-energy of the black hole and liberating a negative mass-energy particle!

Also, because this is right outside the event horizon, the Hawking-Bekenstein radiation has to climb up the gravity well before it reaches the universe at large. Recall that from the viewpoint of an external observer, an object dropped into a black hole will never be seen to cross the event horizon. Spacetime has been bent so much at the horizon that time is enormously slowed as seen from outside. (The viewpoint of the dropped object is another matter.) Just as the light from the dropped object emitted near the event horizon takes a very long time to reach an external observer, the new Hawking-Bekenstein radiation will take a very long time to reach an external observer.

By photon zone, do you mean the lowest region where stable photon orbitals can exist around a black hole?  That is surprisingly not all that close to the event horizon. In a non-rotating (Schwarzschild) black hole, that region is half the Schwarzschild radius above the event horizon. Simplistically put, the Schwarzschild radius is the radius of a Euclidean sphere having the circumference of a black hole. In a real black hole, the radius could be infinite. The Schwarzschild radius is a measure of the ‘size’ of the black hole, where the event horizon lies.  In a rotating (Kerr) black hole, as all black holes in the universe almost certainly are, the photon orbital situation is very complicated and I am not going there right now.

It is important to take note of the qualifier ‘stable’ on orbital. A photon from outside that crosses an orbital can still miss the event horizon and leave the region. Likewise, a photon originating from inside an orbital can also escape. But a photon cannot take up a stable orbit inside the orbital level. It is a consequence of spacetime getting bent.

(1) Then mere grad student Bekenstein had proposed that to prevent a net loss of entropy from the universe when objects went inside, black holes must have entropy, specifically that this entropy was represented in the surface area. Doctor Hawking severely and even sarcastically criticized Bekenstein in front of some professors because it would mean that black holes had a temperature and were not really black. Hawking then proceeded to write a paper on the mechanism of black hole entropy. With Hawking getting the Lucasian Chair and becoming a ‘god’ in the popular imagination, that story did not get told much outside of the physics community and usually not in full detail even today. And it was called just plain Hawking radiation for a long time.