Parameters of Theory of everything.

[MJ kihara]

4 hours ago, Markus Hanke said:

that you cannot simply add together gravitational fields of individual sources to obtain the field of a more complicated system.

Does it mean that every source of gravity in the universe has its own signature gravitational wave? or is it that every point in the universe is unique in its own way given the nature of quantum fluctuation near the source of gravity?

Assuming that we have two similar (in every aspect)sources of gravity in a completely empty space without even quantum fluctuations in the background(just an assumption) can their gravitation field be added together to get the field of the two sources.

[Genady]

1 hour ago, MJ kihara said:

Does it mean that every source of gravity in the universe has its own signature gravitational wave?

No, it does not.

1 hour ago, MJ kihara said:

or is it that every point in the universe is unique in its own way given the nature of quantum fluctuation near the source of gravity?

Ditto.

1 hour ago, MJ kihara said:

Assuming that we have two similar (in every aspect)sources of gravity in a completely empty space without even quantum fluctuations in the background(just an assumption) can their gravitation field be added together to get the field of the two sources.

No, they cannot.

[MJ kihara]

1 hour ago, Genady said:

No, it does not.

Ditto.

No, they cannot.

I doubt your qualifications to answer those questions...not to be personal but after considering a lot of issues in my posts and of course my ongoing learning physics mathematics and relating it to my perspectives...it would be better if you back up your answers with concrete scientific reason ...welcome back 🤗 .

[Genady]

1 hour ago, MJ kihara said:

it would be better if you back up your answers with concrete scientific reason

The reason is given in the post above yours:

 

[studiot]

1 hour ago, MJ kihara said:

I doubt your qualifications to answer those questions...not to be personal but after considering a lot of issues in my posts and of course my ongoing learning physics mathematics and relating it to my perspectives...it would be better if you back up your answers with concrete scientific reason ...welcome back 🤗 .

Genady's first replies are often terse, like mine.

That is because we do not want to waste time on those who are not listening.

But like Marcus Hanke, his replies are usually on the money.

So yes, you have the answers and so you might consider asking for the reasons more politely.

[MJ kihara]

8 minutes ago, Genady said:

The reason is given in the post above yours:

 

You may see those questions as if they are stupid or trivial but if the answers come from our experts-i salute them,I remember Swanson's saying that  'I see far because I stand on the shoulder of giants'-that assurance of answer gives someone guidance in reasoning, especially me.

1 hour ago, MJ kihara said:

...not to be personal but after considering a lot of issues in my posts and of course my ongoing learning physics mathematics and relating it to my perspectives...🤗

You will excuse me for this, but when I was new in the forum with just simple logical reasoning and simple mathematics there was a lot of issues from my ideas that you refuted heavily to the point of appearing as if am hallucinating....however after learning 'some physics e.g GR mathematics' I learned my arguments were probably right..the best thing about learning, there is no limit and once you put more effort you don't remain stagnant... anyway its just a by the way.

[Mordred]

As far as gravity waves you require some anistrophy such as a non uniform spinning object or a merger event such as BH mergers. The BB itself is also considered to generate GW waves but a uniform mass distribution doesn't generate either gravity or gravity waves. Gravity requires a curvature term and that obviously involves the stress energy momentum tensor 

 

For example the Earth with its mountains would generate GW waves but those waves would be far too miniscule for any reasonable means of detection.

Marcus and Genady answer is both correct on the non linearity aspects.

 

Edited October 16 by Mordred

[MJ kihara]

43 minutes ago, studiot said:

So yes, you have the answers and so you might consider asking for the reasons more politely.

I'm sincerely sorry for that,how I make it appear.... however, I fear if I let my temperament go away when facing those controversial issues, then the urge in me to push doing what am trying to achieve will just vanish...all the same I will try to control my temperament...and work hard to appear polite.

[joigus]

10 minutes ago, MJ kihara said:

however, I fear if I let my temperament go away when facing those controversial issues, then the urge in me to push doing what am trying to achieve will just vanish...

What is controversial, that gravity is non-linear, or that sources of gravitational waves do not have a unique signature? Doesn't seem to me like any of those things are controversial.

[studiot]

14 minutes ago, MJ kihara said:

I'm sincerely sorry for that,how I make it appear.... however, I fear if I let my temperament go away when facing those controversial issues, then the urge in me to push doing what am trying to achieve will just vanish...all the same I will try to control my temperament...and work hard to appear polite.

Actually I should not have said polite.

That was the wrong word, I'm sorry.

I should have said sympatico or sympathetic towards others. I realised after I posted.

Others have noted a genuine desire to learn which I applaud. +1

[MJ kihara]

46 minutes ago, joigus said:

What is controversial, that gravity is non-linear, or that sources of gravitational waves do not have a unique signature? Doesn't seem to me like any of those things are controversial.

Am not getting it, Newton gravity or GR gravity?.Realistically,what is the probability of two similar things being 100% identical?....why not 1?

[joigus]

22 minutes ago, MJ kihara said:

Am not getting it, Newton gravity or GR gravity?.

GR, obviously. Newtonian gravity is perfectly linear. Real gravity is much more like GR... Or GR fits much better real gravity, NG being a suitable approximation for weak fields and slow velocities.

23 minutes ago, MJ kihara said:

Realistically,what is the probability of two similar things being 100% identical?....why not 1?

A badger is similar to a skunk, and the probability of them being identical is 0%.

I hope there's a point to this...

[Mordred]

1 hour ago, MJ kihara said:

Am not getting it, Newton gravity or GR gravity?.Realistically,what is the probability of two similar things being 100% identical?....why not 1?

Really not sure what you mean by that gravity under GR is described as a tidal force due to curvature in essence the acceleration term. This is identical for the latter part under Newton gravity being an acceleration.

In both cases Newtons Shell theorem applies. The gradient under Newtons is essentially replaced by curvature.

So could you supply more detail on the last statement ? 

Edited October 16 by Mordred

[joigus]

1 hour ago, studiot said:

Actually I should not have said polite.

That was the wrong word, I'm sorry.

I should have said sympatico or sympathetic towards others. I realised after I posted.

Others have noted a genuine desire to learn which I applaud. +1

And I applaud your applause.

Truth be said, there are few members who are more willing to offer a helping hand.

Edited October 16 by joigus
correction

[MJ kihara]

7 hours ago, Mordred said:

So could you supply more detail on the last statement ? 

Assuming we a have two massive similar but not identical object far away in the universe,how much information can we be able to decode from their respective gravitation waves about their actual composition.

7 hours ago, joigus said:

Truth be said, there are few members who are more willing to offer a helping hand.

It's more than that, it's all about mental picture and how far you are able to navigate others brain while comparing with what you have in yours.I noted that earlier, that's why I become provocative some times to help me access it...the issue is, you put more effort while being flexible then you learn...you offering a helping hand I think helps someone mental flexibility, learning is a continuous process,if you claim you know and stop there,then I think you have stopped learning....the use of 'you' it's for conversation purpose, it's not personal.

[Mordred]

2 hours ago, MJ kihara said:

Assuming we a have two massive similar but not identical object far away in the universe,how much information can we be able to decode from their respective gravitation waves about their actual composition.

The only information one can gain from measuring GW waves is the mass of the source, the direction and momentum.

  For composition one would invariably need to use the EM field via spectography.

Measuring direction is actually interesting as one can use the +× polarizations and the angles recieved of those polarizations.

The other two polarizations are traceless. The transverse gauge is the changes in length while the traceless gauge is the  strain components. Given via the perturbation matrix on a Minkoskii background due to its extreme weak influence.

\[g_{\mu\nu}=\eta_{\mu\nu}+h_{\mu\nu}\]

Which is also used for the weak field limit. The perturbation tensor being after the plus sign.

It's common to seperste any field into other fields in the above case the local metric to the wave being the Minkowskii tensor the global is the LHS of the equal sign. 

So in the above case we have three fields global, local and perturbation each field above being a tensor field which is a combination of scalar, vector and spinor relations.

Renormalizing gravity also employs the same separation of spacetime into seperate fields as described above. Hence you will find the above equation in articles on renormalization.

This is just an FYI the Minkowskii metric or spacetime is one of three Maximally symmetric spacetimes the other two being De-Sitter and anti-Desitter.

How a Maximally spacetime is determined is via killing vectors to determine the non vanishing and vanishing terms of a metric. The easiest to calculate has the least non vanishing terms. Ie Maximally symmetric. 

We renormalize gravity in a Maximally symmetric spacetime we can't when it's not. To put it simply.

Markus would also likely point out the Ricci curvature of a Maximally symmetric spacetime is zero. 

Those same preliminaries involving parallel transport are also involved in the killing vectors.

 

Edited October 17 by Mordred

[Markus Hanke]

17 hours ago, MJ kihara said:

Does it mean that every source of gravity in the universe has its own signature gravitational wave? or is it that every point in the universe is unique in its own way given the nature of quantum fluctuation near the source of gravity?

It means that the gravity of a macroscopic system is in general different from a simple sum of the fields of their individual constituent particles taken in isolation. It also means that just because a volume of spacetime is empty, that doesn’t necessarily mean that it is flat. One has to start with the correct initial and boundary conditions.

[MigL]

Just to add to Markus' always excellent answers ...

Energy is  determined by the configuration of a system ( think potential energy ), so different configurations will have differing energies, even though the systems are comprised of the same individual parts.
These differing energies have different contributions to the stress-energy tensor.

IOW, two systems, comprised of the same individual objects, but arranged differently so as to have different energies, will have different gravity.

[Markus Hanke]

1 hour ago, MigL said:

These differing energies have different contributions to the stress-energy tensor.

This is true, but one must bear in mind the local nature of the field equations - outside the system, in vacuum, the energy-momentum tensor is zero, so the equations you’re solving are actually just the vacuum equations

\[R_{\mu \nu}=0\]

There is no source term at all here, yet you’re still getting a curved spacetime, even far from the central source. This is precisely due to the non-linearity of the theory - the curvature inside the system can “bleed out” into the surrounding vacuum, because curvature at one point is itself a source of curvature for surrounding points. This is encoded in the non-linear structure of the equations themselves.

[chron44]

 

Have in a layman’s manner tried to comprehend how GR works in an elementary manner. Can one easily describe adding mass and/or energy to a vacuum energy volume behaves like this?

 

“I understand that G here is a very important constant (doesn’t change and sets the initial condition) and that the gravitational energy field is affected if mass or energy or both becomes present. One must hence note that the E=mc^2 very much influences the overall rise in this total resulting gravitational energy. -Like this famous "formula" is affecting all involved parts, the mass, the energy and the gravitational field in an intricate manner. In this way the spacetime “fabric” is altered and contributes to GR calculations being non-linear. Does this also mean that the energy related to only the gravitational field to a very extremely small extent is adding energy towards the present mass and energy? Yes, it does. “-Just like the dog is chasing its own tail”. 🙂 In this way it becomes hard to know how the total energy becomes configured. -Especially in extreme astrophysical conditions.”

 

The underlying thought in this GR “statement” is the chase or hunt for the mystic G, the gravitational constant. Which must be an important part of a ToE’s parameters. (If I may alter a bit on the last posts focus.)

[MJ kihara]

In GR,the main point is relating Einstein manifold to energy density content available....Ricci tensor which is part of Riemann tensor ( geometry) are tools helping in constructing Einstein monifold which is encoded in Einstein tensor. Meaning that Ricci tensor may reduce to zero but other aspects of Riemann tensor are still contributing to the manifold.This relationship happens to be the most accurate description of gravity properties in the universe....while modelling this, it turns out the relation( the model) is non linear.

My question is does the Einstein manifold has an interior or it's exterior topology is what matters?

My opinion according to the thread's conversation(in my case from what is in my brain, its more than an opinion) non-linearity of GR may be telling us a more fundamental thing about nature.

[chron44]

2 hours ago, MJ kihara said:

My opinion according to the thread's conversation(in my case from what is in my brain, its more than an opinion) non-linearity of GR may be telling us a more fundamental thing about nature.

 

If I may have some idea or vague opinion (being a layman in physics), is that the "construction" of nature (the physics part especially discussed) is fully dependent on how the universe truly is originated. The cosmological origin and further development set all such linear and non-linear, and other mathematical behavior by the original premises.

I.e. if the BB is the cosmological origin, which much points on, the SM, QFT and the GUTs' among other BB sprung theories and its mathematics, all are part of the BB universal evolution line. Thus, this thread being a ToE parameters scrutiny also alternative cosmological origin ideas must be considered.

Therefore, when GR have been verified so many times, this does NOT by automatics to 100% secure the BB cosmological evolutionary origin.

And for to sum up my maybe a bit "easy and naive" arguing the "correct" cosmological origin does set the "fundamental thing about nature" where the "verified" GR may also suite different evolutionary lines. 

[Markus Hanke]

2 hours ago, MJ kihara said:

My question is does the Einstein manifold has an interior or it's exterior topology is what matters?

What do you mean by this, exactly?

Spacetime is not embedded in anything else, so when we are talking of geometry in this context, what we are referring to is intrinsic geometry on the manifold.

[Mordred]

16 hours ago, chron44 said:

 

Have in a layman’s manner tried to comprehend how GR works in an elementary manner. Can one easily describe adding mass and/or energy to a vacuum energy volume behaves like this?

 

“I understand that G here is a very important constant (doesn’t change and sets the initial condition) and that the gravitational energy field is affected if mass or energy or both becomes present. One must hence note that the E=mc^2 very much influences the overall rise in this total resulting gravitational energy. -Like this famous "formula" is affecting all involved parts, the mass, the energy and the gravitational field in an intricate manner. In this way the spacetime “fabric” is altered and contributes to GR calculations being non-linear. Does this also mean that the energy related to only the gravitational field to a very extremely small extent is adding energy towards the present mass and energy? Yes, it does. “-Just like the dog is chasing its own tail”. 🙂 In this way it becomes hard to know how the total energy becomes configured. -Especially in extreme astrophysical conditions.”

 

The underlying thought in this GR “statement” is the chase or hunt for the mystic G, the gravitational constant. Which must be an important part of a ToE’s parameters. (If I may alter a bit on the last posts focus.)

Your better off applying the energy momentum relation 

\[E^2=(pc)^2+(m_oc^2)^2\] 

This gives a better understanding of how massless particles are also involved (first term RHS) and massive particles (invariant mass second term RHS) are involved as energy being a property doesn't exist on its own.

It is this equation that the Einstein field equations apply as well as the equation that gets integrated into the Klein-Gordon equation of QFT.

 

 

3 hours ago, chron44 said:

 

I.e. if the BB is the cosmological origin, which much points on, the SM, QFT and the GUTs' among othe

While the BB model does not describe how the universe began all equations related to GUT break down at the singularity condition at \(10^{-43}\) seconds after BB. This includes those of GR, the standard model , QFT and the FLRW metric.

Edited October 18 by Mordred

[joigus]

12 hours ago, Markus Hanke said:

What do you mean by this, exactly?

Spacetime is not embedded in anything else, so when we are talking of geometry in this context, what we are referring to is intrinsic geometry on the manifold.

Oh! Such a good question! +1