Parameters of Theory of everything.

[Mordred]

1 hour ago, MigL said:

Gravitational potential is an energy, and as such, it is a source, like momentum, stress, mass, etc.
Rather simplistic, but easily understood for those of us that don't deal with the mathematics on a day to day basis.
Also why I prefer Feynman diagrams to the integrals of QFT.

Lol guess I'm too used to the math side lmao

1 hour ago, chron44 said:

 

End of excerpt.

The famous words of: "Huston, we have a problem.", is in this context a huge understatement. -Though the reasoning of the graviton not being "necessary" in a ToE also has to be noticed.

Concluding issue:
Is this paper really to be considered for the real physics graviton laboratory research situation?

 

 For to answer this issue by myself, or to guess what pro physicists will say:

Yep..!!

Yes but keep in mind this detection method isn't necessarily the only option.

 Although all methods will invariably be incredibly challenging including via particle accelerators in regards to quantum noise and required energy levels.

 

[MJ kihara]

Wikipedia... renormalization.

Renormalization specifies relationships between parameters in the theory when parameters describing large distance scales differ from parameters describing small distance scales. Physically, the pileup of contributions from an infinity of scales involved in a problem may then result in further infinities. When describing spacetime as a continuum, certain statistical and quantum mechanical constructions are not well-defined. To define them, or make them unambiguous, a continuum limit must carefully remove "construction scaffolding" of lattices at various scales.

.....My take is a continuum limit is introduced at various scales for there to be stability in the universe ...for gravity it's the graviton at quantum scale ,structure formation (asteroids,planets,stars, galaxies e.t.c) at global scales and at edges of the universe wherever it is which is ever changing due expansion.Therefore,the issue of gravity not being renormalizable to me it's difficult to comprehend.

[Mordred]

Unfortunately that wiki link doesn't help unless you study the article they got that descriptive from. 

https://arxiv.org/abs/hep-ph/0506330

See the portion near the beginning where the author describes "roughness" ie uncertainties, noise etc when it comes to the wavefunctions defined by the relevant Langrangian.

The problem is that the article and the wiki link are not being clear on the section pertaining to course graining and partition functions.

Here is a relevant paper involving course graining using Wilsonian renormalization.

https://arxiv.org/abs/1412.3148

This is the mathematics pertaining to short range and long range. Specifically pertaining to the following

\[H=H_{IR}\otimes H_{UV}\] 

For the partitioning of the effective degrees of freedom for the short range IR as opposed to the Long range UV effective degrees of freedom with Hilbert action.

PS do not confuse the graphs with physical distances were dealing with Hilbert space which is a type of function space in the same manner as phase or momentum space. These are mathematical spaces pertaining to graphs and not physical spaces.

 

 

 

Edited September 27 by Mordred

[MJ kihara]

On 9/22/2024 at 1:59 AM, Mordred said:

The issue with gravity is the UV divergences. No effective cutoff ie singularity conditions

Going back a little bit for clarification.

When it comes to gravity,where is the effective cutoff/Singularity conditions supposed to be for us to conclude gravity has been renormalised?

[Mordred]

9 hours ago, MJ kihara said:

Going back a little bit for clarification.

When it comes to gravity,where is the effective cutoff/Singularity conditions supposed to be for us to conclude gravity has been renormalised?

A field is renormalized when you have eliminated all infinities. For gravity we have not found an effective cutoff for the high energy end (UV cutoff) IR cutoff is the low energy end. Example g=0 is an effective IR cutoff.

[MJ kihara]

Thanks for the answer.

15 hours ago, Mordred said:

For gravity we have not found an effective cutoff for the high energy end (UV cutoff)

Can this be an indication of new physics?

It seems we need to modify our current understanding of gravity...including introducing more properties of a graviton in a manner consistent with Zero point energy.

Is there a limit to a curvature? 

[Mordred]

More an indication that we do not have a means to test for a limit for gravity aka curvature. 

[MJ kihara]

I suppose limit of a curvature in two dimension is a straight line and a point. A straight line,gravity equals zero while a point in a vacuum there is zero point energy.

Then it's clear that there is a limit at which gravity can be described as a curvature....new concept/concepts  are supposed to be introduced that merges the issue of zero point energy and curvature...since zero point energy is always there,it creates a phantom idea of gravity gravitating (gravity generating more gravity) leading to circular thinking.

Since gravity influence everything including dark matter...I think no new force is supposed to be introduced, however, a new concept in explanation of gravity beyond a curvature is paramount. 

My thinking is something that goes wit;

Normalization condition

The probability that its position x will be in the interval a ≤ x ≤ b is the integral of the density over this interval:where t is the time at which the particle was measured. This leads to the normalization condition

Probability functions should be /if not, must be introduced in explanations of gravity...i think this should help us link quantum world and general relativity world.

 

[Mordred]

If only renormalization of gravity were that easy. It would have been accomplished long ago.

Here is the Hoof.t paper showing one loop divergence renormalization where he further states in the conclusion that it does not renormalize the second order terms.

https://bpb-us-e2.wpmucdn.com/websites.umass.edu/dist/e/23826/files/2014/11/thooft-and-veltamn.pdf

This might give you some idea of the complexity. For the record there is different types of normalization,

Position normalization as well as momentum normalization as two other examples. The equation you have is the position renormalization. 

The link you got that equation from also has the momentum normalization relation.

Edited October 1 by Mordred

[joigus]

On 10/1/2024 at 5:17 AM, MJ kihara said:

it creates a phantom idea of gravity gravitating (gravity generating more gravity) leading to circular thinking.

"Gravity gravitates" does not lead to circular thinking, as far as I know. It only means the equations for the gravity field are non-linear in the gravity field. So the gravity field couples to itself.

Gluons "gluate" too, if you will. The equations become incredibly more difficult to solve, because gluons couple to themselves. But no logical circularity.

On 10/1/2024 at 5:56 AM, Mordred said:

If only renormalization of gravity were that easy. It would have been accomplished long ago.

True. I think @MJ kihara is mixing up "normalisation" with "renormalisation", which are two very different things.

Normalisation is about probabilities adding up to one.

Renormalisation is about some observables growing arbitrarily large when other observables grow arbitrarily large (or small), so you must declare a cutoff for the actual laboratory condition. So it's about asymptotics of observables. Those are different things.

[MJ kihara]

2 hours ago, joigus said:

So the gravity field couples to itself.

With what results?

 

2 hours ago, joigus said:

Renormalisation is about some observables growing arbitrarily large when other observables grow arbitrarily large (or small), so you must declare a cutoff for the actual laboratory condition. So it's about asymptotics of observables. Those are different things.

What is the practical application obtainable by renormalizing gravity and its impact on physical observations made in the universe?

 

3 hours ago, joigus said:

Normalisation is about probabilities adding up to one.

Adding up from which limit?

On 9/28/2024 at 2:18 PM, Mordred said:

A field is renormalized when you have eliminated all infinities.

 

3 hours ago, joigus said:

True.

You know what's  the most difficult thing...? 

Finding the most simple,easy and straight forward solution to any problem.

[joigus]

58 minutes ago, MJ kihara said:

With what results?

All of them?

Deviations of trajectories at intense field values explained

Prediction of black holes confirmed

Lense-Thirring effect

Gravitational time dilation confirmed

Gravitational waves confirmed

Gravitational lensing confirmed

etc.

All of those are consequences of the non-linear structure of GR. Arguably BH's can be sensibly talked about with a linear theory (Laplace).

58 minutes ago, MJ kihara said:

What is the practical application obtainable by renormalizing gravity and its impact on physical observations made in the universe?

Gravity is not renormalisable.

58 minutes ago, MJ kihara said:

Adding up from which limit?

I don't understand. Why do you need a limit in order to adds things up? Maybe you're referring to a continuous spectrum?

1 hour ago, MJ kihara said:

You know what's  the most difficult thing...? 

Finding the most simple,easy and straight forward solution to any problem.

Easier said than done.  

Edited October 2 by joigus
minor correction

[MJ kihara]

51 minutes ago, joigus said:

All of them?

Deviations of trajectories at intense field values explained

Prediction of black holes confirmed

Lense-Thirring effect

Gravitational time dilation confirmed

Gravitational waves confirmed

Gravitational lensing confirmed

etc.

All of those are consequences of the non-linear structure of GR. Arguably BH's can be sensibly talked about with a linear theory (Laplace).

Gravity is not renormalisable.

I don't understand. Why do you need a limit in order to adds things up? Maybe you're referring to a continuous spectrum?

Easier said than done.  

We talking past each other....am asking about you saying gravity field couples with its self,you are telling me the results of non linearity of GR equations.Am not against GR if you have been following the thread keenly.

From the experience i have gotten so far from the forum...someone can have mastered scientific jargon like a pro physicist but  be short of internalized scientific insight.

I hope the Theory of everything will be a theory easily understood by everyone given minimum possible explanations.

I should partially recuse my self from this thread.

[Mordred]

Well Joigus did give a couple of examples of self coupling for gravity. However gravity also can generate its own gravity via the self couplings 

Let's use gravity waves.

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

Now the spacetime locally to the gravitational wave is Minkowskii (local not global). The gravity wave being  transverse traceless  quadrupolar wave has two key polarizations.

These fall under the perturbation tensor \(h+\) and \(h\times\) for the plus and cross poalarizations.

The remaining polarizations are reducable. (Traceless)

They increase the strength of gravity briefly where the perturbation wave is.

This is one example gravity requires using a tensor that linearizes a non linear curve.

It does so through curvilinear coordinates and via covariant and contravariant  vectors and spinars under a tensor field.

The requirement of using tensors for gravity is precisely due to the non linear nature of spacetime curvature.

Another way to see this is via the stress energy momentum tensor.

Edited October 2 by Mordred

[MigL]

3 hours ago, MJ kihara said:

We talking past each other....am asking about you saying gravity field couples with its self,you are telling me the results of non linearity of GR equations.

Gravity is self-coupling; as a result, its equations ( as GR ) are non-linear.
The same issue is being described by you both, but you are failing to connect the two.

 

4 hours ago, joigus said:

Gravity is not renormalisable.

Gravity has to be, or it would not work.
Our model, GR, is not; hence the search for models that don't manifest infinities.

4 hours ago, joigus said:

I don't understand. Why do you need a limit in order to adds things up?

I believe he's still confusing normalization and renormalization.

The simplest 'layman' explanation of renormalization is as follows.
Consider trying to find the charge of an electron by moving a test charge closer and closer to it.
Claasical electromagnetism tells us that, as the electron has no extent, once r approaches zero, the force, and therefore the electron's charge, approaches infinity.
Quantum mechanics rationalizes this by assuming the electron is surrounded by a 'fog' of virtual electrons, that becomes increasingly dense as you approach the electron.
These virtual electrons contribute to the value of the charge, and are the inner loops ( not sure of terminology ) of the Feynman diagram; an infinity of them adding up to infinite charge.

What renormalization does, is subtract all contributions from these inner loops, or contributions from the virtual electron cloud, leaving only the 'bare' electron charge.
Somrtimes it is difficult to see what a mathematical process is physically doing.
I hope I have clarified instead of further 'muddying the waters'.

[Mordred]

10 minutes ago, MigL said:

 

These virtual electrons contribute to the value of the charge, and are the inner loops ( not sure of terminology ) of the Feynman diagram

Propogator or S Channel. A one loop integral will have one progogator inner loop with two incoming and two outgoing external lines typically however you can have further interactions on a particular leg..

Here is an example of a loop integral 

\[\vec{v}_e+p\longrightarrow n+e^+\]

\[\array{ n_e \searrow&&\nearrow n \\&\leadsto &\\p \nearrow && \searrow e^2}\]

The wavy line in the center to the progogator internal loop 

Edited October 2 by Mordred

[geordief]

3 minutes ago, MigL said:

Gravity is self-coupling; as a result, its equations ( as GR ) are non-linear.
The same issue is being described by you both, but you are failing to connect the

I know  that asking "why" is   normally pointless  but I have heard this "gravity is a source of  gravity" thing before. 

I assume the maths  dictate this but  does this presumably  verified fact tell us  something about gravity and curved spacetime?

Is there any  particular insight  involved in that finding?

[Mordred]

5 minutes ago, geordief said:

I know  that asking "why" is   normally pointless  but I have heard this "gravity is a source of  gravity" thing before. 

I assume the maths  dictate this but  does this presumably  verified fact tell us  something about gravity and curved spacetime?

Is there any  particular insight  involved in that finding?

Other than confirming the stress energy momentum tensor is valid under the Einstein Field equations which essentially dictates  the  curvature terms that's the only insight. Once one understands how the stress energy momentum tensor works it becomes rather obvious.

 

Edited October 2 by Mordred

[MigL]

17 minutes ago, geordief said:

I assume the maths  dictate this but  does this presumably  verified fact tell us  something about gravity

That gravitational potential is an energy ...

 

17 minutes ago, geordief said:

and curved spacetime?

... which contributes to the stress-energy momentum tensor.

Which dictates the curvature term ( as per Mordred above ) or what we call gravity.

( yeah ... sometimes it does seem like a 'dog chasing its tail' even to me )

Edited October 2 by MigL

[Mordred]

11 minutes ago, MigL said:

( yeah ... sometimes it does seem like a 'dog chasing its tail' even to me )

Lmao thanks when I read that I immediately visualized the gravity wave polarizations as the dog. Thanks for the amusing visual.

 

[joigus]

5 hours ago, MJ kihara said:

We talking past each other....am asking about you saying gravity field couples with its self,you are telling me the results of non linearity of GR equations.Am not against GR if you have been following the thread keenly.

 

I'm not saying that you are against GR. Sorry if it came across that way.

Let me be a tad clearer about what I said. Some of these effects you could simulate with a linear theory. Eg, you could simulate the precession of Mercury's perihelion by assuming that, instead of the 1/r law for the potential, you had a 1/r^1+something law. This has been tried, and has failed. Also, perturbations with another object which simply is not there. The thing is you cannot concoct a spherically-symmetric field equation as simple as Poisson's field equation for gravity that gives you solutions differing from 1/r law. You simply cannot. Einstein already observed this.

Analogously, you could perhaps concoct a modification of Newton's gravity (and the corresponding generalised Poisson field equation) that gave you all the other effects, like Lense-Thirring, gravitational lensing, etc. So the best explanation we have for all these effects is that the equations are non-linear. A Taylor expansion g=η+h as Mordred has suggested will give you a host of first-order corrections that will do the job.

Edited October 2 by joigus
correction

[Mordred]

14 minutes ago, joigus said:

 A Taylor expansion g=η+h as Mordred has suggested will give you a host of first-order corrections that will do the job.

This is where the Jacobi matrices comes in handy to help keep track of.

https://en.m.wikipedia.org/wiki/Jacobian_matrix_and_determinant

A little side note some people find when learning GR the treatments that tend to lead to comprehension is Fermi-Walker transport or alternately the Rarchaudhuri equations.

For some reason I've seen numerous posters struggle with GR but once they study the those equations they get that Eureka moment of understanding 

Edited October 2 by Mordred

[MJ kihara]

On 10/3/2024 at 12:28 AM, Mordred said:

the Rarchaudhuri equations.

For some reason I've seen numerous posters struggle with GR but once they study the those equations they get that Eureka moment of understanding 

Maybe if you can explain Raychaudhuri equation in a manner that tends to be more visual ( math and diagramatical explanation) it would be of more help to such posters.

[Mordred]

One of the difficulties of understanding geodesics of GR is the parallel transport aspects with the affine connection. Which is rather essential to understanding GR. Where the Raychaudhuri tends to give that eureka moment is that it takes parallel transport and applies even more vectors which allows us to apply geodesic congruence.

Where this comes in particular use by examining the area between these vectors field lines is it gives a better understanding of the stress, vorticy and shear terms.

How this is of particular use with the Einstein field equations is how the stress, vorticity and shear affect the stress energy momentum tensor.

I have been considering writing up something with regards the Raychaudhuri equations showing the above but it will take time to formulate and do properly.

First one would need to explain geodesic motion under parallel transport. Show the affine connection, explain it's relation to the Rayleigh metric and include the Christoffels. That's the preliminary details but those preliminaries don't describe bulk flow. That's where Raychaudhuri becomes useful in connecting the stress energy tensor to those preliminaries.

Raychaudhuri also gives a better understanding of the FLRW metric as well as event horizons including cosmological. There is even a usage and application to Hawking radiation. 

However as mentioned it does require a preliminary understanding of geodesic motion and how parallel transport works with it.

That's where diagrams of course would be particularly useful. 

 

Edited October 16 by Mordred

[Markus Hanke]

On 10/2/2024 at 4:27 PM, MJ kihara said:

With what results?

 

On 10/2/2024 at 10:48 PM, geordief said:

I assume the maths  dictate this but  does this presumably  verified fact tell us  something about gravity and curved spacetime?

Gravity being self-coupling or non-linear (which means the same in this context) means - among other things - that you cannot simply add together gravitational fields of individual sources to obtain the field of a more complicated system.

For example, the spacetime geometry around two bodies in close proximity is not just the sum of two Schwarzschild metrics, especially not if these bodies are in relative motion. This is why you get eg extra perihelion precession with Mercury, which you wouldn’t expect in a linear theory.

Another example are gravitational waves - when they traverse an area of background curvature (like a massive body, or another wave front), they interact in ways that deviate from ordinary linear wave dynamics.

In more technical terms, if you take two metrics, both of which are valid solutions to the Einstein equations, and add them together, then the result is in general not itself a valid solution to the equations.

It also means that a gravitational field can exist in the absence of any “ordinary” sources; for example, exterior Schwarzschild spacetime is everywhere empty, yet nonetheless curved. This is because curved spacetime itself contains energy, which can act as a source for further gravity (caveat: this form of energy cannot be localised, unlike ordinary sources).

This is in contrast to Newtonian gravity, which is completely linear.