1. Originally Posted by Gary A
So, as the U expands cosmologists say entropy (S) is increasing and so, it is not conserved.
That statement does not make any sense.

Redshift is a symptom, not a cause. It is a sign of Hubble expansion.
Obviously

But the consolidation of matter into black holes all over the universe means that entropy is being sucked up by them (and is stored on the quasi-surface of the "event horizon") so that S is reduced in the whole rest of the universe by an amount that may be just equal to the S increase implied by Hubble expansion.
Entropy is being sucked up? WTF is that suppose to mean - do you even know what entropy is?

But, prophets say that the universe is proceeding toward a state wherein all the matter and energy in it will eventually reside in these black holes.
I have no idea who these prophets are, but they certainly aren't cosmologists.

This means that the whole universe will eventually collapse into just one representative SMBH and the U will effectively become a single particle once more.
How could this be possible if the universe continues to expand, as you seem to agree?

Especially, as the universe will eventually reach a state wherein galaxies and their embedded SMBHs will expand beyond "causal contact", the entropy of "the universe", as it must then be defined, must decline by at least as much as may have been gained by expansion.
Just gibberish.

So, entropy may be conserved after all and such conservation may be of crucial importance in discerning the details of the process of accelerating Hubble expansion according to the Friedmann equations under the FLRW relativistic metric. Friedmann uses an analog to the ideal gas equation with a work function, w and with the potential of defining and manipulating thermodynamic quantities like S, "delta S".
More gibberish

No cosmologists are working on this as though gravitational lensing has induced a sort of intellectual myopia.
That is because they are busy doing science.

Maybe you can find a cosmetologist to work with you!

2. Originally Posted by OnlyMe
Yes. It is just very difficult to measure.

Frame-dragging and the curvature of space or spacetime are not entirely the same thing. At least to the extent that the curvature of space is associated with gravitation.

The curvature of space is more like a description of the shape of space, defined by the presence of mass.

Frame-dragging is more like a motion of space associated with the motion of mass through it. While frame-dragging can affect the motion of objects in space it does not add to the gravitational attraction between objects.

There is also a bit of a trap in this description, in that frame-dragging is not space moving with matter. It is a very weak interaction. Any analogy we make can only suggest the relationship. Keeping that in mind, you might think of frame-dragging as the way a stick stirring a pot of honey, very slowly.., pulls the honey in the direction of the stick's motion without making the honey swirl.
Please tell us as much as you can about frame dragging and what sort of resultant effects it could have?

3. Originally Posted by Robittybob1
Please tell us as much as you can about frame dragging and what sort of resultant effects it could have?
Try this site it seems pretty informative!

4. Originally Posted by OnlyMe
Correct!

But not measureablely. For locally flat space and time, where Newtonian Mechanics can still be applied, any affect on the motion of an object is trivial and insignificant.

Though there is little said about how special and general relativity affect the first law, Newton's second law of motion, F = ma, from the perspective of special relativity, becomes $F = ma\gamma$ where $\gamma = \frac{1}{\sqrt{v^2/c^2}$, the Lorentz factor, which acts as a modifier for the influence of relatavistic velocities, in this relationship.

It is more difficult to explain how the Lorentz factor figures into Newton's formula for momentum, p = mv, but it plays a similar role, limiting velocities to less than the speed of light, c.

There is also little discussion as to how all of this affects Newton's third law of motion, "For every action, there is an equal and opposite reaction." If the motion of an object drags on space, then space must resist in some way. Some of the more recent attempts to explain inertia, as an interaction between a moving object and the zero-point field or vacuum energy of QM, begins to touch on this, at least indirectly... However, again this interaction remains insignificant at the classical velocities we are able to achieve at present.
So, Einstein's GR and Newton's 1st Law of Motion are contradictory at lower momentum of a mass .

Which one should be followed at lower momentum ?

There must be some threshold momentum ; above which frame-dragging happens and below which no such frame-dragging can happen .

5. Originally Posted by hansda
So, Einstein's GR and Newton's 1st Law of Motion are contradictory at lower momentum of a mass .

Which one should be followed at lower momentum ?

There must be some threshold momentum ; above which frame-dragging happens and below which no such frame-dragging can happen .
There is no contradiction at low velocities or in weak gravitational fields. What happens is that at low velocities the Lorentz factor is so close to 1 that there is no measureable difference between Newton's formulas and the relativistic formulas.

The difference starts at ether high (or relativistic) velocities or where high gravitational potentials are involved.

Einstein's field equations.., general relativity reduces to agreement with Newton's equations, in locally flat space and time and weak gravitational field potentials.

So for most everyday situations there is no significant difference between what Newton and GR predict.
_______________

I am still looking over the link, origin gave a couple of posts back. So far it seems more focused on the specifics of the GP-B experiment and frame-dragging associated with the geodetic and geodesic aspects.., the curvature of space and the angular momentum of a gravitating body, like the earth.

Frame-dragging is also theoretically involved where the object's motion is linear. We do not at present have the ability to test or confirm this effect. We are unable to accelerate sufficiently large masses to the relativistic velocities required.

It is here in the linear aspect of frame-dragging that some of the implications become debatable and some what speculative. There seems to be a potential connection between some of the more recent attempts to describe inertia as an interaction of the motion of matter through the zero-point field or vacuum energy of QM.

6. Originally Posted by OnlyMe
There is no contapradiction at low velocities or in weak gravitational fields. What happens is that at low velocities the Lorentz factor is so close to 1 that there is no measureable difference between Newton's formulas and the relativistic formulas.
At lower momentum if we measure any variable ( say mass or velocity or force or some other variable) through Newton's-formulas and Relativistic-formulas and subtract them ; will it become zero ?

The difference starts at ether high (or relativistic) velocities or where high gravitational potentials are involved.
Not necessary of relativistic speed , frame-dragging can start at lower non-relativistic speed also . The criteria is momentum and not speed or velocity .

Einstein's field equations.., general relativity reduces to agreement with Newton's equations, in locally flat space and time and weak gravitational field potentials.

So for most everyday situations there is no significant difference between what Newton and GR predict.
Will the both results become identical ?

Can GR predict all the three Newton's Laws of Motion at lower momentum ?

7. Originally Posted by hansda
At lower momentum if we measure any variable ( say mass or velocity or force or some other variable) through Newton's-formulas and Relativistic-formulas and subtract them ; will it become zero ?
.....

Will the both results become identical ?

Can GR predict all the three Newton's Laws of Motion at lower momentum ?
Technically they are never zero unless the object is stationary.
Practically the difference is too small to worry about at lower everyday speeds.
And GR Will "predict all the three Newton's Laws of Motion at lower momentum".

8. Originally Posted by hansda
At lower momentum if we measure any variable ( say mass or velocity or force or some other variable) through Newton's-formulas and Relativistic-formulas and subtract them ; will it become zero ?
They would never be truely equal when an object is in motion, but at the velocities we observe as a matter of experience the difference is so small it cannot be measured. (Except some young hot shot will probably figure a way.)

Originally Posted by hansda
Not necessary of relativistic speed , frame-dragging can start at lower non-relativistic speed also . The criteria is momentum and not speed or velocity .
Frame dragging is present at all velocities but once again at all practical velocities we can achieve, it remains very very small. Even for the GP-B experiment the actual measurements were comparable to the size of Mercury and Pluto as seen from the Earth... And even that requires a significant time frame for the period of observation.

9. Originally Posted by Robittybob1
Technically they are never zero unless the object is stationary.
So , at lower momentum Newton's formulas and Einstein's GR are not identical . So, we will get two solutions for one problem . We have to choose , which one is better solution . Can we say GR is better concept than Newtonian concept at lower momentum ?

Practically the difference is too small to worry about at lower everyday speeds.
The difference though too small to worry about but don't you think , ideally (theoretically) there should not have been any difference at all . So, there must be some mismatch(though too small) somewhere between these two approaches . Should we not worry about this little (too small) mismatch ?

And GR Will "predict all the three Newton's Laws of Motion at lower momentum".
Can you explain Newton's 1st Law of Motion and 3rd Law of Motion with Einstein's GR ?

My understanding was that only Newton's 2nd Law of Motion can be explained by GR .

10. Originally Posted by OnlyMe
They would never be truely equal when an object is in motion, but at the velocities we observe as a matter of experience the difference is so small it cannot be measured. (Except some young hot shot will probably figure a way.)
Even if the small difference can not be measured by any instrument but theoretically or mathematically there will be some difference . Which one is closer to reality at lower momentum of a mass ?

Frame dragging is present at all velocities but once again at all practical velocities we can achieve, it remains very very small. Even for the GP-B experiment the actual measurements were comparable to the size of Mercury and Pluto as seen from the Earth... And even that requires a significant time frame for the period of observation.
Frame dragging may be present at all velocities but not at all momentums .

There must be some critical momentum , below which frame-dragging is not possible . For example gravitaional lensing or the case of sub-atomic particle Neutrino can be considered .

11. Originally Posted by Robittybob1
And GR Will "predict all the three Newton's Laws of Motion at lower momentum".
Do you have any support/reference for your above statement ?

or,

You worked out something to make the above statement ?

12. Originally Posted by OnlyMe

Frame dragging is present at all velocities but once again at all practical velocities we can achieve, it remains very very small. .
The sub-atomic particle Neutrino has a non-zero mass and travels almost at the speed of light/photon . Does it cause any frame-dragging ?

13. Originally Posted by hansda
Do you have any support/reference for your above statement ?

or,

You worked out something to make the above statement ?
Why I said this GM and Newton agree at the lower speeds the "correction factor is so small all experiments must agree. So GM would predict the same result.

14. Originally Posted by Robittybob1
Why I said this GM and Newton agree at the lower speeds the "correction factor is so small all experiments must agree. So GM would predict the same result.
GM or GR ?

I think your GM or GR predicts almost the same result for only Newton's 2nd Law of Motion , which defines force .

What about Newton's 1st and 3rd Laws of Motion ? How GR ( or your GM ) predicts them ?

15. good point GM and GR
I have confused the two

GR = General Relativity
GM = ????????

16. Originally Posted by Robittybob1
good point GM and GR
I have confused the two

GR = General Relativity
GM = ????????
You only coined this term GM in your post #353 .

17. Originally Posted by hansda
The sub-atomic particle Neutrino has a non-zero mass and travels almost at the speed of light/photon . Does it cause any frame-dragging ?
No one can answer this question with any certainty.

If the Cohen-Glashow paper responding to the FTL neutrino data from OPERA is correct then one might assume so.

However, since the neutrino has no charge and interacts only weakly with matter, most of the recent attempts to describe inertia as an interaction between the motion of matter and the ZPF/vacuum energy, all of which relay on the EM nature of particles and matter, may not apply to neutrinos.

We cannot detect or observe neutrinos directly, only through their interactions with matter, which to this point remains confined to weak interactions, and even then relies heavily on theoretical predictions.

I don't believe at this time we have enough information to draw conclussions about the relationship of neutrinos and inertia, gravity or frame-dragging. It may very well turn out that in the end the neutrino will provide a window into the "texture" of space/spacetime and some understanding whether inertia and gravity even have a fine structure limitation.., or component. It could also turn out that we we find they fit into the current model, such that what now appear to be anomalies, are explained without a paradigm shift.

From a position of pure speculation and while awaiting further confirmation or evidence disproving the FTL neutrino data from OPERA, I personally am rooting for a confirmation of the FTL neutrinos and some window of opportunity to better understand inertia and the laws of motion, at quantum scales.., and through that perhaps even the potential to finally find some common ground for a path to the unification of GR and QM.

18. Originally Posted by hansda
You only coined this term GM in your post #353 .
Hansda, it was a typo, he meant GR.

19. Originally Posted by OnlyMe
Hansda, it was a typo, he meant GR.
I also guessed so .

20. Originally Posted by OnlyMe
No one can answer this question with any certainty.

If the Cohen-Glashow paper responding to the FTL neutrino data from OPERA is correct then one might assume so.

However, since the neutrino has no charge and interacts only weakly with matter, most of the recent attempts to describe inertia as an interaction between the motion of matter and the ZPF/vacuum energy, all of which relay on the EM nature of particles and matter, may not apply to neutrinos.

We cannot detect or observe neutrinos directly, only through their interactions with matter, which to this point remains confined to weak interactions, and even then relies heavily on theoretical predictions.

I don't believe at this time we have enough information to draw conclussions about the relationship of neutrinos and inertia, gravity or frame-dragging. It may very well turn out that in the end the neutrino will provide a window into the "texture" of space/spacetime and some understanding whether inertia and gravity even have a fine structure limitation.., or component. It could also turn out that we we find they fit into the current model, such that what now appear to be anomalies, are explained without a paradigm shift.

From a position of pure speculation and while awaiting further confirmation or evidence disproving the FTL neutrino data from OPERA, I personally am rooting for a confirmation of the FTL neutrinos and some window of opportunity to better understand inertia and the laws of motion, at quantum scales.., and through that perhaps even the potential to finally find some common ground for a path to the unification of GR and QM.
If Neutrino with a non-zero mass , travelling at a relativistic speed , caused frame dragging then its relativistic mass would have increased and its speed slowed down . It would not have achieved near light velocity .

So, my guess is that momentum of Neutrino does not cause frame-dragging .