The Theory of Relativity will begin to fall apart in 2016/2017 - Part IV

[Reality Check]

Abysmal "first order in G" in equation 3 ignorance from Michel H

This is a continuation thread from here. As usual the split point is arbitrary and participants are free to quote from previous parts of the thread.

Posted By: Agatha

In the "Strong field tests" section, wikipedia says:..

Repeats
8 June 2021: Michel H persists with "first order in G" ignorance about perihelion precession.
8 June 2021: Abysmal "it has not been quantitatively proved" ignorance from Michel H when he knows about Tests of general relativity - Strong field tests.
And adds
8 June 2021: Abysmal "first order in G" in Equation 3 ignorance from Michel H.
Gravitational Radiation from Point Masses in a Keplerian Orbit (PDF) by Peters and Mathews (1963) has Equation 3 which is a solution from linearized GR with only the "quadrupole approximation" (source dimension is small compared to the wavelength). G only appearing once in Equation 3 is not an ignorant fantasy of dropping higher terms. Multipole expansion is the next page and does explicitly drop J > 3 terms of the Fourier components of the radiation.

 

[catsmate]

Rather off-topic but whenever I'm reminded of Eddington's verification of relativity's predictions in 1919 I have a moment of nostalgia for the Good Old Days of science when verifying laboratory theories involved trekking to the back of beyond with delicate brass and oak instruments and setting them up in places that made the observatory on Ben Nevis seem hospitable. Kids these days.....
BTW I recommend the BBC's Einstein and Eddington.

It's also a reminder of the time in 1932 when the US Navy, attempting to set up a similar test, discovered that One of Our Islands Is Missing....

I now return you to your normal channel of cranks people attempting to avoid accepting that their theories are wrong.

 

[Steve]

Rather off-topic but whenever I'm reminded of Eddington's verification of relativity's predictions in 1919 I have a moment of nostalgia for the Good Old Days of science when verifying laboratory theories involved trekking to the back of beyond with delicate brass and oak instruments and setting them up in places that made the observatory on Ben Nevis seem hospitable. Kids these days.....
BTW I recommend the BBC's Einstein and Eddington.

It's also a reminder of the time in 1932 when the US Navy, attempting to set up a similar test, discovered that One of Our Islands Is Missing....

I now return you to your normal channel of cranks people attempting to avoid accepting that their theories are wrong.

Nit pick: hypotheses, maybe, or ideas. None of these thoughts are consistent or coherent enough to rise to the level of theories.

 

[hecd2]

and then they give the expression for the gravitational power radiated in their equation (3), which is (only) first order in G (like the famous perihelion precession).

What makes you think that there are higher order terms in G in eqn 3?

 

[Reality Check]

Give sources for your "proved quantitatively only to first order in G" assertion

1 June 2021: Give sources for our "proved quantitatively only to first order in G" assertion about the Schwarzschild metric tensor.
That will not be cherry picking arbitrary equations from papers that just have G in them. Next we will have Newton and his gravitational law with a single G in it ! You need the sources that you have read where higher order terms in G are explicitly discarded. You need to cite the papers applying that approximation to observations. For example, where in Two-body problem in general relativity - Precession of elliptical orbits are higher terms in G discarded? The answer is nowhere! This has an exact solution which is expanded by the binomial theorem in orders of 3r_s²/a². It is these terms that are truncated. Presumably because r_{s/a (where a is a length scale) is small so higher powers of it can be ignored.}

 

[Michel H]

What makes you think that there are higher order terms in G in eqn 3?

I believe it is likely. Imagine some masses emit some gravitational waves. General relativity is a nonlinear theory, so these waves are going to interact with the Newtonian gravitational field, and produce some very complicated waves, of orders G², G³ and so on (one can imagine Feynman diagrams).

These authors are using the linearized version of general relativity (only, look at the simple expression for the quadrupole moment in equation (4) of http://gravity.psu.edu/numrel/jclub/jc/Peters_Mathews_PR_131_435_1963.pdf), so they are not probing and testing the whole theory. Yet, this seems sufficient for analyzing the Hulse-Taylor pulsar.

 

[Michel H]

This has an exact solution which is expanded by the binomial theorem in orders of 3r_s²/a². It is these terms that are truncated. Presumably because r_{s/a (where a is a length scale) is small so higher powers of it can be ignored.}

_{I suggest you do a little exercise: calculate the next term of ωr²=ωφ²(1-3rS²/a²)^1/2in https://en.wikipedia.org/wiki/Two-body_problem_in_general_relativity#Precession_of_elliptical_orbits, making a Taylor expansion, and use this to calculate the precession angle δφ to order G² (according to the wikipedia calculation). I think this might help you to understand better that general relativity is quantitatively verified to first order in G only.}

 

[Reality Check]

I suggest you do a little exercise: ...

Ignorant nonsense in reply to my post. There is no expansion in G as I explained and as is explicitly stated in the Wikipedia article.
My full poist:

1 June 2021: Give sources for our "proved quantitatively only to first order in G" assertion about the Schwarzschild metric tensor.
That will not be cherry picking arbitrary equations from papers that just have G in them. Next we will have Newton and his gravitational law with a single G in it ! You need the sources that you have read where higher order terms in G are explicitly discarded. You need to cite the papers applying that approximation to observations. For example, where in Two-body problem in general relativity - Precession of elliptical orbits are higher terms in G discarded? The answer is nowhere! This has an exact solution which is expanded by the binomial theorem in orders of 3r_s²/a². It is these terms that are truncated. Presumably because r_{s/a (where a is a length scale) is small so higher powers of it can be ignored.}

_{Cherry picking the G in rs ^{as what is being expanded is as ignorant as cherry picking the 2, M or c in rs.}}

 

[Michel H]

There is no expansion in G as I explained and as is explicitly stated in the Wikipedia article.
My full poist:

Cherry picking the G in r_s ^{as what is being expanded is as ignorant as cherry picking the 2, M or c in r_s.}

^{There is no need to expand specifically in terms of G; you can expand ω_r²=ω_φ²(1-3r_S²/a²)1/2in terms of r_S²/a². Just keep the quadratic term in the expansion of (1-x)1/2. I expect you'll end up with a term proportional to G², in the final expression for the precession angle.}

 

[Reality Check]

There is no need to expand specifically in terms of G; ...

Repeating that 3r_s²/a² is only G when it is also 2, M, c, 3 and a is just emphasizing your ignorance. Cherry picking the G in r_s is as abysmally ignorant as cherry picking the 2, M or c in r_s or the 3 or a.
1 June 2021: Give sources for our "proved quantitatively only to first order in G" assertion about the Schwarzschild metric tensor.
8 June 2021: Michel H persists with "first order in G" ignorance about perihelion precession.

 

[catsmate]

Nit pick: hypotheses, maybe, or ideas. None of these thoughts are consistent or coherent enough to rise to the level of theories.

True. Perhaps 'rants'?

 

[Steve]

True. Perhaps 'rants'?

That would work.

 

[hecd2]

Double post

 

[hecd2]

What makes you think that there are higher order terms in G in eqn 3?

I believe it is likely. Imagine some masses emit some gravitational waves. General relativity is a nonlinear theory, so these waves are going to interact with the Newtonian gravitational field, and produce some very complicated waves, of orders G², G³ and so on (one can imagine Feynman diagrams).

Gravitational waves observed far from the source are modelled as a perturbation on the Minkowski metric. It seems perfectly rational to me to use the linearised theory in the transverse gauge to do so. Eqn 3 then falls out of the theory with no higher terms in G. Furthermore the simplification by linearising the theory affects the forms of the Ricci tensor and scalar, so it's not clear to me that generalising the theory of gravitational waves will result in expressions with higher tems in G. If you think using the general form of the theory will make different predictions, then it is for you to derive a theory of gravitational waves based on the unlinearised form and show where the higher terms in G appear and that they result in significantly different predictions for the stress energy tensor and, for example, radiated energy per unit solid angle of rotating binaries, the separation distance versus time of rotating binaries and their time to coalescence. I don't think any such significant difference will arise, even if such an analytical solution is possible.

I will agree with you on one thing though - quantitative tests of GR in the strong field regime are not yet definitive - but neither are there any tests which are incompatible with GR in this regime.

 

[Crossbow]

Wow!

It has now been at least four years and four parts of this this thread, and yet the Theory of Relativity still has not fallen apart.

In fact, in the last few years have only served to show just continued validation of the Theory of Relativity.

 

[catsmate]

Wow!

It has now been at least four years and four parts of this this thread, and yet the Theory of Relativity still has not fallen apart.

In fact, in the last few years have only served to show just continued validation of the Theory of Relativity.

Indeed. Though we're seeing more relativity-denying cranks here.

 

[Michel H]

Infinite redshift is of course unobservable, but the predicted redshift has been observed for Sagittarius A* (https://www.mpe.mpg.de/6930756/news20180726).

(link of W.D.Clinger's post in the previous sub-thread: http://www.internationalskeptics.com/forums/showthread.php?postid=13499531#post13499531)

I have read the page by the Max Planck Institute you posted, and I couldn't find any quantitative agreement with General Relativity for gravitational redshift in strong field there.

Besides, an infinite redshift would of course be observable, by continuity (at least in principle: one would observe very large redshifts near the event horizon). But of course an infinite redshift which exists only in the minds of deluded astrophysicists will never be observed in the real world.

As stated by Hawking and Ellis, The large scale structure of space-time, Cambridge University Press, 1973, §5.5, page 149:
It can be seen that this space-time is static, i.e. ∂/∂t is a timelike Killing vector which is a gradient, and is spherically symmetric, i.e. is invariant under the group of isometries SO(3) operating on the spacelike two-spheres {t, r constant} (cf. appendix B). The coordinate r in this metric form is intrinsically defined by the requirement that 4πr is the area of these surfaces of transitivity.

The title of this book is already absurd, in my opinion. How could "space-time" have a structure? (I would understand that a spiral galaxy has a structure, but not space-time). If you tell an experimentalist:

The coordinate r in this metric form is intrinsically defined by the requirement that 4πr is the area of these surfaces of transitivity.

I don't think this is going to help him/her much.

 

[W.D.Clinger]

Infinite redshift is of course unobservable, but the predicted redshift has been observed for Sagittarius A* (https://www.mpe.mpg.de/6930756/news20180726).

(link of W.D.Clinger's post in the previous sub-thread: http://www.internationalskeptics.com/forums/showthread.php?postid=13499531#post13499531)

I have read the page by the Max Planck Institute you posted, and I couldn't find any quantitative agreement with General Relativity for gravitational redshift in strong field there.

ETA: That web page links to the PDF for the scientific paper, which tells the quantitative story.

Quoted from that page (titled "First Successful Test of Einstein’s General Relativity Near Supermassive Black Hole"), with added highlighting (boldface is in the original):

Observations of the Galactic Centre team at the Max Planck Institute for Extraterrestrial Physics (MPE) have for the first time revealed the effects predicted by Einstein’s general relativity on the motion of a star passing through the extreme gravitational field near the supermassive black hole in the centre of the Milky Way.

...snip...

The new measurements clearly reveal an effect called gravitational redshift. Light from the star is stretched to longer wavelengths by the very strong gravitational field of the black hole. And the change in the wavelength of light from S2 agrees precisely with that predicted by Einstein’s theory of general relativity. This is the first time that this deviation from the predictions of the simpler Newtonian theory of gravity has been observed in the motion of a star around a supermassive black hole.

As I wrote, this observation is generally regarded as a strong-field test of general relativity. The gravitational field at "20 billion kilometres from the black hole" at the center of our galaxy is certainly one of the strongest fields for which we have precise observations.

I quoted from The large scale structure of spacetime by Hawking and Ellis. I guess Michel H found it easier to read the cover of that book than its contents:

The title of this book is already absurd, in my opinion. How could "space-time" have a structure? (I would understand that a spiral galaxy has a structure, but not space-time).

To understand how space-time could have a structure, you would first need to acquire some rudimentary knowledge of topology. Before you express an opinion about it in some public forum, you ought also to acquire some rudimentary acquaintance with differential geometry.

 

[Ziggurat]

Besides, an infinite redshift would of course be observable, by continuity (at least in principle: one would observe very large redshifts near the event horizon).

Only in principle, not in practice. Matter actually falling into a black hole will not be visible over the glow from the accretion disk, and the inner edge of the accretion disk is actually a significant distance away from the event horizon. Gravitational redshift is not infinite at this inner edge.

 

[Reality Check]

Abysmal ignorance of physics (spacetime has a mathematical structure) from Michel H

The title of this book is already absurd, in my opinion. How could "space-time" have a structure? (I would understand that a spiral galaxy has a structure, but not space-time).

More evidence against the Ph.D. in By the way, I have a Ph.D. degree in Physics (which does not necessarily mean I am always right)
11 June 2021: Abysmal ignorance of physics (spacetime has a mathematical structure) from Michel H
W.D.Clinger suggests that Michel H gain some rudimentary knowledge of topology and differential geometry before making uninformed opinions. Michel H's post suggests ignorance of even more fundamental mathematical physics. Modern physics textbooks explain that "Euclidean" spacetime and Minkowski spacetime have structures that are written with the basic operations of addition, subtraction, and multiplication with the occasional square root! Euclidean in quotes because it is usually stated as Euclidean space + time. Roger Penrose's "The Road to Reality" book has a Spacetime chapter starting with an E¹ X E³ spacetime for Aristotelian physics.

The rest of the post is Michel H's lack of reading comprehension and what "strong field" means in the tests of general relativity

In the 1970s, scientists began to make additional tests, starting with Irwin Shapiro's measurement of the relativistic time delay in radar signal travel time near the sun. Beginning in 1974, Hulse, Taylor and others studied the behaviour of binary pulsars experiencing much stronger gravitational fields than those found in the Solar System. Both in the weak field limit (as in the Solar System) and with the stronger fields present in systems of binary pulsars the predictions of general relativity have been extremely well tested.

In February 2016, the Advanced LIGO team announced that they had directly detected gravitational waves from a black hole merger.[1] This discovery, along with additional detections announced in June 2016 and June 2017,[2] tested general relativity in the very strong field limit, observing to date no deviations from theory.

This is simply gravitational fields so strong that the weak field limit is not applicable. For example, a very hypothetical "Mercury" planet orbiting close to a supermassive black hole could not be treated to first order in 3r_s²/a² as in Two-body problem in general relativity - Precession of elliptical orbits. The exact solution or more terms or numerical relativity are needed. Numerical relativity is used to successfully model the merging of black holes in the very strong field limit.

1 June 2021: Give sources for our "proved quantitatively only to first order in G" assertion about the Schwarzschild metric tensor.
8 June 2021: Michel H persists with "first order in G" ignorance about perihelion precession.