The Cosmos?

stanley123

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Papist said:
You think I'm a deconstructionist philosopher? That's rich!
Deconstruction involves the attempt to crack open and disturb the tranquillity of a given notion and this is what you are trying to do with gravity by creating the paralysis of a semantical  aporia.
 

Mor Ephrem

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stanley123 said:
Papist said:
You think I'm a deconstructionist philosopher? That's rich!
Deconstruction involves the attempt to crack open and disturb the tranquillity of a given notion and this is what you are trying to do with gravity by creating the paralysis of a semantical  aporia.
We have a winner!
 

stanley123

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Keble said:
All the stuff Hawking is talking about is at a larger scale, galactic in the case of dark matter and intergalactic in the case of dark energy. They are being introduced because the apparent deviation from Newtonian/relativistic motion is most readily explained by keeping the model as is and introducing unseen objects and substances which act within that model to produce the observed deviations. Personally I think dark matter has a better chance of long-term survival as a real phenomenon, but in any case the whole thing is still something of a theoretical kluge that wants more verification. The expansion of the universe is a phenomenon which also needs explanation, but again things are pretty speculative; the notion that we have some idea of what set off the big bang can be rejected out of hand as the purest of speculation.
Dark energy is supposedly responsible for the accelerating expansion of the universe. However, (if I am understanding his proposal and if not, I stand corrected), Christof Wetterich of the university of  Heidelberg proposed that the observed redshift is the result of the masses of electrons and protons being smaller in the past so that the frequencies of the characteristic atomic lines would be smaller thus accounting for the observed redshift. In such a scenario, the universe would not be expanding during the radiation and matter dominated periods. Instead, the Planck mass would grow, with the size of atoms shrinking correspondingly. He introduces a cosmon field whose potential is somehow responsible for the present dark energy. For details please see:
arXiv:1303.6878 (A Universe without expansion).

Also see: http://arxiv.org/a/wetterich_c_1
 

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stanley123 said:
xariskai said:
"In Newton's time and for two hundred years afterwards, physicists spoke of the action of gravity as 'action at a distance,' a  phrase that was accepted as a substitute for explaining the physical mechanism, much as we speak of spirits or ghosts to explain unseen phenomena. The inability to comprehend the mechanism of gravity accentuates the power of mathematics, for Newton's work was, as the title of his Mathematical Principles indicates, entirely mathematical. His work and the additions made by his successors not only provided the calculation of the planetary motions that transcended observations but also enabled astronomers to predict phenomena such as eclipses of the sun and moon to a fraction of a second...

"Contrary to popular belief, no one has ever explained the physical reality of the force of gravitation. It is a fiction suggested by the human ability to exert force. The greatest science fiction stories are in the science of physics. However, mathematical deductions from the quantitative law proved so effective that this procedure has been accepted as an integral part of physical science. What science has done, then, is to sacrifice physical intelligibility for the sake of mathematical description and mathematical prediction..." (Morris Kline, Mathematics and the Search for Knowledge (NY: Oxford), pp. 122-123).

I'm with Papist on this one. And yet we are confident enough of Newton's equations to slingshot ourselves to the moon using mathematical equations of classical mechanics alone. Why does mind mirror nature to such a degree? (cf. Fr. Stanley Jaki's works, and Nobel Prize winner Eugene Wigner's essay (online) "The Unreasonable Effectiveness of Mathematics in the Natural Sciences" http://www.dartmouth.edu/~matc/MathDrama/reading/Wigner.html )
If gravity is a fiction,
That isn't what Kline said. He said the belief that the *physical mechanism* of gravity is known is a fiction. Another point which evidently escapes you is his statement isn't even controversial -in an academic context.

He does not deny there is a consistently present mathematical relationship between physical objects that is present wherever we look. He doesn't deny that we call it "gravity." He is saying we do not know anything about what the *physical mechanism of this relation* actually is.

what causes a ball thrown up in the air to drop and not fly away?
That is for you to tell us (you are the one claiming you know), without simply using the "word" gravity, or mathematical formulae describing a "consistent relationship between physical objects the physical process behind which is *unknown*" (the standard view) and in a manner which explains exactly ***what physical process is behind the word and the formulas and the ball which drops***. That is what Kline states is unknown. If you know better than Kline, just explain to us exactly *the physical process* behind the consistently observed relationship (and claim your Nobel Prize as the first to do so).





 

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stanley123 said:
Papist said:
You think I'm a deconstructionist philosopher? That's rich!
Deconstruction involves the attempt to crack open and disturb the tranquillity of a given notion and this is what you are trying to do with gravity by creating the paralysis of a semantical  aporia.
Except its not semantical. The fact is that bodies move in a certain way, and we don't know why. BTW, even Newton himself said that he was not proposing gravity as an actual cause or force, but rather, as a mathematial abstraction useful for making predictions. :)
 

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xariskai said:
stanley123 said:
xariskai said:
"In Newton's time and for two hundred years afterwards, physicists spoke of the action of gravity as 'action at a distance,' a  phrase that was accepted as a substitute for explaining the physical mechanism, much as we speak of spirits or ghosts to explain unseen phenomena. The inability to comprehend the mechanism of gravity accentuates the power of mathematics, for Newton's work was, as the title of his Mathematical Principles indicates, entirely mathematical. His work and the additions made by his successors not only provided the calculation of the planetary motions that transcended observations but also enabled astronomers to predict phenomena such as eclipses of the sun and moon to a fraction of a second...

"Contrary to popular belief, no one has ever explained the physical reality of the force of gravitation. It is a fiction suggested by the human ability to exert force. The greatest science fiction stories are in the science of physics. However, mathematical deductions from the quantitative law proved so effective that this procedure has been accepted as an integral part of physical science. What science has done, then, is to sacrifice physical intelligibility for the sake of mathematical description and mathematical prediction..." (Morris Kline, Mathematics and the Search for Knowledge (NY: Oxford), pp. 122-123).

I'm with Papist on this one. And yet we are confident enough of Newton's equations to slingshot ourselves to the moon using mathematical equations of classical mechanics alone. Why does mind mirror nature to such a degree? (cf. Fr. Stanley Jaki's works, and Nobel Prize winner Eugene Wigner's essay (online) "The Unreasonable Effectiveness of Mathematics in the Natural Sciences" http://www.dartmouth.edu/~matc/MathDrama/reading/Wigner.html )
If gravity is a fiction,
That isn't what Kline said. He said the belief that the *physical mechanism* of gravity is known is a fiction. Another point which evidently escapes you is his statement isn't even controversial -in an academic context.

He does not deny there is a consistently present mathematical relationship between physical objects that is present wherever we look. He doesn't deny that we call it "gravity." He is saying we do not know anything about what the *physical mechanism of this relation* actually is.

what causes a ball thrown up in the air to drop and not fly away?
That is for you to tell us (you are the one claiming you know), without simply using the "word" gravity, or mathematical formulae describing a "consistent relationship between physical objects the physical process behind which is *unknown*" (the standard view) and in a manner which explains exactly ***what physical process is behind the word and the formulas and the ball which drops***. That is what Kline states is unknown. If you know better than Kline, just explain to us exactly *the physical process* behind the consistently observed relationship (and claim your Nobel Prize as the first to do so).
He didn't say physical mechanism. He said physical reality. The physical mechanism is explained easily enough by the principle of least action or Hamilton's principle from which follows Newton's second law.
 

stanley123

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Papist said:
The fact is that bodies move in a certain way, and we don't know why. BTW, even Newton himself said that he was not proposing gravity as an actual cause or force, but rather, as a mathematial abstraction useful for making predictions. :)
We know that Newton's second law of motion is equivalent to Hamilton's principle of stationarity or the least action principle which is nothing more than a geometric optics Fermat principle for matter waves.
 

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stanley123 said:
Papist said:
The fact is that bodies move in a certain way, and we don't know why. BTW, even Newton himself said that he was not proposing gravity as an actual cause or force, but rather, as a mathematial abstraction useful for making predictions. :)
We know that Newton's second law of motion is equivalent to Hamilton's principle of stationarity or the least action principle which is nothing more than a geometric optics Fermat principle for matter waves.
Have we ever physically shielded the force of gravity?
 

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I think some attribute gravity to space curving, especially around massive objects, such as stars?
 

stanley123

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Papist said:
stanley123 said:
Papist said:
The fact is that bodies move in a certain way, and we don't know why. BTW, even Newton himself said that he was not proposing gravity as an actual cause or force, but rather, as a mathematial abstraction useful for making predictions. :)
We know that Newton's second law of motion is equivalent to Hamilton's principle of stationarity or the least action principle which is nothing more than a geometric optics Fermat principle for matter waves.
Have we ever physically shielded the force of gravity?
I am glad to see that you now believe in the force of gravity, according to the underlying assumptions of the question.
According to a paper by Raymond Chiao and others, two-dimensional superconducting
films whose thickness is less than the London penetration depth can  reflect gravitational microwaves.
http://arxiv.org/pdf/0903.3280v3.pdf
Another way to shield yourself from a gravity wave would be to hide behind a black hole. since the gravity wave will not pass through the black hole.
In EM, you can use a conductor to shield an electric field. Generally, you won't have conductors in gravity, although the Hořava-Witten domain wall is close to it.  But I don't think you could simply place this wall anywhere you wanted to.
 

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stanley123 said:
Papist said:
stanley123 said:
Papist said:
The fact is that bodies move in a certain way, and we don't know why. BTW, even Newton himself said that he was not proposing gravity as an actual cause or force, but rather, as a mathematial abstraction useful for making predictions. :)
We know that Newton's second law of motion is equivalent to Hamilton's principle of stationarity or the least action principle which is nothing more than a geometric optics Fermat principle for matter waves.
Have we ever physically shielded the force of gravity?
I am glad to see that you now believe in the force of gravity, according to the underlying assumptions of the question.
According to a paper by Raymond Chiao and others, two-dimensional superconducting
films whose thickness is less than the London penetration depth can  reflect gravitational microwaves.
http://arxiv.org/pdf/0903.3280v3.pdf
Another way to shield yourself from a gravity wave would be to hide behind a black hole. since the gravity wave will not pass through the black hole.
In EM, you can use a conductor to shield an electric field. Generally, you won't have conductors in gravity, although the Hořava-Witten domain wall is close to it.  But I don't think you could simply place this wall anywhere you wanted to.
You shouldn't assume. :)
 

stanley123

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Gamliel said:
I think some attribute gravity to space curving, especially around massive objects, such as stars?
Right. General relativity has superseded Newton's theory of gravity and in GR, the gravitational force is due to the curvature of space time. However, Newton's theory of gravity is sufficiently accurate for most problems and is most often used because of the ease of its calculations in comparison with GR.
 

stanley123

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Papist said:
Gamliel said:
I think some attribute gravity to space curving, especially around massive objects, such as stars?
In such a case, gravity would not be a force.
What is your definition of a force?
 

stanley123

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Papist said:
stanley123 said:
Papist said:
stanley123 said:
Papist said:
The fact is that bodies move in a certain way, and we don't know why. BTW, even Newton himself said that he was not proposing gravity as an actual cause or force, but rather, as a mathematial abstraction useful for making predictions. :)
We know that Newton's second law of motion is equivalent to Hamilton's principle of stationarity or the least action principle which is nothing more than a geometric optics Fermat principle for matter waves.
Have we ever physically shielded the force of gravity?
I am glad to see that you now believe in the force of gravity, according to the underlying assumptions of the question.
According to a paper by Raymond Chiao and others, two-dimensional superconducting
films whose thickness is less than the London penetration depth can  reflect gravitational microwaves.
http://arxiv.org/pdf/0903.3280v3.pdf
Another way to shield yourself from a gravity wave would be to hide behind a black hole. since the gravity wave will not pass through the black hole.
In EM, you can use a conductor to shield an electric field. Generally, you won't have conductors in gravity, although the Hořava-Witten domain wall is close to it.  But I don't think you could simply place this wall anywhere you wanted to.
You shouldn't assume. :)
You are the one who is assuming, since you have used the term "force of gravity."
 

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stanley123 said:
Papist said:
stanley123 said:
Papist said:
stanley123 said:
Papist said:
The fact is that bodies move in a certain way, and we don't know why. BTW, even Newton himself said that he was not proposing gravity as an actual cause or force, but rather, as a mathematial abstraction useful for making predictions. :)
We know that Newton's second law of motion is equivalent to Hamilton's principle of stationarity or the least action principle which is nothing more than a geometric optics Fermat principle for matter waves.
Have we ever physically shielded the force of gravity?
I am glad to see that you now believe in the force of gravity, according to the underlying assumptions of the question.
According to a paper by Raymond Chiao and others, two-dimensional superconducting
films whose thickness is less than the London penetration depth can  reflect gravitational microwaves.
http://arxiv.org/pdf/0903.3280v3.pdf
Another way to shield yourself from a gravity wave would be to hide behind a black hole. since the gravity wave will not pass through the black hole.
In EM, you can use a conductor to shield an electric field. Generally, you won't have conductors in gravity, although the Hořava-Witten domain wall is close to it.  But I don't think you could simply place this wall anywhere you wanted to.
You shouldn't assume. :)
You are the one who is assuming, since you have used the term "force of gravity."
Don't assume that I am assuming. I  was granting. :p
 

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Gamliel said:
I think some attribute gravity to space curving, especially around massive objects, such as stars?
According to the theory of general relativity gravity not only pulls on matter but also bends space and even time itself. The phenomenon of gravitation itself, however, is a byproduct of a more fundamental phenomenon described by general relativity, which suggests that spacetime is curved according to the presence of matter through a mechanism that is yet to be discovered.

That is to say the physical mechanism responsible for the universally observable and consistently mathematizable effect is unknown. We know what a mathematical relation we call "gravity" does; we do not know what it "is" in the sense of the physical mechanism that is responsible for the universally observable mathematical relation.

stanley123 said:
xariskai said:
stanley123 said:
xariskai said:
"In Newton's time and for two hundred years afterwards, physicists spoke of the action of gravity as 'action at a distance,' a  phrase that was accepted as a substitute for explaining the physical mechanism, much as we speak of spirits or ghosts to explain unseen phenomena. The inability to comprehend the mechanism of gravity accentuates the power of mathematics, for Newton's work was, as the title of his Mathematical Principles indicates, entirely mathematical. His work and the additions made by his successors not only provided the calculation of the planetary motions that transcended observations but also enabled astronomers to predict phenomena such as eclipses of the sun and moon to a fraction of a second...

"Contrary to popular belief, no one has ever explained the physical reality of the force of gravitation. It is a fiction suggested by the human ability to exert force. The greatest science fiction stories are in the science of physics. However, mathematical deductions from the quantitative law proved so effective that this procedure has been accepted as an integral part of physical science. What science has done, then, is to sacrifice physical intelligibility for the sake of mathematical description and mathematical prediction..." (Morris Kline, Mathematics and the Search for Knowledge (NY: Oxford), pp. 122-123).

I'm with Papist on this one. And yet we are confident enough of Newton's equations to slingshot ourselves to the moon using mathematical equations of classical mechanics alone. Why does mind mirror nature to such a degree? (cf. Fr. Stanley Jaki's works, and Nobel Prize winner Eugene Wigner's essay (online) "The Unreasonable Effectiveness of Mathematics in the Natural Sciences" http://www.dartmouth.edu/~matc/MathDrama/reading/Wigner.html )
If gravity is a fiction,
That isn't what Kline said. He said the belief that the *physical mechanism* of gravity is known is a fiction. Another point which evidently escapes you is his statement isn't even controversial -in an academic context.

He does not deny there is a consistently present mathematical relationship between physical objects that is present wherever we look. He doesn't deny that we call it "gravity." He is saying we do not know anything about what the *physical mechanism of this relation* actually is.

what causes a ball thrown up in the air to drop and not fly away?
That is for you to tell us (you are the one claiming you know), without simply using the "word" gravity, or mathematical formulae describing a "consistent relationship between physical objects the physical process behind which is *unknown*" (the standard view) and in a manner which explains exactly ***what physical process is behind the word and the formulas and the ball which drops***. That is what Kline states is unknown. If you know better than Kline, just explain to us exactly *the physical process* behind the consistently observed relationship (and claim your Nobel Prize as the first to do so).
He didn't say physical mechanism. He said physical reality. The physical mechanism is explained easily enough by the principle of least action or Hamilton's principle from which follows Newton's second law.
See above. He said both.
 

stanley123

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xariskai said:
Gamliel said:
I think some attribute gravity to space curving, especially around massive objects, such as stars?
According to the theory of general relativity gravity not only pulls on matter but also bends space and even time itself. The phenomenon of gravitation itself, however, is a byproduct of a more fundamental phenomenon described by general relativity, which suggests that spacetime is curved according to the presence of matter through a mechanism that is yet to be discovered.

That is to say the physical mechanism responsible for the universally observable and consistently mathematizable effect is unknown. We know what a mathematical relation we call "gravity" does; we do not know what it "is" in the sense of the physical mechanism that is responsible for the universally observable mathematical relation.

stanley123 said:
xariskai said:
stanley123 said:
xariskai said:
"In Newton's time and for two hundred years afterwards, physicists spoke of the action of gravity as 'action at a distance,' a  phrase that was accepted as a substitute for explaining the physical mechanism, much as we speak of spirits or ghosts to explain unseen phenomena. The inability to comprehend the mechanism of gravity accentuates the power of mathematics, for Newton's work was, as the title of his Mathematical Principles indicates, entirely mathematical. His work and the additions made by his successors not only provided the calculation of the planetary motions that transcended observations but also enabled astronomers to predict phenomena such as eclipses of the sun and moon to a fraction of a second...

"Contrary to popular belief, no one has ever explained the physical reality of the force of gravitation. It is a fiction suggested by the human ability to exert force. The greatest science fiction stories are in the science of physics. However, mathematical deductions from the quantitative law proved so effective that this procedure has been accepted as an integral part of physical science. What science has done, then, is to sacrifice physical intelligibility for the sake of mathematical description and mathematical prediction..." (Morris Kline, Mathematics and the Search for Knowledge (NY: Oxford), pp. 122-123).

I'm with Papist on this one. And yet we are confident enough of Newton's equations to slingshot ourselves to the moon using mathematical equations of classical mechanics alone. Why does mind mirror nature to such a degree? (cf. Fr. Stanley Jaki's works, and Nobel Prize winner Eugene Wigner's essay (online) "The Unreasonable Effectiveness of Mathematics in the Natural Sciences" http://www.dartmouth.edu/~matc/MathDrama/reading/Wigner.html )
If gravity is a fiction,
That isn't what Kline said. He said the belief that the *physical mechanism* of gravity is known is a fiction. Another point which evidently escapes you is his statement isn't even controversial -in an academic context.

He does not deny there is a consistently present mathematical relationship between physical objects that is present wherever we look. He doesn't deny that we call it "gravity." He is saying we do not know anything about what the *physical mechanism of this relation* actually is.

what causes a ball thrown up in the air to drop and not fly away?
That is for you to tell us (you are the one claiming you know), without simply using the "word" gravity, or mathematical formulae describing a "consistent relationship between physical objects the physical process behind which is *unknown*" (the standard view) and in a manner which explains exactly ***what physical process is behind the word and the formulas and the ball which drops***. That is what Kline states is unknown. If you know better than Kline, just explain to us exactly *the physical process* behind the consistently observed relationship (and claim your Nobel Prize as the first to do so).
He didn't say physical mechanism. He said physical reality. The physical mechanism is explained easily enough by the principle of least action or Hamilton's principle from which follows Newton's second law.
See above. He said both.
He did say both. But I  was commenting on the physical reality quote.
In classical mechanics, gravity is a force, explained by Newton's second law of motion.  Newton's second law of motion is easily derived from Hamilton's least action principle, which in turn is related to a possible  equipartition theorem postulating a symmetry between the average kinetic energy and the average potential energy. 
In general relativity, which arose out of the data on planetary orbits,  gravity is represented geometrically  as curvature of spacetime.  It is claimed that GR shows that gravity is not a force, but a geometrical property of curved space time.  However, on a quantum scale, the quantum effect of gravity-induced phase change which is demonstrated by neutron interferometry, seems to imply that GR is in need of some modification and that we cannot rule out gravity as a force. Also, it can be argued that the stress-energy-momentum tensor of GR has the some of the attributes of a  "gravitational field" .
 

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xariskai said:
According to the theory of general relativity gravity not only pulls on matter but also bends space and even time itself. The phenomenon of gravitation itself, however, is a byproduct of a more fundamental phenomenon described by general relativity, which suggests that spacetime is curved according to the presence of matter through a mechanism that is yet to be discovered.

That is to say the physical mechanism responsible for the universally observable and consistently mathematizable effect is unknown. We know what a mathematical relation we call "gravity" does; we do not know what it "is" in the sense of the physical mechanism that is responsible for the universally observable mathematical relation.
The mechanism for space time curvature is the equivalence principle, at least in part.
 

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stanley123 said:
xariskai said:
Gamliel said:
I think some attribute gravity to space curving, especially around massive objects, such as stars?
According to the theory of general relativity gravity not only pulls on matter but also bends space and even time itself. The phenomenon of gravitation itself, however, is a byproduct of a more fundamental phenomenon described by general relativity, which suggests that spacetime is curved according to the presence of matter through a mechanism that is yet to be discovered.

That is to say the physical mechanism responsible for the universally observable and consistently mathematizable effect is unknown. We know what a mathematical relation we call "gravity" does; we do not know what it "is" in the sense of the physical mechanism that is responsible for the universally observable mathematical relation.

stanley123 said:
xariskai said:
stanley123 said:
xariskai said:
"In Newton's time and for two hundred years afterwards, physicists spoke of the action of gravity as 'action at a distance,' a  phrase that was accepted as a substitute for explaining the physical mechanism, much as we speak of spirits or ghosts to explain unseen phenomena. The inability to comprehend the mechanism of gravity accentuates the power of mathematics, for Newton's work was, as the title of his Mathematical Principles indicates, entirely mathematical. His work and the additions made by his successors not only provided the calculation of the planetary motions that transcended observations but also enabled astronomers to predict phenomena such as eclipses of the sun and moon to a fraction of a second...

"Contrary to popular belief, no one has ever explained the physical reality of the force of gravitation. It is a fiction suggested by the human ability to exert force. The greatest science fiction stories are in the science of physics. However, mathematical deductions from the quantitative law proved so effective that this procedure has been accepted as an integral part of physical science. What science has done, then, is to sacrifice physical intelligibility for the sake of mathematical description and mathematical prediction..." (Morris Kline, Mathematics and the Search for Knowledge (NY: Oxford), pp. 122-123).

I'm with Papist on this one. And yet we are confident enough of Newton's equations to slingshot ourselves to the moon using mathematical equations of classical mechanics alone. Why does mind mirror nature to such a degree? (cf. Fr. Stanley Jaki's works, and Nobel Prize winner Eugene Wigner's essay (online) "The Unreasonable Effectiveness of Mathematics in the Natural Sciences" http://www.dartmouth.edu/~matc/MathDrama/reading/Wigner.html )
If gravity is a fiction,
That isn't what Kline said. He said the belief that the *physical mechanism* of gravity is known is a fiction. Another point which evidently escapes you is his statement isn't even controversial -in an academic context.

He does not deny there is a consistently present mathematical relationship between physical objects that is present wherever we look. He doesn't deny that we call it "gravity." He is saying we do not know anything about what the *physical mechanism of this relation* actually is.

what causes a ball thrown up in the air to drop and not fly away?
That is for you to tell us (you are the one claiming you know), without simply using the "word" gravity, or mathematical formulae describing a "consistent relationship between physical objects the physical process behind which is *unknown*" (the standard view) and in a manner which explains exactly ***what physical process is behind the word and the formulas and the ball which drops***. That is what Kline states is unknown. If you know better than Kline, just explain to us exactly *the physical process* behind the consistently observed relationship (and claim your Nobel Prize as the first to do so).
He didn't say physical mechanism. He said physical reality. The physical mechanism is explained easily enough by the principle of least action or Hamilton's principle from which follows Newton's second law.
See above. He said both.
He did say both. But I  was commenting on the physical reality quote.
You took him to suggest "gravity isn't real," which he never suggested.

What we don't know is what its reality is *physically* We don't know its *physical mechanism*

We know what is done by what we call gravity, to great mathematical precision, but we don't know what it is physically or what its physical mechanism is.

stanley123 said:
It is claimed that GR shows that gravity is not a force... However... we cannot rule out gravity as a force.
Seeing as your claim is that you KNOW what it is why do you suppose anyone is arguing about what it is, Stanley? Why do you suppose there are different ideas about it today? (if, as you claimed, you know what it is).

Somehow it still seems to escape you that if we "knew what gravity was" all argument about what it is or isn't would be over.

While the curvature of space and time affects bodies, conversely when a body moves or a force acts it affects the curvature of space. What is the physical mechanism? (not just the relation).

The mechanism for space time curvature is the equivalence principle, at least in part.
A numerical equality isn't a mechanism. We have said repeatedly that we know the mathematical relation but not a physical mechanism which explains why the mathematical relation pertains.
 
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