How Gravity Works

[newolder]

Einstein wrote c = c0(1 + Φ/c²). He was saying the light goes slower in a region where the gravitational potential is lower, and c is less than c0. Then he talked about Huyghens and deflexion. Read the 1911 paper for yourself:

For measuring time at a place which, relatively to the origin of the co-ordinates, has the gravitation potential Φ, we must employ a clock which – when removed to the origin of co-ordinates – goes (1 + Φ/c²) times more slowly than the clock used for measuring time at the origin of co-ordinates. If we call the velocity of light at the origin of co-ordinates c0, then the velocity of light c at a place with the gravitation potential Φ will be given by the relation

c = c0 (1 + Φ/c²) (3)

The principle of the constancy of the velocity of light holds good according to this theory in a different form from that which usually underlies the ordinary theory of relativity.

4. Bending of Light-Rays in the Gravitational Field
FROM the proposition which has just been proved, that the velocity of light in the gravitational field is a function of the place, we may easily infer, by means of Huyghens's principle, that light-rays propagated across a gravitational field undergo deflexion. For let E be a wave front of a plane light-wave at the time t, and let P1 and P2 be two points in that plane at...

Read what he said for yourself instead of dreaming up a red-herring negative speed. If you go slower and slower and slower, you don't end up with a negative speed. You end up stopped.

http://www.wolframalpha.com/input/?i=c+ ... 6/c%C2%B2)

Wolfram-alpha disagrees. (Edit: The last ')' may need to be added by your self...)

[ChildInAZoo]

Why would one want to spend all this time on a theory the Einstein later rejected and that doesn't actually match the available observations?

[Farsight]

Wolfram-alpha disagrees.

Wolfram-alpha will also agree that carpets exist that measure -4m by -4m. It's bollocks newolder. There is no such thing as a negative length, or a negative speed. These are non-real solutions that only exist in cloud-cuckoo land.

[Farsight]

Why would one want to spend all this time on a theory the Einstein later rejected and that doesn't actually match the available observations?

Because he didn't reject the variable speed of light, instead he reiterated it, see the opening post. And it matches the available observations. When a parallel-mirror light clock in a gravitational potential records a lower reading than one up in space, it's because the light goes slower.

[ChildInAZoo]

But the 1912 theory is not GR. The 1912 theory was abandoned.

And none of this addresses evidence for the specific prediction made about galaxy rotation curves. What is the specific prediction of this theory for galaxy rotation curves?

[newolder]

Wolfram-alpha will also agree that carpets exist that measure -4m by -4m. It's bollocks newolder. There is no such thing as a negative length, or a negative speed. These are non-real solutions that only exist in cloud-cuckoo land.

You do not understand maths nor its application to physics. Wolfram-alpha is bollocks like your work is prize-winning.

Here's a recent (27th April, 2010) post about Shing-Tung Yau and his mathematical discoveries.

Shing-Tung Yau is a force of nature. He is best known for conceiving the math behind string theory—which holds that, at the deepest level of reality, our universe is built out of 10-dimensional, subatomic vibrating strings. But Yau’s genius runs much deeper and wider: He has also spawned the modern synergy between geometry and physics, championed unprecedented teamwork in mathematics, and helped foster an intellectual rebirth in China.

Despite growing up in grinding poverty on a Hong Kong farm, Yau made his way to the University of California at Berkeley, where he studied with Chinese geometerShiing-Shen Chern and the master of nonlinear equations, Charles Morrey. Then at age 29 Yau proved the Calabi conjecture, which posits that six-dimensional spaces lie hidden beneath the reality we perceive. These unseen dimensions lend rigor to string theory by supplementing the four dimensions—three of space and one of time—described in Einstein’s general relativity.

Since then Yau has held positions at the Institute for Advanced Study, Stanford University, and Harvard (where he currently chairs the math department), training two generations of grad students and embarking on far-flung collaborations that address topics ranging from the nature of dark matter to the formation of black holes. He has won the Fields Medal, a MacArthur Fellowship, and the Wolf Prize. …
…
Physicists often talk about the beauty of math. What does that mean to you?
The first time I saw my wife, I thought she was charming—more than charming, shocking to me. I had great motivation to know her more. When I look at the Calabi conjecture, it shocks me too. It’s an elegant, simple construct and explains a great deal. It’s exciting when you go deeper and deeper into a complicated structure that you can spend most of a lifetime working on. It was shocking when it showed up in physics, and it’s beautiful whether it’s true or not.

Your OP contains 1 equation that describes how the speed of light in a vacuum varies with gravitational potential but it is clear you do not understand what the equation models. Your next post concludes:

The energy tied up as the matter of a planet "conditions" the surrounding space to create a non-constant gμνalong with a gradient in c which causes curvilinear motion …

I call bullshit unless you show me reference to this 'gradient in c' in an equation of motion that also contains 'a non constant gμν' and 'the energy tied up as the matter of a planet'.

[Farsight]

Here's a recent (27th April, 2010) post about Shing-Tung Yau and his mathematical discoveries. Shing-Tung Yau is a force of nature. He is best known for conceiving the math behind string theory—which holds that, at the deepest level of reality, our universe is built out of 10-dimensional, subatomic vibrating strings...

Newolder, watch my lips: string theory is garbage. There is no scientific evidence for any of it, it makes no predictions, it isn't science, it's pseudoscience. Like your negative speed.

By the way, the beauty of math does not impress me. I'm a scientist. I'm impressed by a mathematical prediction that matches scientific evidence, and by mathematics that delivers meaning and understanding. If it's beautiful and elegant so much the better. But I'm not impressed by mathematical beauty without those other things. Moonshine is beautiful, but it's still moonshine.

Your OP contains 1 equation that describes how the speed of light in a vacuum varies with gravitational potential but it is clear you do not understand what the equation models.

It's clear I do. All you have to do to be clear on that is read the Understanding Electromagnetism thread.

Your next post concludes:

The energy tied up as the matter of a planet "conditions" the surrounding space to create a non-constant gμνalong with a gradient in c which causes curvilinear motion …

I call bullshit unless you show me reference to this 'gradient in c' in an equation of motion that also contains 'a non constant gμν' and 'the energy tied up as the matter of a planet'.

LOL, you call bullshit? Don't you know that's what Einstein said? And what does an equation of motion have to do with it? Go look at the experimental evidence like the Shapiro delay or the GPS clock adjustment, or the mismatch between parallel-mirror light clocks at different altitudes. We call it gravitational time dilation, but clocks clock up motion, and light clocks clock up the motion of light. Set aside the radial length contraction by holding the clocks flat, and what's obvious? Down here the clock goes slower than it does up there. So the light goes slower. That's a variable c newolder, hidden in plain view, like the nose in front of your face. And if your nose wan't buried in ten-dimensional mathematical fiction, maybe you'd see it.

[Farsight]

But the 1912 theory is not GR. The 1912 theory was abandoned.

But he didn't abandon the variable speed of light. He said that's why the curvilinear motion occurs. In 1916 it isn't gravitation influencing the speed of light any more, it's the gradient in c causing the gravity. The central concentration of energy conditions the surrounding space, making it inhomogeneous, with a radial gradient in gμν and c.

And none of this addresses evidence for the specific prediction made about galaxy rotation curves. What is the specific prediction of this theory for galaxy rotation curves?

There is no specific prediction for galactic rotation curves. But note that Einstein said a gravitational field was inhomogeneous space, and that the energy of a gravitational field operates gravitatively just like any other form of energy. So here we have, within general relativity, inhomogeneous spatial energy causing gravity. That means the assumption that gravity is always caused by matter is wrong. And since we now know about the expansion of the universe being non-uniform as per the raisins-in-the-cake analogy, that means galaxies are of necessity surrounded by a shell of inhomogeneous space. That means the assumption that galactic gravitational anomalies are caused by dark matter is wrong.

[newolder]

Here's a recent (27th April, 2010) post about Shing-Tung Yau and his mathematical discoveries. Shing-Tung Yau is a force of nature. He is best known for conceiving the math behind string theory—which holds that, at the deepest level of reality, our universe is built out of 10-dimensional, subatomic vibrating strings...

Newolder, watch my lips: string theory is garbage. There is no scientific evidence for any of it, it makes no predictions, it isn't science, it's pseudoscience. Like your negative speed.

By the way, the beauty of math does not impress me. I'm a scientist. I'm impressed by a mathematical prediction that matches scientific evidence, and by mathematics that delivers meaning and understanding. If it's beautiful and elegant so much the better. But I'm not impressed by mathematical beauty without those other things. Moonshine is beautiful, but it's still moonshine.

Your OP contains 1 equation that describes how the speed of light in a vacuum varies with gravitational potential but it is clear you do not understand what the equation models.

It's clear I do. All you have to do to be clear on that is read the Understanding Electromagnetism thread.

Your next post concludes:

The energy tied up as the matter of a planet "conditions" the surrounding space to create a non-constant gμνalong with a gradient in c which causes curvilinear motion …

I call bullshit unless you show me reference to this 'gradient in c' in an equation of motion that also contains 'a non constant gμν' and 'the energy tied up as the matter of a planet'.

LOL, you call bullshit? Don't you know that's what Einstein said? And what does an equation of motion have to do with it? Go look at the experimental evidence like the Shapiro delay or the GPS clock adjustment, or the mismatch between parallel-mirror light clocks at different altitudes. We call it gravitational time dilation, but clocks clock up motion, and light clocks clock up the motion of light. Set aside the radial length contraction by holding the clocks flat, and what's obvious? Down here the clock goes slower than it does up there. So the light goes slower. That's a variable c newolder, hidden in plain view, like the nose in front of your face. And if your nose wan't buried in ten-dimensional mathematical fiction, maybe you'd see it.

Bullshit.

[ChildInAZoo]

But the 1912 theory is not GR. The 1912 theory was abandoned.

But he didn't abandon the variable speed of light. He said that's why the curvilinear motion occurs. In 1916 it isn't gravitation influencing the speed of light any more, it's the gradient in c causing the gravity. The central concentration of energy conditions the surrounding space, making it inhomogeneous, with a radial gradient in gμν and c.

This doesn't change the fact that the 1912 theory is not GR and that Einstein abandoned the 1912 theory. If you want to preserve the equation that you lifted from the 1912 theory, then show us where it appears in GR. If you cannot do this, then you are simply picking an equation without any understanding simply because it looks like it fits your preconceived notions. This doesn't sound very scientific.

And none of this addresses evidence for the specific prediction made about galaxy rotation curves. What is the specific prediction of this theory for galaxy rotation curves?

There is no specific prediction for galactic rotation curves.

Really? Then how do we know that there are anomalies? You seem to be contadicting yourself and the available science in the most obvious ways.

But note that Einstein said a gravitational field was inhomogeneous space, and that the energy of a gravitational field operates gravitatively just like any other form of energy. So here we have, within general relativity, inhomogeneous spatial energy causing gravity. That means the assumption that gravity is always caused by matter is wrong.

Plese show us where in GR this is carried out.

And since we now know about the expansion of the universe being non-uniform as per the raisins-in-the-cake analogy, that means galaxies are of necessity surrounded by a shell of inhomogeneous space. That means the assumption that galactic gravitational anomalies are caused by dark matter is wrong.

Please show us how a shell of inhomogeneous space influences galaxy rotation. Please show us how the "raisins-in-the-cake analogy" is evidence that the universe has non-uniform expansion. Please show us how to properly calculate the rotation curve of a galaxy.

[Farsight]

This doesn't change the fact that the 1912 theory is not GR and that Einstein abandoned the 1912 theory. If you want to preserve the equation that you lifted from the 1912 theory, then show us where it appears in GR. If you cannot do this, then you are simply picking an equation without any understanding simply because it looks like it fits your preconceived notions. This doesn't sound very scientific.

But I'm not just picking an equation, I'm also giving the references to Einstein saying the speed of light varies, in 1911, 1912, 1913, 1915, and 1916. Here it all is, in the OP.

Really? Then how do we know that there are anomalies? You seem to be contadicting yourself and the available science in the most obvious ways.

Now you're getting ridiculous. We can see them. We see gravitational lensing, as predicted by GR, but we can't see enough matter to account for it.

But note that Einstein said a gravitational field was inhomogeneous space, and that the energy of a gravitational field operates gravitatively just like any other form of energy. So here we have, within general relativity, inhomogeneous spatial energy causing gravity. That means the assumption that gravity is always caused by matter is wrong.

Please show us where in GR this is carried out.

I've said that already, at the foot of this OP. I'll repeat it for your convenience, with a larger font so it stands out better:

NB: note that it’s energy that causes gravity, not matter per se. Matter only causes gravity because of the energy content. See The Foundation of the General Theory of Relativity and look at page 185 where Einstein says "the energy of the gravitational field shall act gravitatively in the same way as any other kind of energy". A gravitational field is a region of space that contains extra energy and in itself causes gravity, hence an integration approach is required, as per page 201. But we don't consider a gravitational field to be dark matter. We don’t go looking for WIMPs. Yes, space is "dark", and the mass of a system is a measure of its energy content, so if you defined the space around a planet as a system, it has a mass of sorts. But it isn’t matter. It’s just space. What did Einstein say about space? Neither homogeneous nor isotropic. What does the FLRW metric say? ”The FLRW metric starts with the assumption of homogeneity and isotropy of space.” Spot the difference? Gravitational anomalies aren’t evidence for dark matter. Dark matter is just a hypothesis that attempts to explain them. And those who promote it sweep the raisins-in-the-cake analogy under the carpet. The universe expands, but the space within the galaxies doesn’t, because galaxies are gravitationally bound. So each and every galaxy is surrounded by a halo of inhomogeneous space. That’s a gμν gradient. It’s a gravitational field without any matter on the end of it. So when you hear people talking about the hunt for dark matter, bear this in mind.

Oh, and for completeness, Einstein said the space of a gravitational field was neither homogeneous nor isotropic in his 1920 Leyden Address.

Please show us how a shell of inhomogeneous space influences galaxy rotation. Please show us how the "raisins-in-the-cake analogy" is evidence that the universe has non-uniform expansion. Please show us how to properly calculate the rotation curve of a galaxy.

No. Now stop prevaricating and pay attention to what Einstein said.

[ChildInAZoo]

But I'm not just picking an equation, I'm also giving the references to Einstein saying the speed of light varies, in 1911, 1912, 1913, 1915, and 1916. Here it all is, in the OP.

So you are just picking the equation. You like what Einstein said in 1912, even though he soon abandoned that approach to the theory. If you really do understand this theory, then you should be able to show us where this equation has a place in GR.

Now you're getting ridiculous. We can see them. We see gravitational lensing, as predicted by GR, but we can't see enough matter to account for it.

OK, so how can "inhomogeneous space" predict gravitational lensing? And how can it predict galaxy rotation curves? Let's see the predictions.

Please show us where in GR [inhomogeneous space]

I've said that already, at the foot of this OP. I'll repeat it for your convenience, with a larger font so it stands out better:

NB: note that it’s energy that causes gravity, not matter per se. Matter only causes gravity because of the energy content. See The Foundation of the General Theory of Relativity and look at page 185 where Einstein says "the energy of the gravitational field shall act gravitatively in the same way as any other kind of energy". A gravitational field is a region of space that contains extra energy and in itself causes gravity, hence an integration approach is required, as per page 201. But we don't consider a gravitational field to be dark matter. We don’t go looking for WIMPs. Yes, space is "dark", and the mass of a system is a measure of its energy content, so if you defined the space around a planet as a system, it has a mass of sorts. But it isn’t matter. It’s just space. What did Einstein say about space? Neither homogeneous nor isotropic. What does the FLRW metric say? ”The FLRW metric starts with the assumption of homogeneity and isotropy of space.” Spot the difference? Gravitational anomalies aren’t evidence for dark matter. Dark matter is just a hypothesis that attempts to explain them. And those who promote it sweep the raisins-in-the-cake analogy under the carpet. The universe expands, but the space within the galaxies doesn’t, because galaxies are gravitationally bound. So each and every galaxy is surrounded by a halo of inhomogeneous space. That’s a gμν gradient. It’s a gravitational field without any matter on the end of it. So when you hear people talking about the hunt for dark matter, bear this in mind.

This is not GR--this is a repetition of the claims that I am asking you to provide the specific details on. Please show us where in the actual mathematics of GR "inhomogeneous space" is used. (And you might show us exactly where all the cosmologists have gone wrong in their calculations and why all their calculations fit so well with each other anyway.)

Please show us how a shell of inhomogeneous space influences galaxy rotation. Please show us how the "raisins-in-the-cake analogy" is evidence that the universe has non-uniform expansion. Please show us how to properly calculate the rotation curve of a galaxy.

No. Now stop prevaricating and pay attention to what Einstein said.

You are definitely the one prevaricating here. You are making scientific claims and predictions and your only justification is "pay attention to what Einstein said"? Einstein himself claimed that he was wrong from time to time. Einstein was not some sort of deity; we only believe in Special and General Relativity because of the evidence, not because of Einstein's divine nature. You may very well be the Pope of the Great Einstein, but that will never convince anyone but the weak-minded.

Now, forgetting what Einstein said, what is your evidence from within General Relativity for your claims?

[lpetrich]

Newolder, watch my lips: string theory is garbage. There is no scientific evidence for any of it, it makes no predictions, it isn't science, it's pseudoscience. Like your negative speed.

How did you figure that out?

(variable speed of light...)

Go look at the experimental evidence like the Shapiro delay or the GPS clock adjustment, or the mismatch between parallel-mirror light clocks at different altitudes. We call it gravitational time dilation, but clocks clock up motion, and light clocks clock up the motion of light.

Work out "motion" mathematically.

As to those GR time effects, those are global effects, due to communicating across curvature of space-time. I know, because I've worked out the math.

But the 1912 theory is not GR. The 1912 theory was abandoned.

But he didn't abandon the variable speed of light. He said that's why the curvilinear motion occurs. In 1916 it isn't gravitation influencing the speed of light any more, it's the gradient in c causing the gravity. The central concentration of energy conditions the surrounding space, making it inhomogeneous, with a radial gradient in gμν and c.

Einstein eventually folded c into the metric gμν -- the metric is a generalization of Pythagoras's theorem for getting distance values out of space-time intervals.

[lpetrich]

But I'm not just picking an equation, I'm also giving the references to Einstein saying the speed of light varies, in 1911, 1912, 1913, 1915, and 1916. Here it all is, in the OP.

That's a global effect, a side effect of space-time curvature. The local speed of light in a vacuum remains constant.

We see gravitational lensing, as predicted by GR, but we can't see enough matter to account for it.

However, matter with very weak nongravitational interactions can easily account for such discrepancies, as it can do for velocities of stars in galaxies. Farsight, are you claiming that such matter cannot possibly exist?

Oh, and for completeness, Einstein said the space of a gravitational field was neither homogeneous nor isotropic in his 1920 Leyden Address.

I read that, and it seems to me that he was describing the most general case. So I think that you are reading too much into Einstein's comments.

Farsight, since you are so intent on arguing by Einstein-thumping, you may want to read his book The Meaning of Relativity. In it he:

• Acknowledges some homogeneous and isotropic solutions of his equations, the Robertson-Walker cosmological solutions
• Treats time as coequal with space, not a byproduct of motion.

[Farsight]

That's a global effect, a side effect of space-time curvature. The local speed of light in a vacuum remains constant.

Read the OP, lpetrich. The curvilinear motion that we call curved spacetime is the result, not the cause. Einstein said a curvature of rays of light can only take place when die Ausbreitungsgeschwindigkeit des Lichtes mit dem Orte variiert. The speed of light varies with the locality. The local speed of light is always measured to be constant because we define our second and our metre using the motion of light.

Farsight, since you are so intent on arguing by Einstein-thumping, you may want to read his book The Meaning of Relativity...

Noted. And when I do and quote it back at you along with the patent evidence, you won't listen, and instead you'll accuse me of thumping the tub for Einstein. There's nobody home, lpetrich.