How Gravity Works

[Farsight]

Sure I could. But it would take me forever, and nobody would understand it. So there's no point, as you know full well, just as you know that it's just a spoiler to distract from How Gravity Works. However everybody does understand that energy causes gravity, and that matter only causes gravity because of its energy content. This is what relativity told us. It's what Einstein told us in The Foundation of the General Theory of Relativity on page 185 where he said "the energy of the gravitational field shall act gravitatively in the same way as any other kind of energy". He spelled it out. A gravitational field is a region of space with a gradient in energy-density, and we know this isn't made of WIMPs. So there's no reason for anybody to believe that the variations in energy density that cause flat galactic rotation curves are the result of WIMPs. Particularly since there's no evidence for WIMPs. Hide behind arcane mathematics and sweep the raisins-in-the-cake expansion of the universe under the carpet if you like, but it cuts no ice. The game is up.

[ChildInAZoo]

Sure I could. But it would take me forever, and nobody would understand it.

So you are saying that you are able to produce mathematical results that are so advanced that the scientists of today will not be able to understand them? That's a pretty bold claim.

One thing of interest is that you have admitted that you haven't produced these results yet. This means that you haven't actually shown, even to yourself, that your theory can actually match the observations of galaxies that we have today.

So there's no point, as you know full well, just as you know that it's just a spoiler to distract from How Gravity Works.

How can it be a distraction from "How Gravity Works" to ask you to show us how gravity works?

However everybody does understand that energy causes gravity, and that matter only causes gravity because of its energy content. This is what relativity told us. It's what Einstein told us in The Foundation of the General Theory of Relativity on page 185 where he said "the energy of the gravitational field shall act gravitatively in the same way as any other kind of energy". He spelled it out. A gravitational field is a region of space with a gradient in energy-density, and we know this isn't made of WIMPs.

Why can't WIMPs be a source of gravity?

So there's no reason for anybody to believe that the variations in energy density that cause flat galactic rotation curves are the result of WIMPs. Particularly since there's no evidence for WIMPs. Hide behind arcane mathematics and sweep the raisins-in-the-cake expansion of the universe under the carpet if you like, but it cuts no ice. The game is up.

I really don't understand what you are saying here. What is the problem with the specific observations that test for the distribution of the source of gravity in various galaxies? Again you talk of the "raisins-in-the-cake expansion of the universe", but you haven't explained it. What is the proper mathematical representation of the "raisins-in-the-cake expansion of the universe" model that allows us to properly calculate galaxy rotation curves?

[lpetrich]

Farsight shows his aversion to making quantitative predictions yet again. However, such predictions are a major part of many scientific fields, including his field, particle physics.

Farsight seems to think that verbal arguments are much better for making predictions than mathematical ones, because they supposedly get to an underlying reality that mathematical formulas cannot get to. But it's mathematical ones that provoked the development of Newtonian mechanics and its successors. Galileo destroyed Aristotle's hypothesis that more massive objects "naturally" fall faster than less massive ones, and he did so by experiments in timing balls rolling down slopes. He found that in the zero-friction limit, they fall with the same acceleration. In his 1623 book The Assayer, he wrote

Philosophy is written in this grand book, the universe, which stands continually open to our gaze. But the book cannot be understood unless one first learns to comprehend the language and read the characters in which it is written. It is written in the language of mathematics, and its characters are triangles, circles, and other geometric figures without which it is humanly impossible to understand a single word of it; without these one is wandering in a dark labyrinth.

We've since discovered lots of writing with much fancier forms of mathematics, but the principle is still correct.

Notice that Galileo did not confine himself to verbal arguments about some supposed underlying reality. Notice also that he did not quote-mine Aristotle's works while claiming that his beliefs are what Aristotle had really believed.

What motivated Galileo to try this experiment is obscure. He claimed some years afterward that it was from watching hailstones fall. Large hailstones started falling at the same time that small ones did, and if they fall in Aristotle fashion, then small ones would have needed a head start that exactly canceled out the difference in fall time. He decided that this fine tuning was too implausible, so he decided to do his famous experiments on that subject.

[Farsight]

It's not some aversion, lpetrich. It's just that I'm pressed for time, and such an exercise is a red herring because it doesn't address the central issue. Gravity is the result of variations in energy density, and no calculations will distinguish between energy that is within the space itself or within particles in that space. For this we need evidence. And as I've said on repeated occasions mathematics is a vital tool for physics. You're dismissing scientific evidence in the OP on numerous threads, and failing to recognise that you cannot understand the terms used within mathematics using mathematics alone. All you can do is "shuffle the deck", expressing one term in terms of another term, and hence you can't drill down to the underlying reality and make progress. One has to analyse the terms to do this, and you're still not appreciating that this is what I've done. I expect you will eventually.

[newolder]

Gravity is the result of variations in energy density

Yes. Massless energy causes repulsion whilst concentrations of mass attract.

and no calculations will distinguish between energy that is within the space itself or within particles in that space.

Calculations by Weyl disprove this.

For this we need evidence.

Galaxies rotate in bound configurations (to chaotic intervention) and voids expand exponentially in time.

One has to analyse the terms to do this, and you're still not appreciating that this is what I've done.

Pick a term and present your analysis.
[/ ]

[ChildInAZoo]

It's not some aversion, lpetrich. It's just that I'm pressed for time, and such an exercise is a red herring because it doesn't address the central issue. Gravity is the result of variations in energy density, and no calculations will distinguish between energy that is within the space itself or within particles in that space.

OK, so you are advocating a theory of gravity that is different from General Relativity. If you would bother to learn the actual theory, you would see this.

[lpetrich]

It's not some aversion, lpetrich. It's just that I'm pressed for time, ...

Farsight, it seems to me that you can find MUCH more time to advocate your theories than to construct critical tests of them.

Gravity is the result of variations in energy density, and no calculations will distinguish between energy that is within the space itself or within particles in that space. For this we need evidence.

That's demonstrably false, and no amount of quote-mining can change that. Look at the mathematical formulations of Newtonian gravity and general relativity some time, rather than continuing to quote mine.

Furthermore, you have chosen to ignore where Einstein disagrees with you on the nature of space and time.

And as I've said on repeated occasions mathematics is a vital tool for physics.

What do you consider it valuable for?

You're dismissing scientific evidence in the OP on numerous threads,

I'm not -- I'm pointing how it is not contrary to mainstream physics, while you seem to believe that it is.

and failing to recognise that you cannot understand the terms used within mathematics using mathematics alone.

So that's your justification for using nonmathematical arguments?

[Farsight]

It's not some aversion, lpetrich. It's just that I'm pressed for time, and such an exercise is a red herring because it doesn't address the central issue. Gravity is the result of variations in energy density, and no calculations will distinguish between energy that is within the space itself or within particles in that space.

OK, so you are advocating a theory of gravity that is different from General Relativity. If you would bother to learn the actual theory, you would see this.

No, I'm not. 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". It’s energy that causes gravity, not matter per se. Matter only causes gravity because of the energy content. It's cut and dried.

[Farsight]

Gravity is the result of variations in energy density, and no calculations will distinguish between energy that is within the space itself or within particles in that space. For this we need evidence.

That's demonstrably false, and no amount of quote-mining can change that. Look at the mathematical formulations of Newtonian gravity and general relativity some time, rather than continuing to quote mine.

See above. You dismiss what Einstein said as quote mining. It isn't demonstrably false at all.

Furthermore, you have chosen to ignore where Einstein disagrees with you on the nature of space and time.

No, I haven't. See page 31 of The Meaning of Relativity where Einstein says "The non-divisibility of the four-dimensional continuum of events does not at all, however, involve the equivalence of the space co-ordinates with the time co-ordinate". You ignore that, you dismiss it as quote-mining and you insist that space and time are coequal. They simply aren't. I can hop back a metre. Now you try hopping back a second.

And as I've said on repeated occasions mathematics is a vital tool for physics.

What do you consider it valuable for?

Modelling to develop a theory thence prediction to verify it and give direction to application.

You're dismissing scientific evidence in the OP on numerous threads,

I'm not -- I'm pointing how it is not contrary to mainstream physics, while you seem to believe that it is.

I don't. I believe that mainstream theory pays inadequate regard to the fundamental reality that mathematical terms represent.

and failing to recognise that you cannot understand the terms used within mathematics using mathematics alone.

So that's your justification for using nonmathematical arguments?

Yes.

[Farsight]

Sure I could. But it would take me forever, and nobody would understand it.

So you are saying that you are able to produce mathematical results that are so advanced that the scientists of today will not be able to understand them? That's a pretty bold claim.

Nobody here would be able to understand it.

Why can't WIMPs be a source of gravity?

They can. And so can tiny dancing angels. But we have no evidence for the existence of such things.

I really don't understand what you are saying here. What is the problem with the specific observations that test for the distribution of the source of gravity in various galaxies? Again you talk of the "raisins-in-the-cake expansion of the universe", but you haven't explained it. What is the proper mathematical representation of the "raisins-in-the-cake expansion of the universe" model that allows us to properly calculate galaxy rotation curves?

Come off it. You know the explanation for the raisins-in-the-cake analogy. Your demand for a mathematical representation is just another spoiler red-herring.

[ChildInAZoo]

No, I'm not. 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". It’s energy that causes gravity, not matter per se. Matter only causes gravity because of the energy content. It's cut and dried.

But we can distinguish between the different forms that this energy is in, at the very least based on its distribution at a given time. If you would bother to learn the basics of the theory, you would know this.

Sure I could. But it would take me forever, and nobody would understand it.

So you are saying that you are able to produce mathematical results that are so advanced that the scientists of today will not be able to understand them? That's a pretty bold claim.

Nobody here would be able to understand it.

So you simply want to insult everyone here? There is an entire thread here devoted to mathematical physics problems, one that you are suspiciously absent from.

I really don't understand what you are saying here. What is the problem with the specific observations that test for the distribution of the source of gravity in various galaxies? Again you talk of the "raisins-in-the-cake expansion of the universe", but you haven't explained it. What is the proper mathematical representation of the "raisins-in-the-cake expansion of the universe" model that allows us to properly calculate galaxy rotation curves?

Come off it. You know the explanation for the raisins-in-the-cake analogy. Your demand for a mathematical representation is just another spoiler red-herring.

No, really, I don't know what you mean. You are being way too vague. If you would actually give us the solution to the Einstein Field Equation you are using as the basis of your "raisins-in-the-cake analogy" then perhaps we could understand.

[lpetrich]

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". It’s energy that causes gravity, not matter per se. Matter only causes gravity because of the energy content. It's cut and dried.

I will concede that GR treats gravitational self-energy like other forms of mass-energy. In fact, that's a major difference between GR and alternative theories of gravity. That's what one gets from working out the equations, and it does not follow from Einstein-thumping.

The Confrontation between General Relativity and Experiment goes into gory detail about what GR and various alternatives to GR have predicted. Some GR alternatives predict a nonzero "Nordtvedt effect", caused by gravitational self-energy having a different acceleration of gravity than other mass-energy. It makes a perturbation of the Moon's orbit of about 13.1 m * (NP), where NP is the Nordtvedt parameter. This is much smaller than the Sun's Newtonian perturbations of the Moon's orbit, but those perturbations can be precisely calculated, and |NP| is limited to less than 0.001. The Nordtvedt effect has also been searched for in pulsars with white-dwarf companions, and |NP| < 0.1 or so there.

One can easily estimate the amount of gravitational self-energy. For mass m and size r, it is typically around G*m2/r. Total mass-energy is m*c2. Their ratio is thus (G*m)/(r*c2). This is approximately (v/c)2, where v is the typical surface orbit velocity.

For galaxies, v ~ 200 - 250 km/s, yielding a self-energy fraction of around 10-6. That is far too small to account for "dark matter".

Furthermore, you have chosen to ignore where Einstein disagrees with you on the nature of space and time.

No, I haven't. See page 31 of The Meaning of Relativity where Einstein says "The non-divisibility of the four-dimensional continuum of events does not at all, however, involve the equivalence of the space co-ordinates with the time co-ordinate". You ignore that, you dismiss it as quote-mining and you insist that space and time are coequal. They simply aren't. I can hop back a metre. Now you try hopping back a second.

That's due to differences between timelike and spacelike directions, but that's caused by what sort of metric space-time has: locally Minkowskian.

And as I've said on repeated occasions mathematics is a vital tool for physics.

What do you consider it valuable for?

Modelling to develop a theory thence prediction to verify it and give direction to application.

That's all well and good, but you ought to recognize that many important physical theories are formulated with mathematics. Thus, you ignore it at your own peril.

and failing to recognise that you cannot understand the terms used within mathematics using mathematics alone.

So that's your justification for using nonmathematical arguments?

Yes.

Farsight, you deserve some credit for conceding that you consider mathematics irrelevant at some fundamental level.

Sure I could. But it would take me forever, and nobody would understand it.

So you are saying that you are able to produce mathematical results that are so advanced that the scientists of today will not be able to understand them? That's a pretty bold claim.

Nobody here would be able to understand it.

What gives you that idea? What does your mathematics involve?

Why can't WIMPs be a source of gravity?

They can. And so can tiny dancing angels. But we have no evidence for the existence of such things.

What would you consider acceptable evidence of WIMP's?

[Farsight]

I will concede that GR treats gravitational self-energy like other forms of mass-energy. In fact, that's a major difference between GR and alternative theories of gravity. That's what one gets from working out the equations, and it does not follow from Einstein-thumping.

Thank you for conceding the point. But do note that this comes from reading the original general and special relativity. It isn't Einstein-thumping.

The Confrontation between General Relativity and Experiment goes into gory detail about what GR and various alternatives to GR have predicted.

Yes, I've read this paper. Note this section:

2.1.2 Tests of local Lorentz invariance
Although special relativity itself never benefited from the kind of “crucial” experiments, such as the perihelion advance of Mercury and the deflection of light, that contributed so much to the initial acceptance of GR and to the fame of Einstein, the steady accumulation of experimental support, together with the successful merger of special relativity with quantum mechanics, led to its being accepted by mainstream physicists by the late 1920s, ultimately to become part of the standard toolkit of every working physicist. This accumulation included...

Some GR alternatives predict a nonzero "Nordtvedt effect", caused by gravitational self-energy having a different acceleration of gravity than other mass-energy. It makes a perturbation of the Moon's orbit of about 13.1 m * (NP), where NP is the Nordtvedt parameter. This is much smaller than the Sun's Newtonian perturbations of the Moon's orbit, but those perturbations can be precisely calculated, and |NP| is limited to less than 0.001. The Nordtvedt effect has also been searched for in pulsars with white-dwarf companions, and |NP| < 0.1 or so there.

Noted. I can't enthuse with this Nordtvedt effect myself.

One can easily estimate the amount of gravitational self-energy. For mass m and size r, it is typically around G*m2/r. Total mass-energy is m*c2. Their ratio is thus (G*m)/(r*c2). This is approximately (v/c)2, where v is the typical surface orbit velocity. For galaxies, v ~ 200 - 250 km/s, yielding a self-energy fraction of around 10-6. That is far too small to account for "dark matter".

Agreed. I wasn't suggesting that gravitational self-energy was dark matter, but using it as a demonstration of non-particulate spatial energy in pointing to the non-homogeneous expansion of the universe.

No, I haven't. See page 31 of The Meaning of Relativity where Einstein says "The non-divisibility of the four-dimensional continuum of events does not at all, however, involve the equivalence of the space co-ordinates with the time co-ordinate". You ignore that, you dismiss it as quote-mining and you insist that space and time are coequal. They simply aren't. I can hop back a metre. Now you try hopping back a second.

That's due to differences between timelike and spacelike directions, but that's caused by what sort of metric space-time has: locally Minkowskian.

No lpetrich, it's because there is no freedom of motion in the time dimension, because time is a cumulative measure of motion through space. A spatial direction is something real, a time direction is an abstraction. I can point to Sirius. You try pointing to next Tuesday. You really have to understand time to properly understand relativity, thence gravity. I note that you still point out any logical flaws in Time Explained or How Gravity Works.

That's all well and good, but you ought to recognize that many important physical theories are formulated with mathematics. Thus, you ignore it at your own peril.

I recognize it, mathematics is a vital tool for phyiscs. I'm not ignoring it, what I'm trying to do is stop you ignoring the analysis of the terms.

Farsight, you deserve some credit for conceding that you consider mathematics irrelevant at some fundamental level.

Huh? All I've said is that you can't use mathematics to understand the terms you use in mathematics. Mathematics tells you the relationships between terms, but it doesn't define the terms.

What gives you that idea? What does your mathematics involve?

Sorry, you'd understand it. The mathematics would involve the motion of a specimen particle representing a star, and energy distribution instead of mass distribution. It would be mostly a reprise of something you've already read, and it would conclude by saying there's an inhomogeneous energy distribution. It wouldn't say this took the form of particles.

What would you consider acceptable evidence of WIMP's?

Reproducible interactions of a particular nature that can't be explained by known particles.

[Farsight]

But we can distinguish between the different forms that this energy is in, at the very least based on its distribution at a given time. If you would bother to learn the basics of the theory, you would know this.

No, you can't. There's clear evidence for gravitational anomalies, and we are confident that the energy distribution is more non-uniform than is suggested by visible matter. But we cannot distinguish the form of this energy.

So you simply want to insult everyone here? There is an entire thread here devoted to mathematical physics problems, one that you are suspiciously absent from.

No, I don't want to insult veryone here. I'm absent from that thread because my interest lies in fundamental physics rather than mathematical physics problems.

No, really, I don't know what you mean. You are being way too vague. If you would actually give us the solution to the Einstein Field Equation you are using as the basis of your "raisins-in-the-cake analogy" then perhaps we could understand.

You know what I mean. The raisins in the cake analogy Is frequently employed, and it isn't any invention of mine. Again we see a red-herring demand for mathematics as a distraction from the discussion. A solution to the Einstein field equation doesn't tell you the form of the energy that causes the gravity.

[lpetrich]

I will concede that GR treats gravitational self-energy like other forms of mass-energy. In fact, that's a major difference between GR and alternative theories of gravity. That's what one gets from working out the equations, and it does not follow from Einstein-thumping.

Thank you for conceding the point. But do note that this comes from reading the original general and special relativity. It isn't Einstein-thumping.

Waving around Einstein's words like a fundie waving the Bible is what I mean by Einstein-thumping, and you've done plenty of that, Farsight. Complete with being obtuse to those parts of Einstein's writings that are contrary to your beliefs.

The Confrontation between General Relativity and Experiment goes into gory detail about what GR and various alternatives to GR have predicted.

Yes, I've read this paper.

Were you able to understand ANY of its mathematics?

I wasn't suggesting that gravitational self-energy was dark matter, but using it as a demonstration of non-particulate spatial energy in pointing to the non-homogeneous expansion of the universe.

Then you should not have used that example.

No lpetrich, it's because there is no freedom of motion in the time dimension, because time is a cumulative measure of motion through space. A spatial direction is something real, a time direction is an abstraction. I can point to Sirius. You try pointing to next Tuesday. You really have to understand time to properly understand relativity, thence gravity. I note that you still point out any logical flaws in Time Explained or How Gravity Works.

And rainbows and clouds are solid objects, right? They certainly look like solid objects. I'm using that as an example of how your physics "reasoning" works.

No wonder you have to thump Einstein, Farsight. You have to look for things that he had stated that could be conveniently plucked out of their context and misunderstood.

(the importance of mathematics...)

]I recognize it, mathematics is a vital tool for phyiscs. I'm not ignoring it, what I'm trying to do is stop you ignoring the analysis of the terms.

An "analysis" consisting of smuggling in new physical theories whose claimed support is nonmathematical. Reminds

So you simply want to insult everyone here? There is an entire thread here devoted to mathematical physics problems, one that you are suspiciously absent from.

No, I don't want to insult veryone here. I'm absent from that thread because my interest lies in fundamental physics rather than mathematical physics problems.

The trouble is that fundamental physics depends on mathematics rather heavily. Your attitude reminds me of what Martin Gardner had noted about anti-Einstein crackpots and mathematics:

Frequently in the pseudo-scientific literature directed against Einstein, one meets with a violent prejudice against complex mathematical equations. The author, of course, does not understand them, so he rationalizes his ignorance by insisting that nature always obeys simple mathematical laws.