How Gravity Works

[Farsight]

It's very well-established that SR is a local approximation of GR, and Einstein was discussing one of the implications of that. Due to travelling in curved space-time, the speed of light in a vacuum becomes globally variable, even if it is locally constant.

Thanks re the varying coordinate speed of light, but can we clarify cause and effect? Einstein made it clear that energy causes gravity, and that matter causes gravity because of its energy content. He didn't actually say the speed of light varies because it's travelling through curved space-time. He actually said the space was inhomogeneous, and that's why the curvilinear motion occurs. We call this along with gravitational time dilation "curved spacetime", but it's the effect rather than the cause. Here's the relevant passage:

"According to this theory the metrical qualities of the continuum of space-time differ in the environment of different points of space-time, and are partly conditioned by the matter existing outside of the territory under consideration. This space-time variability of the reciprocal relations of the standards of space and time, or, perhaps, the recognition of the fact that ‘empty space’ in its physical relation is neither homogeneous nor isotropic, compelling us to describe its state by ten functions (the gravitation potentials gμν)..."

So what? Einstein did plenty of VERY good work.

I agree. But his good work was between 1905 and circa 1920. After that he seemed to struggle. I don't know why.

Farsight, for all your Einstein-thumping, you have chosen to ignore where Einstein himself had disagreed. That trajectories go through space-time is a reasonable interpretation of Newtonian mechanics, and it's a necessary part of SR and GR, due to space-time unification.

I'm clear on this, lpetrich. We plot lines in spacetime to represent motion through space over time. These lines might be straight, or curved, and in the latter case we can call them trajectories. But a particle doesn't move along this trajectory. There can't be any motion in a mathematical space that has time as one of its dimensions.

Farsight, that sort of attitude will never get your published in a reputable journal. You HAVE to work such things out in order to be taken seriously in the mainstream scientific community.

Noted.

One can work out how different sorts of dark matter would be distributed, like "cold", "warm", and "hot" dark matter. One finds from such working out that cold dark matter is the best fit.

But it doesn't fit with the evidence. It employs an inbuilt presumption that matter causes gravity rather than a non-uniform energy density, and that space is homogeneous. A region of cold dark space with a higher energy-density than the surrounding space will have a mass-equivalence and will cause gravity. And of course the "raisins-in-the-cake" non-uniform expansion of the universe means that we can expect these energy-density variations.

[ChildInAZoo]

One can work out how different sorts of dark matter would be distributed, like "cold", "warm", and "hot" dark matter. One finds from such working out that cold dark matter is the best fit.

But it doesn't fit with the evidence. It employs an inbuilt presumption that matter causes gravity rather than a non-uniform energy density, and that space is homogeneous. A region of cold dark space with a higher energy-density than the surrounding space will have a mass-equivalence and will cause gravity. And of course the "raisins-in-the-cake" non-uniform expansion of the universe means that we can expect these energy-density variations.

Why do you speak out on this matter when you are so clearly ignorant? If you could actually use GR you would see that everything that can be taken into account in dark matter calculations is pretty much taken into account. If you think that there is something extra, then show us what it is.

[lpetrich]

(particulate dark matter...)

It was proposed by Zwicky in 1934. That's 76 years ago. That's a long time to believe in something for which there is no scientific evidence, whilst rejecting what Einstein said about energy causing gravity and describing a gravitational field as inhomogeneous space.

Work out the numbers, Farsight. Your theorizing is empty babble without them, and no amount of quote-mining can change that.

"Dark matter" is not gravitational self-energy, because that self-energy has too little mass to be significant. Relativistic effects have sizes that are typically (v/c)2, where v is a typical velocity. For galaxies, v ~ 200 km/s, so the self-energy will be only 10-6 of the total mass.

So one has to look elsewhere.

The evidence is the measurements. The Shapiro delay is a fact of life, the light goes slower. Mathematical details aren't evidence.

Mathematical details are not evidence??? Farsight, that is blatant scientific illiteracy.

Farsight, for all your Einstein-thumping, you have chosen to ignore where Einstein himself had disagreed. That trajectories go through space-time is a reasonable interpretation of Newtonian mechanics, and it's a necessary part of SR and GR, due to space-time unification.

I'm clear on this, lpetrich. We plot lines in spacetime to represent motion through space over time. These lines might be straight, or curved, and in the latter case we can call them trajectories. But a particle doesn't move along this trajectory. There can't be any motion in a mathematical space that has time as one of its dimensions.

That's illiterate nonsense -- space-time trajectories are an important part of relativity, and one can easily get such trajectories out of Newtonian mechanics. In fact, such trajectories are a very intuitive concept.

[Farsight]

(particulate dark matter...)

It was proposed by Zwicky in 1934. That's 76 years ago. That's a long time to believe in something for which there is no scientific evidence, whilst rejecting what Einstein said about energy causing gravity and describing a gravitational field as inhomogeneous space.

Work out the numbers, Farsight. Your theorizing is empty babble without them, and no amount of quote-mining can change that.

If it comforts you to shield yourself from the argument and general relativity with words like "babble" and "quote-mining", suit yourself. Those numbers will come, not from me, but they will. But you'll still be finding a way to dismiss inhomogeneous space and cling to a 76-year-old myth. All because you don't understand the electron.

("Dark matter" is not gravitational self-energy, because that self-energy has too little mass to be significant. Relativistic effects have sizes that are typically (v/c)2, where v is a typical velocity. For galaxies, v ~ 200 km/s, so the self-energy will be only 10-6 of the total mass.

You still don't get this do you? I didn't say dark matter was gravitational self-energy. I said it's space. Space is cold and dark and it has its vacuum energy. It has a mass-equivalence, and the non-uniform expansion of the universe means space is not homogeneous.

The evidence is the measurements. The Shapiro delay is a fact of life, the light goes slower. Mathematical details aren't evidence.

Mathematical details are not evidence??? Farsight, that is blatant scientific illiteracy.

No it isn't! Evidence is evidence. Not mathematical details. We have good evidence of gravitational anomalies, we can see flat galactic rotation curves and gravitational lensing. But that's where it stops. Regardless of mathematical details, this is evidence for gravitational lensing, it isn't evidence for particulate dark matter in the form of WIMPs. If it was, it could equally be evidence for an alternative hypothesis featuring tiny dancing angels, where mathematical details have been employed to calculate the effect of their wing-beats. You know Lpetrich, I think we're seeing your problem here. You repeatedly dismiss observational scientific evidence and simple iron-clad logic, and you use mathematics as a shield to justify doing so.

That's illiterate nonsense -- space-time trajectories are an important part of relativity, and one can easily get such trajectories out of Newtonian mechanics. In fact, such trajectories are a very intuitive concept.

And those "trajectories" in spacetime aren't trajectories in space. A particle moves through space, along a trajectory. It doesn't move through spacetime. Your intuition that it does is wrong. Think it through. Reduce our three-dimensional world to a two-dimensional plate, draw a dot on it to represent a motionless particle, then sweep the plate upwards to make a block universe, such that the dot traces out a worldline. Now look at this abstract block universe. You're looking at a representation of Minkowski spacetime. Can you see the particle moving through it? No. All you've got is a worldline. You can do this again with a moving particle so that your worldline is angled or even curved, but you still cannot see the particle moving through spacetime. The particle moves through space, not through time, and not through spacetime. It can't, because when it moves through space it takes time to do so. And when you combine the space with the time to make spacetime, the motion has been turned into a line that gives you the particle's full history. All the motion has been frozen out of the picture. Now come on, I can't make it any simpler. Read Time Explained and then you've got a fighting chance of understanding How Gravity Works. Stop all this evasion and give me some worthwhile discussion.

[ChildInAZoo]

But you'll still be finding a way to dismiss inhomogeneous space and cling to a 76-year-old myth.

What is an inhomogeneity? Show us the mathematical description.

All because you don't understand the electron.

You still don't get this do you? I didn't say dark matter was gravitational self-energy. I said it's space. Space is cold and dark and it has its vacuum energy. It has a mass-equivalence, and the non-uniform expansion of the universe means space is not homogeneous.

Einstein worked out the mathematics of vacuum energy---it doesn't work like mass does. It doesn't have a specific distribution. It actually acts to repel particles from each other. If you would learn the physics, you would not write such embarrassing things.

Evidence is evidence. Not mathematical details. We have good evidence of gravitational anomalies, we can see flat galactic rotation curves and gravitational lensing. But that's where it stops. Regardless of mathematical details, this is evidence for gravitational lensing, it isn't evidence for particulate dark matter in the form of WIMPs. If it was, it could equally be evidence for an alternative hypothesis featuring tiny dancing angels, where mathematical details have been employed to calculate the effect of their wing-beats.

The evidence for dark matter is evidence for a theory of tiny angels, if those tiny angels have the properties associated with WIMPs. The angel theory, like your theory, obviously has extra parameters that are not supported by the available observations, and should be discarded because these extraneous aspects place a large burden on the theory that the evidence cannot match.

You know Lpetrich, I think we're seeing your problem here. You repeatedly dismiss observational scientific evidence and simple iron-clad logic, and you use mathematics as a shield to justify doing so.

The case is rather the reverse: we would like to see your evidence and your logic, but you have hidden these away because you refuse to show how statements of your theory actually match the observations. If you want to show the evidence for your theory, you have to show how your theory makes a prediction and how that prediction matches observations.

[Farsight]

An inhomogeneity is a non-uniformity. That's it. A mathematical description offers no further information, being or example Γ1 <> Γ2. But vacuum energy can have a specific distribution, which is why Einstein described a gravitational as inhomogeneous space and spoke of the energy of a gravitational field acting gravitatively just like any other form of energy. Note that this means that a region of space exhibiting a gravitational field has a gradient in vacuum energy density. Sadly Einstein rather struggled with his cosmology, and failed to predict the expanding universe despite talking repeatedly of stress-energy and pressure. People describe it as his "greatest blunder". I myself can't explain why, or why his contribution to physics seems to have diminished from circa 1920.

Here's my evidence and my logic: How Gravity Works. Try countering it. You can't.

[ChildInAZoo]

An inhomogeneity is a non-uniformity. That's it. A mathematical description offers no further information, being or example Γ1 <> Γ2.

But you are using this term in a special way when it comes to galaxy rotation. What is that way? What is the mathematical description of inhomogeneity for a galaxy?

But vacuum energy can have a specific distribution, which is why Einstein described a gravitational as inhomogeneous space and spoke of the energy of a gravitational field acting gravitatively just like any other form of energy. Note that this means that a region of space exhibiting a gravitational field has a gradient in vacuum energy density. Sadly Einstein rather struggled with his cosmology, and failed to predict the expanding universe despite talking repeatedly of stress-energy and pressure. People describe it as his "greatest blunder". I myself can't explain why, or why his contribution to physics seems to have diminished from circa 1920.

You may want to cure your ignorance of cosmology if you want to talk about cosmology. Can you please describe this inhomogeneous vacuum energy using Einstein's theory and mathematical description?

[Farsight]

I'm not using the term in a special way for galaxy rotation. A body's motion is curvilinear because it's moving through inhomogeneous space. The cause of this inhomogeneity is the issue. I have no ignorance of cosmology, you have an ignorance of general relativity and it would seem of the expanding universe. An inhomogeneous energy density causes gravity. A galaxy is gravitationally bound, space expands between the galaxies like the raisins-in-the-cake analogy. But the galaxies aren't expanding. The result is of necessity inhomogeneous space. That's an additional gravitational field. Any description I gave would be a tedious repetition of elements of GR, and a waste of time that detracts from this essential and very simple point that you continue to evade.

[ChildInAZoo]

I'm not using the term in a special way for galaxy rotation. A body's motion is curvilinear because it's moving through inhomogeneous space. The cause of this inhomogeneity is the issue.

See, that was a special use. Please show us this role of inhomogeneity in galaxy rotation curves.

I have no ignorance of cosmology,

You just wrote, "Sadly Einstein rather struggled with his cosmology, and failed to predict the expanding universe despite talking repeatedly of stress-energy and pressure. People describe it as his "greatest blunder". I myself can't explain why, or why his contribution to physics seems to have diminished from circa 1920. " If you had studied cosmology, you would have seen that Einstein's influence on cosmology was great after 1920 and why Einstein is said to have called the cosmological constant his greatest blunder.

you have an ignorance of general relativity and it would seem of the expanding universe. An inhomogeneous energy density causes gravity. A galaxy is gravitationally bound, space expands between the galaxies like the raisins-in-the-cake analogy. But the galaxies aren't expanding. The result is of necessity inhomogeneous space. That's an additional gravitational field. Any description I gave would be a tedious repetition of elements of GR, and a waste of time that detracts from this essential and very simple point that you continue to evade.

On the contrary: since your description conflicts with standard relativistic cosmology (and Einstein's work in cosmology) any detailed description you made would be very illuminating.

[lpetrich]

If it comforts you to shield yourself from the argument and general relativity with words like "babble" and "quote-mining", suit yourself. Those numbers will come, not from me, but they will. But you'll still be finding a way to dismiss inhomogeneous space and cling to a 76-year-old myth. All because you don't understand the electron.

Farsight, your dismissing mathematics reminds me of Martin Gardner on anti-relativity crackpots:

Frequently in the pseudo-scientific literature directed against Einstein, one meets with a violent prejudice against complex mathematical equations.

(me on how "dark matter" cannot be gravitational self-energy...)

You still don't get this do you? I didn't say dark matter was gravitational self-energy. I said it's space. Space is cold and dark and it has its vacuum energy. It has a mass-equivalence, and the non-uniform expansion of the universe means space is not homogeneous.

Farsight, your disdain for mathematics is showing again. Work out the numbers and see what they are like.

Evidence is evidence. Not mathematical details.

Farsight, many observations are mathematical, and many tests of hypotheses are mathematical. Your ideal of a nonmathematical physics is a throwback to Aristotle and before.

You know Lpetrich, I think we're seeing your problem here. You repeatedly dismiss observational scientific evidence and simple iron-clad logic, and you use mathematics as a shield to justify doing so.

There you go again, treating mathematics as irrelevant. Mathematics is an important part of such evidence, whether you like it or not.

That's illiterate nonsense -- space-time trajectories are an important part of relativity, and one can easily get such trajectories out of Newtonian mechanics. In fact, such trajectories are a very intuitive concept.

And those "trajectories" in spacetime aren't trajectories in space. A particle moves through space, along a trajectory. It doesn't move through spacetime. ...

Going through a series of space-time points is not following a trajectory? Farsight, that sort of illogic will get you nowhere.

[Twiglet]

Never mind Gardner, this seems to fit:

The following can indicate a delusion:

1.The patient expresses an idea or belief with unusual persistence or force.
2.That idea appears to exert an undue influence on his or her life, and the way of life is often altered to an inexplicable extent.
3.Despite his/her profound conviction, there is often a quality of secretiveness or suspicion when the patient is questioned about it.
4.The individual tends to be humorless and oversensitive, especially about the belief.
5.There is a quality of centrality: no matter how unlikely it is that these strange things are happening to him, the patient accepts them relatively unquestioningly.
6.An attempt to contradict the belief is likely to arouse an inappropriately strong emotional reaction, often with irritability and hostility.
7.The belief is, at the least, unlikely, and out of keeping with the patient's social, cultural and religious background.
8.The patient is emotionally over-invested in the idea and it overwhelms other elements of his or her psyche.
9.The delusion, if acted out, often leads to behaviors which are abnormal and/or out of character, although perhaps understandable in the light of the delusional beliefs.
10.Individuals who know the patient will observe that his or her belief and behavior are uncharacteristic and alien.

The following features are found:

1.It is a primary disorder.
2.It is a stable disorder characterized by the presence of delusions to which the patient clings with extraordinary tenacity.
3.The illness is chronic and frequently lifelong.
4.The delusions are logically constructed and internally consistent.
5.The delusions do not interfere with general logical reasoning (although within the delusional system the logic is perverted) and there is usually no general disturbance of behavior. If disturbed behavior does occur, it is directly related to the delusional beliefs.
6.The individual experiences a heightened sense of self-reference. Events which, to others, are nonsignificant are of enormous significance to him or her, and the atmosphere surrounding the delusions is highly charged.

[Farsight]

Going through a series of space-time points is not following a trajectory? Farsight, that sort of illogic will get you nowhere.

I am astounded that you still don't understand this. When you consider a block of space and a particle, you see that the particle moves through a series of points in space to follow a trajectory over time. However when you replace this block of space with a block of spacetime, you are showing the particle's worldline. You are showing the particle at all times. The particle doesn't move along this trajectory, because you're already showing it at all times. It would take a further time dimension for any motion through spacetime, and there isn't one. Now read the Nasty Little truth About Spacetime Physics and Time Explained to understand this simple point. Then you'll understand How gravity Works.

[ChildInAZoo]

I am astounded that you still don't understand this. When you consider a block of space and a particle, you see that the particle moves through a series of points in space to follow a trajectory over time. However when you replace this block of space with a block of spacetime, you are showing the particle's worldline. You are showing the particle at all times. The particle doesn't move along this trajectory, because you're already showing it at all times. It would take a further time dimension for any motion through spacetime, and there isn't one. Now read the Nasty Little truth About Spacetime Physics and Time Explained to understand this simple point. Then you'll understand How gravity Works.

You are astounded because you have been lead astray by the crackpot author of "Nasty Little truth About Spacetime Physics". One of the earliest things we did in class learning about relativity was figure out how to describe a curve in spacetime as a function of a single parameter, as if it were a path followed in a specific order. That mathematical description of a path through spacetime is essentially the same as the mathematical description of a path through anywhere. When you actually learn the mathematics of relativity theory, you will actually find that you can understand more. You will finally understand some of what is going on in the theory.

[Farsight]

No, I haven't been led astray, not at all. There can be no motion through a four-dimensional mathematical space that includes time as one of its dimensions. The article is correct, as is Time Explained, along with the mathematics of relativity theory. However your interpretation of that mathematics is incorrect. It is "so trivially proven wrong in fact, that it is insulting to the lay public, the same public that funds most scientific projects".

[ChildInAZoo]

OK, so can you, using the correct mathematics, please show us how to construct a correct cosmological model and how to correctly calculate the rotation curve for a galaxy? Every scientist doing anything in astronomy would like to know.