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Author Topic: What effect does mass-energy density have on gravitational field strength?  (Read 19623 times)

Offline jeffreyH

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Here is a quick sketch of the concept. Comments on this would be appreciated. How wrong am I?

 

Offline Pmb

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The gravitational force experienced between two bodies is related to the mass and distance between them. In some sense, density doesn't matter.
That is incorrect. The greater the mass density is then the greater the mass that occupies the volume the

It's accurate in some sense to think of mass density in gravity as you would charge density in electrodynamics.
 

Offline Pmb

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Does the mass-energy density affect gravity at higher densities? Does any amplification of field strength occur? How could we test if this were true?
Mass-energy is only one source of gravity. Momentum and stress also contribute. You need to take all of these into account to determine what happens. I'm not sure what you mean by amplification effects though. The geometric object which acts as the source of gravity is called the stress-energy-momentum tensor. It's definition is given here http://home.comcast.net/~peter.m.brown/sr/energy_momentum_tensor.htm

I've been playing with different distributions of mass to show how mass-energy comes into play as do momentum and stress. They're at http://home.comcast.net/~peter.m.brown/gr/gr.htm
 

Offline jeffreyH

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Does the mass-energy density affect gravity at higher densities? Does any amplification of field strength occur? How could we test if this were true?
Mass-energy is only one source of gravity. Momentum and stress also contribute. You need to take all of these into account to determine what happens. I'm not sure what you mean by amplification effects though. The geometric object which acts as the source of gravity is called the stress-energy-momentum tensor. It's definition is given here http://home.comcast.net/~peter.m.brown/sr/energy_momentum_tensor.htm

I've been playing with different distributions of mass to show how mass-energy comes into play as do momentum and stress. They're at http://home.comcast.net/~peter.m.brown/gr/gr.htm

It is so good to have someone tell you WHY you are wrong. I will look at both your links and work through any equations. I have just ordered "The Absolute Differential Calculus (Calculus of Tensors) Levi-Civita, Tullio". That should be a fun read!
 

Offline jeffreyH

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Just a thought. Could the zero point energy be an effect of gravity propagating through matter? Could the definition of phonon be equivalent to graviton?
« Last Edit: 04/10/2013 06:42:53 by jeffreyH »
 

Offline Supercryptid

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That is incorrect. The greater the mass density is then the greater the mass that occupies the volume the

It's accurate in some sense to think of mass density in gravity as you would charge density in electrodynamics.

The gravity is only greater because the higher density causes there to be more mass (assuming a constant volume). If distance from the mass and the mass itself are kept constant, then gravity stays the same (regardless of what changes in radius and density may occur).

Just a thought. Could the zero point energy be an effect of gravity propagating through matter? Could the definition of phonon be equivalent to graviton?

Zero-point Energy has to do with Heisenberg's Uncertainty Principle and quantum vacuum fluctuations. Gravity isn't required to explain it.
« Last Edit: 04/10/2013 21:40:13 by Supercryptid »
 

Offline jeffreyH

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That is incorrect. The greater the mass density is then the greater the mass that occupies the volume the

It's accurate in some sense to think of mass density in gravity as you would charge density in electrodynamics.

The gravity is only greater because the higher density causes there to be more mass (assuming a constant volume). If distance from the mass and the mass itself are kept constant, then gravity stays the same (regardless of what changes in radius and density may occur).

Just a thought. Could the zero point energy be an effect of gravity propagating through matter? Could the definition of phonon be equivalent to graviton?

Zero-point Energy has to do with Heisenberg's Uncertainty Principle and quantum vacuum fluctuations. Gravity isn't required to explain it.

Firstly gravity over square surface area must increase if gravity is a particle based field and we take mass-density into account. This causes problems with the inverse square law for reasons I won't go into now.

Secondly I agree the zero point energy is not gravity related after having read up on it a bit more. Also it is not a multi-directional effect.
 

Offline Pmb

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Quote from: Supercryptid
The gravity is only greater because the higher density causes there to be more mass (assuming a constant volume). If distance from the mass and the mass itself are kept constant, then gravity stays the same (regardless of what changes in radius and density may occur).
Not in general relativity. If you have more mass packed into a smaller space and there is more pressure due to this compactness then the pressure also contributes to the gravitational field. GR is much different than Newtonian gravity. It's much more complicated.
 

Offline Pmb

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Just a thought. Could the zero point energy be an effect of gravity propagating through matter? Could the definition of phonon be equivalent to graviton?
Zero-point energy contributes to the gravitational field just like all other sources of energy. But no. The rest is wrong. There is no reason to make such assumptions either. BTW a phonon is a classical entity and the graviton a quantum mechanical one.
 

Offline Pmb

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Quote from: jeffreyH
It is so good to have someone tell you WHY you are wrong.
And its so good to know I can still be useful even though I'm disabled.

There are many good books on geometry such as that of Bernhard F. Schutz. Also Differential Forms and Connections by R.W.R Daring comes highly recommended by a GR expert friend of mine. I myself will be studying it when I'm better (still ill due to lengthy recovery from surgery). Introduction to Vectors and Tensors by Bowen and Wang looks good. I bought a copy a couple of months ago and haven't been well enough to study that either. :(
 

Offline Pmb

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Quote from: Supercryptid
The gravity is only greater because the higher density causes there to be more mass (assuming a constant volume). If distance from the mass and the mass itself are kept constant, then gravity stays the same (regardless of what changes in radius and density may occur).
As I said, that is wrong. At least in general.

I'd like to point out that what was said above only applies to the special situation of a point particle or something of that nature. When its something like a long line of mass then its different. Suppose we wish to determine the gravitational field a distance d from the z axis where along the z-axis is a long line of of constant mass density. The gravitational field at a distance r from the z-axis is proportional to the mass density, not the mass, and inversely proportional to r. So there really are situations where the field is proportional to mass density and not to the entire mass. This will hold for a very long line of matter when we want to look at the field close to the line.

The GR calculation is found here
http://home.comcast.net/~peter.m.brown/gr/grav_field_rod.htm
 

Offline Supercryptid

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Interesting...can the effect of added pressure increase gravity significantly? Does that make the "replace the Sun with a black hole" analogy I mentioned earlier wrong then?
 

Offline jeffreyH

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Interesting...can the effect of added pressure increase gravity significantly? Does that make the "replace the Sun with a black hole" analogy I mentioned earlier wrong then?

I don't think it would but this is only a hunch at the moment.
 

Offline Pmb

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Interesting...can the effect of added pressure increase gravity significantly? Does that make the "replace the Sun with a black hole" analogy I mentioned earlier wrong then?
No. That remains correct.

Each case must really be analzed individually. It's dangerous to form general conclusions. Let me give you an example; you've heard of cosmic strings, right? A straight cosmic string has an enormous linear mass density. It's extremely thin, less than the width of an atom but never ends in an open universe. It has an equally large tension too. Tesion is like pressure but is negative. They contribute equally in the case of the cosmic string. The end effect is that you could be standing right next to a cosmic string and not know it from its gravitational field. The only gravitational effect a cosmic string has is to change tghe topology of the surrounding space from planar to conical. Amazing stuff, isn't it? :)

A vacuum domain wall is another example. In this case the wall is a two dimensional object rather than a one dimensional object like the string. The tension contributes twice as much so the wall has a replusive gravitational field. Interesting thing about the vacuum domain wall is that the gravitaitonal field it generates has zero spacetime curvature.

In three dimensions there is even more repulsion and this is how the accelerating expansion of the universe works.

On the other hand the effective active gravitational mass density of radiation is that the (positive) contribution of the raditation pressure contributes a significant amount to the active-grav-mass.
 

Offline jeffreyH

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Is then gravitation expressed at the event horizon of the black hole as a result of the in falling matter. If so then what part would the original mass play? Or is this looking at it wrong?
 

Offline jeffreyH

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To collapse below the Schwarzchild radius some of the mass is already contained within this volume. Mass outside this region, when collapsing inwards, will approach the radius with escape velocity increasing proportionally. Has anyone tried working this through during the collapse event to calculate the effects on gravity as the process evolves?
 

Offline Pmb

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Is then gravitation expressed at the event horizon of the black hole as a result of the in falling matter. If so then what part would the original mass play? Or is this looking at it wrong?
I'm sorry but I don't understand this question. Can you rephrase it for me please?
 

Offline Pmb

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Quote from: jeffreyH
To collapse below the Schwarzchild radius some of the mass is already contained within this volume.
As observed from outside the event horizon, nothing can pass through the event horizon and go inside.

Quote from: jeffreyH
Mass outside this region, when collapsing inwards, will approach the radius with escape velocity increasing proportionally.
Actually, as matter approaches the event horizon it slows down and comes to a stop at the event horison and never crosses it.

Quote from: jeffreyH
Has anyone tried working this through during the collapse event to calculate the effects on gravity as the process evolves?
I don't understand what you mean by "the effects on gravity." Can you clarify this for me please?
 

Offline jeffreyH

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Quote from: jeffreyH
To collapse below the Schwarzchild radius some of the mass is already contained within this volume.
As observed from outside the event horizon, nothing can pass through the event horizon and go inside.

Quote from: jeffreyH
Mass outside this region, when collapsing inwards, will approach the radius with escape velocity increasing proportionally.
Actually, as matter approaches the event horizon it slows down and comes to a stop at the event horison and never crosses it.

Quote from: jeffreyH
Has anyone tried working this through during the collapse event to calculate the effects on gravity as the process evolves?
I don't understand what you mean by "the effects on gravity." Can you clarify this for me please?

The effects on gravitational field strength. Does it increase or decrease overall? This is assuming a Kerr black hole.
« Last Edit: 05/10/2013 08:50:51 by jeffreyH »
 

Offline jeffreyH

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Is then gravitation expressed at the event horizon of the black hole as a result of the in falling matter. If so then what part would the original mass play? Or is this looking at it wrong?
I'm sorry but I don't understand this question. Can you rephrase it for me please?

I would forget this one. I need to know what I mean myself first. :-)
 

Offline Pmb

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Quote from: jeffreyH
The effects on gravitational field strength. Does it increase or decrease overall? This is assuming a Kerr black hole.
Not sure. I'm not an expert on black holes so I'd rather remain silent on questions requiring great detail like this.
 

Offline Supercryptid

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Interesting...can the effect of added pressure increase gravity significantly? Does that make the "replace the Sun with a black hole" analogy I mentioned earlier wrong then?
No. That remains correct.

Each case must really be analzed individually. It's dangerous to form general conclusions. Let me give you an example; you've heard of cosmic strings, right? A straight cosmic string has an enormous linear mass density. It's extremely thin, less than the width of an atom but never ends in an open universe. It has an equally large tension too. Tesion is like pressure but is negative. They contribute equally in the case of the cosmic string. The end effect is that you could be standing right next to a cosmic string and not know it from its gravitational field. The only gravitational effect a cosmic string has is to change tghe topology of the surrounding space from planar to conical. Amazing stuff, isn't it? :)

A vacuum domain wall is another example. In this case the wall is a two dimensional object rather than a one dimensional object like the string. The tension contributes twice as much so the wall has a replusive gravitational field. Interesting thing about the vacuum domain wall is that the gravitaitonal field it generates has zero spacetime curvature.

In three dimensions there is even more repulsion and this is how the accelerating expansion of the universe works.

On the other hand the effective active gravitational mass density of radiation is that the (positive) contribution of the raditation pressure contributes a significant amount to the active-grav-mass.

Forgive me for taking this a bit off topic, but I find these conclusions rather fascinating. I've heard of domain walls before, but never that they were gravitationally-repulsive. If only we could prove their existence and duplicate them on a tiny, controlled scale. Then antigravity machines may prove plausible. Not that I expect this to happen any time soon.

You sound fairly confident about the gravitational repulsion that causes the Universe's expansion. Yet I've never heard of that explanation before. It does sound like a nice model, as it doesn't invoke a mysterious "dark energy" to explain it. Is this a mainstream theory?
 

Offline Pmb

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Quote from: Supercryptid
Forgive me for taking this a bit off topic, but I find these conclusions rather fascinating. I've heard of domain walls before, but never that they were gravitationally-repulsive.
 If only we could prove their existence and duplicate them on a tiny, controlled scale.
If we could create that kind of matter and control it then we could try it. That's way off in the future if you ask me though.

Quote from: Supercryptid
You sound fairly confident about the gravitational repulsion that causes the Universe's expansion.
That is what the entire cosmology community believes. Who am I to differ?

Quote from: Supercryptid
Yet I've never heard of that explanation before. It does sound like a nice model, as it doesn't invoke a mysterious "dark energy" to explain it. Is this a mainstream theory?
Yes. Please understand that the term "dark energy" is simply the name given to the cause of gravitational repulsion. See
http://news.nationalgeographic.com/news/2012/02/120215-dark-energy-antimatter-physics-alternate-space-science/# - Is Dark Energy Really "Repulsive Gravity"?

See also http://en.wikipedia.org/wiki/Dark_energy
Quote
This accelerating expansion effect is sometimes labeled "gravitational repulsion", which is a colorful but possibly confusing expression. In fact a negative pressure does not influence the gravitational interaction between masses—which remains attractive—but rather alters the overall evolution of the universe at the cosmological scale, typically resulting in the accelerating expansion of the universe despite the attraction among the masses present in the universe.
 

Offline jeffreyH

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I have often thought that collapsing systems such as black holes and neutron stars can only exist in an expanding system. If the system were collapsing we should see white holes. This is why white holes are unstable but in the collapsing system it would be black holes that were unstable.
 

Offline yor_on

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That would make traveling the astronomical 'void' a very dangerous experience me thinks :) when matter and antimatter meet you get radiation, does you not? Shouldn't that be measurable, or is the assumption that this only took place in some beginning never more happening? also it makes me think of a  twisted 'mirror universe' in where half of its existence finds the other half non-existing, as non measurable. A very weird concept which reminds me of Bakers SF (think it was him?) depicting a ultimate 'war of resources',  between beings of matter and anti matter, arranging the universe to a anti matter state, ultimately making it inhabitable for us of matter.
==

It is a nice idea though in the sense of explaining why we then could have a equal amount of anti matter matter, possibly? From a big Bang without those annihilating each other at the moment they emerge. But if they exist in equal proportions, and they should if they do not 'naturally meet', due to gravity/anti gravity, what exactly would make the universe expand, and accelerate? Reminds me of my old idea (my joke actually) about 'virtual particles', although I doubt that one too, it's just too simplistic. You can as easily argue that it then need a equal amount of virtual 'photons' of mass to come into existence, and then you should have no expansion I think, neither a acceleration.

I think geometry holds the answer myself, with probably more degrees of freedom, or less? :) Depending on how you look at it. It all depends on if we got that one right I guess? I can alternatively imagine another sort of topology, solely defined from local measurements, in where the real question becomes what allows a 'local point' to in any way being able to measure another point (connect to). That universe does have a topology (dimensions) defined by our measurements, but its consistency is ultimately a local experience. And ultimately a question of pure logic.

As if what define a universes geometry is a question of some principle allowing local points to measure on other points, a 'point like' universe if one like :) Such a universe, should allow for entanglements easily as our definitions of distance, and motion, would need to be retranslated to fit such a concept.
« Last Edit: 06/10/2013 16:17:45 by yor_on »
 

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