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Thread: Relation of Rubber Sheet Analogy to GR (Part 2)

  1. #1 Relation of Rubber Sheet Analogy to GR (Part 2) 
    KJW
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    I started this new thread as a continuation of the other thread because the forum seems to be having a problem with long threads.


    Quote Originally Posted by AstralTraveler View Post
    One difference between gravitation and the rubber sheet analogy that I don't think you are taking into consideration is that gravitation is a three-dimensional problem whereas the rubber sheet analogy is a two-dimensional problem.
    Yes, but it should be possible to make the same mathematical operations (like scaling) on 2D and 3D objects - you just need to add one dimension more...
    Even if it is possible, it still has to done correctly. For example, in the two-dimensional rubber sheet analogy, if you double the radius of the object, what is the correct change in density so that the mass is unchanged?


    There are no paradoxes in relativity, just people's misunderstandings of it.
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    Quote Originally Posted by AstralTraveler View Post
    I have a test of your theory: explain me physically, what would happen, if we would drop a metal ball on a planet, which is made 100% of water?
    It's not "my theory", it's accepted physics. But, assuming that the metal remains more dense than the water at all pressures, the metal ball will sink to the centre of the water planet. However, if there is a depth at which the water becomes more dense than the metal, the metal ball will sink to that depth and remain buoyant there.


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    Even if it is possible, it still has to done correctly. For example, in the two-dimensional rubber sheet analogy, if you double the radius of the object, what is the correct change in density so that the mass is unchanged?
    True, it has to be calculated correctly... But I'm sure, it can be done. I just want to discuss all the aspects of my claims, before I will start with some calculations...

    It's not "my theory", it's accepted physics. But, assuming that the metal remains more dense than the water at all pressures, the metal ball will sink to the centre of the water planet. However, if there is a depth at which the water becomes more dense than the metal, the metal ball will sink to that depth and remain buoyant there.
    Exactly! Everything can be explained using the forces of pressure and buoyancy - which are strightly related to density of a medium. Also keep in mind, that the metal ball in the center would be influenced by a constant pressure of the entire medium - but how this relates to the current concept, where the whole mass, beyond a given distance from the center, doesn't matter at all? This case shows, that instead to attract towards the center, this mass will "push" more dense objects, with the force of pressure. While object with smaller density, will be "pushed out" from more dense medium, due to it's buoyancy... Those are all forces, connected with gravity...

    And it makes me wonder, why current theory of gravity doesn't include the density of an object and the pressure, which it induces on time-space and other matter... If science would consider the pressure of matter on time-space, everything what I stated about the size and radius of gravity well, would be scientifically correct - and as you possibly noticed, I didn't say anything, what would be contradicted by observations or by General Relativity... Actually, I have the feeling, that my explanation is more consistent with General Relativity, than treating objects as a point-mass...

    If we would use the current concept of gravity, a metal ball, placed in the center of a water sphere, shouldn't be influenced by any force - as the whole matter would be placed outside the center of mass...

    BTW Sorry, that it took me so long to respond - but I didn't notice, that there's continuation of this thread. Thanks for making it! I really enjoy this conversation - and I hope, that others enjoy it as well
    Last edited by AstralTraveler; January 6th, 2018 at 09:41 PM.
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    It seems, that I'm not the first one, who proposed to explain gravity with the force of pressure. Sadly, those are still only theories... But I don't like the fact, that in both publications there's the term: "ether" - as it makes them less scientific...

    https://arxiv.org/abs/0709.0408
    http://cds.cern.ch/record/1003391/files/0612036.pdf

    But I also found this link:
    https://www.quora.com/According-to-E...due-to-gravity

    "You can think of gravity as pressure. the mass/energy has a pressure onto spacetime just as the spacetime has a opposite pressure onto the mass.Gravity is just a description of how this pressure is dispersed (dissipating as to the inverse square law of Newton, and with relativistic effects in gravity wells and inertial frames.
    So you can think of it as:
    Spacetime curvature IS the pressure effects of gravity on mass in spacetime.
    Or alternatively:
    Mass and the associated pressures/curvature of spacetime IS gravity.
    So the trampoline visualisation is used to show the pressures applied by the mass on spacetime and in equal and opposite of spacetime onto mass. "

    Exactly, as I said before - energy/mass and time-space induce pressure on eachother...

    I found more:
    https://arxiv.org/pdf/1511.04305.pdf
    "
    As m(0) = 0, it might be tempting to think that the gravity would also be weak and sothe general relativistic effects could be negligible near the center. This is not correct as itcarries a Newtonian imprint in thinking about gravity. Although the Newtonian gravitationalacceleration, Gm(r)/r2, is small near the center, the relativistic correction to it is significantdue to the contribution of pressure to the gravity."

    Another link - this one describes an educational activity for children, which helps understanding gravity, using the rubber sheet model
    https://www.lpi.usra.edu/education/e...id/planetPull/
    "
    • Planets have measurable properties, such as size, mass, density, and composition. A planet's size and mass determines its gravitational pull.
    • A planet's mass and size determines how strong its gravitational pull is.
    Last edited by AstralTraveler; January 7th, 2018 at 01:34 AM.
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    https://persestudio.org/2015/12/02/g...to-the-planet/

    "Sun has around 28 times more gravity than that of earth. But its radius is 100 times than that of earth, meaning the volume of sun is million times of earth. When we substitute these values into inverse square law, the expected gravitational field increase of sun is around 100 times than that of earth. But the observed solar gravity is around four times less than expected. This is due to the lower density of solar matter.By taking the volume formula of a sphere, and using the definition of density as the quantity of matter contained in a unit volume, we can write gravitational field as a function of density and can show that, for a fixed volume, it is directly proportional to density."
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    https://phys.org/news/2016-01-strong...y-planets.html

    Basically, gravity is dependent on mass, where all things – from stars, planets, and galaxies to light and sub-atomic particles – are attracted to one another. Depending on the size, mass and density of the object, the gravitational force it exerts varies. And when it comes to the planets of our solar system, which vary in size and mass, the strength of gravity on their surfaces varies considerably.

    Sorry, that I post it as another comment, but it was a double post anyway, so I just edited it and pasted new content...
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    Quote Originally Posted by AstralTraveler View Post
    Everything can be explained using the forces of pressure and buoyancy - which are strightly related to density of a medium. Also keep in mind, that the metal ball in the center would be influenced by a constant pressure of the entire medium - but how this relates to the current concept, where the whole mass, beyond a given distance from the center, doesn't matter at all? This case shows, that instead to attract towards the center, this mass will "push" more dense objects, with the force of pressure. While object with smaller density, will be "pushed out" from more dense medium, due to it's buoyancy... Those are all forces, connected with gravity...
    You are conflating gravity and pressure. These are distinct notions. For example, the gravitational field is zero at the centre of the water planet, whereas the pressure is maximum there. Also, you need to know the law of gravitation in order to determine the pressure, so nothing can be explained by the pressure and buoyancy without first knowing the gravity.


    Quote Originally Posted by AstralTraveler View Post
    And it makes me wonder, why current theory of gravity doesn't include the density of an object and the pressure, which it induces on time-space and other matter... If science would consider the pressure of matter on time-space, everything what I stated about the size and radius of gravity well, would be scientifically correct - and as you possibly noticed, I didn't say anything, what would be contradicted by observations or by General Relativity... Actually, I have the feeling, that my explanation is more consistent with General Relativity, than treating objects as a point-mass...
    Where did you get the idea that the current theory of gravity doesn't include the density of an object and the pressure? The central equation of General Relativity, the Einstein equation, equates the Einstein tensor of Riemann geometry to the energy-momentum density tensor (a.k.a. stress-energy tensor) of physics. Birkhoff's theorem is an important result about the vacuum regions of spherically symmetric spacetimes, but hardly constitutes a "theory of gravity".

    Actually, you have raised a topic that is of interest to me: how pressure is manifested by General Relativity. For the moment, I won't go into my own issues with the topic. However, I will point out that the gravity of a planet or star doesn't by itself determine the density or pressure. To determine the density or pressure requires an equation of state. Once one has the density and pressure, these can be placed in the stress-energy tensor as described in the "stress–energy of a fluid in equilibrium" section. Solving the Einstein equation for that stress-energy tensor obtains the gravitation produced by the density and pressure. But note that the gravitation produced by the density and pressure is not the same gravitation that produced the density and pressure to begin with.


    Quote Originally Posted by AstralTraveler View Post
    If we would use the current concept of gravity, a metal ball, placed in the center of a water sphere, shouldn't be influenced by any force
    That is not what is being said. The metal ball at the centre of the water planet is not experiencing any gravity from the water, but the water still exerts pressure on the ball. The force exerted on the ball isn't just the weight of the water in immediate contact, but of all the water above it all the way to the surface, this weight being additive.
    There are no paradoxes in relativity, just people's misunderstandings of it.
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    Quote Originally Posted by AstralTraveler View Post
    https://persestudio.org/2015/12/02/g...to-the-planet/

    "Sun has around 28 times more gravity than that of earth. But its radius is 100 times than that of earth, meaning the volume of sun is million times of earth. When we substitute these values into inverse square law, the expected gravitational field increase of sun is around 100 times than that of earth. But the observed solar gravity is around four times less than expected. This is due to the lower density of solar matter.By taking the volume formula of a sphere, and using the definition of density as the quantity of matter contained in a unit volume, we can write gravitational field as a function of density and can show that, for a fixed volume, it is directly proportional to density."
    You probably should be more selective with your quotes. The above was written by a Year 7 student. As for your other quotes from other posts, I would like to know precisely what it is you are trying to demonstrate.
    There are no paradoxes in relativity, just people's misunderstandings of it.
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    https://phys.org/news/2016-11-theory-gravity-dark.html
    Although this new theory of gravity doesn't fit too well to this subject - as it deals rather with holographic principle and distribution of information - this diagram seems to match nicely with my statements about the radius of gravity well depending on the size and mass/energy distribution of an source object:


    I don't know - maybe it's just coincidence. But I don't believe in such thing...
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    You are conflating gravity and pressure. These are distinct notions. For example, the gravitational field is zero at the centre of the water planet, whereas the pressure is maximum there. Also, you need to know the law of gravitation in order to determine the pressure, so nothing can be explained by the pressure and buoyancy without first knowing the gravity.
    Yes, we need to know the gravitational pull, which a body induces on other objects. But we need to know as well the energy/mass densities of both objects - as it determines the way, in which both objects will interact.

    Where did you get the idea that the current theory of gravity doesn't include the density of an object and the pressure? The central equation of General Relativity, the Einstein equation, equates the Einstein tensor of Riemann geometry to the energy-momentum density tensor (a.k.a. stress-energy tensor) of physics. Birkhoff's theorem is an important result about the vacuum regions of spherically symmetric spacetimes, but hardly constitutes a "theory of gravity".

    Actually, you have raised a topic that is of interest to me: how pressure is manifested by General Relativity. For the moment, I won't go into my own issues with the topic. However, I will point out that the gravity of a planet or star doesn't by itself determine the density or pressure. To determine the density or pressure requires an equation of state. Once one has the density and pressure, these can be placed in the stress-energy tensor as described in the "stress–energy of a fluid in equilibrium" section. Solving the Einstein equation for that stress-energy tensor obtains the gravitation produced by the density and pressure. But note that the gravitation produced by the density and pressure is not the same gravitation that produced the density and pressure to begin with.
    Ok, I understand, that there's an "internal" pressure in all distributions of energy/mass and that it is directed outwards and against the gravitation. From what I understand, those forces nullify eachother, preventing the object from expansion or collapsing.

    And there's also the second kind of pressure - the one, which exists because the gravitational pull induced on a medium, towards a more dense object - like water in ocean or the atmosphere. This is, what I'm interested in - as it defines the way, in which objects behave inside gravitational fields...

    But to be honest, I don't know, which of those forces is better, to explain the curvatures, as a result of pressure, which energy/mass and time-space induce on eachother - and this is, what I'm trying to do, to prove the difference between a force, which is concentrated in a point and a force which is distributed in a volume of space...

    One question: if the stress-energy tensor includes so many variable properties of energy/mass distribution - why all spheres with uniform density are treated as point masses, no matter what is the state/density/pressure/energy of their mass? I mean the stress-energy tensor is probably completely different for a solid matter, liquid, gas or plasma - and still it doesn't change the properties of external gravitational field...

    Maybe it's because I'm not a professional physicist, but it seems logical to me, that an object with big volume and low density (like a nebula) will create a completely different gravitational field, than a small and dense sphere, made of rock or iron... The
    stress-energy tensor should be completely different in both cases...

    That is not what is being said. The metal ball at the centre of the water planet is not experiencing any gravity from the water, but the water still exerts pressure on the ball. The force exerted on the ball isn't just the weight of the water in immediate contact, but of all the water above it all the way to the surface, this weight being additive.


    Yeah, I've learned this today, while I was reading about the
    hydrostatic equation... I'm still learning

    You probably should be more selective with your quotes. The above was written by a Year 7 student. As for your other quotes from other posts, I would like to know precisely what it is you are trying to demonstrate.
    It was made for teachers. Generally, I wanted to show the correlation between the size of objects and the properties of gravity wells... But I'm still looking for something, what would prove my claims
    Last edited by AstralTraveler; January 7th, 2018 at 05:29 PM.
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    I found two nice java applets, which visualise gravitational fields in 3D

    2-D Vector Field Simulation
    3-D Vector Field Simulation

    But there are some issues with the model. First of all, it's possible to change the radius of a sphere only to the point, where given frame of time-space becomes almost completely "flat" - while I would like to see, what would happen, if the sphere would get even bigger. Second issue is with the independence of field strenght and gravity well "depth". From what I understand, strenght of gravitational pull depends on the "depth", which is defined by the energy/mass density. To make it scientifically valid, variable field strenght should be replaced with variable mass - while mass combined with radius should define the radius and "depth" of gravity well, and determine the strenght of gravitational pull...
    Last edited by AstralTraveler; January 7th, 2018 at 07:13 PM.
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    Quote Originally Posted by AstralTraveler View Post
    Yes, we need to know the gravitational pull, which a body induces on other objects. But we need to know as well the energy/mass densities of both objects - as it determines the way, in which both objects will interact.
    How the objects interact is beyond the scope of the original discussion (which has yet to be resolved). The original discussion (the one in which I'm participating) is about the gravitation produced by a non-rotating spherically symmetric matter distribution. Indeed, how a material object interacts with another material object is beyond the scope of any discussion about gravitation because how material objects interact depends on more than gravitation and more than just density and pressure also. For example, you asked about a metal ball in a water planet, but if the water planet was an ice planet, then in spite of the similarity in density between water and ice, the metal ball would behave completely differently, remaining on the surface in spite being more dense than the ice.


    Quote Originally Posted by AstralTraveler View Post
    One question: if the stress-energy tensor includes so many variable properties of energy/mass distribution - why all spheres with uniform density are treated as point masses, no matter what is the state/density/pressure/energy of their mass? I mean the stress-energy tensor is probably completely different for a solid matter, liquid, gas or plasma - and still it doesn't change the properties of external gravitational field...

    Maybe it's because I'm not a professional physicist, but it seems logical to me, that an object with big volume and low density (like a nebula) will create a completely different gravitational field, than a small and dense sphere, made of rock or iron... The stress-energy tensor should be completely different in both cases...
    First, start from a matter distribution that is not rotating and is spherically symmetric, because that is the precondition of the shell theorem and Birkhoff's theorem. Because the gravitation produced by an energy-momentum distribution is unique, the remainder of the spacetime, and hence the entire spacetime, must be non-rotating and spherically symmetric. At any given location, the gravitational field vector must be directed along the radial line, and have a magnitude that depends only on the distance of the given location from the centre of symmetry. This requirement is demanded by the spherical symmetry of the spacetime.

    Contrary to what you may think is the current theory, gravitation in general relativity is a local theory. In other words, the curvature associated with gravitation at any given location depends only on the infinitesimal neighbourhood of that location. In general, this means that gravitation satisfies some system of partial differential equations whose solution is subject to boundary conditions. The energy-momentum distribution which is outside¹ the boundary determines the field values at the boundary, and the field values at the boundary determines the gravitation inside the boundary. It is important to note that regardless of the energy-momentum distribution outside the boundary, if the field values at the boundary are unchanged, so is the gravitation inside the boundary. In simple terms, the gravitational field at locations beyond a particular distance from the centre is determined entirely by the gravitational field at that particular distance from the centre. Because only the magnitude of the gravitational field vector is unconstrained by the spherical symmetry, the boundary condition is a single parameter. This single parameter is all that is available to describe the energy-momentum distribution within the particular distance from the centre, and this may be regarded as a mass value.

    ¹ The terms "outside" and "inside" are with respect to the region of interest that contains the gravitational field solution of the equations, and not with respect to the centre of the spherical symmetry. I hope this avoids confusion.


    Quote Originally Posted by AstralTraveler View Post
    I'm still learning
    Very good.


    Quote Originally Posted by AstralTraveler View Post
    It was made for teachers.
    But it was made by students.


    Quote Originally Posted by AstralTraveler View Post
    But I'm still looking for something, what would prove my claims
    Be careful. This appears to be a case of falling into the trap of confirmation bias.

    How is it that you can reject well established theorems such as the shell theorem and Birkhoff's theorem, yet accept random stuff from the internet including something from a Year 7 student?
    Last edited by KJW; January 8th, 2018 at 11:57 AM.
    There are no paradoxes in relativity, just people's misunderstandings of it.
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    In an earlier post, you suggested that you may want to solve the Poisson equation yourself in order to personally verify its results. While this discussion has been limited to spherically symmetric matter distributions, perhaps I can provide some insight into the general case. Firstly, applying the divergence theorem, one can convert the Poisson equation from its differential form to the equivalent integral form. Now, consider an arbitrary matter distribution, and for some selected region of space, construct the closed boundary of this region (the boundary is not made of anything but is just a set of locations that define a surface entirely enclosing the selected region). At each point on this boundary, consider the component of the gravitational field vector that is perpendicular to the surface. This component can be directed either into or out from the region. If we total the inward components (as magnitudes) over the entire surface and subtract the total of the outward components (as magnitudes) over the entire surface, one obtains the total mass inside the region.

    In the general case, changing the matter distribution within the region does change the gravitational field over the boundary surface, but the net flux described above remains unchanged (indicating that mere redistribution doesn't change the total mass). But in the case of a spherically symmetric matter distribution and spherical boundary, the gravitational field vector at the boundary is both perpendicular to the boundary and constant in magnitude over the boundary. Therefore, any redistribution of matter within the region that maintains spherical symmetry cannot alter the gravitational field at the boundary.
    Last edited by KJW; January 8th, 2018 at 01:37 PM.
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    How the objects interact is beyond the scope of the original discussion (which has yet to be resolved). The original discussion (the one in which I'm participating) is about the gravitation produced by a non-rotating spherically symmetric matter distribution. Indeed, how a material object interacts with another material object is beyond the scope of any discussion about gravitation because how material objects interact depends on more than gravitation and more than just density and pressure also. For example, you asked about a metal ball in a water planet, but if the water planet was an ice planet, then in spite of the similarity in density between water and ice, the metal ball would behave completely differently, remaining on the surface in spite being more dense than the ice.
    Good point! I gues, that it depends on the thermal energy of medium - but I agree, that this is not the subject of this discussion

    First, start from a matter distribution that is not rotating and is spherically symmetric, because that is the precondition of the shell theorem and Birkhoff's theorem. Because the gravitation produced by an energy-momentum distribution is unique, the remainder of the spacetime, and hence the entire spacetime, must be non-rotating and spherically symmetric. At any given location, the gravitational field vector must be directed along the radial line, and have a magnitude that depends only on the distance of the given location from the centre of symmetry. This requirement is demanded by the spherical symmetry of the spacetime.

    Contrary to what you may think is the current theory, gravitation in general relativity is a local theory. In other words, the curvature associated with gravitation at any given location depends only on the infinitesimal neighbourhood of that location. In general, this means that gravitation satisfies some system of partial differential equations whose solution is subject to boundary conditions. The energy-momentum distribution which is outside¹ the boundary determines the field values at the boundary, and the field values at the boundary determines the gravitation inside the boundary. It is important to note that regardless of the energy-momentum distribution outside the boundary, if the field values at the boundary are unchanged, so is the gravitation inside the boundary. In simple terms, the gravitational field at locations beyond a particular distance from the centre is determined entirely by the gravitational field at that particular distance from the centre. Because only the magnitude of the gravitational field vector is unconstrained by the spherical symmetry, the boundary condition is a single parameter. This single parameter is all that is available to describe the energy-momentum distribution within the particular distance from the centre, and this may be regarded as a mass value.
    I don't argue with the spherical symmentry. But let's look at this image:


    The gravity well deepens towards the surface of an spherical object, not it's center... By changing the distance of surface from the center, we disturb the symmetry of gravitational field.

    But it was made by students.

    Be careful. This appears to be a case of falling into the trap of confirmation bias.

    How is it that you can reject well established theorems such as the shell theorem and Birkhoff's theorem, yet accept random stuff from the internet including something from a Year 7 student?
    I wouldn't be sure, if it's made by students, since it's published on Lunar and Planetary Institute official site...

    Very good.
    To be honest, I started to get into the subject of gravitation around 3 weeks, or so... Before I was dealing with another side of space physics - that means MHD and plasma cosmology - but I decided to expand my knowledge. I know, that plasma cosmology explains some space phenomenons in different way, than GR - and I'm interested in finding some common ground for both theories. I know, that it's "rather" hard task for someone, who's not a professional physicist, but I want to try it anyway
    Last edited by AstralTraveler; January 10th, 2018 at 05:33 PM.
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    In an earlier post, you suggested that you may want to solve the Poisson equation yourself in order to personally verify its results. While this discussion has been limited to spherically symmetric matter distributions, perhaps I can provide some insight into the general case. Firstly, applying the divergence theorem, one can convert the Poisson equation from its differential form to the equivalent integral form. Now, consider an arbitrary matter distribution, and for some selected region of space, construct the closed boundary of this region (the boundary is not made of anything but is just a set of locations that define a surface entirely enclosing the selected region). At each point on this boundary, consider the component of the gravitational field vector that is perpendicular to the surface. This component can be directed either into or out from the region. If we total the inward components (as magnitudes) over the entire surface and subtract the total of the outward components (as magnitudes) over the entire surface, one obtains the total mass inside the region.

    In the general case, changing the matter distribution within the region does change the gravitational field over the boundary surface, but the net flux described above remains unchanged (indicating that mere redistribution doesn't change the total mass). But in the case of a spherically symmetric matter distribution and spherical boundary, the gravitational field vector at the boundary is both perpendicular to the boundary and constant in magnitude over the boundary. Therefore, any redistribution of matter within the region that maintains spherical symmetry cannot alter the gravitational field at the boundary.
    I think, that I managed to find something, what might contradict the point-mass concept...
    https://en.wikipedia.org/wiki/Roche_limit
    It is said, that Roche Limit depends completely on the density of objects and their sizes. It's just my guess, but I think, that the limit is conncted with the angle of gravity well "slopes" - objects start to be disintegrated, when the slope becomes almost completely vertical. Considering the fact, that density and radius of a spherical object defines the Roche Limit, it should be possible to conclude, that those two factors have significant meaning, when it comes to the shape of gravity well...
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    Quote Originally Posted by AstralTraveler View Post
    But let's look at this image:


    The gravity well deepens towards the surface of an spherical object, not it's center...
    The graph shows that the gravitational field is maximum at the surface, but the gravitational field is not the same as the gravitational potential. It is the gravitational potential that is referred to as a "well", and this is deepest at the centre.


    Quote Originally Posted by AstralTraveler View Post
    By changing the distance of surface from the center, we disturb the symmetry of gravitational field.
    Changing the radius of a ball does not alter the spherical symmetry.

    If the radius of a ball is increased while keeping the mass constant, the gravitational field at the new larger surface will be the same as the gravitational field at that same distance from the centre of the original smaller ball. In the image, the decreasing curve remains the same, but the increasing straight line has a smaller slope and meets the decreasing curve further from the centre and at a smaller gravitational field.
    There are no paradoxes in relativity, just people's misunderstandings of it.
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    Quote Originally Posted by AstralTraveler View Post
    I think, that I managed to find something, what might contradict the point-mass concept...
    https://en.wikipedia.org/wiki/Roche_limit
    No. The concept underlying the Roche Limit is based on the gravitational tidal field. The tidal field is distinct from both the gravitational field and the gravitational potential. The tidal field is the manifestation of spacetime curvature in general relativity. It does not in any way contradict the shell theorem because tidal forces are not what the shell theorem is about. However, just as the gravitational field doesn't change far enough away from a shrinking ball, neither does the tidal field.
    There are no paradoxes in relativity, just people's misunderstandings of it.
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    Quote Originally Posted by KJW View Post
    In an earlier post, you suggested that you may want to solve the Poisson equation yourself in order to personally verify its results. While this discussion has been limited to spherically symmetric matter distributions, perhaps I can provide some insight into the general case. Firstly, applying the divergence theorem, one can convert the Poisson equation from its differential form to the equivalent integral form. Now, consider an arbitrary matter distribution, and for some selected region of space, construct the closed boundary of this region (the boundary is not made of anything but is just a set of locations that define a surface entirely enclosing the selected region). At each point on this boundary, consider the component of the gravitational field vector that is perpendicular to the surface. This component can be directed either into or out from the region. If we total the inward components (as magnitudes) over the entire surface and subtract the total of the outward components (as magnitudes) over the entire surface, one obtains the total mass inside the region.

    In the general case, changing the matter distribution within the region does change the gravitational field over the boundary surface, but the net flux described above remains unchanged (indicating that mere redistribution doesn't change the total mass). But in the case of a spherically symmetric matter distribution and spherical boundary, the gravitational field vector at the boundary is both perpendicular to the boundary and constant in magnitude over the boundary. Therefore, any redistribution of matter within the region that maintains spherical symmetry cannot alter the gravitational field at the boundary.
    Do you understand the above? Apart from the absence of mathematical notation, it is more-or-less a proof of the shell theorem.
    There are no paradoxes in relativity, just people's misunderstandings of it.
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  20. #19  
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    I found it!!!
    Someone was in fact faster than me - but only by less than 4 years. This publication is from 2013 and explains EVERYTHING, what I'm trying to say from the beginning of this subject...

    http://www.spacetime-model.com/files...time_model.pdf

    Wooow! Somene wrote down everything, what I figured out + a lot more...

    100% scientific explanation of Mass, Gravity and Curvature of Spacetime



    But I still have something to add to this theory...
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  21. #20  
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    According to mr Jacky Jerôme space time induces pressure on a "closed volume" creating "mass effect".


    I would simply use the term "object", which can be freely replaced by the term "medium", as both mean: "mass distributed in a volume of space". However, what I miss in the theory of mr Jacky Jerôme, is the inner pressure inside a medium/object, which is connected with the thermal energy of particles and the state of matter (or maybe I still didn't find it in the publication). In a sphere with uniform mass distribution - let's say made of water or iron - outward pressure of a medium is equalized by inward pressure of time-space. Because of this, particles within an uniform medium don't feel any gravitational pull.
    http://spiff.rit.edu/richmond/asras/sn_bh/sn_bh.html





    This is why, this diagram is incorrect in the case of two objects with the same ratio of size/mass:

    If this would be truth, we wouldn't be able to use submarines. When density of medium is equal to density of an object, there's no gravitational pull in any direction - object floats freely in a medium. Changing the size/mass relation can have two results: inward or outward pressure of medium.

    This is, how looks gravitational field of an uniform sphere for another uniform sphere with the same density:



    Those are the representations of gravitational fields for uniform spheres with different masses and different densities:



    Object is a finite volume of space, separated from the medium. Object makes a local frame inside the frame of a medium. Object will create space-time curvature within a medium if their densities are different. Medium will induce inward or outward pressure, depending on the density of an object.

    That's it... This fixes all my issues with this part physics and explains everything what is connected with gravity and mass/energy distribution in a volume of space. And everything remains consistent with GR

    And from this point, I could proceed further in my quest to fix everything, what science messed up in the standard model... And believe me - couple small fixes can bring back some sense to physics. Physicist should observe the Universe and think, instead of blindly believe in calculations. Math should come at the very end - after a theory is confirmed by observable facts. However scientits love to base their models on factors, which exist only as virtual numbers in calculations. While instead trying to find dark matter/energy, why won't you try to figure out an explanation, which doesn't need those factors... ?

    But it makes me happy, that there are still some REAL scientists, who are not afraid to look at the science from wider perspective. I would love to hear, what mr Jacky Jerôme could tell about such concept... I don't think, that any of my explanations can be contradicted with observations... Maybe I try to contact him...
    Last edited by AstralTraveler; January 16th, 2018 at 10:07 PM.
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