Thread: Question on GR : How is gravity maintained in a box ?

Say i had a concrete closed container moving around randomly under a gravitational influence,
then within the box all the aspects of the surrounding gravity characteristics will be identically maintained,
for instance when going to or coming back from a less gravitational condition.

(Not concerned here about 'the man in the elevator accelarating' issue,
the box could hang still in one place and then later hang still in another place and all the gravity conditions would be contiouously and instantaniously maintained)

How does the fabric of spacetime, spacetime curvage make this happen ?

Not sure I understand the question. Are you concerned about the effect of the mass of the concrete box? Or are you thinking that it would somehow "shield" the external gravitational effects? Or ...?

the box could hang still in one place and then later hang still in another place and all the gravity conditions would be contiouously and instantaniously maintained)

...unless of course you are moving the box closer or further to/from the source of gravity. Also, if the gravitational source is very strong and the box very large, you may have tidal forces to consider.

How does the fabric of spacetime, spacetime curvage make this happen ?

Birkhoff's theorem - the gravitational field of a stationary, spherically symmetric body has Schwarzschild geometry. First and foremost that means the field is static, and static fields act instantaneously ( as opposed to changing fields ).

Originally Posted by Strange

Not sure I understand the question. Are you concerned about the effect of the mass of the concrete box? Or are you thinking that it would somehow "shield" the external gravitational effects? Or ...?

Indeed about shielding, how does the gravity inside the box 'keep track of' gravity outside the box, which it should mimic at all times ?

Originally Posted by Markus Hanke

the box could hang still in one place and then later hang still in another place and all the gravity conditions would be contiouously and instantaniously maintained)

...unless of course you are moving the box closer or further to/from the source of gravity. Also, if the gravitational source is very strong and the box very large, you may have tidal forces to consider.

How does the fabric of spacetime, spacetime curvage make this happen ?

Birkhoff's theorem - the gravitational field of a stationary, spherically symmetric body has Schwarzschild geometry. First and foremost that means the field is static, and static fields act instantaneously ( as opposed to changing fields ).

When i say 'maintain' gravity conditions, i actually mean the ability to maintain the change happening outside the box, in the box.

Say if a certain change of curvage of spacetime etc is happening outside the box as it moves around, according to changing gravitational conditions the bow would encounter on the random path, how does this get transferred to or maintained within the box ?

Originally Posted by Noa Drake

When i say 'maintain' gravity conditions, i actually mean the ability to maintain the change happening outside the box, in the box.
Say if a certain change of curvage of spacetime etc is happening outside the box as it moves around, according to changing gravitational conditions the bow would encounter on the random path, how does this get transferred to or maintained within the box ?

Space-time is everywhere, both in vacuum and in the interior of masses, hence so is gravity, since it is just a geometric property of space-time. You cannot "shield" gravity by putting yourself in a box. Note that the geometry of space-time in the interior of mass-energy is different from the exterior ( vacuum ) - it is described by different solutions to the field equations. However, the equations themselves are valid in both cases.

So am i to interprete that as this :

> Going from vacuum to mass to vacuum (say left to right) :

-in Vacuum : spacetime is curved a certain way (producing the gravitational condition there)
-in Mass : spacetime is curved identically , or is it distorted differently, but still 'connected' to vacuum ?
-in Vacuum : spacetime is curved again as in the leftside vacuum, also still 'connected' to the spacetime in the matter.

?

Originally Posted by Noa Drake

-in Vacuum : spacetime is curved a certain way (producing the gravitational condition there)

Correct.

-in Mass : spacetime is curved identically , or is it distorted differently, but still 'connected' to vacuum ?

It is curved differently in the interior of a mass, but smoothly connected to the metric outside. Note that this difference is very small, unless the mass is substantial.

-in Vacuum : spacetime is curved again as in the leftside vacuum, also still 'connected' to the spacetime in the matter.

Yes. Having said that, the curvature in the interior cavity of the box will very slightly differ from the outside, due to the presence of the mass in the walls. But I think you have understood the basic notion - being that gravity cannot be "shielded", unlike EM radiation.

Suppose one has a hollow spherical shell near some other gravitational source. Without considering the complications arising from the fully general relativistic theory, inside the shell, the gravitation is that of the nearby external gravitational source, while outside the shell, the gravitation is that from the shell itself in addition to the nearby external gravitational source. As Markus Hanke points out, there is no shielding of the external gravitational source by the shell, although inside the spherical shell, there is no contribution from the shell itself (although strictly speaking, Birkhoff's theorem only applies when the entire spacetime is spherically symmetric).

Originally Posted by KJW

Suppose one has a hollow spherical shell near some other gravitational source. Without considering the complications arising from the fully general relativistic theory, inside the shell, the gravitation is that of the nearby external gravitational source, while outside the shell, the gravitation is that from the shell itself in addition to the nearby external gravitational source. As Markus Hanke points out, there is no shielding of the external gravitational source by the shell, although inside the spherical shell, there is no contribution from the shell itself (although strictly speaking, Birkhoff's theorem only applies when the entire spacetime is spherically symmetric).

Gravitational shielding is a controversial subject. To date, no such effect has been detected. It is interesting to see that very reputable physicists, like Majorana, have been experimenting with the concept. Others, like Maurice Allais, pursued the subject despite the ridicule of the mainstream physics .

Originally Posted by xyzt

Gravitational shielding is a controversial subject. To date, no such effect has been detected. It is interesting to see that very reputable physicists, like Majorana, have been experimenting with the concept. Others, like Maurice Allais, pursued the subject despite the ridicule of the mainstream physics .

That's fair enough. Physicists are still testing general relativity (whenever the opportunity arises), and this provides justification for testing ideas that would conflict with GR. I don't know if the full theory of GR would allow some shielding of an external gravitational source, but if it does, it would certainly be a higher-order effect (no shielding in the Newtonian limit).

Originally Posted by KJW

Originally Posted by xyzt

Gravitational shielding is a controversial subject. To date, no such effect has been detected. It is interesting to see that very reputable physicists, like Majorana, have been experimenting with the concept. Others, like Maurice Allais, pursued the subject despite the ridicule of the mainstream physics .

That's fair enough. Physicists are still testing general relativity (whenever the opportunity arises), and this provides justification for testing ideas that would conflict with GR. I don't know if the full theory of GR would allow some shielding of an external gravitational source, but if it does, it would certainly be a higher-order effect (no shielding in the Newtonian limit).

The limits are set to 1 part in !

Not about shielding per say, but this link has to do with an observational test of the strong equivalence principle; Pulsar and companions will put general relativity to the test - physicsworld.com

The article mentions "self gravity", do they just mean mass in this context or something more complex?

Originally Posted by GiantEvil

Not about shielding per say, but this link has to do with an observational test of the strong equivalence principle; Pulsar and companions will put general relativity to the test - physicsworld.com

The article mentions "self gravity", do they just mean mass in this context or something more complex?

It is said that the motion of a test mass in a gravitational field follows a geodesic trajectory in spacetime. A test mass, by definition, is a mass that is small enough to have negligible effect on the spacetime. But for a mass that does significantly distort the spacetime, what does it mean to say that the mass follows a geodesic trajectory? The geodesic trajectories of spacetime depend on the mass itself, and one can't exactly consider the geodesic trajectories in the absence of this mass.

Originally Posted by KJW

Originally Posted by GiantEvil

Not about shielding per say, but this link has to do with an observational test of the strong equivalence principle; Pulsar and companions will put general relativity to the test - physicsworld.com

The article mentions "self gravity", do they just mean mass in this context or something more complex?

It is said that the motion of a test mass in a gravitational field follows a geodesic trajectory in spacetime. A test mass, by definition, is a mass that is small enough to have negligible effect on the spacetime. But for a mass that does significantly distort the spacetime, what does it mean to say that the mass follows a geodesic trajectory? The geodesic trajectories of spacetime depend on the mass itself, and one can't exactly consider the geodesic trajectories in the absence of this mass.

And the strong equivalence principle states that these greater than test masses will still have identical velocities and trajectories to a test mass in an identical gravity field?

Originally Posted by GiantEvil

And the strong equivalence principle states that these greater than test masses will still have identical velocities and trajectories to a test mass in an identical gravity field?

That's my understanding.

Originally Posted by KJW

Originally Posted by GiantEvil

And the strong equivalence principle states that these greater than test masses will still have identical velocities and trajectories to a test mass in an identical gravity field?

That's my understanding.

The larger bodies are subject to tidal forces, the test probes are not.

Originally Posted by xyzt

Originally Posted by KJW

Originally Posted by GiantEvil

And the strong equivalence principle states that these greater than test masses will still have identical velocities and trajectories to a test mass in an identical gravity field?

That's my understanding.

The larger bodies are subject to tidal forces, the test probes are not.

That's true.

Originally Posted by xyzt

The larger bodies are subject to tidal forces, the test probes are not.

I do understand about spaghettification. The sauce comes in a bag.

Originally Posted by KJW

Originally Posted by GiantEvil

And the strong equivalence principle states that these greater than test masses will still have identical velocities and trajectories to a test mass in an identical gravity field?

That's my understanding.

Actually, I answered too hastily. This is actually not correct. A test mass in orbit about a massive object will have a stable orbit (though elliptical orbits undergo perihelion precession), whereas a massive object in orbit about another massive object will have a decaying orbit due to the emission of gravitational radiation.

Originally Posted by KJW

Actually, I answered too hastily. This is actually not correct. A test mass in orbit about a massive object will have a stable orbit (though elliptical orbits undergo perihelion precession), whereas a massive object in orbit about another massive object will have a decaying orbit due to the emission of gravitational radiation.

Indeed. Now, if you add a third massive body to the mix ( as in the article referenced earlier ), you get a holy mess that can only be treated numerically with the aid of supercomputers...isn't GR fun

Originally Posted by Markus Hanke

Indeed. Now, if you add a third massive body to the mix ( as in the article referenced earlier ), you get a holy mess that can only be treated numerically with the aid of supercomputers...isn't GR fun

I read somewhere (I don't recall where) that the general three-body problem has no closed-form solutions in Newtonian theory, the general two-body problem has no closed form solutions in general relativity, and the general one-body problem has no closed form solutions in quantum field theory.

Originally Posted by KJW

Originally Posted by Markus Hanke

Indeed. Now, if you add a third massive body to the mix ( as in the article referenced earlier ), you get a holy mess that can only be treated numerically with the aid of supercomputers...isn't GR fun

I read somewhere (I don't recall where) that the general three-body problem has no closed-form solutions in Newtonian theory, the general two-body problem has no closed form solutions in general relativity, and the general one-body problem has no closed form solutions in quantum field theory.

And the general zero-body problem has no closed-form solutions in string theory.

@Markus

So spacetime curves differently inside the mass.
Does it pervade the atoms ? I would suspect not.
So it distorts ,while staying smoothly connected,around atoms, in an interatomic area ?
Or..?

Could we say then that if density were to increase of the mass, radius staying the same thus,
that the atoms come more closely together? And thus spacetime needs to distort more inside the mass ?


Or is it density of atoms increasing, resulting in another type of matter with more density, so that less spacetime will be present in the matter, hence increasing the strenght of the gravitational field around it ?

Originally Posted by Noa Drake

Does it pervade the atoms ? I would suspect not.

Space-time doesn't have any boundaries, it pervades everything.

So it distorts ,while staying smoothly connected,around atoms, in an interatomic area ?

Same as macroscopic objects - there is vacuum geometry on the outside, and the geometry in the interior of the nucleus. They will slightly differ.

And thus spacetime needs to distort more inside the mass ?

If the mass is stationary and spherically symmetric, there will be no difference on the outside if you increase density while keeping total mass constant. However, space-time geometry in the interior of the mass will change. Same if you induce stresses and strains in the mass.

Or is it density of atoms increasing, resulting in another type of matter with more density, so that less spacetime will be present in the matter, hence increasing the strenght of the gravitational field around it ?

Like I said, space-time is everywhere, so I can't really make much sense of the above comment.

I am referring to this :If mass increases and radius stays the same, then the strenght of the grav field ouside the objekt increases.What is happening then with the spacetime present in the matter/atoms ?I know this more related to my other questiontopic, but one things brings on another.

Originally Posted by Noa Drake

I am referring to this :If mass increases and radius stays the same, then the strenght of the grav field ouside the objekt increases.What is happening then with the spacetime present in the matter/atoms ?I know this more related to my other questiontopic, but one things brings on another.

The time dilation becomes more pronounced.

Originally Posted by KJW

Originally Posted by Noa Drake

I am referring to this :If mass increases and radius stays the same, then the strenght of the grav field ouside the objekt increases.What is happening then with the spacetime present in the matter/atoms ?I know this more related to my other questiontopic, but one things brings on another.

The time dilation becomes more pronounced.

Actually, there will be increased curvature of the three-dimensional space as well, but it's the time dilation (gravitational redshift) that is responsible for the gravity we experience.

Originally Posted by Noa Drake

I am referring to this :If mass increases and radius stays the same, then the strenght of the grav field ouside the objekt increases

As KJW said. If the object is spherically symmetric and stationary, then the exterior geometry is that of Schwarzschild, so that "gravity" as we experience it some distance away from the object depends only on total mass and distance from that mass, but not on internal composition of same. It is then the "time component" of the metric which gives the gravity we experience, whereas the "space components" are responsible for tidal forces.

Ok,that is usefull info on what would happen ouside the mass, but what behaviour or change does the spacetime inside the atom show ?

Originally Posted by Noa Drake

Ok,that is usefull info on what would happen ouside the mass, but what behaviour or change does the spacetime inside the atom show ?

It should be remarked that the magnitude of the curvature is very small. That's why we don't observe it directly in everyday life. Also, curvature manifests itself as tidal effects whose magnitude increases with separation distance. Thus, over the size of an atom, the curvature due to external gravitation (the gravitation from the mass as a whole) has virtually no effect on the atom.

Originally Posted by Noa Drake

Ok,that is usefull info on what would happen ouside the mass, but what behaviour or change does the spacetime inside the atom show ?

Also consider that an atom is largely "empty", in the sense that the probability density of finding an electron is close to zero in large regions of space-time around the nucleus. What happens in the small region of the nucleus itself is really quite complicated due to the quantum nature of the processes there, but what we can say without doubt is that gravity would play a vanishingly small role on such small scales, as compared to the other fundamental interactions.

Originally Posted by KJW

Originally Posted by KJW

Originally Posted by GiantEvil

And the strong equivalence principle states that these greater than test masses will still have identical velocities and trajectories to a test mass in an identical gravity field?

That's my understanding.

Actually, I answered too hastily. This is actually not correct. A test mass in orbit about a massive object will have a stable orbit (though elliptical orbits undergo perihelion precession), whereas a massive object in orbit about another massive object will have a decaying orbit due to the emission of gravitational radiation.

Yes, this correct

^So the article I linked is presenting a simplified and/or incomplete explanation?
My impression is that data is to be gathered to compare the equivalence principle to any potential Nordtvedt effect.

Originally Posted by GiantEvil

^So the article I linked is presenting a simplified and/or incomplete explanation?
My impression is that data is to be gathered to compare the equivalence principle to any potential Nordtvedt effect.

Yes, it is a test of the strong equivalence principle ( as opposed to just the weak one ). Note that the Nordtvedt effect is something which is predicted by a certain class of theories other than GR - if such an effect is found, that would mean that GR isn't the correct theory of gravitation. Hence the significance of this test.