Space-time relativity.

[Physics]

If we think about the space-time relativity graph we of course notice the increase in distortion of space as you get closer to a mass, what happens to space once you penetrate the surface of the mass though? Does the gravity increase or decrease and why?

I would think it would decrease at an increasing rate as you get closer to the center of the object as you have the gravity of the mass behind you working in competition of the mass in front of you.

[Pebble]

To rephrase the question:

Is the volume of a hydrogen atom (nucleus plus orbiting electron) larger or smaller were it in the centre rather than on the surface of the sun - if one could ignore the effects of pressure and temperature. I have no idea!

[Trinoc]

If we think about the space-time relativity graph we of course notice the increase in distortion of space as you get closer to a mass, what happens to space once you penetrate the surface of the mass though? Does the gravity increase or decrease and why?

I would think it would decrease at an increasing rate as you get closer to the center of the object as you have the gravity of the mass behind you working in competition of the mass in front of you.
The gravity inside of a hollow, uniform sphere is zero everywhere. Therefore, if you go below the surface of (say) the Earth, you can think of the gravity affecting you as made up of two parts: (1) That from the mass further out than where you are, which is zero because it is a hollow sphere; and (2) That from the mass closer to the centre from you, which is effectively a smaller planet than the Earth. If the Earth was uniform density all the way down, the gravity would go down linearly, reaching zero at the centre and then increasing in the opposite direction as you climbed up to the opposite side. In practice, the layers of the Earth are not of uniform density, so the gravity actually increases for a while as you go down towards the core. By the time you reach the centre, however, it is always zero. This is just Newtonian gravity - no relativity required.

Regarding your other question about hydrogen in the Sun ... It is not the actual gravity at the centre that compresses it to fusion pressures, but the pressure of all the gas weighing down from above. The actual gravity at the centre is zero as in the case of the Earth.

A hydrogen atom being a quantum entity, it does not gradually get smaller under increasing pressure. The electron cannot occupy an orbital lower than the "ground state". Since the Sun is so hot, there are no actual hydrogen atoms anyway in the core, but just a plasma of protons and electrons. Once the pressure and temperature get high enough the protons can approach each other fast enough to overcome electrostatic repulsion and get close enough to stick with the strong nuclear force, and through a series of stages produce helium and heavier elements.

[Tim the Mage]

If we think about the space-time relativity graph


I'm trying but....

Nope, I can't do this. And isn't the Earth flat any way?

[Physics]

The gravity inside of a hollow, uniform sphere is zero everywhere. Therefore, if you go below the surface of (say) the Earth, you can think of the gravity affecting you as made up of two parts: (1) That from the mass further out than where you are, which is zero because it is a hollow sphere; and (2) That from the mass closer to the centre from you, which is effectively a smaller planet than the Earth. If the Earth was uniform density all the way down, the gravity would go down linearly, reaching zero at the centre and then increasing in the opposite direction as you climbed up to the opposite side. In practice, the layers of the Earth are not of uniform density, so the gravity actually increases for a while as you go down towards the core. By the time you reach the centre, however, it is always zero. This is just Newtonian gravity - no relativity required.

Ahh yes, going into the details of that the mass you have passed would not be canceled out by the gravity of the mass on the opposite side of the object as you are closer to the mass you have passed, making it's pull stronger. So the gravity of the 'smaller planet' as you say would be even weaker?

And yes you're right, Newtonian gravity, didn't think that one through. I'm wondering how you complete a space x gravity graph showing what happens through an object effectively.


Regarding your other question about hydrogen in the Sun ... It is not the actual gravity at the centre that compresses it to fusion pressures, but the pressure of all the gas weighing down from above. The actual gravity at the centre is zero as in the case of the Earth.

A hydrogen atom being a quantum entity, it does not gradually get smaller under increasing pressure. The electron cannot occupy an orbital lower than the "ground state". Since the Sun is so hot, there are no actual hydrogen atoms anyway in the core, but just a plasma of protons and electrons. Once the pressure and temperature get high enough the protons can approach each other fast enough to overcome electrostatic repulsion and get close enough to stick with the strong nuclear force, and through a series of stages produce helium and heavier elements.

Your conclusion is quite correct, but quantum particles have no mass according to the Standard Model theory so the space they are present in also compresses (along with the space between atoms) under increasing pressure, so making the atom smaller. I think. If you think I'm wrong ask Pebble, he understands this better than I do.

EDIT: I'm just wondering about the theory of this, not the practicalities, so let's assume the object is a sphere and has constant density throughout.

[Pebble]

Regarding your other question about hydrogen in the Sun ... It is not the actual gravity at the centre that compresses it to fusion pressures, but the pressure of all the gas weighing down from above. The actual gravity at the centre is zero as in the case of the Earth.

A hydrogen atom being a quantum entity, it does not gradually get smaller under increasing pressure. The electron cannot occupy an orbital lower than the "ground state". Since the Sun is so hot, there are no actual hydrogen atoms anyway in the core, but just a plasma of protons and electrons. Once the pressure and temperature get high enough the protons can approach each other fast enough to overcome electrostatic repulsion and get close enough to stick with the strong nuclear force, and through a series of stages produce helium and heavier elements.

My assumption was that a fictional hydrogen atom occupies a certain amount of space, but gravity distorts space - hence presumably the apparent size of a fictional atom. Of course in reality pressure and temperature prevents anyone testing their model in respect of the question posed - however there must be some mathematical answer - even if I could not understand it.

[Trinoc]

Ahh yes, going into the details of that the mass you have passed would not be canceled out by the gravity of the mass on the opposite side of the object as you are closer to the mass you have passed, making it's pull stronger. So the gravity of the 'smaller planet' as you say would be even weaker?
Nope. I don't remember the maths, but it is a well-established fact that the gravity everywhere inside of a uniform hollow sphere is zero. The mass immediately above you may be closer, but there is a lot more mass pulling in the other direction. The effects cancel out exactly.

See http://en.wikipedia.org/wiki/Shell_theorem.

Also, the bending of space-time by gravity is tiny in any normal situation. The deflection at the surface of the Sun is about 1.75 arc seconds (http://en.wikipedia.org/wiki/Kepler_problem_in_general_relativity#Geodesic_equa tion) (1/2000 degree), and of course at the core of the Sun it is a lot less, becoming zero at the centre.

Regarding hydrogen (or any other) atoms. As much as size as we know it can be said to have any meaning at the quantum level, an atom of a particular element in a particular state always has the same size as seen from its own frame of reference. Relativity may cause it to appear to be distorted when viewed by an observer in rapid relative motion or in a different gravitational field, but the atom itself doesn't notice anything unusual about the situation.

[Physics]

Awesome, thanks for the link.

[Tomolac]

Relativity may cause it to appear to be distorted when viewed by an observer in rapid relative motion or in a different gravitational field, but the atom itself doesn't notice anything unusual about the situation.
gravity works down to the atomic level but no further than that.

Is the volume of a hydrogen atom (nucleus plus orbiting electron) larger or smaller were it in the centre rather than on the surface of the sun - if one could ignore the effects of pressure and temperature.
an atoms volume cannot change.
each atom has a mass, and when you try to;

penetrate the surface of the mass
you get a reaction, you know, a nuclear one.
gravity is affect by mass and density, and mass is effected by velocity and energy.
so as a atom travels to the centre of an object its mass will increase but only due to its motion.

[Trinoc]

gravity works down to the atomic level but no further than that.
Is that known? I thought gravity had only been measured down to millimetre distances, and even then without much accuracy. I've seen suggestions that some of the "extra dimensions" could possibly be as large as a fair fraction of a millimetre without affecting the inverse square law at any scale that we can measure. This would allow the possibility of quantum black holes with much smaller masses than the Planck mass believed necessary at the moment (and hence a lot of fools who believe the LHC will drop one and it will eat up the Earth).


an atoms volume cannot change
Doesn't promoting an electron to a higher energy level increase the effective size of the atom?*

Also, when an atom is cooled down to a ridiculously low temperature the uncertainty in its position becomes greater than the distance to the next atom, and a Bose-Einstein Condensate can form where there are no distinct boundaries between atoms.

[* Just thinking about this a bit ... shouldn't a higher-energy electron have a smaller uncertainty in position, and so be in effect closer to the nucleus? I don't think this is what happens, though.]

[Tomolac]

Is that known? I thought gravity had only been measured down to millimetre distances, and even then without much accuracy. I've seen suggestions that some of the "extra dimensions" could possibly be as large as a fair fraction of a millimetre without affecting the inverse square law at any scale that we can measure. This would allow the possibility of quantum black holes with much smaller masses than the Planck mass believed necessary at the moment (and hence a lot of fools who believe the LHC will drop one and it will eat up the Earth).
possibly, all I know is that the rules governing our world of particles are not the same rules that govern their atoms, but I don't know where the two intersect.

Doesn't promoting an electron to a higher energy level increase the effective size of the atom?*

Also, when an atom is cooled down to a ridiculously low temperature the uncertainty in its position becomes greater than the distance to the next atom, and a Bose-Einstein Condensate can form where there are no distinct boundaries between atoms.

[* Just thinking about this a bit ... shouldn't a higher-energy electron have a smaller uncertainty in position, and so be in effect closer to the nucleus? I don't think this is what happens, though.]
yes I think I may not have been entirely accurate with my statement, so this is the better answer to pebbles rephrase :smiley:

To rephrase the question:

Is the volume of a hydrogen atom (nucleus plus orbiting electron) larger or smaller were it in the centre rather than on the surface of the sun - if one could ignore the effects of pressure and temperature.

[Pebble]

I had regarded the notion of gravity being zero at the centre of planets as being a Newtonian concept. I am unaware of what the situation would be under general relativity, so input welcome.

In terms of the high pressures at the centre of a large mass, why? Is it because too much mass is crammed into too little space, perhaps as a result of temperature? Even if this were true, why must it be greatest near the centre rather than equally great wherever one measures below the surface? Is it because gravity actually increases toward the centre?

[Trinoc]

I had regarded the notion of gravity being zero at the centre of planets as being a Newtonian concept. I am unaware of what the situation would be under general relativity, so input welcome.

In terms of the high pressures at the centre of a large mass, why? Is it because too much mass is crammed into too little space, perhaps as a result of temperature? Even if this were true, why must it be greatest near the centre rather than equally great wherever one measures below the surface? Is it because gravity actually increases toward the centre?
Gravity is zero at the centre (assuming the sphere as a whole is in free fall) due to simple symmetry - which way would the gravity pull? I think this argument applies equally well to General Relativity as to Newtonian gravity.

Pressure is simply due to the weight of matter above. The bits near the centre might have very little weight of their own, but they are still pushed down by the weight of everything further out. I'm sure a fairly simple integral of weight over radius, assuming a uniform sphere, would give a good first approximation to the pressure - but my brain doesn't feel up to the maths right now.

[Pebble]

Gravity is zero at the centre (assuming the sphere as a whole is in free fall) due to simple symmetry - which way would the gravity pull? I think this argument applies equally well to General Relativity as to Newtonian gravity.

Pressure is simply due to the weight of matter above. The bits near the centre might have very little weight of their own, but they are still pushed down by the weight of everything further out. I'm sure a fairly simple integral of weight over radius, assuming a uniform sphere, would give a good first approximation to the pressure - but my brain doesn't feel up to the maths right now.

Now it is this notion of weight above that gets me. Weight = mass x force, the latter being gravity. If at the centre g=0, then weight there should be zero. But pressure = force, created by gravity. So the pressure i.e. gravity generated force is massive, but the weight gravity generated force is zero at the same time and place!

[niggle]

an atoms volume cannot change

The radius of an atom isn't constant and atoms don't have a defined boundary which would yield a measurement.


Doesn't promoting an electron to a higher energy level increase the effective size of the atom?

Actually having more electrons in a period decreases the radius of the atom because the effective charge increases. There are 3 factors which affect the radius: the shells, the charge and the shielding. Broadly, atoms get smaller the further right you go in the periodic table.

[Trinoc]

Now it is this notion of weight above that gets me. Weight = mass x force, the latter being gravity. If at the centre g=0, then weight there should be zero. But pressure = force, created by gravity. So the pressure i.e. gravity generated force is massive, but the weight gravity generated force is zero at the same time and place!
Weight is mass x acceleration due to gravity, not mass x force (though I think that is what you meant). The matter at the exact centre has no weight, but everything above does, and this weight presses down towards the centre by mechanical forces between atoms/molecules of that matter. Just as when you compress the air in a bicycle pump, the end where the air exits feels the pressure even though you are only applying force at the plunger end.