Does Time Slow Down in a Deep Osmium Room?

[alpha_michi]

TL;DR Summary

Could you actually slow down time, when you are in a room that is made out of the densest material on the earth.

So my idea is: Let's say you are in a room, that is 10km in the ground (so its closer to the center of gravity of earth) and made of Osmium.
Could it be that the room, because of its mass, actually bends the space time with the Earth's help more so time could be running slower for you?

If it is indeed possible or worth thinking about, please let me know I want to calculate the time delay in there.

 

[PeroK]

I don't see anything in your idea that would make much difference. You can have differential ageing between someone living on the top floor and someone living in the basement, but it's a negligible difference.

 

[alpha_michi]

I don't see anything in your idea that would make much difference. You can have differential ageing between someone living on the top floor and someone living in the basement, but it's a negligible difference.

I see. But its just the Earth's gravity for them. So if you go closer to the gravity plus the huge mass of the material the room is made of, could that have a noticeable differance?

 

[PeroK]

I see. But its just the Earth's gravity for them. So if you go closer to the gravity plus the huge mass of the material the room is made of, could that have a noticeable differance?

A room made of osmium is not going to give you much in the way of spacetime curvature.

 

[alpha_michi]

A room made of osmium is not going to give you much in the way of spacetime curvature.

And what if we had a material that could be dense enough, that we just didn't discover yet or is on other planets close to us. Could it be possible then?

 

[phinds]

(so its closer to the center of gravity of earth)

Which would DECREASE the gravity in the room and make time move slightly faster than on the surface of the Earth. Do you not understand how gravity works? Google the Shell Theorem.

 

[phinds]

And what if we had a material that could be dense enough, that we just didn't discover yet or is on other planets close to us. Could it be possible then?

If you were able to use the material from a neutron star (you CAN'T) it would be the heaviest material we know of but it would just sink to the center of the Earth, and since you are inside it, the Shell Theorem would ruin your plan. If you were in a box made of the stuff and in outer space so you didn't sink to the center of the Earth, the Shell Theorem would STILL ruin your party (*).

Give up while you are behind. Move on and study some actual physics.

* Actually, you'd be squashed to a paste in a square cubical container of neutron star material and while the Shell Theorem would still apply, in a distorted way, you wouldn't be around to worry about it ruining your plans.

 

[PeroK]

And what if we had a material that could be dense enough, that we just didn't discover yet or is on other planets close to us. Could it be possible then?

A neutron star would give you the mass and density, but then you'd be crushed if you sat on one!

 

[alpha_michi]

Which would DECREASE the gravity in the room and make time move slightly faster than on the surface of the Earth. Do you not understand how gravity works? Google the Shell Theorem.

Ok didn't knwo that. Thank you for that.

 

[Bandersnatch]

Which would DECREASE the gravity in the room and make time move slightly faster than on the surface of the Earth. Do you not understand how gravity works? Google the Shell Theorem.

The gravity would decrease, but gravitational time dilation depends on how deep in the potential well you are, not on the magnitude of gravitational acceleration.

 

[alpha_michi]

If you were able to use the material from a neutron star (you CAN'T) it would be the heaviest material we know of but it would just sink to the center of the Earth, and since you are inside it, the Shell Theorem would ruin your plan. If you were in a box made of the stuff and in outer space so you didn't sink to the center of the Earth, the Shell Theorem would STILL ruin your party (*).

Give up while you are behind. Move on and study some actual physics.

* Actually, you'd be squashed to a paste in a square cubical container of neutron star material and while the Shell Theorem would still apply, in a distorted way, you wouldn't be around to worry about it ruining your plans.

I will, this was just a random idea I got. Just wanted to see if it was worth it.

 

[PeterDonis]

Which would DECREASE the gravity in the room and make time move slightly faster than on the surface of the Earth. Do you not understand how gravity works? Google the Shell Theorem.

Unfortunately I do not think the Shell Theorem can be validly applied to this problem. See below.

The gravity would decrease, but gravitational time dilation depends on how deep in the potential well you are, not on the magnitude of gravitational acceleration.

I don't think the gravity would decrease inside the room.

First, as I said above, I don't think the Shell Theorem applies to this problem. The Shell Theorem says that a spherically symmetric distribution of matter and energy outside some spherical shell has zero effect on the spacetime geometry inside the shell. If our "room" is a spherical shell 10 km deep inside the Earth, the distribution of matter and energy outside it is not spherically symmetric; it is skewed towards the Earth's center. So the Shell Theorem does not apply.

(Another way to see that it can't apply is to note that, if it did apply, it would predict that, in the absence of any gravitating masses inside the shell, spacetime would be flat there. Flat means zero gravity, not just decreased gravity; in other words, if you excavated a spherical chamber 10 km underground, the Shell Theorem, if it applied, would say you could float in it in free-fall. If this were actually true, then, for example, miners in deep mine chambers should at least notice a significant drop in gravity, and they don't.)

I think a sort of generalized "Shell Theorem" could be applied to this case, but the generalized theorem would say, basically, that a spherical shell in a gravitational field has zero effect on either the gravitational potential (this part would be the same as the standard Shell Theorem--see further comments below) or the "acceleration due to gravity" inside the shell. In simple Newtonian terms, the "gravitational pull" of all the parts of the room on any object inside the room, when summed, would cancel out, leaving only the "gravitational pull" due to the Earth that was there in the first place.

As far as gravitational potential and "rate of time flow" is concerned, the standard Shell Theorem already says that the shell has zero effect on the gravitational potential inside it; and, as noted above, I would expect any generalization of it that applied to this problem to say the same thing. So clocks inside the room would go at the same rate as clocks just outside the room.

Note that all of the above applies regardless of what the room's walls are made of. A room with neutronium walls inside a neutron star would behave the same as a room with osmium walls (or walls of any other substance found on Earth) 10 km deep inside the Earth.

 

[PeterDonis]

Moderator's note: Thread level changed to "I".

 

[Bandersnatch]

I don't think the gravity would decrease inside the room.

That bit was referring specificallly to placing the room deeper underground, not building a dense room.

 

[PeterDonis]

That bit was referring specificallly to placing the room deeper underground

Ah, ok. For a constant density sphere, yes, gravity would decrease as you go down. For our actual Earth, because of the density profile, the gravity actually increases until you reach the outer core, which is about 3000 km down.

 

[phinds]

I will, this was just a random idea I got. Just wanted to see if it was worth it.

Not really a great idea on this forum to just throw stuff against the wall to see what will stick. You need to be sure you understand the fundamentals of what you are talking about first. I advise you to concentrate on actual science, not random ideas.

 

[Orodruin]

Which would DECREASE the gravity in the room and make time move slightly faster than on the surface of the Earth. Do you not understand how gravity works? Google the Shell Theorem.

That’s not how gravitational time dilation works. It is dependent on gravitational potential, not gravitational acceleration.

 

[pervect]

I'm not familiar with exactly what would happen in a cubical room - it would take some calculation before I'd hazard a guess. But I'm not sure there is that much interest in the shape of the room with regards to the question to be worth the work it'd take to do the rather messy numerical calculation. Essentinally one would use potential theory to calculate the potential inside the cubical room, and get the tidal forces from the spatial derivatives of the potential. But see also the latter comments about the optimum shapes.

Theoretically inside a spherical room, one would indeed have differential aging between the interior of the room and the exterior of the room, and there'd be no net force on anyone in the interior of the room. There would be the usual gravitation in the exterior of the room. The comparison that is easiest to make is the comparison between someone in the interior of the room, and someone a long distance away from it.

However, the effect on differential aging is proportional to the total mass that one is surrounded by. This means that if the total mass of the room is less than the mass of the Earth, the effect of the room itself would be lower than the effect of the Earth.

To exceed the effect of being in the center of the Earth, one would need a room that massed more than the Earth itself.

There are definitely practical problems with trying to find a room strong enough to keep it's shape just at the center of the Earth, much less anything bigger. Wiki gives the pressure in the center of the Earth as 3 million atmospheres, so one would need a pressure vessel that could survive that sort of pressure without being crushed. We have certainly made strong pressure vessels to descend deep into the ocean, but I doubt they'd be strong enough to remain intact at the center of the Earth. I haven't done any calculations, though.

It's also worth noting that the deep diving submersibles we have made have spherical crew compartments. This is because the spherical shape is optimum for strength. There's a reason pressure vessels are not square boxes, stresses at the corners of the box are very high, and tend to cause early structual failure.

 

[phinds]

That’s not how gravitational time dilation works. It is dependent on gravitational potential, not gravitational acceleration.

So you are saying that time dilation is NOT different from inside the Earth than from on the surface. Doesn't seem right to me. If it's different 1000 Km above the Earth than on the Earth, why is it not different 1000 Km below the surface than on the surface ?

I'm pretending here that the Earth is a perfect sphere.

 

[Orodruin]

So you are saying that time dilation is NOT different from inside the Earth than from on the surface. Doesn't seem right to me. If it's different 1000 Km above the Earth than on the Earth, why is it not different 1000 Km below the surface than on the surface ?

No. The gravitational porential is lower at the center than at the surface so time runs faster on the surface than it does at the core.

 

[PeterDonis]

Theoretically inside a spherical room, one would indeed have differential aging between the interior of the room and the exterior of the room, and there'd be no net force on anyone in the interior of the room. There would be the usual gravitation in the exterior of the room. The comparison that is easiest to make is the comparison between someone in the interior of the room, and someone a long distance away from it.

However, the effect on differential aging is proportional to the total mass that one is surrounded by.

I don't think these statements are correct for this scenario. See my post #12.

 

[Janus]

Theoretically inside a spherical room, one would indeed have differential aging between the interior of the room and the exterior of the room, and there'd be no net force on anyone in the interior of the room. There would be the usual gravitation in the exterior of the room. The comparison that is easiest to make is the comparison between someone in the interior of the room, and someone a long distance away from it.

This is dependent on the thickness of the walls. With thick walls, there will be some difference between inside and outside time dilation. The thinner the walls are, even without changing their total mass, the less the difference. This tends to zero difference as the wall thickness approaches zero.

 

[pervect]

I don't think these statements are correct for this scenario. See my post #12.

We seem to be talking about different scenarios. I am talking about a hollowed out space or room at the center of the Earth. The shell theorem would apply in that case I am considering. Possibly I misunderstood the OP's question.

If instead we considered a room not at the center of the Earth is a more complex question, and seems best avoided, especially since the goal is apparently for a scenario with a lot of differential aging. Having the location of the room at the center of the Earth maximizes the differential aging. To get more differential aging than at the center of the Earth, one would need a room more massive than the Earth.

 

[PeterDonis]

I am talking about a hollowed out space or room at the center of the Earth.

Ah, ok. I agree that if the spherical room is at the center of the Earth, there will be zero gravity inside it. However, it is still true that the potential everywhere inside the room will be the same as just outside it, assuming, as @Janus has pointed out, that the walls are of negligible thickness; there won't be any change in potential at the room's boundary. (The potential inside the room will, of course, be lower than at the Earth's surface.)

However, that scenario is not what the OP is talking about. The OP's room is at a depth of about 10 km beneath the Earth's surface. That's the scenario I was discussing in post #12.

 

[pervect]

Ah, you are right, I should read more carfefully.

 

[phinds]

No. The gravitational porential is lower at the center than at the surface so time runs faster on the surface than it does at the core.

So the gravitational potential at 1000Km above the Earth is less than that on the surface, thus making time run faster at the 1000Km mark.

And then (according to you) the gravitational potential at the center of the Earth is less than at the surface, thus making time run slower than on the surface, despite it also being at a lower gravitational potential.

I don't get it.

 

[PeterDonis]

the gravitational potential at 1000Km above the Earth is less than that on the surface

Actually, it's greater (less negative, i.e., greater).

I suggest rethinking the rest of your post with that in mind.

 

[phinds]

Actually, it's greater (less negative, i.e., greater).

I suggest rethinking the rest of your post with that in mind.

OK, I'm clearly confused. So, the farther from Earth, the greater the gravitational potential?

Of COURSE it is.

I kept wondering why the Frisbee seemed to be getting bigger as it got closer to me. And then it hit me!

 

[Vanadium 50]

This is turning messy.

The Earth is there to confuse you. Remove it.

If I have a hole in the center of a sphere, is the gravitational potential different inside the hole than outside the sphere? Of course it is. Now make the sphere a cube. That changes the numerical value, but nothing qualitative. Now make the walls thin. Voila! A room. The effect is smaller with thin walls, to be sure, but it's still there.

Now you can put it on the earth.

How big an effect will this be? Time dilation on the Earth is roughly the Swarzchild radius divided by the Earth's radius, or 10^-9. Because this goes as potential, it will be smaller by the room length divided by the Earth's radius, or another 10^-6. Let's assume the room walls weigh an enormous 600 tons, so there's another 10^-19. So the entire effect is one part in 10³⁴.

That's one septillionth of a second over the life of the universe.

 

[PeterDonis]

the farther from Earth, the greater the gravitational potential?

Yes. Potential at infinity is zero; as you go inward, it gets more negative, i.e., lesser.

 

[Orodruin]

So the gravitational potential at 1000Km above the Earth is less than that on the surface, thus making time run faster at the 1000Km mark.

No. The gravitational potential at 1000 km is larger. That’s why stuff gains kinetic energy as it falls.

And then (according to you) the gravitational potential at the center of the Earth is less than at the surface, thus making time run slower than on the surface

In exact analogy, yes.

despite it also being at a lower gravitational potential.

Because of, not despite.

 

[phinds]

No.

See post #28