Time dilation in a sphere

[Pugdaddy]

I am not sure if this is the proper place to ask this, but I am sure someone will direct me to the right place if this is not.

I was wondering what the mass and radius a spherical shell would need to be to significantly slow time inside the shell as opposed to outside the shell. Could such a shell be constructed to time travel into the future at any significant rate.

[ajb]

Forgetting general relativity for a moment, recall Newton's shell theorem, basically there is no gravity inside a spherical shell of matter.

 

This generalises to general relativity in the form of Birkhoff's theorem, which tell us that inside a spherical shell the space-time is Minkowski space-time. There are no closed time-like curves here or anything like that.

[swansont]

I am not sure if this is the proper place to ask this, but I am sure someone will direct me to the right place if this is not.

I was wondering what the mass and radius a spherical shell would need to be to significantly slow time inside the shell as opposed to outside the shell. Could such a shell be constructed to time travel into the future at any significant rate.

 

 

There are two ways to have time dilation: move fast, or be in a lower gravitational potential. There's no way to shield gravity, so you can't have the sharp transition between amounts of dilation that you describe. As ajb mentions, the shell itself does nothing. The mass has to be inside, not outside, of the sphere, like standing on a planet.

 

The rate at which time passes (fractional frequancy change of the clock), as compared to someone far away, would be GM/rc^2

(r is your distance from the center of the uniform sphere of mass M)

 

It won't be time travel per se, but someone deep in the well will have time pass more slowly, so you could have someone in the well and only have a year pass while far away, many years have passed. It would be more analogous to hibernation or science fiction hypersleep.

[Pugdaddy]

Thank you for your replies. Time travel maybe wasn't the right terminology, Slowing time inside the shell? Would the gravitational potential at all points inside the sphere be the same as on the surface of the shell? In which case time would pass the same inside the shell as on the surface?

[ajb]

Inside the shell the space-time in the standard Minkowski space-time. There are no interesting gravitational effects inside the shell. It is as if the shell were not there at all.

[Delta1212]

Which would mean time would actually pass more quickly inside of a shell than on the outside surface, wouldn't it?

[swansont]

Which would mean time would actually pass more quickly inside of a shell than on the outside surface, wouldn't it?

 

 

 

No. You would be at the same potential as at the surface, and the potential is the important term for time dilation. There's no gradient of the potential, and thus no force, on the inside.

[Pugdaddy]

I guess the only advantage would be that on a very massive shell, there would be no acceleration or tidal forces inside to squash or pinch you.

[J.C.MacSwell]

Inside the shell the space-time in the standard Minkowski space-time. There are no interesting gravitational effects inside the shell. It is as if the shell were not there at all.

Except time slowing down, correct? And a mass decrease for anything inside? (compared to the same matter with no shell there)

[swansont]

Except time slowing down, correct? And a mass decrease for anything inside? (compared to the same matter with no shell there)

 

 

mass decrease?

[J.C.MacSwell]

 

 

mass decrease?

Isn't this something you made me aware of very recently?

 

Any matter inside is in more of a gravity well than it would be if the sphere wasn't there. The gravity may cancel out, but it is still there.

 

It's still "bottom of the mountain", even with the resultant gravity being essentially zero.

Edited March 17, 2016 by J.C.MacSwell

[swansont]

Isn't this something you made me aware of very recently?

 

Any matter inside is in more of a gravity well than it would be if the sphere wasn't there. The gravity may cancel out, but it is still there.

 

It's still "bottom of the mountain", even with the resultant gravity being essentially zero.

 

 

 

The potential inside is the same as the surface. Being inside doesn't change that.

[J.C.MacSwell]

 

 

 

The potential inside is the same as the surface. Being inside doesn't change that.

Same as the inside surface. Less than the outside surface. Both less than in free space.

 

Say you have 2 kg of lead and you divide it in half, then separate the two halves. You build the hollow sphere around one. Is it not less than 1kg? If it is still 1kg, drill a hole in the sphere and take it out and bring it to the other half. Can it now be more than 1 kg? It is still the same half.

Edited March 17, 2016 by J.C.MacSwell

[Endy0816]

Weight would change, mass wouldn't.

[swansont]

The potential inside is the same as at the surface. It takes the same amount of energy to move them infinitely far away. It takes no net energy at all to move them about inside the shell.

[J.C.MacSwell]

The potential inside is the same as at the surface. It takes the same amount of energy to move them infinitely far away. It takes no net energy at all to move them about inside the shell.

Which surface? There's a gradient through the thickness of the shell.

 

The no shell case is same as infinitely far away...higher mass (for my example lead halves have a mass of 1 kg each...regardless of history)

Inside shell case is in a gravity well...lower mass (for example the half must be less than 1kg)

 

Let me know if any of that is incorrect.

 

I agree with the inside all being at the same potential.

 

How is this conceptual any different from your comment to the Nobel Prize Winner, about the mass of the electron being measured at the bottom or top of the mountain, or my Kg mass of lead moved to the moon from that same thread?

Edited March 17, 2016 by J.C.MacSwell

[swansont]

Which surface? There's a gradient through the thickness of the shell.

 

The no shell case is same as infinitely far away...higher mass (for my example lead halves have a mass of 1 kg each...regardless of history)

Inside shell case is in a gravity well...lower mass (for example the half must be less than 1kg)

 

Let me know if any of that is incorrect.

 

I agree with the inside all being at the same potential.

 

How is this conceptual any different from your comment to the Nobel Prize Winner, about the mass of the electron being measured at the bottom or top of the mountain, or my Kg mass of lead moved to the moon from that same thread?

 

 

If we've gone this far with an idealized thought experiment, I think we get to assume an infinitely thin shell.

 

Bottom or top of the mountain have different potentials. That's why the mass is different.

[J.C.MacSwell]

 

 

If we've gone this far with an idealized thought experiment, I think we get to assume an infinitely thin shell.

 

Bottom or top of the mountain have different potentials. That's why the mass is different.

Fair enough, but a shell massive enough to create a time dilation...so massive enough to affect the mass measurement, at or in the shell vs at infinite or in free space further from the shell. Different potentials, so the mass is different.

Edited March 17, 2016 by J.C.MacSwell

[Pugdaddy]

My original thought was that time slows close to a massive object. The more massive, the larger the gravitational gradient in the vicinity of the object. An object massive enough to slow time any appreciable amount would have a gradient sufficient to stretch and compress anything into strings of spaghetti as it approached the object. But if the object was a spherical shell, something or someone could exist inside the hollow sphere experiencing the time dilation and avoiding the tidal forces that would be present/deadly outside the shell. You would probably need to place the object/person inside the shell and then increase the mass of the shell or else I don't see how else to get inside once the mass was sufficient enough to have a significant time dilation. And then remove the mass to get them out.

[bluescience]

What you could do is have an extremely, extremely, extremely, extremely dense ball or sphere of matter, as dense as the massive black hole that exist at the center of our galaxy.

 

If we could orbit that sphere, Hawking says that a black hole that massive would be able to "slow" time by half for the people orbiting this dense black hole.

So five years for the orbiters would be 10 for people on the earth. So i do not know if that answers your question, However it is possible that we could use something of great mass as a time travel machine, since the people orbiting could come back with earth having gone through twice as much time as the orbiters

 

With the principle of equivalency, we could also use something that is accelerating near the speed of light for time travel. We coulf build a form of transportation, such as a train that would go around the planet at 0.999 the speed of light and the travellers inside would experience time at a much slower place than the people outside of the train. When the people riding the train would stop and come out they would technically have lived longer than possible to see the future.

 

On the matter of travelling back in time, I think i agree with Stephen Hawking that it is impossible, since time paradox's would deem it so.

Edited April 18, 2016 by bluescience