Time Dilation Effects of Hypothetical Zero Gravity Pocket

[NMLevesque]

If you could create a small space on Earth in which a person could fit that was totally unaffected by gravity, or that was sheltered from the gravitational affects of external sources of gravity, what sort of affect on time dilation would be observed? Both for the person in the pocket, and for everyone else outside looking into it.
And as an aside question, what else would happen to the person in the pocket? E.g would they suddenly get flung into the air or what?

 

[WannabeNewton]

A simpler example is that of a spherically symmetric static configuration consisting of a thin shell of mass $M$ and radius $R$. The external space-time geometry will be Schwarzschild but the interior space-time geometry will be flat. This is a result of Birkhoff's theorem. An observer freely falling in the interior will just be hovering in place.

Now suppose a small hole is drilled through the shell so that an observer $O$ freely falling (i.e. hovering) at the center of the shell can access the outside universe by means of signals. A static observer in the external space-time geometry at some $r = r_E > R$ emits a photon that is received by $O$. Now the interior metric at the surface of the shell must agree with that of the exterior. Furthermore the interior itself is flat space-time as noted earlier hence

$\frac{\omega_{O}}{\omega_{E}} = \frac{\omega_{O}}{\omega_{R}}\frac{\omega_{R}}{\omega_{E}} \\= (1)\frac{(1 - 2M/r_E)^{1/2}}{(1 - 2M/R)^{1/2}} \\= (\frac{1-2M/r_E}{1 - 2M/R})^{1/2}$.

 

[NMLevesque]

A simpler example is

Tbh as a laymen I have no idea what most of your reply means, or what phenomenon you've just described. If you could explain it in somewhat plainer English I would be much obliged.

That being said I'll just briefly explain what I understood, hopefully that helps move the conversation forward. You've decided on a sphere as the shape of the aforementioned pocket, this has something to do with a particular theorem of relativity. Inside the spherical pocket spacetime is flat, as a result the observer within it hovers in place. Apparently a hole in the pocket is necessary for the observer inside to have access to the outside universe, and one happens to be drilled. Then an observer on the outside emits a particle of light, the inside observer detects it, and then I went from being kind of lost to being completely lost.

 

[pervect]

Time dilation is controlled not by gravity, but by gravitational potential. For instance, there is no gravity at the center of the Earth, but there is more time dilation there than there is on the Earth's surface.

There isn't any way to shield from gravity, but if you had a dense enough material, you could put a dense object over head to pull up and counteract gravity. Lead wouldn't be dense enough to manage this , you'd need something like white dwarf star densities.

You'd have to calculate the gravitational potential to be sure, but I suspect you'd find that you had more time dilation with the compensating mass present than you did without it.

 

[WannabeNewton]

Then an observer on the outside emits a particle of light, the inside observer detects it, and then I went from being kind of lost to being completely lost.

Yes and all I did was derive the gravitational blueshift between the observer inside the shell (where space-time is flat i.e. where there is a zero net gravitational field in a very loose sense-I won't go into the caveats of this) and the observer hovering outside of the shell (where there is space-time curvature i.e. there is some gravitational field). Gravitational time dilation is a straightforward consequence of the gravitational blueshift so that formula is what you seek for this very simple setup. You can find tons of reading material online on the relationship between gravitational time dilation and gravitational redshift/blueshift.

 

[NMLevesque]

Time dilation is controlled not by gravity, but by gravitational potential.

As far as I understand gravity creates gravitational potential, making that sort of a semantic difference as far as my question is concerned. I mean, if it wasn't wouldn't it be called gravitational potential time dilation?

There isn't any way to shield from gravity

Assume for the sake of my question that there is one. I'm not so much interested in how it would be possible to do so. Rather in the consequences of having done so on what human observers (one inside, one or more outside) would perceive due to time dilation.

 

[NMLevesque]

You can find tons of reading material online on the relationship between gravitational time dilation and gravitational redshift/blueshift.

I'm sure, but I kind of came here because I don't understand it. Maybe I wasn't very clear on exactly what sort of information I'm looking for. Just assume the pocket is possible, it's not an incidental fact of a spacetime peculiarity, it's as if gravity inside the pocket can be turned on and off with a switch. That's about all you need to assume for the sake of the question, I just want to know about the perception of human observers as a result of this (and possibly whether the person inside it would be flung around by the centrifugal force of the Earth with gravity 'off'). There's a laymen in the pocket, and a laymen outside it, they're both looking at each other, light and sound can be transmitted to and from both of them. What would they say to each when trying to explain what's different about how time appears to be passing where the other is?

 

[Dale]

Assume for the sake of my question that there is one.

We cannot do that. Since you have posted the question on physics forums then presumably you would like an answer based on the laws of physics, rather than fantasy or science fiction. Surely you can see that the laws of physics cannot be used to answer a question involving a violation of the laws of physics. That would be starting from a self-contradiction, which can then lead to literally any conclusion.

What we can do is answer a closely related question which is compatible with the laws of physics: the time dilation in the interior of a spherical shell of mass, i.e. a spherical ball of mass with a hole in the center. Inside such a shell the spacetime is flat and a person would "float" as though they were in deep space. However, signals from outside would be blueshifted based on the gravitational potential.

 

[Dale]

Just assume the pocket is possible, it's not an incidental fact of a spacetime peculiarity, it's as if gravity inside the pocket can be turned on and off with a switch.

This can be done. You cannot shield from gravity, but you can move mass around so that you go from curved to flat spacetime and back. Consider a spherical ball of matter which can quickly expand into a spherical shell filled with vacuum. A location outside the ball's radius and inside the shell's inner radius would go from being in curved spacetime to being in flat spacetime. The gravitational time dilation at that location would be determined by the potential on the inside of the shell.

 

[pervect]

As far as I understand gravity creates gravitational potential, making that sort of a semantic difference as far as my question is concerned. I mean, if it wasn't wouldn't it be called gravitational potential time dilation?

We may be talking past each other, I'm not sure if this can be rectified or not.

The derivative, or slope, of the (Newtonian) gravitational potential gives you "gravity". The example of an object at the center of the earth, or an object at the center of a hollow sphere, illustrates why the distinction is important. It has no "gravity" (in the Newtonian sense), but it has a lot of "gravitational time dilation". Thus if you are thinking of "gravity" as causing "time dilation" you will be confused by the fact that an object experiencing no "gravity" experiences a significant amount of gravitational time dilation.

I'd encourage you to try to think about this a little, and see if you can see my point, what I"m trying to communicate, focusing in particular by focusing on the example situtations I described.

I'm afraid I don't , at this point, see any other way of answering your question other than to repeat what I said, and if that doesn't make sense, it won't do much good to keep repeating it.

I'm afraid I also can't definitely answer why the literature uses the terms it does.

Assume for the sake of my question that there is one.

How? The theory basically makes certain assumptions, it's how the theory works. So the problem statement needs to be consistent with the theory.

It's impossible for a theory to make valid predictions about questions that aren't in the framework of the theory.

Distributions of matter are within the framework of the theory of general realtivity, I'll skip the exact technical language as I dont' think it'd be helpful.

If your idea about "shielding" can be described by a distribution of matter (as per my suggestion of a heavy, dense object overhead), then your question can be answered, in principle. If your question can't be put in the framework of the theory (i.e. by describing some distribution of matter as an input to the theory), it doesn't have an answer within the theory and it would be irresponsible of me to claim that it did.

Note that part of the theory is the "principle of equivalence". Part of the idea of the principle of equivalence is that gravity doesn't depend on the details of an objects construction, so that for instance in a vacuum, the rate at which an object falls doesn't depend on what it's made of. If your question requires matter that doesn't satisfy the principle of equivalence (example, the fictional Cavorite from the HG Wells novel), then it's not consistent with GR because it violates the principle of equivalence.

 

[A.T.]

Assume for the sake of my question that there is one.

Then you can also assume any answer you wish to your question.

 

[NMLevesque]

In response to all the comments saying that it's unreasonable to make my assumption for the sake of the question, seriously? I have to be honest that comes off as really anal retentive. As if theoretical physicists don't regularly just say, well what if this was that what would happen? I mean string theory for one, I just read an article on scientific american where someone basically went, well what if quantum entanglement was caused by wormholes for another. And einstein's tachyonic antitelephone, parallel universes, hell even dark energy. Scientists always wonder, well what if this rule or that is just wrong, or what if there's some ridiculous exception we never considered, and even well what if there was some completely undetectable thing that had exactly these qualities that could conveniently explain this. As though it's impossible to make an educated guess as to how a humans perception of time might be affected, it's not like I'm asking you for a concrete fact. It's a hypothetical, use your imagination, take chances, make mistakes, get messy!

 

[WannabeNewton]

I gave you a static physical system consisting of an infinitely thin spherical shell of mass in which the exterior has a non-vanishing gravitational field but the interior does have a vanishing gravitational field (up to a choice of gauge) and then derived the gravitational blueshift formula between an observer freely falling in the interior and an observer hovering in the exterior. It's a simple matter to then reinterpret the result in terms of gravitational time dilation. I have no idea what more you want really; you can't avoid the math if you want to understand physics not to mention the math involved in the aforementioned gravitational blueshift formula is very simple anyways.

 

[PAllen]

In response to all the comments saying that it's unreasonable to make my assumption for the sake of the question, seriously? I have to be honest that comes off as really anal retentive. As if theoretical physicists don't regularly just say, well what if this was that what would happen? I mean string theory for one, I just read an article on scientific american where someone basically went, well what if quantum entanglement was caused by wormholes for another. And einstein's tachyonic antitelephone, parallel universes, hell even dark energy. Scientists always wonder, well what if this rule or that is just wrong, or what if there's some ridiculous exception we never considered, and even well what if there was some completely undetectable thing that had exactly these qualities that could conveniently explain this. As though it's impossible to make an educated guess as to how a humans perception of time might be affected, it's not like I'm asking you for a concrete fact. It's a hypothetical, use your imagination, take chances, make mistakes, get messy!

Your assumption is undefined. You don't seem to know enough to define a physically useful "what if" question (e.g. not seeming to understand potential versus gravitational force in Newtonian physics). Physicists do play "what if games", but for them to be worth anyone's time (publishable anywhere) they start from some mathematical statement - a toy theory related to some real theory, a formally described type of matter that isn't known to exist, etc. This allows meaningful answers to the what if question. For example, there are many what if questions in GR relating to what you could do if you could arbitrarily manipulate matter with negative energy. No one has seen a lump of matter with negative energy, but it happens to be easily expressible in the equations of GR.

So, people have asked for clarification: gravity in GR is curvature of spacetime. Do you mean a pocket where curvature disappears? If so, you have been answered in detail by WannabeNewton and Pervect, because the inside of a spherical shell of matter is exactly such a case. Do you mean a pocket where the rest of the universe doesn't matter? Here no one can think if a way to even represent this in GR, other than perhaps you go off into your universe, and then the question is uninteresting - nothing can be said about.

Finally, if you did formulate speculative modification to GR, and asked people to do the work for you to figure out its consequences - then you would be violating the rules of this forum, which I hope you have read. In particular, these forums are specifically not the place to do "new physics".

 

[Vanadium 50]

I have to be honest that comes off as really anal retentive.

And we're done here. The OP has an answer. He may not like it, but he has it.