A puzzle on a Faraday cage "eating up" information

[Happiness]

Imagine an uncharged solid spherical conductor. Inside this spherical conductor, there is a cavity of a weird shape carved out of it. And somewhere inside this cavity, there is a charge +q.

The charge +q induces an opposite charge -q on the wall of the cavity of the conductor, which distributes itself in a such way that its electric field cancels out that of +q for all points exterior to the cavity. Since the conductor carries no charge, this leaves +q to distribute itself uniformly over the surface of the sphere.

The information about the shape and the location of the cavity seems to be lost, so does the information about the location and distribution of the charge +q within the cavity. I find this rather unsatisfying, unacceptable to my intuition. Is there a way to figure out the shape and the location of the cavity and of the charge without "cutting open" the conductor? I would have intuited that the charge distribution on the outer surface of the conductor should not be uniform and that one should be able to deduce the information about the cavity and about the charge within it from any asymmetry in the charge distribution on the outer surface. But apparently this is not true, so what is wrong about this intuition? In clearer words, what must I believe to be true for me to have such an intuition? I am thinking, roughly speaking, that information cannot be destroyed and should, in principle, be retrievable, even though the process of retrieving it (such as the measurement or calculation) may be very difficult in practice. But physics is seemingly now saying that the information is not retrievable even in principle and is forever lost to no where and for no reason.

 

[Nugatory]

I find this rather unsatisfying, unacceptable to my intuition.

You'll find plenty of other examples. For example... Have you noticed that the radius of the sun doesn't appear in any of the solutions of planetary motion? All spherically symmetric distributions of the mass of the sun yield the exact same orbits for objects outside the surface of the sun, and therefore the information about the distribution of mass within the sun is hidden from us if we limit ourself to observing gravitational effects. On the other hand, that information is not "destroyed"; we can and do figure it out through other means such as direct visual observation. Likewise, the external electrical field doesn't tell you anything about the internal structure of your conductor, but other techniques (ultrasound? X-rays?) do, so no information is destroyed - you just have to look for it the right way.

Of course irreversible processes routinely destroy information. Write a message on a piece of paper, then burn the paper... the information on the paper is gone forever.

 

[rumborak]

I think a distinction must be made between actual destruction of information, and the simple occlusion of it. In the OP example, the information is still there (go inside the sphere, and you can distinctly retrieve the existence of the charge), it's just occluded to the outside. I mean, it's really no different than not being able to see the sun behind a pillar. The information about the existence of the sun didn't really get destroyed; somebody else just "consumed" it (here, the pillar) and transformed it into something (heat) you can't easily use to retrieve the original information.
Similarly, in your scenario being outside the sphere means you're standing in the "shadow" of that sphere. The sphere "knows" very well of the existence of the charge, and thus the information is fully alive.

 

[Happiness]

I think a distinction must be made between actual destruction of information, and the simple occlusion of it. In the OP example, the information is still there (go inside the sphere, and you can distinctly retrieve the existence of the charge), it's just occluded to the outside. I mean, it's really no different than not being able to see the sun behind a pillar. The information about the existence of the sun didn't really get destroyed; somebody else just "consumed" it (here, the pillar) and transformed it into something (heat) you can't easily use to retrieve the original information.
Similarly, in your scenario being outside the sphere means you're standing in the "shadow" of that sphere. The sphere "knows" very well of the existence of the charge, and thus the information is fully alive.

I find the idea that information may be "perfectly" occluded similarly discomforting. I would rather believe that there must exist some way to retrieve the information without having to "go inside" the sphere. If information can be perfectly occluded, then a sphere with a cavity inside it looks exactly the same from the outside in every way as one without any cavity. So to someone without any knowledge about the existence of the cavity, he would not have any motivation to suspect and to "go inside" the sphere. That would mean that the detection of the cavity will only happen randomly, by chance, when someone decides to "cut it open" out of the blue one day. In that sense, I find the distinction between the actual destruction of information and the "perfect" occlusion of it rather repulsive, even heretic. Or if you insist, the distinction is only "conceptual"; it must be a law of physics that the actual destruction of information is equivalent to the "perfect" occlusion of it. But that just makes things more confusing than if we just say: there is no such thing as a perfect occlusion.

 

[phinds]

I find the idea that information may be "perfectly" occluded similarly discomforting. I would rather believe that there must exist some way to retrieve the information without having to "go inside" the sphere. If information can be perfectly occluded, then a sphere with a cavity inside it looks exactly the same from the outside in every way as one without any cavity. So to someone without any knowledge about the existence of the cavity, he would not have any motivation to suspect and to "go inside" the sphere. That would mean that the detection of the cavity will only happen randomly, by chance, when someone decides to "cut it open" out of the blue one day. In that sense, I find the distinction between the actual destruction of information and the "perfect" occlusion of it rather repulsive, even heretic. Or if you insist, the distinction is only "conceptual"; it must be a law of physics that the actual destruction of information is equivalent to the "perfect" occlusion of it. But that just makes things more confusing than if we just say: there is no such thing as a perfect occlusion.

In the case of your example, it would be impossible to totally hide the information about the shape of the inside since it can be retrieved from the outside in any number of ways. On the other hand if there are no possible tests that could be performed from the outside of something to discern something about the inside, then what difference does it make? That is, information that really is unobtainable and does not show up on any tests is irrelevant.

If you care about the inside and think there might be something there that does not show up from the outside, then yeah, you're going to have to go inside. I don't get why that's an issue.

 

[rumborak]

@Happiness I think I would agree with you if there was a way to *completely* destroy any evidence of a charge. Likely, completely destroy, not just mangle it into a high-entropy jumble (called heat) or just shadow it.
But neither of these scenarios qualify; your scenario has all the information alive inside the sphere.

EDIT: Are you aware of Dyson Spheres? Do you have the same fundamental objection to Dyson Spheres in that they totally cover the information about the sun inside?

 

[Happiness]

In the case of your example, it would be impossible to totally hide the information about the shape of the inside since it can be retrieved from the outside in any number of ways. On the other hand if there are no possible tests that could be performed from the outside of something to discern something about the inside, then what difference does it make? That is, information that really is unobtainable and does not show up on any tests is irrelevant.

If you care about the inside and think there might be something there that does not show up from the outside, then yeah, you're going to have to go inside. I don't get why that's an issue.

I mean I believe that information, however small, have to "leak out". There cannot exist a seal or a wall or a shield that perfectly blocks the "broadcast" of information to the outside such that if you do not detect such information from the outside, you can, in principle, be 100% sure that the cavity or whatever anomaly is not present inside.

 

[rumborak]

Why? That, no offense to you, sounds like you're postulating your intuition as law.

But, on a completely theoretical level, because of invariable heat-related movements of charges and such, even the Faraday cage will never be perfect. It takes time for the charges to settle in the equilibrium that counteracts the internal charges. So, there will actually be information about leaking to the outside, but at a vastly attenuated level.

 

[Happiness]

@Happiness
EDIT: Are you aware of Dyson Spheres? Do you have the same fundamental objection to Dyson Spheres in that they totally cover the information about the sun inside?

I'm not aware. Are they structures built around a star to capture all of its energy? I believe you can capture most but not all the energy.

Why? That, no offense to you, sounds like you're postulating your intuition as law.

I guess it's because I believe all places in the universe are "connected" in some way.

 

[Drakkith]

I guess it's because I believe all places in the universe are "connected" in some way.

That's nice. I believe that this thread is now locked since we don't discuss personal beliefs or non-mainstream science.