Problems with Pocket Dimensions

I wanted to work on worldbuilding, but ended up realizing something more general.

Whether it’s pokeballs in Pokemon, sealing scrolls in Naruto, or any number of other ‘hammerspace’ or ‘pocket dimensions’ effects, the ability to store large objects inside a much smaller volume is a common trope in speculative fiction.

But it presents problems, if you want your setting to be consistent and systemic.

For my purposes, I will call these magic storage devices ‘capsules’, the act of storing things inside them ‘sealing’, and retrieving them ‘unsealing’.

Put briefly, if your (realistic) setting has magic capsules, then one of the follow must be true:

Capsules reduce volume, but not mass. Sealing a boulder in a capsule will not make it any lighter (and, technically, makes it heavier, since capsules probably themselves have mass)
Storing objects is merely a side effect, an implementation detail. Your setting actually has time machines. Every magic capsules can predict the future.
Capsules require energy to maintain their seal, and this energy draw is variable. If you record the variability, they function as potential energy detectors. (Oh, and it might still be a time machine.)
Stored objects are ‘cursed’ in a way I’ll describe below.
Capsules let you construct perpetual motion machines.

If not the mention of potential energy, then ‘perpetual motion’ probably clued you in to the gist of my argument. But I’ll elaborate anyway.

A simple scenario illustrates the problem. Go to a lake or stream, and seal a large volume of water into a capsule. Then, take the capsule to where you can unseal the water into the resevoir of a turbine. The flow of the water through the turbine will produce energy.

Here we come to the first fork. Since energy came out of the system, either that energy was created (violating energy conservation, easily getting you option E, perpetual motion), or that energy came from somewhere else. There are four places the energy could have come from.

The mechanical energy of transporting the capsule.
The sealing energy of storing the water.
The maintenance energy drawn from the capsule itself.
The unsealing energy required to release the water.

If it’s 0, then we have option A: capsules do not reduce mass.

In cases 1, 2, and 3, it’s important to recognize that the energy input must be proportional to the eventual potential energy. For instance, if sealing an object is simply very energetically expensive, or is proportional to the mass of the object, it’s not sufficient. Potential energy is determined by an object’s relation to other objects; a boulder ten meters above the surface of the moon has less potential energy than the same boulder ten meters above the surface of the earth, and the capsule doesn’t know where it’s going to be released. (I don’t think you can determine an object’s maximum potential energy just by looking at the object in itself, but I’d need someone who understands physics to confirm.)

Thus, if we’re assuming i) the energy requirements for sealing, carrying, and unsealing an object are low enough sealing is at all viable (why include magic storage if no one can actually use it?), and ii) magic capsules do not allow perpetual motion machines, then we’re left with one conclusion: sealing a boulder and carrying up a mountain takes more energy than sealing it and walking the same distance on level ground.

In case 0, it’s simply because the capsule has the boulder’s weight.

In case 1, the capsule knows whether you’re going to climb the mountain before you actually do. And if you commit to only climbing the mountain conditional on a certain future event occuring, then what amount of energy the seal requires tells you whether that event will occur.

In case 2, the capsule must be hooked up to a power source. And if you monitor that capsule’s power drawn, by construction it must (somehow) correlate to its potential energy. I’m having trouble convincing myself this entails time travel – sensing potential energy seems like it necessarily means sensing an object’s future path – but I can’t quite contrive a scenario to illustrate. Nevertheless, the idea of somehow sensing potential energy is spooky enough, I think.

Edit: Wait, I thought of something. Does it draw energy even if you fake it out? Say, if I seal a ton of water, then bring it to where I can release it into a resevoir, has the maintence energy already spiked? What if I never unseal it? Or, alternatively, does it still exact more energy to seal a boulder and walk up a mountain, then walk back down without unsealing? (Versus just remaining stationary.)

Actually – and apologies, this tangent is getting embarassingly stream of consciousness-ish – this isn’t so strange if we reframe it. Imagine the capsules work by shunting the object along a fourth axis, acting as a sort of anchor. Whenever the anchor (capsule) moves, it applies force to drag the object along with it. In this case, the capsule would no more be a violation of energy conservation (or causality) than cars or conveyor belts are.

Finally, case 3. A similar sort of reasoning to the above can be applied, where storing pushes an object into extradimensional space, and when unsealed, the object is at once pulled through that space, making the energy required proportional to the work needed to move the object from where it was sealed to where it is unsealed. This has odd knock-on effects, like delays in unsealing, or collisions in hyperdimensional space.

Otherwise, the unsealing process must magically determine how much energy is required to not violate conservation, potentially through past or future divination.

There is a fourth possibility, which entails stepping outside the frame we’ve used until now. Rather than requiring any special energy to seal, carry, or unseal, capsules could instead apply a special property to any object unsealed. It becomes “cursed”, and the curse represents the energy deficit. Removing the curse requires the same amount or more energy than was ultimately gained from unsealing the object. There’s a few ways you could handle this – the object is unsealable until the curse is removed, or the curse has some deleterious effects. An obvious choice is the curse leeches energy from the environment until balance is restored.

(Sidenote: there’s a last, insignificant wrinkle: the energy cost could be paid before the object is even sealed, via the energy required to create a capsule in the first place. This way, the more a capsule is used, the more it degrades. But I don’t think this seriously changes the analysis; you could just view the structural integrity of the capsule as a source of energy.)

And that, I think, is it. Five-ish consistent ways to handle the physics of magic capsules. Some of them, in my opinion, are far more workable than others.