How can it be bigger on the inside

Question

We have these "magical" items everywhere in fiction; from the classic rabbit coming out of a hat illusion, to the TARDIS from Doctor Who, to Newest Magical Beast Newt Scamander Briefcase. These items all share same characteristic: a container with interior spaces that are much larger than they appear to be externally.

My question: Are there any possibilities of how this could be done based on science theorems and/or hypothesis?

To narrow things down I will set some rules:

1. A teleportation answer is not acceptable. The answer must take some form of a container, not Portal's hula-hoop like gate.

2. All item inside aren't just compressed, at least if we get inside we wouldn't feel that our body had been shrunk down.

3. Main question is about Volume differentiation. However you can try to answer the weight differentiation of the interior vs exterior, but its not necessary.

Bonus: If there exist possibilities, would there be some limit to the difference of the exterior volume vs the interior volume?

Can we put a portion of our universe with some galaxies inside a peanut size container?

Answer 1

In such matters, it's always helpful to scale things down to the familiar. So, imagine for a moment that you are a 2-dimensional being. You can move freely left or right, back or forward, but you have no conception at all of up or down. Then suppose that your house exists on a sheet of paper.

I, a three-dimensional being, can take that piece of paper and fold it several times. Each time its size halves, while at the same time having exactly the same surface area inside the folds.

By the time I've folded it several times, I can place it easily inside a small square in your 2-dimensional world. As long as I line up the entrances carefully, you can pass through a gap in the square and walk back and forth across the surface of the sheet of paper. Because it's folded through a dimension you have no access to, your perception is that the paper is bigger on the inside.

Answer 2

D&D's Bag of holding (and other spells & effects) describe the use of pocket dimensions to achieve this. Also see: Rope Trick. The bag does not compress or use a portal; the inside of the bag is an actual extradimensional and finite space with rigid boundaries. For the Bag of holding, these boundaries have some connection to the physical outside of the bag: If the bag is pierced, within or without, the bridge to the dimension disappears and you lose all your stuff forever.

Answer 3

I have done some thinking about making an “abcess” or “bleb” of folded spacetime on the far side of a throat that’s smaller than the room it contains.

I’ll illustrate using flatland. Draw a small circle. Inside that circle, push the flat sheet perpendicular to the plane, making a deep dent; continue stretching as if to make a wormhole. Then inflate the dead-end like blowing up a balloon.

The flatlanders outside the circle are not affected. Upon reaching the circle they find a tunnel to a room that’s “bigger on the inside”.

When I came up with this, I had been thinking that the throat could be shrunk to microscopic size and a submarine can be inside, providing miniaturization. Access to the outside world is through this throat, so I was speculating on how it would appear.

The “mass” is essentially screened, appearing (on the outside) as a constant mass of the wormhole stabilizing structure, or an apparent mass that being what would cause the same curvature of spacetime seen near the wormhole mouth.

That is, consider a normal wormhole, where you assume that the mouths can be moved independantly. If it’s the same for a wormhole leading to a pocket universe or a rented warehouse in this universe, moving the mouth does not make you drag around everything you have stored too.

So, I have a mechanism whose only purpose is to support the wormhole mouth and hold the door. It might look like a prehung door for sale at the hardware store, or might need more support equipment so it's like a small phone booth. You can move that around and it’s just the mass of the door and the mouth. But if you go through the door the warehouse at the far end holds a huge amount of mass.

Now just having a wormhole to a warehouse elsewhere is too mundane. Lead to a pocket universe, but keep the ability to move the two mouths independently and not pulling on the pocket universe space.

Answer 4

You can construct Einstein metrics which have the property of "Bigger on the Inside". For example

$$ ds^2 = -c^2 dt^2 + a(r)^2 \left( dr^2+r^2 d\theta^2+r^2 sin^2 \theta \, d\phi^2 \right)$$

with $a(r) =1 $ for $r > R$ and $a \gg 1$ for, $r < R$. If you calculate the volume inside a sphere of radius $R$ you will find a much greater volume than normal but a standard surface area.

You can calculate the Einstein tensor of this geometry to find the matter configuration needed to create this geometry (I believe it would violate certain energy conditions.)

Answer 5

Some theories about Space time I have heard imply that it can expand not only indefinitely (Big rip theory, which is that the universe never stops expanding), to being able to expand in such vast quantities that the spacetime between 2 objects, and hence the distance between them, can increase so that if both objects emmited light that went at C for eternity toward eachother, they would never meet (One of the theories about the Big Bang was that it became light years in diameter in at most a few seconds). It is common that Space time is not limited to things such as the speed of light, and even today we observe Redshift of galaxies that implies that light being sent from us now will never reach them because of the amount of space being created between us and them.

So what does all of this have to do with Hammerspace and the like? Its simple, Because space can theoretically expand like this, then the idea that we can selectively make it expand in a contained area is also not far fetched. There is no Teleportation or anything, Its just the physical space inside of a container has been forcefully expanded, and is contained in the container.

Of course, We are no where near technologically advanced enough to determine if this is actually possible, and what would actually happen to surrounding space time and the container if we tried, but so long as this is not a Hard Science universe, Hand wavium away.

Answer 6

The space is shrunk, but it doesn't seem like it.

Things in the container effectively are shrunk. But you don't feel shrinking nor does it look shrunk if you look inside. That's because everything including your hands and even light gets shrunk too. As the light exits the space, paths are bent in such a way that everything looks normally sized.

Answer 7

Take a page from String Theory

There are many flavours of String Theory. My favorite is called type IIB, for two reasons: it reminds me of a very lovely robot and it has a very creative quantum description of black holes.

In general relativity, a black hole is a body so dense that it has an event horizon: a region around it with an escape velocity greater than that of light. That necessitates a singularity at the center and creates more troubles for physics than it solves. You read enough about this, and you get ideas about wormholes, time travel and information paradoxes.

In IIB, a black hole is more properly described as a fuzzball. The whole of the black hole is its surface (the event horizon). There is no inside. From PBS Spacetime (one of my favorite shows) (also the emphasis below is mine):

As a fuzzball is forming, all of the matter - now dissolved into stringy mess, is pushed up to the surface and the interior grid of spacetime is deleted from the universe.

Funny thing: the reason why the fuzzball has, externally, all the same properties as your regular black hole is that it behaves kinda like an interiorless katamari: everything that touches it becomes part of it, including light. Unlike a katamari, though, it won't break if you hit it with any force at all.

IIB also stipulates that the universe has 10 dimensions (or branes), with four being time and space, and the other six being really compacted. These dimensions can be distorted just like the strings in them, which is what allows for the fuzzball to be a region of space with no inside.

Just the same, it is very theoretically possible to poke a hole into a fuzzball and then refill the space inside it. And the space inside can then become arbitrarily large, not being bound by the outside in any manner. You can also loop the branes inside. You can have a separate, possibly infinite universe in there if you mess around enough.

Now, regardless of what is inside, the outside will only ever notice the mass of the fuzzball itself (without the contents of the branes you put in)! Just the same, those inside will not notice anything from the universe outside. The only interaction between the inside and outside is through the aperture through which you inserted the branes. Close the gap, and you have two parallel universes.

The only thing you need now to avoid killing everyone in a very messy manner is to put some surface over the fuzzball so that people don't touch it, because remember: you touch it, you become part of it FOREVER. No, really: every string that makes the particles in your body gets disassembled and is absorbed by the more complex strings forming the fuzzball. There is no going back.

So in order to make Newt's suitcase, for example:

1. Make a microscopic black hole. For comparison, a coin-sized one might be as massive as the Earth. We are really talking microscopic here so it weights no more than a suitcase.
2. Contain it somehow (static, maybe? Black holes can have electric charge). Make the container look like a suitcase.
3. Poke a hole on the fuzzball. This is the magic part of this, as even string theory offers little help here (even though it kinda implies it is possible).
4. Insert some branes (i.e.: spacetime and other dimensions) into the hole.
5. Stretch the aperture of the fuzzball to fit the open suitcase, and stretch the inside as well.
6. If you want the inside to have comfortable gravity, you can either make it spin (makes keeping the opening relatively static complex), or have a planet inside the fuzzball and build the "interior" of the suitcase on top of it.
7. ???
8. Profit!

Answer 8

A simple mathematical way to get around the problem is to use the concept of diffeomorphism. According to this concept, if there are two different manifolds which are continuous and differentiable everywhere, one can map every point from manifold 1 to some point on manifold 2 or vice-versa. In other words, there is a one-to-one correspondence between them.

Now, for a three dimensional volume, it can get a bit tricky to do. But we can do it for sure. Consider an object which is solid and it can be cut off into many 2 dimensional manifolds by peeling it off. Take the outer most layer as a manifold and label it as $M_1^1$. Take a container whose volume is smaller than the solid object's volume and imagine an imaginary 3-d 'hollow' shape inside it. Now take the outermost layer of this 'hollow' shape and label it as manifold $M_2^1$. Now map each point of $M_1^1$ to each point of $M_2^1$ as $M_1^1 \rightarrow M_2^1$. Next take the next outermost layer from both solids as $M_1^2$ and $M_2^2$ respectively. Go on taking subsequent mappings as $M_1^i \rightarrow M_2^i$, (where $i$ is the ordinal number of the manifold taken, starting from the outermost and all the way to the central point) and you will have complete mappings from the points of solid object to the points of the 'hollow' object inside of the container and the solid object would fit inside the container even though the container's volume is smaller than solid's volume.