How does space between ends of a wormhole work?

Question

I am writing up a system of wormhole-based gates to allow "fast travel" in a far-future setting. My description is an extrapolation of the way I understand a flatlander's experience of the following illustration of an Ellis wormhole:

Right now, there are the following specific questions that I am not sure about whether my interpretation is correct:

1. Am I correct that there is a maximum "aperture" width at the throat of the wormhole? And that a ship that was too big yet forced itself through would essentially fill the entire throat up, thereby "looping around" in this non-Euclidean deformed space within the wormhole and bump into ITSELF, crushing itself?
2. Am I correct that objects of sufficient hardness (ie. lack of elasticity) would crack/pulverize when forced through a wormhole due to the curvature of the space?
3. If so, would they "resist" going into space with increased curvature before they do? As in, would a diamond inside a ship passing through a heavily curved wormhole (seem to) respond to some force that stopped it from moving further without cracking? Ie. the diamond would start moving towards the back of the ship as the curvature of space pushed back against it harder than it did against the softer materials of the ship.

For completeness' sake, here is the full description as I have it planned right now.

A network of gates spans the known parts of the galaxy. These gates come in various sizes, but are consistently ring-shaped. The rings consist of ancient, self-powering, self-repairing technology yet to be understood by modern civilizations. The area circumscribed by the ring holds a spherical field that appears very much like a soap bubble, with various colorful distortions slowly drifting and mingling. However, unlike a soap bubble, one cannot see through this field; instead the opaque bubble acts as a mirror, showing a reflection of the surrounding space.

What we know of them is that they come in pairs (the matching gate is always of identical size) and function like wormholes. The space between gates features high levels of geometric distortion, but is otherwise safe to traverse without any special equipment.

Because of this geometric distortion, there is a maximum to the size of the ships that can use a gate (which is smaller than the size of the gate sphere). Think of the gates as entrances to tunnels, with the width of the tunnel at the narrowest part being the limiting factor. Of course, within this distorted space there are no walls as such, the tunnel walls simply represent where space starts looping around on itself, and a ship that is too big risks bumping into or even crushing itself.

The geometric curvature of the space between the gates has been and still is an important field of study to ensure the safety of inter-gate travel. Conventional spaceships and most lifeforms are usually not in any danger using a gate, but materials with very high hardness (diamonds and harder) have spontaneously pulverized when transported through gates with relatively high curvature.

As a general rule, the minimum size of a gate is defined by the minimum width of the tunnel and the maximum amount of curvature; the bigger a gate is, the wider the tunnel can be at the same maximum curvature, or conversely, the bigger a gate is, the lower the curvature can be when not changing the tunnel aperture.

The bubbles are theorized to modulate the size and curvature of, and hold stable the wormholes connecting them. Perhaps the civilization that created these gates had ways of changing these parameters of existing gates, but as far as is currently known, gates are static in curvature and aperture width. Inactive and broken gates have been found, some of which had tiny regular wormholes - lacking the distinctive bubble - at their centre.

Answer 1

The wikipedia article already shows a modelled Ellis (traversable) wormhole:

I must admit I would have problems to use that thing. :)

But essentially wormholes only exist in dimensions one higher than the dimension in it was created. That means the entry is not a 2D hole, but a 3D sphere, you can enter it from each direction and move out from each direction. Essentially it also makes much more sense than Hollywood wormholes like Stargate:

Because using a plane as separator forces a progression from one side to the other which asks the question how something which passes the barrier is not seperated immediately (one part is suddenly a world away). A correct wormhole has no barrier, you can enter and leave it continously at will.

It has boundaries which cannot be violated, so if something is too big, it won't get through (at least not without collapsing the hole). The tunnel itself consists of at least a 5-dimensional entity (yes, literally hyperspace) so if you are inside the tunnel, effects are unknown, but light and matter should pass through and also time is felt normally.

Forget only the thing with the space-time curvature. There is no effect on materials, remember the thing has one dimension more than normal (5-dimensional containing 4D space-time), so it does not restrict anything which is transported. Both ends could be on completely different sets of time and location.

While an Ellis wormhole does not show sign of gravitation because it was specifically constructed to do so, some other wormholes may not be so unforgiving. What a traveller may experience with the curved space-time in the transition zone which creates the dizzying effect is very strong gravitation. So once you get too near to other wormholes than the Ellis case, you will be sucked in literally. Depending on the size and dimensions it could lead to deadly spaghettification or only strong acceleration. The main problem of wormhole traversal will then to get out of the wormhole again.

Answer 2

From the comments on the excellent summary answer by Thorsten S., it appears you still have specific questions: I’ll address just that, without going over the rest again.

It’s generally OK to work in a flatland analogy so you can visualize it and make physical models, as with your picture.

There is some question about whether the items in the space perceive the same curvature and distortion that you see from your hyperspace model. The answer is that it doesn’t have to be the same.

Start with a rubber sheet model of a plane. Draw your X-Y grid on it, and this becomes your metric. Roll up the sheet and the citizens won’t know or care. Stretch and distort the sheet, and it looks funny to you; but the metric is what controls the experience for those on the inside. Mr. A.Square’s rulers will stretch by the same amount, and he only cares about the passing tickmarks, not how they are seen by you. Picture looking at the plane through a funhouse mirror: it does not affect the plane itself.

Now if you made holes in the plane such that some gridlines were cut, they would notice that on the inside. If you distort the topology of the metric such that it’s not Euclidian, they would notice.

In the case of a wormhole, you have a topological feature which restricts how you can draw your metric. Approaching the bridge, you have a choice of having abrupt boundries where gridlines just end, or a hyperbolic geometry where parallel lines get squeezed together (the case you illustrate).

Yes an object can be too large to pass and will wrap around so that the right edge bumps into its own left; you could reach out and take our own hand.

Because of parallel lines converge (or diverge coming out) a ship will be squeezed and stretched as the ship’s sides, initally taking parallel tracks, are forced together. A large ship must travel slowly enough to deal with the resulting stresses, and perhaps be built with joints to absorb this!