Methods of travel between the Infinite Realms and the Living Realm
Note: it is tempting to think of the division, or Veil, as a membrane between the realms. In reality, it is not a skin or wall made of any substance. Rather, it is simply the place where an ectoplasmic reality-space and a mundane-matter reality-space rest against one another. It is less like a film of oil floating on a body of water, and more like the glassy surface of the body of water itself. The water holds itself together with surface tension and you can see the divide, but there is nothing actually separating the water and the air. We will colloquially refer to the Veil as "self-healing", but it's really more like it is settling. Simply the increasingly-entropic nature of the mundane reality and the decreasingly-entropic nature of the ectoplasmic reality finding a steady point they're both happy with.
1. Slicing a hole in the division.
Some ghosts specialize in this. It's fairly easy if you have a good sense of fourth-dimensional space and a sharp edge. The cut will self-heal, though, especially if it's messy, so it can be difficult to open a wider gap or leave it open for more than a moment. The mechanics of the slicing are fairly simple; like a shark fin about to surface, a blade that's almost touching the division causes currents that disrupt the fields enough to allow for the tip to easily pass through (see Method 3 below for further explanation), and then the wider part of the blade increases the size of the cut. The trick is in not touching the tip to the Veil before it's been destabilized. Perfektigas Tranĉadon is a good practical guide.
2. Punching a hole in the division.
With enough force (the true amount necessary is not exactly known, but it is known to be colossal), the division can be pushed and broken. This results in a hole which takes a long time to close on its own and produces a number of "shards" or "bubbles" of the division, which can knock their surroundings askew in the fourth dimension. These shards introduce incontinuities in spacetime, which will quickly equalibriate but momentarily pose a threat to laws maintained by continuous spacetime. The punching process also results in a jet of reality-material from the entrance side to the exit side. For further information, consider reading Continuous Space: Geometry and the Infinite Realms. This is the method perfected by the Ring of Rage, and it can also be achieved by any object with enough momentum (that is, velocity times the sum of ectoplasmic mass and mundane mass) being flung at the right fourth-dimensional angle.
3. Exciting the division until it is permeable.
If the spaces in realities on either side of one area are sufficiently energized, the Veil in that area can loosen up into a chaotic mixture of mundane and ectoplasmic space, which is not practically impossible to pass through like a smooth division is. This creates an illusion of a smooth gradient between mundane and ectoplasmic reality— in actuality, a space cannot be simultaneously ectoplasmic and mundane. This would be an impossibility, and, if it impossibly came to be, result in totality-altering paradoxes¹. It's more like tiny pockets of reality too interspersed to be noticeable, like an emulsion of milkfat in water (milk) or an aerosol of water in air (fog). The biggest issues with this method are (1) exciting the ectoplasmic field and quantum field simultaneously and (2) containing the excitement such that it doesn't dissipate in the Living Realm and/or coalesce in the Infinite Realms. Thus far, this is the only portaling method managed by mundane technology, and it is also the one usually used by summonings which do not rely on the summoned ghost for transportation (or fail to peovide transportation at all). Use of Ectoenergetic Excitement Alongside Gauge Field Dynamics in Ectoplasmic Portalling, being written by living scientists, is not a perfect explanation of the "how" or "why", but it explains the "what" pretty nicely.
Ghosts with an ability to rewrite their position in spacetime, via whatever method, generally have no more issue moving interdimensionally than moving intradimensionally. The division only acts as a barrier when moving continuously. If your "teleportation" has issues with interdimensional movement being stopped at the division, it is possible you are actually moving continuously and simply too quickly or abstractly to notice.
5. Simply shifting your balance.
An item or entity which is positioned perfectly on the division can "tip over" onto one side or the other without facing any resistance. This is largely not an actionable method, as it is practically-impossible to obtain the perfect positioning and would require using one of the other methods to obtain it in the first place. Additionally, the smallest destabilization in fourth-dimensional space will tip the object, and the "fall" is not reversible. While a balance on the division is technically at equilibrium, it is a weak equalibrium in this sense and is not stable. An object which is stable in a state of being wholly ectoplasmic and mundane simultaneously (an entity fitting this description is known as a "true halfa", "Limenarch", "owuw-uwow", or y'know just their name that they go by for once) is, however, always positioned perfectly along that balance, and can shift one way or the other without being disrupted. There is no other writing published on this topic that I can find, so you'll just have to take my word on it.
6. Bringing one space to another.
On rare occasions, usually the work of powerful beings with domains in space or reality, such as certain Ancients or the Ghost King, an area of one reality is moved to an area previously occupied by another. In this circumstance, the shift generally causes enough chaos and mixing that the division is permeable. If it happens quickly or instantaneously, though, and the reality that was previously occupying the space is not moved out of the way, the impact with the division can be sudden and dangerous.
7. Entering a black hole.
I'm not entirely sure why this happens. The mundane matter that enters a black hole in the Living Realm measurably becomes a part of the black hole itself, so why does it also appear in the Infinite Realms? Does this disrupt the conservation of matter/energy, or are the two dimensions already on opposite sides of that coin? It seems impossible to tell, as the Infinite Realms have an infinite hypervolume. This is a puzzle that hasn't been solved yet, to my knowledge. Grab something made out of mundane matter and try it sometime, if you can survive immeasurable gravitational pull. It's pretty mind-boggling.
8. Using a natural portal.
Most of the phenomena described above can happen without intentional cause, thus forming a short-lived natural portal. When influenced by certain currents in ectoplasmic flow, these passages can be at odd temporal angles as well as spacial. Thus a natural portal is more likely to cross time than an intentional portal, only a few methods and users of which have been noted to be capable of transtemporal travel. There are not currently any known instances of mundane matter or energy causing a portal which crosses time. Most community centers in the Infinite Realms will have resources available for tracking natural portals.
