# Can you cross a space from which a two dimensional plane is missing?

If I travel through 3d space, will my travel be stopped abruptly if I encounter a 2d plane without space? That is if a 2d plane of space is missing?

You can consider every type of motion, continuous, step-wise, accelerating with an arbitrary value, or whatever, as long as you don't take refugee to 4d space.

• Are you assuming that trajectories must be continuous? Commented Jun 15, 2021 at 21:50
• does this question really make sense ? Commented Jun 16, 2021 at 11:47
• @armand Not at all!
– user52804
Commented Jun 16, 2021 at 11:48
• @Methadont This is an empirical question, and nobody is ever likely to know the answer because it certainly won't happen that a 2D-slice of space goes missing. Commented Jun 16, 2021 at 13:26
• @Speakpigeon In the epokyrotic universe two infinite hyper volumes are separated a very small distance from each other. There is space between them. If they touch (or almost touch) a new big bang starts. What makes this different from the example above? That the gap I presume is in the space itself (which makes it discontinuous)? Why shouldn't it be possible that somewhere a piece of space(time) is missing? oes space have to be continuous? This nicely extends to Zeno's paradox.
– user52804
Commented Jun 16, 2021 at 13:34

If I travel through 3d space, will my travel be stopped abruptly if I encounter a 2d plane without space? That is if a 2d plane of space is missing?

The 2D missing plane is an interruption of continuity in the 3D space you are moving in, so essentially your body just disappears as it moves out of the 3D space. It doesn't reappear on the other side because continuity has been interrupted.

For all intent and purposes, the part of your body out of your side of the 3D space would have disappeared altogether. It would be as if your body had just lost one half.

If you stayed only a few seconds half-in, half-out, then some of your blood for example would keep moving out of 3D space and disappearing. Your blood pressure would drop very quickly and you would probably die very quickly. An eyeball half-out would also empty like a glass of water tipped 90° to one side.

If you kept moving, for example from inertia, you would just completely disappear never to come back.

It all depends of course on what you mean exactly by a missing bit of space, but this is what would happens if this bit of space really no longer existed.

Maybe the really interesting question rather is what would happen to space itself. If space does not exist in itself, that is, if space is an epiphenomenon, then it cannot go missing either, so that would make your hypothetical scenario totally impossible.

If there is, however, something like the fabric of space, then such a space might conceivably be inside another space, for example a 4 or 5D space or whatever. In such a case, I think the effect of a missing bit in it would broadly be the same as the one described above.

The more plausible situation, however, is that spacetime as we think of it, including in General Relativity, is essentially a model based on empirical experience, empirical experience we have no means of deciding whether it is complete of reality. So, we can only answer this sort of question on the basis of what we understand, i.e., on the basis of our model, and scenarios that are counterfactual to our model, as this one is, have almost zero plausibility. The answer can only be as good as our model and our model is most plausibly false of reality, even if it is true of our empirical experience.

• Why do you think it's most plausibly false of reality? Why do we have no means of deciding whether it's complete of reality?
– user52804
Commented Jun 19, 2021 at 11:14
• @Methadont All we have is empirical experience. So how could you possibly decide that it is complete of reality? We can always assume it is, but that may not be true. For practical purposes, we assume it is. This is not even a rational decision. We just do it. And, broadly, it works. But science demonstrated that our trust was misplaced. Reality appears to be much, much weirder than anything anyone anticipated. Commented Jun 19, 2021 at 15:29
• We may not have empirical evidence, but why is this needed to ascertain something (or falsify)? The atom seems 100% certain to exist. It is 100% certain it exists. Or what about elementary particles? More objective than them it can't get. There may be a smaller subdivision of the Standard Model ones, but more elementary it can't get (except for searching ways to circumvent their supposed point-likeness). The eventual two really elementary particles must be the most elementary.
– user52804
Commented Jun 19, 2021 at 15:39
• @Methadont "The atom seems 100% certain to exist. It is 100% certain it exists." Science itself says certainty is a psychological state. Commented Jun 19, 2021 at 16:30
• But it is a certainty.
– user52804
Commented Jun 19, 2021 at 16:53

You should be unable to reach anything on the other side of the plane. Whether you are stopped abruptly is not clear, as there are issues revolving around the underlying metric of the space (e.g if things shrink as you approach the missing plane, you may never stop, as the perceived distance to it is always 'further away').

Depends on what you mean by "stopped abruptly". The question can be answered from multiple perspectives:

The notion of a continuous, smooth space in physics is tied to the mathematical term of a smooth manifold. However, there are generalizations like connected space, which is the simplest mathematical structure with geometrical meaning. Though in mathematics, nothing prevents you from defining discrete spaces. Connected Spaces don't even require a metric, which is a function giving a sense of "distance" to a space, to be defined on it. Topology is the mathematical theory in which very primitive notions of space can be studied.

So when is a space no longer continuous and smooth in physics, such that you can be "stopped abruptly"? Well, "singularities" are what capturing this best;

In Relativity, gravitational singularities are 0-dimensional points in spacetime, where all geodesics end. Space and Time are "ending" at this point. The specifics are clarified by the Penrose-Hawking Singularity Theorems.

In String Theory, there are generalizations to higher dimensional singularities, like 1D Cosmic String and 2D Domain Walls. ​

To the best of current physical understanding, hitting any singularity would imply you ceasing from existence. There are theoretical debates whether the information content of your body would be re-constructible in the case of 0-dimensional gravitational singularities (Black Hole Information Paradoxon).

More generalized spoken from the perspective of the perspective of Modal Realism, none of the above mentioned results are logical necessities though and you could axiomatically probably construct logically possible worlds where other outcomes happen when you hit "the end" of a connected space.

To understand the question you may consider the analogue with two dimensions less: Can one travel along the real line when one point is removed?

I consider the problem underdetermined, it needs more context to be well-posed.