“Yet the longer you lived in Summerland, the stranger things became. Your hypersight grew more acute, and little by little, you developed an awareness of two additional directions that were invisible to the living. One was the ana direction, four-up. Towards ana lay the world of the living, in its own thin slice of the aether. It was the direction of the Unseen, the mysterious source of hyperlight and soul. Luz stones fell from ana, lodged themselves in dense aetheric configurations like brains at birth. Upon death, the luz detached and fell below the plane of the living world in the kata direction – the equivalent of down in the fourth [spatial] dimension.”
In “Summerland” by Hannu Rajaniemi
I don’t know how much physics people reading this post know. So, here’s a very, very, very brief synopsis on how objects in 1D, 2D, 3D, 4D space move:
Dimensional space Movement that can be made in that space
1D Forward, backward
2D Forward, backward, right, left
3D Forward, backward, right, left, up, down
4D Forward, backward, right, left, up, down, ana (imagine the object coming down from heaven), kata (imagine the object going up from hell)
As you can see, in 4D space we’ve got two additional directions: ana and kata. If want more than this by way of explanation, you’ve got to look elsewhere.
Rachel White and Peter Bloom, the main protagonists of Rajaniemi’s novel, live literally on different planes of existence: life vs. the afterlive. I’ve been told that if one found themselves in a higher dimensional space they would flop and fold in very much the same way that a piece of paper (nearly 2D) does in our 3-D world. In higher dimensions we’re all surface. However a 4-D person sticking their hand in our 3-D space would reveal an internal cross section in the same way our 3D hand crossing through a 2-D Universe would be a cross section. Could our hand be physically cut by the 2D plane? So lower beings going in reverse to higher dimensions would then reveal their entire internal and external surfaces? In essence are they ripped into one flat piece of meat? If they ended up in 5D hyperspace devoid of any laws of physics would they flop around helplessly, and at least stay together in that one flat piece?
The problem with extra dimensions is that our brains have specifically evolved, or adapted if you prefer, to recognise 3D space. If when we try think of 1 & 2D our mind sees them embedded in 3D. 2D animals might exist if they didn’t have a digestive/colon tract because it is this that would separate the 2 halves of the animal. We might be embedded in 4D. However, dimensions don’t have to be macro and might exist on the quantum level as in Superstring theory and compactification. However, we are never likely to be able to prove this since there is no known way to probe at this level.
Here’s a way to visualise the “innards” of a 2D person. Take a piece of paper to be the 2 dimensional world; we will create a person to live in it. First draw a basic outline of a person on the paper. In order to “live” the 2-D person will have to have organs: draw a brain in its head, heart and lungs in its chest, a stomach in its belly and pipes connecting its mouth to the lungs and stomach (note that the mouth has to be on the side of its head so that it opens up into the rest of the paper), as much detail as you feel like. This 2D person lives only in the piece of paper. It therefore considers the organs you just drew to be its innards, since the only way to get to them from the edge of the paper is to pass through its “skin” (the outline of your drawing). However you have a 3D perspective, so you can touch the organs without passing through the skin. This means that what it considers to be innards, the 3-D universe does not, so they would fall out if you ever able to lift the person of the paper.
There would be a few problems for 3D matter existing within 4D space, let alone a human surviving within 4 dimensional space! The first problem is that 4D matter as we understand it would be very unlikely, simply because orbits (or the 4D equivalent) are unstable in 4D space. So, electrons could not remain in orbit around a nucleus, likewise planets would not remain in orbit around a star (or again, their 4d equivalents). The reason for this is, (in the case of a planet) the way gravity falls-off much more rapidly in 4D. (Being proportional to 1/r^3 rather than 1/r^2). So, gravity would be unable to ‘balance’ centripetal force and the slightest perturbation of the orbit would result in the planet either flying-off into ‘space’, or spiralling into the star. Likewise, the force holding the electron in orbit around the nucleus would behave in much the same way, so if electrons & proton/neutron nuclei exist in 4D, they would do so as a 4d soup of charged particles.
The other rather major problem is that a 3D object in 4D space would have no substance, exactly like a 2D ‘object’ in 3 space. A 2D object would extend over only 2 dimensions, much like a sheet of paper with no thickness, it would simply not exist. That fact that a 3D object has no 4D component means that it simply could not exist in 4 space. It would be exactly analogous to the infinitely thin sheet of paper (representing a 2D object) in 3D space.
Question: As I understand it, the compactification scale within 3D space is a similar order of magnitude to the Plank length? Answer: the plank length would be greater in 4D space, (by several orders of magnitude?) so it should follow that the compactification scale in higher dimensional space is also increased (for the remaining 9, 10 or 25 dimensions, as one of the previously compactified dimensions in 3D space in now BIG in 4D space!). However, wouldn’t it be true to say that the scale is still sub-micro, i.e.: the dimensions still being many orders of magnitude smaller than any 4D subatomic particle and also so small that gravitational effect would be negligible to non-existent? I suppose I have also ‘conveniently’ ignored the recollection I have that ‘G’ in 4D space is quite a bit larger than in 3D space. I don’t think that changes the suggestion that ‘orbits’ (both of them!) are unstable in 4D.
I have a different idea of time and although I have worked some equations I still have problems so it remains an idea and not a theory. The idea is that time as we use it (‘arrow of’, sequence of events, progression of change, etc.) is a manifestation of something more fundamental which I refer to as Component Time. In this, C.T. is multidimensional and I’m considering 4D C.T. where one of those is the part we recognise. However, it needs to be an evolving system and what I call ‘repeatable relative function’ as the math to describe it. The nearest analogy would be a ‘time gene’. Certain numbers appear to be constants some of which, coincidentally, are very close to what we use in space/rocket science. If such an idea was applied to macro extra D then each 3D instant might be a ‘patch’ on an expanding 4D (or 4+xD) surface. This could mean that the past still exists as ‘patch’ and that opens the flood gates doesn’t it. I have posted some of these ideas but they remain just ideas.
I’ve always wondered something. If 3D beings can place objects in 2D space, and that 2D space beings would have no conception of how it got there or what it’s for, couldn’t we argue that a 4 dimensional “being” may have placed something in our 3D space at the beginning of the universe thus solving the mystery of how something (our universe and the big bang) came from nothing? I say this because we have no concept of how it’s even possible to make something of nothing like how 2D beings have no concept of a 3D object placed in there space, even though us as 3D beings have full understanding of how it’s possible (for example, picture your life as a dot on a piece of paper and a 3D being set down a coffee mug. What would you see? You would see nothing but a flat plane in front of you, but even though there is still something there).Could different higher level dimensions create other lower dimensions? If a 4D “object” was placed in our 3D universe it would have to have mass based on the theory of relativity, otherwise it would just be traveling at the speed of light. So assuming this object has mass it would HAVE to have energy (gravitational potential) thus making something come from nothing (from a 3D beings perspective of course). Are these “objects” from a 4D world being placed in our dimension, dark matter? Dark matter, of course, is not observable from a 3D perspective (does not absorb or reflect light) but we know it has to exist because it alters gravitational pulls in our observable universe. A final question to leave with would be… could a 4D being see dark matter as we see the very coffee cup we placed on the piece of paper? How can we say a 2D object cannot exist in a world with three dimensions? Maybe they can exist here, but due to their lack of a third dimension and therefore volume we simply cannot observe them. Perhaps it works in the same way for 3D objects in a world with four dimensions. The 3D object can exist there, but will simply be unobservable to a being living in that world with four dimensions, due to it lacking that fourth dimension.
I tend to think the concept of wormholes or the like are linked with the fourth dimension. The idea that you can take a 2D object in a 2D world and move it into the third dimension (think having a 2D picture on a page and you pull a piece of that picture off the page) and then back into the 2D world at a different location (think placing that object back on the page in a different spot), this object, to an observer in the 2D world, would appear to have ‘teleported’ (because the 2D observer cannot see what is occurring in the third dimension). This might also hold true in our three-dimensional world. An object is pulled into the fourth dimension and is then returned to the three-dimensional world in a different location. This would give to us (the observer in the three-dimensional world) the appearance that that object ‘teleported’.
The earliest conception of “modern” space-time by Minkowski in his space-time diagrams was that objects (including us) are all really examples of a four dimensional manifold, the world-lines of their particles stretching from the Big Bang to an unknown distant future. We as 4-manifolds do not experience all the events of our lives simultaneously, but as successive moments of time — successive 3-d “slices” of the 4-manifold. This is probably because causality has a speed limit — the speed of light — which essentially fragments what our consciousness can perceive into the enormous number of “frames” (3D cross-sections or individual moments) of our lives. This is because of relativity of simultaneity demanded by Einstein’s Special Relativity, which makes successive moments possible. The mystery is how our “conscious selves” at each one of these moments experiences a transition from one “frame” (3D slice) to the next. The perceived “Arrow of Time.” It is what physicist David Park called “the fallacy of the animated Minkowski diagram.” I am not a single conscious entity aware of my entire life, but something resembling a train of boxcars, with each boxcar a conscious self-observing an instant at a time, with each boxcar moving forward. Some thinkers use this as an argument for consciousness being not an emergent property but rather something “outside” of the material world.
Rajaniemi constructed a wonderful world wherein the existence of higher dimensional creatures ‘a la H.P. Lovecraft would explain certain phenomena, such as so-called poltergeist manifestations, where, for example, objects sometimes disappear from locked cupboards or safes, only to reappear after a time back there or somewhere else. It is as if some mischievous 4D creature reaches down into our 3D world and grabs something. I thought hard about what Rajaniemi is trying to tell us in a fictionalized way and I too ask the question as follows: if energy (in our case it’s matter in space and time) never dies, could it change its form in a dimension beyond ours? But I am grappling right now with how our notion of “energy” might have to be changed. In 1926 Sir Arthur Eddington said on the verge of the astonishing realization of quantum physics, “something unknown is doing we don’t know what.” I think we’re in the same place here. Who knows what other dimensions there are because as mere mortals we do not really know for sure; however, some people believe in ghosts or spirits, and some people claim evidence of such. If this is true then the realm they live in could be another dimension of existence. Everything is happening at once. Different aspects of ourselves do exist in other dimensions and I believe that certain energies can indeed be allowed entrance (this is what my SFional self wants to believe…). As Rajaniemi says: "The material world was invisible, except for electricity and the soul-sparks of the living."
Bottom-line: 4D space has an extra spatial ‘direction’ at right angles to the other three. (So, in addition to up/down, left/right and back/forth, there’s ana/kata as Rajaniemi uses in his book – see quote above). We don’t live in a ‘dimension;’ we live in a three dimensional space, with time being considered to be analogous to a 4th dimension. Stating that we live in our ‘dimension’ is not really correct, it’s simply convenient shorthand for saying the ‘3 dimensional space’ we live within. Whether beings are entering our 3D space from a space with more dimensions (= a higher dimension, in this case!) as ‘spirits’ is really a matter for pseudo-scientific speculation. It might turn out to be the case, but somehow I very much doubt it…
Sorry for this long review. Hannu Rajaniemi and Greg Egan are two of the most extraordinary SF writers of the hard stance kind of tone. You should read them for the science. Not so much for the stories. Incidentally, Summerland’s spy story is a little bonkers…5 stars for the physics, 1 star for the story: 3 stars altogether.
NB: SF = Speculative Fiction.