The original question was: Assuming we had four (or more) spatial dimensions in which to freely move around, like say a 4+1 dimensional universe, how might one extend our 3+1 dimensional physics to that universe?
Side note: When someone says “3+1 dimensions”, what they mean is “3 regular space dimensions, and one time dimension” which is exactly the situation we live in (apologies to our pan-dimensional readers).
Physicist: Right off the bat, more dimensions means more freedom of movement. One of the more mundane effects of that is that in 4 dimensional space there’s an extra direction you can move and/or fall over in. So if you want to build a working bar stool you’d need at least 4 legs instead of just 3. In fact, in D-dimensional space bar stools need at least D legs, or they’ll fall over. Just one of the subtle economic effects of higher dimensional living.
You’d also find that in 4 or more dimensions, you’d be able to do a lot of tricks impossible in 3 dimensions, like creating Klein bottles or (equivalently) taping the edges of two Möbius strips together. Sailing knots could take on stunning complexities. In fact, they’d need too! All of the knots that work in 3 dimensions fall apart immediately in 4.
In four dimensions you could make this surface without worrying about it intersecting itself.
Most physical laws are already written in a dimension-free form. For example, in Newton’s second law, 
There are some laws that are usually written in a 3-D form, but that’s generally a matter of convenience more than necessity. For example, we talk about the “angular momentum vector”, which is defined to be perpendicular to the plane of rotation. It’s convenient because in three dimensions there’s always exactly one perpendicular direction to a plane, whereas in 4 dimensions (for example) there are 2.
In 3-D we can formulate laws about spinning things in terms of the one direction that isn’t spinning (h), the “axis of rotation”. But we can always formulate laws in terms of the two directions that are spinning, regardless of dimension.
This is pretty easy to fix and generalize, it just becomes a little more difficult to work with. All that said, while our physical laws can be generalized to any number of dimensions, the manifestation of those laws are wildly different. So, living in higher dimensions would be pretty alien.
Based on our understanding of gravity (gained from studying this podunk universe), gravitational force should drop by 
The “effective potential” representing the balance between the gravity and centrifugal forces of an orbiting object. Orbits can be stable in 2 and 3 dimensions. In all other dimensions planets and moons will always either spiral in or fly away. Shown here is the potential energy from gravity and the centrifugal force combined. If there’s a “cup” you can form a “bound orbit” in it.
In 4 or more dimensions orbits are always unstable, and in 1 dimension the idea of an orbit doesn’t even make sense.
Most physicists consider light to be native to only 3 dimensions, because light is an EM wave and it’s direction of propagation is perpendicular to both its Electric and Magnetic fields. (Fun fact: the direction that light points is called the “Poynting vector“, after John Henry Poynting. Life’s funny.) In 4 or more dimensions this direction isn’t unique, and in two dimensions there’s no direction at all. However, you can express EM waves just in terms of “E” in any dimension without problem.
Assuming light can exist in higher dimensions, it would behave very strangely. Sound waves too. In odd dimensions other than 1 (3, 5, 7, …) waves behave the way we normally see and hear things: a wave is formed, it moves out, and it keeps going. However, in even dimensions, and 1 as well, (1, 2, 4, 6, …) waves “double back” on themselves. You can see this in ripples on the surface of water (2-D waves). Ripples are more complex than just a ring; the entire circle within the ripples is disturbed.
In even dimensions (like the 2-D surface of water), waves propagate in a more complex way than we’re used to. Instead of a simple pulse, you get an “area filling” wave.
If you set off a firecracker in 3, 5, 7, etc. dimensions, then you’ll see and hear the explosion for a moment, and that’s it. If you set of a firecracker in 4, 6, 8, etc. dimensions, then you’ll see and hear the explosion intensely for a moment, but will continue to see and hear it for a while. For light the effect would be fairly subtle, except for extremely long-distance effects, like somebody reflecting a bright light off of the moon. You probably wouldn’t notice the effect day-to-day. However, it would ruin the experience of sound. In 4 dimensional space the firecracker, even in open air, would sound like thunder; loud at first, and leading into a drawn out boom. It may not even be possible to understand people when they speak.
All the fundamental particles should still exist, but how they interact would be pretty different. Which elements are stable, and the nature of chemical bonds between them, would be completely rearranged. Some things would stay the same, like electrons would still have two spins (up or down). But atomic orbitals, which are determined by spherical harmonics (which in turn are more complicated in higher dimensions), would generally be able to hold more electrons. As just one example (for our chemistry-nerd readers), you’ll always have 1 S orbital in every energy level, but in 4 dimensions you’ll have 4 P orbitals in each energy level, instead of the paltry 3 that we’re used to. This messes up a lot of things. For example, in 4 dimensions Magnesium would be a noble gas instead of a metal. Every element after helium would adopt weird new properties, and the periodic table would be longer left-right and shorter up-down.
So, while the laws of physics are actually the same, if you lived on a four-dimensional Earth in a four-dimensional universe you’d find that (among other things): your bar stool may need an extra leg, Earth wouldn’t be able to orbit anything, you’d never be able to hear anything crisply, and the periodic table of the elements would be seriously rearranged.
Ok, this is a dumb question, but the dimension number does NOT effect the magnitude of a force vector or the total energy right? As in 10 J in 1-D is the same as 10J in 3-D which is the same as 10J in 10-D in terms of magnitude?
@Anon
That’s a great question! Kinetic energy shouldn’t have anything to do with the dimension of the space.
Thanks a lot
there are a few people i know that just don’t listen to this distinction
they think a higher dimension immediately = infinitely more energy
oh also, mass too is a dimensionless quantity right?
@Anon
Maybe? We’d need to look at some 2 or 4 dimensional matter and see how it behaves. My guess is that it’s a dimensionless quantity.
Well the important difference is dispersion, advection. transport. because in 2d radiation from a point result in 1/dist. using the law of triangles, and particle model, foe example, 10j will do more damage. Or transmit more information, as in music , loud, and, reverb, and echo, since it lingers. if gravity is 1/dist not 1 /dist sq, orbits can be stable, but not in 4 d. So, it is the same but scales differently with other qualities such as distance..unless theres is some string theory to change this, it is a different universe with flat molecules..its first have to have our laws exactly. I only think life is possible in 2d space and 3d. 4d. Seems too far from the sweet spot.. Also doesn’t help me understand 3d of space and time.
If matter took on strange new properties then who knows what life can be made of. For all we know a 4d universe’s life could have gold or uranium as a base instead of carbon.
in our world, most of the heavy metals are formed from supernova.. then they end up in the cores of planets when they are cooling down.. ( gold is heavier than iron)… so carbon, is common and has many connectors, so its used by life. After reading the Planiverse and working on the 2d simulator, i’m convinced 2d life can and maybe does exits, although we cannot interact with it. The mass is flat. There are no physical laws that would govern interaction between 3d matter and 2d matter. ( someone its I watched this video, i became more skeptical on 4d space creatures, because, there are more things that have to go right. https://www.youtube.com/watch?v=vDmMnSKEYnIv=vDmMnSKEYnI Also I think 2d creatures can look cool, or weird, but how a 4 creature looks i cant imaging at all.. I guess i go back to 2d mans shoes and try to imaging him thinking about what we look like, he could certainly have a set of set points, or a surface for our face, wih depth info..To visualize it i guess he would slide it along the symmetry where one eye is above the other. That is wrong he would soon turn it and see the L and R symmetry.. We could look a bit like him ..But i havent any proposals on 4d creaturse ( 5d, is needed, if can move or have poses) , expresented as a 3d image or a 4d database. I have invented my plausible 2d one though. Flatland has none, but Planverse has plently. I just think the creature would be aboble to jump , not waddle around. Especially the way things scale with strength. 2 d is stronger bones betcause less ways to break..flux is 1/r. In 4d spacetime, our world, smaller means stronger ( relative to body lenght because of volume scaling with r cubed, and strenght with cross section, thats r squared. so the bigger the slower. Im sure the rules can change but its more enlightenting to me to make analogies, keep the rule similar, and of course consistent, no magic.
I was wondering. What would happen if a creature of 2-dimensions went into a 3-dimensional universe? Would it die because of a total new set of laws of physics or would it adapt to 3-D?
Most “alternate universe” thinkers say there could be no physical interaction at all. Just pass right through. They would not even see a cross-section of the 3d world. This is because their atoms and molecular forces are flat and very different. Seems like even if a 2D cross section of a 3d atom, with its electron cloud, passed through their plane, isn’t going to give them something they could see, even if the scales by luck, matched enough. But , it could..just -maybe-When an electron crosses the plane, they could it guess bounce from one of their atoms. But, tunnelling could be the issue. Very likely the matter on a big scale, would enter into the middle of a planet and disrupt and and destroy it. The chance of it being near the edge, and the creatures, without disturbing the inner planet and causing massive volcanic leaks or breaking the planet before it can repel out, is unlikely unless steered by something or someone very nice to the flat peoples.
When “The Planiverse” came out A. K. Dewdney said that some sort of electronic resonance occurred between the worlds, and brain of one of the creatures, a special one with a desire to know beyond his limits, became linked, so the 3d people , via computer, could see the world and speak to the creature. A lot of people thought it was a true story because it was written in that style, without any silly fiction.
For a 2d creature, we should be able to see its future and past if time were a 3d space line dimension.. but not if the scale was light years to a creatures year. So that was not in the book. We could see inside the creature though. It is possible we are just data in a simulation. We wouldn’t know unless we we very clever. Some think we found clues as to limits of the resolution of the data, but that proves nothing.
On the very popular “Flatland” has that the square “creature” he gets to see 3d..feels gravity for the first time .. (in 2d land gravity for disk planets, you walk around is not much different than ours, so they would not be impressed with gravity), Flatland, was written in 1884, it is not educational science fiction, its OK, but so silly that i’m disturbed it always comes up. The square with no feet? the triangle creature ? the Yndrd in Planiverse, is not even that strange in the planiverse. I thin Planiverse is too scientific for most people who don’t see beauty in science and math because the teachers failed to show them. I simulated some fish for my online game project Kontrol and they are similar to 3d fish.. Wiggle side -to- side and move, using the 2d versions of our laws of physics equations.
As for the Planiverse creatures affecting us, I cant imagine a way unless their time flowed in sync with ours ( things with any sort of interaction do tend to sync, if time were like a flow and such fluids) so that to keep them near some part of us, say, so one creature can see part of my left eye when its near the computer as usual. Then the creature keeps chopping and otherwise messing with the mysterious thing that changes shape, until I go insane or blind.. or… they spoke to someone via brain waves, then we might probably lock him up and medicate him.
the fact that i cannot picture a 4-d universe only makes me want to try harder. how much torture must the 3-d universe be going through, just to try a imagine if we existed and this torture keeps going on until you get to the nth-d. i believe in a 4-d universe the concept of time becomes a reality i.e in the 3-d universe both time is perceived through movement and expansion of space, thus, spacetime. but in a 4-d universe time exist independent of space and vice versa. i believe if life was to exist in a 4-d universe it would be able to move through space and time separately.
You said more dimensions means more freedom of movement, so will there be any kind of blink or teleportation? Can somehow 3-D creature like human sneak into a higher dimensional space?
We as humans can’t comprehend what it would actually be like to see what the 4th dimension looks like as a reality. We can only imagine. However things not possible in 3 dimensions can be possible in 4-D. Since there is more freedom of movement normal knots you’d tie in 3D simply wouldn’t work in 4D. Also light and sound would behave strange in 4D as well.
On a side note its an awesome coincidence the last two posts were also posted on the 25th haha.
What about the power of love (or more specifically the electrochemical potential of excited [lol] synapses in a 4th dimensional beings nervous system)? I don’t hear anyone asking about this in a higher dimension.
Want to know how neural networks might behave in 4 D or higher Ds , how would algorithms work and will AI exist in 4D
This topic could be the most important subject in modern physics.
It is becoming clear that the universe we inhabit is not a 3D Big Banged construction.
At the very least it is a 3D surface on a 3-sphere or 4-dimensional sphere.
What we see as the beginning of the Universe could just be the point where we cannot see around the edge of the underlying sphere.
For example:
For compact 2-dimensional surfaces without boundary, if every loop can be continuously tightened to a point, then the surface is topologically homeomorphic to a 2-sphere (usually just called a sphere). The Poincaré conjecture, proved by Grigori Perelman, asserts that the same is true for 3-dimensional spaces.
The more facts we know about multi dimensional geometry the better for our understanding of our 3D world.
You got the idea on how 2d plus 1d turns into 3d… 4d is the distance traveled from the center outwards… Because you can travel in all directions and it happens all at once as everything happens everywhere this becomes a multiverse of parallel realities. Also the speed it takes.. So when you think about it in a ball you expand the ball or bubble outwards from the center as it reaches the limit it explodes and this is how I picture the big bang… A soup of different matter encased in a container being feed from an outside force to the point that the dark matter container that has dark energy in it explodes forming carbon and anything else that was encased in it… We can access other realms that have not been explored within we have the power to do this as well other things… I love science and its literately my bible I love creative thought and I don’t learn this from a book its just little bits of data I pick up to better understand what I am…..
I once heard this hypothesis about “2D life”: that there could be magnetic plasma aliens on the surface of the stars (like Sun). Now wouldn’t this be just Crazy? ^_^ They would be TOTALLY 2d, while existing in our 3D universe, just like this stuff with this Perelman spheres.
Interesting that you would describe sounds in some higher dimensions as sounding like thunder, considering: Job 37:2, 4-5; Job 38:1 & Job 40:9. It’s not proof of anything, just interesting.
There are just 2 energy devolving structures in any dimension: Divergence and rotation.
Thunder is a divergence phenomenon.
Mathematically the divergence of the thunder’s mathematical function is represented by the time derivitive of all motions in 3 coordinate axes (3 -x,y,z) ie. a 3-vector in our 3D world and the time derivitive of all motions in 4 coordinate axes(4-x,y,z,a) as a 4-vector in an alien 4D world.
Rotations are also defined as the curl of the thunder’s mathematical function over 4 dimension and it’s well defined even for someone in 3D space.
In a Thunder storm rotations would be propagting vortices.
These formulae tell us what motions to look for, over time, in 3D, 4D or any higher space.
Would it be possible to make a virtual reality experience in higher or lower dimensions?
yes. I see that i did mention it earlier but i wrote this before i scrolled up, 🙂 Anyways a game is a virtual reality so ill mention it again, as I might revive this project. Inspired by the book, The Planiverse in 1984, and the logical consistency of the 2D universe describe in it, I for a long time dreamed of making a program like the 2DWORLD as made by the students in the book, which reads like a nonfiction about contact with such an alien race of 2d creatures. I was working as a software engineer around 2008 and with two helpers I hired for this sideproject, when we got our creature , a 2d biped, to take his first steps and walk a few body lengths before falling. We used earth gravity, and human scales, to make it familiar and since it works for us. Until then we struggled with basic 2d physics, but when we pulled in the standard Box2D physics engine used in Angry Birds things took off. You can still play mine at http://www.puppetarmyfaction.com but only in internet Explorer, (not Edge)run iexplore. exe. It has been blocked due to Microsoft abandonment and the project development has to stop a few years back. It might get retarted again as a phone game since the physics stickman games are quite popular now. I think its very fun and we use physics for all the animation, using robot controllers and I believe in near future all games will be done this way, its just more natural and less work, once you get the universal air , earth , first and water anything can happen and it can be amazing. If restarted it will need support, before it had a small but very dedicated cult audience all over the world. I want to make a game that does not teach wrong physics, and introduct more aircraft that is using actual wind modeling, unlike the AAA flight simulations coming out now in 2020 which dont have any wind effects at all, and turn on the physics engine only when characters die and fall. Its unbelievable since the goal animators have is to make things physical-seeming.
As for 4D there is one game here at https://miegakure.com , but this is not true to physics if matter was 4d and spacetime 5D. its more of a teleporting version of a hit game called Fez, its not physics-based. One can argue that 4D matter would not stay in stable orbits and the kind of life would be alot less like ours. However 2d is amazingly similar, planet would be like a disk, you walk around the edge, the universe spacetime could be even be extrinsically curved like in those rubber sheets used to depict general relativity. I think in 2D when concepts are tough, and 4D doesn’t give me any insight at all. Looking at 2d creatures we can see inside everything as if gods, or 4D beings looking at us, 3D spacetime where a closed universe with past, present and future could all be a solid sphere, is actaully pretty easy to visualize, big bang right there in the center as scientists from Einstein to Hawking have used this 2d creature though experiment.
Hello! I’m so glad I found this article— I’ve had a lot of trouble finding info on this subject… Could anyone direct me to further reading on it; scientific articles, books, websites, or otherwise?