We can’t physically see or understand how complex numbers exist or work in our world in a nice way, but we know they do exist. Because we’ve made massive advancements in science and technology off the assumption that they exist and work, and our understanding of many things in the world including stuff as basic as the solutions to quadratic equations would fall apart. By the same token, there are many problems for which vectors and problem spaces of nth degree are used, where n>3, and there’s that whole adage where time is considered a 4th dimension. In that way, we often solve many problems, even rudimentary linear algebra ones, using sets in R⁴, R⁵, etc, and there are many, many invisible forces at work in our world such as gravity. We know how easily our brain can trick us, we still are easily fooled by optical illusions even when we know they’re there and what they are/how they work, despite our visual cortex being the one of the most powerful and most used part of our brain. So the idea of forces and things which we don’t have the capacity to perceive existing in the world is not anything new or foreign. There are frequencies we can’t hear, colors we can’t see, etc which other animals can and do. So why is the concept of n dimensions in the world so widely rejected? There must be a simple reason, I have heard that it has to do with the volume of a gas in a container being proportionate to its dimensionality or something
In: 2497
I don’t think we know there are three. I think we just know we can only perceive three?
Because we know what a dimension is.
We have three spacial dimensions and one time dimension. There are three orthogonal directions a spacial object can be rotated in, and they are interchangeable. There is no fourth one. That’s pretty easy to test. This is what makes a spacial dimension a spacial dimension.
Since dimensions are mathematical we can call other things dimensions too. Say every fundamental particle is a dimension, then we live in an four-dimensional field of 18-dimensional vectors.
If you want to say some fifth non-time-non-space time-like dimension exists, then sure, but it won’t be a spacial dimension, and if it has no impact on our world then saying it exists is quite pointless.
As an aside, it is possible that we do have more spacial dimensions that are incredibly small, since we cannot measure small enough we can’t directly test this like we can with space as a whole.
If there are more than 3 spatial dimensions, we cant perceive or interact with them, so it doesnt matter and can be Occam Razor away.
Here is a good video that describes how we can have infinitely high mathematical dimensions without ever needing to ask if they actually exist in the physical world. https://www.youtube.com/watch?v=6_yU9eJ0NxA
Imagine you are holding a cube made of wires (along the edges, ie. 12 wires), outside in the sun. When you rotate the cube, its shadow (2d projection from 3d space) changes shape quite markedly.
Imagine now that there is a 2 dimensional creature with no perception into the third dimension looking at that shadow. They see an object which is changing shape and conclude that it is an object with varying geometry, not a fixed object simply being rotated.
Now search for “Tesseract animation”, you’ll see examples of 4d “Cubes” rotating in 4d space. To us, 3 dimensional creatures, it looks like these objects have varying geometry but they are fixed geometry objects being rotated, then projected into 3d space from 4d space.
The fact that we don’t observe objects changing shape like that suggests we’re not just 3d creatures living in a higher dimensional world only perceiving 3 dimensions, but are actually in a universe with only 3 ordinary spatial dimensions.
There may be higher dimensions, but they do not appear to ordinary ones like our known 3.
Couple ways to answer this. The simplest is, because we see three dimensions. If there were more spatial dimensions, we would expect to see a lot of weird things that we just don’t see. For example, objects would sometimes just disappear, as they move along another dimension (as an analogy, imagine an ant on a piece of paper: it can see a crumb on the paper with it, but if you pick up that crumb then to the ant, it just disappeared). We don’t see objects randomly disappear, so we can be pretty confident there are only three spatial dimensions.
You mention time as a fourth dimension, and that is 100% true. However, it isn’t a spatial dimension, in the sense that you can’t freely move through time like you can move up/down, forward/backward, and left/right. Getting into the nitty-gritty of how time is a dimension and all the implications that go along with that is complicated, but the important point is that unless you’re a physicist, it’s not a dimension in the same sense that space is three dimensional.
Final point is that yes, there could theoretically be more spatial dimensions that we can’t see. In fact, string theory in physics predicts at least 11 spatial dimensions, with some theories predicting 26 or more. However, we have never detected any sign of these dimensions existing, so if they do exist or not, we will still only experience a 3D world, so there’s not much point in saying otherwise (unless you’re a physicist doing calculations that require them, but that is not most people).
Math can describe a lot of things. Physics is finding math models that predict behavior in nature.
You can use Newtonian Gravity to understand the water pressure in a deep pool or in a hydro dam. It is not a perfect description of nature, but a useful one.
General Relativity describes spacetime as a four dimensional thing that is warped by energy and momentum, and we can move through. This allows us to predict the orbital position of Mercury, the deflection of starlight when passing close to the Sun, and the time dilation of GPS satellites. Again, an imperfect yet very useful model.
There are many other proposed models in development that have extra dimensions, such as String Theory. The problem is so far nobody has been able to construct a version that matches the existing observations of nature, and also makes new predictions that we can test that would be different from General Relativity or Quantum Physics. So while these higher dimensional models are clever math, they are not yet useful.
This would be the same for any model, gravity or evolution or quantum physics, it only gets trusted when it makes testable predictions, we test it, and it continues to be correct.
Edit: strong theory
This question and the top answer is pretty relevant: [https://physics.stackexchange.com/questions/110876/a-sketch-of-various-combinations-of-numbers-of-space-and-time-dimensions](https://physics.stackexchange.com/questions/110876/a-sketch-of-various-combinations-of-numbers-of-space-and-time-dimensions)
To summarize: we could conceive of worlds with more than three spatial dimensions, but it would have some undesirable properties. To quote:
>If we have more than three spatial dimensions central potentials like the Sun’s gravity have no stable orbits so the Solar System wouldn’t be stable and we wouldn’t be here. This singles out three spatial dimensions as the only case in which humans can exist.
We don’t. There is a prominent theory that unifies general relativity and quantum mechanics called String Theory, and it’s based on the idea that the universe is actually 10, maybe 11 dimensions.
We are only able to interact in 3 spacial dimensions and we have seen no indication of 4d objects moving through our 3d space (which would look like a 3d object that changes as it moves in weird ways) but it’s also important to understand that the dimensions described mathematically don’t have to be spacial dimensions. Instead they can be a time dimension, which is fairly commonly used or a temrature dimension. Each point in 3d space could be represented by an x,y,z coordinet and a temperature reading for 4 dimensions of data.
> How come we know there’s only 3 dimensions
A better way to phrase that statement is to say we’ve found no evidence of any dimensions exceeding the three we’re familiar with. Scientists are certainly open to the possibility of more. There are even some theories that predict they might exist. We’ve just haven’t found any experimental evidence they exist. The best phrase is therefore, to date, we have no evidence any spatial dimensions above three exist.
What we know physics is consistent with a universe that only has three dimensions. If any forces were disappearing into higher dimensions, that would reflect in the equations that model how those phenomena propagate. Take light for instance. When we compare the amount of light an object outputs versus what we predict, we find none of it is disappearing into a higher dimension. All of it’s there, and the equation that models the way it spreads perfectly correlates to three dimensions.
There are some theories that predict extra dimensions, but they lack experimental evidence. Right now they only exist on paper. Most of them predict dimensions higher than four! One thing to keep in mind is that higher dimensions aren’t necessarily large and infinite. Some theories predict extra spatial dimensions to be crumpled up into impossibly small spaces. So even if extra spatial dimensions exist, you might be unable to enter a bank vault by shimmying down the fourth dimensional axis.
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