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
Math allows for technically and literally anything. Its only a system of extrapolating rules once you have some base rules set. Currently a large portion of the maths we know (and is popular) has high practical value. That is, it is almost as if we have explored parts of maths that are useful.
Now, just because it’s useful, does not mean the universe obeys any maths rules. Not only are there infinite ways of constructing math, there will be infinite different rules. The universe just is. You are finding rules that seem to work out in the universe.
Complex numbers don’t Exist in physical sense. They are a concept which we can use to simplify certain calculation in a certain framework of math. Numbers don’t exist either. You can still assume they ‘exist’ and play around with the idea and see what things can be explained using that math, but it will eventually be insufficient or inconsistent.
TLDR – math is just a tool. If something can exist based on some math, doesn’t mean it should exist in the universe. Universe doesn’t give a F about our math.
There is a lot of physics that you don’t understand. “Frequencies we can’t hear, colors we can’t see” This has nothing to do with dimensions. Physics can explain these things perfectly. Just because you don’t understand something, doesn’t mean it’s wrong or supposed to be looked at with skepticism.
Complex numbers are a catalyst in mathematics. They show the results to equations for electronics. It’s in no way an argument for weird unknown things like more spatial dimensions existing.
We can perceive three spatial dimensions. There are NO experiments that prove any more spatial dimensions exist.
String theory mathematics works out if there are 10 spatial dimensions. This doesn’t prove that there are more spatial dimensions, and string theory isn’t proven either.
So right now we have no evidence to believe there are more spatial dimensions, and we can only ever perceive three, so it’s like the flying spaghetti monster: There’s no reason to believe it or not believe it, it’s an arbitrary idea with no backing.
This has to be the most Eli25 Question I have seen in Eli5!
Pretty amazing responses though 🙂
Math is the language used to describe many ideas, but just like English can be used to describe fictional universes, math can be used to describe relationships that don’t exist in reality. If you have some hypothesis about how reality works you can use math to calculate what the consequences would be if that hypothesis is true, but critically, you have to compare those predictions against reality to see if your hypothesis is accurate.
Simply put as others have expressed well, we dont see them.
However that is not to say there arent other dimensions and physicists, myself included, have spent a lot of time looking for them. Sadly to this date, we’ve so far uncovered zero evidence that they exist which is disappointing to say the least.
There are two popular models of extra dimensions in particle physics (although less popular these days as the LHC has found no evidence of them), [large extra dimensions](https://en.wikipedia.org/wiki/Large_extra_dimensions) and [warped extra dimensions](https://en.wikipedia.org/wiki/Randall%E2%80%93Sundrum_model)
These models postulate very small extra dimensions which we are simply too big to observe (even the large ones are a relative term..). Think of it this way, say you are walking along a tightrope. You can only move in one dimension. However if there is an ant on the tightrope, it can move around the tightrope as well as its much smaller and thus can move in 2 dimensions. But to you that extra dimensions is so small it simply doesnt exist for you.
Now why do physicists spend a lot of time looking for extra dimensions? The reason is gravity is a very odd force and one of its oddities is that is extremely extremely weak compared to the other know forces, like stupidly weak. As in size of a grain of rice vs size of the milky way style difference
One explanation is that gravity is actually the roughly the same strength but there are extra dimensions which it spreads out in. So we only see a fraction of the strength of gravity, ie thinking the only water in the lake is its surface. Warped extra dimensions achieve this another way but thats more ELI A PHD.
We’ve spent a lot of time looking at the LHC for evidence of these particles (we can either see a particle leaving our 3+1 D world or see a resonance effect from the confinement of the extra dimensions) but sadly we’ve seen zero evidence of them and as far as we can tell we’re just a 3+1 D universe. We’re still looking though and maybe one day we find some evidence as honestly it would be pretty cool if this was the case!
And as a final parting comment, complex numbers are amazing and you can literally see the effect of them on the real world as light is a consequence of them in our theories. The equation of free electron being symmetric with respect to a complex phase shift requires that the photon must exist otherwise it all falls apart!
A rather cute, somewhat theatrical and definitely not ELI5 explanation is [here]( https://users.hep.manchester.ac.uk/u/twyatt/electrodynamics/R_Barlow_1990_Eur_J_Phys_11_008.pdf)
>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.
They don’t “exist”. We invented them so we can explain things better.
Others have explained the 3D part, so I won’t expand further, but..
The problem with models is that they can model anything you imagine, whether it’s physically true or not, this then becomes an important fact: models are not inherently connected to reality.
This is boiled down in a great quote: “All models are wrong, some are useful”
There are three things that get confounded: physical _reality_, our _perceptions_, and our _models_ of it.
What we perceive is clearly 3D. Our world behaves in such a way that our brains have evolved to interpret position and velocity as 3D. There are left-right, front-back and up-down, and maybe time. Not more, not less, according to every human. So we can be pretty sure that our perception says we live in three spatial dimensions, not more, not less.
Our models of physics also work quite fine with 3+1 dimensions. We modelled the world based on our perception and found that it can describe a lot of things very well. So we stuck with it, as no other dimensional count so far has done equally good or better. There are a few propositions of there actually being more (or even less) dimensions in string theory and holographic universe, but those are mere suggestions without any verified example where they work better than the 3D theories; they even usually explain how all sane amounts of mass and energy result in exactly 3D behaviour.
The true reality, if that is even a thing, however might be quite different. We could be 2D holograms considering themselves 3D, or shadows of 23-dimensional objects. Quantum physics (just a model again!) already involves infinitely-dimensional things, so that is also an option. Maybe the concept of dimension doesn’t even apply to the actual universe!
However, if the universe at least satisfies some structures we consider “sane”, we could claim that the part we actually interact within, what is called a _submanifold_, might truly be 3 space and 1 time dimension. So there is more, but it is forever impossible to perceive or interact in any way, and the part left to us is truly the size we think. We could never actually verify that, but that doesn’t change that it _might_ be that way.
OP, you should hold that thought, and learn about the difference between invention and discovery. I think you’re missing some key points that would show you some of your assumptions are not correct.
Let’s break this down:
**1. Do we really live in just 3 dimensions?**
While our daily experience is primarily rooted in three spatial dimensions (length, width, height), theoretical physics suggests more dimensions, especially when exploring concepts like string theory.
**2. Time as the Fourth Dimension:**
Yes, time is often referred to as the fourth dimension. In relativity theory, time and space are intertwined into a 4-dimensional spacetime continuum. So, when we talk about events in our universe, we reference them in four dimensions (3 space + 1 time).
**3. Higher Dimensions in Theoretical Physics:**
Some theories in physics, especially string theory, postulate the existence of more than four dimensions. One common version of string theory proposes 10 dimensions. Here’s a simple breakdown of these dimensions:
– **0th Dimension:** A point in space.
2. **1st Dimension:** A line connecting two points.
3. **2nd Dimension:** A plane, having length and width.
4. **3rd Dimension:** Depth is added to the plane, forming a volume.
5. **4th Dimension:** Time, forming the spacetime continuum.
6. **5th Dimension:** This is where the idea of a multiverse comes in. At this level, we can imagine another world slightly different from ours.
7. **6th Dimension:** A plane where all possible worlds with the same start conditions exist. If you imagine a world where, say, you turned left this morning instead of right, it would be in this dimension.
8. **7th Dimension:** A plane containing all possible universes with different start conditions.
9. **8th Dimension:** All possible worlds, starting with all possible start conditions and laws of physics.
10. **9th and 10th Dimensions:** The specifics get even more theoretical here, but in essence, these dimensions encompass all possible universes, histories, and laws of physics. Every possible universe exists in these dimensions.
**4. Why don’t we see/experience these higher dimensions?**
Just because certain dimensions might exist doesn’t mean we can perceive or interact with them. Much like a 2D being on a flat plane wouldn’t be able to perceive or understand the third dimension, we, as 3D beings, might be limited in our perception of higher dimensions.
**5. Gases and Higher Dimensions:**
The argument you referenced about gas volume comes from a physics thought experiment. If our universe had more than three easily perceivable spatial dimensions, the behavior of gas molecules would be different than what we observe. The inverse square law governing forces like gravity and electromagnetism would be different in a universe with more than three spatial dimensions. Our observations match a universe with three spatial dimensions and one of time.
In conclusion, while our immediate experiences are grounded in a 4D spacetime, theoretical physics delves deep into the possibility of higher dimensions. The exploration of these ideas is ongoing, and it’s one of the many intriguing aspects of modern science!
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