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
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)
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