this post was submitted on 30 Jun 2024
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I saw a video on higher dimensional geometry the other day and it said something at the end that gave me the following question: How do we know for sure that anything we perceive in our 3D world is actually only in 3D and not simply what we can perceive of higher dimensions?
Because we see no evidence of a 4th spatial dimension. So if there is a fourth dimension, our universe doesn't seem to have access to it.
If there are higher dimensions, say the extra seven asserted by String Theory, then we have breadth (thickness?) along each axis that is non zero. The higher-order string theory dimensions (which communicate particle information like gravity) are tightly rolled up.
Brian Greene uses the metaphore of an ant on a wire who can move along the wire freely, but can't go far laterally. They may be so small that our quantum bits can't drift anywhere, so our liver doesn't abandon us drift along a high-level axis.
If there are flat higher level dimensions, then either a force or some kind of membrane would have to exist to keep our blood from leaking.
That said, when we have pure elements, or even pure minerals or chemicals, they retain the same density (mass to volume, sometimes affected by temperature) which suggests nothing is hiding away in other dimensions whenever we take measurements. If there is room along higher axes for unseen activity, it doesnt bug us enough to work out consistent properties.
We actually kinda do perceive a fourth dimension: time. Sure, we infer it from our memories and come up with cause and effect relationships to help us understand it. But we do know it's there.
Okay, sure, but the question still remains, how do you know that there isn't some 5th dimension for some random objects.
I think that's one of the theories for explaining dark matter (i personally like the idea because it can also possibly address why gravity seems to be so much weaker of a fundamental force, but i'm a chemist, not a physicist, so take that with a grain of salt).
We don't! When I was younger I had a theory that the brain is a 3D representation of an organ that exists in a higher dimension. Granted, I had (and still have) no relevant expertise to properly speculate on how that could work, but it was fun to think about.