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What's interesting there is that our understanding of elements is almost entirely theoretical. The math works out, but we might be missing entire particle structures or interactions. We observe atomic forces and give them names, but it's all built on particle theories that started as one lump and have been honed over time.
Aliens might have a periodic table of dimensional harmonic wave frequencies. Our concept of elements to aliens might be like when we meet an uncontacted culture which does not have numbers larger than 4.
Some parts of the theory have been demonstrated. For instance:
https://www.newscientist.com/article/2279115-this-is-the-most-detailed-look-at-individual-atoms-ever-captured/
This is a scanning electron microscope image of a crystal structure (PrScO~3~). The bright spots are atomic nuclei.
The full paper is here: https://www.science.org/doi/10.1126/science.abg2533
To interact with us in any meaningful way I think we have to assume that the aliens exist in our universe composed of atoms. Regardless of how they perceive the atomic structure, the structure would be the same.
Sure, but even that is based on perceiving electromagnetic waves visually. The electron microscope represents the smallest particle that we can bounce off of another particle. That's why we can't visualize things on a smaller scale. Then we have the Planck length which is the theoretical limit of what we can predict physics are like at tiny scales.
But imagine a life form that evolved to perceive gravitational waves instead of electromagnetic waves (light). Or maybe there's some other force that we aren't even aware of.
So much of our understanding of the universe is a reflection of some Precambrian paramecium mutating an eyespot or cilia that can detect sound waves.