When I think about describing what it means for something to have a certain size, I keep running into tautological explanations:
- An object has size if you can compare its size to something else (that has size)
- An object is large if it is bigger than another
- An object has size if it can be described as spanning distance in at least one physical dimension.
All of these arguments invoke variants of the same notion; big, small, distance, etc. The best lay analogy I can think of for this problem is the question of what time is. However, in that case I can understand intuitively how time could be an emergent phenomenon (e.g. if there is a 4th dimension in which slices of 3 dimensional space interact in such a way as to give the illusion of the passage of time). Quantum mechanics also explains how many physical properties are emergent, but even the Schroedinger equation's wave function has spatial coordinates as an input.
Is there a fundamental description or some kind of explanation for what the physical dimensionality of an object actually is? Can size be explained as emergent from some deeper understanding (or hypothesis) of reality?
I'm not a physicist so the tools at my disposal for answering this question are severely limited.
