Invariants are the conserved quantities (time-independent, space-independent).
Invariants in particle physics
- charge
- spin
- mass
- Other conserved quantities
Invariants in graph theory
There may be invariants of neural networks. We can develop algorithms to discover them. These algorithms may employ AI. The invariants of neural networks can be very useful to build models of cognition.
- Can Deep Networks Learn Invariants?
- Machine Learning Topological Invariants with Neural Networks
- Measuring Invariances in Deep Networks
Other types of invariants
- frequency spectrum
- phase-space
Both procedures (frequency spectrum and phase-space) extract a static picture from dynamical processes.
Cosmological constant
There is some evidence that energy density of space is invariant.
“In cosmology, the cosmological constant (usually denoted by the Greek capital letter lambda: Λ), alternatively called Einstein’s cosmological constant, is the constant coefficient of a term that Albert Einstein temporarily added to his field equations of general relativity. He later removed it. Much later it was revived and reinterpreted as the energy density of space, or vacuum energy, that arises in quantum mechanics. It is closely associated with the concept of dark energy.” – Wikipedia
Fine structure constant
There is extensive literature on the significance of the invariant known as the fine structure constant.
For an introduction to the fine structure constant, I recommend this article. Many physicists speculated about the significance of this constant.
“Where does α come from; is it related to π, or perhaps to e? Nobody knows, it is one of the great damn mysteries of physics: a magic number that comes to us with no understanding by man. You might say the hand of God wrote the number and we don’t know how He pushed his pencil.” – Richard Feynman
Michael Atiyah could not resist writing about the fine structure constant either.
Suresh Emre
Renaissance Universal 