Disclaimer: I am not a physicist.

Einstein has discovered that some physical properties are relative.

In this blog post I present the conjecture that essentially all physical properties are relative. I do not formulate exact details of this theory, a thing which could be measurable, but just a broad class of specific theories. Nevertheless the theory which I formulate in this blog post is mathematically exact.

Let $latex P$ be the set of (relative) physical properties. We will make $latex P$ into poset by the order of which properties are more relative and which are less relative. (With the axiom that less relative properties may be always restored knowing more relative properties.)

Consider the filter $latex F$ characterizing positive infinity (that is infinitely least relative properties) on the poset $latex P$, that is the filter $latex F$ defined by the base of all strict sets $latex \uparrow X\setminus\{X\}$ where $latex X\in P$ and $latex \uparrow X$ denotes the principal filter induced by the element $latex X$ (if such a base exists). Note that $latex \setminus\{X\}$ is essential: Otherwise we could consider the principal filter $latex F$ induced by the maximum element of $latex P$ and the corresponding property would be absolute (non-relative).

My conjecture: The only really existing (non-relative) physical properties are values of relative properties on the filter $latex F$.

Formally: The only really existing physical object is a monovalued reloid whose domain is the filter $latex F$.

My theory may become into something verifiable by experiment if someone specifies what is $latex F$ exactly.

I’ve explained what the “positive infinity filter on a poset” means, and corrected some mathematical errors (or rather a vague explanation) in this blog post.