Ciro Santilli @cirosantilli  40

Generally means that he form of the equation $f(x)$ does not change if we transform $x$.

This is generally what we want from the laws of physics.

E.g. a Galilean transformation generally changes the exact values of coordinates, but not the form of the laws of physics themselves.

Lorentz covariance is the main context under which the word "covariant" appears, because we really don't want the form of the equations to change under Lorentz transforms, and "covariance" is often used as a synonym of "Lorentz covariance".

TODO some sources distinguish "invariant" from "covariant": invariant vs covariant.

Does not appear to refer to any one specific phylogenetic level, it usually refers to either:

Size: 10 micrometers.

Genome:

Proteins per cell: 42m: www.cell.com/pb-assets/journals/research/cell-systems/cels_384.pdf

Division time: 100 minutes.

Minimization project: en.wikipedia.org/wiki/Saccharomyces_cerevisiae#Synthetic_yeast_genome_project | syntheticyeast.org/

Named after radio pioneer Heinrich Hertz.

In the Galilean transformation, there are two separate invariants that two inertial frame of reference always agree on between two separate events:

However, in special relativity, neither of those are invariant separately, since space and time are mixed up together.

Instead, there is a new unified invariant: the spacetime-interval, given by:

Note that this distance can be zero for two events separated.