Since white is our perception of reflection of light, why are mirrors and other metallic objects that are more grey or silvery capable more reflective than a white object?
This is somewhat related: What is the difference between a white object and a mirror? but I'm wondering why more white objects aren't mirrors.
An object is white when it reflects more or less any color – any frequency – and it reflects it in a random direction: the light gets scattered.
For this reason, the photons arriving from a specific point of the white object (e.g. a point on the paper) are photons that arrived there from random directions in the space and they have random colors. Because the white object mixes the directions, it mixes the colors, too, and the mixture of all colors (including red, green, blue) looks like white light.
A mirror is an object that reflects the photons in a specific direction – the direction that only changes the sign of the angle between the photon and the (tangent to the) surface of the object.
An ideal mirror would reflect all colors perfectly so it would appear colorless. However, there's some scattering from metals such as silver, platinum, and iron. This is mostly independent of the frequency so the metals appear color-neutral i.e. grey.
Copper, gold, and others tend to scatter especially longer [thanks for the fix] (redder) wavelengths, so they appear redder – orange or yellow (shiny yellow i.e. golden) etc. Incidentally, individual gold atoms not bound in the macroscopic body would appear greenish, not yellow.
This is similar to why a glass of water and a glass of milk look different. We can use geometric optics (used in 3D animation ray tracing) to explain this.
When a light ray (of any color) hits a mirror, it reflects as another light ray. But for a white nonreflective surface, it is scattered in all directions.
From the perception side, a eye gathers incoming light rays to form image on the retina. From a mirror, a light ray on a point originated from a single light ray from elsewhere. From a white surface, a light ray originates from contributions from multiple directions, which usually averaged out to white, i.e., combination of wavelengths that stimulates all color pigments in the retina.
Note that I'm assuming our eye is a pin hole camera, so a point in the retina image corresponds to a single light ray direction. The purpose of the lens though is gather multiple light rays (in multiple directions) eminating from a point back to a point again. So if your eyes are unfocused, colors can get blended.
