Readers to these pages (not all in mobile ready form) may also enjoy this modern physics teaser for our How Things Work students, using mainly concepts that are discussed during the course itself:

**Quantum weirdness recap:** __Refracted photons__ & __quantum copy protection__ use "explore-all-paths" to create *a combined path of least time* provided "no-one is looking", __LASERs__ use herd behavior by photons, __solid state diodes__ & __atomic spectra__ use the 720^{o} exclusion rule for electrons, while __flash memory__ & __alpha decay__ use the uncertainty principle's quantum tunneling. The pairings between scalar quantities time t and energy E, and vector quantities position **x** and momentum **p**, show up in the uncertainty relations {ΔEΔt ≥ h/(4π), Δp_{x}Δx ≥ h/(4π)} and in the free particle relations to temporal-frequency *ν* and spatial-frequency **g** as E = h*ν* and **p** = h**g** (first seen as deBroglie's h/λ).

**Spacetime weirdness recap:** __Traveler-time__ elapsed δτ is connected to __map-distance__ traveled δx and __map-time__ elapsed δt by a "Pythagorean" __metric equation__ of the form (cδτ)^{2} = (cδt)^{2} - (δx)^{2} where "lightspeed" c is the number of meters in a second. As a result __coordinate-speed__ v ≡ δx/δt has an upper limit of c and requires synchronized clocks to measure, while __proper-speed__ w ≡ δx/δτ equal to __momentum per unit mass__ m does not. Furthermore motion, along with gravitational and inertial forces, is associated with __differential aging__ γ ≡ δt/δt that gives rise to __kinetic energy__ and __potential energy__ differences of the form (δt/δτ-1)mc^{2}.
This relation reduces to the usual Newtonian relations for kinetic
energy and "geometric force" potential energies, in the case of low
speed (δx/δτ) << c and weak fields/accelerations.

**Informatics weirdness recap:** The equation S = k ln[W] on Ludwig Boltzmann's 1906 tombstone may be more familiar today as #choices = W = e^{S/k} = 2^{#bits}. We now know that thermodynamics is a special case of __statistical inference__ from the __correlation between objects and models thereof__,
which can be no greater than the correlation (also measured in bits)
between those objects and the world around them. These insights: __connect information to ordered energy__ and to the 2nd law of thermodynamics, mean that __coldness__ (reciprocal temperature between ±∞) is energy's uncertainty-slope dS/dE e.g. with room-temperature (22^{o}C)
coldness about 1/kT ≈ 39.3[nat/eV] ≈ 44.3[GB/nJ], and have applications
in quantum computing, molecular biology, electronic communications, and
our understanding of the __bloom and decline phases__ of gene/culture co-evolution.