Relativity and Quantum Mechanics: the elevator pitch

Physicist: A woman on the subway, about two stations away from her stop, asked us “what are relativity and quantum mechanics?”
So, this is a two-stop elevator pitch for the two most pivotal sciences since slicedbreadology.

Elevators: Wonderful, mechanical rooms, quietly skirting the ever-thinning line between broom closet and robot.

Relativity: Speed is just distance over time (as in “miles per hour”). Normally when you change you’re own speed, the speeds of everything else changes (for your point of view). For example, if you’re walking slowly down the street everyone else will be moving quickly (and, for the sake of this example, in the same direction), but if you pick up the pace and walk normally, then everyone else will barely be moving at all.

But the speed of light is different. No matter how you move, it will always stay the same. Since that particular speed refuses to change, distance and time have to change instead.  Relativity is the study of how distance and time change with speed, and the consequences that follow from those changes.

Quantum Mechanics: When you look at very, very small objects, like individual particles, you begin to find that they don’t behave right. If particles were like ordinary objects, but smaller like tiny billiard balls, then you’d expect them to act like ordinary (but tiny) objects. Instead, they “ooze” from place to place, move through impassable barriers, exist in several places at the same time, and interfere with each other. It’s impossible even to say exactly where they are.
All of these are impossible (or at least very unlikely) behaviors for solid “particle-ish” objects. But all of these behaviors are explained, and even expected, if all of matter is actually some kind of wave.
So, quantum mechanics is the (more-accurate-than-every-other-science) study of the universe from the perspective that everything, at the lowest levels, is made up of some kind of waves.