Free Fall, Elevators, and Weightlessness

The falling elevator

Einstein called it "the happiest thought of my life." Imagine you are standing in an elevator and the cable snaps. For the few seconds before the crash, something strange happens: you, your phone, the coffee cup you dropped — everything falls together, at exactly the same rate. Relative to the elevator, the cup just hangs in the air beside you. You feel weightless. There is no experiment you could do inside that sealed box to tell whether you are falling toward Earth or drifting peacefully in deep space.

Why astronauts really float

Here is a myth worth killing. People often say astronauts on the Space Station float because they are "beyond Earth's gravity." They are not. The station orbits only about 400 km up, where Earth's gravity is still about 90% as strong as on the ground. Astronauts float for the very same reason as the person in the snapped elevator: the whole station and everyone in it are in continuous free fall. They are falling around the Earth — moving sideways so fast that they keep missing it.

  Newton's cannonball: fall + sideways speed = orbit

          .  -  -  -  .
       .'              '.        slow shot:
     /      ___           \      falls back to ground
    |     .'   '.    ()----+---->  faster shot:
    |    | EARTH |    \          curves down but the
    |     '.___.'      \         ground curves away too
     \                  \
       '.              .'  ----> just-right speed:
          '  -  -  -  '          it falls forever = ORBIT

   An orbiting astronaut is always falling, never landing.

Free fall is the natural motion

Notice what you actually *feel*. In the falling elevator you feel nothing — no push, no pull, no weight. Standing on the ground, by contrast, you feel the floor shoving up on your feet every second of the day. Einstein took this seriously and flipped the usual story: free fall is the relaxed, force-free, natural state of motion. What needs a force, and what you actually feel, is being *stopped* from falling — by the floor, by your chair, by the ground pressing back.

1. Standing on the ground: the floor pushes up on you. You feel weight. You are being held *off* your natural path.
2. Jumping off a diving board: for a moment nothing pushes on you. You feel weightless — you are back on your natural path.
3. Orbiting in the station: nothing ever pushes on you. You float for hours — endless free fall, endless natural motion.

The first hint of curved spacetime

Now comes the leap. In empty space, a force-free object moves in a straight line — the *straightest possible* path. We just decided a freely falling body is also force-free, the most natural motion there is. So a thrown ball, the Moon, and a falling apple should all be tracing the *straightest possible* paths too. Yet their paths through space are obviously curved. The only way to keep both ideas is breathtaking: the spacetime they move through is itself curved, and they are simply following the straightest path available in it. That straightest-possible path has a name — a geodesic.