Caption: The Alien in an elevator.

Features:

1. Newton's 2nd law of motion (AKA F=ma) applied to bodies (e.g., the Alien) in the elevator in the vertical direction (taking upward as positive) is

       ma = F_net = F_other + m(-g) ,

   where m is the body's mass, a is the acceleration of the body (more exactly of its center of mass), F_net is the net force on the body, g = 9.8 m/s**2 is the Earth's gravitational field strength with fiducial value 9.8 m/s**2, -g is the gravitational field (which points downward hence the explicit minus sign), -mg is the gravitational force on the body, and F_other is the net force on the body except for the gravitational force.

2. Note that in both Newtonian physics and relativistic physics , there is NO way the Alien can determine the velocity of the elevator from just of the inside of the elevator---it could be rising, sinking, or at rest relative to the outside world.

   The Alien can determine the elevator's acceleration with the right equipment and from knowing the gravitational field.

3. Now we subtract off from both sides of the above equation ma_el (which is the body's mass times the acceleration of the elevator) to get

       m(a-a_el) = ma_rel = F_other - m(g+a_el) = F_other - mg_eff

   or

       ma_rel = F_other - mg_eff ,

   where a_rel the body's acceleration relative to the elevator and g_eff = g+a_el is the effective gravitational field strength.

4. From the last equation, we see that relative to the elevator it's as if the gravitational field strength had been changed from g to g_eff=g+a_el

   Some examples elucidate the situation:

   1. Say a_el = -g which gives g_eff = 0. This means the elevator is accelerating downward in free fall.

      Everything in the elevator is weightless. The Alien is floating carefree---until the elevator hits the bottom of the elevator shaft, of course.

   2. Say a_el = 0. The elevator is in uniform linear motion and the effective gravity is just the ordinary gravity.

   3. Say a_el = g or g_eff = 2g. Now the Alien and everything in the elevator have effectively doubled their weights.

      Really, the elevator has to push up on the Alien's feet with normal force m*(2g) to counter gravity on the Alien and accelerate the Alien upward at rate g.

      Likewise internally, every layer of the Alien's body has to counter gravity on every layer above itself and accelerate every layer above itself at rate g.

      So the Alien feels twice as heavy as normal.

      In rocket jargon, the Alien is experiencing a G-force of 2g.

      In an unaccelerated elevator, the G-force is 1g which is what we all normally experience.

   If you have ever been in a rapidly accelerating elevator, you know the above cases are true for yourself.

5. The quantity -ma_el is called an inertial force. Inertial forces are NOT real forces, but are an effect of being in a non-inertial frame like an accelerating elevator.

   Inertial forces act equally per unit mass on all bits of a body---just like gravity. For this reason, they are considered body forces