Absolute Acceleration?
Most recent answer: 10/22/2007
Q:
How can the theory of general relativity state that there’s no absolute inertial reference system while a foucault pendulum seems to oscillate with respect to such a system?
- david (age 26)
montreal
- david (age 26)
montreal
A:
Here’s an expanded version of what we think you’re asking, just to
make it clearer to other readers.
Newtonian physics makes a clear distinction between inertial reference
frames, in which Newton’s laws take their simplest form, and non-inertial
coordinate systems, in which the motion of objects is more complicated, with extra forces coming from nowhere. The rotation of the oscillation plane of a Foucault pendulum in a coordinate system fixed to the room in which the pendulum swings
is a classic example of an effect arising from the fact that the
room’s coordinate system, which is tied to the Earth’s spinning surface,
is not an inertial reference frame. So how can General Relativity claim
that you can use the same laws of physics in a broad class of frames,
including ones like the room where you see the pendulum’s plane
rotate?
The General Relativistic laws include all sorts of effects from
the curvature of spacetime. In a frame tied to a room on Earth, those
effects are quite big. The biggest effect is the fact that the pendulum
swings back and forth (if the room’s coordinate system were an inertial
reference frame, the pendulum would float freely). A smaller but
very noticeable additional effect is the rotation of the pendulum plane. So
why don’t we just pick a frame where those effects are zero, call it
inertial, and forget all the complications? It turns out that so long as
gravity is present, there are no global inertial reference frames,
only local ones, which describe infinitesimal regions of space and time.
The Newtonian description of gravity as a force in flat spacetime
is not correct and experimental evidence strongly favors General
Relativity over the Newtonian model.
General Relativity allows us to do our calculations in any coordinate
system we like and get the same predicted behavior if we use any other
coordinate system. The locations and times of events, such as the
pendulum bob knocking over a wooden peg standing on the floor, have
to be converted from one set of coordinates to another, of
course. In practice, we use the simplest coordinates possible.
There are very interesting related experiments which
test the predictions of General Relativity. For example, see
the web site of
at Stanford University, which is an experiment to measure the
precession induced in rotating spherical gyroscope balls in orbit
around the spinning earth. The description of what the experiment
is all about is in .
Tom and Mike
make it clearer to other readers.
Newtonian physics makes a clear distinction between inertial reference
frames, in which Newton’s laws take their simplest form, and non-inertial
coordinate systems, in which the motion of objects is more complicated, with extra forces coming from nowhere. The rotation of the oscillation plane of a Foucault pendulum in a coordinate system fixed to the room in which the pendulum swings
is a classic example of an effect arising from the fact that the
room’s coordinate system, which is tied to the Earth’s spinning surface,
is not an inertial reference frame. So how can General Relativity claim
that you can use the same laws of physics in a broad class of frames,
including ones like the room where you see the pendulum’s plane
rotate?
The General Relativistic laws include all sorts of effects from
the curvature of spacetime. In a frame tied to a room on Earth, those
effects are quite big. The biggest effect is the fact that the pendulum
swings back and forth (if the room’s coordinate system were an inertial
reference frame, the pendulum would float freely). A smaller but
very noticeable additional effect is the rotation of the pendulum plane. So
why don’t we just pick a frame where those effects are zero, call it
inertial, and forget all the complications? It turns out that so long as
gravity is present, there are no global inertial reference frames,
only local ones, which describe infinitesimal regions of space and time.
The Newtonian description of gravity as a force in flat spacetime
is not correct and experimental evidence strongly favors General
Relativity over the Newtonian model.
General Relativity allows us to do our calculations in any coordinate
system we like and get the same predicted behavior if we use any other
coordinate system. The locations and times of events, such as the
pendulum bob knocking over a wooden peg standing on the floor, have
to be converted from one set of coordinates to another, of
course. In practice, we use the simplest coordinates possible.
There are very interesting related experiments which
test the predictions of General Relativity. For example, see
the web site of
at Stanford University, which is an experiment to measure the
precession induced in rotating spherical gyroscope balls in orbit
around the spinning earth. The description of what the experiment
is all about is in .
Tom and Mike
(published on 10/22/2007)