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)*