Does Einstein's Theory of Relativity Apply to Everyday Gravity on Earth?

[Simon Bridge]

This is why I question the practicality of GR on earth.
Perhaps its because I haven't studied GR in depth but I cannot grasp the 2 previous Einstein statements.
They directly contradict Newton which is what I was taught in motion physics.

GR replaces Newtonian physics.
Newtonian physics is a subset of General relativity - it provides a very useful approximation for the set of phenomena that it covers.

I'm a little concerned about your understanding of Newtonian physics though:

A body at rest has a velocity that remains at zero. How does something accelerate without even moving?

But you already know that happens in Newtonian mechanics too
- if an object starts with velocity vi and acceleration ai where a<0,
- then at some time it's velocity will be zero (it is "at rest" for an instant) but it's acceleration is still non-zero. So you are quite familiar with the idea of stationary objects having acceleration.

An example would be a thrown ball at the top of it's trajectory or an object bouncing off a solid surface, or a pendulum bob at each end of the swing.

This is not what happens with gravity though:

Another examples: A body may also be at rest in an accelerating reference frame and, therefore, accelerating in an inertial one. Even in Newtonian mechanics you need to be careful about which reference frame you are talking about.

If an object is stationary in an inertial frame and it is viewed from an accelerating frame, the object will appear to that observer to be accelerating.

A lot of the concepts in GR also exist in Newtonian physics. i.e. pseudo-forces.

In Newtonian mechanics, centrifugal force is treated as fictitious - an artifact of being in a non-inertial reference frame. You call it a pseudo-force. You will realize that the surface of the Earth is not an inertial reference frame, so we see centrifugal and coriolis effects.

General relativity just treats gravity as a pseudoforce. The acceleration of gravity is an artifact of being in a non-inertial reference frame. When you treat it that way, a lot of tricky maths gets simpler - which is why the idea caught on. It extends the concept of a non-inertial frame beyond what is in Newtonian mechanics.

The Newtonian idea of the equivalence of inertial frames (there is no experiment you can do, locally, to determine absolute uniform motion) is, in GR, extended to gravitation in a similar manner. It's hard to grasp, but the usefulness of the idea is confirmed by experiment.

The usefulness of Newtonian physics is not in dispute.
On small scales GR gives pretty much the same answers as Newtonian physics.
We also don't bother with the Newton's Law of Gravitation all that much... replacing it with a constant force because it doesn't change much close to the surface of the Earth.

 

[Chestermiller]

This is why I question the practicality of GR on earth.
Perhaps its because I haven't studied GR in depth but I cannot grasp the 2 previous Einstein statements.
They directly contradict Newton which is what I was taught in motion physics.
A body at rest has a velocity that remains at zero. How does something accelerate without even moving?

Suppose you're on that ride at the amusement park where the platform is rotating, and you are situated against the cylindrical vertical wall. We used to call this ride the "Roundup." At some time, the floor drops out, but you are still pinned against the wall. From the perspective of your frame of reference inside the cylinder, you are at rest. Yet you are experiencing an acceleration. This is somewhat analogous to what happens with gravity in GR (although, there, the time dimension is participating in the acceleration effect). If you are at rest in proximity with a large gravitating mass like the earth, then you are not in an inertial frame of reference.

Chet

 

[Dale]

This is why I question the practicality of GR on earth.

If all you want to do is describe apples falling and satellites and rockets flying around the solar system, then GR is not practical. Newtonian gravity is almost as accurate and easier to compute.

If you want to describe very fast objects, very strong gravity fields, or very sensitive measurements then you cannot avoid GR.