# Inertial Equivalence

#### Woody

I have seen a number of posts indicating that while it seems impossible to identify any difference between the inertia from acceleration and the inertia from gravity, there has been no theoretical reason discovered why they must be the same

As an object is accelerated, its space-time co-ordinate system is changing relative to its original space-time co-ordinate system.
We normally don't consider this effect until the velocity difference reaches a substantial fraction of the speed of light, but it does still happen at "normal" speeds.

One might expect such a change to require the transfer of energy,
(which with suitable mathematical shenanigans should lead to F=mA).

The gravitational distortion of space-time by a mass also causes a change of an objects space-time coordinate system.

Can the effects of these two methods of altering the space-time coordinate system be equated?
If so, could not the acceleration and gravitational inertia also be sensibly equated?

Note that is really just idle speculation on my part.
Please feel free to pull the idea apart, the reasoning against it will be instructive.

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#### HallsofIvy

I have seen a number of posts indicating that while it seems impossible to identify any difference between the inertia from acceleration and the inertia from gravity, there has been no theoretical reason discovered why they must be the same
Really? That's what general relativity is all about!

1 person

#### Woody

I think I must have misapprehended those previous comments.
Perhaps they were intending to suggest that there had been no obvious reason to assume the link between gravitational inertia and accelerational inertia,
but by making that assumption, Einstein was able to show that his theory arose as a consequence.

#### Woody

Just been re-examining the old threads, I think that my memory is playing tricks with me.

The particular post that I was remembering actually said:
inertial mass, gravitational mass and relativistic mass are not the same thing
Rather than that inertia from acceleration and from gravity were different.

I will go back and re-examine that thread in more detail....

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#### Woody

Ok the first paragraph of my initial post in this thread was wrong,
However, I think the rest is reasonable.

Following that line of thought,
Inertia is the resistance to moving a mass from one inertial reference frame to another.
It seems intuitively reasonable that changing the reference frame of a mass should be resisted,
However, what generates that resistance?
Are we distorting the (local) space-time geometry by accelerating the mass?