[Physics] About "logical errors"

[Ilja Schmelzer]

2016-11-10 16:22 GMT+01:00, mike at mlawrence.co.uk <mike at mlawrence.co.uk>:
> But I disagree that it does not matter what is
> providing the acceleration. .... In the acceleration due to gravity, there is the
> mass of the Earth being included in the calculation.
> ... In the acceleration case, in the FOR of the object there is
> a force acting to move the object faster...... but you don't include the
> source of that force in your calculation.

Indeed, according to GR, there is a big difference in the formulas for
computing clock time dilation. If the force is non-gravitational,  one
can use the SR formula, all what matters is the actual velocity, and
the SR time dilation factor computed for that velocity.

If gravity is involved, one has to know the gravitational field, and
has to use the formula for a clock in some gravitational field.

\[ \tau = \int \sqrt{g_{mn}(x,t) dx^m(t)/dt dx^n(t)/dt} dt \]

This mathematical (and physical - different formulas mean different
observable predictions for clocks) difference is behind those many
vague talking about gravitational force not being a force and so on.