- #1

beyondthemaths

- 17

- 0

When there are gravitational accelerations present, as for example in the

gravitational field of the earth, the space cannot be the flat Minkowski space. Indeed,

in the Minkowski space we can have

$$\Gamma^{\lambda}_{\mu\nu}=0$$

everywhere. This should then be interpreted as meaning that the sum of the inertial

and the gravitational acceleration could be made equal to zero everywhere. This

**does**,

however,

**not correspond to our experience about gravitational accelerations: When**

gravitational accelerations exist, it is not possible to make them vanish everywhere.

gravitational accelerations exist, it is not possible to make them vanish everywhere

**We can only make them vanish at one point, or approximately in a small region, by the**

use of an appropriate coordinate system.Therefore, when a gravitational field is

use of an appropriate coordinate system.

present, the space will be necessarily a curved Riemannian space. The gravitational

field will then appear as the expression of the fact that we are in a curved riemannian

space and no longer in the flat Minkowski space.

For the sentence in bold, what

**experience**that tells us so about gravitational accelerations (that we can not make them vanish everywhere except in a small region)? How do we know that?