Acceleration/gravitation equivilence

[The Geoff]

One of the foundations of GR as we were taught at school is that there is no way to differentiate between a force felt due to acceleration and a force of the same magnitude caused by a gravitational field.

 

However, the acceleration caused by a rocket (for example) is linear, everything is being pushed in the same direction. A gravitational field, however, is invariably curved in some way....if I hold my arms out and drop a coin from each hand they won't fall in the same direction, they'll converge slightly because they're both heading towards the same place, the centre of the Earth.

 

So given that an infinite plane (to give a perfectly linear gravitational field) is impossible, you can always differentiate between acceleration and gravity if your experiment is sensitive enough.

 

Does this cause GR any problems? Or is it one of those "good lies" to try and explain the maths?

[ajb]

Interpreting the weak equivalence principle this way is fine for "small enough regions".

 

 

Imagine a sealed box, in which we observe freely falling particles. Provided the gravitational field does not vary over the box then it is impossible to distinguish this situation from the box being constantly accelerated by only observing the particles in free fall.

 

The weak equivalence principle states that inertial and gravitational mass are the same. This is why the above is true.

 

The same would not hold if we considered charged particles in an electromagnetic field. By examining different charges we would "see" the electromagnetic field.

 

Now this can be extended to a stronger version of the equivalence principle, which states that in a small enough region you can not distinguish gravity from constant acceleration by any experiment. More precisely, all the laws of physics reduce to those of special relativity.

 

I don't know what the experimental situation is with the second stronger version of the equivalence principle, but it is not difficult to construct theories that don't obey it. (Non-minimally couple fields to gravity for example.)

[swansont]

One of the foundations of GR as we were taught at school is that there is no way to differentiate between a force felt due to acceleration and a force of the same magnitude caused by a gravitational field.

 

However, the acceleration caused by a rocket (for example) is linear, everything is being pushed in the same direction. A gravitational field, however, is invariably curved in some way....if I hold my arms out and drop a coin from each hand they won't fall in the same direction, they'll converge slightly because they're both heading towards the same place, the centre of the Earth.

 

The inability to properly recreate/simulate the gravitational field does not mean the principle is wrong.

[kleinwolf]

The equivalence is locall..this means your rocket should have a different acceleration depending on space and time...for example :

 

In the gravitational field of a point (or sphere), the equivalent acceleration at a certain (constant) radius is constant a®=GM/r², if you are farther away the acceleration of your rocket changes