Proper Work

I am confused about Einstein's equivalence principle. Consider a book sitting on the Earth's surface. The book has a non-zero proper acceleration. But I thought it took work to accelerate an object. Specifically, from the point of view of a freefalling observer (an inertial observer according to the equivalence principle) there is a net force on the object and the object is travelling in the direction of the force ... work = force * distance ... and the book is gaining kinetic energy according to the inertial observer. Where is the energy coming from that allows the earth to continually accelerate the book? Furthermore, since it is the proper acceleration that is non-zero, all observers and coordinate systems will agree the book is indeed accelerating. I must be misunderstanding the equivalence principle as it seems to lead to contradictions. Please help, Ben
- Benedek (age 16)
Birchham, AL, USA

Ben- Very deep question. Yes, in the free-fall frame there is a force from the Earth pushing the book 'up' and doing positive work on it. However, there is also an exactly equal force from the book on the Earth pushing 'down' and doing equal negative work on it. (Remember Newton's 3d law and that the displacements of the book and Earth are equal.) So whatever problems we have in translating our conservation of energy laws into a General Relativistic framework, there is no problem with conservation of energy arising from these ordinary forces.

Mike W.

(published on 05/16/2013)