In classical mechanics, the equation that describes the force of gravity between two objects is given by Newton's law of universal gravitation:
F = (G * m1 * m2) / r^2
Where:
- F represents the force of gravity between the two objects,
- G is the gravitational constant (approximately 6.67430 × 10^(-11) m^3 kg^(-1) s^(-2)),
- m1 and m2 are the masses of the two objects, and
- r is the distance between the centers of the two objects.
This equation provides a good approximation for the gravitational interaction between macroscopic objects.
However, when it comes to incorporating gravity into the framework of quantum mechanics, the situation becomes more complex. The theory that aims to describe the gravitational force within the framework of quantum mechanics is called quantum gravity. While a complete and universally accepted theory of quantum gravity is yet to be developed, there are several candidate theories that researchers have been exploring, such as string theory, loop quantum gravity, and others.
In these theories, the equations describing gravity are significantly different from the classical equations. They involve intricate mathematical formulations and are generally expressed using advanced mathematical tools like differential geometry and functional analysis. The specific equations differ depending on the particular approach or theory being considered.
For example, in string theory, the equations involve vibrating strings and higher-dimensional spacetime, whereas in loop quantum gravity, the equations involve discrete quantum properties of spacetime. The precise form of the equations depends on the details of the theory and the specific aspects of gravity being considered.
It's worth noting that quantum field theory, which is highly successful in describing other fundamental forces (electromagnetism, weak nuclear force, strong nuclear force) in the framework of quantum mechanics, has not yet been able to fully incorporate gravity. The development of a consistent theory of quantum gravity remains an active area of research in theoretical physics.