If there’s anyone who can, please let me know if the similarities between these two formulas imply a relationship between gravity and electrical attraction or hint at a unified theory, or if it’s just a coincidence or a consequence of something else.
It’s really simple, they are both radial fields with a 1/r potential, thus a 1/r² force.
Newtonian gravity is just a weak field approximation of general relativity, where you have very different equations, for example Einsteins field equations…
One electric charge creates an electric field, and another charge will interact with it, but the motion itself still depends on the mass of the second charge.
Matter instead curves spacetime itself, and the curved spacetime tells matter how to move.
Source: MS in physics.
Doubtful but interesting thinking. It’s actually a rather simple equation that explains how two equally weighted forces affect one another over distance. The numerator expresses that both forces carry equal weight in the interaction (if they are both the same kind of force, eg gravity or electromagnetism, this makes sense) and they are constructive interactions (both add to the intensity of the interaction) hence multiplying one by the other. The denominator just indicates that the distance between the two things exponentially degrades the force at a power of 2, since the force is spreading out in 2 dimensions (imagine a cone starting at one point and extending to the second, so that when you reach the second point the force is spread across the cross section of that cone, but the only part of the force affecting that second point is the part that touches it).
If there’s anyone who can, please let me know if the similarities between these two formulas imply a relationship between gravity and electrical attraction or hint at a unified theory, or if it’s just a coincidence or a consequence of something else.
The most accepted theory among physicists is that “shit’s crazy, yo”.
It’s really simple, they are both radial fields with a 1/r potential, thus a 1/r² force. Newtonian gravity is just a weak field approximation of general relativity, where you have very different equations, for example Einsteins field equations… One electric charge creates an electric field, and another charge will interact with it, but the motion itself still depends on the mass of the second charge. Matter instead curves spacetime itself, and the curved spacetime tells matter how to move. Source: MS in physics.
Doubtful but interesting thinking. It’s actually a rather simple equation that explains how two equally weighted forces affect one another over distance. The numerator expresses that both forces carry equal weight in the interaction (if they are both the same kind of force, eg gravity or electromagnetism, this makes sense) and they are constructive interactions (both add to the intensity of the interaction) hence multiplying one by the other. The denominator just indicates that the distance between the two things exponentially degrades the force at a power of 2, since the force is spreading out in 2 dimensions (imagine a cone starting at one point and extending to the second, so that when you reach the second point the force is spread across the cross section of that cone, but the only part of the force affecting that second point is the part that touches it).