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Newton's first law provides a guide: "Every object persists in its state of rest or uniform motion in a straight line unless it is compelled to change that stat

Newton's first law provides a guide: "Every object persists in its state of rest or uniform motion in a straight line unless it is compelled to change that state by forces impressed on it." So, the definition of a force as something that causes an object to change its movement from a "straight line" comes to us from Newton's laws. > Why does the existence of a transformation that makes movement under a supposed force actually follow a straight line mean it's not really a force? It's not just the fact that the transformation exists that means we don't really consider gravity to be a force. It's that the transformation exists, and provides useful predictions about the universe that turn out to be backed by experiment. Under the theory of general relativity gravity isn't a force, because the fundamental premises of general relativity assume that gravity is actually a distortion of spacetime caused by mass. We say that "gravity" isn't a force simply because the predictions made by general relativity have been validated by a number of experimental observations—at least on the macro scale. > For the other forces (e.g. electromagnetism) can we say that there's _no way_ to exhibit a transformation that causes charged particles travel on "straight" lines? I'm certainly not an expert, so I can't really comment on this. My best guess is that there doesn't exist any such transformation that causes charged particles to travel on "straight" lines that makes experimental predictions as well as our current scientific theories.

marta_morena_28 6y ago
So what you are saying is that if we assumed that all particles, including light are magnetic, and everything that has a mass, emits a corresponding magnetic field with a strength relative to its mass, we could not form a similar theory of "general magnetic relativity" in which the frame of reference under magnetic fields would behave in a similar way it does for gravity? That seems kinda odd. What exactly would provide this difference? How is magnetism different from gravity? Is it that gravity doesn't have a mass, but magnetic fields do?
- handol 6y ago
  There's no emitting magnetic fields, no diverging fields allowed. The right analogy is between mass and electric charge, only mass is limited to positive values.
- ncallaway 6y ago
  I think (and, again, I'm absolutely not an expert) that a fundamental difference between the two is that from our perspective gravity "effects" particles with 0 mass, while the electromagnetic field does not effect particles with 0 charge. So a photon, which has 0 mass is still bent by gravity. Everything that we've observed that moves through spacetime is bent by gravity. That's why we say that gravity is a warping of spacetime itself, where electromagnetism isn't. If you tried to build the "general electromagnetic theory of relativity", then 0 charged particles wouldn't follow a straight line on a geodesic of spacetime. With gravity, everything follows a straight-line on the geodesic of a curved straight line, regardless of its mass. As to why such a difference exists between gravity and electromagnetism, that's well above my pay grade.
esc_colon_q 6y ago
Actually it's quite easy to cast electromagnetism into a purely geometrical form, you just add a few extra curled up dimensions to a flattish spacetime in general relativity and you basically get Maxwell's equations for free. There are other reasons that's not a great theory (IIRC sources and self-action get nasty and you have to make arbitrary choices about scale, etc), but it's straightforward to get force laws out of pure geometry.

marta_morena_28 6y ago

So what you are saying is that if we assumed that all particles, including light are magnetic, and everything that has a mass, emits a corresponding magnetic field with a strength relative to its mass, we could not form a similar theory of "general magnetic relativity" in which the frame of reference under magnetic fields would behave in a similar way it does for gravity? That seems kinda odd. What exactly would provide this difference? How is magnetism different from gravity? Is it that gravity doesn't have a mass, but magnetic fields do?

handol 6y ago
There's no emitting magnetic fields, no diverging fields allowed. The right analogy is between mass and electric charge, only mass is limited to positive values.
ncallaway 6y ago
I think (and, again, I'm absolutely not an expert) that a fundamental difference between the two is that from our perspective gravity "effects" particles with 0 mass, while the electromagnetic field does not effect particles with 0 charge. So a photon, which has 0 mass is still bent by gravity. Everything that we've observed that moves through spacetime is bent by gravity. That's why we say that gravity is a warping of spacetime itself, where electromagnetism isn't. If you tried to build the "general electromagnetic theory of relativity", then 0 charged particles wouldn't follow a straight line on a geodesic of spacetime. With gravity, everything follows a straight-line on the geodesic of a curved straight line, regardless of its mass. As to why such a difference exists between gravity and electromagnetism, that's well above my pay grade.

esc_colon_q 6y ago

Actually it's quite easy to cast electromagnetism into a purely geometrical form, you just add a few extra curled up dimensions to a flattish spacetime in general relativity and you basically get Maxwell's equations for free. There are other reasons that's not a great theory (IIRC sources and self-action get nasty and you have to make arbitrary choices about scale, etc), but it's straightforward to get force laws out of pure geometry.