I’ll preface this by saying that I have a very good understanding of Newtonian mechanics, but only an amateur’s understanding of Einstein’s relativity.
I understand that Newton’s law of gravitation is insufficient to accurately describe and predict certain physical phenomena, and that Einstein’s relativity “fixes” this. I don’t understand, however, why we must do away with the model of gravity as a force to build a better model. Couldn’t Newton’s law of gravitation be amended to account for the discrepancies? It looks to me as if it’s a question of which mental model we prefer. Saying that gravity isn’t a force, it is a curvature, or vice-versa, sounds to me like saying that positive charges are actually negative and negative charges are actually positive, i.e., a matter of convention. Whether gravity >is< one or the other seems to me much more a matter of philosophy than physics properly.
So why is this such a central point?
In: Physics
The central premise of general relativity is that gravity is not a force. The rest is built from the premise, it’s not an interpretation, but rather than starting axiom Einstein worked with. Warped spacetime comes from taking gravity to not be a force, not the other way around.
What do we mean when we say gravity is not a force?
Well, let’s start with centrifugal force. That’s a force, right? Well no, it isn’t. It’s just inertia, there is no force. If you’re on a bus going straight, and it turns, nothing pushed you into the wall when it turns. There is no force. The wall just comes to you and pushes you to make you turn, to accelerate you. The reason we think there is this fictitious centrifugal force is because of this flawed choice of the bus as a reference frame. It’s a non inertial reference frame. The bus is accelerating, in this case, changing directions. How strong is the centrifugal force? Well, the easy answer is it depends on how fast you are turning or spinning. Yes, that. But the revealing answer is it depends on mass. All objects feel the same acceleration, so the force they feel is proportional to their mass. Because it’s not really a force, but just inertia, therefore it happens to scale with mass. Sound familiar? Mass is not a charge of centrifugal force, it doesn’t belong in a force law like electric charge. Inertia manifests this fictitious force, so obviously inertia mass relates to it. Same goes for other fictitious forces, like coriolis force.
So what do we mean when we say gravity is not a force. The EXACT same thing. We mean gravity is a fictitious force. Gravity manifests from choosing a non inertial reference frame. And gravity will depend on mass because it’s just inertia with a mustache disguising it. If you understand why centrifugal force isn’t real, you already understand why gravity isn’t real. You just need to make the leap to non Euclidean geometry with time as a coordinate, which is, admittedly, quite a hard leap to make for the human brain.
You’re on an elevator in space. Or rocket. Whatever, take your pick. It’s a box that can move up or down. The box moves up with you in it. What do you feel? You feel a force pushing you into the floor. You feel weight. If the box goes up at 9.8m/s/s, you feel the same weight as you do on earth. Any object in this box feels the same acceleration. And the force, the weigh, scales with mass. There is no force pushing you down, only the floor pushing you up. But from a reference frame of the box, this downwards force manifests. Now, this sounds exactly like gravity. And Einstein’s insight, it IS the same thing as gravity. It’s the equivalence principle. And if the box stooped accelerating, you’d just float. That’s the same thing as freefall, be it orbit or falling to the ground..
So this is what gravity is not a force means. It means gravity is not real. It’s a fictitious force that arrives simply from the property of inertis and the choice of a non inertial, and accelerating reference frame.
So now, the obvious counter you have to me. The surface of the earth is accelerating. If gravity wasn’t real, and the ground was pushing me up, the ground needs to be accelerating.
Yes, it would. And that’s where the weirdness of taking Einstein’s insight to its logical conclusion comes from. Spacetime is bent. The ground is accelerating. The only force on you is this pushing you up. Not gravity pulling you down. And that’s why every object falls at the same speed. It’s actually really, really weird that we all took Newton on his word when he assumed mass, the thing that responds to gravity, and mass, the thing to do with intertia in Newton’s F=ma were the same thing. That was a wild ass assumption Newton was making. For good reason, it appeared to be true. And Einstein figured out it wasn’t a coincidence. There was only one mass, the inertia one.
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