The Equivalence Principle
The equivalence principle states that acceleration and gravity are interchangeable, and the effects of one versus another cannot be distinguished. In the example of Newton and the apple, one possible interpretation is that Newton is actually accelerating toward the apple, while the apple is at rest. Though the concept is slightly unfamiliar and a very different way of thinking than usual, it is not too uncommon as it can be thought of as almost a reversal of the traditional roles.
The equivalence principle states that the effects of gravity and acceleration are indistinguishable. For example, when an apple falls, it accelerates downward due to gravity, while Newton feels the same gravitational pull standing still. If Newton were in a rocket ship accelerating upward at the same rate as gravity, he would feel just like he does on Earth. This idea can feel strange because it challenges our usual understanding of gravity as a force that pulls objects down, making us rethink what it means to be "at rest."
This might be completely wrong and might sound weird (it does sound weird to me) but i was thinking: if Newton is at rest relative to the earth and hence feeling the gravitational field pulling him down, as if he was accelerating upwards at 9.8 m/s², it would mean that Newton is not ACTUALLY at rest, since he can feel acceleration. As for the apple: it is in a free fall, it does not feel acceleration at all, thus, if we ignore air resistence, we could say that the apple could claim to be at rest since it does not feel anything at all. This would mean that if we consider the system Newton-apple, Newton would be "moving" toward the apple, and not the other way around. But this is very weird because for Newton to be moving towards the apple, it means that the earth would be moving towards the apple, and this sounds very weird, because its not REALLY moving. If you conider that its moving towards the apple, since the gravitational field surounds the whole planet, you would have to affirm that the earth is moving upwards in ALL directions and THAT sounds literally impossible. Unless if you dont consider movement as the changing of distances between objects but rather as a feeling of motion caused by acceleration.
And yes it all does feel very unfamiliar to me because we never learn these kind of things at school, and its a quite complex subject.
The motion of an object or its lack thereof depends on the reference frame in which we are considering the object. Motion is relative. In general relativity, Newton is "at rest," while the apple moves under the influence of Earth's gravitational field, which manifests as the curvature of spacetime, leading to the apple falling to the ground.
For me, the idea that spacetime is constantly curving is strange because I am unfamiliar with this concept, and it's difficult to imagine.
In general relativity, Newton is "at rest." The force of gravity is indistinguishable from acceleration, so the apple can feel that it is accelerating. But Newton is not accelerating, i.e. Newton is in an inertial frame. The gravitational field of the Earth manifests itself as a curvature in spacetime, and this causes the apple to fall towards the Earth.
The thing that feels most strange to me is the sense of how spacetime is curved. It is very hard to imagine what that would look like.
Whether one object is in motion or not depends
on the system that the objects in question are
considered within. If the system considered is
the apple and the Earth, then the apple will
be in motion. But if the system is the apple,
earth, and Newton, then both Newton and the
apple will be in motion. Motion is relative.
To me, the idea that spacetime is
curving constantly around me is strange
because it is an idea that I'm unfamiliar
with. This course has been teaching me that a
lot of things are relative, and almost nothing
is absolute!
According to general relativity, the Earth curves spacetime around it due to its mass. When you drop an apple, it follows a geodesic, which is the natural path in the curved spacetime. This geodesic represents the object's free-fall motion towards the ground.
Only considering the Earth and the apple, the Earth will be "at rest", and the apple will free-fall towards the Earth as described above.
This does feel unfamiliar for me because it is very different from Newton's explanation, where gravity is thought of as a force pulling objects towards one another. Instead, general relativity describes …
This is how I see it: The apple starts at rest in a local frame. Since an accelerometer on the apple reads 0 it remains at rest in that frame. The ground also starts at rest in the same local frame, but since an accelerometer on the ground reads 1 g upwards it accelerates upwards at 1 g and pushes Newton's head into the stationary apple.
Newton described gravity as a force acting on an object. So the free fall is the result of this force pulling on the "falling" object, which Einstein disagreed with. Gravity doesn't pull you down; it accelerates upwards. In other words, gravity is …
