Comment by JumpCrisscross
4 days ago
> According to general relativity, you (and the ground) are accelerating at 1g
I don't believe this is correct. If I lock two rockets in opposition to each other, they aren't accelerating. They're pushing at each other. And their propellant is accelarating away. But their displacement and orientation are unchanging, which means their velocity is zero which means acceleration isn't happening.
Similarly, the normal force resists your gravitational force to produce zero net acceleration. (An object at rest in a gravity well is its own local frame.)
> If you jump off a cliff, you'll stop accelerating for a bit, until the ground hits you
I don't believe this is correct. In GR, free fall is still inertial motion. You're just free of fictitious forces and thus following the curvature of spacetime.
As I understand it, in GR acceleration is indistinguishable* from gravity, so while you're on the ground feeling 1 gee, you're being accelerated up at 1 gee, and so is the ground.
When you're in free-fall, that's when you're in a non-accelerating frame, even though a non-relativistic description** would say that you are, in fact, accelerating.
Caveat: I only do physics as a hobby, neither academically nor professionally, so take with appropriate degree of doubt.
* for point-like observers at least
** ignoring rotation and curved orbits
That is incorrect. Acceleration generates a force that is indistinguishable from gravity (and vice versa) but that does not mean they are the same thing.
It is correct, and you're also right that two rockets tethered to each other would not feel acceleration. The acceleration we feel in Earth's gravitational field is affecting our speed, though - it's slowing down the speed at which we move towards the future.
> you're also right that two rockets tethered to each other would not feel acceleration
I just realized that the energy of the exhaust would warp local spacetime. So one might feel acceleration depending on how that geometry settles.
Declaring some forces as "fictitious" is just a convention and in my opinion it is a useless convention that brings more complexities than simplifications.
In my opinion, a much healthier way of thinking is to not apply any such conventional labels to some forces and to just treat all forces equally, which is simpler, and it also matches the real world, where there is no practical difference between "fictitious" and "non-fictitious" forces.
If you treat all forces equally, then the rule (a.k.a. Newton's 2nd law) is that the resultant of all forces that act in a point is always null. From this, the conservation of energy is an obvious consequence, because whenever that point moves the total mechanical work is null.
The mechanical work of the "fictitious" forces is the variation of the kinetic energy, in the same way as the mechanical work of other forces is equal to the variation of some corresponding kinds of energy. For instance, the mechanical work of an elastic force is the variation of a potential elastic energy.
A "fictitious" force can squish you like a bug exactly like a "non-fictitious" force, and when that happens you would not be saved by the thought that the force is "fictitious".
There is a baseless claim that "fictitious" forces can be distinguished from "non-fictitious" forces because they depend on the system of reference. However the same is true for some of the so-called "non-fictitious" forces, which are functions of velocities and accelerations of bodies, in the same way as the inertial forces. Moreover, what actually varies between systems of reference is how forces are distributed into various kinds of components, not the resultant forces.
If you are pressed on a wall by a so-called "fictitious" inertial force, no change in the system of reference will change the compression force that you feel, but it may change the interpretation of the kind of forces that result in the compression that you feel.
In general relativity the "fictitious" forces do not disappear, but like in classic mechanics where you can define the "fictitious" forces using the variation of the kinetic energy, in relativistic mechanics there is an analogous definition based on the variation of the momentum-energy quadri-vector. In the gravitation theory of Einstein you can compute this inertial 4-force using the gravity force that is derived from the "curvature" of the space (which is in turn determined by the spatial distribution of the momentum-energy 4-vector of matter). The rule of a null resultant 4-force remains true in general relativity, so for a body that moves freely, like a satellite or a body in free fall, the inertial 4-force is equal in magnitude and opposite in sign with the gravitational 4-force.
In some problems of general relativity, you do not need to compute the inertial forces, because e.g. the trajectory of some body might be along a geodesic and that is all that is of interest for you. This is the same like when you use kinematics to determine the possible movement of a mechanism, where you want to know the path on which something moves, but you do not care which forces are exerted on the parts of the mechanism. However, in other problems of general relativity, you may want to know the forces that act upon a body, for instance for computing the required strength of materials, and then you may need to compute inertial forces, exactly like in classic mechanics.
The physics as taught in schools is full of such useless conventions caused by historical accidents. Moreover, besides conventions that just make things more complex than they should be, the standard textbooks contain definite mistakes that have been perpetuated for generations, like wrong definitions for all physical quantities related to rotation motions. In conclusion, trusting the "authority" of the school textbooks is a mistake and people must attempt to verify with their minds all that they are taught, instead of trusting. As a schoolboy I was more skeptical than most, so some of the less competent teachers feared my questions, but I still believed much of what I was being taught and only years later I realized that I was duped.
The fact that the AI models are trained on scientific literature that contains widespread inefficient methods or even mistakes, guarantees that they will provide wrong answers in comparison with really competent humans.