The specific part is here and deals with the Schwarzchild metric and curvature of space-time. Here is the trouble I’m having with it. Two bodies are side by side near a gravitational body, one in freefall (inertial) and one maintaining its distance from the body by accelerating. Insert frames and voila, the accelerating body maintains its distance and to that observer the inertial body gets closer to the the gravitational body.
But that seems to be begging the question. Why do we presuppose (and not assuming gravity for a second) that acceleration is needed to maintain your distance from another body?
If there is no gravity, then you do not need to accelerate. Or have I misunderstood you?
ETA the curved space-time is gravity, maybe that was not clear. As for maintaining your distance, a free-falling object will fall towards the centre (because of the curvature); if you want to follow a different trajectory, that is where the acceleration comes in.
The video ISTM is begging the question in that it assumes gravity to show that gravity exists due to the curvature of space-time.
If there were no gravity, then space-time would not be curved and particles would not be accelerated towards the center. I watched the part you linked to and the spacetime is already curved, so either this is assumed, or was there something earlier that I overlooked? The curvature is supposed to be generated by something (e.g., a massive particle) via gravity. Different masses will have different effects, for example.
It might help to go back to something called the equivalence principle (don’t know if this was mentioned in the video). This states that the laws of physics, as seen in a freely falling reference frame, are locally equivalent to the laws of physics as seen in the absence of gravity. Roughly speaking, this is the statement that if you’re in an elevator and someone cuts the cord, you become weightless. So when you’re near any massive object, you can either freely fall, remaining weightless; or you can maintain your separation from the object, requiring constant acceleration.
Notice I haven’t said anything about curvature, yet; this is all a statement about the laws of physics will look to observers under the influence of gravity, however we choose to describe it. The notion of spacetime “curvature” is needed to describe how different freely falling observers can get closer to each other or farther apart from each other due to gravity’s effects, as well as to account for the effects of special relativity.
I’m not sure I understand the basis of your confusion but here’s another way of looking at it that may help. The key is that the presence of mass warps space-time, not just space. Even an object that is stationary with respect to another mass is still moving through time, describing a geodesic through four-dimensional spacetime. That geodesic is altered by the presence of the other mass in such a way that the arrow of time points slightly more toward that mass. Taken to an extreme, this is consistent with the conjecture that beyond the event horizon of a black hole the space dimension between an infalling object and the singularity becomes entirely timelike, rendering any escape impossible.
With that in mind, this spacetime curvature produces what we perceive as an attractive force between masses, proportional to their mass. So we can answer your question without invoking gravity as a given by saying that acceleration is needed to maintain your distance from another body because the other body is creating an apparent accelerating force for the reason given above, and to maintain your distance you have to exert an equivalent force in the opposite direction. In everyday life we do this by standing on the ground or sitting in a chair.
I’m puzzled by your framing of this question. It’s not really a question of “presupposing” anything. Relativity does not derive from abstract principles that must be true. It is a mathematical model that turns out empirically to correctly describe the way our universe behaves.
(Although it can be said if certain fundamental principles are empirically true in the universe then other things follow, and the theory was developed by following this kind of reasoning.)
The video does. It presupposes that an inertial body near a gravitational body falls towards it and uses this premise to show … an inertial body near a gravitational body falls towards it and that is gravity.
I still don’t know what you mean by “presupposes” here. The video “presupposes” that GR is the correct model for our universe, and describes how things behave in a specific case under that mathematical model.
Is your question is why we should assume GR is correct? We shouldn’t assume it, it’s an empirical question. All the evidence we have from observation is consistent with GR, but the purpose of this video is not to describe the empirical evidence supporting GR.
OK, I carefully watched the video and he begins by saying, “What does the curvature of space and time around a massive body look like?” Then he writes down some metric (of a curved manifold). That’s it.
If you want to derive that form, you need a theory of gravity, which he never talks about but he does mention the name “Einstein”.
After writing down the “curved spacetime metric: Schwarzschild coordinates” you are done, though; an test body will inexorably be accelerated towards the center, that is not an assumption he makes. You have to solve for the radial velocity of a test particle (for example, if you just drop it, or if it is orbiting the black hole, or whatever) and see that there is an effective potential pulling it towards the hole.
Yeah I get all that. My issue is that at the point I cued up in the video, he says that an inertial body is in free-fall and a body must accelerate to maintain its distance from the body. The inertial body will be in free-fall. OK, yes I get that.
He then goes on to show that because of this and the curvature of space-time, that the inertial body that is in free-fall is, believe it or not, in free-fall and that’s called gravity. Sooooooooo assuming the inertial body is in free-fall we see that the inertial body is in free-fall. That smacks of in petitio principii. I’m not arguing the science, I’m just questioning his explanation as a logical fallacy (Begging the Question) and wondering if I am missing something in his argument.
He’s not making an argument. He’s making a video about what it means to describe space time with GR.
General relativity cannot be derived purely logically. The Einstein Field Equations might be in general, but the solutions that they create require plugging in the Newtonian Theory of gravity, or some other theory for how the universe works, as the limiting case. You start by assuming that two bodies in free fall attract each other, because that’s what experiments have proven happens. General relativity then provides a framework for how that spooky action at a distance actually manifests, by saying that energy and mass curve spacetime and force objects’ timelines to come closer together in space as time progresses.
That is not how I understood it. The gravity comes in in the very first minute of the video when he writes down a curved space-time, before he talks about bodies in free-fall. (This is certainly not derived in any detail—he says something like, this is what you get after solving Einstein’s magic equation.) Later he talks about the effect of gravity on a test body, so he says, assume it is in free fall, let’s see where it goes.
It is possible he said something incorrect which I overlooked, but I do not think any type of logical argument is being made. He is starting out with such-and-such a gravitational field, no explanation given, and saying this particle goes this way, that particle goes that way (again, not in any detail).