Fednis, I'm going to give an answer that is not going to be popular, but there is no such thing as an inertial frame once we consider gravity fields. This is true even for a free-falling body because, (uh oh, here comes that word again) technically, gravity fields are never uniform and, technically, point masses are unphysical. Therefore, objects will always be subject to tidal forces, and an object experiencing tidal forces is not inertial; it undergoes the same physical stresses that it would under proper acceleration. It goes without saying that the tidal forces can be so small as to be negligible, but I've found that many don't consider tidal forces of ANY strength to invalidate the inertial status of a free-falling object, and I disagree with this. Of course, we could theoretically construct a lab where gravity fields were uniform (e.g. Newton's shell theorem) but if we're talking about theory would could also allow for point masses, etc... [Originally made in response to this post - mod]
Quote links are still a bit buggy so they don't always point back to where the quote originates. That issue aside what was or is your point?
I don't see why anybody would think that's unpopular. Einstein called a real gravitational field a "special" gravitational field, so people might quibble about the details. But I don't think anybody would argue strongly for a uniform gravitational field that doesn't diminish with distance.
Actually my comment isn't as relevant here! In the other thread Fednis was asking a question about Newtonian inertial frames, though there was side discussion specifically about the OP hypothetical. This seems a more general discussion about inertia.
In Fednis' thread, the point at x=1/2 would feel a pull. I expected the standard answer to be that a free-floating body at x=1/2 would be inertial but it wouldn't stay at x=1/2. I was jumping ahead of that expected answer by pointing out that even this isn't technically correct...
RJBeery: perhaps you aren't thinking hard enough about what inertia is supposed to be. Also consider motion in a gravitational field; if you drop an object with (inertial) mass, it doesn't need a push to get it moving: acceleration towards a center is constant--the "freely falling" object is weightless as soon as you release it. If you want to make the same object move across the field you have to push it that way--the object's inertia resists this, but there is none of this resistance when you drop it.
Newton worked very hard to ensure that nothing that he did required that we ever encounter an inertial frame. Most of the theorems of the Principia are accompanies by corollaries that establish that they hold very approximately in conditions where there is acceleration on the systems that is close to parallel. So all he needs to do is show that his predictions hold approximately. In addition, he developed his theory in a way that once we have the approximations, we can look to the deviations from a perfect inertial frame to determine possibilities for corrections to the ideal. So we can look to the deviations of the orbits of Jupiter and Saturn to determine that this is due to their mutual interaction. We can look to the deviations of many planets to determine the mass and position of Neptune.
I hope not. Surely everybody has heard of "spaghettification" wherein tidal forces become extreme for the observer falling into a black hole.
There are members here who literally deny that spaghettification occurs anywhere but at R=0 of the black hole. See here
Noted. Bruce is wrong about that. And on this thread he related the force of gravity with the local spacetime curvature. That's wrong, the tidal force relates to local spacetime curvature. We've been through this before. On the depiction of gravitational potential the slope at some location denotes the force of gravity at that location, and the degree of curvature at some location denotes Riemann curvature and tidal force. Please Register or Log in to view the hidden image! CCASA image by AllenMcC, see Wikipedia arfa brane: acceleration towards the centre isn't constant. The force of gravity reduces with distance. I presume you know this, and what you said was some typo or talking at cross-purposes.
