Earlier quoted context omitted.
Spherical mass can be replaced with a point mass. Earth however is not spherical (biggest deviation is polar flattening). And even then, Einstein's model, unlike Newton's, says it's not an ellipse even for a point mass. So, moral of the story - we have to be not too pedantic.
> Spherical mass can be replaced with a point mass I'm not a physicist, but that doesn't sound right. One example is that if you are inside of the sphere, at least some of the mass will be pulling you away from the point at its center. I think what you mean is that a point mass closely approximates a spherical mass, but the degree to which that is true becomes less and less the closer you get to the center. I don't t…
Gravity is not a force – free-fall parabolas are straight lines in spacetime
121–130 of 451 posts
Re: Gravity is not a force – free-fall parabolas are straight lines in spacetime
#122Earlier quoted context omitted.
Under special relativity, everyone and everything moves at a constant speed `c` through spacetime. If you feel like you're not moving, it's because all your speed is being put towards travelling faster through time. Conversely, if you manage to move very fast through space, the world around you will appear to speed up, because you've had to trade off some of your forward travel through time so as to travel in space;…
I've always intuitively understood this to be the reason why it would take infinite force to achieve light speed for a massive object. When we apply a physical force, it is applied in the spatial axes, so it is always perpendicular to the time axis. Acceleration is just rotating some magnitude of your fixed velocity vector out of the time axis and into the spatial axes. When your spatial velocity is apparently zero,…
This is a useful way to think about it, but you have to keep in mind that (even flat) spacetime is not Euclidean but Minkowskian: in the distance metric, time has an opposite sign to the spatial dimensions. So when you "rotate" a four-vector, it actually follows the surface of a hyperboloid rather than a sphere, which means that rotation has a discontinuity at Θ = π/4 (in normalized units) and the vector escapes to infinity! Only massless objects can travel "at the speed of π/4", everything else can only approach but never reach that speed.
Re: Gravity is not a force – free-fall parabolas are straight lines in spacetime
#123I heard an interesting question at one point: "how come, when you throw a ball up on Earth, the parabola is so strongly curved? Spacetime is nearly flat, so how can a straight line become such a steep parabola?" I'll answer this question as I understand it, but I only took four lectures of General Relativity before I gave it up in favour of computability and logic, so if there is a more intuitive and/or less wrong an…
Are we flat in the time dimension? Or what is our time size?
>Or what is our time size?
That's just another way of describing the total time you exist.
Re: Gravity is not a force – free-fall parabolas are straight lines in spacetime
#124My enlightening moment about general relativity: apples do not fall on the ground, instead, the earth is inflating, and the inflation of the earth is accelerating at 9.8 m/s^2. Eventually, the ground catches the apple. Of course, you are going to tell me that the earth is not inflating, obviously, because it is still the same size after so many years. But here is the trick: the earth is inflating at the same rate as…
my visualization of this view:
https://landgreen.github.io/physics/notes/relativity/general...
Re: Gravity is not a force – free-fall parabolas are straight lines in spacetime
#125Would not an electron and a positron trace out an identical line/parabola? Would that mean electromagnetism is not a force either? What is the difference between the two that makes one a force and one not a force?
This is a great question!
Re: Gravity is not a force – free-fall parabolas are straight lines in spacetime
#126Earlier quoted context omitted.
> Spherical mass can be replaced with a point mass I'm not a physicist, but that doesn't sound right. One example is that if you are inside of the sphere, at least some of the mass will be pulling you away from the point at its center. I think what you mean is that a point mass closely approximates a spherical mass, but the degree to which that is true becomes less and less the closer you get to the center. I don't t…
In Newtonian physics, a sphere and point mass are exactly interchangeable as long as you are not inside the sphere. If you are outside the sphere, the equivalence is exact, regardless of distance. Proving this is a classic problem in undergraduate physics.
Thanks! Shame I never took undergraduate physics but now that you've rung my bell I think we may have discussed this in high school. What an unintuitive result that being even a meter under ground breaks what is, up to that point, a fine model.
Re: Gravity is not a force – free-fall parabolas are straight lines in spacetime
#127Earlier quoted context omitted.
In Newtonian physics, a sphere and point mass are exactly interchangeable as long as you are not inside the sphere. If you are outside the sphere, the equivalence is exact, regardless of distance. Proving this is a classic problem in undergraduate physics.
We are inside the atmosphere at least...
And that brings fluid dynamics into the picture, which produces discrepancies orders of magnitude greater than the parabolic/elliptical/etc. distinction!
Re: Gravity is not a force – free-fall parabolas are straight lines in spacetime
#128I heard an interesting question at one point: "how come, when you throw a ball up on Earth, the parabola is so strongly curved? Spacetime is nearly flat, so how can a straight line become such a steep parabola?" I'll answer this question as I understand it, but I only took four lectures of General Relativity before I gave it up in favour of computability and logic, so if there is a more intuitive and/or less wrong an…
Are we flat in the time dimension? Or what is our time size?
> The creatures can see where each star has been and where it is going, so that the heavens are filled with rarefied, luminous spaghetti. And Tralfamadorians don’t see human beings as two-legged creatures, either. They see them as great millepedes—“with babies’ legs at one end and old people’s legs at the other,” says Billy Pilgrim.
—Kurt Vonnegut, Slaughterhouse-Five
Re: Gravity is not a force – free-fall parabolas are straight lines in spacetime
#129Earlier quoted context omitted.
In Newtonian physics, a sphere and point mass are exactly interchangeable as long as you are not inside the sphere. If you are outside the sphere, the equivalence is exact, regardless of distance. Proving this is a classic problem in undergraduate physics.
Thanks! Shame I never took undergraduate physics but now that you've rung my bell I think we may have discussed this in high school. What an unintuitive result that being even a meter under ground breaks what is, up to that point, a fine model.
The way the result works is that if you are a meter underground, it is equivalent to standing on top of a sphere with the top meter of mass removed.
Or equivalently, if you are inside a shell (sphere outside, hollow sphere inside) then the gravitational effect is zero. This can be explained by analogy with light which also follows the inverse square law--changing your position inside a hollow sphere does not change the fact that you see the sphere all around you. Same reason that there is no electrical field inside a hollow conductive object.
Re: Gravity is not a force – free-fall parabolas are straight lines in spacetime
#130I'm curious, how does the "gravity is not a force" viewpoint relate to the hypothesized graviton particle [1]? Are they incompatible viewpoints, or just different perspectives on the same thing? (E.g. are gravitons hypothesized to disappear depending on frame of reference?) I'm assuming they're incompatible (that we need the theory of everything [2] to reconcile them) but would love to know if there's something I'm m…
In quantum physics the particles are excitations of a particular field. The gravitons correspond to (excitations in) the curvature of space-time. The other force bosons correspond to (excitations in) the curvature of other fields, such as the electromagnetic field.
Interestingly the Yang-Mills equations (used in quantum mechanics) and the Einstein-Hilbert action (used in general relativity) are pretty much identical if you use general enough mathematics.