This video really cleared up a lot of misunderstandings for me: https://www.youtube.com/watch?v=wrwgIjBUYVc I had never visualized it this way in my head before, and it all makes a lot more sense now. Highly recommend!
What a fantastic video.
Gravity is not a force – free-fall parabolas are straight lines in spacetime
211–220 of 451 posts
Re: Gravity is not a force – free-fall parabolas are straight lines in spacetime
#212Earlier quoted context omitted.
Off topic, but in reality, the trajectory of a ball thrown on Earth is not a parabola, but an ellipse [1]: > under the laws of gravity, a parabola is an impossible shape for an object that's gravitationally bound to the Earth. The math simply doesn't work out. If we could design a precise enough experiment, we'd measure that projectiles on Earth make tiny deviations from the predicted parabolic path we all derived in…
It's a parabola in a uniform gravity field, an ellipse in a circular gravity field coming from a point mass. So if you want to be really pedantic, it's never an ellipse because the Earth is not a point mass. It would be equivalent to a point mass if the Earth were a perfect sphere of uniform density, but it isn't. In reality it's a potato like mass blob that's approximated by what geodesists call the "geoid". So in o…
. . and then you have to account for the moon's gravity in the equation depending on where it is at th3e moment you throw the ball . . .
Re: Gravity is not a force – free-fall parabolas are straight lines in spacetime
#213I 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…
Great answer!
It’s also why I despise the popular portrayal of space time curvature. It looks at space in isolation rather than space time as a whole, and provides no intuition as to why objects traveling at different speeds follow different trajectories.
FWIW I think that in general it is better to just teach people that gravity is an acceleration in classical spacetime (as opposed to a force or curvature). It is simply too hard to create intuition for laymen around minkowskian spacetime, and even harder for curved minkowskian spacetime.
Re: Gravity is not a force – free-fall parabolas are straight lines in spacetime
#214Seems rather tricky to invent anti-gravity when gravity is just an emergent phenomenon of distortions in the spacetime fabric.
Re: Gravity is not a force – free-fall parabolas are straight lines in spacetime
#215Can anybody sane tell us what gravity is in the case of flat space-time?
Re: Gravity is not a force – free-fall parabolas are straight lines in spacetime
#216Earlier quoted context omitted.
Good point; this becomes more obvious if you imagine throwing the ball up and then immediately collapsing all the mass of the Earth into a single point at the centre. What path does the ball follow now? It's probably following a path we would more usually call an "orbit", and it sure looks a lot like an ellipse. Now just put the mass of the Earth back where it was, and notice that the ball hits the ground before it c…
Despite both being conic sections, cutting up an ellipse won't yield you parabolas. An ellipse has two focal points to which the sum of the distances is constant, while a parabola has a focal point and a directrix line to which the difference of the distances is constantly 0. Two different things.
More symmetrically, Every comic section has one focus and one directrix (and a semi-major axis for scale), eccentricity is the ratio of distance. Ellipse has eccentricity less than 1, and a parabola has eccentricity equal to 1.
Re: Gravity is not a force – free-fall parabolas are straight lines in spacetime
#217Earlier quoted context omitted.
> The difference is that light travels through space, but not time This is a common pop science statement, but it's not correct. A correct statement is that the concept of "speed through spacetime", which is what has to be split into "speed through space" and "speed through time" in the pop science statement, does not apply to a light ray. In more technical language, the tangent vector to the light ray's worldline is…
I wouldn't say it's incorrect at all. From the point of view of a photon, no time elapses between its the origin and destination endpoints.
> From the point of view of a photon, no time elapses between its the origin and destination endpoints.
No, this is not correct. The correct statement is that the concept of "elapsed time" does not apply to a photon; it only applies to timelike worldlines, not null worldlines.
To put it another way, if your statement were true, it would mean that the origin and destination events were the same point in spacetime. But they're not; they're distinct points in spacetime. Which means that, since the spacetime interval along the worldline is zero, you can't use the interval to distinguish points on the photon's worldline. And the concept of "elapsed time" requires that you be able to do that. So the concept of "elapsed time" can't be used for a photon.
Re: Gravity is not a force – free-fall parabolas are straight lines in spacetime
#218Earlier 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.
Check out gauss law for electromagnetism and gravity. It says that total flux through closed surface is proportional to strength of field sources inside the surface. Flux from outside sources cancels out.
You can use this law to see what's the gravity fields as you move under ground and in other very symmetrical cases.
Re: Gravity is not a force – free-fall parabolas are straight lines in spacetime
#219Earlier quoted context omitted.
> if you are inside of the sphere, at least some of the mass will be pulling you away from the point at its center If the mass is spherically symmetric, this will not be the case; all of the Newtonian forces from the masses further away from the center than you are will cancel out. This is called the "shell theorem", and it turns out to hold even in General Relativity.
I don’t think this is correct. I think the shell theorem says that the gravitational forces cancel if you are on the inside of a hollow sphere and all mass is on the surface. A perfect sphere of uniform density would not meet the shell theorem assumptions.
> I think the shell theorem says that the gravitational forces cancel if you are on the inside of a hollow sphere and all mass is on the surface.
No, it's stronger than that. It says that any spherically symmetric distribution of matter outside a certain radius exerts no "gravitational force" on anything inside that radius, whether there is matter inside that radius or not.
Re: Gravity is not a force – free-fall parabolas are straight lines in spacetime
#220F = ma
F means force. Gravity is a type of acceleration, not a force without being multiplied by a mass!