Gravity is not a force – free-fall parabolas are straight lines in spacetime • Hacker News Board

Re: Gravity is not a force – free-fall parabolas are straight lines in spacetime

#21

Post by kubanczyk » Sun, Oct 18, 2020, 9:59 PM UTC

a3w wrote: post #12

Somewhere I read that a free fall parabola does not even take into account earth's curvature. Although I cannot remember, what kind of function describes the reference system specific ``path, as a function of time''. Could this be named more correctly: Gravity is not a force – free-fall hyperbolas are straight lines in spacetime (timhutton.github.io) ?

The planet's curvature is not very relevant to the article, but, yes, if an object is in a free fall at a slow speed (I mean non-orbital) its trajectory is:

- parabola if you assume flat&infinite ground,

- ellipsis if you assume a spherical planet (an ellipsis is crossing the planet's surface).

This is Newton, not GR.

Re: Gravity is not a force – free-fall parabolas are straight lines in spacetime

#22

Post by umvi » Sun, Oct 18, 2020, 10:01 PM UTC

montagg wrote: post #10

shireboy wrote: post #8

I saw this and the related Veritasium video, but am still scratching my head about something. Does this mean that away from all gravity a body does not experience any time? ie a person on a spacecraft stopped in intergalactic space would not age relative to persons on planets?

I believe (from my limited knowledge from Interstellar ) that it’s the opposite: higher gravity environments move slower relative to lower gravity environments, which enabled the “go down to high gravity planet for a couple hours and come back and it’s ten years later” plot point in the movie. So if you’re in intergalactic space, time is actually passing very quickly in the higher gravity environment of a galaxy. But…

I don't think that is quite right. If you travelled near the speed of light and then slowed down again it would look (from your perspective) like you jumped 10 years into the future. So high gravity environments "moving slower" shouldn't result in a jump to the future upon exit.

Instead I think what is happening is that massive objects actually stretch the fabric of spacetime somehow so that the closer you are to the object, the slower you travel through both space and time. And the more massive the object, the more stretched space and time become as you get closer to it.

Hence if you go near a very massive object, from an outside observer it looks like you are frozen in time because time is so stretched it takes forever for you to move through it.

As you mentioned though, from any given frame of reference time will always feel the same. 1 second will always feel like 1 second.

Re: Gravity is not a force – free-fall parabolas are straight lines in spacetime

#23

Post by dreamcompiler » Sun, Oct 18, 2020, 10:03 PM UTC

frutiger wrote: post #6

True gravitational force is something that can’t be transformed away by an arbitrary choice of frame (even an accelerating one). As a brief example, consider two objects in downwards free fall toward the centre of some massive object. Since they head towards the centre, in a free falling frame the two objects actually get closer to each other until they collide as they reach the centre. This is known as the tidal eff…

I take your point, but I think the author's main point was that because objects in free-fall merely follow spacetime geodesics, it makes calling gravity a "force" a little bogus, at least compared to the other forces. Tidal effects don't change that; tidal effects mean the spacetime curvature "over here" is different than the spacetime curvature "over there", which means the principle of equivalence isn't true in a global sense. But objects still follow spacetime geodesics, which is a concept that's hard to reconcile with the notion of a "force."

Re: Gravity is not a force – free-fall parabolas are straight lines in spacetime

#24

Post by vbezhenar » Sun, Oct 18, 2020, 10:05 PM UTC

Smaug123 wrote: post #14

I 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 moving through time with constant speed? Or we're constantly accelerating through time?

Re: Gravity is not a force – free-fall parabolas are straight lines in spacetime

#25

Post by Smaug123 » Sun, Oct 18, 2020, 10:06 PM UTC

umvi wrote: post #7

vbezhenar wrote: post #4

Earlier quoted context omitted.

I don't understand it. How can it accelerate towards anyone on its surface? Where does it get energy to accelerate? We generally need to burn fuel to accelerate something in the space.

"in curved spacetime, an object needs to accelerate just to stay still" I don't really understand why, that was just the explanation Derek gave.

This amounts to a confusion over notation: "proper acceleration" (e.g. as measured by an accelerometer) vs "coordinate acceleration" (the acceleration an observer observes an object to be undergoing).

The acceleration an observer sees you undergoing is the same as the inherent "proper" acceleration you're undergoing, minus the acceleration of their coordinate frame with respect to yours. For me to stay still with respect to you, if you're in a frame that is accelerating away from me, I need some proper acceleration to catch up and counteract the fact that our frames are diverging. But if spacetime is curved, your frame probably is accelerating relative to mine - c.f. the example on the Earth's surface, where our frames inexorably accelerate towards each other as we move parallel to each other. So for me to stay still with respect to you, I need to have some proper acceleration to balance out the coordinate acceleration derived from the fact that our frames are moving in a curved space.

Re: Gravity is not a force – free-fall parabolas are straight lines in spacetime

#26

Post by tim_hutton » Sun, Oct 18, 2020, 10:06 PM UTC

layoutIfNeeded wrote: post #5

How would periodic “free-fall” motion look in this setup? E.g. a point mass orbiting around a body, or a point mass oscillating back and forth in a 1D gravity well.

With two space dimensions and one time dimension (2+1), an orbit in Newtonian physics is a helix. In general relativity that same helical path would be a straight line in an interestingly curved spacetime.

Likewise I guess for the 1D gravity well case, where a sine wave would become a straight line in spacetime.

Re: Gravity is not a force – free-fall parabolas are straight lines in spacetime

#27

Post by Smaug123 » Sun, Oct 18, 2020, 10:07 PM UTC

paulpauper wrote: post #17

Smaug123 wrote: post #14

I 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…

>I 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?" Air resistance, wind, and horizonal acceleration. Over long vertical distances, these perturbations in the x-axis cause an arc. Nothing to do with general relativity.

I assert that if you throw a ball upwards in a vacuum chamber on Earth, it will in fact still fly in a parabola.

Re: Gravity is not a force – free-fall parabolas are straight lines in spacetime

#28

Post by c06n » Sun, Oct 18, 2020, 10:08 PM UTC

pininja wrote: post #2

The video for this page provides great context https://youtu.be/XRr1kaXKBsU

I do not understand how you can have acceleration without changing position (at 10:06). Acceleration is the derivative of speed, which is the derivative of position change. If the position change is zero, how can the acceleration be non-zero?

Re: Gravity is not a force – free-fall parabolas are straight lines in spacetime

#29

Post by mytailorisrich » Sun, Oct 18, 2020, 10:09 PM UTC

Smaug123 wrote: post #14

I 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…

> the parabola is so strongly curved? Spacetime is nearly flat, so how can a straight line become such a steep parabola?

I suspect that the answer is that this is a false comparison.

Re: Gravity is not a force – free-fall parabolas are straight lines in spacetime

#30

Post by Smaug123 » Sun, Oct 18, 2020, 10:10 PM UTC

vbezhenar wrote: post #24

Smaug123 wrote: post #14

I 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 moving through time with constant speed? Or we're constantly accelerating through time?

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; the rest of the world is moving forward in time faster than you are.

So you can change your acceleration through the time dimension of spacetime, by dint of changing your acceleration in the spatial ones.