Stones and Apples | Hacker News Reader

Stones and Apples

blog.mathspace.co

55 pointsoxplot12 comments

This was awesome. I’ve taken astronomy and physics in high school and then later physics and mechanics at university. But this article explained gravity way better than anything I’ve encountered before.

The viewpoint presented in the article looks "way better" only because you've been exposed to it much more recently than what you've studied in the past. Newer = shinier.

Also, you've not been asked to solve any chapter exercises using this shiny theory, where you have to obtain correct numerical answers.

Ash and Bernard crawling from the apple's equator to its stem is cute, though.

This is a great mental model, but I'm getting hung up on a more minor point. The masses wouldn't be moving around on a static spacetime model because, as the text says, the masses are what bend the spacetime. So spacetime would be more curved close to each mass, which in turn means they would accelerate toward each other even harder as they got closer to each other.

Curved spacetime is not required to explain anything in classical mechanics.

The presented concepts are poorly developed and do not account for forces other than gravity. Suppose A and B are oppositely charged and electrostatically attracted together with great vigor over a considerable distance. Next to A there is a C, which is not charged, and not attracted to B (other than mildly due to gravity). A begins to move toward B rapidly, whereas C hardly moves toward either of them. Are A and C situated in a differently curved spacetime, even though they start off right next to each other in both space and time?

You didn't learn it this way in school because it's bunk. The equations of motion together with fields that are responsible for forces provide a coherent theory that actually solves problems.

It's....complicated. That's why The Three Body Problem is not just a great scifi book, but a real mechanics brain teaser. That doesn't take away from the strength of this illustration, which is explanatory in nature, not authoritative.

They do! Gravity is an r-squared law.

(If you're confused about constant acceleration due to gravity, Galileo's experiment and all that, well different masses fall to earth with the same acceleration from the same height, but g decreases with distance from the Earth. It takes the familiar 9.81 m/s value as an agreed averaged value at the surface).

I know they do in real life. It's the illustrations showing a static curve that the masses slide over that I'm taking issue with.

Oh yeah, I see what you mean. I think the models in the article are deliberately simplified. At least some of those plots demonstrate a constant force, rather than a gravitational-type force. And the well-known weights-on-a-rubber-sheet analogy is notoriously unhelpful. I guess the real equations work for real curved spacetime.

I noticed that too. Presumably, modeling a dynamic curve over time would have dramatically complicated the diagrams and explanations without really adding much to the core concept. That's at least my assumption for why it was passed over.

These diagrams look upside down to me. I think of gravity Wells like those coin donation wells: https://i.pinimg.com/736x/1e/c8/de/1ec8de8c6c3d15ff0df8cafa8...

MinutePhysics on YouTube was the first place I saw a good explanation of spacetime curvature, but this write-up is equally good.

Very interesting read... I wonder at what distance the expansion of the universe itself nullify the gravitation attraction?

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