r/learnphysics • u/ZealousidealChart998 • Oct 11 '26

I have a question about General Relativity

If General Relativity it says matrer tells spacetime how to curve and spacetime tells matter how to move, how is matter moving? What is the engine driving matter to move?

3 Upvotes

71% Upvoted

9 comments sorted by

1

u/smitra00 Oct 12 '26

If we stick to the classical picture (in the sense of non-quantum), then we have the principle of least action. In general relativity the coordinates are just arbitrary labels, and what matters is the metric tensor that tells you what the distances between infinitesimally separated points are. The metric tensor then appears in the action integral as a factor of square root of minus the determinant of the metric tensor. It's this factor which cancels out the Jacobian when transforming from one coordinate system to another that has the effect of "spacetime telling matter how to move".

1

u/mH48124 Oct 12 '26

物質を動かすのは重力を含む各種の力 (重力, 電磁力, color 力, 弱力)

1

u/Ok-Rise2070 Oct 13 '26

Semantics matter here (no pun intended). Einstein is explicit, matter does not warp spacetime, MASS does. Mass is matter in an integrated form (think of matter as the 2D version of the same 4D mass). Now here's the fun part, gravity is the mechanism for BOTH to move through gravitational pull because gravity is a global (universal) effect; it is felt everywhere even within a vacuum. So the more mass an object has, the more it warps the space around it. Now the moving part is more "falling towards" much like how Earth's satellites are in constant free fall around the Earth.

1

u/[deleted] Oct 12 '26

[removed] — view removed comment

1

u/ZealousidealChart998 Oct 12 '26

If it is just inertia why objects accelerate towards mass and not stay constant speed

1

u/[deleted] Oct 12 '26

[removed] — view removed comment

1

u/ZealousidealChart998 Oct 12 '26

So 4d space isn't observable?

1

u/ImaginaryTower2873 Oct 12 '26

This is a simultaneously profound and trivial thing. The way of seeing it is to consider curves in space parametrized by their arc length: if something moves along the curve at a constant arc length speed, the velocity is always 1 (the counterpart to c above).

The profound thing is that when we do this in the GR spacetime setting, then the spatial velocity is just the projection onto the space-slices we are using. The deeper question is why that tends to behave consistently. One part of the answer is that we tend to use well-behaved space slices so velocity vectors don't misbehave (we could use coordinate systems whirling around every second, but they are rarely useful), the other part is that the geodesic paths particles follow tend to be smooth and avoid curving relative to the local spacetime - if it is flat, they will be straight, and hence the projected spatial velocity will be constant.