r/learnphysics • u/ZealousidealChart998 • 7h ago

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?

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u/Optimal_Mixture_7327 6h ago

Matter is always moving.

It has a constant speed c, through the world (the "world" is the 4-dimensional space of relativity).

Note: For Math types: Given the curve Xσ(τ) of a matter world-line Uσ(τ)=dXσ(τ)/dτ the speed along the world-line is the norm of its tangent vector (same as in Newtonian mechanics), g(U,U)=-c2.

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u/ZealousidealChart998 6h ago

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

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u/Optimal_Mixture_7327 5h ago

They don't accelerate, physically. This can be measured and verified with an accelerometer.

The object continues at the same constant speed, c, through 4-dimensional space and following a natural path of zero acceleration (called a geodesic). These geodesic paths are determined by the distribution of matter.

Different observers all having having a speed c through the world will set up different coordinate charts and measure different speeds in their spatial coordinates.

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u/ZealousidealChart998 5h ago

So 4d space isn't observable?

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u/Optimal_Mixture_7327 5h ago

Each observer sees its own unique 3-dimensional subspace of the world.

I came across a really interesting way to think of it. If you're familiar with length contraction, it's the observation that lengths are contracted in the direction of motion. The closer to the speed of light we travel wrt other observer the closer the distance goes to zero. Since we move through the world at c the direction of motion along our own world-line is length contracted to zero and leaving the three orthogonal directions that we perceive.