# How does mass affect space?

according to einstein the mass go straight in the curved space because the sun makes the space curved and so the earth circle the sun. but i dont understand why this "geometrical" explanation is a replacement for the gravity. how does the mass (of the sun for example) makes the space curved?
thanks!

andrewkirk
Homework Helper
Gold Member
Nobody knows. Einstein produced an equation we can use to calculate the curvature of spacetime if we know the distribution of mass-energy. Using that equation, we can calculate how bodies like the planets will move around a larger body like the sun. But as to why that equation works, nobody knows. Right now it's a question for philosophical speculation, and perhaps for some more advanced science of the distant future.

Ibix
2020 Award
We don't yet have an explanation, as Andrew says. We can make very precise predictions using general relativity and test them, and the theory gives good predictions. But it doesn't say why spacetime (not just space!) is curved by stress-energy, only that it is.

On a slightly philosophical note, this is true of all scientific theories on some level. For example, Newton's theory of gravity simply says that masses exert a force on one another, but it doesn't say how they do it.

• stoomart
Dale
Mentor
2020 Award
how does the mass (of the sun for example) makes the space curved?
I am not sure if you are asking "how" or "why". How mass (stress energy) curves space is described by the Einstein field equation. But why that equation rather than some other one is not.

but i dont understand why this "geometrical" explanation is a replacement for the gravity.

Newton's gravitation law ##F=G\frac{mM}{r^2}## ,dividing by m, ##\frac{F}{m}=G\frac{M}{r^2}=a##.

any m around M receive the same acceleration a. Thus M generate acceleration field around itself.

As deriving Maxwell's equation from Coulomb's law in electromagnetism, this relation is expressed as ## div\ a=4\pi G\rho ## where ##\rho## is mass density.

So in non relativistic mechanics already mass (density) generates ## div\ a## which is a kind of geometry.

Dale
Mentor
2020 Award
@sweet springs You may want to look into Newton Cartan gravity. It is a geometrized version of Newtonian gravity along the lines of what you mention, but correctly formalized.

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Thanks for information. I will try.

It begs the very similar question: if space-time is curved as in the quotes, does that mean that - mass attracts space , and space attracts mass, but mass does not attract mass as such ?

does that mean that - mass attracts space , and space attracts mass, but mass does not attract mass as such ?
It seems you are unconsciously using concepts of Newtonian theory into Einstein's theory.

Note that in Einstein's theory, it doesn't make sense to talk about attraction in the way you seem to be thinking of. Gravity is, in Einstein's theory, the curvature in the underlying space-time which is the framework for the mathematical part of the theory, and that's it.