Mass and Curved Space Question

[Dorje]

According to General Relativity, the presence of mass curves space, and this curvature causes the effects of "gravity". Do Einstein's equations give us a clue as to the mechanism by which mass is able to do this? In other words, how does mass curve space? How does it "know" to curve space? And why is it that more mass results in more curvature?

The source of these questions comes from a reflection upon the old Newton's Law of Gravity. Newton's Law of Gravity provided a very accurate quantitative description of gravity, but did nothing to account for the cause of gravity (aside from the construct of the "field" later on). General Relativity is supposed to clear this up by suggesting that gravity is caused by curved space due to the presence of mass. This doesn't seem to be a complete answer though.

 

[Mike2]

The question is only raised when matter is viewed as point particles. For then we wonder what properties are there in a point that can possibly curve space. However, if matter is an extended object, a submanifold of space-time, then we can easily invision curvatures on the submanifold of matter giving rise to curvatures in space-time that surrounds it. In other words, matter particles themselves are regions where curved space is conserved through time, and the curved space-time of gravitation is where space-time gradually changes in a continuous manner to match the flatness of empty space.

 

[R0man]

Einstein's equations do not explicitly tell us the mechanism by which mass is able to curve space. They provide a mathematical framework for understanding the relationship between mass, space, and gravity, but they do not give us a direct answer to how mass is able to curve space.

One possible explanation for this is that mass itself is a property of space-time. In other words, mass is not a separate entity that exists within space-time, but rather it is an inherent property of space-time itself. This means that as mass is present in a certain area of space-time, it causes a curvature in that space-time, much like how placing a heavy object on a trampoline causes a depression in the surface.

As for how mass "knows" to curve space, this is still a topic of debate and research. Some theories suggest that mass has a type of "gravitational charge" that interacts with the curvature of space-time, while others propose that mass and space-time are inseparable and always interact with each other.

The reason why more mass results in more curvature can be understood through the concept of density. The more mass there is in a certain area, the more densely packed it is, and this density leads to a stronger curvature in space-time. Think of it like placing more and more weights on a trampoline - the more weight there is, the more the surface will curve.

In conclusion, while Einstein's equations provide us with a way to mathematically describe the relationship between mass, space, and gravity, they do not give us a definitive answer to how mass is able to curve space. It is an ongoing topic of research and debate in the scientific community, and further studies and experiments may shed more light on this fascinating phenomenon.