# Why does matter curve space time? [duplicate]

I am under the impression that Einstein never explains in his General Theory of Relativity, why matter curves spacetime; could explanations please be given?

Should physics make an ultimate answer to the why questions? In my opinion, it is not the physicist's aim, and moreover it is beyond the scope of physics.

Physics mostly builds theories as our tools to understand and predict some aspect of the surrounding infinitely complicated world. Sometimes we come to a theory that is of such a generic applicability that it also gives one elegant theoretical unification to multiple disconnected observations.

But, to my knowledge, the curvature of space-time has so far no such underlying explanation. Thus I believe the general relativity is not a consequence of other theory (yet), it just seems to be compatible with nature and has an exceptionally great predictive and explaining power.

• Yet couldn't one argue that Newtonian gravity was unable to explain why gravitational force was exerted by mass yet GR provides somewhat an explanation for why- matter curves spacetime. – PDMurray Apr 20 '16 at 15:00
• Sure, but the motivation behind GR, as far as I know, was not the question "why there is gravity" but the decision for building an elegant theory. – dominecf Apr 20 '16 at 19:47

The curvature of space-time is provided by the solutions of Einstein equation $$R_{\mu\nu} - \frac{1}{2} g_{\mu\nu} R - \lambda g_{\mu\nu} = 8\pi G T_{\mu\nu},$$ where $R_{\mu\nu},R$ denotes respectively the Ricci tensor and Riemann scalar. It is important to note that these quantities are provided as a function of the metric tensor $g_{\mu\nu}$, characterizing the curvature of space-time. The mass term is then included inside the energy-momentum tensor $T_{\mu\nu}$ which, considering the famous relation between mass and energy $E=mc^2$, it does not vanish when a mass term is considered. Then, it is possible to show that the $g_{\mu\nu}$ solution of Einstein equation describes a curved (non-minkowskian) space-time.

Summarizing:

1. The mass term provides a non-vanishing energy-momentum tensor $T_{\mu\nu}$.
2. Due to this term, it is possible to solve the Einstein equation and compute the space-time metric $g_{\mu\nu}$, which describes a curved space-time.

No it cannot be explained why or how matter can curve space. Unfortunately like Dominect suggest many have the attitude that we should not even be concerned with the why.

• Notice I only wrote that physics does not aim to answer the "why?" questions; its method is in proposing and developing of theories. If a new theory predicts observations or some other less general theories, then it indirectly answers the associated "why?" question. The latter approach is much more fortunate, since it is rigorous, it inherently avoids getting stuck at unsolvable mysteries or ill-posed "whys", and most importantly, it also allows harmonic co-existence of multiple different approaches that may both be partially applicable to some aspect of the field. – dominecf Apr 20 '16 at 8:11
• I deleted some apparently obsolete comments. – David Z Apr 20 '16 at 13:47