I have studied physics in high school and like to watch documentaries. I was intrigued with Einstein's concept of gravity and I had this question. I may not be precise asking this question, but I hope you will pay more attention towards intention behind this question rather than my inability to ask question in technical terms.

In the world of Newton, the gravity is an inherent property that is exhibited by the objects. But unlike Newton, Einstein's notion of gravity is of time-space. Where due to object the space bends.

So, my question is,

What is the critical mass required to observe the bending of the space?

My personal rationale behind this question is to know that, if space behinds irrespective of how small mass may be or it stops bending after certain critical mass. If so, then there is no point on working on unification theory using Quantum Mechanics and Relativity.

Can we calculate the curvature near classical objects?

  • $\begingroup$ Maybe this is beside the point of the question, but even if some minimum amount of mass were required in order to bend spacetime, why would that mean that quantum theory and general relativity don't need to be unified? The sun bends spacetime, and the sun is made of quantum ingredients (electrons, protons, and so on), so quantum physics and general relativity must be reconciled somehow. Curious people want to understand how. $\endgroup$ Nov 7, 2020 at 20:08
  • $\begingroup$ @ChiralAnomaly My question is wrong? Why I am not getting any answer? $\endgroup$
    – Ubi.B
    Nov 7, 2020 at 23:52
  • $\begingroup$ Gravity is such a weak force that it is extremely difficult to detect for small masses. Don't expect an answer based on experimental evidence. Are you familiar with the Planck scale? Some theories postulate that space itself is quantized at this scale $\endgroup$ Nov 8, 2020 at 3:04

1 Answer 1


What is the critical mass required to observe the bending of the space?

In General Relativity, arbitrarily small and arbitrarily large masses cause spacetime curvature. GR is not a quantum theory and it imposes no theoretical lower or upper limit on the amount of mass that can cause curvature. Actually, in GR, you don’t even need mass at all to cause curvature; you just need a nonzero density or flow of energy or momentum.

There is no accepted theory of quantum gravity, so no one knows whether limits will eventually be known.

Whether we can “observe” spacetime curvature depends on what experimental technique you are willing to consider an observation of curvature. We can definitely measure the gravitational attraction of laboratory-sized objects, and today we understand that attraction as being due to spacetime curvature. But for non-astronomical objects it is much simpler to think about their attraction in terms of Newtonian gravity, without thinking about spacetime curvature at all.

Can we calculate the curvature near classical objects?

Yes. It’s particularly straightforward if the object is spherically symmetric. We can easily calculate, for example, the curvature of spacetime outside a grapefruit, the Earth, or the Sun using the Schwarzschild metric.

However, spacetime curvature is a somewhat complicated concept mathematically. In a general non-symmetric four-dimensional spacetime, it takes 20 numbers at each point to completely describe the curvature there.


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