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This question already has an answer here:

Einstein theorized that gravity is a phenomena manifested by the curvature of spacetime, in effect it IS the curvature of spacetime. If this is so, why do we need a graviton to convey the force of gravity? If I have mis-understood Einstein then I would appreciate a little help in grasping the relationship between warped space and gravity.

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marked as duplicate by heather, JDługosz, Ben Crowell, John Rennie gravity Jan 1 '18 at 10:09

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

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    $\begingroup$ Welcome to 2018. This is a question of why we think quantum gravity is a "must happen". Can you search this here? I am sure this has been asked before. $\endgroup$ – DanielC Dec 31 '17 at 22:42
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    $\begingroup$ It can likewise be shown that electromagnetism arises as the curvature of the internal space of U(1) transformations. Having a geometric interpretation or formalism doesn’t preclude or contradict field quantization. $\endgroup$ – bapowell Jan 1 '18 at 2:13
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The short answer is that we need $G_{\mu\nu}$ to be quantised because $T_{\mu\nu}$ is. You can try getting around that by e.g. replacing the stress tensor with its own expectation in the Einstein field equations, but that causes all sorts of headaches people have investigated, such as nonlinear quantum mechanics.

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  • $\begingroup$ This is IMO a poor answer, because it makes it seem that there is some highly technical reason specific to gravity that makes it hard to couple a classical gravitational field to a quantized system. There are simple, totally generic reasons why it doesn't fundamentally work if you couple a classical field to a quantized system, and these have been understood since 1927. The issues you're referring to are reasons to worry about whether semiclassical gravity works as an approximation. They're not the fundamental reasons why we think gravity has to be quantized fundamentally. $\endgroup$ – Ben Crowell Jan 1 '18 at 2:09
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the (mostly) non-mathematical answer is that any time we have a field in physics, there will be defined for that field an associated quantum, which can be considered an excitation of that field. when that field is responsible for transmitting forces between objects, that process can be modeled as the exchange of those quanta between those objects. For the electromagnetic field, the associated field quantum is the photon. for the gravitational field, the associated field quantum is the graviton.

the mathematics of the process by which a certain field is quantized defines the characteristics of the quantum of that field. Even before we go out and try to catch one of those quanta as it propagates through the universe, we know in advance what its properties are.

in the case of the electromagnetic field, the quantum of the field must be massless and possess a spin number of one. for the gravitational field, it too must be massless and have a spin number of two.

in studying how gravity works, we can visualize the process of gravitational forces acting between two massive objects as occurring because mass bends spacetime and thereby alters the trajectories of those objects, or equivalently by visualizing it involving instead the exchange of gravitons between those objects.

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  • $\begingroup$ This is just an argument by analogy, that if other fields are quantized, gravity probably should be too. We have much stronger reasons to believe that gravity must be quantized, as discussed in the answers to the question that this question duplicates. $\endgroup$ – Ben Crowell Jan 1 '18 at 2:10
  • $\begingroup$ ...I stopped where I did because 1) I figured that more detail might be over the OP's head, and 2) I knew there were others here who could provide that detail far more thoroughly and rigorously than I could. BTW I am now going to go read the answers you mentioned. -NN $\endgroup$ – niels nielsen Jan 1 '18 at 2:21

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