Stress-energy tensor as source of gravity

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Hello. This is a question for the philosophers. I know just a little bit about QT and GR, but have a solid background in QM, classical physics and some particle physics.

I was wondering about the stress energy tensor. I know that the graviton must have spin 2 because the source of gravity is a rank 2 tensor.

Now, the stress energy tensor contains properties like mass density, pressure and shear stress. These are large scale macro-properties, no? Seems like a continuum hypothesis for the mass/energy is assumed. So my question is how can one make a quantum theory of gravity while using these concepts? Seems like trying to make a quantum theory of atoms or particles using properties like bulk-modulus and mass density?

If one looks at the mass as a collection of many many single particles. Then, the contribution to the warping of space-time from each single particle shouldn't contain concepts like shear or pressure? Couldn't, in this picture, the source of gravity be a rank 1 tensor (i.e. four-momentum), and the 2nd rank only comes after we consider the effect of all these single particles?
 
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Quantum gravity is a difficult topic, so I would suggest you to first consider a simpler but analogous question in quantum electrodynamics. The charge current is a continuous source of electromagnetic field, so how can it be compatible with a quantized electromagnetic field (photons)?
 
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Good question! I do not know, but would love a lead. Any tips on reading for this?
 
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Quantum gravity is a difficult topic, so I would suggest you to first consider a simpler but analogous question in quantum electrodynamics. The charge current is a continuous source of electromagnetic field, so how can it be compatible with a quantized electromagnetic field (photons)?
I would say because the charge/current four-vector can be derived from the four-vector potential, A, which can be quantized and is what we work with in QED.
 

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