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For force carriers the interacting field theory determines the spin. A scalar field yields spin 0; the Higgs is the only example; a vector field yields spin 1, the photon, W, and Z are examples; a tensor field yields spin 2. Since gravitational field theory requires a tensor field for General Relativity, quantized gravity, in the weak-field, linearized ...

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Peter is right. The tensor nature requires it to be a spin 2 field, and the graviton is its presumed quanta. But there have been and are theories of gravity that include a spin 0 field. Brans-Dicke theory was one (I think mostly or fully disporved), and some theories for dark energy are spin 0 - quintessence is one, it assumes the cosmological constant is ...

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Suppose you have two systems $S_1,S_2$ with Hilbert spaces $H_1,H_2$ with a density matrix $\rho$ on $H_1\otimes H_2$. The partial trace of $\rho$ over the Hilbert space of one of the systems, $H_1$ say gives you a reduced density matrix $\rho_2$. The reduced density matrix predicts the expectation values of all the measurements you can conduct on $S_2$ ...

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