The _stress-energy tensor_, also referred to as the _momentum-energy tensor_ is a [symmetric](Bilinear%20form.md#symmetry) [Bilinear form](Bilinear%20form.md) that contains the information needed to understand the flow of [[4-momentum]] as a continuum flow in [Spacetime](Spacetime.md) associated with a particular event on a [Field](Field.md). As such it encodes the measurable [[energy density]], [[Momentum density]], and [[stress]] at an event (i.e. a point in space time). # Equation of motion [Equations of motion](Equations%20of%20motion.md) # Relation to the Lagrangian and Hamiltonian densities ## Scalar fields For a [[scalar field]] in [Minkowski Space](Minkowski%20Space) described by a [[Lagrangian density]], $\mathscr{L}$, and [Hamiltonian density](Hamiltonian%20density.md) $\mathscr{H},$ The energy momentum tensor is defined as $T^{\mu\nu}=\frac{\partial \mathscr{L}}{\partial(\partial_\mu \phi(x))}\partial^\nu \phi(x)-\eta^{\mu\nu}\mathscr{L}$ ### $T^{00}$ We find that $T^{00}$ is equivalent to the [Hamiltonian density](Hamiltonian%20density.md). #Mechanics/SpecialRelativity #Mechanics/ClassicalFields