In relativity, symmetric Energy momentum tensor is $$ T^{ij} $$ where $T^{00}$ is energy density and $\frac{1}{c}T^{10}$ is momentum density. Thus $$ (\frac{1}{c}T^{00}dV, \frac{1}{c}T^{10}dV)$$ is four momentum. Under Lorentz transformation, this should transform like four vector where $$ \frac{1}{c}T^{00}dV=\frac{\frac{1}{c}T'^{00}dV'+\frac{v}{c^2}T'^{10}dV'}{\sqrt{1-\frac{v^2}{c^2}}}\\dV=dV'\sqrt{1-\frac{v^2}{c^2}}$$ After simplification, we have $$ T^{00}=\frac{T'^{00}+\frac{v}{c}T'^{10}}{1-\frac{v^2}{c^2}}$$ But if we apply transformation to the tensor directly we can get $$ T^{00}=\frac{T'^{00}+\frac{v}{c}T'^{10}+\frac{v^2}{c^2}T\ ^{11}}{1-\frac{v^2}{c^2}}$$ What makes the difference? I think the first is wrong but have no idea why. Thanks.