We have constrained possible new interactions which produce nonrelativistic potentials between polarized neutrons and unpolarized matter proportional to $alphavec{sigma}cdotvec{v}$ where $vec{sigma}$ is the neutron spin and $vec{v}$ is the relative velocity. We use existing data from laboratory measurements on the very long $T_{1}$ and $T_{2}$ spin relaxation times of polarized $^{3}$He gas in glass cells.Using the best available measured $T_{2}$ of polarized $^{3}$He gas atoms as the polarized source and the earth as an unpolarized source, we obtain constraints on two new interactions. We present a new experimental upper bound on possible vector-axial-vector($V_{VA}$) type interactions for ranges between $1sim10^{8}$m. In combination with previous results, we set the most stringent experiment limits on $g_{V}g_{A}$ ranging from $simmu$m to $sim10^{8}$m. We also report what is to our knowledge the first experimental upper limit on the possible torsion fields induced by the earth on its surface. Dedicated experiments could further improve these bounds by a factor of $sim100$. Our method of analysis also makes it possible to probe many velocity dependent interactions which depend on the spins of both neutrons and other particles which have never been searched for before experimentally.
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