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We have constrained possible new interactions which produce nonrelativisticpotentials between polarized neutrons and unpolarized matter proportional to$\alpha\vec{\sigma}\cdot\vec{v}$ where $\vec{\sigma}$ is the neutron spin and$\vec{v}$ is the relative velocity. We use existing data from laboratorymeasurements on the very long $T_{1}$ and $T_{2}$ spin relaxation times ofpolarized $^{3}$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 anunpolarized source, we obtain constraints on two new interactions. We present anew experimental upper bound on possible vector-axial-vector($V_{VA}$) typeinteractions for ranges between $1\sim10^{8}$m. In combination with previousresults, we set the most stringent experiment limits on $g_{V}g_{A}$ rangingfrom $\sim\mu$m to $\sim10^{8}$m. We also report what is to our knowledge thefirst experimental upper limit on the possible torsion fields induced by theearth on its surface. Dedicated experiments could further improve these boundsby a factor of $\sim100$. Our method of analysis also makes it possible toprobe many velocity dependent interactions which depend on the spins of bothneutrons and other particles which have never been searched for beforeexperimentally.

Probe Spin-Velocity Dependent New Interactions by Spin Relaxation Times of Polarized $^{3}He$ Gas