We have constrained possible new interactions which produce nonrelativistic potentials between polarized neutrons and unpolarized matter proportional to α σ · v where σ is the neutron spin and v is the relative velocity. We use existing data from laboratory measurements on the very long T1 and T2 spin relaxation times of polarized 3 He gas in glass cells. Using the best available measured T2 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(VV A) type interactions for ranges between 1 ∼ 10 8 m. In combination with previous results, we set the most stringent experiment limits on gV gA ranging from ∼ µm to ∼ 10 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 ∼ 100. 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.PACS numbers: 13.88.+e, 13.75. Cs, 14.20.Dh, 14.70.Pw In recent years, various models of new physics beyond the Standard Model have been studied in which new massive particles such as the axion, familon and majoron, etc. were theoretically introduced [1]. New macroscopic interactions meditated by WISPs (weakly-interacting sub-eV particles) have also been theoretically proposed. The interaction ranges of these new forces range from nanometers to astronomical distance scales. The fact that the dark energy density is on the order of (1 meV) 4 corresponding to a length scale of 100 µm also encourages people to search for new physical phenomena around this scale [2]. Various experiments have been performed or proposed recently to search for a subset of these new interactions which could couple to the spin of the neutron/electron. Polarized neutron beams were used in the experiments presented in Refs. [3,4]. Polarized noble gases were used in Refs. [5][6][7][8]. Atomic magnetometers were applied in Refs. [9,10]. Experimental schemes using polarized atom beams have been recently proposed in Ref. [11].The idea that exotic new interactions might be spin/velocity dependent is quite fascinating. For example, the theoretically proposed photinos interact with nuclei only through spin-dependent forces [12]. Ref. [13] analyzed the possible nonrelativistic potentials between spin-1/2 fermions from spin 0 and spin 1 boson exchange and found 16 possible new interactions, 10 of which depend both on the spin states and the relative velocity be- * Corresponding author: hyan@caep.cn tween particles. Torsion, a twisting of spacetime coupled to intrinsic spin, which has been included in many models which extend general relativity [14,15], can also induce spin-velocity dependent interactions between an unpolarized source and the spin. Har...