The model presented in this paper describes simultaneously three different experimental techniques applied to different monodisperse polymer melts: neutron spin-echo (NSE), linear rheology, and diffusion. First, it shows that the standard tube model cannot be applied to NSE because the statistics of a one-dimensional (1D) chain in a three-dimensional (3D) random-walk tube become wrong on the length scale of the tube diameter, whereas all available NSE data are for scattering vectors in this range. Then a new single-chain dynamic slip-link model on the basis of a recent network model by Rubinstein and Panyukov is introduced. Instead of solving the model analytically, which would require uncontrolled approximations, the model is formulated in terms of stochastic differential equations, suitable for Brownian dynamics simulations. I perform these simple simulations, demonstrate that the model describes individual experiments well, and then compare the results with experiments on monodisperse polyethylene, polyethylene-propylene, polyisoprene, polybutadiene, and polystyrene. For all polymers, model parameters from one experiment are obtained, and the others are predicted without fitting. The results show some systematic discrepancies, suggesting possible inadequacy of the Gaussian chain model for some of the polymers, and possible inadequacy of time-temperature superposition.