Modern vision-language models (VLMs) excel at many multimodal tasks, yet their grasp of temporal information in video remains weak and has not been adequately evaluated. We probe this gap with a deceptively simple but revealing challenge: judging the arrow of time (AoT)-whether a short clip is played forward or backward. We introduce AoT-PsyPhyBENCH, a psychophysically validated benchmark that tests whether VLMs can infer temporal direction in natural videos using the same stimuli and behavioral baselines established for humans. Our comprehensive evaluation of open-weight and proprietary, reasoning and non-reasoning VLMs reveals that most models perform near chance, and even the best model lags far behind human accuracy on physically irreversible processes (e.g., free fall, diffusion/explosion) and causal manual actions (division/addition) that humans recognize almost instantly. These results highlight a fundamental gap in current multimodal systems: while they capture rich visual-semantic correlations, they lack the inductive biases required for temporal continuity and causal understanding. We release the code and data for AoT-PsyPhyBENCH to encourage further progress in the physical and temporal reasoning capabilities of VLMs.