Light as a carrier of information and energy plays a fundamental role in both general relativity and quantum physics, linking these areas that are still not fully compliant with each other. Usually the quantum nature of light is described in the frequency domain. Even for broadband quantum states with a well-defined carrier frequency, a quasi-continuous-wave picture is still applicable. However, recent access to subcycle quantum features of electromagnetic radiation promises a new class of time-dependent quantum states of light. Paralleled with the developments in attosecond science, these advances motivate an urgent need for a theoretical framework that treats arbitrary wavepackets of quantum light intrinsically in the time domain. Here, we formulate a consistent time-domain theory of the generation and sampling of few-cycle and subcycle pulsed squeezed states, leading to a relativistic interpretation in terms of induced changes in the local flow of time. Our theory enables the use of such states as a resource for novel ultrafast applications in quantum optics and quantum information.