Stephen Hawking discusses the psychological reality of time, where people feel there is a unidirectional flow and succession of events. Let me see if I can summarize well what Hawking states about time:
To explain how time can be conceived, Stephen Hawking starts from light, whose speed is always the same regardless of the speed its source has. An event under observation will therefore show a dot-like present time, a cone-like future time (formed by the light spreading out from the event and creating a three-dimensional cone within the four-dimensional timespace) opened in the direction of time flow, and a cone-like past time (standing for the set of events that the light impulse can reach to the event under observation) opened in the opposite direction of time flow.
Stephen Hawking also mentions the difficulty scientists have in combining quantic mechanics and gravity. By using imaginary numbers (that is those that result in negative numbers when multiplied with themselves), scientists can obtain a Euclidean spacetime where the distinction between time and space disappears completely. Stephen Hawking points out that the utilization of this ‘imaginary time’ and the Euclidean spacetime is a mathematical artifice that can offer answers regarding real spacetime.
Different ideas converge in Stephen Hawking’s effort to find the meaning of time. First, time is finite but with no boundaries. Second, the universe changes from a homogeneous and orderly state to a heterogeneous and disorderly one. Third, the universe expands constantly. Hawking’s remark is that intelligent life can only exist in an universe whose initial state must show order and homogeneity and which can only happen if time is finite but with no boundaries. Under these circumstances, the psychological reality of time where we can remember the past but not the future is intertwined with (1) the cosmological reality of the universe, where constant expansion seems to be essential for the very existence of this universe and (2) the thermodynamic reality of our universe, where entropy increases over time.