The past is part of the present, in the sense that part of the present is the same as the past, or is based on something of the past. For example, “I was 10 years old in the past” is the necessary condition for “I am 20 years old in the present”.
However, not all of the past is still part of the present, because some of the past is already lost. In other words, some of the past is not stored in the present.
You need physical macroscopic law (induction) in order to get the cumulative property of time.
Microscopically, due to the unitarity of the Schrödinger equation, any past quantum state has a one-one correspondence to a quantum state at any particular future moment. So any future quantum state already has all the information needed to deduce its past state. In this sense, there is no time microscopically.
Time is not cumulative microscopically, because the past is not part of the future.
We can also say that time is 100% cumulative microscopically, because the past is all of the future; instead of being part of any future quantum state, the past quantum state already has all the (equivalent) information of a quantum state at any particular future moment.
— Me@2013-08-10 07:45 PM
— Me@2021-04-21 04:24 PM
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