The Rate of Flow of Subjective Time

I believe that time's rate of flow is constant.

Note however: "Memory" can mislead us into thinking that time varies in its flow-rate.

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Scenario 1 (S1)

Let us consider two events, A and B. Event A occurs at the moment t1, and event B occurs 10 minutes later at the moment t2.(1)

Suppose an observer, Ann, observes these two events. Ann sees event A occur at t1. She sees event B occur at t2.

When Ann observes event B, she recalls event A. However, she does not have a wrist watch and does not know that A took place 10 minutes before B. She relies on her memory and makes a judgment about how long ago event A took place. Ann's memory is not reliable, however. At the moment t2, her memory misleads her into thinking that event A took place 20 minutes before event B.

A little while later, at a moment t3, Ann looks at a clock and discovers that event A took place 10 minutes before B (not 20 minutes before B, as she thought). At this moment, t3, Ann is convinced that time passed very slowly between events A and B. At t3, she claims that the 10-minute gap between A and B seemed like 20 minutes.

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Scenario 2 (S2)

Let us consider a slightly different scenario, S2. This scenario is the same as the first scenario, S1, between the moments t1 and t2. However, at moment t2, S2 differs from S1.

At t2 in scenario S2, Ann's memory misleads her into thinking that event A took place 5 minutes before B.

At t3, in S2, Ann looks at a clock and discovers that event A took place 10 minutes before B (not 5 minutes before B). At this moment, t3, Ann is convinced that time passed very quickly between events A and B. At t3, she claims that the 10-minute gap between A and B seemed like 5 minutes.

In the first scenario described, Ann claims that the 10-minute period between events A and B seemed like 20 minutes. In the second scenario, she claims that the 10-minute period between A and B seemed like 5 minutes.

Note however: The only difference between the two scenarios is the content of Ann's memory at the moment t2. Ann's experience of temporal passage is actually the same in the two scenarios!

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Notation

In the example above, the Actual Time (AT) between events A and B is 10 minutes: AT = 10

In scenario 1, at the moment t2, Ann's memory misleads her into thinking that event A happened 20 minutes before event B.

Thus, the Time According to Memory (TAM) in this scenario is 20: TAM = 20

Note: In this scenario, the Time According to Memory is greater than the Actual Time: TAM > AT (i.e., 20 > 10)

In scenario 2, at the moment t2, Ann's memory misleads her into thinking that event A occurred 5 minutes before event B.

Thus, the Time According to Memory (TAM) in this scenario is 5: TAM = 5

Note: In this scenario, the Time According to Memory is less than the Actual Time: TAM < AT (i.e., 5 < 10)

Notes

1. The argument presented above can be made for any two events, A and B, where B occurs after A. (In the example above, I arbitrarily choose two events, A and B, where AT = 10 minutes.)