The Nature of Uncertainty: Past vs. Future

Postdiction: Subjective Ignorance of the Past

There is only one macroscopic reality in the past.

• Uncertainty in Postdiction: When we attempt to predict the past, known as postdiction, the uncertainty we deal with is essentially a subjective ignorance of macroscopic data.
• Observer's Role: An observer who possesses more data about the past will naturally have less ignorance compared with others. This suggests that the depth of historical knowledge directly impacts the accuracy of postdictions.

Prediction: Objective Ignorance of the Future

However, when we shift our focus to the prediction of future events, the nature of uncertainty changes.

• Objective Ignorance: Here, uncertainty is not just subjective; it's an objective ignorance of the future state of the physical system.

Two Dimensions of Future Uncertainty:

1. Non-Existence of Future Data: By definition, data from the future does not exist for any present observer. This makes predicting the future inherently uncertain.
2. Microscopic State Indistinguishability:
   • The ignorance also encompasses the uncertainty about which of the macroscopically indistinguishable microscopic states the system will be in.
   • Entropy as Ignorance: This aspect of uncertainty is where entropy plays a crucial role, representing part of the objective ignorance.

   
   

   For instance, in processes like diffusion, the uncertainty about "which microstate the system is in" only increases with time, illustrating how entropy contributes to our objective ignorance of future states.

By understanding these distinctions, we not only gain insight into the mechanics of time and observation but also appreciate the profound differences in how we approach knowledge about the past versus the future.

-- Me@2025-01-31 07:13:22 AM

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2025.02.11 Tuesday (c) All rights reserved by ACHK