In quantum mechanics, time plays a role unlike any other observable. We find that measuring whether an event happened, and measuring when an event happened are fundamentally different - the two measurements do not correspond to compatible observables and interfere with each other. We also propose a basic limitation on measurements of the arrival time of a free particle given by 1/Ek where Ek is the particle's kinetic energy. The temporal order of events is also an ambiguous concept in quantum mechanics. It is not always possible to determine whether one event lies in the future or past of another event. One cannot measure whether one particle arrives to a particular location before or after another particle if they arrive within a time of 1/E of each other, where E is the total kinetic energy of the two particles. These new inaccuracy limitations are dynamical in nature, and fundamentally different from the Heisenberg uncertainty relations. They refer to individual measurements of a single quantity. It is hoped that by understanding the role of time in quantum mechanics, we may gain new insight into the role of time in a quantum theory of gravity.
I expound on QM formalism, to reach conclusions on several topics of interest, and answer some questions:1. What is the amount of information in measuring device output?2. What determines the output of measuring device, aka quantum state?3. What is the amount of information required to set device to a certain configuration?4. What is the relation between preparation and measuring device?5. What is the relation between quantum state and quantum ensemble?6. Is there a boundary between measuring device and measured entity?7. Does quantum state (aka wave function) collapse upon measurement?8. Are event outcomes truly probabilistic as commonly believed?9. What is the significance of global phase?10. What is the boundary between measuring device and observer?11. What is the role of observer, debated since very inception of quantum mechanics?
The main mystery of quantum mechanics is contained in Wheeler's delayed choice experiment, which shows that the past is determined by our choice of what quantum property to observe. This gives the observer a participatory role in deciding the past history of the universe. Wheeler extended this participatory role to the emergence of the physical laws ("law without law"). Since what we know about the universe comes in yes/no answers to our interrogations, this led him to the idea of "it from bit" (which includes the participatory role of the observer as a key component). The yes/no answers to our observations ("bit") should always be compatible with the existence of at least a possible reality - a global solution ("it") of the Schrodinger equation. I argue that there is in fact an interplay between "it" and "bit". The requirement of global consistency leads to apparently acausal and nonlocal behavior, explaining the weirdness of quantum phenomena. As an interpretation of Wheeler's "it from bit" and "law without law", I discuss the possibility that the universe is mathematical, and that there is a "mother of all possible worlds" - named the "Axiom Zero".