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?
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?
What is the observer's role in quantum measurement? Obviously, observers prepare the apparatus, observe and interpret the measured results. Although the observer will have a certain influence on the measurement results by setting up the measuring apparatus, we don't believe human consciousness cause reducing of wave packet; also observers are certainly required to interpret the measured results with physical meanings. We believe observers build up their experience of the external world by playing games with nature, and then "decode" the nature based on their experiences. We propose a quantum decision theory approach to explain the role of the observer in quantum measurements, and pointed out that a set of quantum decision trees (strategies to answer natural questions with yes/no logic) can be optimized to deal with the challenges of nature through quantum genetic programming based on maximization of the expected value of the observers; Quantum decision trees can discover the dynamics rules of quantum entities and Just as classical mechanics uses the principle of least action to obtain the trajectories of particles, we use the principle of maximum expected value to approximately obtain the kinematic "trajectories" of quantum entities by learning from natural historical "events" (measured results); even we can "reconstruct" the past of quantum entity, because we don't know the prior information of quantum entity, it is very difficult to predict the future of the nature.
Intersubjective consistency asks when different observers of a physical system, reasoning from a shared theory, will agree on their probability assessments. Classical probability theory provides a benchmark in the form of the Agreement Theorem (Aumann, 1976). We study the quantum mechanics (QM) analog to the classical Agreement Theorem in a finite-dimensional tripartite setting in which two observers obtain information via local projective measurements. We represent their mutual awareness by common certainty, which is formally an infinite hierarchy of certainty operators concerning the probability of an event of interest. We first prove that if the observers' measurements commute with one another and with the property of interest, common certainty forces their probability assessments to coincide, thereby recovering a QM analog to the classical Agreement Theorem. We then construct a one-parameter family of qutrit-qubit-qubit models in which one observer's measurement does not commute with the property and common certainty of disagreement occurs -- a distinctively QM phenomenon. The mechanism is coherence between branches distinguished by one but not the other observer's measurement. When measurement outcomes are stored in a classical register, the resulting dephasing removes this coherence and restores agreement. Finally, we prove that QM does not permit the extreme 0-1 configuration in which Alice is certain of a property and is also certain that Bob is certain of its negation. These results aim to turn debate in QM about observer-dependent facts into precise mathematical conditions for when intersubjective agreement or disagreement in QM can be sustained.
The interactive interpretation I have presented here leaves many interesting questions unresolved. In conclusion, I shall raise several such questions, and discuss their significance for the interpretation. These may be divided roughly into two kinds: Some are merely requests for a more complete development of the view expressed here, whereas others represent unresolved challenges to its adequacy as an interpretation of quantum mechanics. What these questions all have in common is that at the present time I cannot myself adequately answer them. I raise the questions here to commend them to others, as suggesting interesting topics for further research of a kind that holds out hope for an improved understanding of the quantum world, as well as of our current best theories of it. The first such question concerns the dynamics of quantum systems during interactions. The present interactive interpretation rests on certain rather weak assumptions about how the dynamical state of a quantum system changes during an interaction: It would clearly be of great interest to explore further details of this process. Such an exploration requires both theoretical and experimental research. If the present interpretation of quantum mechanics is along the right lines, then not only does a quantum system have a well-defined dynamical state at each moment, but also there is an interesting stochastic element to the evolution of that dynamical state during an interaction. Although the present interpretation constrains this stochastic behavior, it neither specifies nor determines it.
A new scientific truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die, and a new generation grows up that is familiar with it. – Max Planck, 1936 The only way quantum theory allows us to interact with quantum systems is via quantum processes. Thus, the only way we can extract information about the state of a quantum system is to apply some non-deterministic process and observe which of the branches happened. For that reason, many people refer to the act of applying certain quantum processes as measurement and sometimes even as observation . A consequence of this unfortunate terminology is that one of the most touted ‘strange’ features of quantum theory is often misleadingly described as follows: ‘The mere act of observing a quantum state changes it.’ ‘Misleading’, since the concept of measurement described in the previous paragraph is far from the passive concept of observation familiar from our macroscopic world, but is rather a non-trivial process that will almost always drastically affect the quantum state. So, the mysterious aspect of quantum theory is not that ‘observation’ alters the quantum state but, rather, that it is impossible, even in principle, to ‘observe’ a quantum system in the classical sense. Given this fundamental restriction on how we can extract information from a quantum system, what can we learn about that system by means of a quantum process? The answer is, in fact, very little! First, performing a particular measurement could, for the vast majority of quantum states, yield any outcome i with a non-zero probability. In that case, obtaining an outcome i doesn't tell us much about what the state of the system was. Second, we say ‘was’, because the measurement will moreover irreversibly change the state according to the outcome. So rather than revealing the state of a system, a quantum measurement typically erases that state from history! Nonetheless, these quantum measurements are crucial to quantum theory since they constitute the only interface between us, in our classical world, and the quantum world. The great insight of the quantum computing community is that the non-deterministic changes induced by these quantum measurements are not a nuisance, but rather an extremely useful resource.
Although time is one of our most intuitive physical concepts, its understanding at the fundamental level is still an open question in physics. For instance, time in quantum mechanics and general relativity are two distinct and incompatible entities. While relativity deals with events (points in spacetime), with time being observer dependent and dynamical, quantum mechanics describes physical systems by treating time as an independent parameter. To resolve this conflict, in this work, we extend the classical concept of an event to the quantum domain by defining an event as a transfer of information between physical systems. Then, by describing the universe from the perspective of a certain observer, we introduce quantum states of events with space-time-symmetric wave functions that predict the joint probability distribution of a measurement (observation) at $(t,\stackrel{P\vec}{x})$. Under these circumstances, without assuming collapse, we propose that a well-defined instant of time, like any other observable, arises from a single event, thus being an observer-dependent property. In this manner, we obtain a stationary quantum state written as a sum of a sequence of normalized states of events with increasing memories. As a consequence, a counterfactual asymmetry along this sequence of events gives rise to the flow of time as being successive ``snapshots'' from the observer's perspective. In this proposal, which contrasts strikingly to the view in which time is an illusion, it is the many distinguishable states in which the observer stores information that makes the existence of time possible.