We derive the Hilbert space formalism of quantum mechanics from epistemic principles. A key assumption is that a physical theory that relies on entities or distinctions that are unknowable in principle gives rise to wrong predictions. An epistemic formalism is developed, where concepts like individual and collective knowledge are used, and knowledge may be actual or potential. The physical state
S corresponds to the collective potential knowledge. The state
S is a subset of a state space
S={Z}, such that
S always contains several elements
Z, which correspond to unattainable states of complete potential knowledge of the world. The evolution of
S cannot be determined in terms of the individual evolution of the elements
Z, unlike the evolution of an ensemble in classical phase space. The evolution of
S is described in terms of sequential time
n∈N, which is updated according to
n→n+1 each time potential knowledge changes. In certain experimental contexts
C, there is initial knowledge at time
n that a given series of properties
P,P′,… will be observed within a given time frame, meaning that a series of values
p,p′,… of these properties will become known. At time
n, it is just known that these values belong to predefined, finite sets
{p},{p′},…. In such a context
C, it is possible to define a complex Hilbert space
HC on top of
S, in which the elements are contextual state vectors
SˉC. Born's rule to calculate the probabilities to find the values
p,p′,… is derived as the only generally applicable such rule. Also, we can associate a self-adjoint operator
Pˉ with eigenvalues
{p} to each property
P observed within
C. These operators obey
[Pˉ,Pˉ′]=0 if and only if the precise values of
P and
P′ are simultaneoulsy knowable.
An operational description of the controlled Markov dynamics of quantum-mechanical system is introduced. The feedback control strategies with regard to the dynamical reduction of quantum states in the course of quantum real-time measurements are discribed in terms of quantum filtering of these states. The concept of sufficient coordinates for the description of the a posteriori quantum states from a given class is introduced, and it is proved that they form a classical Markov process with values in either state operators or state vector space. The general problem of optimal control of a quantum-mechanical system is discussed and the corresponding Bellman equation in the space of sufficient coordinates is derived. The results are illustrated in the example of control of the semigroup dynamics of a quantum system that is instantaneously observed at discrete times and evolves between measurement times according to the Schroedinger equation.
The space‐time is empirically perceived as a pre-existing property of the universe. However, a special kind of perception that takes place in near-death-experiences (NDEs) is challenging this idea. Here, I will illustrate how understanding of this particular state of consciousness (named the bodiless consciousness) helps us re-think the space‐time structure of the physical world. I first speculate that the bodiless consciousness perceives the physical world as nonlocal 4D. I then propose that the space‐time is a “derived” feature subsequent to the emergence of perception of the bodiless consciousness, rather than a pre-existing and unchangeable property. Next, I explain that the space structure only takes place in the classical (or macroscopic) world rather than in the quantum (or microscopic) world, due to its intrinsic imperceptibility to the bodiless consciousness. Without a presupposed structure of the space, the strangeness of the quantum world is expected. Then, I bring up the old measurement problem. I will argue that it is the bodiless consciousness that may entangle with the superposed state of an observed system and trigger the collapse. Finally, I will briefly discuss the potential relationship between electromagnetic wave and consciousness.