Observer in the QM universe
... This is a rough draft ...
Despite the many successes of quantum mechanics generally physicists are still suspicious to its many properties. Words like “spooky action at a distance”, "collapse of the wave function" dominates well established entanglement and decoherence terms. Inherent non-locality and non-causality of the quantum mechanics is still looked upon with suspicion. More or less obvious fact that the macro scale systems are ruled by the same laws as the micro scale is still not quite obvious to many. There are more than ten popular interpretations of quantum mechanics, ranging from the orthodox Copenhagen interpretation to the freakish Many-Minds one. Only recently one of the corner-stone of quantum mechanics - the measurement problem have been more or less satisfactory resolved by the modern Decoherence interpretation of the quantum mechanics.
And still there are some ghosts left. Observers. Apparently they have magical properties. No. They are not governed by the same micro-scale laws. They can "collapse wave functions". They can stay above it all and do "measurements". They can bring causality and locality into the intrinsically non-local and non-casual world. And obviously they insist that they own history is the central one and the only one existing. Strangely, sometimes they can also explain how a quantum computer performs several operations in parallel.
From the bird perspective the universe is defined by the universal wave function. Mathematically this wave function can be formulated in several ways, namely the path-integral formulation (generalizing the action principle) or the Schrödinger equation (generalizing the conservation principles).
From this view there is only a state space. There is no time. There is no space.
The observer perspective is different. The entanglement produces time and space. The decoherence (again entanglement) produces the familiar classical mechanics. But still, ultimately, the observer experience is derived from the quantum level.
Every classical observer have a beginning. From the very first particle entangling with the environment the observer decreases its own internal entropy. The level of the total entanglement with the environment grows with the time, resulting in a more and more complex and well defined observer. At some point, if the conditions are right, the complexity increases to a level when we can consider the observer to be alive.
The evolution of the observer is not deterministic, the only part that is defined is the entanglement with the environment. The entanglement is final, it never goes away with the time evolution. The environment that is not yet entangled with the observer does not have any limits on the possible states, in fact the observer entangles with the every possible eigenstate, having different experience in every specific case.
The probabilities to experience one or the other outcome of every event can be derived from the path-integral formulation - the action principle on all possible paths. The most probable experience would correspond to the minimum action path.
The entanglement of the observer with the environment comes at a price however, with the time, entangling more and more with the environment possible future space state configurations are becoming more and more limited. Ultimately, at the end, the entanglement with the environment reaches its maximum, limiting the configuration of the observer to one exact eigenstate of the universal wave function. At this point the evolution of the observer finally is deterministic, being the evolution of the universal wave function itself.
Definition of an observer
To approach the definition of the observer we need to start from a few assumptions:
- All isolated systems evolve according to the Schrodinger equation (1);
- Decoherence is the mechanism by which the classical limit emerges out of a quantum (2);
Assuming that, we can give a generic definition to the universe and an observer (in that universe) in terms of the QM:
- The universe - a closed system with the corresponding state vector .
- The observer - an open system with the corresponding state vector .
In the classical limit the observer can also be described in classical terms as an open or continuous classical system.
The classical behavior emerges from the quantum due to the decoherence.
Lets define as the probability of an observer to find itself in some specific state of the universe .
According to the postulates of the QM:
Given the initial conditions on the state vector U should evolve according to the Schrödinger equation, the evolution of the state vector is deterministic. As a result of that at any given moment of we can consider U(t) as a constant and calculate the probability . This probability would only be a function of time and the state vector .
This dependence on time makes sense, consider the observer consisting of atoms - the probability of such an observer to find itself in the universe in a state |U> very early in the evolution when it consists mainly of photons is very low. The observer consisting of biomoleculas have much higher probability of finding itself in the state of the universe that have stars and planets in it. In other words - the anthropic principle.
Via integrating by time we can find the total probability . Now this probability is only a function of the state .
Probability of an observer to find itself in the universe in the state |U> is a function only of the state |U> of the observer itself.
Living observer evolves with the subjective time and continuously observes the 'collapse' of the wave function of the universe resulting in observing of some observables of some certain states |U>. Given the observer finds itself in some universe at the subjective time T with the state |U> let us consider the probability P' of it finding itself in the universe with the state |U'> at the subjective time T+dt.
Generally this probability P' depends on the state |U>, but again, considering the semi-classical observer we may find that this probability mostly depends on the |O> - subspace of |U> - the state of the observer itself.
P` = F(|O>) (4);
In summary the probability of an observer to find itself in some specific state of the universe depends entirely on the state of observer itself. The probability to observe some specific events in the subjective future again mostly depends on the state of the observer itself.
Path-integral formulation of the QM is a likely way to analyze the probability distributions for the observer. It is intuitive that the action principle should define the most probable path of the observer.
Consequences for the classical observer
Generally the observer can NOT be described in the classical terms. But the observer functioning in the high temperature noisy environment can be described in semi-classical terms. 'Described' = we can associate a bit string describing the classical state of the observer. This bit string K in terms gives us some boundary conditions on |O>.
Coarsely, for the observer consisting of atoms, this bit string S should contain positions of atoms, atomic numbers and their state. Part of that bit string would include the memory of the observer MEM. Lets consider some substring of MEM - M.
It is interesting that the bit string M imposes some strong boundary conditions on |O> and in its terms on |U>. For example consider the string "the world is made of atoms" in the memory of the observer and its effect on probability P of the observer finding itself early in the state of the universe with no stars evolved. Considering the boundary conditions on |O> the bit string M can also affect the probability P' (see (4)).
P = F(M), P' = F(M) (5);
It is reasonable to suggest that P would be higher for some state |U> where M is more frequent.
Some rough ideas:
- Correlation between the frequency of occurences of
some bit string M in the memory of the observer and the and the probability for the observer to receive that string;
- Correlation between the length of the new random bit string added
into the memory of the observer and the probability for the observer to receive that string (consider enthropy/energy);
- Interference effects of the MEM with itself;
- Anthropic bias observation selection effects
(e.g. color or shape preference).