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Th1. Macroscopic systems are all quantum systems.
Proof: the union of two quantum systems is always a quantum system, so the union of any number of quantum systems is a quantum system. Microscopic beings are all quantum. Macroscopic beings are made up of a large number of microscopic beings so they are all quantum.
For the following theorems we need the fundamental quantum principle: we can add the states of a physical system like vectors and thus obtain new states.
Th2. Don Juan can spend the night with a thousand lovers at the same time.
Proof: consider the system made up of Don Juan and his thousand lovers. For each lover l, there is at least one state Nl of the system for which Don Juan is with her (Nl means a night with lover l). Since we can add all these states like vectors, there is also a state of the system, the vector sum of all Nl for all lovers l, for which Don Juan is at the same time with his thousand lovers.
Th3. A particle can spread out over an arbitrarily large region of space.
Proof: there is at least one state of a particle for each of its possible positions. Since states can be added like vectors, a particle can be at all positions in any region at the same time.
Th4. A spinning top can spin in one direction and the other at the same time.
Proof: there is at least one state of the top for each of the two directions of rotation. The vector addition of states suffices to conclude.
Th5. A cat can be dead and alive at the same time.
Th6. The Moon can be everywhere in the sky at the same time.
The proofs of theorems 5 and 6 are similar to the previous ones.
Th7. A state of a compound system can be completely determined without the states of the components being completely determined.
Proof: let a system consist of two components A and B. a1 and a2 are two possible states of A, b1 and b2 two possible states of B. a1b1, a1b2, a2b1, a2b2 are four possible states of the system AB. a1b1 + a2b2 is also a possible state of the system, since the states can be added like vectors. If the system is in this state, neither A nor B are in determined states. One could believe that A is in the state a1 + a2 and B in the state b1 + b2, but a short calculation shows that this is false: (a1 + a2)(b1 + b2) = a1b1 + a1b2 +a2b1 +a2b2 which is different from a1b1 + a2b2.
States such as a1b1 + a2b2 are said to be entangled. An entangled state is a determined state of a system for which its components are not all in determined states. Entanglement is one of the most fundamental concepts of quantum physics.
Th8. After an observation, the destiny of an observer can be divided into several different destinies.
Proof: let an observer O who is about to observe whether a being A is in a state a1 or in another state a2. Let o0 be the initial state of the observer before the observation. Let s1 be the state of the system AO when the observer observed a1. Similarly s2 is the state of the system after the observation of a2. The observation therefore changes the AO system from a1o0 to s1, and from a2o0 to s2. Since states can be added like vectors, A can initially be in the state a1 + a2. The observation then makes the system AO go from (a1 + a2)o0 to s1 + s2. The state s1 + s2 cannot represent a unique destiny of the observer, because in a unique destiny one cannot observe at the same time two incompatible results. s1 and s2 therefore represent two different destinies which separate from the initial state (a1 + a2)o0 of the AO system.
The existence of multiple destinies of an observer is a theorem, not a new postulate. It results from the Schrödinger equation when applied to the evolution of an observer. In the above proof we used the linearity of the Schrödinger equation to assert that the observation changes the AO system from (a1 + a2)o0 to s1 + s2. Some quantum theories want to correct the Schrödinger equation by adding principles that mysteriously make multiple destinies disappear in favor of only one, because theorists are embarrassed by the existence theorem of all these destinies. But we do not need these additional principles. They distort the Schrödinger equation and serve no purpose, because the existence of multiple destinies does not contradict observations.
If the observation is ideal, s1 = a1o1 and s2 = a2o2 for states o1 and o2 of O. s1 + s2 is then the entangled state a1o1 + a2o2. The observation made the AO system go from the non-entangled state (a1 + a2)o0 to the entangled state a1o1 + a2o2. Relative to O the state of A before the observation was a1 + a2, after the observation it is a1 in the destiny which follows o1 and a2 in the destiny which follows o2. Everything happens from the point of view of O as if the observation had reduced the initial state a1 + a2 of A to one of its components a1 or a2. Physicists call this wave packet reduction.
Th9. Observed reality can be a component of initially observable reality.
Proof: in the previous example, the observation has selected a part of the initially observable reality of A. The observed states a1 or a2 of A are components of the initial reality a1 + a2 of A.
Th10. Observed and experienced reality is only one component of reality.
Proof: in the previous example, the observed and experienced reality is represented by the state a1o1 or by the state a2o2 of the AO system. These two states are components of the reality a1o1 + a2o2 of AO after the observation.
Theorems 9 and 10 show why theorems 2 to 6 do not contradict observations.
As soon as an observation leads to several destinies of the observer, it selects a part of reality. Observed reality is relative to the destiny of the observer. There are as many observed realities as there are destinies of the observer. They all exist, but each is only a component of the total reality that unites them all. Physicists sometimes call the state that represents total reality the universal wave function (Everett 1957). Observed and experienced reality is only one branch of this wave function. Total reality can be seen as a forest that intertwines the multiple destinies of many observers with each other and with those of all other observed beings. The forest of intertwined destinies reveals to us the meaning of the Schrödinger equation when applied to a community of observers of the real world.
Th11. Two beings can coexist in the same place without being able to meet.
Proof: Let A and B be two beings, 1 and 2 two distant places, a1 and b1 states of A and B in place 1, a2 and b2 states of A and B in place 2. If the system AB is in state a1b2 + a2b1, A and B are both in place 1 and place 2. They each have two different destinies, one where A is in place 1 and B in place 2, the other where A is in place 2 and B in place 1. In neither of these two destinies can they meet, because 1 and 2 are distant places. They therefore cannot meet each other when AB is in the state a1b2 + a2b1, even though they are both in the same places.
Th11. Two beings can coexist in the same place without being able to act on each other.
Proof: Let A and B be two beings, 1 and 2 two distant places, a1 and b1 states of A and B in place 1, a2 and b2 states of A and B in place 2. We suppose that 1 and 2 are places sufficiently far apart that A and B cannot act on each other when one is in place 1 and the other in place 2. In state a1b2, A is in place 1 and B in place 2, so they cannot act on each other. In state a2b1, A is in place 2 and B is in place 1, so they cannot act on each other either. Since they cannot act on each other neither in the state a1b2 nor in the state a2b1, they also cannot act on each other in the state a1b2 + a2b1 whereas they are both in the same places.
Why say that A and B are in the same place if they cannot meet? Because they can both meet the same being C present in this place. Proof: let c1 be a state of a being C in place 1. In state a1b2c1 + a2b1c1, A and B can both meet C, but they cannot meet each other.
The multiple destinies of all observers are all in the same space. They are separated because they cannot meet, not because they occur in different universes. In the same place, myriads of beings can coexist which can never meet.
When destinies cannot meet, we can say that they are incomposable.
To make the quantum theory of truth-producing devices, we study a system made up of a community of observers who communicate with each other, and who therefore observe each other, and who observe a world outside them. Their evolution is determined with the Schrödinger equation (the fundamental equation of motion in quantum physics). The quantum theory of observation thus obtained can be considered as a chapter of naturalized epistemology (the application of physics, biology and psychology to the theory of knowledge, Quine 1969).
Remarks
Quantum physics is generally presented with the principle of wave packet reduction: after an observation, only one of the components of the wave function remains, the one which corresponds to the observed result. This is the Copenhagen interpretation, defended by the pioneers, Bohr, Heisenberg, Dirac, and many physicists. Dirac gave a proof of this principle: two successive observations must give the same result if one is made immediately after the other, therefore after the first observation, the wave function must be reduced to a single component. But this proof is false, because it ignores the entanglement between the two successive measurements. If we take this into account, we do not need the reduction of the wave packet to explain the identity of the results observed during the two observations. This proof better be false, because if it were true, the theory would be contradictory: the evolution of a physical system is always linear, according to the Schrödinger equation, and is not always linear, according to the wave packet reduction principle. But a contradictory theory is always false: all statements and their negations can always be proven. It is curious that our best physical theory is presented as a contradictory theory, with the wave packet reduction principle. But one should know that this principle is useless, that it bears no fruit, that all the knowledge of quantum physics is obtained without it. If one wants to do quantum physics, one has to forget it as soon as one hears it.
Quantum entanglement leads to a revolution in the theory of space, geometry. That two beings can be in the same place without being able to meet is incomprehensible from a classical point of view. But quantum space is not classical space. We must not project our prejudices about the nature of space onto quantum theory. The problem posed by Einstein, 'does quantum entanglement lead to instantaneous action at a distance?' is a false problem, because it comes from our classical prejudices about the nature of space. When we reason about quantum space, the problem no longer arises. Quantum space is much more than what Euclid, Newton and Einstein taught us about the nature of space.
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