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Complex-Time Geometry and Perpetual Creation of Space

by Mohamed Haj Yousef

Search Inside this Book  Schroedinger’s Cat

In line with the EPR paradox just explained in section 4.4.6 above, in order to illustrate what he saw as the problem of the Copenhagen interpretation, Schroedinger proposed, also in 1935, another thought experiment; this time using a macroscopic living organism. The scenario presents a cat that may be in a superposition state, being simultaneously both alive and dead, as a result of being linked to a random subatomic event that may or may not occur. In the course of developing this thought experiment, Schroedinger coined the term Verschrankung, meaning: entanglement, as we described in section 4.4.7.

To further illustrate the paradox, Schroedinger described how one could, in principle, create a superposition in such a large-scale system by making it dependent on a quantum particle that was in superposition state. He proposed a scenario with a cat in a locked steel chamber, wherein the cat’s life or death depended on the state of a radioactive atom, whether it had decayed and emitted radiation or not. According to Schroedinger, the Copenhagen interpretation implies that the cat remains both alive and dead, until the state is observed.

Schroedinger wrote in his article: “One can even set up quite ridiculous cases. A cat is penned up in a steel chamber, along with the following device: in a Geiger counter, there is a tiny bit of radioactive substance, so small, that perhaps in the course of the hour one of the atoms decays, but also, with equal probability, perhaps none; if it happens, the counter tube discharges and through a relay releases a hammer that shatters a small flask of hydrocyanic acid. If one has left this entire system to itself for an hour, one would say that the cat still lives if meanwhile no atom has decayed. The first atomic decay would have poisoned it. The psi-function of the entire system would express this by having in it the living and dead cat mixed or smeared out in equal parts.” Greenstein and Zajonc (2006)

This thought experiment highlights the implications that accepting uncertainty at the microscopic level has on macroscopic objects. A cat is put in a sealed box, with its life or death made dependent on the state of a subatomic particle. Thus a description of the cat during the course of the experiment, having been entangled with the state of a subatomic particle, becomes a superposition of living and dead cat. But this can’t be accurate because it implies that the cat is actually both dead and alive, until the box is opened to check on it. The wave-functionmeans that, once the cat is observed, there is a 50% chance it will be dead, and 50% chance it will be alive.

This thought experiment poses the following question: when does a quantum system stops existing as a superposition of states and becomes one or the other? Copenhagen interpretation is very clear about this, because it already confirmed that the wave-function is only a mathematical description that can calculate the probabilities of each particular state, which may or may not become real only after the actual measurement is performed. The cat could be either dead or alive, but we may only know that after the box is opened, and we look at it.

However, other later interpretations had been proposed that give different answers to the questions posed by Schroedinger’s cat, of how long superpositions last and when or whether they collapse. In the many-worlds interpretation, explained further in section 4.5.5, every event is a branching point in our particular history, so the cat is both alive and dead at the same time, regardless of whether the box is opened or closed, but the alive and dead cats are in different branches of the Universe that are equally real in their own corresponding branch of reality, but cannot interact with each other because there is no effective communication or interaction between them.

When opening the box, the state of the observer becomes entangled with the state of the cat; so in one branch of reality the cat is dead and in another the cat is alive, and quantum decoherence ensures that the different outcomes have no interaction with each other.

The same mechanism of quantum decoherence is also important for the interpretation in terms of consistent histories, as explained further in section 4.5.10, where only the dead cat or the alive cat can be a part of a consistent history. In the objective collapse theories, explained in section 4.5.12, superposition states are destroyed spontaneously, irrespective of external observation, when some objective physical threshold, such as time, mass, or temperature, is reached. Thus, the cat would be expected to have settled into a definite state long before the box is opened, but its state is known only at the time of opening the box.

The Duality of Time agrees with the Copenhagen interpretation that the superposition state is only a probabilistic description of reality, and then combines that with the above conclusion of objective collapse theories that the states are always spontaneously collapsing, whether they are being externally observed or not. Observation only provides knowledge of the otherwise independent and dynamic reality. At the same time, however, as we shall see further in chapter VI, the mere consciousness of all possible observers are inevitably part of any otherwise closed systems that they may be concerned with at the time, and thus they may have individual or collective influences on the outcome of each spontaneous collapse that is continuously happening at every instance of time. The effect of consciousness builds up, just as any other objective physical thresholds, but being intrinsically metaphysical, this effect of consciousness, though it is extremely very weak compared to other direct physical causes, it could become strong enough in special cases of concentrated and focused mental contemplation or any inherently strong correlation with the object in question, such as for example when someone is tremendously anxious about his own gorgeous cat being in such fatal circumstances locked inside the box! This effect of consciousness is only conceivable based on the actually indivisible oneness of the Universe, in the real metaphysical flow of time, that is spreading into the physical multiplicity that seems to be evolving apparently unconnected, or remotely connected, on the normal level of time. So in reality there are no closed systems apart from the whole Universe, because the observer’s consciousness is always part of it, while if no observers are outside a closed system no one would know that it even exists. Any abstract awareness that something exists entangles the corresponding consciousness with it, and this may affect its continuing spontaneous evolution. This revolutionary connection that results from the reality of the indivisible oneness of the Universe has extremely deep implications that will be discussed in chapter VI.

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I have no doubt that this is the most significant discovery in the history of mathematics, physics and philosophy, ever!

By revealing the mystery of the connection between discreteness and contintuity, this novel understanding of the complex (time-time) geometry, will cause a paradigm shift in our knowledge of the fundamental nature of the cosmos and its corporeal and incorporeal structures.

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Mohamed Haj Yousef

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