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Roman Republic: Res publica Romana • View topic - INFINITAS – The Concept of Infinity

INFINITAS – The Concept of Infinity

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INFINITAS – The Concept of Infinity

Postby Gaius Florius Lupus » Sun Nov 26, 2017 6:06 pm

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Re: INFINITAS – The Concept of Infinity

Postby Gaius Florius Lupus » Sat Dec 02, 2017 5:50 pm

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Re: INFINITAS – The Concept of Infinity

Postby Gaius Florius Lupus » Wed Dec 13, 2017 2:36 am

Salvete amici!

When we discuss the concept of infinity, there is one question left to ask: Is the infinite number of worlds as suggested by Epicurus the same as the worlds in the Many-Worlds interpretation of modern quantum mechanics?

Epicurus taught that an infinite number of worlds exist and that therefore any possible world must also exist in an infinite universe, even if it is beyond our event horizon and therefore not real for our consciousness since it is beyond the perception of our senses.

Now let us look at a short summary of the Many-Worlds interpretation of quantum mechanics:
From quantum physics we have learned that the world can be described by the Schroedinger equation, which is a wave function. This means it provides only probabilities for the possible states of a particle including its location and impulse. When we observe the particle, then it has a random state that cannot be predicted by any laws of causality. However the particle behave statistically, as if their states were determined by waves. According to the Many-Worlds interpretation in each case of a non-deterministic event, this means when the wave function of the Schrödinger equation offers more than one possible outcome, our world splits in distinct parallel worlds. In the case of the double-slit experiment the world would split in one world where the particle passes through the left slit and another one where the particle passes through the right slit. For a short period of time the two worlds would still be interconnected and could interact with each other, so that we would get the resulting interference pattern on the screen. But then the worlds would be irreversibly separated and continue their own path of events.
Since such non-deterministic events occur in an incredible number every millisecond, the universe would permanently split in an uncountable number of parallel universes where every possible outcome of events occurs. Everything, which is only remotely possible, would therefore happen somewhere in some of the uncountable number of alternative universes.

From this description we can already see a difference. While Epicurus talks about different worlds in one universe, the Many-Worlds interpretation assumes entirely different universes.
But the question is not that easily answered. We have to ask first, what “identical” and "different" means.

For this purpose we have to consider the second axiom of Classical Logic, the Law of the Excluded Middle (Axioma Exclusi Tertii, everything is either A or not A). If A and not A is the same, then the term A is meaningless and its use not logically valid. In the empiric world this means that an abstract concept must have distinct consequences from its negation. If a concept and its negation have the same consequences, then the concept is meaningless.

In our example we have to ask: Does a different world in the same infinite universe (but beyond the observable horizon) have any distinct consequence from a different world in a different universe?
The answer is: No, because both are not causally connected to us and therefore have no consequence for us. Different worlds in different universes are no distinct concept from different worlds in the same infinite universe. These parallel universes would be contained in our infinite universe. The use of the word “parallel” in this context makes no sense. It is an identical concept, because it has no distinct consequences.

The Many-Worlds interpretation of quantum mechanics however assumes that the parallel universes are shortly superpositioned to each other before they separate permanently and that they can shortly affect each other by interference.
Epicurus’ infinite worlds would not necessarily interfere with each other. This means a remote world that differs only in the position of one particle from our world would not necessarily have any connection with our world that would allow an interference as described by the Schroedinger equation. Nevertheless we have not excluded this possibility by any experiment. Neither has the Many-Worlds interpretation and the temporary superimposition of parallel universes been proved by any experiment. This is one of the reasons why most physicists prefer the Copenhagen interpretation over the Many-Worlds interpretation.
Actually the Many-World interpretation has exactly the same problem as the assumption that similar remote worlds in one infinite universe have a non-local connection with each other. If the one proves false, the other one would prove false too. We know that non-local connections can exist in quantum physics where particles are connected regardless of time and space from experiments. It is called “quantum entanglement”. Therefore we cannot discard the possibility that two remote places are somehow connected with each other. We can only discard the possibility that information or causality can travel that fast.

So what can we finally conclude from the fact that the universe is infinite?
The answer is, we know for sure that in an infinite universe similar worlds to ours must exist, just as described by the Many-Worlds interpretation of quantum mechanics. We do not know, whether or not the Many-Worlds interpretation is correct regarding a temporary interference between them in order to explain the wave function of the Schroedinger equation.

As we have seen the concept of infinity may appear simple and Epicurus’ conclusions may seem trivial to us today, but in fact they have consequences and implications that are relevant even in the face of the latest discoveries of quantum physics.
The main problem is that most of us believe that we have understood what infinity means while in fact we have not.

Valete!
C. Florius Lupus
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