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Space and Dimension

What is space? We know that it is a fundamental element of the universe. It gives us our sense of locality. We can also sense that it has three dimensions within which objects can move. The special theory of relativity assumes space and time as real entities that are the background and benchmark of the universe. However, these entities are not rigid or inert.

Space and time are bendable and play a very active role in the forming reality as we see it. Einstein mentions that singularity cannot contain topological space. In mathematics, singularity theory is the study of the failure of manifold structure. This means there is no spatial dimension to singularity. In other words, singularity is a mathematical point. In such a realm, the notion of distance disappears and co-existence prevails.

Steven Hawking, George Ellis, and Roger Penrose have worked on the theory of relativity and its implications regarding the notion of time. In 1968 and 1970, they published papers in which they extended Einstein’s theory of general relativity to include measurements of time and space. According to their calculations, “Time and space had a finite beginning that corresponded to the origin of matter and energy. The singularity didn’t appear in space; rather, space began inside of the singularity.”[14]

According to the Big Bang theory, space started at time 0 and has been expanding ever since. Inside the inescapable zone of black holes (event horizon), space gets twisted and disappears. The Heisenberg uncertainty principle (discussed in the section “Quantum Mechanics”) suggests that at the small scale, location is blurred. Therefore, we can deduce that at the scale of the ultra small, the notion of space disintegrates. We will discuss this in further detail later. The following arguments support the assertion that space did not exist in singularity.

If we deny that matter was the origin of universe, we have to consider its energy equivalent as the initiator. The equation for the enormous energy that built our space-time universe can be written as follows:

Ψ(E) = E max e i(kr^n-wt)

In this equation, Ψ (E) is energy function, i is an imaginary number, k is a wave number, nr is the number of dimensions, w is the angular velocity, and t is time.Ψ (E) = E max e i(kr^n-wt).

In singularity, t = 0, then

e -iwt = e 0 = 1.

Therefore, Ψ (E) = E max ei knr

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If we take energy as maximum in singularity, then Ψ (E) = E max,

therefore e i knr = 1.

If i krn = 0, we may conclude that n = 0, which means there are no dimension in singularity. Consequently, we can claim that the singularity does not contain space.

Furthermore, Assertion C3 implies that space, as a measurable entity, cannot exist in singularity. Interestingly, in the supersymmetry model, the size of superspace, which lies beyond familiar space, is zero.

Assumption S3: Space is not a property of singularity.

Bell’s theorem defies the notion of locality for subatomic particles. Quantum entanglement suggests that Subatomic particles have a mysterious instant connection with each other, even if they are worlds apart in space-time. The entanglement of particles points to a realm where locality doesn’t exist and therefore immediate connections can happen.

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