According to the current concepts in Cosmology, the Space-Time Fabric of our Universe is a continuum. This a natural humanistic view of our world since as humans we only see the Arrow of Time expanding out to infinity. Our mathematics is based upon the real number system in which we support the concept of +/- infinity. As the old story goes, if you step half of the distance between you and a wall on each step, then you will never reach the wall. We see this as a logical conclusion. But is this the true Reality? Our mathematics is only an invention of our experience of Reality (see: The Road To Reality by Roger Penrose for an excellent review on the development of mathematics).
Because we believe that Space-Time is infinite (i.e. a continuum), Physics encounters a problem with a discontinuity at the singularity point. Our Physics breaks down inside Black Holes. The Big Bang becomes impossible to describe at the initial moment since the size of Space-Time is infinitely small according to our mathematics. But what if we have taken the wrong approach? What if Space-Time is a Quantum region?
String Theory proposes that the smallest size in the 10-dimensional Space-Time is equal to one Planck Length 1.6 x 10-35 m or about 10-20 times the size of a proton. Indeed if this is the smallest size, then Space-Time should be a Quantum Space-Time. Returning to our old story, if the smallest step we can make as we approach the wall is only one Planck Length, then we should be able to reach the wall upon the next and final step when we are exactly one Planck Length away from the wall. This logic implies that Space-Time is Quantized and is not a Continuum. If this is the true Reality, then our Physics does not break down. There are no discontinuities. The minimum size of the Universe at the moment of the Big Bang was 1.6 x 10-35m . Infinity is just a mathematical concept.
Not only is Space quantized, but so is Time. The Planck Time is the time it would take a photon traveling at the speed of light to cross a distance equal to the Planck length. This is the ‘quantum of time’, the smallest measurement of time that has any meaning, and is equal to 10-43 seconds. From our perspective as human beings, we cannot experience these Planck Limits. We see the Universe as a Continuum of 3 expanding dimensions and one of time. String Theory proposes 6 more closed dimensions curled up upon themselves and finitely small. These extra dimensions are invisible to us. So is the quantized "ticking" of our clocks. As macro objects of matter, we cannot experience these small dimensions and periods of time.
The advantage of all of this is that our mathematics does not fail us if we view the Universe in a quantized Space-Time matrix. Maybe this same quantization occurs in other Multi-Universes assuming William Jame's theory is correct. Perhaps we need to take another look at things. Instead of using calculus, finite summation mathematics should be sufficient to describe our Universe.
In my next posting, we will take a look at the concept of Bubble Universes (Chaotic Inflation theory). I wonder if they are comprised of different forms of matter than those we see in our Standard Model. Why are there only 3 levels of matter in our Universe? Could it be that there are more forms? And if so, could the entire Multiverse be a collection of Universes where the higher energy Universes are degenerated according to the Pauli Exclusion Principle? More on that later.
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