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Chapter 10 M-Theory, Heaven and Earth?


Is the universe actually a giant quantum computer? According to Seth Lloyd—Professor of Quantum-Mechanical Engineering at MIT and originator of the first technologically feasible design for a working quantum computer—the answer is yes. This wonderfully accessible book illuminates the professional and personal paths that led him to this remarkable conclusion.
Programming the Universe by Seth Lloyd
As in a play, we need to introduce the characters one by one to get a sense of who is who and to get to the enthralling story of quantum mechanics and M-Theory.

String theory

No one could link quantum mechanics and Einstein’s general theory of relativity. They both match reality nigh-on flawlessly in the domains they refer to atomic and cosmological. However, putting them together with our current equations would mean the Universe would have instantaneously collapsed, and we would not exist. Various scientist proposed various string theories to join the two domains together, but they were inconsistent and only worked in specific parts of Quantum mechanics. Then in 1990 M-Theory arrived.

M-theory

For a more complete description of M-theory see Wikipedia on M-Theory.
For an abridged simpler version read on.

Until 1990, there were seven separate string theories, five in 10 dimensions, 10D for short, and two bosonic string theories in 26D. They were the best theories so far at uniting Gravity and quantum mechanics. Explaining how the supergravity expected by relativity can work at the tiny distances of quantum mechanics in specific scenarios. However, the five separate string theories had five distinct 10D explanations of supergravity. Then in 1990, Edward Witten demonstrated that using two mathematical transformations S-Duality and T-Duality, he could connect the 5 different sets of 10D formulae for supergravity into one using an 11D theory of supergravity. Combining the 5 separate theories into one overriding theory.  He called this mathematical mapping between them M-theory, M for Magical, Mysterious or Mathematical, depending on how you felt about it, or when a More fundamental explanation arrives, rename it accordingly. M-theory is far from complete.

Although M-Theory is itself not string theory, it suddenly meant that the five 10D string theories were no longer in conflict with each other. This gave a considerable boost to the efforts being ploughed into each of these areas of study individually. Their conjoined research is now called superstring theory.

However, this left the two 26D bosonic theories unconnected to the others. So, M-Theory joins various string theories together in an attempt to unite quantum mechanics and Einstein’s general theory of relativity into one supergravity theory in 11D.
None of the string theories is complete, and they all leave some things unexplained or unconnected.

M-theory is the search for that unified set of equations that works at the cosmological scale and the tiny subatomic scales while leaving Earth as a viable place for us to live on somewhere in the middle of these two ranges. M-theory changes almost every year as people find contradictions that exclude possible options and narrows the search to a different set of possibilities. Or think up new theories that give alternative explanations.


Planck dimensions

The smallest unit of measurement is the Planck length.  Consider the Planck length as the number 1 for measuring the quantum world.
The visible Universe is approximately 8.4 x 10184 Planck lengths cubed. See note at the end of this chapter, if you want to know how I arrived at this number.

I use this number as an estimated upper limit as to the number of hidden manifolds containing the wrapped up dimensions of space that we cannot see in the Universe. The actual number is likely to be a lot smaller. While this is a colossal number, so vast that I could be out by a factor of 1 x 1030  it would hardly matter to our understanding of it. It also very definitely not infinite.

p-branes, D-branes, NS-branes and M-branes

While I do not appreciate some of the language used in the comments. This is the most concise and clear description I have found of the difference of these branes was found at What is the difference between p-branes, D-branes, M-branes, etc...?

M-branes are the branes visible in M-theory.  There are only 2D and 5D stable M-branes. These map onto the various other branes in string theory.

p-branes is a generic term for p dimensional branes used in the associated string theories. Strings are in general 1-dimensional branes. Strings can be closed loops or open with two loose ends.

D-branes are a specific sort of open string. All D-branes are p-branes, but not all p-branes are D-branes. NS-branes are normal string branes also called F-branes for fundamental branes.

According to the theory, p-branes vibrate and have harmonics. The p-branes has energy dependent on its frequency and tension. All the other particles are made up of p-branes vibrating at different rates and under different tensions. These two parameters give p-brane all the other features usually associated with a sub-atomic particle such as mass, electric charge, weak force and strong force.

Reaching to infinity

According to two very brilliant mathematicians, Eugenio Calabi who proposed a theory in 1954 and 1957 and Shing-Tung Yau who "proved" them in 1970, there is a mapping, using one of the family of Calabi Yau Manifolds into the hidden 6 dimensions of space.

http://en.wikipedia.org/wiki/Calabi_Yau

http://en.wikipedia.org/wiki/Calabi_Yau_manifold

When being specific about Calibi Yau manifolds, I will use CY-manifold as an abbreviation. There are several other sorts of manifold such as Kahler manifolds of which CY-manifolds are a subset.
There are many possible variants of the CY-manifolds, and it is expected that only 1 might match the actual physics and there is no guarantee that any do.

Kahler manifolds use complex mathematics. That means that each individual number is represented as two numbers. See note at the end of the chapter for an explanation of complex numbers. So all this family of manifolds always have even number of dimensions, and there are many such manifolds. Even the 6-dimensional variants of CY-manifolds there is a vast range of possible CY-manifolds that could match our knowledge of this Universe's Laws of Physics.

The 10 dimensions of space in superstring theory are split between the visible 4 dimensions we can see and the 6 compact dimensions we cannot see. Apparently, as in all mathematics, there is an infinite amount of space inside these 6 real dimensions, or 3 complex dimensions.

A last point, other types of manifold also match our current understanding of the Laws of Physics. So reality may not involve CY-manifolds at all.

Now here is where the mystery of infinity begins. A point of perspective when is the inside the outside?

In CY-manifolds, it is impossible to tell if you are inside or outside the manifold. The further you go into a the CY-manifold apparently the more room there is just a,s in the "y = 1/x" description of infinity, there is as much space inside as outside. There is a mathematical transformation that allows the external universe to flip into and out of these tiny spaces. There is also a hypothesis that at the end of the universe will "implode" into one of these CY-manifolds. Or is that explode out of a CY-manifold? No one could tell the difference.

There is also no guarantee that a CY-manifold is the correct explanation.

In actual fact, we cannot see the hidden dimensions that CY-manifolds are trying to explain, let alone see inside them. So the rest of this chapter is pure speculation. Logical speculation, but it is still a wild guess just the same.

All suggested manifolds are as large inside as outside. CY-manifolds have the same form inside them as outside them. They could already contain multiverses inside them. The fact that there is a transformation between them means that communication is possible. If the space inside is as expected a mathematical manifold, whether a CY-manifold or not, has the same structure as outside it, Those multiverses will similarly have manifolds within themselves. Each of the up to  8.4 x 10184 manifolds could have a separate multiverse inside it. We really do not have a clue how big the Multiverse is.

I suspect it is infinite because these manifolds are as big on the inside as on the outside. The physics inside does not need to be the same as on the outside. While we will never usefully measure sub-Planck lengths in this Universe, using, what would be sub-Planck lengths for us, from within some of these manifolds, and CY-manifolds in particular, has just become a very valid thing to do.

Going back to our understanding of infinity and there is as much space within any volume as, outside it. Quantum mechanics no longer measures just the tiny but also the infinitely vast space inside each manifold. Each manifold could contain several billion galactic empires, and they could be trying to communicate with us through the manifolds. Although that is pure speculation, in the world of abstract existence, every possibility exists.

Could the Multiverse be intelligent?

These CY-manifolds may be our Universe’s dendrites branches into other multiverses within the CY-manifolds inside each manifold. Our Multiverse may have an Axon into an even bigger entity, thus making the whole system whatever it is called truly intelligent.

However, just because the Universe may be intelligent does not mean that it is the mind of God. Remember God includes all abstract worlds including, for example, 15 dimensional, 27 dimensional or 17,343-dimensional worlds. The Word is truly limitless. To suggest that there is equality with The Word in and an intelligent version of the visible Universe is ridiculous.

However, using the mathematics of infinity, a perfect image of the outside can be held from within. This does imply that God can be seen from within The Universe, and so the Universe could contain God.

The Word is full of paradoxes because He, She or It contains everything.

Note on the calculation of the volume of the Visible Universe in Planck Lengths.

While the Universe is 13.7 billion years old, space has expanded, each unit cube of space has effectively grown in size over time. So the diameter of the visible universe is 93 billion light-years across.
#ValueDescription
  12.99792000000000E+008Speed of Light in m/s
  29.30000000000000E+010The Diameter of visible space in Light Years
  33.65242500000000E+002Days in a year (leap years and non-leap centuries)
  48.64000000000000E+004Seconds in a day (24 hours x 60 minutes x 60 seconds)
  53.15569520000000E+007Seconds in a year (value 3 x value 4)
  69.46052175398400E+015A light year in metres (value 1 x value 5)
  78.79828523120512E+026The Diameter of visible space in meters
  84.39914261560256E+026The Radius of visible space in meters (Diameter halved)
  91.61622938000000E-035Planck Length (The length discovered by Planck)
102.72185536907055E+061The radius of visible space in Planck lengths(value 8 x value 9)
118.44663529018872E+184The volume of space in cubed Planck lengths 4/3 pi r3(r is value 9)


Note on complex numbers

There is no real square root of any negative number. So the square root of -1 has been given the name i, for imaginary and is not found on the real line but on a plane. Complex numbers are a combination of a real component and an imaginary component. With a real number associated with each, e.g. 10 + 5i.

Real numbers are the numbers we use every day, except they include the infinite number of numbers or cardinality, we do not usually think of when using them. We think of and use the decimal approximations, that are practical to use, and we ignore the infinite cardinality.