Do you recall reading this: What is the destiny of science? Until now, scientific research has not embraced the internal world of cause, but only the external world of result; not the world of essence, but only the world of phenomena. Today science is entering a higher dimension; it is no longer concerned exclusively with the external world of result and phenomena, but has begun to examine the internal world of cause and essence as well. (Divine Principle, 5th ed, 1977. p. 18)

One day, I am confident, this will be recognized as a prophecy of the first rank. You see, the remarkable thing is, that while the work of figuring out Quantum Mechanics was completed by the fifties, its meaning was buried in a multitude of detail and the esoterica of matrix mechanics and complex vector-spaces. It is only now, decades later, that the real import of quantum mechanics is beginning to emerge yet the Introduction to the Principle confidently asserted that it was already examining "the internal world of cause and essence." It had, to be sure, but no one on the physical plane at least realized back then.

What is only now emerging is that the conceptual framework developed by the quantum physicists, put simply, links the external world of space and time with the internal world of mind.

As is always true, such a development has not occurred in a vacuum, it is based on the work of many over a period of many years.

In fact. a good case can be made that the story starts thousands of years ago in the mud of the annual flood of the Nile. The dilemma this imposed on the Ancient Egyptians was how to figure out whose bit-of-land was whose, after the waters had subsided leaving everything covered with a layer of concealing ooze.

Fighting was the solution at first, but eventually the priestly class came up with a much better way using large triangles measured from fixed features such as a pyramid or mountain. They found particularly useful a remarkable triangle with sides in the ratio of 3, 4 and 5 which always contained a perfect right angle which was helpful in giving everyone their fair-squares of land back after the flood.

The next step along from this modest beginning happened just across the Mediterranean in Greece where, just about twenty five hundred years ago, an inquiring mind became socially acceptable and the Egyptian observation was explained by a philosopher from the island of Samos.

Using pure logic, he found that the 3-4-5 triangle was just one of an infinite number of different triangles, all described by the theorem that has engraved the name "Pythagoras" into the minds of countless school children down the millennia:

In any right-angle triangle, the square of the side opposite the right angle is equal to the sum of the squares of the other two sides.

This is what mathematicians generalize as the relationship between the size of an object, s, and its projections as height, width and breadth; x, y and z. This relationship is simply expressed algebraically (a convenience not available to Pythagoras, of course) as s2 = x2 + y2 + z2.

Now, while the size of a 2-by-4 piece of wood, say, does not change just because you twirl it around; the rotation alters its projection from being a tall and narrow post to that of a short and wide beam.

In a somewhat grandiose manner, science states that size remains "invariant" under the operation of rotation.

The simple Pythagorean relationship was clearly significant which is why it was passed down to us through the dark ages but no one thought to say why it was so significant until, almost 2000 years later, when in renaissance France, Descartes, one of the philosophical founders of our modern age, decided that spatial extension must be what distinguished matter from mind.

The things of the mind realm the Res Cogitans as he called them were characterized by what they didn't have and what they didn't have was spatial extension. In a nutshell, they didn't have size, they didn't follow the Pythagorean relationship. On the other hand, he said, things in the matter realm did.

The historical consequence of this separation of mind from body Cartesian Dualism, as his explanation came to be called was spectacular, to say the least.

You see, before Descartes, people, such as Aristotle had mind-things and matter-things all mixed up. The tree falls because of its desire to go to the earth, was how Aristotle explained things, and he must have made a lot of sense because no one disagreed with him for over two thousand years and Descartes' freeing matter-stuff to be examined without reference to mind-stuff.

Within a century, Sir Isaac Newton had abolished the barrier between the heavens and the earth. He found that with his description of gravity he could explain how the apple fell from the tree as well as what moved the moon and the planets through the heavens.

In a moment of quite uncharacteristic modesty he acknowledged those, such as Decorates, who had opened the way by declaring that, "If I have seen further, it is by standing on the shoulders of giants."

It is widely recognized that the birth of Western science can be traced back to the foundation established by Newton's work.

It took another genius to substantial enlarge the foundation created by Newton.

Einstein, just this century, found that it was not really the spatial extension that was invariant, but rather the extension in time-and-space that was the real invariant.

He found that something as simple as a lighted match, with a length of two inches and a duration of one minute, would look very different if you were moving very, very quickly past it would be one inch long but last for two minutes.

It is the same match and its objective reality, which he called its worldline, w, is related to the spatial and temporal extensions s and t in a simple extension of the Pythagorean relationship: w2 = s2 + t2.

The worldline is the invariant but, just as the width and height of an object seem to change with rotation, the spatial and temporal extensions seem to change with linear motion. Or, putting it another way, the worldline is invariant under the operation of linear motion. The only reason we don't usually notice this is because we habitually travel around at speeds significantly slower than that of light.

Einstein later told a friend that he was horrified by the "everything's relative" social misuse of his work and wished that he'd used the much more accurate "Principle of Invariance" instead.

"Everything's invariant, man!"

This change in perspective continued stimulated by the highly sophisticated development of the impulse of every child to pull things apart to see what they are made of.

It was found that when such smashing was taken to the extreme, everything turned out to be made up of various combinations of just two so-called fundamental particles the electron and the quark. And, as quarks live a convent-like confined life in the atomic nucleus and play little part in everyday life, almost everything could be understood if we understand the electron.

So scientists took a close look at the electron.

They fully expected the electron, of course, to behave just the way things made of electrons behave basically they expected electrons to conduct themselves just like tiny pool balls.

It seems obvious, but the important thing about pool balls, to both the punter and the scientist, is that you know where they are when you start and you can know, through either the laws of mechanics or shooting a lot of pool, just where the balls are going to end up.

Scientists, therefore, expected that they would be able to pinpoint the electron and that, once they had figured out the appropriate laws, they would be able to predict what the electrons would do.

So you can imagine their surprise when it turned out that the electron doesn't play pool at all, rather it plays the subatomic equivalent of roulette.

It turned out that was impossible, in principle, to know where an electron is and where it is going with certainty. Just like roulette, all you can know about the electron is the probability of finding it in a particular state.

Such behavior is not-at-all common sense but, when common sense conflicted with probability, probability won every time. In some set ups, for example, the electron might sometimes be found at one spot and sometimes at another but never anywhere in between. This "tunneling", as it is called, occurs because the electron has a probability of being in one place and the other but no probability of being anywhere in between.

The only reason, it turns out, why things made of electrons such as you and me don't teleport with ease long a possibility in the creative imaginations of science fiction writers is that this tendency cancels out and things tend, instead, to stay in the same place.

The explanation for such non-pool ball behavior, it turned out, does not involve the time-and-space extension of the electron, rather, it involved an aspect of the electron that had never been noticed in matter before, an extension that physicists called the wave function usually labeled with the Greek letter sigh, y and its projection as sigh-squared, y2.

In non-technical terms, sigh can be thought of as a measure of the tendency to follow a particular history.

It turned out that the worldline of Einstein only dealt with the past of an object where it was and what it did while the future history was a combination of this worldline extension and the sigh extension.

When there is a choice of future paths, all the factors involved which, for a simple system such as an electron, are described by the action equation' of the electron combine to create the sigh extension which you will not go very-far-wrong in thinking of as an arrow: big sigh, big arrow; little sigh, little arrow.

The key insight in the development of quantum physics was the realization that the probability of a particular history being followed was simply sigh-squared, that the probability of following a particular path was just the projection of the tendency, the probability was sigh-squared, Y2.

So the invariant is not the worldline, rather it is something we can call the world graph of an object.

In the illustration, at time zero the future opens up with all its possibilities each of which has its associated probability (indicated by the width of the gray line. This graph-in-gray is an extension in time-and-space but is a potential extension, not an actual one. A little later, time 1, one of these paths was followed, a probable one here, and the worldline is now an actual extension in space-time. A little later still, the worldline has progressed further still, at one point following a less-probable path which occasionally happens. You will see, however, that the world net is unchanged, all the other ramifications becoming might-have-beens.

The connection between the worldgraph, symbolized by the Greek letter W, and the time, space and sigh extensions is just the Pythagorean one again: W2 = s2 + t2 + y2. Succinctly, quantum physics has that the worldgraph of an object is invariant under the operation of movement through time. That, believe it or not, is the simple essence of quantum physics though you'll probably need to go to graduate school to fill in all the details.

So, to summarize, the size of an object is invariant under the operation of rotation; the worldline of an object is invariant under the operation of linear motion; and the worldgraph of an object is invariant under the operation of movement through time.

It is the worldgraph that is the real object of scientific study, it is this that is created by the natural laws. It is the worldgraph that underlies all phenomena. What actually happens is history, what particular branch of the graph was followed. While modern physics has an excellent understanding of both aspects the principles that govern the sigh extension of particles (expressed as the action equation, remember) as well as the actual history, their creation in the Big Bang modern biology is almost wholly constrained to the historical description of what actually happened and has little understanding of the underlying principles.

It is this worldgraph that theologians are speaking of when they say that, "God Knows Everything!" It is the worldline that theologians are speaking of when they say that the universe is autonomous, it runs without God tinkering to keep it moving. Most theologians agree that, while God knows what you can do, He does not know what you will do. Quantum mechanics makes this apply to everything: while God knows what path an electron can follow, and the probability of each path; He does not know which path the electron will follow.

Now I am sure there is least one question left unanswered if the sigh extension of the wave function is not pointing in the spatial dimensions, and its not pointing in the temporal dimension, then just where is it pointing?

Our current level of scientific understanding answers this question but only in a fashion with the explanation that the wave function extension is internal, it is pointing not in an external dimension, such as space and time, but in an internal dimension.

Well, you might ask at little exasperatedly, just what is an internal dimension, where is this internal space? Ahh, the scientist will answer with a wry shake of the head, we don't know the answer to that question, but then we don't know what the external dimensions of time and space are either!

Now I have a confession to make. I have sort of hinted that modern science explains the mind. Well, that is a bit of a come on since science does not understand the human mind at all, it does not even have a handle on the mind of plants and animals or even cells for that matter.

But the internal extension of the electron, the sigh-wave-function aspect, is what a non-scientist might call the mind of the electron, the invisible, intangible, internal aspect that determines its future, its inherent directive nature.

And what electrons have we can confidently expect things made of electrons to have as well.

Classical physics (which includes Einstein's worldline) was puzzled by the "arrow of time" as all the laws of nature were thought to work on the external extension and be reversible in time. There were, to be sure, the thermodynamic arrow (things get disordered technically entropy increases and broken crockery doesn't spontaneously reassemble), the cosmological arrow (the universe is expanding) and the physiological arrow (we remember the past but not the future) but how were they connected to each other.

The new physics connects them all: the tendency of things to be in the most probable states (the disordered, unfortunately) is directly related to the sigh extension of things; the tendency of the universe to expand (at the start when it was most crucial) can be calculated and was highly probable; and memory involves the worldline not the worldgraph. The arrows of time are all connected to the sigh extension and its expression as the worldline.

One thing emerges, though, Descartes got it wrong the difference between mind and body is not that matter has extension while mind does not the difference is actually that of an extension in an internal space and an extension in an external space.

There you have it, as predicted, the way that modern science "is no longer concerned exclusively with the external world of result and phenomena, but has begun to examine the internal world of cause and essence as well."

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