MY STRING THEORY HAS KNOTS - THINKING LONGER AND HARDER

(- Copyright 2016 by Mike Stewart -)

I am rational, you are rational, and now we are saying PI is rational. In the case of PI, we mean that it is a number with a definite value.

We began our consideration of String Theory by listing six of possibly many sub-string theories and decided to look more closely at these. The first said matter (you and me) did not exist and Einstein was wrong when he said nothing could go faster than light.

Looking closely at the first, I thought we could drill down, moving from our world to the microscopic, then the world of DNA and large molecules, then to atoms, electrons, and maybe quarks, and then on to see what might be happening at the string level. We have reached the atomic level, and maybe a little further, and along the way come up with what I hope are some interesting speculations. We are, however, nowhere near string level. And, we haven't even looked at the other five sub-string theories.

There is a ray of hope. I believe I can rationalize covering the other five in much less detail.

There is a ray of doom. Newer theories may have replaced String Theory.

There is another ray of hope. It is unlikely that new theories can invalidate my wild speculations.

There is a Theory you may have heard of. It is called the Big Bang Theory.

Before we discuss the Big Bang Theory, let me tell you why I am bringing it up now. We have been talking about some very large and some very small numbers. Planck's time, for example, is the shortest duration of time possible. Part of the Big Bang Theory is concerned with our universe when it was very young. Planck's time is equal to 10 E-43 seconds. Our universe cannot be younger than 10 E-43 seconds. The Big Bang Theory says that the universe did not existed at the super microscopic string level, but that it suddenly sprang into existence with a ripe old age of one unit of Planck time.

When I say suddenly, you can't get any more sudden than 10 E-43 seconds. At this point, PI is probably equal to 3.0 and the circumference of the universe is three Planck's lengths. What I want to think about is how did our universe go from not existing at string level scales to developing existence when time started.

The Big Bang Theory is a theory that attempts to explain how we came to exist. It is not the only theory, but it is the most popular. Over the years, science has accumulated a lot of evidence to support it.

What happens at the string level, "before existence" remains an area of speculation and can include, for the religious, images of God.

Edwin Hubble's discovery, in 1929, that the universe was expanding, was probably the cornerstone of the Big Bang Theory. If the universe was of a certain size and expanding at a certain rate, you could imagine running time backwards until everything in the universe was at one point.

There is a paragraph on the website http://www.big-bang-theory.com/ that adds to our discussion and introduces a couple of concepts that may be useful:

"According to the standard theory, our universe sprang into existence as "singularity" around 13.7 billion years ago. What is a "singularity" and where does it come from? Well, to be honest, we don't know for sure. Singularities are zones which defy our current understanding of physics. They are thought to exist at the core of "black holes." Black holes are areas of intense gravitational pressure. The pressure is thought to be so intense that finite matter is actually squished into infinite density (a mathematical concept which truly boggles the mind). These zones of infinite density are called "singularities." Our universe is thought to have begun as an infinitesimally small, infinitely hot, infinitely dense, something - a singularity. Where did it come from? We don't know. Why did it appear? We don't know.".

In the above quoted discussion, I think there is a typo - 'as "singularity"' should have been 'from a "singularity"'. Scientists and laymen like me are very interested in what is happening in "singularity zones" - in this case, we are talking about what is happening at the moment of the Big Bang in the zone between Planck's world and the world of strings.

Before we go there, however, let's talk a little more about the Big Bang.

When our universe sprang into existence, everything was confined to a universe that had a circumference of three Planck's lengths (remember that on this scale, PI was probably equal to 3.0 and when we multiply this by the diameter of one Planck's length, we get the circumference).

What is the volume of our universe at "the very beginning"? In our world, the volume of a sphere is equal to ((4 divided by 3) times PI times R times R times R) where R is the radius of the sphere. We are assuming that the initial universe is a sphere, that is, it has an equal thickness in all directions. It would still have the same problem I am about to describe if it had any thickness at all (even zero). It probably wouldn't have this problem if its thickness was negative, but we don't know what that means.

The problem is with the radius R. It is equal to one-half of the diameter or one-half of one Planck's length. By definition, however, nothing can be less than one Planck's length. The entire equation, to my mind, becomes meaningless, and we come to the conclusion that our universe entered our reality sporting an imaginary volume. Maybe we can say it was partly in and partly outside of reality.

What happens next? In our reality, next is one unit of Planck's time later and the entire universe has to "quantum leap" to this point. We will pursue this, but note that since the universe is not entirely within our reality yet, it may not have to follow this rule. In fact, maybe reality itself is relative, with our universe, and us along with it, moving toward "true" reality. Our universe may, or may not, ever reach this reality.

OK, our universe quantum leaps to a point one unit of Planck's time later. The minimum distance it can expand is one Planck's length - thus the diameter of the universe could now be two Planck's lengths (scientist argue that the universe could expand faster than this, but we will discuss this more later).

The Radius R is now equal to one Planck's length and we can use our equation for Volume V:

V = ((4 divided by 3) times PI times R times R times R).

V = ((4 divided by 3) times 3.0 times 1 times 1 times 1) .

V = 4 cubic Planck's lengths.

The entire universe is now confined to a very small, but to what we recognize as, a real volume.

If we continue this process of quantum leaping forward, however, we will find a result analogous to our calculations for circumferences. Based on the precision used for PI and whether or not R is a whole number, V can be either a real or imaginary number. Or we could say we only have a probability of a particular value of V.

Once we have a very small, but very real volume, and we put our entire universe in it, we realize it must be very dense in there and the temperature must be very high. As the volume increases, the density of matter and energy will decrease and the temperature will fall. In fact, we can calculate the temperature after 13.7 billion years of expansion, that is, what the temperature should be Today.

Cosmic Background Radiation had been theorized to be energy left over from the Big Bang. It was discovered in 1964 and had a temperature, as predicted, of slightly below three degrees above absolute zero. This was major support for the validity of the Big Bang Theory.

We are, however, going the wrong way. I want to go down, toward strings; not up, toward the reality we know.

If I want to have any chance of successfully exploring the non-reality world of strings, I will need to try to adhere to a few rules.

I do think I can use analogies to physical processes that occur in our reality - this includes weird quantum stuff.

I think I should try to avoid the "digging to China" syndrome where I believe that the next shovelful of facts is going to tell me the secret of string reality when I still have millions of shovelfuls to dig.

Since I see no reason why any reality has to accept Occam's razor, I will not do so either.

Occam's razor is a problem solving technique attributed to William of Ockham, an English Franciscan friar who lived in the 14th century. Most scientists believe, based on his philosophy, that if there are two or more possible explanations for some experimental results, the simpler explanation is usually the correct one.

The sub-string theory we have been considering has 26 dimensions. I am sure this is based on a mathematical model that few in the world can understand. I wonder if the math might have also implied more dimensions, like fifty-two or five million. Scientists may have ignored these possibilities because scientist are taught to subscribe to Occam's razor.

If there are 26 dimensions, we are aware of four, namely height, width, length, and time. The rest of very small - billions and billions of times smaller than a Planck's length. They have impossible smallness. Each of these is curled up, taking up only a small part of the three space dimensions. These small dimensions are intertwined within themselves and are too small for us to be aware that they exist.

We can take a closer look at the three space dimensions. Height is the distance traveled by a dimensionless point in a particular direction. Width and length can also be defined in the same way. The only difference in these three dimensions seems to be the direction of travel. We think of length as traveling horizontally. We think of height as traveling vertically. We think of width as traveling "across" or horizontally and at a right angle to the other two dimensions.

Each small dimension, besides being smaller, is often described as traveling at right angles to other dimensions and moving in a direction that only exists for that dimension.

Since my head is beginning to spin, we should probably try to look at our string realm differently. Before we do, however, a comment or two on the other dimension, time.

Time is very important in our reality. One of the chapters in this book is "Time is of the Essence". Time is ubiquitous in scientific equations. The speed of anything, including light, is the distance that "anything" travels during a specific time.

Almost all multi-dimension theories in science assume space dimensions, but only one time dimension. This seemed strange to me so I googled "multiple time dimensions" and Wikipedia told me that "The possibility that there might be more than one dimension of time has occasionally been discussed in physics and philosophy".

Maybe when we try to explore the realm of strings, we should consider more than one time dimension. But I have a better idea.

What if we try to imagine the realm of strings as being all existence. By all existence, I mean every universe that can exist. In a particular universe, you may have time and space, but, in the realm of strings, such concepts have no meaning.

A useful analogy might be a traveler on the surface of the earth. He can travel anywhere and he can look west, north, east, and south. There are only two exceptions - if he is standing on the North Pole or on the South Pole. In both cases, east and west no longer have any meaning. At the North Pole, north also loses all meaning. Our traveler can only look south. Similarly, at the South Pole, south loses all meaning. Our traveler can only look north.

When we enter the realm of strings, it seems to me that we need to question every "normal" question we may have. For example, when we talk of all existence and every universe that can exist, we might wonder how many universes can exist. In such a strange land, however, maybe first we should ask, at least in passing, questions like:

Will our math work there?

Is two greater than one?

Can we have half a universe?

In the normal world of quantum physics (I never thought I would use that phrase), we can have bosons and fermions. Bosons are the particles that transmit force. Bosons usually can occupy the same space at the same time. Fermions are the particles that make up matter. Two of them cannot occupy the same space at the same time.

If we believe our math works in the realm of all existence, we can ask how many universes exist "there". Maybe each universe is like a boson and untold numbers can exist together.

At the string level, time no longer exists. Distance, which we define as how long, that is, the time, it takes to move from point A to point B, must also disappear. Even point A and Point B have vanished. Motion no longer has a meaning. Without distance, we cannot calculate volume. We might say size has disappeared. Is there anything left? Maybe just the fabric of all reality.

We have been thinking of a string as a very, very small thing that we would have to have a super-microscope to see. If a string could think, however, that is not how it would view our reality. With no concept of distance or time, events occurring a mile away would be the same as events happening on the other side of the universe. With no concept of size, an elephant would be neither larger or smaller than our entire galaxy.

With no concept of time, at the string level, all events are equal. Now is the same as a million years ago or a million years in the future. We can ask what caused the Big Bang, but we shouldn't look for a time based answer - what we call cause and effect.

When you require cause and effect, you can get into interesting and funny discussions involving elephants, tortoises, and God.

Stephen Hawking related the following in his 1988 book "A Brief History of Time" (from Wikipedia):

A well-known scientist (some say it was Bertrand Russell) once gave a public lecture on astronomy. He described how the earth orbits around the sun and how the sun, in turn, orbits around the center of a vast collection of stars called our galaxy. At the end of the lecture, a little old lady at the back of the room got up and said: "What you have told us is rubbish. The world is really a flat plate supported on the back of a giant tortoise." The scientist gave a superior smile before replying, "What is the tortoise standing on?" "You're very clever, young man, very clever," said the old lady. "But it's turtles all the way down!".

This story highlight what is one of the major obstacles in our quest to understand reality. It seems like we can always ask what is the last turtle standing on. We need to always remember what I call the "Turtle Problem".

Wikipedia goes on to report:

Hawking's suggested connection to Russell may be due to Russell's 1927 lecture "Why I Am Not a Christian". In it, while discounting the "First Cause" argument intended to be a proof of God's existence, Russell comments:

"If everything must have a cause, then God must have a cause. If there can be anything without a cause, it may just as well be the world as God, so that there cannot be any validity in that argument. It is exactly of the same nature as the Hindu's view, that the world rested upon an elephant and the elephant rested upon a tortoise; and when they said, 'How about the tortoise?' the Indian said, 'Suppose we change the subject.'".

At the string level, effects do not have to have causes, or, at least, an effect does not have to be tied to a cause by time. Suppose a traveler, standing on the North Pole, where all directions are SOUTH, asks "Where is God?". Can the answer be "You are close. It is important that you find him because he made everything. He is on the other side of that hill WEST of you"?

We don't know where the Big Bang, and thus, our entire universe, came from. It just sprang into existence. In fact, we don't know where other universes, if they exist, came from either. Or where they are. But we do know that when time does not exist, the answer becomes as meaningless as "He is on the other side of that hill WEST of you". Without time, we cannot construct distances or volumes to put things in. All possible universes are nowhere, or everywhere. Or perhaps we should just say we are all in Never Never Land.

But this doesn't mean we can't ask what may happen in Never Never Land.

Scientists have said that our universe has three space dimensions that we can all see and maybe some dimensions we can't see. I must confess that sometimes when people are talking about other dimensions, I wonder if they are talking about other universes.

We have spoken of Schrodinger's fictional cat. This story highlights my dimension universe confusion. When in a box, the cat is either living or dead. Until we open the box, we don't know. The cat in the box is half dead and half alive. Only when we open the box does the cat become truly dead or truly alive. The strange part is, according to quantum theory, that if we find the cat dead, there is another universe where the box is opened and a live cat is found.

We could say this other universe is a parallel universe. What does that mean? Has it always existed or is it created when we open the box? If it is created, does that mean opening the box sends a signal back to the fabric of reality asking for a new universe, identical to ours, except that the cat is now alive?

Let us temporarily use occam's razor, that is, chose the slightly simpler explanation, to resolve the Schrodinger's cat problem. It would be simpler if, after creating a universe, reality let that universe run on its own. In this case, when Schrodinger opened the box, one or more new dimensions would be created. One Schrodinger and a dead cat would occupy one group of dimensions while another Schrodinger and another cat would live in another set of dimensions.

Now we can return to Never Never Land. Or, to be more exact, to almost Never Never Land.

Our universe has just sprang, or quantum leaped, into existence. It has a circumference of three Planck's lengths, but an undefined thickness. It is a quintillion quintillion times larger than the strings we have been considering. Except you can't say that. Never Never Land has no time, no size, no distance. You cannot compare the size of our universe, as it initially existed, or as it is today, with the size of a string.

At this point, the dimension of time (if it is a dimension) appears in our reality. Length and height have appeared, but width is still in Never Never Land. Since length and height seem to be dependent on time, it seems unlikely they are really separate dimensions. On the other hand, width is not yet in our realty even though time does exist. The only apparent difference is our frame of reference. We can have one dimension or a quintillion dimensions. A question that makes no sense until time exists is "in what order did the dimensions jump into existence?".

A Google Snippet defines "frame of reference" as a system of geometric axes in relation to which measurements of size, position, or motion can be made. This means that we can rotate our frame of reference so that width becomes either height or length while either height or length becomes width. What we are saying is we can put a dimension into either reality or Never Never Land just by how we look at it. Weird.

It is also possible that we cannot have any frame of reference until time comes into existence. We can ask how many times time can come into existence. It could be a quintillion quintillion, but let's look at just two.

The first time that comes into existence creates our frame of reference containing what we call our universe. The second time that comes into existence creates a second frame of reference and a second universe. This frame of reference could be moving at, relative to our universe, at a speed a million times the maximum speed allowed in our universe (that is, the speed of light). As far as we are concerned, this universe is still deep in Never Never Land, but it could be as rich and as varied as our universe. This universe is moving rapidly relative to our universe, but the speed of both of this universe and our universe have no meaning in Never Never Land.

It was mentioned earlier that our universe sprang into existence as a "singularity", a zone of such extreme density and temperature that they defy our current understanding of physics. Since such conditions are also thought to exist at the core of "black holes", maybe if we take a closer look at these "black holes" we can gain some insight into what happened the moment everything was born (or even "before").

On a very simple level, black holes are easy to imagine. The mass of the earth creates the force of gravity. Einstein said it is bending space time, whatever that means. If you put the mass of a large star, and certainly the mass of an entire galaxy, into a small space, the gravity will be so great that not even light can escape.

As experiments have shown, a light wave (a photon) is affected by gravity. This would not be true if its properties were perfectly wave-like, but it also behaves, to a certain extent, like a particle. If anything, including you or me or a photon, gets too close to a black hole, it would be drawn into the black hole, never to escape. Since light cannot escape from a black hole, we cannot see its surface. A black hole is just black.

To get an idea of how powerful gravity has to be to keep light from escaping, think about escape velocity. Escape velocity is the minimum speed an object must have to escape from the gravitational attraction of a massive object like the earth. The escape velocity of the earth is about twenty file thousand miles per hour or seven miles per second. On the other hand, the escape velocity of the sun is about 384 miles per second. All of this means that if you could throw a ball straight up with a speed of less than seven miles per second, eventually the earth's gravity would stop the ball and it would fall back to earth. If, on the other hand, the speed of the ball was greater than seven miles per second, the earth's gravity could not stop the ball and it would never return.

A black hole must contain enough mass so that its escape velocity is greater than the speed of light, or about 186,000 miles per second.

If light passes near a black hole, its trajectory is changed - just like a rocket passing near a planet. In fact, it seems like at a certain distance from the black hole, a light beam (photon) could go into orbit. Einstein wondered what it would be like riding on a light beam. What would it be like riding on a photon orbiting a black hole?

Of course, this is viewing the photon as a particle. If we viewed the photon as a wave, we could only say there is a certain probability it would go into orbit. There is a possibility it would whip around the black hole and go in another direction, maybe returning to its source (perhaps a laser on earth). There is also a possibility it would get too close to the black hole and not be able to escape. There is a possibility that this photon might disappear from our reality. I would think that a photon orbiting a black hole would have a fifty-fifty chance of staying in our reality.

This is an area ripe for additional questions like "what about photons not near black holes?", but let's move on.

If a photon (or anything else) drops through what is called the "event horizon" of a black hole, it seems to disappear from our reality. Inside the event horizon, the escape velocity for the black hole is greater than the speed of light. Wikipedia defines an event horizon as follows:

"In general relativity, an event horizon is a boundary in spacetime beyond which events cannot affect an outside observer. In layman's terms, it is defined as "the point of no return", i.e., the point at which the gravitational pull becomes so great as to make escape impossible, even for light.".

The event horizon is the only part of the black hole we can see. We see one black hole as larger than another if its event horizon forms further from its center. This happens if the larger black hole contains more mass and thus has a more powerful gravitational field.

Stephen Hawking, the famous physicist, is perhaps best known for his speculations about black holes. I thought he had received a Nobel Prize for his work, but I have learned that Nobel Prizes are usually reserved for discoveries and inventions. Hawking's work is brilliant, but unverified, speculation. New research, both by Hawking himself, and others, may eventually give the needed support and a Nobel Prize would be very likely.

Dr. Hawking became famous by suggesting forty years ago (I assume he was backed up by lots of fancy math) that something could escape from a black hole - that something is what is now called Hawking radiation. Escaping radiation would cause the black hole to shrink and eventually evaporate.

Although Dr. Hawking changed how we thought about black holes, he didn't solve a problem created by the very existence of black holes. This problem is what is commonly called the information paradox. You can google this if you want descriptions from scientists or science writers, but the following is my understanding of the information paradox and the basis of some of my speculations.

Particle Physics depends on the equivalency of mass and energy. Particles may break down into other particles plus energy. The excess energy may imply the existence of new, undiscovered particles. Both the old and new particles conserve certain properties in certain ways. Information about particles (their properties) is never lost - unless one or more of the particles fall into a black hole.

One way I look at the wave nature of an electron is we can't be sure exactly where an electron is - the electron is really spread out over a large, perhaps infinite area, with a high probability of being at a particular point - but the "true" electron is the total of all the places it could be. The problem is if the area containing the electron also contains a black hole, part of the electron is not in our reality. Part of what we would call the properties of an electron are missing. Is it still an electron?

Even an electron or other particle that is far from a black hole would still have some part of its existence overlapping a black hole, impacting particle physics calculations adversely. When you consider that string theory postulates that electrons and other particles are infinitely long strings vibrating in many dimensions, you can wonded as multiple entangled particles - giving rise to what Einstein called, when faced with the quantum nature of reality, "spooky action at a distance".

We can look a little closer at Hawking radiation occurring near an event horizon by bringing up virtual particles. At the quantum level (not the string level), a particle can, for no known reason, suddenly exist, and then, just as suddenly, cease to exist. Virtual particles help make up (possibly completely make up) what are called bubbles in the quantum foam.

A Google Snippet says that Quantum foam (also referred to as space-time foam) is a concept in quantummechanics devised by John Wheeler in 1955. The foam is supposed to be conceptualized as the foundation of the fabric of the universe.

I immediately have a problem with "foundation of the fabric of the universe" part of this snippet. Although quantum foam is small, the fabric of the universe has to reside where time and size have no meaning (Never Never Land).

A bubble in the quantum foam is also called a quantum fluctuation or a quantum vacuum fluctuation or a vacuum fluctuation. A bubble is caused by a temporary change in the amount of energy at a point in space and is related to Heisenberg's uncertainty principle. Quantum Mechanics requires that energy cannot be created or destroyed, but this virtual energy comes and goes so fast it doesn't cause a problem - usually. Since energy and mass are equivalent, virtual energy can also be viewed as a virtual particle. A quantum bubble is the smallest possible size that can exist in our universe - one Planck length. Apparently, it only has one size dimension. A quantum bubble lasts for the shortest duration possible - one Planck time. Virtual particles are part of a lot of the mathematical models that support Quantum Physics.

Things happen in the foam that would usually take time. One example is particle anti-particle pairs can spontaneously form next to each other (bubble to bubble). Ordinarily, they usually meet and annihilate each other or return to Never Never Land. If, however, the pair forms at the event horizon of a black hole, the anti-particle will be attracted toward the black hole, falling through the event horizon. The particle will be pushed away and could be detected as Hawking radiation.

What happens as the anti-particle drops into the black hole?

When Dr. Hawking first speculated on what became known as Hawking radiation, it was viewed as a method whereby a black hole would slowly evaporate or suddenly explode. I take it that this view is saying that over time more and more anti-particles drop into the black hole. This rain of anti-particles eventually makes the black hole unstable.

As a stupid layman, I could follow this argument if a massive star was being subjected to an anti-particle rain, but not a black hole. A neuron star, for example, is massive. Its core is made up of, surprise, neurons. Every time an anti-particle hit one of these neurons, energy would be produced and the entire star would become slightly more negatively charged. As the electrical charges built up, the repulsion force between these charges, which is much more powerful than the gravitational attraction between particles in the star, could tear the star apart.

The situation, it seems to me, should be somewhat different in a black hole. On to what are the anti-particles raining down?

The anti-particle rain has entered a timeless area that I have called Never Never Land. What is the surface of a black hole, if it exists, like? What happens when the anti-particle arrives? Keep in the back of your mind that, in a timeless region, even the phrase "when the anti-particle arrives" is problematic.

Some think that at the center of a black hole matter has been compressed out of existence. Yet this matter continues to warp space and time to such a degree that light itself cannot escape. This matter, which does not exist, warps space and time in an area where space and time do not exist.

Let us think about this situation a little more. When I used the phrase "in an area", I had to mean Never Never Land. Never Never Land is anything inside the black hole's event horizon.

Suppose we have our universe with time ticking along, moving "forward" every Planck unit of time. Suppose we also had in our universe a massive star that needed one more atom (or subatomic particle) to become a black hole. To an outside observer, the intense gravitational field would slow the passage of time, but if an observer could stand on the star, everything would seem normal.

Now suppose we move forward one Planck unit of time. Everything is the same - except one additional atom has crashed into the star and time has ceased to exist.

With the addition of one more atom, light can no longer escape from the star. An event horizon is created. Where is this event horizon created? To our way of thinking, this event horizon can only be created above the surface of the star, below the surface of the star, or on the surface of the star.

If the event horizon is created above the star surface, we have to ask how far above. Yet, distance has no meaning within the event horizon. We, and our mathematical models, cannot answer this question. I am going to assume the event horizon is not going to form above the surface of the star.

Perhaps the event horizon exists in the shape of a sphere within the star (we are thinking three dimensional rather than multi-dimensional). As matter falls into the star, the event horizon grows. When it reaches the surface, the star vanishes and we have a black hole.

I am suspicious of the growing event horizon concept. Additional outside matter would not be required. Once such an event horizon forms, it would eat the star from within. I don't know if scientists can compute, from our viewpoint, how long it would take for this eating process to complete, but when it did we would have a black hole.

To sum up, we don't know how to think about an event horizon forming above the surface of a star. When a black hole forms, the event horizon, which makes the black hole black, must either form on the star's surface or rise to the star's surface.

Now let us return to the particle, anti-particle pair being spontaneously created near the event horizon with the particle moving away as Hawking's radiation and the anti-particle dropping through the event horizon into Never Never Land. In an environment where there is no time and no distance, where and when is the surface?

Some say that when a black hole forms, all the matter in the star collapses to an infinitesimal point and effectively disappears from our reality.

There is also speculation that black holes have surfaces somewhere "below" their event horizons. One theory, for example, is they have a surface made up of quarks. The intense gravity has compressed neutrons and protons so much that quarks flow around freely. Quark Stars are only theoretical. If they exist, they would be black like black holes, but have somewhat different properties (escaping radiation would be different). My point is, "true" black holes may, or may not, have a surface.

What if our poor little anti-particle drops through an event horizon of a black hole with no surface?

To speculate on the answer to this question, either remember or google Schrodinger's cat. The cat was considered to be both alive and dead. One possibility was there were two parallel universes, one with a live cat, another with a dead cat.

Maybe the live cat anti-particle dropped through the event horizon and collided with the surface. Maybe the dead cat anti-particle passed through the black hole and out the other side.

Our live cat anti-particle arriving on the surface would quickly encounter a "normal" particle and both would be annihilated. Some of the anti-particle's properties, such as charge, would persist. As more live cat anti-particles arrived, this process might make the black hole more and more unstable, eventually destroying it.

Although I believe this live cat anti-particle speculation is reasonable, we need to remember a couple of things. I used the words "quickly" and "eventually". In a region with no time, both these words could mean much more quickly than a unit of Planck's time or forever. This, in turn, means that we need to ask (not now) if anything can happen faster than one unit of Planck's time and does "forever" exist.

It is hard to imagine how a creature like me or you, made up as we are of quintillions of elementary particles, getting through the event horizon and being able to stand beside our anti-particle and see what is going on. The probability that all our particles would "tunnel through" this barrier at the same time seems very remote.

It may be hard to imagine, but not impossible. It would be worthwhile and interesting if we imagined a way to get through an event horizon. I may even take a shot at it. But right now it is easier to imagine something else.

If our dead cat anti-particle passes through the black hole and out the other side, it could combine with other anti-particles to form an anti-matter universe. Creatures similar to us, made of anti-matter, could be born on the other side of an event horizon.

These creatures might wonder what is on the other side of an event horizon, but they could not imagine it would be us. Time would be normal in their universe, but would be undefined and impossible to understand in our universe. They would wonder why there was so much more anti-matter than matter in their universe.

String Theory speculates that elementary particles are really one dimensional objects (strings) that propagate through space and interact with each other. Our universe contains a quintillion quintillion particles, each defined by the way these strings vibrate as they float through ten or twenty six dimensions. Our virtual particle that spontaneously forms near a black hole is one of these. Maybe the live cat and dead cat anti-particles that drop through the event horizon are two more.

We could look at these particles another way - a way that initially seems more complex and thus goes against Occam's razor.

From now on, I am going to use quintillion quintillion to mean a big number. It could just be a quintillion, or it could be more than a quintillion quintillion quintillion.

Our virtual particle near a black hole may be a string vibrating in a quintillion quintillion dimensions. Can this view of our virtual particle actually make things easier to understand and can we address the "Turtle Problem"?

Let us take this view of our virtual particle, make a few wild speculations, and see where it leads.

Suppose there is only one particle in all of reality, a true God particle.

Suppose this particle contains enough dimensions to account for every elementary particle we have ever found or will find.

Suppose that outside this particle time and space do not exist. Without time, there is no outside of this particle. There never has been and there is no reason to believe there ever would be an "outside".

In String Theory, a string is thought of as a string vibrating as it moves through multiple dimensions (or is at least affected by the multiple intertwined dimensions). What is vibrating? Perhaps slight differences in potential between pieces of reality - this potential being similar to energy fluctuations on a quantum level and being governed by laws like quantum probability laws. These fluctuations become strings when they move as one dimensional points.

Suppose these points move as they travel through dimensions. One point out of quintillion quintillion could move through one dimension out of a quintillion quintillion. What does it mean for this point to be one dimensional - having length but no width and no height? Perhaps it means that time, for this dimension, is directional.

I suspect (the math is way above my pay grade) that if, for a particular dimension, time is directional, you could set up a time value so that, from our perspective, the string length could stretch across the universe and back. The value of time in other directions would cause width and height to approach zero (also implying a super Planck's time).

A point on a string could be affected by other strings passing through other dimensions. A point on a string could correspond to a place and a time in our universe.

A top spinning in a vacuum will spin forever. These quintillion quintillion strings, intertwined in a quintillion quintillion dimensions, have always vibrated and always will. They have always defined reality and always will. There is no bottom turtle.

Return to INTRODUCTION TO THINKING LONGER AND HARDER. Or, if you liked this, send an email to Mike Stewart. - mike@esearchfor.com

MY STRING THEORY HAS KNOTS - THINKING LONGER AND HARDER

 

 
 

(- Copyright 2016 by Mike Stewart -)

I am rational, you are rational, and now we are saying PI is rational. In the case of PI, we mean that it is a number with a definite value.

We began our consideration of String Theory by listing six of possibly many sub-string theories and decided to look more closely at these. The first said matter (you and me) did not exist and Einstein was wrong when he said nothing could go faster than light.

Looking closely at the first, I thought we could drill down, moving from our world to the microscopic, then the world of DNA and large molecules, then to atoms, electrons, and maybe quarks, and then on to see what might be happening at the string level. We have reached the atomic level, and maybe a little further, and along the way come up with what I hope are some interesting speculations. We are, however, nowhere near string level. And, we haven't even looked at the other five sub-string theories.

There is a ray of hope. I believe I can rationalize covering the other five in much less detail.

There is a ray of doom. Newer theories may have replaced String Theory.

There is another ray of hope. It is unlikely that new theories can invalidate my wild speculations.

There is a Theory you may have heard of. It is called the Big Bang Theory.

Before we discuss the Big Bang Theory, let me tell you why I am bringing it up now. We have been talking about some very large and some very small numbers. Planck's time, for example, is the shortest duration of time possible. Part of the Big Bang Theory is concerned with our universe when it was very young. Planck's time is equal to 10 E-43 seconds. Our universe cannot be younger than 10 E-43 seconds. The Big Bang Theory says that the universe did not existed at the super microscopic string level, but that it suddenly sprang into existence with a ripe old age of one unit of Planck time.

When I say suddenly, you can't get any more sudden than 10 E-43 seconds. At this point, PI is probably equal to 3.0 and the circumference of the universe is three Planck's lengths. What I want to think about is how did our universe go from not existing at string level scales to developing existence when time started.

The Big Bang Theory is a theory that attempts to explain how we came to exist. It is not the only theory, but it is the most popular. Over the years, science has accumulated a lot of evidence to support it.

What happens at the string level, "before existence" remains an area of speculation and can include, for the religious, images of God.

Edwin Hubble's discovery, in 1929, that the universe was expanding, was probably the cornerstone of the Big Bang Theory. If the universe was of a certain size and expanding at a certain rate, you could imagine running time backwards until everything in the universe was at one point.

There is a paragraph on the website http://www.big-bang-theory.com/ that adds to our discussion and introduces a couple of concepts that may be useful:

"According to the standard theory, our universe sprang into existence as "singularity" around 13.7 billion years ago. What is a "singularity" and where does it come from? Well, to be honest, we don't know for sure. Singularities are zones which defy our current understanding of physics. They are thought to exist at the core of "black holes." Black holes are areas of intense gravitational pressure. The pressure is thought to be so intense that finite matter is actually squished into infinite density (a mathematical concept which truly boggles the mind). These zones of infinite density are called "singularities." Our universe is thought to have begun as an infinitesimally small, infinitely hot, infinitely dense, something - a singularity. Where did it come from? We don't know. Why did it appear? We don't know.".

In the above quoted discussion, I think there is a typo - 'as "singularity"' should have been 'from a "singularity"'. Scientists and laymen like me are very interested in what is happening in "singularity zones" - in this case, we are talking about what is happening at the moment of the Big Bang in the zone between Planck's world and the world of strings.

Before we go there, however, let's talk a little more about the Big Bang.

When our universe sprang into existence, everything was confined to a universe that had a circumference of three Planck's lengths (remember that on this scale, PI was probably equal to 3.0 and when we multiply this by the diameter of one Planck's length, we get the circumference).

What is the volume of our universe at "the very beginning"? In our world, the volume of a sphere is equal to ((4 divided by 3) times PI times R times R times R) where R is the radius of the sphere. We are assuming that the initial universe is a sphere, that is, it has an equal thickness in all directions. It would still have the same problem I am about to describe if it had any thickness at all (even zero). It probably wouldn't have this problem if its thickness was negative, but we don't know what that means.

The problem is with the radius R. It is equal to one-half of the diameter or one-half of one Planck's length. By definition, however, nothing can be less than one Planck's length. The entire equation, to my mind, becomes meaningless, and we come to the conclusion that our universe entered our reality sporting an imaginary volume. Maybe we can say it was partly in and partly outside of reality.

What happens next? In our reality, next is one unit of Planck's time later and the entire universe has to "quantum leap" to this point. We will pursue this, but note that since the universe is not entirely within our reality yet, it may not have to follow this rule. In fact, maybe reality itself is relative, with our universe, and us along with it, moving toward "true" reality. Our universe may, or may not, ever reach this reality.

OK, our universe quantum leaps to a point one unit of Planck's time later. The minimum distance it can expand is one Planck's length - thus the diameter of the universe could now be two Planck's lengths (scientist argue that the universe could expand faster than this, but we will discuss this more later).

The Radius R is now equal to one Planck's length and we can use our equation for Volume V:

V = ((4 divided by 3) times PI times R times R times R).

V = ((4 divided by 3) times 3.0 times 1 times 1 times 1) .

V = 4 cubic Planck's lengths.

The entire universe is now confined to a very small, but to what we recognize as, a real volume.

If we continue this process of quantum leaping forward, however, we will find a result analogous to our calculations for circumferences. Based on the precision used for PI and whether or not R is a whole number, V can be either a real or imaginary number. Or we could say we only have a probability of a particular value of V.

Once we have a very small, but very real volume, and we put our entire universe in it, we realize it must be very dense in there and the temperature must be very high. As the volume increases, the density of matter and energy will decrease and the temperature will fall. In fact, we can calculate the temperature after 13.7 billion years of expansion, that is, what the temperature should be Today.

Cosmic Background Radiation had been theorized to be energy left over from the Big Bang. It was discovered in 1964 and had a temperature, as predicted, of slightly below three degrees above absolute zero. This was major support for the validity of the Big Bang Theory.

We are, however, going the wrong way. I want to go down, toward strings; not up, toward the reality we know.

If I want to have any chance of successfully exploring the non-reality world of strings, I will need to try to adhere to a few rules.

I do think I can use analogies to physical processes that occur in our reality - this includes weird quantum stuff.

I think I should try to avoid the "digging to China" syndrome where I believe that the next shovelful of facts is going to tell me the secret of string reality when I still have millions of shovelfuls to dig.

Since I see no reason why any reality has to accept Occam's razor, I will not do so either.

Occam's razor is a problem solving technique attributed to William of Ockham, an English Franciscan friar who lived in the 14th century. Most scientists believe, based on his philosophy, that if there are two or more possible explanations for some experimental results, the simpler explanation is usually the correct one.

The sub-string theory we have been considering has 26 dimensions. I am sure this is based on a mathematical model that few in the world can understand. I wonder if the math might have also implied more dimensions, like fifty-two or five million. Scientists may have ignored these possibilities because scientist are taught to subscribe to Occam's razor.

If there are 26 dimensions, we are aware of four, namely height, width, length, and time. The rest of very small - billions and billions of times smaller than a Planck's length. They have impossible smallness. Each of these is curled up, taking up only a small part of the three space dimensions. These small dimensions are intertwined within themselves and are too small for us to be aware that they exist.

We can take a closer look at the three space dimensions. Height is the distance traveled by a dimensionless point in a particular direction. Width and length can also be defined in the same way. The only difference in these three dimensions seems to be the direction of travel. We think of length as traveling horizontally. We think of height as traveling vertically. We think of width as traveling "across" or horizontally and at a right angle to the other two dimensions.

Each small dimension, besides being smaller, is often described as traveling at right angles to other dimensions and moving in a direction that only exists for that dimension.

Since my head is beginning to spin, we should probably try to look at our string realm differently. Before we do, however, a comment or two on the other dimension, time.

Time is very important in our reality. One of the chapters in this book is "Time is of the Essence". Time is ubiquitous in scientific equations. The speed of anything, including light, is the distance that "anything" travels during a specific time.

Almost all multi-dimension theories in science assume space dimensions, but only one time dimension. This seemed strange to me so I googled "multiple time dimensions" and Wikipedia told me that "The possibility that there might be more than one dimension of time has occasionally been discussed in physics and philosophy".

Maybe when we try to explore the realm of strings, we should consider more than one time dimension. But I have a better idea.

What if we try to imagine the realm of strings as being all existence. By all existence, I mean every universe that can exist. In a particular universe, you may have time and space, but, in the realm of strings, such concepts have no meaning.

A useful analogy might be a traveler on the surface of the earth. He can travel anywhere and he can look west, north, east, and south. There are only two exceptions - if he is standing on the North Pole or on the South Pole. In both cases, east and west no longer have any meaning. At the North Pole, north also loses all meaning. Our traveler can only look south. Similarly, at the South Pole, south loses all meaning. Our traveler can only look north.

When we enter the realm of strings, it seems to me that we need to question every "normal" question we may have. For example, when we talk of all existence and every universe that can exist, we might wonder how many universes can exist. In such a strange land, however, maybe first we should ask, at least in passing, questions like:

Will our math work there?

Is two greater than one?

Can we have half a universe?

In the normal world of quantum physics (I never thought I would use that phrase), we can have bosons and fermions. Bosons are the particles that transmit force. Bosons usually can occupy the same space at the same time. Fermions are the particles that make up matter. Two of them cannot occupy the same space at the same time.

If we believe our math works in the realm of all existence, we can ask how many universes exist "there". Maybe each universe is like a boson and untold numbers can exist together.

At the string level, time no longer exists. Distance, which we define as how long, that is, the time, it takes to move from point A to point B, must also disappear. Even point A and Point B have vanished. Motion no longer has a meaning. Without distance, we cannot calculate volume. We might say size has disappeared. Is there anything left? Maybe just the fabric of all reality.

We have been thinking of a string as a very, very small thing that we would have to have a super-microscope to see. If a string could think, however, that is not how it would view our reality. With no concept of distance or time, events occurring a mile away would be the same as events happening on the other side of the universe. With no concept of size, an elephant would be neither larger or smaller than our entire galaxy.

With no concept of time, at the string level, all events are equal. Now is the same as a million years ago or a million years in the future. We can ask what caused the Big Bang, but we shouldn't look for a time based answer - what we call cause and effect.

When you require cause and effect, you can get into interesting and funny discussions involving elephants, tortoises, and God.

Stephen Hawking related the following in his 1988 book "A Brief History of Time" (from Wikipedia):

A well-known scientist (some say it was Bertrand Russell) once gave a public lecture on astronomy. He described how the earth orbits around the sun and how the sun, in turn, orbits around the center of a vast collection of stars called our galaxy. At the end of the lecture, a little old lady at the back of the room got up and said: "What you have told us is rubbish. The world is really a flat plate supported on the back of a giant tortoise." The scientist gave a superior smile before replying, "What is the tortoise standing on?" "You're very clever, young man, very clever," said the old lady. "But it's turtles all the way down!".

This story highlight what is one of the major obstacles in our quest to understand reality. It seems like we can always ask what is the last turtle standing on. We need to always remember what I call the "Turtle Problem".

Wikipedia goes on to report:

Hawking's suggested connection to Russell may be due to Russell's 1927 lecture "Why I Am Not a Christian". In it, while discounting the "First Cause" argument intended to be a proof of God's existence, Russell comments:

"If everything must have a cause, then God must have a cause. If there can be anything without a cause, it may just as well be the world as God, so that there cannot be any validity in that argument. It is exactly of the same nature as the Hindu's view, that the world rested upon an elephant and the elephant rested upon a tortoise; and when they said, 'How about the tortoise?' the Indian said, 'Suppose we change the subject.'".

At the string level, effects do not have to have causes, or, at least, an effect does not have to be tied to a cause by time. Suppose a traveler, standing on the North Pole, where all directions are SOUTH, asks "Where is God?". Can the answer be "You are close. It is important that you find him because he made everything. He is on the other side of that hill WEST of you"?

We don't know where the Big Bang, and thus, our entire universe, came from. It just sprang into existence. In fact, we don't know where other universes, if they exist, came from either. Or where they are. But we do know that when time does not exist, the answer becomes as meaningless as "He is on the other side of that hill WEST of you". Without time, we cannot construct distances or volumes to put things in. All possible universes are nowhere, or everywhere. Or perhaps we should just say we are all in Never Never Land.

But this doesn't mean we can't ask what may happen in Never Never Land.

Scientists have said that our universe has three space dimensions that we can all see and maybe some dimensions we can't see. I must confess that sometimes when people are talking about other dimensions, I wonder if they are talking about other universes.

We have spoken of Schrodinger's fictional cat. This story highlights my dimension universe confusion. When in a box, the cat is either living or dead. Until we open the box, we don't know. The cat in the box is half dead and half alive. Only when we open the box does the cat become truly dead or truly alive. The strange part is, according to quantum theory, that if we find the cat dead, there is another universe where the box is opened and a live cat is found.

We could say this other universe is a parallel universe. What does that mean? Has it always existed or is it created when we open the box? If it is created, does that mean opening the box sends a signal back to the fabric of reality asking for a new universe, identical to ours, except that the cat is now alive?

Let us temporarily use occam's razor, that is, chose the slightly simpler explanation, to resolve the Schrodinger's cat problem. It would be simpler if, after creating a universe, reality let that universe run on its own. In this case, when Schrodinger opened the box, one or more new dimensions would be created. One Schrodinger and a dead cat would occupy one group of dimensions while another Schrodinger and another cat would live in another set of dimensions.

Now we can return to Never Never Land. Or, to be more exact, to almost Never Never Land.

Our universe has just sprang, or quantum leaped, into existence. It has a circumference of three Planck's lengths, but an undefined thickness. It is a quintillion quintillion times larger than the strings we have been considering. Except you can't say that. Never Never Land has no time, no size, no distance. You cannot compare the size of our universe, as it initially existed, or as it is today, with the size of a string.

At this point, the dimension of time (if it is a dimension) appears in our reality. Length and height have appeared, but width is still in Never Never Land. Since length and height seem to be dependent on time, it seems unlikely they are really separate dimensions. On the other hand, width is not yet in our realty even though time does exist. The only apparent difference is our frame of reference. We can have one dimension or a quintillion dimensions. A question that makes no sense until time exists is "in what order did the dimensions jump into existence?".

A Google Snippet defines "frame of reference" as a system of geometric axes in relation to which measurements of size, position, or motion can be made. This means that we can rotate our frame of reference so that width becomes either height or length while either height or length becomes width. What we are saying is we can put a dimension into either reality or Never Never Land just by how we look at it. Weird.

It is also possible that we cannot have any frame of reference until time comes into existence. We can ask how many times time can come into existence. It could be a quintillion quintillion, but let's look at just two.

The first time that comes into existence creates our frame of reference containing what we call our universe. The second time that comes into existence creates a second frame of reference and a second universe. This frame of reference could be moving at, relative to our universe, at a speed a million times the maximum speed allowed in our universe (that is, the speed of light). As far as we are concerned, this universe is still deep in Never Never Land, but it could be as rich and as varied as our universe. This universe is moving rapidly relative to our universe, but the speed of both of this universe and our universe have no meaning in Never Never Land.

It was mentioned earlier that our universe sprang into existence as a "singularity", a zone of such extreme density and temperature that they defy our current understanding of physics. Since such conditions are also thought to exist at the core of "black holes", maybe if we take a closer look at these "black holes" we can gain some insight into what happened the moment everything was born (or even "before").

On a very simple level, black holes are easy to imagine. The mass of the earth creates the force of gravity. Einstein said it is bending space time, whatever that means. If you put the mass of a large star, and certainly the mass of an entire galaxy, into a small space, the gravity will be so great that not even light can escape.

As experiments have shown, a light wave (a photon) is affected by gravity. This would not be true if its properties were perfectly wave-like, but it also behaves, to a certain extent, like a particle. If anything, including you or me or a photon, gets too close to a black hole, it would be drawn into the black hole, never to escape. Since light cannot escape from a black hole, we cannot see its surface. A black hole is just black.

To get an idea of how powerful gravity has to be to keep light from escaping, think about escape velocity. Escape velocity is the minimum speed an object must have to escape from the gravitational attraction of a massive object like the earth. The escape velocity of the earth is about twenty file thousand miles per hour or seven miles per second. On the other hand, the escape velocity of the sun is about 384 miles per second. All of this means that if you could throw a ball straight up with a speed of less than seven miles per second, eventually the earth's gravity would stop the ball and it would fall back to earth. If, on the other hand, the speed of the ball was greater than seven miles per second, the earth's gravity could not stop the ball and it would never return.

A black hole must contain enough mass so that its escape velocity is greater than the speed of light, or about 186,000 miles per second.

If light passes near a black hole, its trajectory is changed - just like a rocket passing near a planet. In fact, it seems like at a certain distance from the black hole, a light beam (photon) could go into orbit. Einstein wondered what it would be like riding on a light beam. What would it be like riding on a photon orbiting a black hole?

Of course, this is viewing the photon as a particle. If we viewed the photon as a wave, we could only say there is a certain probability it would go into orbit. There is a possibility it would whip around the black hole and go in another direction, maybe returning to its source (perhaps a laser on earth). There is also a possibility it would get too close to the black hole and not be able to escape. There is a possibility that this photon might disappear from our reality. I would think that a photon orbiting a black hole would have a fifty-fifty chance of staying in our reality.

This is an area ripe for additional questions like "what about photons not near black holes?", but let's move on.

If a photon (or anything else) drops through what is called the "event horizon" of a black hole, it seems to disappear from our reality. Inside the event horizon, the escape velocity for the black hole is greater than the speed of light. Wikipedia defines an event horizon as follows:

"In general relativity, an event horizon is a boundary in spacetime beyond which events cannot affect an outside observer. In layman's terms, it is defined as "the point of no return", i.e., the point at which the gravitational pull becomes so great as to make escape impossible, even for light.".

The event horizon is the only part of the black hole we can see. We see one black hole as larger than another if its event horizon forms further from its center. This happens if the larger black hole contains more mass and thus has a more powerful gravitational field.

Stephen Hawking, the famous physicist, is perhaps best known for his speculations about black holes. I thought he had received a Nobel Prize for his work, but I have learned that Nobel Prizes are usually reserved for discoveries and inventions. Hawking's work is brilliant, but unverified, speculation. New research, both by Hawking himself, and others, may eventually give the needed support and a Nobel Prize would be very likely.

Dr. Hawking became famous by suggesting forty years ago (I assume he was backed up by lots of fancy math) that something could escape from a black hole - that something is what is now called Hawking radiation. Escaping radiation would cause the black hole to shrink and eventually evaporate.

Although Dr. Hawking changed how we thought about black holes, he didn't solve a problem created by the very existence of black holes. This problem is what is commonly called the information paradox. You can google this if you want descriptions from scientists or science writers, but the following is my understanding of the information paradox and the basis of some of my speculations.

Particle Physics depends on the equivalency of mass and energy. Particles may break down into other particles plus energy. The excess energy may imply the existence of new, undiscovered particles. Both the old and new particles conserve certain properties in certain ways. Information about particles (their properties) is never lost - unless one or more of the particles fall into a black hole.

One way I look at the wave nature of an electron is we can't be sure exactly where an electron is - the electron is really spread out over a large, perhaps infinite area, with a high probability of being at a particular point - but the "true" electron is the total of all the places it could be. The problem is if the area containing the electron also contains a black hole, part of the electron is not in our reality. Part of what we would call the properties of an electron are missing. Is it still an electron?

Even an electron or other particle that is far from a black hole would still have some part of its existence overlapping a black hole, impacting particle physics calculations adversely. When you consider that string theory postulates that electrons and other particles are infinitely long strings vibrating in many dimensions, you can wonder if the string might pass near a black hole in other dimensions.

When I think of a string passing through multiple dimension, maybe I could visualize this string as multiple strings, giving a super microscopic fuzzy texture to reality. Since this fuzz passes through a timeless area, it could be viewed as multiple entangled particles - giving rise to what Einstein called, when faced with the quantum nature of reality, "spooky action at a distance".

We can look a little closer at Hawking radiation occurring near an event horizon by bringing up virtual particles. At the quantum level (not the string level), a particle can, for no known reason, suddenly exist, and then, just as suddenly, cease to exist. Virtual particles help make up (possibly completely make up) what are called bubbles in the quantum foam.

A Google Snippet says that Quantum foam (also referred to as space-time foam) is a concept in quantummechanics devised by John Wheeler in 1955. The foam is supposed to be conceptualized as the foundation of the fabric of the universe.

I immediately have a problem with "foundation of the fabric of the universe" part of this snippet. Although quantum foam is small, the fabric of the universe has to reside where time and size have no meaning (Never Never Land).

A bubble in the quantum foam is also called a quantum fluctuation or a quantum vacuum fluctuation or a vacuum fluctuation. A bubble is caused by a temporary change in the amount of energy at a point in space and is related to Heisenberg's uncertainty principle. Quantum Mechanics requires that energy cannot be created or destroyed, but this virtual energy comes and goes so fast it doesn't cause a problem - usually. Since energy and mass are equivalent, virtual energy can also be viewed as a virtual particle. A quantum bubble is the smallest possible size that can exist in our universe - one Planck length. Apparently, it only has one size dimension. A quantum bubble lasts for the shortest duration possible - one Planck time. Virtual particles are part of a lot of the mathematical models that support Quantum Physics.

Things happen in the foam that would usually take time. One example is particle anti-particle pairs can spontaneously form next to each other (bubble to bubble). Ordinarily, they usually meet and annihilate each other or return to Never Never Land. If, however, the pair forms at the event horizon of a black hole, the anti-particle will be attracted toward the black hole, falling through the event horizon. The particle will be pushed away and could be detected as Hawking radiation.

What happens as the anti-particle drops into the black hole?

When Dr. Hawking first speculated on what became known as Hawking radiation, it was viewed as a method whereby a black hole would slowly evaporate or suddenly explode. I take it that this view is saying that over time more and more anti-particles drop into the black hole. This rain of anti-particles eventually makes the black hole unstable.

As a stupid layman, I could follow this argument if a massive star was being subjected to an anti-particle rain, but not a black hole. A neuron star, for example, is massive. Its core is made up of, surprise, neurons. Every time an anti-particle hit one of these neurons, energy would be produced and the entire star would become slightly more negatively charged. As the electrical charges built up, the repulsion force between these charges, which is much more powerful than the gravitational attraction between particles in the star, could tear the star apart.

The situation, it seems to me, should be somewhat different in a black hole. On to what are the anti-particles raining down?

The anti-particle rain has entered a timeless area that I have called Never Never Land. What is the surface of a black hole, if it exists, like? What happens when the anti-particle arrives? Keep in the back of your mind that, in a timeless region, even the phrase "when the anti-particle arrives" is problematic.

Some think that at the center of a black hole matter has been compressed out of existence. Yet this matter continues to warp space and time to such a degree that light itself cannot escape. This matter, which does not exist, warps space and time in an area where space and time do not exist.

Let us think about this situation a little more. When I used the phrase "in an area", I had to mean Never Never Land. Never Never Land is anything inside the black hole's event horizon.

Suppose we have our universe with time ticking along, moving "forward" every Planck unit of time. Suppose we also had in our universe a massive star that needed one more atom (or subatomic particle) to become a black hole. To an outside observer, the intense gravitational field would slow the passage of time, but if an observer could stand on the star, everything would seem normal.

Now suppose we move forward one Planck unit of time. Everything is the same - except one additional atom has crashed into the star and time has ceased to exist.

With the addition of one more atom, light can no longer escape from the star. An event horizon is created. Where is this event horizon created? To our way of thinking, this event horizon can only be created above the surface of the star, below the surface of the star, or on the surface of the star.

If the event horizon is created above the star surface, we have to ask how far above. Yet, distance has no meaning within the event horizon. We, and our mathematical models, cannot answer this question. I am going to assume the event horizon is not going to form above the surface of the star.

Perhaps the event horizon exists in the shape of a sphere within the star (we are thinking three dimensional rather than multi-dimensional). As matter falls into the star, the event horizon grows. When it reaches the surface, the star vanishes and we have a black hole.

I am suspicious of the growing event horizon concept. Additional outside matter would not be required. Once such an event horizon forms, it would eat the star from within. I don't know if scientists can compute, from our viewpoint, how long it would take for this eating process to complete, but when it did we would have a black hole.

To sum up, we don't know how to think about an event horizon forming above the surface of a star. When a black hole forms, the event horizon, which makes the black hole black, must either form on the star's surface or rise to the star's surface.

Now let us return to the particle, anti-particle pair being spontaneously created near the event horizon with the particle moving away as Hawking's radiation and the anti-particle dropping through the event horizon into Never Never Land. In an environment where there is no time and no distance, where and when is the surface?

Some say that when a black hole forms, all the matter in the star collapses to an infinitesimal point and effectively disappears from our reality.

There is also speculation that black holes have surfaces somewhere "below" their event horizons. One theory, for example, is they have a surface made up of quarks. The intense gravity has compressed neutrons and protons so much that quarks flow around freely. Quark Stars are only theoretical. If they exist, they would be black like black holes, but have somewhat different properties (escaping radiation would be different). My point is, "true" black holes may, or may not, have a surface.

What if our poor little anti-particle drops through an event horizon of a black hole with no surface?

To speculate on the answer to this question, either remember or google Schrodinger's cat. The cat was considered to be both alive and dead. One possibility was there were two parallel universes, one with a live cat, another with a dead cat.

Maybe the live cat anti-particle dropped through the event horizon and collided with the surface. Maybe the dead cat anti-particle passed through the black hole and out the other side.

Our live cat anti-particle arriving on the surface would quickly encounter a "normal" particle and both would be annihilated. Some of the anti-particle's properties, such as charge, would persist. As more live cat anti-particles arrived, this process might make the black hole more and more unstable, eventually destroying it.

Although I believe this live cat anti-particle speculation is reasonable, we need to remember a couple of things. I used the words "quickly" and "eventually". In a region with no time, both these words could mean much more quickly than a unit of Planck's time or forever. This, in turn, means that we need to ask (not now) if anything can happen faster than one unit of Planck's time and does "forever" exist.

It is hard to imagine how a creature like me or you, made up as we are of quintillions of elementary particles, getting through the event horizon and being able to stand beside our anti-particle and see what is going on. The probability that all our particles would "tunnel through" this barrier at the same time seems very remote.

It may be hard to imagine, but not impossible. It would be worthwhile and interesting if we imagined a way to get through an event horizon. I may even take a shot at it. But right now it is easier to imagine something else.

If our dead cat anti-particle passes through the black hole and out the other side, it could combine with other anti-particles to form an anti-matter universe. Creatures similar to us, made of anti-matter, could be born on the other side of an event horizon.

These creatures might wonder what is on the other side of an event horizon, but they could not imagine it would be us. Time would be normal in their universe, but would be undefined and impossible to understand in our universe. They would wonder why there was so much more anti-matter than matter in their universe.

String Theory speculates that elementary particles are really one dimensional objects (strings) that propagate through space and interact with each other. Our universe contains a quintillion quintillion particles, each defined by the way these strings vibrate as they float through ten or twenty six dimensions. Our virtual particle that spontaneously forms near a black hole is one of these. Maybe the live cat and dead cat anti-particles that drop through the event horizon are two more.

We could look at these particles another way - a way that initially seems more complex and thus goes against Occam's razor.

From now on, I am going to use quintillion quintillion to mean a big number. It could just be a quintillion, or it could be more than a quintillion quintillion quintillion.

Our virtual particle near a black hole may be a string vibrating in a quintillion quintillion dimensions. Can this view of our virtual particle actually make things easier to understand and can we address the "Turtle Problem"?

Let us take this view of our virtual particle, make a few wild speculations, and see where it leads.

Suppose there is only one particle in all of reality, a true God particle.

Suppose this particle contains enough dimensions to account for every elementary particle we have ever found or will find.

Suppose that outside this particle time and space do not exist. Without time, there is no outside of this particle. There never has been and there is no reason to believe there ever would be an "outside".

In String Theory, a string is thought of as a string vibrating as it moves through multiple dimensions (or is at least affected by the multiple intertwined dimensions). What is vibrating? Perhaps slight differences in potential between pieces of reality - this potential being similar to energy fluctuations on a quantum level and being governed by laws like quantum probability laws. These fluctuations become strings when they move as one dimensional points.

Suppose these points move as they travel through dimensions. One point out of quintillion quintillion could move through one dimension out of a quintillion quintillion. What does it mean for this point to be one dimensional - having length but no width and no height? Perhaps it means that time, for this dimension, is directional.

I suspect (the math is way above my pay grade) that if, for a particular dimension, time is directional, you could set up a time value so that, from our perspective, the string length could stretch across the universe and back. The value of time in other directions would cause width and height to approach zero (also implying a super Planck's time).

A point on a string could be affected by other strings passing through other dimensions. A point on a string could correspond to a place and a time in our universe.

A top spinning in a vacuum will spin forever. These quintillion quintillion strings, intertwined in a quintillion quintillion dimensions, have always vibrated and always will. They have always defined reality and always will. There is no bottom turtle.

Return to INTRODUCTION TO THINKING LONGER AND HARDER. Or, if you liked this, send an email to Mike Stewart. - mike@esearchfor.com