Wednesday, March 9, 2011

Why Quantum Indeterminacy Must Exist

(In Order For Anything to Exist)

1.  Introduction

It may seem like a silly question, at first.  But if you know anything about quantum physics, the question gets less and less silly the more you think it through.
     The question is this:  how does the universe keep track of everything?
     Of course, the question implies an anthropomorphic universe, a universe that has to think things through before doing them.  The universe is not like that.  So maybe we should phrase the question differently.  But no matter how we ask the question, no matter how we word it, the question addresses a principle that underlies all of nature.  That question involves how the universe is organized.  Is there some immutable natural law at work, or is it all randomness?
      We might never have had to ask such a question were it not for quantum physics.  In a purely Newtonian universe, we could say that each separate thing in the universe would “keep track,” so to speak, of itself.
      But in the quantum universe of Neils Bohr,[1] we confront the reality that human consciousness, human perception, is part and parcel of reality.[2]  So we cannot simply define the universe as a sterile clockwork of atoms.  We must find better analogies to describe reality.
      The analogy selected here is that of a computer.  Can we compare the workings of the universe to those of a computer?  As an analogy, I contend that it is far superior to the analogy of a mechanistic clockwork.
      Here, then, is an excursion into that analogy.
      Decades ago, I programmed an old apple 2c computer that had only 128,000 bits of random access memory, a minuscule amount compared to today’s average home computer.  Using that primitive system, I was able to “construct” an elaborate labyrinth, a game map, of 1,000 rooms, each with doors, tunnels, creatures and stairways, giving each room a large number of details, such that no two rooms were alike.  Since the end result was more than 128,000 details on the map, how could this have been done? 
      Is this how the universe keeps track of everything?
      I kept track of everything in my virtual world by using some well known programming techniques. With them, I was able to overcome the fact that there was not enough capacity in the computer to define each room individually.  Without going into the details of these techniques, the feat was accomplished by setting up a table of rules for what features, what details, rooms could and could not contain, and then applying these rules as needed, but only when a room was being “used” in the game.
      In this way, a very small amount of computer memory was needed to process very large amounts of detail.  In some ways, this technique mimics certain aspects of how quantum physics describes the universe, and why quantum indeterminacy is necessary to it.  For, in quantum physics, we use the rules of probability.
      To a degree, the universe can be thought of as a vast, programmed information system, a sort of self-contained computer.  Like a computer, the universe operates according to a program (natural law), and processes data (natural events).  If we use this analogy, then some important conclusions follow.
      Let’s begin by considering the classic case of the apple that fell from a tree--- the one that according to legend, caused Isaac Newton to describe gravity as the mutual attractive force of any two objects.
      This event could be described as being programmed to happen.  The earth and the apple are represented in two arrays of data in the computer memory.  The gravity is part of the computer program, a formula embedded in the computer’s processing circuitry, or perhaps the firmware.  Once the apple is no longer constrained by the tree, the computer applies the inverse proportion law, and then the apple falls to the ground.  Of course I have left out a great many details, but this is only a start.  As we have seen, even an ordinary desktop computer, even a primitive one, can be programmed to mimic physical reality by means of what we call, virtual reality, or virtual worlds.[3]
      But unlike a computer, the universe is a system which operates only on itself, rather than on data objects outside of it.[4]  In other words, the computer (the universe) is both the programmed instruction set (that is to say, natural law), and also, the data being processed by that program (the particles, spaces, forces and constants of nature), as well as the circuitry (the hardware and firmware) and the signals along those circuits.
      It quickly becomes apparent that this presents a logical paradox.  First, no computer can thoroughly model itself in every detail.  Second, no computer, no matter how vast and complex, can do all the things that the universe does, not even if that computer is as large as the universe. For unlike an ordinary computer, the universe controls itself, measures itself, records itself, and processes itself as data. The universe “knows” (so to speak) where everything in it is, what everything in it is doing, and how each particle is interacting with every other particle. 
      The universe never loses track of any detail. 
      Every possible permutation and combination is instantly calculated, and the resulting operations are continually carried out.  Yet the universe has no separate storage banks for memory.  It is its own memory storage device, its own processing device, and perhaps even its own input/output device.[5] 
      This is a far different thing than programming a desktop computer to carry out simulations of things outside itself.  A computer can contain a map of something outside itself.  But can it contain a map of itself?  Can a map contain a map of itself?
      If your desktop computer were programmed to contain a model of itself, it would face the need for an infinite sequence of models, within models, within models. Each memory cell would have to have another memory cell to record it, resulting in a never ending procession of more memory cells. You could never achieve this capacity with your own computer, no matter how large it would be.  Yet, the universe itself faces the same problem. Presumably, it cannot contain an endless regression of models of itself.[6]  So how then, how can the universe contain all the information needed to carry out its operations?
      Can this paradox be resolved?  Or does it invalidate the analogy?
      The problem can be resolved, but only if somehow the computer can generalize its data, or represent it in some abstract form, so that it does not have to keep a separate memory location for each of its parts.  Again, there are well known programming techniques that accomplish this.
      We can therefore conclude that the enclosed system, the one we call a universe, cannot store, compute, and correlate each datum individually.  Nor need it.  Instead, most of the data can be compressed (in a manner of speaking) by being defined in group terms, with only a few parameters common to all of them.  The universe does this by defining most of its data statistically, or more precisely, by means of quantum indeterminacy.
      In the universe, when a particular datum must be “used” (so to speak) for a specific operation, then the statistical nature of that datum is collapsed, or “solved,” for a specific allowable value.[7]  After being used, or processed, the datum can then be returned to its statistical set until needed again.  Only a limited amount of specified data need be kept in operating memory, datum by datum.  The remainder are arrayed into statistical sets.
      The explanation of the “whys” and “hows” (of how the universe does this) are of course conceptual, a framework for creating a model that explains why quantum indeterminacy exists at all, and why it is a vital principle on which the universe operates.  It provides a possible stepping stone to a more mathematical model.
      It is to be noted that the collapse of statistical values to a specific value is inextricably linked to the consciousness of system users, or perceivers, otherwise known as us.  The question then arises as to whether the users (we) are entirely internal to the system, or do we represent an external source of inputs to it?  While such a question involves speculation, it may be a useful bridge to larger ideas, ideas that heretofore, usually have been considered to be outside the proper scope of science.
      In order to fill in the details of this concept, it may be necessary for some readers to be informed (or reminded) of the context in which the ideas are expressed.  That context, provided below, includes a layman’s description of quantum physics.

2.  A brief consideration of probability clouds

Quantum physics is a field of science that seems to violate all common sense.  It contradicts many of our normal everyday ideas of what things are.  Ordinarily, we think of things as being definite, solid objects, located in definite, exact places.  We think of them as being external to ourselves. We think of things as being independent of whether we see them or not.
      But, according to quantum physics, things are not as they seem.  Quantum physics says that things are not definite, objective realities independent of our senses.  Instead, the reality of objects is indeterminate.  This is called quantum indeterminacy.
      Quantum Indeterminacy is the principle in physics that tells us that things do not really exist--- at least not in any specific sense--- until they are perceived.  To put it more simply, the object that is in the next room is not really there, not until you see it.
      That, of course, is too simple, but it gets us to the fact of the matter.  A better example would be the electron.  When we see a diagram of an atom, we often see the electron portrayed as a dot, orbiting a much larger nucleus.  But the electron is not a particle in the normal sense.  It is better described as a wave, and even more accurately yet, as a probability wave.  Even better yet, it is more aptly described as a probability cloud, the idea being that with a cloud, there is no one place that you can point to and say, that is the cloud.  Indeed, in a cloud, there is no one place that you can point to and say that here begins the cloud, and there it ends.  Instead, the cloud is a wispy thing with fuzzy edges.
      So it is with the electron, but in a statistical sense.  Just as a cloud may be more dense at the center, than at the edges, so also, an electron may have a higher probability of being found, or perceived, in one location than in another.  A wave has low points, and also a high point (or points).  An electron is a wave of lower probabilities and higher probabilities.  So if you ask where an electron actually is, you can only say where it is more likely to be, and less likely to be, until you actually perceive it as being in one specific location.
      The average computer programmer could easily employ a similar technique in creating a virtual world.

3.  A brief consideration of the collapse of a probability wave

Suppose that we flip a coin, high in the air.  Our supposition includes the reasonable givens that the coin has two sides (heads and tails) and that the coin must land unpredictably either heads side up, or tails.
      While the coin is in the air, its result is neither heads nor tails. We must wait for it to land.  During this time, the coin flip result is indeterminate (regarding whether it lands head or tails).  It is a statistical set of probability, fifty percent heads, fifty percent tails (assuming ideal conditions).  When it does land, the statistical probabilities become resolved into a definite result.  We then perceive that the coin landed tails side up (in this case).  In quantum physics, the correlating event is called the collapse of a probability wave.
      While this analogy is not perfect, it gives us a helpful way to think of quantum probability.  Electrons are coins tossed into the air.  They are neither here nor there (that is, neither heads nor tails) until they land.  They land only when they are measured, or perceived, at which time, we know whether they are “up” or “down” electrons (referring to the two directions of quantum spin).

4.  A brief consideration of entanglement

A more difficult concept to grasp is that of quantum entanglement.  In experiments, it has been shown that the state (for example spin direction) of one subatomic particle is inextricably linked to (or entangled with) its pair.  The state of each particle is indeterminate, or statistical, (a coin flip in the air), until that state is measured, or perceived.
      What is astonishing is that, even when the particle is separated from its pair by vast distances (even billions of miles!), and the two are moving apart from each other at the speed of light, even then, the collapse of one particle’s probability wave results in the immediate collapse of its pair, and into the opposite state of the one being measured.  This brings up the question, perhaps anthropomorphic:  how did the second particle “know” what state the other had collapsed into?
      These experiments reveal the principle of quantum entanglement.  One might say that the paired objects became entangled with each other when they became paired.  They may have become paired when they were split apart from another particle.  In any case, each particle, if by definition its state is the opposite of its pair, must collapse into the opposite state of its pair, and must do so exactly when its pair-mate collapses.
      The implications of entanglement are so profound as to merit a bit more discussion.  For example, entanglement challenges our very notion of whether any two separate objects are really separate at all, even if they are separated by vast distances.  Are such distances merely an abstraction?  According to the Big Bang Theory, everything in the entire universe was originally a single point-particle.  When the explosion occurred (or implosion, or inflation), all particles in the universe separated from each other.  The question is, then, did this primordial point-particle cause everything in it to entangle with everything else? 
      If so, then it may be concluded that everything in the universe “knows” exactly where everything else is, and what it is doing.  Perhaps everything after all, is one and the same thing.
      If so, then perhaps that is why the universe must be abstract and statistical, not determinate.

5.  A brief consideration of quantum information

The word, “information,” has many meanings depending on the context.  In this discussion, the word has to do with its concept in physics. Since I am not a physicist, I will limit the discussion to a few fundamentals, those which apply to the ideas introduced at the very beginning of this article.  But one should bear in mind that there are also very complex ideas involved in the quantum principle of information.  I am not qualified to discuss these complexities.  So I shall restrict my discussion to descriptions authored by those who are qualified, and which are in the popular literature.
      To give you an idea of what “information” means in physics, let us return to the earlier example we gave of the coin flip.  Let us acknowledge that there are a few problems with the example we used.  These problems concern the idea of “information.”
      In the macro world of coin tosses, it can be said that once the coin is in the air, the end result is no longer truly random, even if it is (in practice) unpredictable.  If we know all the myriad factors involved in the coin toss, including such details as the mass of the coin, its angular momentum, air density and the characteristics of the landing site--- then in principle (even if not in practice), there is a predetermined outcome that defines what the result of the coin toss will be.[8]
      This is another way of saying that once the coin is in the air, it contains information.  That information consists of all the factors that we said went into the flip.
      Another example is that of a baseball that has just been hit.  Assuming that no player will touch it (this is batting practice), we could, with complete, perfect knowledge of all the inputs, predict exactly where the baseball will come to rest, and when.
      Of course, we never have complete, perfect knowledge of all the inputs.  Even if we did know all of the immediate inputs, there would still be an entire universe of additional inputs, for example the moon’s gravity, a gust of wind that comes into play after the initial strike of the bat, and so forth.  Most of these would of course be very, very tiny, but all of them considered, would have some effect, even if only very small.
      Finally, there are unknowable inputs in the examples we gave above.  That is because every atom contains subatomic particles governed by the Uncertainty Principle.  This gets us back to the statistical values touched upon earlier in this writing.  Even though the exact state of a subatomic particle does not actually exist, there is nevertheless information (in the physics sense) in it.  That it is statistical information does not change the fact that it is information.
      A more difficult concept is the idea that there is always the same amount of information in the universe.  None of it is ever lost, and no new information is ever created.  I do not feel too badly about not being able to understand this concept, since it has at times confused even the most expert and renowned physicists in the world.  (However, it must be pointed out that their confusion was at a much higher level than I could ever attain.)
      But if no information is ever created or lost, does this not mean that all the information now present in the universe, was also present in the primordial point-particle that generated the universe?  Was the Big Bang itself analogous to the initial execution command (launch) of a universal computer program?
      Just as a computer processes information, so also, can we think of the universe as a sort of giant computer, processing information.
      But let us look further int the question of why such a computer would rely on quantum indeterminacy in order to function.

6.  Why Quantum Indeterminacy is needed for the universe to operate

A small computer, such as the one on your desk, operates on precise, binary digits.  Because of the way the computer is constructed, and due to the manner in which it is programmed, it responds to specific operator inputs, the operator being you, or another person. 
      Let us say that the computer in question is being used as the accounting system for a medium sized company.  The company has hundreds of customers, each of which must be recorded in terms of what they are buying, how much they are paying, and how much they owe the company, just to name a few of the sorts of things the computer must keep track of for the manager.  There are also employees, vendors, and inventory involved, so the operation of the computer can be quite complex, even for a relatively small company.
      It would therefore be very foolhardy for the computer operator to instruct the computer to act upon imprecise information.  A customer who is overcharged even by a trifling amount can feel that he is not being treated with the kind of respect he could get from one of your competitors.  Likewise, a customer who is underpaying his account can bleed the company of resources.
      So then, every operation of the computer must be based on an exact and precise number, or datum, whether that number be a dollar amount or an account identifier, whether that datum be a name or a date.
      However, computers can also deal with imprecise data in the forms of statistics and probabilities.  For example, a life insurance company may use actuarial data to predict how many people in a given category will die this year.  Such data are imprecise, yet they provide enough of a degree of reliability to be used to arrive at the price of an insurance policy.  Note that the actuaries do not predict precisely who will die this year (at least I hope not!).  They don’t need to.  They lump all the members of a given category (let’s say for example, married men aged 45 who do not smoke or sky dive) into a statistical set.  Only when an actual person dies, does the company identify that particular policy for payment.
      As we have illustrated before, the universe, in a somewhat analogous fashion, can lump all similar items together into categories without having to identify each and every one individually.  A limited number of parameters can define all electrons in the universe.  But when a particular electron is perceived, or measured, then the universe identifies it specifically with its own parameters of location, energy, and spin etc.

7.  How Quantum Indeterminacy works

The universe contains an unimaginably large number of objects.  Electrons, photons, atoms, stars, planets, and discarded beer bottles, there are too many objects for any computer to keep up with--- even if that computer is the universe itself.
      So, rather than our universe/computer assigning to each object a precise location, momentum and mass, and a precise array of all the factors acting upon that object--- it averages them out.  Well, not exactly, but that gets across the idea.
      First, the universe assigns an identical rest mass to all electrons, and another to all protons.  This is remotely like assigning the same value to every penny in the United States economic system.
      Second, the universe sets common rules that apply to all electrons regarding their location and velocity.  These rules are statistical.  This is remotely similar to money, in the sense that, if you have a thousand dollars and fourteen cents in a US bank account, there is no need to define each penny’s location precisely.  Indeed, you do not even need to know which branch office it is located in.  If you decide to withdraw eleven dollars and four cents, the bank will give it to you no matter which branch you visit.
      But once you have withdrawn the money, if you withdraw the actual cash, it now has a definite location.  This is analogous to the observation of a particular electron.  Before it is observed, it exists only somewhere in a universal bank account, but in no particular branch.  But once it is observed, when it is “withdrawn” from that account, and placed in your pocket or purse, that is to say, in your consciousness, then it assumes a specific location.  After that, if you spend it or deposit it, it goes once again into its former statistical existence.
      In this manner, a computer can keep track of trillions of dollars, right down to the penny, without having to track each penny separately.

8.  Further Questions and Conclusions from Quantum Indeterminacy

You have probably noticed by now that we have defined computers as things that require human interaction.  This indicates that there is a binary interaction between the two.  Computers do not create themselves.
      True, in theory, a lightning strike in a silicon field could by happenstance generate a working computer.  But that computer would be nothing if it had no function, no purpose.  And even if it could operate with no purpose, it could not generate within itself an infinite regression of models within models.
      Similarly, in quantum physics, we find clues that the universe cannot exist apart from human consciousness, at least not in any specific sense.  At most, it would be an uncondensed probability cloud, a void without form or substance.[9]
      The question then arises, could the void generate its own users, conscious humans, who give to the void its substance and form?  For, if nothing existed with any certainty in the probability cloud, then what could possibly give it form and substance in the form of conscious humans?
      Of course we are dealing with speculative questions here.  There are those who say that from simple, unorganized chaos, there can spontaneously arise complex, organized systems.  The only evidence for that is that, complex organized systems are seen to exist.  But that is scarcely strong support for the theory of emergent complexity.  It is simply an assertion--- that the observed systems arose from chaos, and not from something else.
      One might just as validly state that the organizing principle of the universe comes from a divine Creator.

[1] who said that if we are not shocked by what quantum physics tells us, it is only because we have not understood what it says 
[2] witness the results of the double slit experiment
[3] One might disagree with the analogy entirely, and instead assert that the universe does not operate like this at all.  However, whatever disadvantages it has, this analogy has the advantage of not requiring advanced mathematics.
[4] Which is why one might be inclined to discard the analogy entirely.  But I persist in pursuing it, for now.
[5] Finally, and most peculiarly, the universe performs the seemingly self-definitional function of measuring itself without an outside standard of measurement.
[6] Although the Hindus say that it’s turtles all the way down, one might argue that there is no “all the way” down.
[7] For example, when the location of a specific electron is detected, its probability wave is collapsed.
[8] Of course, we can never know all these things, but the principle of information does not depend on whether we can know that information.

[9] See Genesis 1:2