In the 1999 motion
picture film The
Matrix,
the actor Keanu Reeves plays a character, Neo, who is forced into the
horrific realization that the world he lives in – indeed, that
everyone he has ever known and loves lives in – is not the
objective real universe at all, but only a virtual reality created by
an artificial intelligence, an intelligence that has enslaved
humanity for its own purposes. Neo’s realization of this truth is
the result of his liberation from the Matrix by an individual known
as Morpheus (played by Laurence Fishburne). Upon ingesting a red
pill, Neo awakens in his own, true, body; a body which is naked and
hairless and is curled up in a fetal position in an artificial womb,
kept alive via tubes and cables leading into important orifices.
More important and unbelievable than this however, is the fact that
he is but one body, one virtually identical to the billions that
surround him in a vast menagerie of wombs, stretching as far as the
eye can see.
Well, what do you
think? Could it be true? Could we all be living inside a virtual
universe created by an intelligent entity? Could the seeming
solidity of the world around us be merely an illusion created by a
computer program, and we unfortunate souls slaves to the master
programmer who has created this mirage?
I’m guessing your
answer to these questions is an unqualified NO!
That The
Matrix,
as entertaining as it was in the movie theater or in your home, or
even as compelling, is the paranoid fantasy of any mind bizarre
enough to think it even possible. Sure, logically it could
be true; but that can be said about any paranoid delusion.
No, there is no
Matrix, no master programmer, and we are not slaves except to the
extent that we are ignorant of our true condition. But what is true
is that the world we experience and perceive is not actually an
objective existence “out there” but a virtual reality simulation
of that existence, one that is going on inside our own heads, in our
fabulously complex and wondrous brains, twenty-four hours a day,
throughout our entire lives. The only difference between this simple
fact and science fiction is that, as I said, there is no master
programmer: all the programming is done by a combination of our
genes and experiences working together, each blind to what it is
doing and without any plan at all, yet together a combination far
more powerful and brilliant that the greatest software engineer in
the world.
This statement may
astound you, but in fact there is nothing either particularly
original or controversial about it; not, at least, to any philosopher
or biologist or neuroscientist you might care to mention it to. That
is why I say you can go through the process of digesting it and
retain your sanity. The only question is, why do so? What purpose
beyond an abstract, and somewhat macabre exercise in philosophical
musing could it possibly serve? Moreover, given the theme of this
book, what does it have to do with curiosity and our capacity to
comprehend the universe?
Before answering
these questions, it is worthwhile to examine this concept of living
inside a virtual reality of the mind in more detail. I need to
convince you that, all your experience and perceptions to the
contrary, it is true beyond any reasonable doubt. At the same time,
and perhaps even more importantly, I also need to make clear just
what I mean by it and, just as critical, don’t
mean by it. Here, in fact, might be the best place to begin the
examination.
A good way to
describe anything is by means of an analogy, or metaphor, and the
most natural one that suggests itself here, to me at any rate, is the
so-called “desktop” of a modern personal computer. I am assuming
that you have experience with this phenomenon, whether in the form of
a Windows PC, a Macintosh, or one of the several flavors of graphical
desktops available on UNIX or other machines. If you do not, the
example below (taken from my own PC, naturally) ought to give you the
general flavor of what I am talking about:
This
is an example of what you might see, looking at the monitor screen of
my computer. The first thing that might strike you is that the term
“desktop” is indeed a fairly apt one: we see a background of
blue as a true desktop might actually have, covered with things you
might expect to find on a desktop. For example, there are what are
known as “icons” in the upper left hand corner; these could be
considered as kinds of folders, or perhaps drawers containing folders
and files. The center is dominated by the four open “folder
windows” (hence the name Windows, although other graphical
interfaces sport the same appearance), each appearing exactly like
that; an open folder some of which containing list of still more
folders (the rectangular, yellow icons) and open files (e.g.,
“Chapter 1.doc, Chapter 2.doc, which incidentally are the chapters
of this book at the time of writing). There are also two windows
representing open and running programs or “applications”: the
Notepad Editor, and the Calculator program; you probably find them
easy to think of as an open paper notepad and calculator on a real
desktop for they really appear as physical applications you might
have on a true desktop.
I
will ignore the bar at the bottom of the screen, although this does
provide more interesting information as well. Basically, what we see
are things, or at least by the appearances of things, that we can
interact with in an intuitively obvious manner. By using the mouse (
a handheld instrument which you manipulate across your actual
desktop) for example, when I maneuver a small arrow (not shown) over
any of the icons or windows, or parts of windows, and either singly
or doubly clicking a button on the mouse, I cause something to
happen. If, for example, I position the arrow over the “file”
that says Chapter 3.doc and double-click, a program called Microsoft
Word will start, and will load the Chapter 3.doc file so that I can
read and or edit it, rather like conjuring up a (very powerful!)
typewriter with loaded pages. Double-clicking any of the folder
shaped icons on the “My Documents” window will likewise “open”
the folder to reveal its contents: most likely, a mixture of more
folders and files. Double-clicking any of the upper left corner
icons will open a window showing their contents, usually a collection
of folders, files, and other icons. Clicking on the calculator
program will allow me to enter numbers in the top white bar and
perform all sorts of mathematics on them just as with a “real”
calculator, while the notepad application allows me to type in text
and save it to a file.
I
do not want to belabor the point here, for if you have any experience
with a modern computer – which I am assuming you do – you are
quite familiar with the kinds of actions I am talking about. You are
familiar with how you genuinely appear to be working with a real
desktop, one containing icons, windows, and applications you can
interact with in a way so intuitive and simple a manner it is almost
childlike. The point I want to emphasize is that despite this it is
nevertheless no more than a virtual reality simulation, one designed
to conceal the details of what is really going on while making using
the computer so simple and easy. In truth, the desktop and all its
icons and windows and toolbars (at the bottom) are but phantoms for
the eye; useful phantoms, as they make the computer easy to use, but
misleading ones, as they conceal from us and seriously mislead us as
to what is actually going on inside that humming box of dumb
electronics and other gizmos we are working with. We see a bunch of
icons and folders and files, just as we might on an actual desktop.
We might even be fooled into thinking that is what we are working
with. But it is not, not at all. It is a mirage, through and
through.
For
what we are really working with are patterns of bits (basically, on /
off type switches) which make up two primary parts of the computer
physically: its working memory, and its permanent storage, or disk
drives. The point is, if we were to study those patterns of on / off
switches and try to decipher what they are saying directly, let alone
work with them in any direct fashion, we should very quickly find
ourselves hopelessly and helplessly overwhelmed by the complexity and
non-intuitiveness of the task (to instill some appreciate and
admiration in you, however, that is pretty much just what the users
of the original computers, some fifty plus years ago, had to do).
Designers of an earlier generation of computers, before the graphical
interfaces so common today, would simplify using computer by
providing a “command console” in which you would type, via a
keyboard, the names of programs you wished to run, the files you
wanted to work on, or any other commands the computer understood.
Even this was no easy task, so when the first graphical interfaces
came out in the early / mid 1980s (by the Apple Macintosh), it
revolutionized the personal computer, making it a household object
much like the television or telephone. Other companies followed suit
with their own graphical interfaces, such as Microsoft Windows and
the various UNIX interfaces, and the computer revolution was in full
steam. With the advent of the internet in the 1990s, and high speed
permanent connections in the 2000s, most of us now regard our desktop
or laptop machine as indispensible and valuable as our refrigerators.
Life, indeed, seems hardly conceivable anymore without it.
* * *
If
I keep going on this way, I will stray too far from my subject and
my point. Let us recapitulate: there is reality, and there is, or
can be, a virtual simulation of that reality such that it has the
effect of making it much easier to interact with that reality than
directly. The virtual simulation is a model which corresponds to
objective reality, but in a way that allows us to interact with it
much more effectively. If you can imagine setting bits in a computer
memory or disk off or on, instead of working with icons, windows,
folders, and files, you should have no problem grasping the advantage
of this.
What
I am saying goes further, however. Just as the desktop of your
computer provides a useful, albeit inaccurate description of its
objective reality, your brain does the same with the objective world
all around you.
Let’s take a few
moments to let that sink in. I am saying that the “objective
world” that we all deal with and handle every day as we move
through our busy lives is in fact a simulated reality in our own
brains. If you find that impossible to believe then, allow me to
prove it with a sensual (in this case, optical, but you can fool your
other senses as well) illusion, one of the usual stock in trade in
books on how the brain works. Have a good look at the object below:
Perhaps
you have seen this illusion before. Here’s the upshot: the
squares marked “A” and “B” are, all irresistible appearances
to the contrary, exactly the same shade of grey. Don’t believe it?
Good, don’t take my word: cover the entire image with a cutout
which conceals all parts of the figure except these two squares and
see what happens. You will see that they immediately jump out as the
exact same shade of grey, improbable as that seems. Improble? No,
impossible, for take the cutout away and it literally is impossible
to not perceive B as much brighter than A.
What
is going on here? Quite simply, your brain, which has nothing more
to go on than a pattern of photons on your retinas, is creating a
model of reality as best as it can, based on rules wired into it by
your genes and experience. That model insists that square B must be
brighter than square A, despite the actual facts as demonstrated by
applying our cutout.
As
illusions go, however, this is small potatoes for something as
complex and sophisticated as your brain. For a better example – in
truth, and the basic point of this chapter –take a look at one of
your hands. Make it your left hand (if for no better reason than I’m
left-handed). What do you perceive? Solid flesh overlying even more
solid bone, if you are like me. Press it against the surface on an
object, such as a real desktop, and that perception is made all the
more stronger. Now wiggle your fingers. What has happened? No
doubt, you feel as though you simply just decided to wiggle your
fingers, and then did so. Same if you clench and unclench your hand
in a fist, or scratch your nose, or write (oops – if you are
right-handed this probably isn’t easy), or deftly pick up an object
such as a pen and manipulate it in some way, such as twirling it like
a baton. In each case, you are aware of what a marvel of engineering
your hand is, and you sense the seemingly miraculous gift of being
able to use it the many myriad ways that you do.
As
marvelous and miraculous and real as it seems, though, it too is an
illusion; a virtual reality created inside your brain for you to
interact with. Furthermore, this is true not only of your hands, or
any other part of your body, but of the entire – yes, a
lá The Matrix
– objective world you live and function in. You do not interact
with the universe in any direct sense at all, but only through models
of that universe created by your brain using the rather limited
sensory information it gets from your eyes, ears, sense of touch, and
so on. As much as it seems that you are indeed interacting directly
with the universe the fact is that you are not; do not, and can
not, because the data taken in by your senses is quite insufficient
to allow you to do so.
Precisely
then, what is going on? The virtual model created in your brain is
obviously not arbitrary. On the contrary, it bears a very close
correlation to the actual universe around you, as indeed it must if
you are not to walk into trees or off cliffs, fail to run away or
hide from tigers, feed and take care of yourself, interact with the
other human beings, fall in love and procreate, and raise children;
all the things, in other words, that we and our ancestors stretching
back millions of years have had to do to survive and pass on their
genes in the great experiment known as Evolution by Natural
Selection. The fact that you have genes that code for a brain that
models the world so effectively is no accident. Nature has been
honing those genes a long, long time, under relentless and
unforgiving evolutionary pressure.
* * *
The
problem with this model in your head, and the reason I mention is, is
that it can seriously interfere with your understanding the
scientific explanation of things. I discovered this often during my
own education: sometimes my problems understanding a subject were
due to an “intuitively natural” concept of things, a concept that
in fact wasn’t true. Or to give a specific example: when studying
optics as an undergraduate, a fellow student was hopelessly and
distressingly lost trying to follow the subject material. It took a
little conversation to reveal that the problem was due to the basic
concept of optics that she had; instead of light from the sun and
other sources bouncing off objects and entering our eyes, she viewed
the light as emanating from her own eyes to illuminate objects, much
as the ancient Greeks did. Once she erased this false concept from
her mind and adopted the correct one, her problems diminished
greatly.
To
emphasize this in our current situation, look at your hand again. It
appears solid and continuous, which is why it doesn’t pass through
whatever it is resting on. But you know, even from your elementary
school education, that that isn’t really true. Matter isn’t
solid or continuous at all, not even the heaviest and densest of
things we normally encounter. All things, as you learned in school,
are composed of extremely tiny elemental motes of matter known as
atoms. You may even have learned that atoms consist mostly of empty
space; an extremely dense but small nucleus of protons and neutron,
around which tiny things called electrons orbit.
* * *
I
recall my father introducing me to the concept of atoms over the
dinner table when I was about seven or eight. He sat at the head of
the table, and I was the first one on his right (at the left end
because, as I have just mentioned, I’m left-handed). The details
are lost to me now but I’m quite clear that one day, as we were all
sitting down to dinner, he introduced the concept to me. Mind you,
my father was not a highly educated man. I don’t believe he ever
even finished high school. But he worked for a chemical company, and
had picked up enough science to give me my first taste of the
subject. That first taste was that everything – yes, everything –
is made of atoms (a story I later learned was not entirely true).
Look
upon your hand again. Yes, it is made of atoms. If you are curious
(and if you are not I cannot imagine why you are reading this book),
the atoms are mostly carbon, oxygen, hydrogen, and nitrogen, with
some phosphorus and sulfur thrown in, along with a smattering of
iron, calcium, sodium, potassium, chlorine … you get the idea. My
hope is that you begin to see why I began this chapter as I did:
your perception of your hand and what your hand actually is
are quite different things. The perception is for the purposes of
your survival and reproduction. The is
is what science tells us: the objective reality. Do you begin to
see why satisfying our curiosity as to the nature of things is so
difficult? Because it so often requires we think about things in a
way that is utterly foreign to our normal experiences. We do not
experience atoms, either in our hand or, for that matter, as what air
is made of. We have this built-in concept of matter as being solid
and continuous. But that concept, or instinct if you prefer, is
wrong. It is misleading. It blocks the path to comprehension. So
if we are to comprehend, very often we are required to cast our
instincts and concepts aside, and look at the world with fresh eyes.
One of the ambitions of this book is to help you to do precisely
that.
Again,
stare at your hand and try to see it, not as the solid, continuous
thing it appears to be, but as a vast collection of exquisitely small
but exquisitely alive, vibrating atoms, interacting with each other
and with the environment around them. If you find this difficult to
do at first, don’t worry, or give up. You are not being asked to
hallucinate (fascinating as such an hallucination would be), only to
imagine it – remembering that you cannot truly picture it, you can
only simulate the image by making the atoms much larger in your mind
than they actually are. So just relax and imagine you are some
Lilliputian being transported into this world, observing what such a
tiny creature would imagine. Do you have it? Good.
(I
can’t resist. There is a scene in the original The
Matrix
movie, in which Neo at last directly perceives the artificial reality
people live in as a stream of symbolic logic symbols; this is truly
his moment of liberation, more than anything else. What I am talking
about here roughly corresponds to that moment in the movie.)
Now
that you have this image before your eyes, I am going to do something
cruel: I am going to take a sledge hammer and … no, I am not that
cruel. Besides, I don’t need to completely smash that image,
however; just enough to let us begin on the next leg of our long
journey toward truth – a journey which never actually ends but does
take us to the most fantastic worlds and universes. Actually, the
general picture you probably absorbed from your schooling is, in the
basics, correct: the atom is composed of a a tiny, dense nucleus
composed of protons and neutrons, and a cloud of electrons which are
somehow around the nucleus – probably you picture them as orbiting
the nucleus, in much the same way as Earth orbits the sun, but that
is the part I am going to smash, so I won’t emphasize it. The
essential picture is, in many ways, correct, especially the part
about the atom being almost entirely empty space, meaning that
ordinary matter is almost entirely empty space, our perceptions
notwithstanding.
It
is correct enough to explain why your hand seems solid and cannot
pass through walls or desktops. The electrons at the outer edges of
your hands encounter the electrons on the wall or surface, where they
electrically repel each other so strongly that you would have to rend
the matter of your hand and / or the surface of the wall into tiny
shreds to make your hand pass through it. That’s right, the
apparent solidity is in fact just electrons repelling each other via
the electromagnetic force, which is astonishingly powerful – some
1039
times as powerful as gravity (no doubt this seems hard to believe;
why gravity appears to be the stronger force is something we will
explore later). Your sense of solidity has nothing to due with
understanding what is really going on. Nothing to do whatsoever.
Remember this. The world is not what it seems. Implant this in your
mind, and nourish it like a rich garden. It the key to satisfying
curiosity.
* * *
Actually,
perhaps you think that atoms are obvious. After all, you went to
school where the subject was introduced, and now it may seem as
commonplace as other unlikely truths, such as the sphericity of
Earth, or the fact that Earth is orbiting the sun and not, as your
eyes plainly tell you, vice-versa. But it is not obvious at all.
Reflect on the fact that, for a century after John Dalton first
proposed the modern concept of atoms in the early 1800s, using the
reasoning of the whole number proportions of elements that went into
reactions, the great majority of scientists rejected the idea of
atoms being real right up to the early 1900s. Nor were they fools
for doing so, because the idea of atoms leads to serious conflicts
with Newton’s Laws of Motion and the Laws of Thermodynamics as they
were then understood. The reason for this is that Newton’s Laws of
Motion are time reversible – that is, you cannot distinguish
between a process happening in forward time as from one happening
backwards; while the Laws of Thermodynamics, in particular the famous
Second Law, and its greatest creation, the concept of entropy, state
that energy – in the 1800s regarded as a form of fluid – moved
inexorably from regions of low entropy / high order in time to
regions of high entropy / low order at later times. The bottom line
of this view was the so-called “heat death” of the universe,
which appeared inevitable, at least from 19’th century
perspectives. But if matter were indeed composed of atoms, the
reasoning went, then their interactions, as derived from Newton’s
Laws, would be time reversible, in violation of the Second Law, which
says that entropy – disorder – must always increase. There
appeared to be an irreconcilable contradiction here, one that led
most scientists, and philosophers, to dismiss the actual existence of
atoms as a phantom, despite the increasing evidence from the work of
men such as Rutherford and J. J. Thompson that they did indeed exist.
* * *
It
took the brilliance of one Ludwig Boltzmann to reconcile the
seemingly unreconcilible, which he did by devising a new, subtly
different definition of entropy, or disorder. Assuming atoms were
real, Boltzmann deduced that the Second Law still held if one took a
statistical view of entropy, rather than an absolute view of it. To
appreciate Boltzmann’s insight, consider a deck of cards. If the
deck is perfectly ordered – i.e., ace of spades, king of spades,
queen of spades, etc., down through all the other houses in similar
order – then obviously any shuffling of the cards will invariably
destroy that order. The order is unlikely to be completely
destroyed, however; if we examine the deck after one shuffling, we
will still find that isolated pockets of order have survived, both
large and small. One might say that the deck is still semi-ordered;
that its entropy, while not zero any longer, is still fairly low. It
is certainly much lower than a deck of cards that has been shuffled
many times, so that all order is lost, but much higher than our
original, perfectly ordered deck.
Now
consider the second, or third, shuffling. Again, we regard it as
likely that the cards will be in less order with each shuffling; or
conversely, will possess more entropy. But the key word here is
“likely”; it is possible that, purely through the vagaries of
chance, that a shuffling will result in an increase
of order. In truth, a truly random shuffling will result in a
completely unpredictable order of the cards; this in fact is
practically the definition of random. But if the order is truly
unpredictable, than it very well can be a more
ordered arrangement of the cards than before the shuffling! Here is
where the key insight lies. It can be, but is unlikely to be, more
ordered, simply because if one examines all
possible arrangements of the cards, there are many more disordered
arrangements than ordered ones. This is why we expect shuffling to
decrease the disorder; it is purely a statistical assumption, yet an
excellent one simply because there are so many cards. If, instead of
fifty-two cards, there were fifty-two thousand, the ratio of
disordered arrangements to ordered arrangements would be vastly
greater and the likelihood of increasing disorder / entropy by
shuffling proportionately greater.
Let
us move from card decks to actual, ordinary realities. A single
cubic centimeter of air contains not fifty-two thousand but over ten
million trillion molecules of various gasses. Thus, the odds of any
random process decreasing its entropy (increasing its order) is so
infinitesimally small that we regard it as essentially certain not to
happen. Indeed, it is so small that we simply say that entropy
always increases.
But we are wrong.
Entropy doesn’t always
increase. It is a purely probabilistic law, which says that order is
almost certainly likely to decrease, especially in a system with more
than a few dozen or so parts. But almost certainly isn’t always.
It may be so often that in the entire lifetime of the universe we
never observe its overall order decrease. But nothing says that it
can’t happen. It is just overwhelmingly unlikely to happen.
Boltzmann’s
insight neatly resolved the apparent conflict between the Second Law
and Newton’s Laws of Motions. The evidence coming out of
Rutherford’s and Thompson’s laboratories, among others, convinced
the scientific world of the truth of atoms in the early nineteen
hundreds. Sure, entropy almost
always increases, so almost that we never observe the opposite
however long we observe, but it is not impossible. For tiny systems,
however, it can and has
been observed to happen. Newton’s laws and thermodynamics agree
after all.
* * *
This
book is not meant primarily as the history of scientific ideas. But
sometimes it is impossible to both pique and gratify our curiosity
without covering the grounds that minds before us have covered. The
atom is a perfect case in point. It is both obvious (mainly because
we are taught it) yet devilishly elusive at the same time. The above
discussions shows a part of the reason why this is true. But – and
now we enter Alice in Wonderland territory – it is not the only
reason. If anything, in fact, things become truly strange from here
on. So buckle your mental seat belts and lets prepare for a wild
ride.
Even
as atoms were being accepted as real in the early twentieth century –
for the record, Einstein’s experiments on Brownian motion probably
clinched the case as much any other work – physicists were still in
an utter quandary over just how they could be real. By all known
laws of physics up to the twentieth century, atoms were simply
impossible. Just that: impossible.
The
reason for this has to do with the well known analogy between atoms
and solar systems, what atoms were modeled from. Earth and the other
tiny planets orbit the massive sun, in a seemingly infinitely stable
manner, in much the same way as the tiny electrons were proposed to
orbit the massive nucleus of protons and neutrons. It is a very
natural analogy, which Rutherford initially proposed. And which
everyone saw at once could not possibly work.
Analogies
are tricky things. We humans naturally employ them when explaining
phenomena hitherto unexplained. Analogies can be very powerful, and
often form the basis for new insights and explanations in the natural
world. Scientists and laymen alike have been using them with
wonderful successes for centuries. But there is a nasty snare in
this whole process of analogizing, which is why, as Richard Dawkins
laments in The
Blind Watchmaker
“… analogies can be immensely fruitful, but it is easy to push
analogies to far, and get overexcited by analogies that are so
tenuous as to be unhelpful or even downright harmful. I have become
accustomed to receiving my share of crank mail, and have learned that
one of the hallmarks of futile crankiness is overenthusiastic
analogizing.”
The
main reason for this, I suspect, lies in the fact that analogies are
just that: compendia of likenesses between something we do
understand with the phenomena we are struggling to make sense of.
The problem is, almost nothing is really exactly
like something else. The appearances of similarity may in fact be
purely superficial, and so lead us nowhere (the “Argument from
Design”, so often employed by people who reject evolution is, I
think, a good example of this). More often however, and this is
where the snares are baited and waiting and the unwary are in
greatest danger of being caught, come from analogies that work quite
well to a certain depth of understanding, but fail at a deeper level
of analysis. The analogy between atoms and solar systems fall right
into the middle of this dangerous pit; so enticing to the casual eye,
but lethally flawed to those who have looked deeper.
Here
is the problem as concisely as I can give it. The planets orbit the
sun in what appear
to be eternally stable orbits, but that it is not actually true.
According to classical physics, any object accelerating through a
force field (in this case, a gravitational field), where accelerating
means either speeding up, slowing down, or changing direction,
gradually but inexorably radiates energy away. In the case of
planets, the energy lost is in the form of gravitational waves, which
are extraordinarily weak. The net result is that the planets’
orbits about the sun are only approximately stable; eventually they
will fall into the sun, but not for many trillions of years and more,
a time period in which much more serious things are going to happen
to the solar system, such as the sun running out of hydrogen fuel and
blowing up into a red giant, roasting or destroying all the inner
planets, then contracting to a white dwarf, leaving all remaining
planets in an eternal deep freeze.
For
a single electron orbiting a single proton, the simplest atomic
model, the hydrogen atom, the same physics apply, but the time scales
are vastly different. Remember the 1039
difference between gravity and the electromagnetic force, the force
which attracts the electron in the hydrogen atom to its proton
nucleus? Do the necessary calculations and you find the electron
radiating away all its energy as electromagnetic radiation and
crashing into the nucleus in a tiny fraction of a second. All the
other atoms must suffer the same fate, and if indeed this is how
physics works at this level, then matter as we know simply could not
exist.
And
so, by the early twentieth century it was clear from indirect and
direct experiments on the nature of atoms that there was no choice
but to conclude that, in fact, physics was incomplete, and did not
provide a true description of nature at this scale. A new model and
new laws were needed, laws that might seem counter-intuitive to
common sense (always the bane of science) and even to the known laws
of physics. Of course it couldn’t completely overthrow those laws,
as they had explained so much as about how reality works, but it must
give a deeper, subtler, and more complete description of those laws.
The
first attempt to square the now accepted reality of atoms with
physics was made by Neils Bohr, in 1913. Bohr accepted the basic
Rutherford model of the atoms, of electrons orbiting a tiny, dense
nucleus, but added a caveat to the system, based on work previously
done by Max Plank and Einstein: He arbitrarily decided that the
electrons, unlike planets orbiting the sun, couldn’t have any
energy but were restricted to certain, “quantized” values. Atoms
didn’t collapse because the lowest allowed quantized level was not
zero (an assumption Bohr had no justification for except that it made
his model work). To speak strictly correctly, Bohr didn’t quantize
the energy of the electrons but their angular momenta, but the
difference need not concern us here; what is important is that he was
able, for the hydrogen atom, to construct a model with quantized
electron orbits, which perfectly explained all the properties of this
atom, especially its spectral lines, which were the result of
electrons “jumping” (Bohr had no concept for what actually
happened when an electron switched orbits) from outer to inner
orbits, and releasing the energy in the form of light photons of a
specific wavelength.
Bohr’s
model for the hydrogen atom was a stunning success and showed the
world he was on the right track, but many puzzling problems remained.
First, Bohr could not make a working model for any other atom in the
periodic table, or any molecule, which are combintations of atoms
bound together. Second, his arbitrary assumption of quantized energy
levels was just that: arbitrary. It made his model work in an ad
hoc
fashion, but there was no deep, underlying physical explanation which
lay beneath it, an explanation which was satisfying to physicists of
the day. Clearly, something more was required. It was that
something more, however, which was to set the scientific – indeed
the philosophical – world on its heels. For what was required was
nothing less than a reevaluation of the very nature of physical
reality itself; a reevaluation which still has scientists and
philosophers debating to this day.
* * *
In
a book about curiosity, it is fitting that what follows is probably
the most curious thing scientists have ever uncovered about nature.
Echoing the theme from chapter one, it demonstrates just how amazing
and profound and unexpected our discoveries will be whenever we are
overcome by our desire to know and just have to peek under the covers
a little to see how nature genuinely works. It also extends the
theme with which I began this chapter, on how scientific
understanding undermines and even obliterates our cozy and seemingly
so real perceptions of reality and shows that we must look at the
world with fresh eyes and imaginations if we are to have any chance
of comprehending it. For the world of quantum physics, the bizarre
Alice-In-Wonderland world we are about to enter, not only obliterates
our perceptions; it challenges our capacity to think at all. It is
like a dream in which nothing makes sense, and fades instantly the
moment the dreamer awakens.
It
is probably the ultimate irony that in the human quest to satisfy our
curiosity, we have been ultimately humbled by the inescapable fact
that our answers shall always be inherently uncertain. The quest for
knowledge has yielded the knowledge of the limitations of that quest.
Perhaps we should have seen it coming. We can certainly enjoy the
cosmic joke it has played on us. I have no words to match those of
Jacob Bronowski, who captured the new view of reality in chapter 11
(“Knowledge or Certainty”) of The
Ascent of Man:
One of the
aims of the physical sciences has been to give an exact picture of
the material world. One achievement of physics in the twentieth
century has been to prove that aim is unattainable.
Take a
good, concrete object, the human face. I am listening to a blind
woman as she runs her fingertips over the face of a man she senses,
thinking aloud. ‘I would say that he is elderly. I think,
obviously, that he is not English. He has a rounder face than most
English people. And I should say that he is probably Continental, if
not Eastern-Continental. The lines in his face would be lines of
possible agony, I though at first they were scars. It is not a
happy face.
This is
the face of Stephan Borgrajewicz, who like me was born in Poland. In
plate 175 it is seen by the Polish artist Feliks Topolski. We are
aware that the these pictures do not so much fix the face as explore
it; and that each line that is added strengthens the picture but
never makes it final. We accept that as the method of the artist.
But what
physics has now done is to show that that is the only method to
knowledge. There is no absolute knowledge. And those who claim it,
whether they are scientists or dogmatists, open the door to tragedy.
All information is imperfect. We have to treat it with humility.
That is the human condition; and that is what quantum physics says.
I mean that literally.
No absolute
knowledge? All information imperfect, to be treated with humility?
The only method to knowledge that of the artist? Just what is going
on here? Hasn’t all our curiosity been about getting to the
ultimate and final truth? Yet what we seem to be hearing here is
that there is no so such thing; worse, that we are in danger of
falling into dogmatism and even tragedy if we insist on pursuing it
to that end.
* * *
Partly
by design, partly by accident, this chapter has meandered through
several different, though interrelated, themes, the main one being
science, our best and in my opinion only realistic hope of satisfying
curiosity, repeatedly demanding that we use our imaginations to view
reality in ways we had never considered, and which often seem
counter-intuitive. Part of that imaginative use means accepting that
things are often not at all what we perceive them to be. Another
part, the part we are coming to, is that what must even be careful
about relying on any intuitions or “common-sense” if we are to
understand the way the universe works. I do not mean to say,
however, that intuition, perceptions, and common-sense are always
wrong or useless; by no means is this so. But we must proceed
cautiously and with open minds and eyes if we are to make progress.
Once
again, look at your hand and visualize the tiny, vibrating atoms
which compose it, much the same way that the tiny, vibrating bees
constitute a hive. We left off with Bohr’s description of these
atoms, which said that the electrons did indeed orbit their nuclei,
albeit in fixed, quantized orbits. We noted that Bohr himself had no
explanation why nature should work this way at this scale, instead of
continuous orbits like those of the planets around the sun. This was
a weakness in Bohr’s original visions, which of course he realized;
Bohr understood only too well that what he was suggesting was nature
was something more bizarre and counter-intuitive than our senses
captured for us.
* * *
This
is not a history on the development of quantum mechanics, so I will
leave out quite a bit of interesting detail here (like de Broglie’s
wave model of electrons, which was actually quite critical to the
final vision). What I’d like to do at this point is use the
cherished method of analogy again, to help you appreciate the true
situation of how electrons behave in atoms and molecules. Again, I
think this is more helpful for the layman to start this way.
My
analogy is that of a tennis match. Imagine that you are watching the
ball sail back and forth between the players (this could be a bit
tough if you are picturing modern professional players, who hit those
seemingly impossibly hard shots from all angles; so try to make it a
friendly game on a local court somewhere). As you watch the ball,
even in this friendly match, you are aware that it still seems a blur
much of them time. At no particular moment can you make out exactly
where the ball is, or how fast it is moving, or its precise
direction.
That’s
fine. What you are experiencing is simply the limits of your visual
acuity system, involving your eyes, optics nerves, and the parts of
your brain which process the information. They can follow the
situation only so quickly, and the result is that things seem
somewhat blurred to you. Still, and despite this, you accept the
proposition that, at any given moment in time, the ball has
an exact location, and has
an exact speed and direction. You can’t pick it up, but certainly
a sensitive enough piece of equipment – say a strobe camera
operating at high speed – could do so easily. You take that as
given. It is just “common sense” you might say.
Yet
– and here is the part where you must starting thinking in as
unorthodox a manner as possible – you would be wrong. However, in
our hypothetical tennis match, not even the most sensitive instrument
ever built would show you that you are wrong. That is because the
mass of a tennis ball is simply too overwhelmingly huge. Indeed, the
mass of a dust mote would be too overwhelmingly huge as well. This
is why we don’t ordinarily notice our error; from the viewpoint of
creatures our size moving amongst objects that we can see and touch,
the error is so small it would never show up. Thus, our brains and
sensory systems, which have been attuned by natural selection to deal
with objects of approximately our sizes, has a hard time grasping the
concept what I am about to tell you. But electrons, which are vastly
smaller in mass than anything we shall ever come in contact with,
don’t behave the way that the analogy with tennis balls would
suggest. They don’t behave that way at all, simply because they
are so small in mass. The most concise way of expressing their real
behavior is, with all due apologies because I want to avoid math as
much as possible, is with an equation:
x × s
≤ h
/ m
Hopefully,
this is not too complicated a piece of math to throw at you if you
are tucked way in front of a roaring fireplace, all comfy and cozy.
Or reading it over your three minute egg at breakfast. But I am
going to ask that you look at this equation and drill into your mind,
for you shall miss much of what is to come if you don’t. Oh, and
before proceeding, this equation is just one version of what is
commonly referred to as the Heisenberg Uncertainty Principle, after
Werner Heisenberg, who first elucidated it in the 1920s. Some
definitions are in order here. First, the
sign refers to an uncertainty. In the case of x,
what it means is that there is an inherent uncertainty of the
position of a particle (tennis ball, dust mote, or electron) at any
given moment. Understand something very clearly here: we do NOT
mean an uncertainty due to the limitations of any measuring devices;
we mean that nature herself does not allow us to say exactly where in
the region of uncertainty the particle is – it is as though the
particle doesn’t even have an exact position in the region of
uncertainty, it is just somewhere within it. Take some time and let
that sink in, odd as it sounds, for it is contrary to all your
intuitive, common-sense view of how the world works; yet it is
critical to understanding the ideas that will be developed here and
later. Yes, I am saying that there is inherit uncertainty, and no
measurement can reduce or eliminate it; it is built into the
foundation of nature’s laws as strongly as the law of gravity or
the laws of thermodynamics.
Likewise, the symbol
s
is an expression of the uncertainty in the speed of the particle,
tennis ball, dust mote, or electron, at any given instant. We do not
know exactly how fast it is travelling; we can only determine it’s
speed within certain limits. Again, this is another oddly-shaped
brick in the foundation of natural law. Accept it, strange and
counter-intuitive though it might sound as well.
One thing you should
see that comes out of the equation is that as x
increases,
s
must
grow smaller, and vice-versa. Why? Because their product is a
constant, the [h
/ m]
part on the right side of the equation. Thus, if we could measure
the position of a particle exactly (x
= 0)
then s
would become infinitely large, while if we measured its speed with
perfect precision (s
= 0)
then x
becomes infinite . The second salient point I must mention here is
that the product of the two uncertainties, x
× s,
is always equal to or less than the quantity h/ m,
whatever that is. It turns out that h
is
exceedingly small, on the order of 10-34
newton-seconds,
which, I assure you, is a minuscule quantity. It is, for all you
scientific pedants out there, a symbol representing the so-called
Planck’s constant, which Planck devised around 1900 while working
with blackbody radiation, and which Einstein used later to explain
the photoelectric effect and Bohr to construct his model of the
hydrogen atom (actually, the real constant is h-bar,
which is
h
divided by 2π). m,
on the other hand, which is the mass of the object being measured,
makes this ratio smaller or larger, depending on its own size. You
will all breathe a sigh of relief when I tell you that for m
on the scale of a tennis ball or even a dust mote, x
× s
or h/ m
is so infinitesimally small that, as I have said, it is to small to
be measured with even our most powerful and sensitive instruments.
Hence, in the world we experience, tennis balls and dust motes and
cars and planets, the equation x
× s
≤ h
/ m
for all practical purposes might as well not even exist. Whew! What
a relief, I suspect you are saying, for if it were significant the
world would be fantastically different from what we actually
experience. Here’s the important point, however, and why I harp on
the equation and demand that you absorb and digest it. For an
electron, where m
(mass) is excruciatingly tiny indeed, this equation – Heisenberg’s
Uncertainly Principle -- dominates its behavior. In the next
chapter, the one on matter and chemistry, we will explore the
consequences of being at the low mass end of things.
And so on to matter
and chemistry, and how all this uncertainly stuff fits in.
