The Supernatural Element in Nature

 

Axioms and Evidence

 

In his 1888 book "Evolution" [Le Conte 1888] Joseph Le Conte, professor of Geology and

Natural History at the University of California, writes:

 

 "Intermediate links may be wanting now, but they must, of course, have existed

  once--i.e., in previous geological times, and therefore ought to be found

  fossil.  In distribution in space or geographically, organic kinds may be

  marked off by hard-and-fast lines but, if their derivative origin be true, in

  their distribution in time or geologically, there ought to be many examples

  of insensible shadings between them.  In fact, if we only had all the extinct

  forms, the organic kingdom, taken as a whole and throughout all time, ought

  to consist not of species at all, but simply of individual forms, shading

  insensibly into each other...But this is not the fact.  On the contrary, the

  law of distribution in time is apparently similar in this respect to the law

  of distribution in space, already given.  As in the case of contiguous

  geographical faunas, the change is apparently by substitution of one species

  for another, and not by transmutation of one species into another.  So also

  in successive geological faunas, the change seems rather by substitution than

  by transmutation.  In both cases species seem to come in suddenly, with all

  their specific characters perfect, remain substantially unchanged as long as

  they last, and then die out and are replaced by others.  Certainly this looks

  much like immutability of specific forms, and supernaturalism of specific

  origin...The reason for this, given by Darwin and other evolutionists, is the

  extremely fragmentary character of the geological record...While it is true

  that there are many and wide gaps in the record...yet there are some cases

  where the record is not only continuous for hundreds of feet in thickness,

  but the abundance of life was very great, and the conditions necessary for

  preservation exceptionally good...and yet, although the species change

  greatly, and perhaps many times, in passing from the lowest to the highest

  strata, we do not usually, it must be acknowledged, find the gradual

  transitions we would naturally expect if the changes were effected by gradual

  transformations."

 

Le Conte also acknowledges that natural selection cannot explain the

appearance of new features:

 

  "...neither can it [natural selection] explain the first steps of advance

  toward usefulness.  An organ must be already useful before natural selection

  can take hold of it to improve on it."

 

After acknowledging that the only direct evidence, the fossil record, does

not support the idea of gradual change, and that the only theory ever taken

seriously as to the causes of these changes cannot explain anything new, Le

Conte nevertheless concludes:

 

  "We are confident that evolution is absolutely certain--not evolution as a

  special theory--Lamarckian, Darwinian, Spencerian...but evolution as a law

  of derivation of forms from previous forms.  In this sense it is not only

  certain, it is axiomatic...The origins of new phenomena are often obscure,

  even inexplicable, but we never think to doubt that they have a natural

  cause; for so to doubt is to doubt the validity of reason, and the rational

  constitution of Nature."

 

Le Conte illustrates the optimism which prevailed in science in the late 19th

century.  Science had made such progress explaining previously mysterious    

phenomena that there was no reason to believe, it was felt, that any of the  

secrets of Nature, even the secrets of life itself, would long endure the    

assault of scientific investigation.  In Le Conte's day, nearly all

scientists held the view that everything that happens in our world is

completely determined by the laws of Nature, that the only limits to our

ability to understand what has happened, and predict what will happen in

the future, are practical limits on the extent of our knowledge.

Olan Hyndman, in "The Origin of Life and the Evolution of Living

Things," [Hyndman 1952], calls Darwinism "the most irrational and illogical

explanation of natural phenomena extant."  Yet he says "I have one

strong faith, that scientific phenomena are invariable...any exception

is an unthinkable as to maintain that thunderbolts are tossed at us

by a man-like god named Zeus," and so he goes on to develop an

alternative (and even more illogical) theory of the causes of evolution.

 

The Advent of Quantum Mechanics

 

Surprisingly, only about 30 years later, Le Conte's axiom was shattered

by the discoveries of quantum mechanics, which introduced, quite literally,

a "supernatural" element into science.

 

 

             

                                           

 

                Figure 5.1 Wave Diffraction

 

To understand the background for the discoveries of quantum mechanics, let

us start with a classic diffraction experiment.  Suppose two wave sources

in phase and of the same wavelength, l, are placed a small distance

apart as shown in Figure 5.1.  We can imagine these to be sound waves,

for example.  At a point on a wall, A, chosen to be equally distant

from each source, the waves from the two sources will arrive in phase,

and reinforce each other.  However, at a point B, chosen to be exactly

l/2 further from one source than the other, the waves will arrive

one half cycle out of phase, and cancel each other at all times.  We will

also observe this cancellation at the points whose distances from the two

sources differ by 1.5, 2.5, 3.5,... wavelengths, and so as we move up the

wall we will encounter alternating points of reinforcement and cancellation.

Experiments with light diffraction had been carried out, in which light

from a distant source is passed through two narrow slits on a plate

perpendicular to the direction to the source.  Since the two slits are

equally distant from the source, the light should hit the two slits in

phase, and the two slits can thus be considered to be separate light

sources in phase with each other.  Where the light from these two

"sources" hits a wall, a diffraction pattern with alternating light and

dark bands will be observed.  If one slit is covered up, the dark bands

go away!

 

It is easy to see why, at the beginning of the 20th century, it was

unanimously agreed that light must consist of waves.  If light consists

of particles, it is hard to see how light from one source could cancel

the light from another source!

 

Some new experiments, however, seemed to be inconsistent with the wave

theory of light.  In the photoelectric effect, for example, it was

observed that when a metal plate was illuminated, the energy delivered

by the light caused some electrons to be stripped from their host

atoms and ejected from the plate.  Since an electron must reach a

certain threshold energy level before it can escape the metal,

experimenters were surprised to find that even when light of extremely

low intensity was aimed at the plate, a few electrons were immediately

able to absorb enough energy to be ejected.  If light were propagated

through waves we would expect the light energy to be spread more evenly

over the metal, and at very low intensities we would expect to have to

wait a while before any electron could absorb enough energy to

escape.  When the intensity of the light was increased, another

unexpected result was observed.  The number of electrons emitted

increased with the intensity, but the energies of the individual emitted

electrons were unchanged.  The ejected electrons, it seemed, had

received a packet, or "quantum", of energy whose magnitude was

independent of the light intensity; increasing the intensity seemed

only to increase the number of such packets available.

 

A particle theory of light would explain these results: even at very

low light intensities, a few electrons (those hit by the light

"particles") would be immediately ejected, and increasing the intensity

(the number of light particles bombarding the metal) would cause more

electrons to be knocked out, but the energy of an individual ejected

electron would depend only on the energy of the light particle which

struck it, not on the number of light particles.  Further experimentation

showed that while the energy of an individual ejected electron did not

vary with the intensity of the light, it did change with color,

increasing as the wavelength of the light was decreased.

 

For a while, light had to be considered to have a dual nature, since

some experiments (such as diffraction) could only be explained using

the wave theory, while others (such as the photoelectric effect) could

only be explained using the particle theory.  The spectroscope, a tool

used by astronomers, separates out the different wavelengths of light by

bending them through different angles.  It was designed using the wave

theory of light and it should not work, according to the particle theory.

The Geiger counter, on the other hand, is designed to count individual

"particles" of electromagnetic radiation, such as light.

 

In the early 1920's, the two opposing views of light were reconciled

by the following theory: Light consists of particles (photons), but

there is a wave associated with each photon, whose intensity at a given

point gives the probability of finding a photon at that point.

In other words, light consists of particles whose motions are guided

by probability waves.

 

In 1924 French physicist Louis de Broglie further suggested that this

dual wave/particle nature was characteristic not only of electromagnetic

waves, such as light, but of all "particles".  He concluded that any

particle of momentum p is guided by a probability wave of wavelength

l=h/p, where h is called Planck's constant.  This would explain

why, in the photoelectric experiment, the electrons knocked out by

the lower wavelength light came off with a higher energy: the lower

wavelength photons have a greater momentum.  Spectacular confirmation

of de Broglie's conclusion came in 1927, when electron diffraction was

first observed, by Davisson and Germer at Bell Telephone Laboratories.

The electron's particle nature was undisputed: we find 1,2,3... electrons

in an atom; we never find the electronic charge or mass in other than

integral multiples.  Yet electrons were observed to diffract--a

phenomenon unique to wave motion, involving cancellation--when passed

through a metal crystal.  Because electrons typically pack a much

greater momentum than photons, and thus their associated wavelengths

are much smaller, the electron diffraction pattern is only observable

when the spacing between slits is very small.  That is why electron

diffraction was first observed using the tiny spaces between atoms in

a metal crystal as "slits".  Other atomic particles such as neutrons

have since been made to exhibit the diffraction characteristic of waves

as well. 

 

The governing equation of the new quantum physics is the Schrodinger

equation, which can be used to calculate the "probability distribution"

of particles.  For example, Figure 5.2 shows the probability distribution

associated with the second lowest energy level, for an electron in the

vicinity of two protons, as calculated by my partial differential

equation solver, PDE2D.  Note that there is no attempt to say exactly

where the electron is at any given time (until it is directly observed),

we can only say where it "probably" is.

 

             

 

   Figure 5.2 Probability Density for Electron Near Two Protons

 

To fully appreciate why science was forced, to the dismay of many, to

drag "probability" into the picture, let us go back and repeat the two

slit diffraction problem of Figure 5.1, only this time let us use a

beam of electrons rather than a beam of light, and let us replace the

wall with a photographic plate.

 

Let us set the intensity of the electron beam at such a low level that

we can assume that only one electron at a time passes through the

diffraction apparatus.  Each electron which is not stopped by the

plate will pass through one of the two slits and hit the film at a

particular point, marking its impact with a dark spot.  After these

dark spots begin to accumulate, however, we begin to observe the

familiar wave diffraction pattern of alternating light and dark bands

on the film.  The individual electrons impact the film at specific

spots, yet the collection of impact marks conforms to the diffraction

pattern expected for a wave whose wavelength is given by the de Broglie

formula.  In other words, a particular electron may hit the film

almost anywhere, but when a large number of electrons pass through

the slits, the result is highly predictable.

 

Suppose we repeat the experiment, only this time instead of leaving

both slits open long enough for N electrons to pass through, we

block the top slit and leave the bottom slit open until N/2 electrons

have passed through it; then we block the bottom slit and let another

N/2 electrons pass through the top slit.  Surely the results will be

the same as in the first experiment.  How could it possibly matter

whether we allow the electrons to alternate randomly between slits,

or force the first batch of electrons to pass through the bottom slit

and the second batch to pass through the top slit?  But it does matter:

in the first experiment we get a diffraction pattern, while in the second

we get only a more or less uniformly exposed film.  Incredibly, the behavior

of an electron passing through one slit seems to be affected by whether or

not it could have passed through the other!  We can explain these

results only if, when both slits are open, we think of each individual

electron as a probability wave, passing through both slits--and yet

each electron strikes the film as a particle!  In other words, until

it is actually observed, we must think of the position of the electron

as inherently ill-defined, specified only by a probability

density function; when it is finally observed (when it hits the film)

it has a very definite position.

 

Philosophical Implications

 

The introduction of "probability" into physics has enormous philosophical

implications.  For the first time, science had to face the fact that no matter

how well we prepare for any experiment, no matter how much data we accumulate,

we cannot predict with certainty the outcome of the experiment.  British

Astronomer Sir Authur Eddington, in his classic work "The Nature of the Physical

World," [Eddington 1929], says that according to quantum theory, "the future is a

combination of the causal influences of the past together with unpredictable

elements--unpredictable not merely because it is impracticable to obtain the

data of prediction, but because no data connected causally with our experience

exist."

 

Einstein objected to quantum mechanics with its introduction of chance and

the "uncertainty principle" into science, saying "God does not play

dice", but the quantum theory has been so successful in explaining

scientific phenomena that it is now universally accepted.

 

If we look at a single electron in an electron beam, we can make an

educated guess, based on the probability wave associated with the electron,

as to where it will hit the target--but we may be way off.  If we

consider a particular atom of a radioactive substance whose half-life

is 100 years, we may guess that it will decay after about 100 years or

so, but it may surprise us and decay tomorrow.  And it doesn't matter

how much we learn about that electron, or that radioactive atom, or

its neighbors, we will never be able to predict with certainty what

the electron or atom will do.  For it is not the practical constraints

of our experiment, but the theory itself, that limits our predictive

powers.  

 

One of the philosophical implications of the "uncertainty principle"

introduced by quantum mechanics is that the idea--so contrary already

to our intuition--that all human actions are strictly determined (in

a complicated way) by external influences, is shown once and for all

to be wrong.  For even the individual particles which make up the

brain have a "free will" of their own; even their behavior is not

strictly predictable.  Eddington says [Eddington 1929], "It is meaningless

to say that the behavior of a conscious brain is precisely the same as

that of a mechanical brain, if the behavior of a mechanical brain is left

undetermined."  Further, he states that with the advent of quantum

mechanics, "science thereby withdraws its moral opposition to freewill."

 

It could be added that science must also withdraw its moral opposition

to religion, for if we define the "supernatural" to be that which is

forever beyond the ability of science to predict or explain, then

there is, quite literally, a "supernatural" element to all "natural"

phenomena.  Eddington says that quantum mechanics "leaves us with no

clear distinction between the Natural and the Supernatural." 

 

When we say that the result of a coin toss, for example, is determined

by "chance", we really mean that it is determined by factors too

complicated to predict in practice, but we assume that if we knew the

initial conditions and forces with sufficient accuracy we could predict

whether it would land heads or tails.  But with quantum mechanics, when

we talk about "chance", we mean something very different, we do not mean

a factor too complicated to predict in practice, but rather a factor

which is inherently impossible to predict.  Science can say what

will "probably" happen in a given situation, but what actually happens

is decided by something that science does not understand, and never will

understand.  The introduction of this "supernatural" element into Nature

by no means makes science useless, it can still be used to predict

macroscopic phenomena with probabilities approaching certainty.  But it

does mean that those who claim that science has eliminated the supernatural

from Nature have a view of science that has been out of date for 80 years.