This is the first of three parts explaining, in non-technical
terms, the brilliant "Theory of Elementary Waves" of Lewis
Little. If you normally shy away from discussions on physics,
please give this a chance - it was especially written for you.
Although I love and revere mathematics, I firmly believe if you
cannot explain a principle of physics in common language and
terms, then you probably do not fully grasp the principle in the
first place. Little's theory is extremely broad-ranging and if I
can successfully communicate the highlights of his achievement I
would consider that to satisfy my goal.
-----------------------------------------------------------------
PART 1
------
Quantum physics focuses primarily on the atomic and sub-atomic
level, and the evolution of its mechanics spans almost a century.
In 1900 Max Planck developed an empirical formula which described
certain experimental observations about energy. When looking for
a theoretical basis for his formula he advanced the idea that
energy, which at that time was thought to be a continuous flow of
waves, actually consisted of small individual pieces, called
quanta. Several years later Albert Einstein conceived the idea
that light was composed of both waves and particles, and later
the name photon was given to that particle of light. About 1913
Niels Bohr, utilizing the idea of Planck's quanta, created a
model of atomic structure. The next decade saw many physicists
involved in quantum mechanics research, and in 1926 Erwin
Schroedinger formulated what was to become the cornerstone of
this new theory, his quantum wave equation. The decade
following Schroedinger's discovery ushered in the world of
nuclear physics which has continued quantum research through
today.
In the seven decades since the wave equation was created, the
strangeness of this new field of physics has been transformed
into the 'weirdness' of quantum mechanics. The standard theory is
replete with effects without causes and the assertion that matter
exists in an indeterminate state. The 'weird' behavior, according
to the theory's interpreters, is worn as a banner of proof, as if
this difference from known facts of reality should be taken as
evidence to substantiate the theories. In 1996 the physicist
Lewis Little published his paper "The Theory of Elementary
Waves". For the first time since Planck's quanta in 1900, a
rational basis for quantum mechanics has been established. The
purpose of this article is to outline Little's revolutionary
theory, in non-technical terms, and to identify the kinds of
problems that his ideas have resolved. I will present some
highlights of the theory. A full explanation requires a much more
substantial analysis.
The sagacious Caltech physicist, Richard Feynman, was fond of
presenting essentialized models of experiments to his beginning
physics students in order to illustrate basic physics principles.
Feynman believed (rightfully so) that a particular kind of
experiment, one called the double-slit experiment, embodied the
essence of the fundamental issues in quantum mechanics. Following
Feynman, we will look at a few examples of these models, keeping
in mind that, in principle, the actual experiments can and have
been performed. We will then explore some fundamentals of
Little's theory and re-evaluate the experiments in light of what
we have learned.
A particle is usually understood to be an individual coherent
object possessing a specific identity which can be localized in a
given region of space. It is easier to grasp the actions of
quantum particles by first looking at the behavior of a more
familiar particle - a bullet. Figure 1 shows a gun (our 'source')
that shoots a continuous stream of bullets. The source sprays
bullets, in a fan-like manner towards a wall which has two slits
just big enough to allow the bullets to pass through. Some
distance behind the wall is a backdrop which stops the bullets as
well as counts the number of bullets that impinge anywhere along
its surface. Intuitively, if we think of what is the likelihood
of where the bullets going through slit 1 will wind up, we can
see that the maximum number of bullets will be along an angle
from the source directly through slit 1 and, as the bullets
bounce off the edge of the slit, the likelihood of finding
bullets will decrease as we get further in each direction from
the slit. The number of bullets detected having gone through slit
1 is shown as 1's. Similarly the number of bullets going
through slit 2 is shown as 2's. The important point here is that
the total number of bullets counted is just the sum of the
bullets going through slit 1 had we closed off slit two plus the
sum of those going through slit 2 had we closed off slit 1.
F I G U R E 1
--------------
| 21111111|
| 211111111|
| 2111111111|
| 21111111111|
| 211111111111|
-slit 1 2221111111111|
22221111111111|
/ - 222222111111111|
/ | 2222222111111111|
/ | 22222222211111111|
source - - - | 222222222211111111|
(bullet)\ | 22222222211111111|
\ | 2222222221111111|
\ -slit 2 222222222111111|
22222222221111|
- 2222222222111|
| 222222222221|
| 22222222221|
| 2222222221|
| 222222221|
| 22222221|
WALL BACKDROP
In contrast to particles, mechanical waves are usually understood
to be a disturbance in some continuous medium; the disturbance
propagates through the medium. Water waves and sound waves are
two common examples of this simple wave phenomenon. We can
perform the same double-slit experiment using a wave for a source
instead of the bullets. Figure 2 shows a similar experimental
setup where now the source makes circular water waves. The
backdrop, instead of counting the bullets as before, now has the
ability to measure the intensity of the wave impinging on its
surface. If we cover slit 2 and measure the intensity of the
waves coming through slit 1, and then cover slit 1 and measure
the intensity of the waves coming through slit 2, we get a
distribution that looks very much like the count distribution for
the bullets in Figure 1. However, when we measure the intensity
with both slits open, unlike the case with the bullets, the total
intensity does not equal the sum of the intensities from slit 1
and slit 2 alone. In fact, we get a total intensity which
sometimes is more than and sometimes less than the sum of the
intensities from slits 1 and 2. This difference of wave behavior
as compared to particle behavior is a consequence of the
interaction of the waves coming through each of the slits. This
is actually a very common wave occurrence which you can see if
you watch the waves that result from the passing of two boats.
If the waves meet when both are at their crest the resultant wave
of their combination is larger than the sum of the originals. On
the other hand, if one wave is at its crest and the other at its
trough, the waves cancel each other and you can observe
relatively smooth water. This interaction of two waves is called,
in physics, interference. Constructive interference is the
additive process when the two waves are 'in phase' with each
other; destructive interference is the subtractive process when
the waves are 'out of phase'.
F I G U R E 2
--------------
| 211111|
| 2111111|
|) 211111|
| ) 2111|
) | ) 21|
) - slit 1 211|
) ) ) ) 21111|
) ) - ) ) 2211111|
) ) | ) 222111111|
) ) ) | ) 22221111111|
source-)- -)- -)| ) ) 222222111111|
(water ) ) ) | )) 22222221111|
wave) ) ) | )) 222222111|
) ) - ) ) 2222211|
) ) ) 22221|
) - ) 221|
) | slit 2 21|
| ) 2221|
| ) 222221|
| 2222221|
| 222221|
WALL BACKDROP
Now that we have seen how classical objects like particle-bullets
and water waves respond to the double-slit experiment, the next
step is to investigate the response of quantum mechanical
particles. All we need do is to use as a source an electron (a
charged particle) or a photon (a quantum of light). When we
perform the double-slit experiment using photon particles, the
result is _not_ like the bullets in Figure 1. In fact, the
interference pattern seen in the wave source of Figure 2 is
observed. The experiment seems to be telling us that the photon
particle acts like a wave. How we don't know, just somehow. This
observation has led quantum mechanic theorists to use the ideas
of particle-wave, or wave-particle. The connotation of this is
that a photon is a particle with wave-like properties, but it is
completely unclear what this means in reality other than pointing
to the results of the experiment. It is possible to detect that
the photons are arriving as discrete packets, so it seems
reasonable to assume a particle goes through either slit 1 or
slit 2. But, if we block off slit 2 we just get the same
distribution for slit 1 as we got for the counting of bullets.
Likewise for closing off slit 1. Only by keeping both slits open
do we get the interference pattern. Clearly there is some kind of
wave interaction.
If we try to 'peek' and see which slit each particle is going
through (a particle is always detected as going through slit 1 or
slit 2), the results of the experiment are again just like the
counting of bullets. So the theorists conclude that we cannot
definitely say that the particle goes through either slit 1 or
slit 2, since the act of determining that fact changes the
outcome. When speaking about the experiment, the standard theory
treats probability as if it had physical characteristics. There
is a certain probability of the particle going through either
hole, and probability interference (somehow acting like real wave
interference) is what causes the wave-like result. If you can
detect a particular particle, that changes the probability
pattern. So there is a ghost-like quality to the actions of these
particles, where probability replaces a real existent. In fact,
the standard theory is saying that the very act of observing
forces a particular probability and it is then that something
_becomes_ real.
It is this ghost-like quality which leads us to the Schroedinger
wave equation. The solution to the equation is known as the wave
function; it gives the probability of locating a particle at a
particular place and at a particular time. The Schroedinger
equation, then, associates a wave with a particle. A
characteristic of the equation is that if you have separate
solutions, they can be combined together - a process known as
superposition. Think of a particle at the source vanishing and
being replaced by a host of ghost particles that follow different
paths to the backdrop. These ghost-like particles somehow
interfere with each other, which results in the pattern we have
seen for wave-like behavior. These ghosts relate to the wave
function which is a solution to Schroedinger's equation. When we
observe the particle, all of the probability waves disappear
except for the one associated with the real object. This is the
act you may have heard described as the 'collapse of the wave
function'. Nothing is real, until we look at it. This is pure
Kantianism.
Let me try to succinctly sum up what we have learned about the
standard theory. Experiment shows that quantum particles seem to
behave sometimes like particles and sometimes like waves. This
'weirdness' is enshrined in an anti- concept of particle-wave (or
wave-particle) which refers to nothing in reality. Real objects
are replaced by probability functions which somehow govern the
overall wave-like behavior that results in the patterns seen in
experiments. There is absolutely no attempt to establish a causal
basis; in fact this lack is proudly offered as proof of the
theory since 'why should we think quantum reality is anything
like what happens on a larger scale'. In one sense this is true,
in that quantum behavior is uniquely defined, but does that mean
we must abandon all pretense of causality and maintain a
ghost-like existence of matter in some indeterminate state? Yes,
says the standard theory. No, says Lewis Little's Theory of
Elementary Waves.
In one sense the Theory of Elementary Waves (TEW) is very
profound and requires a detailed technical analysis to see how it
operates and how it applies to quantum phenomena. In another
sense, though, it is quite simple, in that it identifies and
integrates some very fundamental parts of reality. As a starting
point to understand his approach, consider some of Little's
thinking regarding the double-slit experiment. Although standard
theory is hesitant to even pronounce judgment as to which slit a
particle goes through, Little realizes that each particle must go
through a single slit and that it must follow a specific
trajectory while doing so. At the outset he rejects the effect
without cause of standard theory. Figure 3 shows the double-slit
setup with a set of supposed trajectories for each particle.
Little now argues that if we moved the target to another
position, B, then as the particles follow the same trajectories
they would intersect the detector at different points than before
and, therefore, would not show the standard pattern. However,
experiment shows that in fact the pattern occurs _wherever_ the
target is placed. This experimental fact cannot be explained by
the standard theory if we are to simultaneously maintain cause
and effect. It can be explained, however, if you consider the
experiment as evidence that there is motion _from_ the target
_to_ the particle source. This is exactly opposite to the way of
thinking in the standard theory.
F I G U R E 3
--------------
(B)
| | |
| | x|
| x x| |
| x x | |
| x x | |
slit 1 -x x | |
x x y x | |
x - x y x | |
x | x x y | |
x | x x y | |
source x | x | y|
(photon x | x x y | |
particle) x | x x y | |
x - x y x | |
x x y x | |
slit 2 -x x | |
l x x | |
| x x | |
| x x| |
| | x|
| | |
WALL target
What is it, then, that moves from the detector to the source.
Little's theory states that it is the quantum wave that moves in
this reverse direction. But, as we saw before, a wave is thought
of as a disturbance of some medium and the wave propagates
through the medium. What is the medium in this quantum case, and
what is the cause of the disturbance? It is in answer to this
question that Little breaks with tradition and establishes a base
on which to explain the 'weirdness' of quantum mechanics. It is
not a wave in the usual sense at all - it is an elementary wave -
a _fundamental constituent of reality_. In effect, it _is_ the
medium. I cannot stress strongly enough the importance of this
idea. Little's theory identifies the most basic 'stuff' of
existence. This is not just the mathematical representation of a
phenomenon, this is a _real_ wave. The elementary wave cannot be
understood by appealing to anything more basic to explain it -
there is nothing more basic. The elementary waves have a
structure and the effects of the changes in that structure are
all we can know about them. So the ghost-like packets of waves in
the standard theory have been replaced by a real existent, and
the behavior of that wave is contrary to standard interpretation
- the wave moves in reverse, from the target, or more generally
from the detector, towards the source.
In a way, Little's elementary wave is less like a traditional
wave and closer to the idea of the elusive ether, in that it is
like a flow, or a flux of material, while realizing that it makes
no sense to talk about what kind of material it is - it just is.
Twenty-five hundred years ago Parmenides said (and more recently,
as Leonard Peikoff is fond of saying) the universe is a "plenum".
That is, there are no gaps, no voids, no place where there is
nothing. That is what Little's theory has identified, the
elementary waves are what fill the universe - they are
omnipresent. According to Little's theory the waves exist for
every possible quantum state, for every variable parameter that
is possible.
Before we can revisit the double-slit experiment in the light of
elementary waves, we first need to understand what a particle is
in this new theory. In Little's view the elementary waves are
primary in the sense that they carry dynamic quantities such as
mass, momentum, energy, etc. It is the wave that triggers the
emission of the particle at the source; the state of that
particle, the dynamics of its motion, is determined by the
particular wave that stimulates, or induces, the emission. The
particle then follows the path of the wave; thus the wave moves
from the detector to the source and the particle travels from the
source to the detector. We should keep in mind that these are
_elementary_ waves, not waves in some medium. The wave itself is
moving from the detector to the source; no dynamic information
propagates through the wave; the wave carries the information as
it moves. That is why, as mentioned above, the elementary waves
may be best understood as being a flux or a flow. As a general
statement then, a particle will follow the straight line motion
opposite to its elementary wave, and will continue such motion
unless there is some interaction with another particle which can
change its direction. As in the case with Little's elementary
waves, Little's particles are not ghost-like, they are real.
There is no 'collapse of the wave function' which selects from an
array of probability waves a packet of waves which describe a
'real' photon. In the TEW, _all_ of the elementary waves and
_all_ of the particles are real existents.
Now we can look back at the quantum double-slit experiment and
try to make sense of the experiment using TEW as a guide. We
understand that there are elementary waves, which correspond to
all possible quantum states, that exist as real objects filling
the space around us. Further, think of coherence as a certain
likeness of waves which can then combine by one rule, and
incoherence a certain dissimilarity in waves which can then
combine by another rule. When the target, or detector, is placed
in position, the particles of which the detector consists impose
an 'organization' or coherence upon the existing waves. From
every point on the detector flows a complete set of waves that
uniquely reflect the state of the particle which imposed the
organization on the wave and they are all coherent with each
other; but they are incoherent with the waves flowing from other
points. So for any given point on the detector, the reverse
waves travel back towards the wall with the two slits, through
the slits and continue onwards to the particle source. These are
real waves which will interfere with each other; so, in some
cases there will be constructive interference and in others
destructive interference. The resulting intensity of the wave,
after interference, determines, at the particle source, the
likelihood of inducing the emission of a particle. The particle
then follows the path of the wave back to the detector.
Therefore, the pattern we see at the detector _is_ a consequence
of the interference of waves and the transmission of particles;
but, these are real waves and real particles and the pattern
occurs due to real processes. It is the intensity of the
elementary wave as seen at the source that determines the number
of particles that are induced. The pattern at the detector, then,
is due to the particles that follow the path of each wave back
from the source. In addition, all of the usual quantum mechanical
mathematics remains essentially the same - this new theory,
however, explains _why_ the mathematics works.
To see the dramatic contrast between the standard theory and the
TEW, we can summarize as follows: The standard theory creates a
wave-particle (or particle-wave) out of thin air. It is a
nebulous concept without referents in reality. In opposition to
the standard theory, the TEW identifies the existence of
elementary waves, which are real, primary, fundamental
constituents of reality, and it logically asserts, also in
opposition to the standard theory, the existence of real,
fundamental particles. These real, elementary waves are what
interfere with each other, accounting for the observed
interference pattern on the detector. While standard theory is
unable to state that particles go through either one of the
slits, the TEW unequivocally does so state and gives the
mechanism by which it is accomplished - the particle following
the path of the reverse wave. While standard theory has
ghost-like objects that disappear with 'wave collapse' in order
to give birth, so to speak, to a 'real' object, the TEW always
deals with real objects that do not 'disappear' when the
experiment is done. So, unlike the standard theory, the TEW
establishes a causal basis for the actions of real entities,
and completely contravenes the theory of the existence of matter
in some indeterminate state. This is why I stated above: For the
first time, the TEW has established, a rational basis for quantum
mechanics.
In Part 2 we will look at the famous 'uncertainty principle' in
light of what we have learned so far about the TEW, as well as delve
a little deeper into the mechanics of the TEW by discussing
additional experiments.
sjs@compbio.caltech.edu
Copyright (C) 1998 Stephen Speicher
Caltech 
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