This is the second part of a three-part article focusing on Lewis
Little's revolutionary Theory of Elementary Waves. It is
prefaced by a short digest, an "Executive Summary" highlighting
key elements of the article, leaving out technical details and
substantive information. It may also be helpful to establish the
overall context before reading the entire article.
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"Executive Summary" - Part 2
----------------------------
Schroedinger's wave equation is the mathematical cornerstone of
quantum mechanics. Heisenberg's uncertainty principle represents
the intellectual underpinnings of the standard theory.
The standard theory: if anything is definite in quantum
mechanics, it is mathematical; if anything is physical, it is
indefinite; there are uncertainties in the nature of matter that
cannot be overcome. The essence of the standard theory: It is the
measurement of particles that create their reality.
Heisenberg's uncertainty principle: there are fundamental limits
to which the accuracy of pairs of quantum variables can be
specified and measured. Examples: the uncertainty relation
between energy and time means that if you were able to localize a
particle at a given instant, it would not have any definite
energy; the more accurately you are able to determine the
location of a particle the less precise you can be about its
momentum.
The TEW identifies that the uncertainty is a consequence of the
anti-concept of wave-particle, along with the mistaken notion of
the forward motion of the wave.
Part 1 explained the TEW which posits the existence of real
fundamental particles and real fundamental elementary waves which
travel in the reverse direction of what has previously been
considered to be the case.
The standard theory interpretation of the Schroedinger wave
equation relies on probabilities which inherently possess
uncertainties which, in logic and according to the TEW, do not
exist for the real particle and the real wave. The uncertainties
are due to a mathematical construct and an illogical physical
interpretation.
In the TEW, the elementary waves exist as real objects. In the
standard theory, a particle exists as ghost-like particles,
giving rise to the alleged uncertainties. In the TEW, the
elementary waves exist as independent objects and there are no
uncertainties for any quantity or quality of real particles and
real waves.
The TEW refutes the Heisenberg uncertainty principle by
essentially exposing its false philosophical base and illogical
acausal premises.
The EPR experiment: Einstein and colleagues use a 'thought
experiment' to question the lack of causality in quantum
mechanics. EPR becomes a 'real' experiment and appears to violate
causality.
The standard theory interpretation of the experiment says that
even if two particles are separated by half the distance of the
entire universe there is a 'connectedness' between them. The
theory requires 'spooky action-at-a-distance' to explain
interactions that occur instaneously regardless of the distance
of separation.
Another theory: 'hidden variables', a kind of reality that lurks
behind quantum reality. To explain the EPR experiments our choice
seems to be between the acausal ghost-like reality of the
standard theory and the causal view of a 'hidden' reality that
cannot be seen.
The TEW says: again the assumed forward direction of the quantum
waves have misled the theorists; with that assumption causality
was doomed. The TEW explains the experiment with reference to
real particles, real waves, and the identification that the waves
move in the opposite direction of what has been supposed. There
is no 'spooky action-at-a-distance' required and strict causality
is restored.
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PART 2
------
In the late 1970's, I attended Richard Feynman's graduate seminar
at Caltech which was based on his book "Quantum Mechanics and
Path Integrals". Feynman told me that there were only two ways
to unseat Heisenberg's uncertainty principle: either you defeat
it experimentally or you find some other way to explain the
results of quantum mechanics. Feynman was right - Lewis Little
accomplished it by the latter of the two methods via his Theory
of Elementary Waves (TEW).
Just as Schroedinger's wave equation is the mathematical
cornerstone of quantum mechanics, Heisenberg's uncertainty
principle represents the intellectual underpinnings of the
standard theory. But, while Schroedinger had some interest in
physical reality, Heisenberg was not confined to such
restrictions. Heisenberg once said:
"The very fact that the formalism of quantum mechanics
cannot be interpreted as visual description of a
phenomenon occurring in space and time shows that
quantum mechanics is in no way concerned with the
objective determination of space-time phenomena".
More succinctly, the standard theory says, in effect, that if
anything is definite in quantum mechanics, it is mathematical,
and if anything is physical, it is indefinite. Quantum variables
are measurable things pertaining to the field of quantum
mechanics which can change, such as position, momentum, energy,
and time. Heisenberg's uncertainty principle states that there
are fundamental limits to which the accuracy of pairs of these
quantum variables can be specified and measured. That is the
uncertainty _principle_. There are many particular uncertainty
_relations_. For instance, the uncertainty relation between
energy and time means that if you were able to localize a
particle at a given instant, it literally would not have any
definite energy. There are similar relations between other pairs
of quantum variables. The most well-known uncertainty relation is
between position and momentum, where momentum is usually
understood to be the product of mass times velocity. The more
accurately you are able to determine the location of a particle
the less precise you can be about its momentum. More formally
stated, the uncertainty in location multiplied by the uncertainty
in momentum can never be less than a certain quantity. That
quantity, which is extremely small, is known as Planck's
constant.
As an illustration of how the standard theory views these
uncertainties, consider the single-slit experiment shown in
Figure 4. In this essentialized model our source consists of
electrons; the single slit in the wall has a width which is
denoted by 'Y'. The (by now) familiar interference pattern is
shown as the intensity experienced at the detector. When an
electron goes through the slit we then know its position, at
least to the accuracy determined by the width 'Y'. Since the
electron is considered to also be a wave, when it goes through
the slit, the wave interference results in the pattern seen at
the detector. Due to the probabilistic nature of the solution to
the wave equation we discussed in Part 1, the intensity due to
that particular electron is only known within a given
uncertainty. If we try to make a more precise determination of
the position of the electron by reducing the width of the slit,
the pattern on the detector widens, increasing the uncertainty in
the determination of the intensity due to this particle at this
particular location. The more precisely we are able to measure
the _position_ of the particle, the less precisely we can
determine its intensity. This is a concretization of Heisenberg's
uncertainty principle.
F I G U R E 4
--------------
| IIIIII|
| IIIIIII|
| IIIIII|
| IIII|
| II|
| III|
| IIIII|
| slit IIIIIII|
- - IIIIIIIII|
IIIIIIIIIII|
source- - -> Y (width) IIIIIIIIIIII|
(electrons) IIIIIIIIIII|
- - IIIIIIIII|
| IIIIIII|
| IIIII|
| III|
| II|
| IIII|
| IIIIII|
| IIIIIII|
| IIIIII|
WALL DETECTOR
These uncertainties are neither a consequence of our inability to
build more precise instruments for measurement nor a limitation
of the resolution of the devices that are used. The basic idea,
according to the standard theory, is that there are uncertainties
in the nature of matter that, _in principle_, cannot be overcome.
That is the intellectual cornerstone of modern quantum mechanics.
Heisenberg's uncertainty principle, with its various uncertainty
relations, embodies the essence of Kantianism: there are barriers
to our knowledge, limitations on what is measurable, and it is
impossible even to speculate on what cannot be measured.
In the TEW, Little identifies the fact that this whole view of
uncertainty is a consequence of, an artifact of, the anti-concept
of wave-particle, along with the mistaken notion of the forward
motion of the wave. When the particle is thought to be the wave
and when the wave is thought to move in a forward direction from
the source to the detector, the interpretation of the wave
function solution to the Schroedinger wave equation becomes a
probabilistic function that _inherently_ possesses uncertainties.
But these uncertainties do not exist for the _real_ particle and
the _real_ wave; the uncertainties are due to the mathematical
construct and physical interpretation underlying the standard
theory.
Recall that in the TEW, the elementary waves exist as real
objects and are available in a complete range of quantum states.
The waves travel from the detector towards the source, through
the slit, interfere and induce the emission of particles at the
source. The particle then follows the path of the waves back to
the detector. The intensity pattern has already been determined
by the dynamics of the waves prior to the particles even reaching
the detector. In the standard theory a particle exists in
multiple states, the ghost-like particles we discussed
previously, and gives rise to the uncertainties inherent in that
theory. In the TEW, it is the elementary waves that exist in
multiple states, but they exist as independent objects and do not
gain their reality by the 'collapse of the wave function'. In the
TEW there are no uncertainties for any quantity or quality
associated with the real particles and the real waves.
Little is careful to distinguish 'unpredictability' from
'uncertainty'. We may not know which particular wave leads to
particle emission at the source and, therefore, we may not know,
in advance, the particle momentum. But this fact is just a
consequence of our ignorance, our lack of knowledge, of not
knowing in advance the particular parameters which determine the
particle and which characterize the source. There is nothing that
is inherently uncertain in this process, nothing which by its
nature is indeterminate. The entire quantum process as described
by the TEW is determined by the nature of the waves and the
particles and by how they interact. There is nothing _in
principle_ that stops us from identifying the nature of the
parameters involved in the exact determination of particle
emission - it is just our current ignorance, not some inherent
uncertainty, of what strictly determines this level of quantum
processes.
Heisenberg published his uncertainty principle in 1927 and, along
with Niels Bohr, he became one of the founders of the standard
theory, which is sometimes referred to as the Copenhagen
interpretation of quantum mechanics. At that time some
theorists, most notably Albert Einstein, expressed concern over
the lack of causality in the theory. This concern of Einstein
engendered a debate with Niels Bohr in 1927 which, amazingly,
lasted until Einstein's death, almost three decades.
Unfortunately, very little was ever resolved. In 1935 Einstein,
along with Boris Podolsky and Nathan Rosen, published a paper
attacking the standard theory's view of physical reality. As they
stated in their paper, they concluded that "the description of
reality as given by a wave function is not complete." Although
their paper cannot be considered to be a fundamental or
devastating attack, the 'thought experiment' they offered
underscored a major problem with the standard theory. In honor of
the authors Einstein-Podolsky-Rosen, this experiment was dubbed
EPR and it has persisted these many decades through today.
There are elements in this 'thought experiment' which are
somewhat subtle, but EPR can generally be thought of in the
following way. Assume we have two particles (1 and 2) which have
interacted with each other and are now moving in opposite
directions at the same speed. If you can measure (without
disturbance) the position of particle 1, then you will
automatically know the position of particle 2, since they are
both moving at the same speed. According to EPR, if we can
predict with certainty "the value of a physical quantity, then
there exists an element of physical reality corresponding to this
physical quantity." Therefore, our knowledge of the position of
particle 1 itself establishes the reality of the position of
particle 2 without in any way making a measurement or observation
of particle 2. But this is contrary to the standard theory which
holds that the reality of particle 2 exists only when an act of
measurement or observation of the particle is performed. In
addition, since we already have an accurate measurement of the
position of particle 1 (which also then tells us the position of
particle 2) we could then accurately measure the momentum of
particle 2 directly. These independent measurements can be made
accurate to whatever precision we like. But this would be
contrary to the uncertainty principle which places limits on the
degree of our accuracy in measuring these combined quantities.
Bohr used his response to Einstein to further entrench his
wave-particle view of the quantum world; his idea of
'complementarity', the joining of wave and particle, was a
scientific pluralism applied to matter. Bohr firmly implanted his
view that an act of measurement, an observation, was what made a
particle 'real'. He identified an 'ambiguity' in the EPR idea;
namely that it presumed the ability to measure _without any
disturbance_ to the overall system. He argued that since no
measurement was taken of particle 2 (which act would have
established it's own reality) then the measurement of particle 1
must be responsible for the 'reality' of particle 2. The
presumption, therefore, is that a wave function must exist that
applies to particles 1 and 2, and the 'collapse of the wave
function' upon measuring particle 1 gives 'reality' to particle
2. This principle of Bohr's applies whether the particles are
separated by an inch or by a light-year. This is the source of
the famous 'spooky action-at-a-distance' (Einstein's words) idea
associated with the standard theory of quantum mechanics. It
represents the complete destruction of the idea of local
causality.
While the EPR 'thought experiment' is interesting from a
philosophic point of view, one might ask in what way does this
relate directly to science and to the TEW? The reason we have
spent time outlining the 'thought' experiment is that in the
decades since the original paper on EPR, a whole family of
_actual_ experiments has been devised. As with the double slit
experiments, the EPR experiments highlight the absurdity of the
standard theory and afford the TEW another opportunity to present
a rational explanation for observed events. In order to
understand the basis for these experiments, we must first
introduce and explain what is known as Bell's theorem, or more
precisely, Bell's inequality. (With apologies to the physicist
Heinz Pagels, who has presented a similar treatment, albeit with
a completely different objective in mind.)
Consider the essentialized model shown in Figure 5. Here we have
a source, similar to the ones we have used previously, except
that this particular source (a gun) is unique - it is a 'No. 2
pencil with eraser' gun. When the gun shoots, two pencils are
ejected simultaneously, each going in opposing directions. The
pencils move sideways; that is, rather than the eraser or the
pointed end facing forward, the length of the pencils face
towards the direction they move. The orientation of the pencils,
as they are ejected, is completely random, meaning that the
eraser end can be pointed anywhere within a circular direction in
the plane of its motion. Each successive _pair_ of pencils,
however, will have exactly the same orientation. Each of the
pencils, call them pencil A and pencil B, move in a direction
towards wall A and wall B respectively. Each wall has a wide
cutout in them allowing pencils of a certain orientation to fit
through. We will call these wall-cutout arrangements
'polarizers', since they allow pencils with a certain orientation
to pass through but effectively block out others. The angle of
these 'polarizers' can be changed during the course of our
experiment, but initially both have the same alignment. Behind
each wall are counters which keep records of the pencils that get
through the 'polarizers' and those that do not.
F I G U R E 5
--------------
_ _
| | | |
_ | | | | _
| | | | | | | |
| | | | | | | |
| | | | A * B | | | |
| | --- | |---------<----- *** ----->---------| | --- | |
| | | | * | | | |
| | | | | | | |
| | | | Source | | | |
|_| | | (pencils) | | |_|
Counter A | | | | Counter B
|_| |_|
Wall A Wall B
With the 'polarizers' aligned in the same direction, we would
expect the counters to record pencil events that looked something
like this.
A 010010010001100000100100000100...
B 010010010001100000100100000100...
The counters record a '1' for each pencil going through the
'polarizer' and a '0' for an event where the pencil did not make
it through. As would be expected, the events recorded for A
precisely match the events recorded for B, since the pair of
pencils are correlated (that is, they both have the same
orientation) and each of the 'polarizers' have the same
alignment.
Now let us change the alignment of the 'polarizers'. We will
rotate 'polarizer' A clockwise through an angle (say 20 degrees)
relative to B. Since each of the 'polarizers' do not have the
same alignment anymore, some of the pairs of pencils will not be
recorded the same for each counter. Some pencils getting through
A will not get through B, and vice versa. The recorded events
might look like this.
A 000010011000001010001010100010...
B 010010010000001010001010000010...
As indicated, the counting record shows there are events that no
longer match up between A and B due to the different alignment of
the 'polarizers'. In fact, the mismatch is 1 in every 10 events,
a 10% mismatch rate. Had we rotated 'polarizer' B
counterclockwise by the same angle, instead of 'polarizer' A
clockwise, we would expect the results to be essentially the
same. By fixing one 'polarizer' and rotating the other we are
creating results where the mismatches between the two act in an
independent manner. This makes sense. Why should the outcome of
the counter at A have any effect on the counter at B? One of the
counters is always used as the standard to judge the mismatches
with the other counter. If we were to double the angle of
'polarizer' A (from 20 degrees to 40 degrees) we would reasonably
expect the mismatch rate to exactly double.
If, however, we rotate A an angle of 20 degrees clockwise and
then rotate B an angle of 20 degrees counterclockwise, we
introduce a new possibility. By rotating A we lose the standard
for B and by rotating B we lose the standard for A. That means
when we compare the two counts for A and B, we will completely
overlook any double mismatches that may have occurred. That is,
if a particular event would show up as recording a pencil to go
through the 'polarizers' for both A and B when the 'polarizers'
are perfectly aligned, it might be that they both record a
failure to see the pencils at both A and B when the 'polarizers'
are both rotated in opposite directions. Therefore what might
have been a 1 and a 1 at both A and B is now a 0 and a 0; i.e. a
double mismatch has occurred. Therefore, the best case for
mismatches at a double angle would be twice that of the single
angle. The worst case, however, would not include the double
mismatches which would be undetectable. Therefore, stated more
formally, the mismatch for a double angle is always less than or
equal to twice the mismatch for a single angle. Mathematically,
this is:
M(2*angle) <= 2*M(angle)
This is known as Bell's inequality. These are the results we
would expect from a system that was governed by local causality:
that is, influences in the state of a system are a consequence of
a change in the system itself or are due to energy changes
transmitted into the system. In other words, Bell's inequality
should hold without regard to, or consideration of, 'spooky
action-at-a-distance'.
With this as background we can now look at an actual EPR
experiment. We require pairs of photons that are to be
polarized; that is, similar to the orientation of the pencils,
there is a precise direction in space associated with each
photon. Figure 6 shows a typical setup which appears similar to
the essentialized model we used with the pencil gun. The purpose
of our source is to generate photon pairs, moving in opposing
directions, which have their polarizations correlated, i.e.,
photons which have the same orientation in space. The orientation
of each pair of photons is random, but the correlation requires
the particular pair to possess the exact same orientation. In
general, these kinds of EPR experiments use sources such as
calcium or positronium atoms to generate the polarized photon
pairs. Actual polarizers replace our wall-cutout apparatus to
permit passage of photons possessing the correct orientation, and
photomultipliers (the counters) are used to detect and record the
photon events. There are many more details to these types of
experiments, but the above reflects their essence, which is all
we need in order to understand what is going on.
F I G U R E 6
--------------
_ _
| | | |
_ | | | | _
| | | | | | | |
| | | | | | | |
| | | | A * B | | | |
| | --- | |---------<----- *** ----->---------| | --- | |
| | | | * | | | |
| | | | | | | |
| | | | Source | | | |
|_| | | (photons) | | |_|
Counter A | | | | Counter B
|_| |_|
Polarizer Polarizer
A B
As in our 'pencil gun' experiment, we first keep both polarizers
aligned with each other so that the angle between them is zero.
The source generates pairs of photons which go off in opposing
directions towards each polarizer. Each pair of photons has the
same orientation, but the particular orientation of each pair is
random. If the orientation of the photon aligns to the
orientation of the polarizer, then the photon passes through and
is counted as a '1' event. If the photon does not pass through,
it is a '0' event. The results of such an experiment are shown
below and are very much like the results from the 'pencil gun'.
As we would expect, since each pair of photons has the same
orientation and the A and B polarizers are aligned the same, the
counts for A and B match perfectly.
A 001000110001001100000100001000...
B 001000110001001100000100001000...
When we rotate polarizer A a small angle, say 25 degrees, we find
results that are very similar to the 'pencil' experiment; that
is, we find a small number of mismatches between the A and B
count. The differences between the A and B count occur 1 in 10, a
10% mismatch rate.
A 001100110001001100000100001000...
B 001000110000001100000100001010...
When we double the angle of rotation for polarizer A to 50
degrees, the event counts are as indicated below.
A 101000110001011000010100001010...
B 001010110000001101000101001000...
The mismatches that have been counted are now 3 out of 10, a
mismatch rate of 30%. According to Bell's inequality, the
mismatch rate for twice the angle should be less then or equal to
twice the mismatch rate for the single angle. In other words,
since the single angle had a 10% mismatch rate we would expect
the double angle mismatch rate to be less then or equal to 20%.
The experiment shows, however, that the rate observed is not 20%,
but 30%. Bell's inequality has been violated! Recall that this
means, philosophically, that the idea of local causality has been
violated. This experiment has been performed repeatedly and the
results are essentially the same in all cases. This appears to be
a substantial confirmation of the 'weirdness' of quantum reality.
The standard theory is perfectly poised to explain this strange
phenomenon; it is, after all, just another example of the ideas
developed by Heisenberg and Bohr. We can speak of a
'connectedness' between these pairs of photons that have
interacted, whether their separation be measured in inches or
they are distanced by the size of the entire universe. We can
speak of how changing the alignment of polarizer A influenced the
polarization of the photons counted at B even if the polarizers
were light-years away. We can speak of the 'collapse of the wave
function' and the role it plays in the final result. We can
speak of these, and many other things, but the real essence of
the explanation of the standard theory lies in the _fundamental_
ideas of Bohr and Heisenberg - speculation about the underlying
reality of this experiment is nonsense. It is a fantasy to think
of the photons existing in a definite state. It is the
measurement we make of the particles that create their reality
and such measurements change the conditions of the experiment.
We really do not know that the polarizations of the pairs of
particles were originally correlated and the act of measurement
changes the very conditions upon which Bell's inequality was
derived.
Bell, like the physicist David Bohm, did not subscribe directly
to all these views; he thought that local causality could be
saved by postulating 'hidden variables', a kind of reality that
lurks behind quantum reality. Our choice seems to be between the
acausal ghost-like reality of the standard theory and the causal
view of a 'hidden' reality that cannot be seen. In the six
decades since Einstein and his colleagues published the EPR, it
was not until Lewis Little and the TEW that a rational
explanation could be given to this 'weird' EPR phenomenon.
Recall that in the TEW, elementary waves exist for all quantum
states which include all values of polarization. There are
elementary waves that flow from the 'counter' as well as waves
that flow from the polarizer itself. The polarizer is able to
impose a coherence, a similarity, on some of the 'counter' waves
with the same orientation as the polarizer. An opposite
orientation wave flows directly from the polarizer. These are
real, independent waves which arrive at the photon source and
independently induce emission of a photon. Each individual photon
will follow its reverse wave back to the source of the wave,
either the counter or the polarizer. The same process as
described, of course, occurs from each of the two opposite sides
(A and B) of the experiment.
The question that now arises is: how does the whole process
change when one polarizer is rotated at an angle relative to the
other? Assume a photon is first induced by an elementary wave
flowing from the detector; the photon will follow this reverse
wave back to the detector. But recall that the photon source is
such that it emits particles in pairs with the same orientation.
Since the polarizers are angled apart, there may not be an
elementary wave coming from the opposite direction that has the
proper orientation required for the induced emission. The waves
from the opposite direction may be offset in their polarization
by the angle that the polarizer has been rotated. Recall from our
discussion of the double slit experiment that it was the
intensity of the elementary wave, as seen at the particle source,
which accounted for the probability of stimulated emission of a
particle. That is exactly the case here, where the offset of the
polarizer reduces the probability of the particle emission at
least as far as the required polarized orientation is concerned.
The wave that corresponds to the opposite orientation associated
with the polarizer will induce emission of a photon, but the
photon will traverse its reverse wave back to the polarizer and
is never seen by the 'counter'. The dependence of the mismatches
on the angular rotation of the polarizer is therefore explained
without reliance on 'spooky action-at-a-distance' or otherwise
acausal behavior; the elementary waves _at the particle source_
determine the entire dynamic outcome of the experiment. The
dependence on the degree of angular rotation of the polarizer
turns out to be a consequence of the intensity of the elementary
waves experienced there, whose characteristics have already been
determined due to the reverse direction of the wave.
Of necessity, there were a number of simplifications that were
made in describing the above process. One area in particular, in
which the TEW clarifies a particle physics process, is in the
emission of the two correlated photons. The TEW represents the
cascade, the rapid succession of particles, to be all of a single
quantum process. This is important because it underscores that it
is the elementary wave interactions which determine all of the
dynamics prior to the emission of a single particle. This is lost
in the standard theory because of the anti-concept of
wave-particle, where the real elements of particle and wave
physics are disembodied.
It should be mentioned that there is a whole class of EPR
experiments which change the structure of the experiment while
the photons are in flight. For instance, the rotated polarizer
may be brought back into alignment after the photon particles
have been emitted. There is, in fact, one experiment, referred to
as a double delayed choice (both polarizers independently rotated
after particle emission), where the results, under certain
circumstances, are predicted by Little to validate the TEW while
contradicting the expectations of the current theory. It is
beyond the scope of this article to detail the process involved.
Suffice it to say that there is nothing fundamentally different
required for the TEW to make sense of such experiments. I just
want to note here that the TEW does not require a particle to
always follow a single reverse wave back to its source in all
instances. Such a rigid requirement could not and would not
account for any dynamic system changes that might occur, which is
the case for most conditions outside of the laboratory
environment. The TEW details the physics of the 'jump'
conditions which permit a particle to follow more than just one
wave. This 'jump' also helps explain the scattering of particles
where their direction changes at a point of interaction. The
actual 'jump' of a photon requires the annihilation of the
original along with the creation of a new particle, which in turn
is dependent on the organization of the wave which produced the
scattering in the first place.
In summary, we have seen in Part 2 how the TEW refutes the
Heisenberg uncertainty principle by essentially exposing the
false intellectual base upon which it rests. Bell's inequality
and a whole class of EPR experiments were explained without
consideration of the philosophically illogical acausal premises.
As in Part 1 with the explanation of the double slit experiment,
a rational analysis is made possible primarily by positing the
existence of real fundamental particles and real fundamental
elementary waves which travel in the reverse direction of what
has previously been considered to be the case.
In Part 3 of this article we will focus on relativity and how it
relates to the TEW. We will also briefly mention some of the
philosophic and scientific concerns about the TEW theory.
sjs@compbio.caltech.edu
Copyright (C) 1998 Stephen Speicher
Caltech 
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