Auto Dynamics
Warren Dixon
Over the past few days I have been posting to news groups over the theories
opposing Einstein's theories of relativity, as part of my A Level R&A
Project. The main one I have been trying to gather information on is
Autodynamics as this seems to be the most documented. This has provoked
some "Very" different come backs.
Not only have people been posting to the news groups, but I have received
Nemours E-mails (which are very insightful) and there are very strong
opinions both for and against. My problem is that although I have received
MANY more responses in support of Einstein's theories, they all seem to
follow the same format...... "Einstein's theories are accepted, accept this
yourself". The several that I have got from AD supporters are very
passionate, and they tend to go out of there way to give me information on
the subject.
I have tried to Instigate arguments (or discussions) but I keep Receiving
the same belligerent answers and hope that Someone can 'show me' that one or
the other can be proven and if it is "unrealistic" why!
My last word is sorry to Todd, who I have really tried to get to argue with
me as he offered real answers and tried too show me (although I dug my heels
in). Todd, I have been listening, thanx.
Jim Carr
... research newsgroup snipped for the moment, relativity group
added with followups set there ...
"Warren Dixon" <xo...@dial.pipex.com> writes:
>
>Over the past few days I have been posting to news groups over the theories
>opposing Einstein's theories of relativity, as part of my A Level R&A
>Project.
I have not seen any posts on that subject in any of the newsgroups
this was sent to: sci.physics, sci.physics.particle, and the moderated
sci.physics.research newsgroup.
>The main one I have been trying to gather information on is
>Autodynamics as this seems to be the most documented.
You don't need to "gather" information on AutoDynamics, it is all
right there on their newsgroup. It would make a good "A levels"
project for you to sort out the history of that work and the way
the theory has narrowed its scope over time. It would make an
even better one if you spotted the two big mistakes they have on
their web site.
>I have tried to Instigate arguments (or discussions) but I keep Receiving
>the same belligerent answers and hope that Someone can 'show me' that one or
>the other can be proven and if it is "unrealistic" why!
Again, I have not seen any examples of that in the newsgroups this
article was initially posted to. That is, no examples of "instigating
arguments" on AutoDynamics or "belligerent answers" to same.
--
James A. Carr <j...@scri.fsu.edu> | Commercial e-mail is _NOT_
http://www.scri.fsu.edu/~jac/ | desired to this or any address
Supercomputer Computations Res. Inst. | that resolves to my account
Florida State, Tallahassee FL 32306 | for any reason at any time.
Tom Roberts
Here is one of two articles I posted to sci.physics.relativity in November
of 1996 about Autodynamics. I have NOT visited their web site since, and
make no claims whether or not the errors and confusions described below
remain true about their web site todsy.
Tom Roberts tjro...@lucent.com
--- BEGIN INCLUDED ANCIENT ARTICLE ---
Subject: A Physicist's Refutation of Autodynamics
ADMINISTRIVIA
-------------
Notation:
A paragraph indented by a <TAB> indicates an aside or comment not part
of the main text. Such a paragraph beginning "OBJ" or "ANS" indicates
my anticipation of an objection and my answer to it.
Math: A * B indicates multiplication; A / B is division; X ** Y indicates
exponentiation; = is mathematical equality (NOT the FORTRAN meaning);
== means "is identically the same as"; sqrt(X) is the square root of X.
A PHYSICIST'S REFUTATION OF AUTODYNAMICS
----------------------------------------
by Tom Roberts, tjro...@lucent.com
In this article I will give a strong argument on why Autodynamics
is not a viable theory.
All of my sources for Autodynamics come from the Web page
http://www.autodynamics.org, on November 1, 1996. While it
may be "untraditional" to critique a theory from a Website
rather than from papers published in technical journals, in
this case it is my only option (Autodynamics has a very
sparse literature, and I don't have access to the journals
mentioned in the Website).
In this discussion I will not quibble about individual experimental
details or how Autodynamics purports to more properly explain them.
Instead I will discuss the central equations of Autodynamics, and why
they inherently imply unacceptable consequences. Thus, my refutation
rests not in experiments, but upon general theoretical grounds.
I will show that Autodynamics does not conform to some very basic
requirements of any physical theory.
In the Autodynamics section "...FRAMES: Derivation 2"
[http://www.autodynamics.org/Frames/Deriv2New.html], equation 19
gives the Autodynamics "Simplified Lorentz Equations". These are then
used to derive equations relating velocities, forces, and Kinetic Energy
among various coordinate systems. The problem with the entire approach
is that these transformation equations do not form a group (see Appendix
for proof; it is trivial and unenlightening, so I have relegated it to
an Appendix).
Einstein said "Keep things as simple as possible, but no simpler."
The Autodynamics "Simplified Lorentz Equations" went too far, and
in their simplification they lost an essential component of the
meaning. The original Lorentz Equations, of course, do form a group.
If my audience were composed of physicists, I would end right here,
present the Appendix, and be done (though most of the audience would
wonder why I bothered...). As this is sci.physics.relativity and not
the "Physical Review", I will expand upon why it is essential that
coordinate transformations form a group.
OBJ1: But equations 19 are NOT transformation equations. We
never claimed they were.
ANS1: You're right, in a far deeper sense than you probably
realize. They are indeed not transformation equations because
they do not provide a 1-to-1 mapping from one set of coordinates
to another (and also because they do not form a group). But
then why do you differentiate them to find the transformation
of velocities, forces, and KE? The only justification for doing
that is if they are indeed the transformation equations. As far
as I can tell, eqn 19 serves as transformation equations in the
derivation. In "...LIGHT SPEED" it says "To shift from one
observer to another, the velocity transformation equation is used
[...]." This equation is derived from equation 19. (See my
"Opinions" article for more discussion of the steps from eqn 19
to eqn 21.)
OBJ2: Your so-called refutation rests purely on theoretical
grounds. Science rests on EXPERIMENTS. Autodynamics provides
a simpler explanation of several experiments.
ANS2: The theoretical grounds upon which I base my refutation
are the distillation of literally billions of experiments --
you cannot just dismiss them out-of-hand. They are also an
explicit statement of basic modes of human thought and
perception, and seem so fundamental that any theory which does
not adhere to them MUST at least provide a detailed description
of how these ideas need to be modified, and why. Autodynamics
does not do this. See my "Opinions" article for more discussion
of this important point. Autodynamics displays such a blatant
disregard of the physics literature that the third statement in
OBJ2 is highly suspect (see my "Opinions" article).
The fundamental assumption of all physics is that there is an underlying
"something" out there which is independent of all observers, and which
is basically understandable by humans. That is, that there are regular
and quantifiable Laws which govern phenomena in the real world. And
these Laws exist independent of which observer applies them -- both the
phenomena and the Laws that govern them are independent of an observer's
point of view, position in space, position in time, or any other personal
attribute of the observer.
Now consider multiple observers making measurements of the same set of
phenomena. We will neglect the organizational issues of how they arrange
to not bump into each other (etc.). We will also permit each observer
to select her own coordinate system, in whatever manner she chooses.
{Free suggestion to the next Einstein: many of our conceptual
difficulties center around coordinate systems; can you formulate
physical laws WITHOUT using any coordinate system? Autodynamics
makes no attempt to do so, and I will not pursue this aside.}
As each observer is observing the same phenomena, there must be a
definite relationship between their individual measurements.
If observer A uses a coordinate system F to make measurements,
and observer B uses coordinate system F' for measurements, and they both
observe the same phenomena, then there MUST be some definite relationship
between their measurements because they are measuring the same phenomena.
If observer A uses F to measure everything of importance about F', then
these measurements (using F) of F' should enable A to relate A's measurements
of the phenomena (using F) to B's measurements of the same phenomena
(using F').
We call this relationship between measurements in two different
coordinate systems a "coordinate transformation". In a quantitative
mathematical environment there must be definite equations specifying
this transformation. From the physical situation, measurements in F of
F' must be sufficient to relate measurements in F' to measurements in F.
In the above discussion we could exchange the labels A and F with the
labels B and F'. We immediately see that the transformation equations
relating F to F' must be the inverse of the equations relating F' to F.
And if F and F' are merely different labels for a single coordinate
system, there must also be an Identity transformation which relates
a coordinate system to itself.
If instead of two observers there are three (call the third C and her
coordinate system F"), any of the labels in the above discussion
could be replaced by the labels C and F". There must be transformation
equations relating all three coordinate systems in pairs:
F -> F' F' -> F
F -> F" F" -> F
F' -> F" F" -> F'
And moreover, all of these transformation equations must be consistent.
As all three observers are measuring the same phenomena, it cannot
matter whether one relates the measurements of A and C by using F -> F"
or by using F -> F' and F' -> F".
EXAMPLE 1: let A use CGS units, B use MKS units, and C use
English units. Then it is clearly possible to relate each
set of measurements to the other sets. And it makes no
difference by which path the relationship is followed
(within experimental errors and arithmetic accuracy).
EXAMPLE 2: consider the Gregorian, Mayan, Julian, Hebrew,
Hindu, Chinese, Sumerian, and Islamic calendars.
You clearly need the measurements in one calendar of the
origin of another calendar before you can relate dates
among the different calendars (you also need additional
measurements because months are not the same length, etc.).
But it is clearly possible to do so, because the underlying
phenomena (days, seasons, moon phases, etc.) are the same.
The details may be difficult, but in principle it is possible.
These are trivial examples based on scale and origin differences.
They do, however, illustrate the principle that different
coordinate systems can be related to each other via the
underlying physical phenomena.
The above discussion has not specified anything about A, B, or C, or
F, F' or F". Thus it must apply to all possible observers and to all
possible coordinate systems.
This is now enough to declare: The set of all coordinate transformations
must form a group. The group composition rule is clearly successive
application of transformation. The above discussion has established
the four group criteria:
1. There is an Identity in the group.
2. The composition of any two members of the group is also
a member of the group.
3. Every group member has an inverse which is in the group.
{The composition of any member with its inverse gives
the Identity member.}
4. The composition of any 3 group members is associative.
That is, (A*B)*C = A*(B*C), where '*' represents composition.
{O.K. I have not established item 4. I leave that as an
interesting exercise for the reader. It is not used below.}
{O.K. I have glossed over some mathematical details. This is a
physics discussion, not mathematics. Start a new thread if you
insist on discussing this.}
It is important to remember that it is coordinate transformations which
form a group, not coordinate systems. The Identity transformation maps
any given coordinate system to itself -- this has no relation whatsoever
to any concept of "absolute space" or any "preferred reference frame".
The understanding that coordinate transformations form a group is a
compelling (and powerful) observation about how observers and phenomena
interrelate. It has no dependence upon Special Relativity, and depends
only upon the implicit physical situation of multiple observers
measuring phenomena.
But it is a strong underpinning of Special Relativity. See
my recent article posted to sci.physics.relativity --
Subject: A Physicist's Derivation of Special Relativity.
That article uses this group requirement to deduce the
transformation equations of SR.
The "Simplified Lorentz Equations" of Autodynamics fail item 2.
The successive application of two such transformations does not
generate another such transformation. This is the kiss of death
for a theory, because it implies that the form of the transformation
is not the same for all observers. That is, the physical laws of the
theory are not independent of the personal details of an observer.
That is completely unacceptable.
Note that the Autodynamics website contains several statements to the
effect that Einstein's error was to surreptitiously introduce a third
coordinate system into the discussion, and that his approach does not
make sense without this third coordinate system. I was unable to follow
their argument, but I suspect they will jump with glee on the above
discussion, pointing out that it inherently requires three observers
and three coordinate systems. I merely point out that it makes no
sense to propose a theory which artificially limits the world to one or
two observers. Science is inherently ecumenical -- any number can play.
While the above discussion happens to use three observers, it clearly
generalizes to any number.
The fact that Autodynamics fails such a fundamental tenet of scientific
theory is both interesting and disappointing. My second article
discusses this further. It is
Subject: A Physicist's Opinion of Autodynamics
Tom Roberts tjro...@lucent.com
APPENDIX -- PROOF THAT AUTODYNAMICS TRANSFORMATIONS DO NOT FORM A GROUP
-----------------------------------------------------------------------
In the Autodynamics section "...FRAMES: Derivation 2"
[http://www.autodynamics.org/Frames/Deriv2New.html], equation 19
gives the Autodynamics "Simplified Lorentz Equations". In my ASCII
notation they are:
x' = v1 * t / sqrt(1 - B1**2) 1
t' = t / sqrt(1 - B1**2) 2
Here x and t are measurements in F; x' and t' are measurements in F';
B1 is "beta-sub-1"; B1 == v1/c for the motion of F measured in F'.
This holds for any arbitrary v1 (velocity between frames F and F').
Introducing observer C (coordinate system F"), we also get from their
equation 19:
x" = v2 * t' / sqrt(1 - B2**2) 3
t" = t' / sqrt(1 - B2**2) 4
Here x' and t' are measurements in F'; x" and t" are measurements in F";
B2 is "beta-sub-2"; B2 == v2/c for the motion of F' measured in F".
This holds for any arbitrary v2 (velocity between frames F' and F").
We can also use their equation 19 to directly relate F" to F:
x" = v3 * t / sqrt(1 - B3**2) 5
t" = t / sqrt(1 - B3**2) 6
Here x and t are measurements in F; x" and t" are measurements in F";
B3 is "beta-sub-3"; B3 == v3/c for the motion of F measured in F".
This holds for any v3 (velocity between frames F and F").
Note that B1, B2, and B3 relate the reference frames, not measurements
of phenomena (ditto for v1, v2, v3).
Substituting 1 and 2 into 3 and 4:
x" = v2 * t /( sqrt(1-B1**2) * sqrt(1-B2**2) ) 7
t" = t /( sqrt(1-B1**2) * sqrt(1-B2**2) ) 8
For these transformation equations to form a group, equations 5 and 6
must be the same as equations 7 and 8. As these transformation equations
hold for all x and t (and all x" and t"), we can equate the factors
of t:
v3 / sqrt(1 - B3**2) = v2 /( sqrt(1-B1**2)*sqrt(1-B2**2) ) 9
1 / sqrt(1 - B3**2) = 1 /( sqrt(1-B1**2)*sqrt(1-B2**2) ) 10
Substituting 10 into 9 we get:
v3 = v2 11
Substituting 11 into 10 we get (remember B1 == v1/c, etc.):
1 = 1 / sqrt(1 - v1**2 / c**2) 12
Solving for v1 we get:
v1 = 0 13
This is very strange -- we started out with arbitrary v1 and v2, but
have concluded that v1=0. Clearly we have a contradiction.
Thus, when composing two Autodynamics transformations, the result will
be another Autodynamics transformation ONLY when one of the original two
transformations is the identity transformation (V=0).
Clearly the set of Autodynamics transformation do not form a group,
because the composition of any two transformations does not give
another transformation.
Dries van Oosten
On 19 Feb 1998, Warren Dixon wrote:
> Over the past few days I have been posting to news groups over the theories
> opposing Einstein's theories of relativity, as part of my A Level R&A
> Project. The main one I have been trying to gather information on is
> Autodynamics as this seems to be the most documented. This has provoked
> some "Very" different come backs.
>
> Not only have people been posting to the news groups, but I have received
> Nemours E-mails (which are very insightful) and there are very strong
> opinions both for and against. My problem is that although I have received
> MANY more responses in support of Einstein's theories, they all seem to
> follow the same format...... "Einstein's theories are accepted, accept this
> yourself".
I distance myself from people who say that. I myself have made a posting
here in which I have described my previous encounters with AD supporters.
If you want, I can send you (through personal email, these groups have
seen enough of AD) a description with why the AD people are wrong in their
accusations to SRT and why their own derivation is unacceptably sloppy.
Also, Mr. Carr (or wasn't it you?) has pointed out a few times already in
these groups that there have been experiments with autodynamics and the
data didn't look good for the AD people. The reason that the people who
have actually thought about don't respond is because they have done so so
many times already.
> The several that I have got from AD supporters are very
> passionate, and they tend to go out of there way to give me information on
> the subject.
>
> I have tried to Instigate arguments (or discussions) but I keep Receiving
> the same belligerent answers and hope that Someone can 'show me' that one or
> the other can be proven and if it is "unrealistic" why!
If you want to know, mail me personally about it, because I don't want to
start the discussion on this group again.
Dries van Oosten
// No more drugs for that man.
// Standard disclaimer applies.
[Sci.physics.research moderator's note: given Tom Roberts' post refuting
autodynamics, we urge that further discussion of the subject be taken
to sci.physics, and we have taken the liberty of setting followups to
that group. - jb]
Tom Roberts
Here is the second Article about Autodynamics which I posted in November 1996.
Again, I have not visited their site since, and have no idea whether or not
the errors and confusions I describe are still present on their site.
Tom Roberts tjro...@lucent.com
--- BEGIN ANCIENT INCLUDED ARTICLE ---
Subject: A Physicist's Opinion of Autodynamics
ADMINISTRIVIA
-------------
Notation:
A paragraph indented by a <TAB> indicates an aside or comment not part
of the main text. Such a paragraph beginning "OBJ" or "ANS" indicates
my anticipation of an objection and my answer to it.
Math: A * B indicates multiplication; A / B is division; X ** Y indicates
exponentiation; = is mathematical equality (NOT the FORTRAN meaning);
== means "is identically the same as"; sqrt(X) is the square root of X.
Abbreviations:
AD == Autodynamics
SR == Special Relativity
GR == General Relativity
wrt == with respect to
A PHYSICIST'S OPINION OF AUTODYNAMICS
-------------------------------------
by Tom Roberts, tjro...@lucent.com
My earlier article (Subject: A Physicist's Refutation of Autodynamics)
presented a technical refutation of AD (http://www.autodynamics.org).
This article presents a collection of random musings which occurred
to me while investigating that Website and preparing an article on
why I believe that Autodynamics will not ever enter mainstream physics.
I have separated my posting into two articles, because I expect a
protracted flame war from the advocates of AD. That's understandable --
they have clearly expended a lot of effort on their Website and enormously
more emotional energy in their devotion to "The Cause".
Mass Marketing comes to physics. Their Website even advertises
T-shirts touting Autodynamics (!).
I expect that this article will generate more flames than the first one;
by separating the two parts I hope to permit people interested in the
narrow technical aspects to not get drowned out by those who disagree with
my personal opinions and suggestions.
This article contains the following sections:
1. Thoughts on general aspects of physical laws.
2. Thoughts on physicists and their reactions to crackpots.
3. Thoughts on scholarship and accuracy in publications.
4. Observations about Autodynamics.
5. Conclusions
I decided to prepare and post these articles initially because I felt
that the AD advocates at www.autodynamics.org presented an
unwarranted "paranoid" case about physicists in general (see section
2 below). I visited the Autodynamics Website out of curiosity and a
faint hope that they had actually discovered something important and
useful; as I said in the last paragraph of my first article, I was
truly disappointed to learn they had not.
My other motivation for preparing and posting these articles is a
desire to advance people's knowledge about physical theories. I feel
that the anti-science "Creationists" are still a menace to science,
freedom, and intellectual discourse, and that the more people who have
some understanding of what physics is really about, the more likely we
are to prevail.
Autodynamics and its advocates are no danger at all. Not
because their ideas are wrong (which happens....), but because
they are honestly pursuing their cause in an intellectual
manner. The Creationists pursue their cause in a political
arena, seeking to banish intellectual discourse from the
entire political process (including the public schools!).
I would also like to think that my articles might convince the people
who have spent so much time and energy on AD to redirect their
efforts to some real physics. If not that, then I at least hope to
save other people the time and effort of pursuing a dead end.
I hope these articles will serve as a "primer" to others who think they
have a new theory which will replace all others. There are extremely
strong constraints on physical theories, and if the crackpots would
first make sure their theories take them into account, then their
writings would be much more likely to receive attention from the physics
community. This would be a service to BOTH the crackpots and to the
community as a whole. There are similarly strong constraints on the
scholarship of the authors of any putative theory -- understanding
those as well would be a service.
The most interesting new theories of the past have all involved major
modifications to the then-current constraints on physical theories --
I expect this to remain true in the future. But all theories which have
become mainstream have dealt with this explicitly and convincingly.
I just wish the crackpots would realize this simple truth.
1. THOUGHTS ON GENERAL ASPECTS OF PHYSICAL LAWS
-----------------------------------------------
There are some very general assumptions we all make which inherently
influence and direct our thinking. Many of them are inescapable ("I exist"),
and many are subject to historical accident (the use of English, having 10
fingers). Scientists have discovered many important truths about the world
which are so fundamental that any proposed theory which is incompatible
with them is usually rejected out of hand. These are very basic attitudes,
including such things as:
1. A theory must be falsifiable.
Thus, a theory "God makes everything happen" is not scientific,
because ANY phenomena can be explained by "God made it happen",
and any unobserved phenomena can be explained by "God didn't
make it happen". No counterexample could ever be found to such
a theory. Such a theory is also useless, as it can make no
predictions (no description of "God" is given).
2. The laws of physics are understandable and discoverable by humans,
at least in principle.
Without this, no physics is possible. Some parts may require
too high energies to ever be accessible, and other areas may
be inaccessible for other reasons. Some laws may be of only
statistical nature. All are probably subtle.
In particular, the laws of physics do not change for different
people or cultures. Culture and personalities may well affect
the path of discovery (and LACK of discovery), but not the laws
themselves. Sentient aliens are presumably included....
** Some of the consequences of this are that the laws of physics
cannot depend upon the personal attributes of an observer, and
that the laws of physics must be invariant for any reasonable
choice of coordinate system.
3. A theory must be able to make predictions about the real world.
That is, there must be some consequences of a theory which
can be tested. This is closely related to (1) above.
4. A theory should conform to other theories when their regions of
applicability overlap.
This is a powerful statement. The "classical limit" is a strong
touchstone for SR, Quantum Mechanics, and many other theories.
5. A theory must permit multiple observers to reconcile their
measurements.
That is, if multiple observers (people) observe a single
experiment, they should be able to confer and agree that
they all saw the same thing (at least in principle).
Physics is inherently ecumenical; any number can play.
(This is intimately related to 2 above.)
** One consequence of this is that the transformations among
coordinate systems must form a group.
6. Observations made on a physical system inherently interact with
and modify that system. Such actions cannot be ignored.
Observations are not a "special" operation independent of the
system being observed, but are an integral part of it. The
state of the observer cannot (in general) be separated from the
state of the system. In the "normal" world, and in the world
of AD and SR, typical observations can be shown to be negligible,
so this principle is not used below.
In addition, there are some general symmetries which it seems impossible
to avoid:
7. A theory should be isotropic and homogeneous in space.
That is, there should be no "preferred direction" or "preferred
origin" in the theory. An amazing new theory which carefully
explained WHY it does not meet this criteria might also be
acceptable, but the explanation would have to be convincing.
General Relativity is an example of a theory which required
modifications to this principle (in GR homogeneity is only local,
not global).
** Two consequences of this are that momentum is conserved and
angular momentum is conserved (with suitable definitions).
8. A theory should be independent of time.
That is, it should not behave differently at different times.
Objects of the theory may well have time dependencies, but the
theory itself should not. Again, a convincing explanation of
why this is violated might be acceptable.
** One consequence of this is that energy is conserved (with a
suitable definition of energy).
** A consequence of 7 and 8 combined is that only relative motion
is observable (motion of one object with respect to another).
Observe that the "Law of Conservation of Momentum" and the "Law of
Conservation of Energy" are not explicitly listed here. They are
consequences of what I consider to be more fundamental and basic
symmetries.
Note, however, that major revolutions in physics usually end up modifying
such basic concepts. Fish never see the water, and when somebody has a
major new insight about basic assumptions, it usually is revolutionary.
SR, GR, and Quantum Mechanics are three of the most well-known revolutions
in physics (not to mention Galileo, Copernicus, etc.). All of these
involved major changes in then-current basic attitudes.
{Free suggestion to the next Einstein: I have flagged with "**"
some of the more important consequences of these basic concepts.
They are all well known and described in the physics literature.
As previous revolutions in science have all included modifications
to these basic attitudes, study these consequences well and find
a hole in one of them -- that is the way to revolutionize physics.
AD has made no attempt to do so, and I will not pursue this aside.}
2. THOUGHTS ON PHYSICISTS AND THEIR REACTIONS TO CRACKPOTS.
-----------------------------------------------------------
First off, remember that physicists are people. As such we have a limited
professional lifetime. TIME is the primary coin of a professional career,
and spending it wisely is the sine qua non of success.
Crackpot theories have been proposed since science began. I label
a theory "Crackpot" if it meets most or all of the following:
A. It is described only in a "hand-waving" manner.
B. Its presentation exhibits a clear lack of understanding
of general physical principles (such as 1-8 above).
C. It is presented with obscure and/or confusing notation.
D. It is presented in a deliberately obfuscatory way.
E. It uses standard notation in a deliberately perverted way
(or in an inadvertently perverted way).
F. Its presentation is full of trivial errors or omissions.
G. Its presentation shows a clear lack of familiarity with
the relevant literature.
H. It makes wildly optimistic claims about revolutionizing
the foundations of science.
I. Its presentation claims to point out errors in existing
theory, without a detailed proof they are really errors.
J. In attempting to disprove an established theory, it uses
an erroneous or oversimplified description of that theory.
These items are not absolute, and it is certainly possible that a
"real" theory might meet many of them. These are more a sort of
check list to save time (and effort). A new theory which exhibits
many of these stigmata will probably be ignored by most scientists
-- not because they fear new ideas, but because it just probably isn't
worth their time and effort.
In another context, James "The Amazing" Randi said "Extraordinary
claims require extraordinary proof." While he was talking about claims
of the paranormal, the same principle applies here. If a new theory is
going to supplant or replace an existing one, it must be carefully
explained and meticulously documented. Slipshod scholarship will
not get anyone to listen, and will not convince anyone but other
crackpots.
3. THOUGHTS ON SCHOLARSHIP AND ACCURACY IN PUBLICATIONS.
--------------------------------------------------------
Scholarship and accuracy are basically an issue of being honest and
fair to the reader:
a. It is not fair to quote the one article which supports your
point while ignoring hundreds of others which refute it.
b. It is not fair to the reader to make trivial arithmetic or
spelling mistakes, because they cause confusion and delay.
c. It is not fair to make deliberately misleading statements.
d. It is not fair to take quotations out of context so their
full meaning is hidden or distorted.
e. It is not fair to use standard terminology or notation in
an unusual or misleading manner.
f. It is not fair to change notation and/or its meaning in the
middle of an article or series of articles.
g. It is not fair to make the reader guess what your notation
means; all notation should be defined.
h. It is not fair to the reader to be ignorant of the relevant
literature on the subject.
i. It is not fair to report inaccurate or erroneous results, as
that can cause confusion and wasted efforts.
j. It is not fair to omit discussions of experimental errors,
biases, or known inadequacies.
k. It is not fair to omit proofreading your writing and removing
gross mistakes.
l. It is not fair to make the reader guess which previous paper is
being discussed or criticized; references are essential.
m. It is not fair to omit references to other relevant papers;
neither to the reader nor to the other authors.
In summary, good scholarship requires time and effort on the part of
the author.
OBJ3: O.K. wise guy, how about your (lack of) scholarship in
these articles?
ANS3: Admittedly my scholarship is not perfect here -- I am matching
it to the medium (USENET), which is noted for its frequent lack of
any common sense at all (!). I believe my scholarship and accuracy
are adequate for the task, and are sufficiently higher than that
of the theory I am criticizing that the result is credible. As
always, it is a question of how much time to spend.
So far, I have not seen ANY seriously-studied analysis of AD
on sci.physics.relativity, but only the typical USENET flamewar
consisting of "you said" - "I did not, but you said" ... confusion.
While some of the messages included real and cogent criticism, none
so far have included what I consider to be the "stake through
the heart" which I am trying to describe here. I believe this article
significantly exceeds the usual USENET standard of scholarship.
Specifically, my list above in section 1 is arbitrary, and completely
a product of my own memory and biases. A more proper list would
be a summary of the many books and articles in the history and
foundations of science. At present I have neither the time nor
the inclination to prepare such a survey; the list above seems to
me to be adequate for the task at hand.
4. OBSERVATIONS ABOUT AUTODYNAMICS.
-----------------------------------
All of my sources for Autodynamics come from the Website
http://www.autodynamics.org, on November 1, 1996. While it may be
"untraditional" to critique a theory from a Website rather than
from papers published in technical journals, in this case it is my
only option (AD has a very sparse literature, and I don't have
access to the journals mentioned in the Website).
References to specific articles are as follows:
[Gal Simp] http://www.autodynamics.org/Frames/Deriv1.html
[Frames Lay] (URL lost) header is "...FRAMES: Layman"
title is "Frames in Relative Movement"
[Derivation 2] http://www.autodynamics.org/Frames/Deriv2New.html
[Muon Decay] http://www.autodynamics.org/Engaging/Engaging.html
Heading: TIME DILATION - Muon Decay
[Lorentz Inv.] http://www.autodynamics.org/Engaging/Engaging.html
Heading: LORENTZ INVARIANCE
[Neutrino] http://www.autodynamics.org/Engaging/Engaging.html
Heading: NEUTRINO SPECTRUM
[Entropy] http://www.autodynamics.org/Cosmos/Entropy.html
[Paper] http://www.autodynamics.org/Experiments/MuonDecy.html
In addition, I will occasionally reference my own recent postings
to sci.physics.relativity:
[Refutation] Subject: A Physicist's Refutation of
Autodynamics
[Derivation of SR] Subject: A Physicist's Derivation of
Special Relativity
If you cannot obtain a copy of these, email me at
tjro...@lucent.com for a copy.
According to the Website, AD is over 50 years old.
I would expect that such a mature theory would have a derivation
and arguments which have been carefully honed over five decades, so
that no details were omitted, no trivial or elementary errors would
remain, and no fundamental flaws appeared in the theory. In other
words, I would expect to find at least a sturdily-built edifice to
compare to the towering monument which is Special Relativity.
Instead, I found cobwebs. Cobwebs full of holes. Enormous holes.
During the past 50 years they have amassed a paltry amount of writing
(comparable in quantity to 3 or 4 weeks of homework in a graduate physics
program, but not in quality). What they have is poorly argued, lacking
in detail, full of elementary and trivial errors, and contains several
fundamental flaws. It appears to me that even the authors of AD
do not take it seriously, OR DO NOT EVEN HAVE A CLUE OF WHAT IT MEANS TO
TAKE A PHYSICAL THEORY SERIOUSLY.
This section is by no means a complete review of the Autodynamics
Website. It will merely record those thoughts and observations I had
while touring it, and while reading the papers I printed out.
This section contains the following subsections:
4.1 Specific technical errors
4.2 Examples of lack of understanding of basic physical concepts
4.3 Lack of scholarship
4.1 Specific Technical Errors
-----------------------------
4.1.1 The AD transformation equations do not form a group
-------------------------------------------------------------------
This was the conclusion of my first article [Refutation]; I will not repeat
it here. I will reiterate, however, that the physical consequences of
this fundamental failure of AD are devastating. It implies that the
"Laws of Autodynamics" change for each and every observer, and that
multiple observers cannot reconcile their observations with each other.
This is completely unacceptable in this post-Einstein world.
4.1.2 Absence of justification for Equation 10
----------------------------------------------
In [Derivation 2], in the sentence preceding equation 10, it says
"Without the extra coordinate system, AD describes position and time for
one frame of reference as only a function of time". No explanation
is given of why this is justified or possible. This is merely an "Ansatz",
or statement out of the blue. The entire argument beyond this point is
pure speculation, and based upon this Ansatz.
OBJ4: But isn't that what other theories do? Don't they
simply postulate some hypothesis and see where it leads?
ANS4: Well, yes and no. First, mainstream theories which do
such a thing make it explicitly clear when they do so; AD
buried it in the middle without any notice to the reader.
Second, mainstream theories make at least a passing argument
why the Ansatz makes physical sense; AD did not. And third,
mainstream theories like SR and GR have since found alternative
derivations which do not depend upon any Ansatz; AD has not.
OBJ5: But we DID justify this with a physical argument. Just
look at [... somewhere else, I don't know where ...].
ANS5: If you are going to derive a theory, you must either
include the entire argument or include references to places where
the reader can find the complete argument. You did neither.
4.1.3 Use of Incomplete Transformation equations
------------------------------------------------
In [Derivation 2] the argument leading from Equations 19 to equations 21
involves differentiation to obtain velocity transformation equations.
This is only justified if the Equations 19 are indeed transformation
equations. But they cannot be, because they do not form a 1-to-1 mapping
of one coordinate system (F) onto another (F').
OBJ6: But that doesn't matter. In F, the point P is always
at the origin (x = 0), so we don't need to consider any other x.
ANS6: By differentiating Eqn 19 you are saying in effect: "If
an object is moving wrt F and has its velocity measured in F,
then we can relate its velocity in F to its velocity in F' by
equations 21". But the argument leading up to equations 19 implicitly
requires x == 0. In the discussion immediately following equation 3
of [Derivation 2], it states "Yet Equation (3) has 3 velocities even
though it must only have 2." This is one of the few places in the
Website where I found a real physical argument, and the AD authors
completely ignored its implications (!). The act of differentiating
Eqn 1 to obtain eqn 3 is implicitly considering motion in F, but
the authors are puzzled why the term dx/dt appears in eqn 3 (dx/dt
is velocity measured in F, and appeared because of the differential
nature of differentiation). Their dogmatic claim that P is at rest
in F is incompatible with differentiation to obtain the velocity
transformation equations. In other words, they are trying to claim
that F can only be used to measure a single point, and simultaneously
are differentiating (which inherently involves neighboring points).
Please note the difference between x = 0 in OBJ6 and
x == 0 in ANS6.
4.1.4 Differentiation of Transformation Equations done improperly
-----------------------------------------------------------------
In [Derivation 2] the argument leading from Equations 19 to equations 21
involves differentiation with respect to t'. It is done using the
invalid rule:
dx'
--
dx' dt
-- = --------- {INVALID !}
dt' dt'
--
dt
Differentiation is NOT division, and this "rule" is invalid. This error
is in pure Calculus, not physics at all. The proper way to compute this
derivative is via the chain rule:
dx' dx' dt {valid only if x' is a function of t only,
-- = -- * -- and t is a function of t' only, which
dt' dt dt' don't necessarily hold.}
The proper equations require partial derivatives wrt both x and t, for
which my ASCII notation is woefully inadequate; this gives the basic
concept. Note that computing the second factor requires inverting equations
19 to obtain t as a function of t'.
Because of the specific form of equations 19, the invalid rule actually
gives the correct answer. The same error was used between equations 2
and 3, again fortuitously obtaining the correct answer.
OBJ7: Aren't you being overly pedantic, after all they got
the right answer.
ANS7: This goes right to the heart of the credibility of the
authors of AD. Not only do they not justify important steps
of the derivation, but some of their justifications are plain
wrong (though this particular error is correctable).
4.2 Examples of Lack of Understanding of Basic Physical Concepts
----------------------------------------------------------------
4.2.1 Lack of Understanding of what a Coordinate System is
----------------------------------------------------------
In [Gal Simp] the authors of AD attempt to show that using more than
one coordinate reference frame is "[...] useless, inoperative, and
superfluous" [para 4 of [Gal Simp]]. They base this argument on the
claim that "self observation of a point is absolutely impossible"
[Para 18 of [Gal Simp]].
In modern physics, a coordinate system (or frame of reference) is
no more (or less) than the ability to make measurements. In particular
it is NOT a physical entity, but is an abstract "ruler" against which
events can be marked and measured. An example is the lines of latitude
and longitude on the surface of the earth (this example is neither
inertial nor Euclidean, but it is still a valid and useful coordinate
system); the satellite GPS is a way of making direct measurements in it.
I don't know precisely what is meant by "self observation of a point"
(because measurement is certainly NOT "self observation"), but there
is surely nothing wrong with using a co-moving coordinate system to
measure the location of point P. Yes, it will be dull, and every
measurement will give the same x value, but it is not meaningless
and may well be important. Imagine that successive events will occur
at point P (e.g. the creation of a particle, and its subsequent decay).
Then the measurement that both occur at the same x value (in F) is probably
important.
Note that restricting the world to a single coordinate system is
extremely limiting: in a colliding beam experiment there are
three different reference frames (coordinate systems) of interest:
the Center of Mass (i.e. the laboratory), and the rest frames of
the two incident particles. You will need to do computations in
multiple coordinate systems if you ever want to compare colliding
beam experiments with fixed target experiments (in which one of
the incident particles is at rest in the laboratory). As I have
mentioned before, it is also unphysical to make such a restriction.
4.2.2 Lack of Understanding of What Relative Motion is.
-------------------------------------------------------
Paragraphs 2 and 3 of [Frames Lay] discuss a thought experiment in which
only you and Ricardo exist in the universe. The analogy "Now imagine that
velocity is now acceleration [...]" is hopelessly naive. It says "[...]
there is no reference point [...]", but there are TWO obvious reference
points: yourself and Ricardo (not the "infinite number" disparaged in the
next sentence). It then claims "Something must be different between the two
which answers the question 'who is moving?'". But that is NOT true. One
can choose to take your point of view (coordinate system) or Ricardo's
point of view (coordinate system). The answer to "Who is moving?" depends
upon which point of view is taken (and the equations of SR apply equally
well to either choice). From the way this last sentence is phrased, it
is clear that the authors simply don't understand this concept.
The conclusion that only relative motions are observable
is not limited to SR. It is a profound consequence of the
homogeneity, isotropy, and time invariance of space.
In the preceding paragraph (paragraph 2 of [Frames Lay]), the author lists
only three possibilities of interpreting a relative motion observed by
both you and Ricardo: "(1) you are moving and Ricardo is stationary,
(2) Ricardo is moving and you are stationary, or (3) both of you are moving
at one of an infinite possible summations of the observed speed." The
author doesn't understand that another choice is possible: (4) all of the
above. And that is the correct choice.
The concept "motion" cannot be divorced from the selection of a coordinate
system; in other words, "motion relative to this" (as a coordinate system
is abstract, there need not be a physical object involved). By choosing a
system comoving with Ricardo, (1) is the answer; by choosing a system
comoving with you, (2) is the answer; and by choosing any other coordinate
system (not comoving with either), (3) is the answer. The whole point of SR
is that you can do physics (and apply the SR equations) in ANY of these
coordinate systems (as long as the coordinate system used satisfies the
requirements of SR - inertial, etc.).
Similarly, the answers to the questions of para 3: "Who is getting
smaller?", "Whose clock is slowing?", "Whose mass is decreasing?"
all depend upon the answer to the prior question "Who is asking
these questions?". If you ask "Whose clock is slowing?", you will
answer "Ricardo's", and if Ricardo asks "Whose clock is slowing?"
he will answer "Yours". AND THERE IS NO INCONSISTENCY HERE.
If you and Ricardo were to consult with a third observer, that
observer would tell you "Yes, when you measure Ricardo's clock
you perceive it as running slower than yours. And yes, when
Ricardo measures your clock he perceives it as running slower
than his. And yes, when you each tell me how much slower the
other's is running, I can bring both measurements into agreement
with my own measurements by applying the appropriate Lorentz
transformation to the results." The fact that the Lorentz
transformations form a group ensures that this reconciliation
is possible.
Please note that the third observer is NOT essential to this
discussion. For you can also say "Yes, I agree, when I apply
the appropriate Lorentz transformation to Ricardo's measurements,
I obtain agreement with my own." And Ricardo can say "Yes, when I
apply the appropriate Lorentz transformation to your measurements,
I obtain agreement with mine."
The "Relativity Principle" being discussed here is merely a direct
consequence of the fact that whenever a question such as "Whose clock
is slowing?" is asked, SOMEBODY did the asking. And the answer can
depend upon who is asking (I assume that the question is retorical,
and is answered by the same person doing the asking; I did not frame
the discussion in this awkward way, the AD author did).
Note that this is in no way inconsistent with items 2 and 5 of
section 1 above. The LAWS of physics must be independent of an
observer's personal details, but the MEASUREMENTS of each observer
certainly can depend upon the details of the observer's coordinate
system (etc.) -- imagine coordinate systems using CGS and MKS units;
their values will differ, but they can be reconciled using the
appropriate coordinate transformation. While the differing answers
to the question "Whose clock is slowing?" are contrary to our
everyday experience, they are NOT inconsistent with each other
(when properly interpreted) or with the basic expectations of
physical theories of section 1.
This same lack of understanding is exhibited explicitly in the "frames tour"
(http://www.autodynamics.org/FrameTour/FTStart.html), which claims to be
a visual description of relative motion. In the 5th step of the tour
(FT5.html), the pictures are stated to be from "your video display boom
camera", but (1) no boom is visible, and (2) your image MOVES later in the
tour (FT10.html, again in FT11.html, ...). The author has gratuitously
introduced a THIRD reference frame, that of the camera.
Yes, this particular error could easily be fixed. But it
illustrates how basic and pervasive is the authors' lack of
understanding of concepts central to their argument.
4.2.3 Lack of Understanding of What Entropy Is.
-----------------------------------------------
In paragraph 3 of [Entropy] the author equates entropy with energy.
Entropy is NOT energy, and the difference is profound (and interesting).
4.2.4 Lack of Understanding of what Invariance Means
----------------------------------------------------
In paragraph 2 of [Lorentz Inv.], it says "From the moment AD discards
two frames in relative motion, the concept of 'invariance' becomes
meaningless". The concept of invariance is simply that the laws of physics
cannot depend upon which coordinate system you happen to choose -- the laws
are INVARIANT regardless of this choice. AD can certainly choose to use
only one frame (coordinate system) in their derivation, but they cannot
arbitrarily dismiss observations made using other coordinate systems.
Invariance is not "meaningless", even if their derivation doesn't use it.
And if they truly mean to impeach the modern concept of invariance,
then they need a cogent and compelling argument of why this is so.
Here (and elsewhere) it is merely stated as if it were an obvious
fact, with no supporting argument whatsoever.
4.2.5 Lack of Understanding of Experimental Errors and Environment
------------------------------------------------------------------
In paragraph 3 of [Neutrino] it says "A mass of 20 eV is accepted,
and simultaneously that this Neutrino is traveling at light speed. The
contradiction is evident throughout SR".
{I strongly suspect that this should have read "An upper limit
on the rest mass of the neutrino of 20 eV is accepted ..."
As far as I know, there is no experiment which rules out a
rest mass of 0, while I do remember quotes of an upper limit
around 20 eV. I have not looked recently, and there are probably
new experiments and papers which are relevant.}
As no references are given, I cannot go to the original papers to verify
that the original authors really did expect a 20 eV neutrino to travel
at light speed, but I seriously doubt it. As SR is a pervasive part of the
intellectual environment of such an experiment, such an expectation would
be unusual indeed! Rather, I suspect the situation is more like "We cannot
rule out a non-zero neutrino mass as long as it is less than 20 eV." The
experimenters probably made no stronger statement than that. The SR
environment would then imply "A non-zero rest mass would of course mean
that the neutrinos travel at slightly less than the speed of light, but
we did not measure this directly."
I suspect that these experiments involve neutrinos with energies
of at least several MeV. In SR, a 20 MeV object with a rest mass of
20 eV would travel at 0.999999 c. Many experiments might not be
able to distinguish that from 1.000000 c. The neutrino experiment
in which I participated included neutrinos of 1 to 50 GeV, which
SR and a 20 eV rest mass would imply travel at approximately
0.999999999 c. Our apparatus was completely incapable of measuring
either the neutrino velocity or its rest mass (neither was of
interest in that experiment).
The above-quoted "contradiction" is NOT "evident throughout SR". It is
only the AD authors' lack of understanding of the experimental environment
which caused them to perceive a contradiction at all.
4.2.6 Lack of Understanding of Special Relativity
-----------------------------------------------
In paragraph 7 of [Muon Decay] (beginning "Gamma is equal ..."), the
author claims "[...] it is necessary to eliminate the the position term
(v x)/c^2 from [the Lorentz equations]". He calls this "surreptitious"
elimination "magic".
Note that the AD author's notation "(v x)/c^2" would be
"(v * x)/c**2" in my ASCII notation.
There is nothing "surreptitious" or "magic" about this. Given the physical
situation described, the "gamma" of the AD article is relating a frame
co-moving with the particle to a frame at rest in the laboratory. In
the unprimed frame (co-moving with the particle), let the particle be
located at any x; clearly this value remains constant for the duration of
the experiment. Observe that in the discussion only time DIFFERENCES
are used; the origin of time is NOT significant. When using the Lorentz
equations to compute time differences, this position term will cancel
out (because both v and x are constant). Alternatively, you are free to
select the origin of the co-moving frame such that the particle is always
at x = 0; then this term is always zero (and still cancels out).
In any case, the "position term" is not "eliminated", it merely does not
contribute to anything of physical significance in this particular situation.
4.3 Lack of Scholarship
-----------------------
To anyone who has actually read a scientific paper, the lack of scholarship
exhibited throughout the AD Website is immediately obvious. I will
discuss only a few of the most blatant examples.
Scholarship is NOT an outmoded requirement of the past, or an incidental
or optional part of scientific discourse. The ability of others to
"check your work" is an integral part of the scientific process.
Besides, poor scholarship is extremely impolite, to both the reader and
to the original authors in the field.
4.3.1 Criticism of SR without ANY supporting argument
-----------------------------------------------------
In several places above I have pointed out where the AD authors claim
SR "made an error", or "performed magic", etc. In NONE of these cases
did the AD author bother to explain precisely how the error was made,
or argue or explain why it is an error. They simply claim an error was
made, and proceed with their (usually flawed) argument.
This is simply unacceptable. AD claims it is attempting to either "replace"
or to "supplant" SR (the verb depends upon which part of the Website you
look at). If they are really going to do this, they had better explain in
no uncertain terms what is wrong with SR. They have not done so; they have
not even tried.
As I quoted above, "Extraordinary claims require extraordinary proof."
Today it is extraordinary to claim that SR is wrong, and AD has presented
not a single shred of proof.
4.3.2 Absence of References
---------------------------
The AD Website contains MANY mentions of SR, but contains not a single
reference to any description of it. Thus they leave the reader guessing
about what precisely it is they are discussing. It is also grossly
ungracious and impolite to the original authors of SR. Good scholarship
demands the accurate citation of sources, so that the reader can verify
that the author interpreted the referenced material correctly. By
omitting references, the AD authors prevent a precise verification of
their claims.
This lack of references is intimately related to section 4.3.3.
4.3.3 Lack of Balance in Literature Usage
-----------------------------------------
Throughout the Website there is consistently a lack of a proper literature
search. In the few instances where specific papers are cited, they
consistently select one paper which indicates a possible incompatibility
with SR, or the one paper which supports their case. They completely
ignore numerous other papers which do not support their case, and they
totally ignore the numerous papers reporting experiments which have
been performed to specifically test SR. They offer no AD analysis of
these latter, giving no opportunity to really examine AD in detail or
to compare AD and SR directly.
When discussing neutrinos, they cite primarily an ancient paper by
Buechner and Van de Graaff, completely ignoring hundreds of experiments
since.
OBJ8: Isn't this just sour grapes? After all, you did work on a
neutrino experiment.
ANS8: No. The experiment I worked on was not directly applicable
to their argument. But I am a bit puzzled because AD
claims that the neutrino simply doesn't exist; we sure saw
lots of evidence for interactions which were completely
consistent with both electron and muon neutrinos, and were
inconsistent with any other known particles.
4.3.4 Egregious Typographical Errors
------------------------------------
In the Website version of [Paper], there remains an egregious typographical
error in the title. While not notable by itself, I believe that it does
indicate the level of self-criticism exhibited by the AD authors (i.e.
virtually none).
In the title, one of the destination e+ must really be an e-.
5. CONCLUSIONS
--------------
Autodynamics is not a credible theory. The presence of basic, fundamental
errors is devastating to the derivation of its basic equations. The lack
of scholarship by its authors lends no credibility to their work. It has
languished for 50 years in a well-deserved oblivion, and I have every
expectation that it will continue to do so.
OBJ9: Oh come now, do you have to be so cruel?
ANS9: I have to be honest. The authors of AD claim to have a
theory which will "supplant" or "replace" Special Relativity.
They have failed to make their case. Utterly.
OBJ10: So how could it be "fixed" or "improved" ?
ANS10: Frankly, I seriously doubt that AD could be salvaged at all.
The basic errors described above in sections 4.1.1, 4.1.2, and
4.1.3 are central to the theory -- if they were truly resolved (in
the obvious way) then the resulting theory would be isomorphic to
SR.
For a discussion of this point see [Derivation of SR].
That article shows that the basic concepts described
in section 1 above are enough to derive the equations
of SR. In particular, the constancy of the speed of light
is a conclusion, not an hypothesis.
If the authors really and truly think that their central ideas
are correct and SR is incorrect, and that they have a truly novel
resolution of their errors, then they should at least improve
their scholarship to a credible level. They MUST deal with the
basic issues presented in this article if they ever hope to
attract attention from the physics community at large (not simply
because I say so, but because of the general "inertia" of a large
community and the lack of time from individual members -- they
must get past the "crackpot filters"). The AD authors MUST
include a cogent and compelling argument of how and why existing
basic attitudes must be changed to accommodate Autodynamics.
In closing, I hope that future proponents of alternative theories will
read these articles and learn their lessons:
1) Think about basic attitudes and expectations of physical theories,
and their relationship to your theory.
2) Make sure that your theory is compatible with these basic attitudes
and expectations, or that you include a cogent and compelling
discussion on how and why they must be changed.
3) Spend the time to make your arguments complete and scholarly,
or you will lose all credibility.
OBJ11: Whew! Thank goodness that's over! Why did it have to be
so long? You surely used an enormous sledgehammer on a fly!
ANS11: Yes, this did get out of hand, and is VERY MUCH longer than
I expected when I started. It all comes back to scholarship:
I wanted to make mine so good that I could criticize theirs with
a clear conscience.
In summary, I have done to Autodynamics what most zealots and crackpots
should fear the most: I took them seriously.
Tom Roberts tjro...@lucent.com