Bogus Physics
Ken Arromdee
>> absolute rest. You _can_ say that the sun goes around the earth; the math
>> is just easier the other way.
>> Kenneth Arromdee
>
>Oh come on folks!!! The sun (universe) does not twirl around the earth!!!
>Einstein never even implied such a thing.
>Motion is relative *only* when considering inertial reference frames,
>as determined by Lawrence transformations.
>Rotation is definitely not an inertial reference frame.
>It is not a matter of mathematical complexity,
>the earth really does rotate.
>Put simplistically (as we must when posting to this newsgroup),
>if the universe spun around the earth, it would fly apart,
>and even nearby galaxies would be traveling faster than light.
>Similarly, the earth revolves around the sun,
>and the solar system revolves within our galaxy.
>These are not arbitrary conventions, they are facts.
>The amount of bogus physics in this newsgroup is astonishing.
> Karl Dahlke
This originally started with a challenge to a creationist to provide examples
of his statement that there are empirical propositions more established than
evolution, and he responded by saying the earth goes around the sun. Would
net.physics readers please tell me how accurate my response was, as far as
physics goes? (I am not a physics major, and it is quite possible I was wrong).
--
"We are going to give a little something, a few little years more, to
socialism, because socialism is defunct. It dies all by iself. The bad thing
is that socialism, being a victim of its... Did I say socialism?" -Fidel Castro
Kenneth Arromdee
BITNET: G46I4701 at JHUVM and INS_AKAA at JHUVMS
CSNET: ins_...@jhunix.CSNET ARPA: ins_akaa%jhu...@hopkins.ARPA
UUCP: {allegra!hopkins, seismo!umcp-cs, ihnp4!whuxcc} !jhunix!ins_akaa
David S Fry
>> Motion is relative *only* when considering inertial reference frames,
>> as determined by Lawrence transformations.
>> Put simplistically (as we must when posting to this newsgroup),
>> if the universe spun around the earth, it would fly apart,
>> and even nearby galaxies would be traveling faster than light.
>> Similarly, the earth revolves around the sun,
>> and the solar system revolves within our galaxy.
>> These are not arbitrary conventions, they are facts.
>> The amount of bogus physics in this newsgroup is astonishing.
>> Karl Dahlke
I don't intend to get involved in the evolution argument, but if the
universe would fly apart when rotating about the earth, it will just as
surely disintegrate when rotating about the sun. So that reasoning falls
apart. Nothing really rotates strictly about anything.
It is correct that Einstein spoke about inertial reference frames, but
a note to Mr. Dahlke: name calling begins at home. Refering to Lorentz
transformations as "Lawrence transformations" shows that your knowledge
in this field is also "bogus".
- David Fry
...!seismo!umcp-cs!aplcen!jhunix!ins_adsf
Johns Hopkins University
--------------------------------------------------------------------
"Rien n'est beau que le vrai, le vrai seul est aimable."
- Boileau
Kendall Auel
>>> The amount of bogus physics in this newsgroup is astonishing.
>>> Karl Dahlke
>
> I don't intend to get involved in the evolution argument, but if the
>universe would fly apart when rotating about the earth, it will just as
>surely disintegrate when rotating about the sun. So that reasoning falls
>apart. Nothing really rotates strictly about anything.
David Fry has just proven Karl Dahlke's point. The amount of bogus physics
_and_ bogus logic in this newsgroup is sometimes unbelievable.
^ ^
/O O\ Kendall Auel
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bhu...@sjuvax.uucp
>...
>>> Motion is relative *only* when considering inertial reference frames,
>>> as determined by Lawrence transformations.
>...
>>> Put simplistically (as we must when posting to this newsgroup),
>>> if the universe spun around the earth, it would fly apart,
>>> and even nearby galaxies would be traveling faster than light.
>>> Similarly, the earth revolves around the sun,
>>> and the solar system revolves within our galaxy.
>>> These are not arbitrary conventions, they are facts.
>>> The amount of bogus physics in this newsgroup is astonishing.
>>> Karl Dahlke
>
>
> I don't intend to get involved in the evolution argument, but if the
>universe would fly apart when rotating about the earth, it will just as
>surely disintegrate when rotating about the sun. So that reasoning falls
>apart. Nothing really rotates strictly about anything.
> It is correct that Einstein spoke about inertial reference frames, but
>a note to Mr. Dahlke: name calling begins at home. Refering to Lorentz
>transformations as "Lawrence transformations" shows that your knowledge
>in this field is also "bogus".
>
>
> - David Fry
> ...!seismo!umcp-cs!aplcen!jhunix!ins_adsf
> Johns Hopkins University
What reasoning falls apart? I fail to comprehend the (apparently)
extraordinary leap of logic that is required to reason from the specific
proposition, 'the universe does not rotate around the sun' to the general
proposition, 'nothing ... rotates ... about anything'. Fry owes us, at
least, an elaboration of this argument.
I cannot see either that misspelling 'Lorentz' nullifies any of Dahlke's
argument, which should be judged on its own merits.
In fact, the relativity theories currently in vogue provide for an intrinsic
determination of 'inertiality' of any frame. It is possible for an observer
to determine whether a frame is accelerated or not. Knowing this, one can
easily determine, through observation alone, the rates of rotation of most
objects about other objects. This is the subject matter of most modern
physics texts, so I refer you to them for elaboration.
As to name-calling, I read none of that in Dahlke's article. It is only
natural that someone who is even modestly acquainted with modern physics
would become upset at the plethora of unsupported assertions that appear
in this newsgroup. There is nothing the matter, per se, with being wrong:
having the opportunity to make mistakes is what learning and investigation
are all about. Making an assertion without any support is to maintain
a position solely on one's personal authority. Such a stance is rarely
illuminating.
Fry's point is, I think, that this newsgroup could be used more constructively
were we a little more tolerant of error.
Bill Huber
Pete Zakel
> transformations as "Lawrence transformations" shows that your knowledge
> in this field is also "bogus".
>
> - David Fry
So he didn't remember how to spell "Lorentz". That makes his knowledge bogus?
I know many programmers that can't spell or construct grammatical sentences.
They are still quite good programmers. How does lack of spelling knowledge
relate to physics knowledge?
--
-Pete Zakel (..!{hplabs,amd,pyramid,ihnp4}!pesnta!valid!pete)
Clayton Cramer
Misspelling "Lorentz" as "Lorintz", or "Larentz" would suggest that Mr.
Dahlke has at least read something about "Lorentz transformations" but
couldn't remember the spelling. Turning it into "Lawrence" suggests he
hasn't ever read anything on the subject -- just relying on what he heard
on the radio or at a party.
Michael McNeil
>In article <20...@jhunix.UUCP> ins_...@jhunix.UUCP writes:
>>>> 1) According to Einstein, it's relative--there _is_no_such_thing_ as
>>>> absolute rest. You _can_ say that the sun goes around the earth;
>>>> the math is just easier the other way.
>>>> Kenneth Arromdee
>>>Oh come on folks!!! The sun (universe) does not twirl around the earth!!!
>>>Einstein never even implied such a thing.
>>>Motion is relative *only* when considering inertial reference frames,
>>>as determined by Lawrence transformations.
>>>Rotation is definitely not an inertial reference frame.
>>>It is not a matter of mathematical complexity,
>>>the earth really does rotate.
>>>Put simplistically (as we must when posting to this newsgroup),
>>>if the universe spun around the earth, it would fly apart,
>>>and even nearby galaxies would be traveling faster than light.
>>>Similarly, the earth revolves around the sun,
>>>and the solar system revolves within our galaxy.
>>>These are not arbitrary conventions, they are facts.
>>>The amount of bogus physics in this newsgroup is astonishing.
>>> Karl Dahlke
>> I don't intend to get involved in the evolution argument, but if the
>>universe would fly apart when rotating about the earth, it will just as
>>surely disintegrate when rotating about the sun. So that reasoning falls
>>apart. Nothing really rotates strictly about anything.
>> It is correct that Einstein spoke about inertial reference frames, but
>>a note to Mr. Dahlke: name calling begins at home. Refering to Lorentz
>>transformations as "Lawrence transformations" shows that your knowledge
>>in this field is also "bogus".
>> David Fry
>What reasoning falls apart? I fail to comprehend the (apparently)
>extraordinary leap of logic that is required to reason from the specific
>proposition, 'the universe does not rotate around the sun' to the general
>proposition, 'nothing ... rotates ... about anything'. Fry owes us, at
>least, an elaboration of this argument.
>
>I cannot see either that misspelling 'Lorentz' nullifies any of Dahlke's
>argument, which should be judged on its own merits. {...}
>
>As to name-calling, I read none of that in Dahlke's article. It is only
>natural that someone who is even modestly acquainted with modern physics
>would become upset at the plethora of unsupported assertions that appear
>in this newsgroup. There is nothing the matter, per se, with being wrong:
>having the opportunity to make mistakes is what learning and investigation
>are all about. Making an assertion without any support is to maintain
>a position solely on one's personal authority. Such a stance is rarely
>illuminating.
> Bill Huber
Come on, people! It isn't just the misspelling, it isn't just the
strong language (whether you call it name-calling or not) -- Karl's
argument is completely wrong! Einstein's theory of general relativity
was published more than seventy years ago (1915) -- and it certainly
*does* allow non-inertial reference frames! Only Einstein's *special*
relativity (1905) is restricted in its application to inertial frames.
It's a shame knowledge of Einstein's theory isn't more widespread
(especially in net.physics!) so many years after it was published.
Though, I suppose, like they say of churches, net.physics isn't a
temple for saints, but a hospital for sinners. I imagine it must
be the memories of all those undergraduate physics classes, where
inertial reference frames were ground into our flesh, never to be
forgotten, while terms like "special" (applied to what one knew) and
"general" (applied to what one did not know) gradually slip away.
I *highly* recommend that people learn *more* about relativity!
An excellent up-to-date reference for those with a modicum of college-
level physics background is *Gravitation*, by Charles W. Misner, Kip S.
Thorne, and John Archibald Wheeler, published in 1973 by W. H. Freeman
and Co., San Francisco. This 1,310-page tome declares itself to be
"a textbook on gravitation physics (Einstein's `general relativity'
or `geometrodynamics')." The book is designed to provide a full-year,
rigorous, graduate-level course in gravitation physics -- intending,
as it says, "to give a competence in gravitation physics comparable to
that which the average Ph.D. {in physics} has in electromagnetism."
There is also an alternative route through the text ("Track 1") which
is less thorough. "It is suitable for a one-semester course at the
junior or senior level or in graduate school; and it constitutes --
in the opinion of the authors -- the indispensable core of gravitation
theory that every advanced student of physics should learn."
Mathematical prerequisites for Track 1 are "only vector analysis and
simple partial-differential equations." I highly recommend the book.
Additional references in relativity theory and gravitation physics:
Albert Einstein, *The Meaning of Relativity*, Fifth Edition,
Princeton University Press, Princeton, 1956. A mathematical
introduction to both the special and general theories.
Albert Einstein, *Relativity: The Special and General Theory*,
Crown Publishers, Inc., New York, 1961. An elementary
exposition of the relativity theories; only algebra is needed.
Bertrand Russell, *The ABC of Relativity*, Revised Edition,
George Allen and Unwin, Ltd., or Signet Science Library, 1958.
Another elementary introduction -- but no algebra is required.
Returning to Ken's original point, which started off this whole series
of articles, in the above reference Bertrand Russell writes as follows:
But in the modern theory the question between Copernicus and
his predecessors is merely one of convenience; all motion
is relative, and there is no difference between the two
statements: `the earth rotates once a day' and `the heavens
revolve about the earth once a day.' The two mean exactly the
same thing, just as it means the same thing if I say a certain
length is six feet or two yards. Astronomy is easier if we
take the sun as fixed than if we take the earth, just as
accounts are easier in decimal coinage. {Signet, pp. 13-14}
I would think this would finish the debate over what Einstein "never
even implied." However, it is still relevant to ask, what is the
status of Einstein's theory of general relativity in modern physics?
The following two sections from Misner, Thorne, and Wheeler's
*Gravitation* explore this question of alternative theories of gravity.
39.1. Other Theories
Among all bodies of physical law none has ever been found that
is simpler or more beautiful than Einstein's geometric theory
of gravity {...}; nor has any theory of gravity ever been
discovered that is more compelling.
As experiment after experiment has been performed, and one
theory of gravity after another has fallen by the wayside a
victim of the observations, Einstein's theory has stood firm.
No purported inconsistency between experiment and Einstein's
laws of gravity has ever surmounted the test of time.
*Query*: Why then bother to examine alternative theories
of gravity? *Reply*: To have "foils" against which to
test Einstein's theory.
To say that Einstein's geometrodynamics is "battle-tested"
is to say it has won every time it has been tried against a
theory which makes a different prediction. How then does one
select new antagonists for decisive new trials by combat?
Not all theories of gravity are created equal. Very few,
among the multitude in the literature, are sufficiently
viable to be worth comparison with general relativity or with
future experiments. The "worthy" theories are those which
satisfy *three criteria for viability: self-consistency,
completeness, and agreement with past experiment*.
*Self-consistency* is best illustrated by describing several
theories that fail this test. The classic example of an
internally inconsistent theory is the spin-two field theory
of gravity [Fierz and Pauli (1939) {...}], which is equivalent
to linearized general relativity {...}. The field equations
of the spin-two theory imply that all gravitating bodies move
along straight lines in global Lorentz reference frames,
whereas the equations of motion of the theory insist that
gravity deflects bodies away from straight-line motion.
(When one tries to remedy this inconsistency, one finds
oneself being "bootstrapped" up to general relativity {...}.)
Another self-inconsistent theory is that of Kustaanheimo
(1966). It predicts zero gravitational redshift when the
wave version of light (Maxwell theory) is used, and nonzero
redshift when the particle version (photon) is used.
*Completeness*: To be complete a theory of gravity must be
capable of analyzing from "first principles" the outcome of
every experiment of interest. It must therefore mesh with
and incorporate a consistent set of laws for electromagnetism,
quantum mechanics, and all other physics. No theory is
complete if it *postulates* that atomic clocks measure the
"interval" dTau {...} constructed from a particular metric.
Atomic clocks are complex systems whose behavior must be
calculated from fundamental laws of quantum theory and
electromagnetism. No theory is complete if is *postulates*
that planets move on geodesics. Planets are complex systems
whose motion must be calculated from fundamental laws for
the response of stressed matter to gravity. {...}
*Agreement with past experiment*: The necessity that a theory
agree, to within several standard deviations, with the "four
standard tests" (gravitational redshift, perihelion shift,
electromagnetic-wave deflection, and radar time-delay) is
obvious. Equally obvious but often forgotten is the need to
agree with the expansion of the universe (historically the ace
among all aces of general relativity) and with observations at
the more everyday, Newtonian level. Example: Birkhoff's
(1943) theory predicts the same redshift, perihelion shift,
deflection, and time-delay as general relativity. But it
requires that the pressure inside gravitating bodies equal the
total density of mass-energy, p = rho; and, as a consequence,
it demands that sound waves travel with the speed of light.
Of course, this prediction disagrees violently with experiment.
Therefore, Birkhoff's theory is not viable. Another example:
Whitehead's (1922) theory of gravity was long considered a
viable alternative to Einstein's theory, because it makes
exactly the same prediction as Einstein for the "four standard
tests." Not until the work of Will (1971b) was it discovered
that Whitehead's theory predicts a time-dependence for the
ebb and flow of ocean tides that is completely contradicted
by everyday experience {...}.
39.2. Metric Theories of Gravity
Two lines of argument narrow attention to a restricted class
of gravitation theories, called *metric theories*.
The first line of argument constitutes the theme of the
preceding chapter {i.e. Chapter 38 -- "Testing the Foundations
of Relativity"}. It examined experiment after experiment, and
reached two conclusions: (1) *spacetime possesses a metric;
and* (2) *that metric satisfies the equivalence principle*
(the standard special relativistic laws of physics are valid
in each local Lorentz frame). *Theories of gravity that
incorporate these two principles are called metric theories*.
In brief, Chapter 38 says, "For any adequate description of
gravity, look to a metric theory." *Exception*: Cartan's
(1922b, 1923) theory ["general relativity plus torsion"; see
Trautman (1972)] is nonmetric, but agrees with experiment and
is experimentally indistinguishable from general relativity
with the technology of the 1970's.
The second line of argument pointing to metric theories begins
with the issue of completeness (preceding section). To be
complete, a theory must incorporate a self-consistent version
of all the nongravitational laws of physics. No one has found
a way to incorporate the rest of physics with ease except
to introduce a metric, and then invoke the principle of
equivalence. Other approaches lead to dismaying complexity,
and usually to failure of the theory on one of the three
counts of self-consistency, completeness, and agreement with
past experiment. *All the theories known to be viable in 1973
are metric*, except Cartan's. [See Ni (1972b); Will (1972).]
In only one significant way do metric theories of gravity
differ from each other: their laws for the generation of the
metric. In general relativity theory, the metric is generated
directly by the stress-energy of matter and of nongravitational
fields. In Dicke-Brans-Jordan theory {...} {Brans and Dicke
(1961); Jordan (1959); Dicke (1962)}, matter and nongravita-
tional fields generate a scalar field phi; then phi acts
together with the matter and other fields to generate the
metric. Expressed in the language of section 38.7, phi is
a "new long-range field" that couples indirectly to matter.
As another example, a theory devised by Ni (1970, 1972) {...}
possesses a flat-space metric eta and a universal time
coordinate t ("prior geometry" {...}); eta acts together with
matter and nongravitational fields to generate a scalar field
phi; and then eta, t, and phi combine to create the physical
metric g that enters into the equivalence principle.
All three of the above theories -- Einstein, Dicke-Brans-
Jordan, Ni -- were viable in the summer of 1971, when this
section was written. But in autumn 1971 Ni's theory, and many
other theories that had been regarded as viable, were proved
by Nordtvedt and Will (1972) to disagree with experiment.
This is an example of the rapidity of current progress in
experimental tests of gravitation theory! {pp. 1066-1068.}
--
Michael McNeil
3Com Corporation "All disclaimers including this one apply"
(415) 960-9367
..!ucbvax!hplabs!oliveb!3comvax!michaelm
Rather than have one global frame with gravitational forces
we have many local frames without gravitational forces.
Stephen Schutz, statement in January 1966
final examination in course in relativity,
Princeton University
[To Ernst Mach, regarding confirmation at a forthcoming eclipse]
... If so, then your happy investigations on the foundations of
mechanics, Planck's unjustified criticism notwithstanding, will
receive brilliant confirmation. For it necessarily turns out
that inertia originates in a kind of interaction between bodies,
quite in the sense of your considerations on Newton's pail
experiment. The first consequence is on p. 6 of my paper.
The following additional points emerge: (1) If one accelerates
a heavy shell of matter S, then a mass enclosed by that shell
experiences an accelerative force. (2) If one rotates the shell
relative to the fixed stars about an axis going through its
center, a Coriolis force arises in the interior of the shell;
that is, the plane of a Foucault pendulum is dragged around
(with a practically unmeasurably small angular velocity).
Albert Einstein's appreciation to Ernst Mach, written on
June 25, 1913, while working hard at arriving at his
November 1915 formulation of standard general relativity
Ian Ferris
a short list of good books on relativity theory. Here's another:
*Einstein's Theory of Relativity* by Max Born, available from Dover
This is another book "for the general reader" but it's much more
detailed than most such books and also goes into the historical
background more thoroughly than any other book at this level I
know of. If you understand the physics but wonder how
Einstein ever thought of it, try
*'Subtle is the Lord ... ': The Science and the Life of Albert Einstein*,
by Abraham Pais, Oxford University Press (Hardback 1982, Paperback 1983)
Supposedly the reader can skip the mathematical and physical details
in this book, but I doubt the validity of this claim -- I regard
working it all out as a sort of lifetime homework assignment.
Dave Richards
>Dahlke has at least read something about "Lorentz transformations" but
>couldn't remember the spelling. Turning it into "Lawrence" suggests he
>hasn't ever read anything on the subject -- just relying on what he heard
>on the radio or at a party.
So as I understand it, knowledge that I acquire by word of mouth, ie.:
the radio, friends, a lecture by a professor; these sources are all
"bogus". So all the stuff that's important is printed, like in books,
magazines; like National Enquirer, etc.
Aside from that, you are still making a conclusion about the poster of the
article which may or may not have any validity. In fact, it sounds remark-
ably like a put-down.
Dave "Holler when you're hit!" Richards
Gadfly
> a note to Mr. Dahlke: name calling begins at home. Refering to Lorentz
> transformations as "Lawrence transformations" shows that your knowledge
> in this field is also "bogus".
>
> - David Fry
The hell it does. Think, Mr. Fry. Scientifically, even. By what
plausible hypothesis could a person know his subject matter cold but
make the blatant (hint: but homonymic) spelling error above? After
all, we've all seen Lorentz's name in the literature so often...
...Or have we? Well, I won't keep you in suspense any longer, Dave.
Mr. Dahlke, whom I know personally, is totally blind. If I were
you, Dave, I'd feel mighty small right now, but who knows, it might
just be a (no, stop Ken, don't inflict this pun on the world--you
promised to use your skill only for good, never for evil--no, please!)
Lorentz contraction.
--
*** ***
JE MAINTIENDRAI ***** *****
****** ****** 13 Mar 86 [23 Ventose An CXCIV]
ken perlow ***** *****
(312)979-7753 ** ** ** **
..ihnp4!iwsl8!ken *** ***
Jim Giles
>Returning to Ken's original point, which started off this whole series
>of articles, in the above reference Bertrand Russell writes as follows:
>
> But in the modern theory the question between Copernicus and
> his predecessors is merely one of convenience; all motion
> is relative, and there is no difference between the two
> statements: `the earth rotates once a day' and `the heavens
> revolve about the earth once a day.' The two mean exactly the
> same thing, just as it means the same thing if I say a certain
> length is six feet or two yards. Astronomy is easier if we
> take the sun as fixed than if we take the earth, just as
> accounts are easier in decimal coinage. {Signet, pp. 13-14}
Whatever Bertrand Russell's qualifications in mathematics are, no one
would ever accuse him of being a great physicist. One of the paramount
features of General Relativity is that the laws of physics should
appear the same in ALL reference frames. In a reference frame which
is fixed with respect to the average motion of the nearby stars, those
stars all appear to be traveling with low (relatively) velocities. In a
'reference frame' which is fixed to the spinning Earth, the nearby stars
appear to be traveling MUCH FASTER than the speed of light. (Consider A-
Centauri: radius of 'orbit' around Earth is 4.2 light years, it 'orbits'
once per day, total distance traveled per day is 2*4.2*PI light years or
about 26 light years per day.) The consequences of stars being tachyons in
one 'frame' and not being tachyons in the other would cause the observers
in the two frames to come to different conclusions about the laws of
physics in Earth local space (that is, the only way to reconcile the two
observations is to assume that there is a space-time singularity between
the two observers, but when they go to look they won't find one).
The bottom line is that rotation is LOCALLY discernable and is therefore
NOT a property of Einstein's reference frames (whether they are lorentz
frames or not). One way of locally measuring rotation is with a foucault
pendulum (which you even mentioned). Meanwhile ALL Einstein frames are
LOCALLY indistinguishable from lorentz frames.
For the definition of 'frame' and 'local' I suggest you read the first few
chapters of MTW ('Gravitation') again. I just did - fascinating stuff!
J. Giles
Los Alamos
gw...@brl-smoke.uucp
>strong language (whether you call it name-calling or not) -- Karl's
>argument is completely wrong! Einstein's theory of general relativity
>was published more than seventy years ago (1915) -- and it certainly
>*does* allow non-inertial reference frames! Only Einstein's *special*
>relativity (1905) is restricted in its application to inertial frames.
The idea that centrifugal force can be explained by the inductive
effect of all matter in the universe is known as Mach's principle.
This principle appears to be necessary for any theory that claims
that there is no absolute motion. Einstein originally supported
Mach's principle and tried to deduce it from general relativity,
but in later years he became less convinced of its necessity. The
concepts of "absolute", "relative", and "motion" are more subtle
than they appear, it turns out.
Because of the emphasis on teaching the special theory of
relativity, far too much emphasis is placed on so-called "inertial
frames" of reference. From a more general viewpoint, one has an
inertial frame (locally) whenever the metric is diagonal. It is
not always possible to diagonalize the metric by a differentiable
change of coordinates, let alone one corresponding to a "motion";
this observation has led to attempts to extend general relativity
using a more general notion of metric.
> 39.2. Metric Theories of Gravity
>
> Two lines of argument narrow attention to a restricted class
> of gravitation theories, called *metric theories*.
It should be noted that Einstein and other early workers in
relativity theory determined that the general theory was
incomplete, and attempted to extend it in various ways. Some
of these attempts generalized the idea of metric, but the most
successful theories were formulated in terms of the affine
connection of the tangent bundle, with metric introduced only
comparatively late in the formal development of the theories,
as a derived notion or as an independent-but-related notion.
My favorite formulation of the general theory, Schr" odinger's,
introduces the metric purely as shorthand for an entity that
can be produced from the affinity field. The emphasis on metric
has its origins in the Gauss/Riemann development of differential
geometry; related concepts have spread throughout linear
mathematics. The main complaint I have against Misner/Thorne/
Wheeler is that the book does not adequately prepare one for
understanding or investigating the more general theory, which
does not track the usual development of differential geometry.
The "pure affine" field theory yields a number of interesting
symmetries beyond those of general relativity. These are
expected to correspond to physical laws other than the
gravitational field equations. This was the motivating idea
behind the "unified field theory" program pursued by Einstein
and others, which has almost universally been called a failure
by textbooks. If one compares the structure of theories such
as Einstein/Straus/Kaufman with present-day non-Abelian gauge
field theories, it becomes apparent that Einstein as usual
knew what he was doing and was simply ahead of his time.
Gene Ward Smith
>In article <4...@3comvax.UUCP> mich...@3comvax.UUCP (Michael McNeil) writes:
>>Returning to Ken's original point, which started off this whole series
>>of articles, in the above reference Bertrand Russell writes as follows:
>>
>> But in the modern theory the question between Copernicus and
>> his predecessors is merely one of convenience; all motion
>> is relative, and there is no difference between the two
>> statements: `the earth rotates once a day' and `the heavens
>> revolve about the earth once a day.' The two mean exactly the
>> same thing, just as it means the same thing if I say a certain
>> length is six feet or two yards. Astronomy is easier if we
>> take the sun as fixed than if we take the earth, just as
>> accounts are easier in decimal coinage. {Signet, pp. 13-14}
>
>Whatever Bertrand Russell's qualifications in mathematics are, no one
>would ever accuse him of being a great physicist. One of the paramount
>features of General Relativity is that the laws of physics should
>appear the same in ALL reference frames. In a reference frame which
>is fixed with respect to the average motion of the nearby stars, those
>stars all appear to be traveling with low (relatively) velocities. In a
>'reference frame' which is fixed to the spinning Earth, the nearby stars
>appear to be traveling MUCH FASTER than the speed of light. (Consider A-
This "faster than light" motion is merely conventional. It has NOTHING
WHATEVER to do with tachyons or real faster than light motion. Russell is
correct (almost) in his quote above. You are dead wrong. Try writing a rotating
coordinate frame in GR (not hard) and you will see.
>For the definition of 'frame' and 'local' I suggest you read the first few
>chapters of MTW ('Gravitation') again. I just did - fascinating stuff!
You need to do more than read it (we both have, apparently). You need
to understand it. Read it again, using your noggin.
ucbvax!brahms!gsmith Gene Ward Smith/UCB Math Dept/Berkeley CA 94720
Fifty flippant frogs / Walked by on flippered feet
And with their slime they made the time / Unnaturally fleet.
Matthew P. Wiener
>>Returning to Ken's original point, which started off this whole series
>>of articles, in the above reference Bertrand Russell writes as follows:
>>
>> But in the modern theory the question between Copernicus and
>> his predecessors is merely one of convenience; all motion
>> is relative, and there is no difference between the two
>> statements: `the earth rotates once a day' and `the heavens
>> revolve about the earth once a day.' The two mean exactly the
>> same thing, just as it means the same thing if I say a certain
>> length is six feet or two yards. Astronomy is easier if we
>> take the sun as fixed than if we take the earth, just as
>> accounts are easier in decimal coinage. {Signet, pp. 13-14}
>
>Whatever Bertrand Russell's qualifications in mathematics are, no one
>would ever accuse him of being a great physicist.
So? BR's statements were essentially correct. The only possible point
to challenge is his assertion that there is 'no difference', but that is
a matter of semantics, not physics.
> One of the paramount
>features of General Relativity is that the laws of physics should
>appear the same in ALL reference frames.
The laws that are invariant are the ones in covariant form, which is
essentially a circular definition. The essence of General Relativity is
that space-time is a four-dimensional manifold with a Lorentzian metric,
that the laws of physics hold on the manifold in an invariant way, and
that local observers can put local frames on the manifold and make
measurements that way. The local observers can put ANY coordinate frame
they want on it, "rotating" or not.
> In a reference frame which
>is fixed with respect to the average motion of the nearby stars, those
>stars all appear to be traveling with low (relatively) velocities. In a
>'reference frame' which is fixed to the spinning Earth, the nearby stars
>appear to be traveling MUCH FASTER than the speed of light. (Consider A-
>Centauri: radius of 'orbit' around Earth is 4.2 light years, it 'orbits'
>once per day, total distance traveled per day is 2*4.2*PI light years or
>about 26 light years per day.)
This is complete nonsense. The nearby stars in the rotating frame are
travelling at a NUMBER which is much larger than the number obtained by
measuring light in an inertial rectangular coordinate frame. The fact
that the one number in the one frame is bigger than another number in
another number is meaningless. Is Alpha Centauri suddenly whipping
9490 times faster than the photons it is omitting in the (apparent)
direction of motion? Of course not. The fact that Alpha Centauri is
seen moving slower than light in ONE frame means it moves slower than
light in ALL frames.
> The consequences of stars being tachyons in
>one 'frame' and not being tachyons in the other would cause the observers
>in the two frames to come to different conclusions about the laws of
>physics in Earth local space (that is, the only way to reconcile the two
>observations is to assume that there is a space-time singularity between
>the two observers, but when they go to look they won't find one).
It also leads to natural explanations of the Bermuda triangle, I'm sure.
>The bottom line is that rotation is LOCALLY discernable and is therefore
>NOT a property of Einstein's reference frames (whether they are lorentz
>frames or not). One way of locally measuring rotation is with a foucault
>pendulum (which you even mentioned). Meanwhile ALL Einstein frames are
>LOCALLY indistinguishable from lorentz frames.
The first two sentences are correct. The last one is completely wrong.
Frames locally indistinguishable from Lorentz frames are called inertial.
In such frames, special relativity as standardly presented is valid. SR
can be done in accelerated frames, but care must be taken.
But rotation can be detected more generally. For example, in a universe
with just one rotating black hole, ie, a Kerr metric, the local geometry
is a Kerr geometry, no matter WHERE in the universe you measure. And
given enough local information (a Cauchy surface), the entire metric is
determined uniquely.
>For the definition of 'frame' and 'local' I suggest you read the first few
>chapters of MTW ('Gravitation') again. I just did - fascinating stuff!
I suggest YOU read the first few chapters again.
ucbvax!brahms!weemba Matthew P Wiener/UCB Math Dept/Berkeley CA 94720
Matthew P. Wiener
>>Dahlke has at least read something about "Lorentz transformations" but
>>couldn't remember the spelling. Turning it into "Lawrence" suggests he
>>hasn't ever read anything on the subject -- just relying on what he heard
>>on the radio or at a party.
>
>So as I understand it, knowledge that I acquire by word of mouth, ie.:
>the radio, friends, a lecture by a professor; these sources are all
>"bogus". So all the stuff that's important is printed, like in books,
>magazines; like National Enquirer, etc.
You don't understand the complaint then . Knowledge of relativity is not
trivial, and somewhere along the line, if you are going to learn any, you
will have to look in a book somewhere. "Lawrence" is just too wide of the
mark.
>Aside from that, you are still making a conclusion about the poster of the
>article which may or may not have any validity. In fact, it sounds remark-
>ably like a put-down.
But it probably is valid and it is a deserved put down. Passing off as real
knowledge something you don't really understand is annoying to those of us
with real knowledge, and confusing to those of us who are just learning, and
misleading to those of us who are just curious. Such cocktail party level
knowledge should stay where it comes from.
David desJardins
>
>The idea that centrifugal force can be explained by the inductive
>effect of all matter in the universe is known as Mach's principle.
>This principle appears to be necessary for any theory that claims
>that there is no absolute motion.
Am I stupid? I have reread the first sentence above many many times
and can't make any sense out of it. In an empty (flat) universe some
frames are accelerated and some are not. This is in the absence of any
matter. What does "the inductive effect of all matter in the universe"
have to do with centrifugal force??
This is not an attack, just a request for explanation...
-- David desJardins
Doug Gwyn
>In article <18...@brl-smoke.ARPA> gw...@brl.ARPA writes:
>>The idea that centrifugal force can be explained by the inductive
>>effect of all matter in the universe is known as Mach's principle.
>>This principle appears to be necessary for any theory that claims
>>that there is no absolute motion.
>
> Am I stupid? I have reread the first sentence above many many times
>and can't make any sense out of it. In an empty (flat) universe some
>frames are accelerated and some are not. This is in the absence of any
>matter. What does "the inductive effect of all matter in the universe"
>have to do with centrifugal force??
No, David, there are some subtle issues involved here. The nonlinear
system of PDEs that constitutes Einstein's general relativistic field
law can be expected to have different solutions for different
"boundary conditions". For instance, the original 1915 theory with
asymptotically "flat" (Rijkl -> 0) spacetime might be a cosmological
model; this particular model happens not to support Mach's principle.
For another example, suppose the universe were to have some positive
average density of matter; then spinning it around an axis would mean
that a humongous amount of mass is being moved, most of it at great
distances from the axis. If Mach was right, this would have an effect
on local physics, indistinguishable from rotating the local frame
in the opposite direction in a static universe. The "inductive effect"
appears to actually exist for laboratory-scale mass motions, although
it is hard to detect experimentally.
Einstein was very much aware of the importance of boundary
conditions. Since he (originally) strongly believed in Mach's
principle, he looked for ways to make sure it was obeyed. One
such attempt was the introduction of the "cosmological term"
into the field law; another (not entirely unrelated) was to
avoid boundary conditions altogether by imposing topological
constraints on the space-time manifold (e.g. closed universe).
In my favorite unified field theory, there is no such thing as
an empty universe, which nullifies your objection. (This is a
prediction of the theory, not an assumption.) Indeed, that
theory produces the interesting effect that its universe is
locally self-gauging, which has all sorts of ramifications,
Mach's principle probably included.
P.S. In conventional general relativity, flat => empty but
not conversely.
P.P.S. A fairly good discussion of Mach's principle from the
conventional point of view can be found in Chapter 10 of
"Principles of Relativity Physics" by James L. Anderson
(Academic Press, 1967).
Matthew P. Wiener
>In article <12...@ucbvax.BERKELEY.EDU> wee...@brahms.UUCP (Matthew P. Wiener) writes:
>>... The fact that Alpha Centauri is
>>seen moving slower than light in ONE frame means it moves slower than
>>light in ALL frames.
>
>than light in ALL frames. Therefore, a coordinate system anchored the
>the Earth in NOT a 'frame' - which is what the Russell quote implies.
>Attaching vectors x0 - x4 to a rock and calling it a frame is NOT an
^^^^^^^ and he built a crooked house, eh?
>application of relativity.
What is this? Your argument to prove that attaching vectors etc. ... does
not lead to a frame is completely bogus. You concluded that Alpha Centauri
was moving 9490 times faster than light in the rotating frame, which no
frame can allow, and therefore concluded it was not a frame. But in the
rotating frame, your calculation does NOT show Alpha Centauri is moving
faster than light, and so you CANNOT conclude that the rotating frame is
not a frame. Reread my article to see what your calculation does show.
For your information, a frame is nothing more than a coordinate system.
I think you might be confused on this point because Misner Thorne and
Wheeler never defined what a frame is in general. Try reading some other
GR books for a change. Or better yet, actually DO some GR instead of
yelping about it all the time.
Matthew P. Wiener
In article <5...@lanl.ARPA> j...@a.UUCP (Jim Giles) writes:
Actually, the definitions are not in the book.
>> You need to do more than read it (we both have, apparently). You need
>>to understand it. Read it again, using your noggin.
>Note: I have always said 'local reference frame', which in GR is ALWAYS
>a Lorentz frame.
It is? Do you make this up as you go along? Is it congenital?
As a matter of fact, all GR frames are Lorentzian, which is totally different
than saying all frames are Lorentz frames, which, as you admit is what YOU'VE
been saying all along. The preference for Lorentz frames IS a mathematical
convenience: "Physics is simple only when analyzed locally." There is
nothing physical about coordinate systems per se. That is the whole point of
emphasizing the geometry of space-time in the first place. And if you do not
realize that, then you just do not understand GR at all.
A rotating frame is still a frame. It is not a Lorentz frame, but it is
still Lorentzian.
Why do you think Einstein called it the GENERAL theory? Since it holds
under ALL frames, not just the special relativity Lorentz frames.
Bertrand Russell IS correct, and I wish you'd stop spewing your nonsense.
You are worse than Ted Holden actually: even the non-experts can tell that
he spouts gibber, but your misreadings of MTW might confuse a lot of people.
> See box 1.3 in "Gravitation". End of Note.
Try READING the box, not just looking at it. And the surrounding text:
These theorems lend themselves to empirical test in the
appropriate, very special coordinate systems: ... local
Lorentz coordinates ... in the local Lorentz geometry
of physics. However, the theorems rise above all coordinate
systems in their content. [pp 19,23]
Jim Giles
>>Attaching vectors x0 - x4 to a rock and calling it a frame is NOT an
> ^^^^^^^ and he built a crooked house, eh?
>>application of relativity.
I was expecting someone to nit-pit this! I didn't want to exclude
anyone, so I gave the timelike dimension twice - once for the people
who put it at x0 and one for those who keep it at x4. (:-)
>
>For your information, a frame is nothing more than a coordinate system.
When I mean 'coordinate system' I say 'coordinate system'. I always use
'frame' as short for 'Lorentzian frame', and the geometry of spacetime is
locally Lorentzian everywhere. I made this distinction pretty clear in my
first submission. A rotating coordinate system is NOT a Lorentzian frame!
It is the lack of this distinction which I objected to in the Russell
quote, he implied that a rotating coordinate system was indistinguishable
from a non-rotating one. Since this is not true (at least, you have yet to
give ANY evidence or documentation supporting that view), I objected.
>I think you might be confused on this point because Misner Thorne and
>Wheeler never defined what a frame is in general. Try reading some other
>GR books for a change. Or better yet, actually DO some GR instead of
>yelping about it all the time.
I AM reading other GR books, MTW just happens to be the most complete.
I assumed that YOU didn't read or do GR since you never mention any
problems, references, research, or facts to support your view. All
you have done so far is spout high sounding terminology without any
evidence that you understand it. Unlike you, I have tried to keep
my submissions simple enough for the other readers of the net to follow,
and then leave references for people to follow it up in more detail.
Now, don't get me wrong. I don't claim that you don't know the subject,
you just haven't given any evidence of it yet. I'm not unwilling to
change my mind if presented with evidence and information instead of
rhetoric.
You don't really know a subject unless you can explain it
clearly in layman's terms.
Charles Greeley Abbott
Former secretary of
The Smithsonian Institution
J. Giles
Los Alamos
P.S. I don't plan to continue this discussion unless new EVIDENCE is
presented. If you can't stop yelping out rhetoric and begin a
discussion in layman's terms, perhaps it's better to take the
discussion off the net and just use email or not discuss it at
all.
Note: I have put 'name calling' back on the list of keywords to this
discussion. An ad hominem attack is the last resort of one without
further valid arguments. I'm sorry to see that Mr. Wiener saw fit
to resort to it.
Jim Giles
>>Note: I have always said 'local reference frame', which in GR is ALWAYS
>>a Lorentz frame.
>
>It is? Do you make this up as you go along? Is it congenital?
The reference is: "Gravitation", Misner, Thorne, and Wheeler, 1973:
W.H. Freeman and Co., p.21:
"STATEMENTS OF FACT
... The geometry of spacetime is locally Lorentzian
everywhere."
The emphasis is theirs. There is, therefore a local Lorentzian frame
everywhere (actually, an infinity of them). On page 23 the text goes on
"... these theorems [about spacetime] rise above all coordinate systems in
their content. They refer to intervals or distances." "All coordinate
systems" here refers to the infinity of available Lorentzian frames which
you might select for computational purposes. Any non-Lorentzian coordinate
system causes the theorems in question to be completely reformulated for
that system (mainly because the metric (a word which actually doesn't
appear yet) is no longer valid - intervals don't behave properly in a
non-Lorentzian coordinate system).
There seems little point in continuing a discussion with someone who can
only spout rhetoric and resort to ad hominem attacks. If you can give
references, information, or understandable explanations which support
your view, then do so. But quit playing meaningless word games with
terminology that does no more than muddy the waters of understanding.
And, certainly, if all you can do is resort to name calling, you shouldn't
even post your article.
>Bertrand Russell IS correct, and I wish you'd stop spewing your nonsense.
>You are worse than Ted Holden actually: even the non-experts can tell that
>he spouts gibber, but your misreadings of MTW might confuse a lot of people.
Bertrand Russell's remark implied that there was no difference between a
rotating and a non-rotating coordinate system. Since this is NOT true, I
don't see how you can hold that he is correct. But, on the off chance that
you have any EVIDENCE, I wish you would present it. I, on the other hand,
have presented several ways to distinguish a rotating coordinate system
from a non-rotating one; I have given references; and I have refrained from
the use of jargon and terminology which would confuse the lay readership on
the net. I have also (until now) refrained from ad hominem attacks.
Now, if you have ANY evidence which shows a rotating coordinate system is
indistinguishable from a non-rotating one - PRESENT IT. Any other garbage
you put on the net I (for one) will ignore.
J. Giles
Los Alamos
Tom Courtney
that in school too, but then I read an article claiming that if the universe rotated
around the earth, the pendulum would do the same thing. Sorry, I don't remember the
article or justifications. Does anyone have a proof, one way or the other?
Doug Gwyn
>Hmm, the way a foucalt pendumlum behaves proves that the earth is rotating?
>I was taught that in school too, but then I read an article claiming that
>if the universe rotated around the earth, the pendulum would do the same thing.
It would, if Mach's principle is true. Is Mach's principle true?
If you believe in conventional general relativity, Mach's principle
is true only if certain cosmological constraints exist. Are these
constraints true? Who knows?
Burch
It is an accelerated frame, and one can determine by measurement... A ring
laser gyro of sufficient sensitivity can detect the rotation of the earth
as can simpler implements like foucault pendulums. An object's apparent
velocity only makes sense in an inertial frame.
--
-David B. (Ben) Burch
Analyst's International Corp.
Chicago Branch (ihnp4!aicchi!dbb)
"Argue for your limitations, and they are yours"
Matthew P. Wiener
>>In article <5...@lanl.ARPA> j...@a.UUCP (Jim Giles) writes:
>>>Note: I have always said 'local reference frame', which in GR is ALWAYS
>>>a Lorentz frame.
> "... The geometry of spacetime is locally Lorentzian everywhere."
Lorentz frame is not the same as Lorentzian geometry. And your assertion
is completely false as stated.
>The emphasis is theirs. There is, therefore a local Lorentzian frame
>everywhere (actually, an infinity of them). On page 23 the text goes on
>"... these theorems [about spacetime] rise above all coordinate systems in
>their content. They refer to intervals or distances." "All coordinate
>systems" here refers to the infinity of available Lorentzian frames which
>you might select for computational purposes. Any non-Lorentzian coordinate
>system causes the theorems in question to be completely reformulated for
>that system (mainly because the metric (a word which actually doesn't
>appear yet) is no longer valid - intervals don't behave properly in a
>non-Lorentzian coordinate system).
Read what you just quoted. There are no non-Lorentzian coordinate systems
in a Lorentzian geometry. But whatever you are talking about, the theorems
in question rise above coordinate systems, just like MTW said in your quote,
and unlike your last sentence. If a law or theorem is expressed in covariant
form, ie with tensors, it is true in all coordinate frames. That is why we
use tensors in the first place: to identify the underlying geometric meaning
behind the coordinate systems.
David desJardins
Yes, exactly. This is the point that Matt Wiener and others have been
trying to make (I hope I can speak for him). From the fact that these two
descriptions lead to the same result, we conclude that it is meaningless
to say that the universe is rotating about the Earth (since it is equivalent
to the simpler assumption that the Earth is rotating). Meaningless but
definitely not wrong.
For an intuitive (mathematically non-rigorous) derivation of this see
MTW pp. 547-49.
-- David desJardins
j...@lanl.uucp
>in a Lorentzian geometry.
I'm surprised to see you admit this! You have been talking all along about
rotating 'frames' (which aren't Lorentzian). Now, you have finally admitted
this to be inappropriate. Bravo!
J. Giles
Los Alamos
David desJardins
>> I don't know which "theorems are referred to," but you did in fact make
>> the *demonstrably false* statement that "in GR all local frames are Lorentz
>> frames." If you want I will find the article and quote it to you.
>
>I never said that ALL local frames in GR are Lorentz frames.
Well, then, please explain the following:
>Article 3198 of net.physics:
>From: j...@lanl.ARPA (Jim Giles)
>Message-ID: <4...@lanl.ARPA>
>.... One of the paramount features of General Relativity is that the
>laws of physics should appear the same in ALL reference frames.
>.... The bottom line is that rotation is LOCALLY discernable and is
>therefore NOT a property of Einstein's reference frames (whether they are
>lorentz frames or not). One way of locally measuring rotation is with a
>foucault pendulum (which you even mentioned). Meanwhile ALL Einstein
>frames are LOCALLY indistinguishable from lorentz frames.
Here you seem to be saying that all "Einstein frames" (a phrase which
has not been defined, and which I take to mean all frames that can be
used to solve Einstein's equations) are local Lorentz frames. False.
Article 3233 of net.physics:
>From: j...@lanl.ARPA (Jim Giles)
Message-ID: <5...@lanl.ARPA>
.... Note: I have always said 'local reference frame', which in GR is
ALWAYS a Lorentz frame. See box 1.3 in "Gravitation". End of Note.
Here you are very explicit. All local reference frames used in GR
are Lorentz frames. False.
Article 3246 of net.physics:
>From: j...@lanl.ARPA (Jim Giles)
Message-ID: <8...@lanl.ARPA>
.... When I mean 'coordinate system' I say 'coordinate system'. I always
use 'frame' as short for 'Lorentzian frame' ....
In other words, your terminology is incorrect. You are confusing an
arbitary local frame with a "Lorentzian [sic] frame" (presumably you mean
Lorentz frame).
Back to the letter:
>I DID say ....
Nobody is denying that you later said some true things. I just want
to know if you admit that some of the things you said are in fact wrong.
>Since you can't tell which theorems I am talking about, I can only assume
>that you don't even HAVE a copy of MTW to check the context of my remarks -
>much less have you read it!
Since you didn't tell me in your letter what theorems you were talking
about, it was hard for me to guess which ones you meant. I do in fact have
MTW sitting right in front of me, and have had for this whole discussion.
Was reading MTW supposed to make me a mind reader so I could guess what
theorems you were talking about?
>> But the *point* of the above is that you *can* do GR in *any* local
>> frame, and the results are the same *because* of the analysis you describe
>> above! What you are saying is, "Einstein realized that *if* you do your
>> analysis in a rotating coordinate frame, the influence of all of that
>> rotating mass gives you the same answer after all." Don't you realize
>> that you need to be able to do GR in rotating frames in the first place
>> for this to even make sense?
>
>I never claimed that you COULDN'T do GR in any coordinate system you wanted
>to.
YES YOU DID! See the above quotes. This is the whole problem.
>You can invent a hyperbolic coordinate system with singularities in it
>(even for an empty region of space) if you want to - and, with sufficient
>mathematical sophistication, you can correctly work out what's going on.
>This has NOTHING to do with the question: is rotation 'merely' a matter of
>convenience? The answer is NO! The Earth rotates once per day, the Moon
>once per month. Both the Earthling and the Selenite agree that their
>pendulums and gyroscopes are linked to the distant stars, NOT the Earth or
>the Moon. By claiming this to be 'merely convenience' is to disregard this
>effect as purely coincidental.
Using that particular coordinate system to do your computations is merely
a matter of convenience. But neither Matt nor I nor anyone else has said
that there is not a preferred frame, or that there is nothing special about
nonrotating frames. All we have been saying is that GR says things about
*geometry* of space-time that are true *independent* of which particular
frame you choose to do your computations in. For example the coordinate-
free statements in your favorite box, 1.3.
>The effect makes perfect sense without rotating coordinate systems (it is,
>after all, a Newtonian effect as well). Now, as you say, you should be
>able to compute the effect in GR for rotating frames as well. This does
>NOT imply that such rotating frames will satisfy the theorems of Special
>Relativity (as you and Mr Weiner have actually said) - rotating 'frames'
>DON'T obey the theorems of special relativity.
NEVER has either of us said this. I can quote you the places in which
you have said the things I attribute to you. You cannot, because we have
not said those things!
>No matter how long you and Mr. Weiner bang on your keyboards, you can't
>make rotating coordinate systems obey the theorems of Special Relativity.
Nor would we claim to.
>Don't send me more mail about this issue until you have read and under-
>stood at least chapter 1 of MTW or some other adequate text. It's a
>useless discussion until you start making sense instead of meaningless
>diatribes.
I know so much more differential geometry than the small amount that
is in MTW that this is just ludicrous. I have spent years as a graduate
student studying geometry. I don't know how to convince you of this,
except to repeat the same things I have been saying, and to point out
the inconsistencies in the things you have said.
-- David desJardins
k...@warwick.uucp
>>Hmm, the way a foucalt pendumlum behaves proves that the earth is rotating?
>>I was taught that in school too, but then I read an article claiming that
>>if the universe rotated around the earth, the pendulum would do the same
>>thing.
[David desJardins]
> Yes, exactly. This is the point that Matt Wiener and others have been
>trying to make (I hope I can speak for him). From the fact that these two
>descriptions lead to the same result, we conclude that it is meaningless
>to say that the universe is rotating about the Earth (since it is equivalent
>to the simpler assumption that the Earth is rotating). Meaningless but
>definitely not wrong.
If the two descriptions lead to the same result (I don't disagree with this)
then how can one be considered "meaningless" unless we also consider the
other to be identically "meaningless"? Surely all we may say is that the
two descriptions are restatements of "the Earth and the Universe have relative
rotation"? The principle of parsimony may indeed lead us to prefer the
first description on grounds of local utility, but it does not allow us to
affirm that the second is meaningless.
Kay.
--
"I AM; YOU ARE; HELLO: all else is poetry"
... mcvax!ukc!warwick!kay