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From: Thnktank@concentric.net (Eleaticus)
Newsgroups: sci.physics,sci.physics.relativity,alt.sci.physics.new-theories,sci.answers,alt.answers,news.answers
Subject: Unknown Functions & Einstein's Incompetence (FAQ)
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Followup-To: sci.physics.relativity,sci.physics
Date: 22 May 1999 12:39:38 GMT
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Summary: Creating new mathematical equations; with applications
to physics/mechanics, and with reference to Einstein's
incompetent derivation of the Special Relativity time
transform.
X-Last-Updated: 1998/07/19
Originator: faqserv@penguin-lust.MIT.EDU
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Archive-Name: physics-faq/functions-unknown
Version: 0.06.01
Unknown Functions & Einstein's Incompetence (FAQ)
(c) Eleaticus/Oren C. Webster
Thnktank@concentric.net
The tutorial version of this FAQ is being revised
for notation improvement. In the meantime, this
less tutorial and more general form is provided.
------------------------------
Subject: 1. Purpose
Einstein violated simple logic (many times), common sense,
the basic principles of analytic geometry, vector algebra,
and elementary measurement theory in deriving the transfor-
matin equations at the heart of Special Relativity.
We explicate many of his absurdities.
In all cases we are discussing his 1905 paper in which
he presented the derivation of SR. We are using the Dover
edition of "The Principle of Relativity" in which the
title page is on p-35.
By the way, our frequently asked question - often asserted
as fact - is in one form or another:
Isn't Special Relativity silly?
-----------------------------------------------------------
Note: Everywhere in this document, we use @ to represent
the curly deltas used for partial derivatives. Einstein
used the curly deltas.
-----------------------------------------------------------
------------------------------
Subject: 2. Table of Contents
1. Foreword and Intent
2. Table of Contents
3. The light direction absurdity.
4. The really strange and marvelous magical gamma absurdity.
5. The amazing transverse gamma absurdity.
6. The time increases as distance decreases absurdity.
7. Simultaneity and Measurement Prologue.
8. The data scale degradation absurdity.
9. The absolute simultaneity SR transforms.
10. The Relativistic Maxwell absurdity.
11. The Twins Paradox absurdity.
12. The "how does an absurd SR work" non-absurdity.
13. The "strange effects of nothing" absurdities.
14. The "lasting effects of no effect" absurdity.
15. The "brag about your absurdities" absurdity.
16. Einstein's anti-simultaneity argument.
17. A straightforward pro-simultaneity argument.
------------------------------
Subject: 3. The light direction absurdity.
Having derived his differential equation and subse-
uent tau function based on light moving in both
directions, he then substitutes - for t - an expression
for time that is valid only for one light direction.
This creates a transform formula that could be valid only
for one direction. Substituting the opposite direction
expression is just as invalid, and results in a diff-
erent transform for x to x'.
-----------------------------------------------------------
At one point, Einstein attains a formula for what we'll
call X', the transformed x; it is based on the tau equation
he got from from his differential equation:
X' = c*tau = ac(t-vx'/(cc-vv)).
He then returns to the time arguments of his unknown tau
functions, where he had t=x'/(c-v). He substitutes this
expression into the X' formula above, to get:
X' = accx'/(cc-vv).
Remembering that Einstein's model, his unknown tau functions,
his differential equation, and resultant tau function are
all about light going BOTH directions, we see that using the
time expression for just one light direction is an error, and
time in the other direction, t=x'/(c+v), is just as valid,
- which is to say not at all valid. The algebra works out
just a bit differently:
X' = ac(x'/(c+v)-vx'/(cc-vv)).
= ac(x'(c-v)-vx')/(cc-vv)
= ac(cx'-vx'-vx')/(cc-vv)
= ac(cx'-2vx')/(cc-vv).
QED. Einstein's derivation of the x' transform is invalid
by reduction to the absurd; the transform depends on the
direction of the light movement in the time term substituted
for t in the X'=c*tau equation, an absolute violation of the
principles of Special Relativity. It is one thing to realize
that an expression in one case differs from the other, but
a very different thing to let your one and only transform
formula's derivation depend on an arbitrary choice of just
one light direction.
------------------------------
Subject: 4. The really strange and marvelous magical gamma absurdity.
Perhaps the most marvelous thing about Einstein's Special
Relativity derivation is the math he used to get from his
tau function in t and x' to his tau=f(t,x) transform.
[We let his a=phi(v)=1, as he concludes later.]
[1] tau = (t-vx'/(cc-vv)).
[2] tau = (t-vx/cc)/sqrt(1-(v/c)^2).
First of all, to get to [2], we certainly have
to rid [1] of x'. x'=x-vt.
[3] tau = (t-v(x-vt)/(cc-vv))
= (tcc-tvv-vx-vvt)/(cc-vv)
= (tcc - vx)/(cc-vv)
Now, divide numerator and denominator on the right
by cc:
[4] tau = (t-vx/cc)/(1-vv/cc).
There's only one way to get [2] from [4]. Let
tau<>tau, a logical absurdity in this situation;
Einstein has proceeded far beyond tau the unknown
function. The only unknown is a, which he later
says is phi(v)=1.
And if it is legal to get [2] by multiplying only one side
by sqrt(1-vv/cc), then it is also correct to multiply
only one side by (1-vv/cc), and get the galilean transform.
Or to multiply one side by pi and get "t and -vx/cc
are really circle diameters" transforms. [You know,
the circumference of a circle is Pi*diameter?]
But in all cases - both the absurd Einsteinian and Pi
transforms - it is not legal to treat only one side of
an equation in a non-identity fashion. The left side of
the tau function would not be tau, but gamma*tau or Pi*tau.
The appearance of gamma is just as magically marvelous
in the X' transform (we used X' for the moving system
x value coordinate, remember?):
X' = ccx'/(cc-vv).
= (ccx-ccvt)/(cc-vv)
= (x-vt)/(1-vv/cc).
Not X' = (x-vt)/sqrt(1-vv/cc).
------------------------------
Subject: 5. The amazing transverse gamma absurdity.
Gamma=1/sqrt(1-vv/cc) (he called it beta, but tradition now
calls it gamma) appeared magically in Einstein's t' and
x' transforms, replacing the mundane 1/(1-vv/cc) without
cause, reason, or justification.
But Einstein did cause it to appear in expressions for
the transformed y and z axes. All he had to do was say
light movement along these transverse axes was at the
rate sqrt(cc-vv).
Remember, the (c-v) and (c+v) expressions Einstein used
were not due to non-c light velocity, but due to the
movement of objects toward which the light was moving.
That condition does not hold in the y and z directions
in his derivation.
"In an analogous manner we find, by considering rays
moving along the other two axes, that
Y' = c*tau = ac(t-vx'/(cc-vv))
when t=y/sqrt(cc-vv), x'=0."
When x'=0, we find that Y' = c*tau = act, just as every
SRian in the universe agrees.
In any case, the t=y/sqrt(cc-vv) line is the full,
ridiculous justification Einstein gives for the
existence of the expression sqrt(1-vv/cc).
Ridiculous? Sure, x'=0 is a rather small subset of
the possibilities for x'; how do you generalize to
the full range of the universe from x'=0?
And there is not even the hint of a justification for
replacing (1-vv/cc) with its square root in his time
and space (x) transforms.
QED: Einstein's SR time transform derivation is invalid
by reduction to the absurd: it is eithered based on the
premise that x'=0 and not x'<>0, or based on nothing.
------------------------------
Subject: 6. The time increases as distance decreases absurdity.
Einstein uses his distance to the mirror x' with which
to derive the differential equation and tau function from
which he derives the t' and x' transforms of Special Rela-
tivity. The greater that distance, the more time it takes
for the light to travel either direction, and roundtrip.
But Einstein concludes that the slope of tau wrt the dist-
ance to the mirror is the inverse of the slope wrt the time
it takes.
Einstein's x' is the distance to the mirror, which also
defines the distance back to the source at the moving origin.
This distance shows up in the time expressions in his un-
known tau functions, and when differentiated wrt x' gives
a value of 1.00, proving that the x' of the @tau/@x' term
is indeed the distance to the mirror and not the other x'
in his model (yes, there are two; the other is the location
of the light and/or the clock in use at the time).
The greater the distance, the greater time it takes
for light to cover the total and part-wise distances.
But Einstein's differential equation and his resultant
tau equation say that although tau increases when the
distance increases, tau decreases when time increases,
and vice versa.
His differential equation is:
(@tau/@x') + (v/(cc-vv))(@tau/@t) = 0.
We put the two terms on opposite sides:
(@tau/@x') = - (v/(cc-vv))(@tau/@t).
Thus, either v must always be negative or the slope
of tau with respect to x' is the negative of the slope
of tau with respect to t. Yet, his model - for that
very x' - is that x' and v together fully define t,
and that the time - with a constant v, which is how
Einstein treated v - increases as x' increases.
This aburdity is repeated in his immediately
consequent tau function:
tau = a(t-vx'/(cc-vv)).
There can be no doubt that the x' in the differential
equation and the resultant tau function are the x'
that is the distance to the mirror. When he different-
iates the time expressions in his unknown taus wrt x',
the slope of that distance x' is 1 wrt to the differen-
tiating x'.
QED, by reduction to the absurd, his derivation of the
SR transformations is nonsense. It is based on a model
in which tau increases with a greater x' and/or a greater
t - t being an increasing function of an increasing x'
- but Einstein's conclusion is that tau increases with
one when it decreases with the other.
Objection:
But, you say, you said there were two x' usages.
Surely the tau at the time the light returns to the
moving origin, at location L=0, is later than the tau when
light reaches the mirror at L=x'. That's a negative
relationship.
OK. That is saying tau is an obvious inverse function of
the location coordinate.
But the tau at emission is surely less than at either
of the other occasions, and its L is zero also, making
it a direct function of the location coordinate, by
the same argument.
------------------------------
Subject: 7. Simultaneity and Measurement Prologue.
Einstein - and Special Relativity - not only
mixes apples and oranges, but treats indepen-
dent variables as dependent variables, and vice
versa.
One of the first things a child learns about
algebra is to not add apples and oranges.
Special Relativity adds apples and orangutans.
Apples and oranges are at least both fruit, so
you could add them and get a fruit total.
But Special Relativity adds space and time, and
does so without justification. Yes, there is a
derivation process (with some of the absurdities
outlined above) but in no way does that derivation
specify any reason why one should treat time and
space as dimensions similar enough to add them
up together.
Yes, the units in the transform equations that
mix the two together are compatible, but it is
not a set of compatible measures that are con-
sidered a four-D coordinate system. It is not
space and ct that are the four axes, it is space
and t.
Should we also consider heat and space similar
dimensions because a balloon will rise to greater
heights as its gasses warm up?
Should we also consider velocity and distance
similar measures because we can multiply the
one by time and get distance? That's identical
to the math that makes time and space suppos-
edly compatible measures.
-----------------------------------------------
The worst thing about mixing time and space as
does SR, is that there is no macro-world evidence
whatsoever that time can ever be a dependent
variable, which is what the SR transforms make
of it.
A dependent variable is one that you can control
indirectly, through control of other variables.
You can REALLY control how great a distance you
go by choosing to move for only some certain time
period at the given velocity and then not going
further than that distance.
But you can NEVER control how long a time you 'go',
no matter what you do, unless you consider suicide
as accomplishing that control.
Time is not a dependent variable, but when you
decide that t'=g(t-xv/cc), you are saying time
is just such a dependent variable.
--------------------------------------------------
But it is only by imagining that time is a dependent
variable - that you can add it somehow with space -
that allows SR to imagine its transforms are
rotations and not translations.
Imagine x as the verticle axis on your graph, time
as the horizontal axis.
If x'=gx-gvt is just moving the x-axis to the right,
more and more as time goes by, then the transformation
is just a shift in the axis with no implication that
x (space) and time are the same stuff.
If x'=gx-gvt is a rotation, as SR says, then the
graphical equivalent is to tilt the x-axis somewhat
toward the horizontal, somehow becoming part time
and part space.
------------------------------
Subject: 8. The data scale degradation absurdity.
The SR transforms and the Galilean transforms both
convert good, ratio scale data to inferior interval
scale data. The effect is corrected, allowed for,
when the transforms are conducted on the generalized
coordinate forms specified by analytic geometry - and
vector algebra, for that matter - but SR refuses to
do it right. The consequence is the appearance that
simultaneity does not hold across inertial frames,
and the consequence of that is the Twins Paradox
absurdity.
Both sets of transforms are 'translations' - lateral
movements of an axis, increasing over time in these
caes - but with the SR transform also containing a
rescaling. It is the translation term, -vt in the x
transform to x', and -xv/cc in the t transform to t',
that degrades the ratio scale data to interval scale
data.
SR likes to consider its transforms just rotations,
however, and in the case of 'good' rotations, ratio
scale data quality is indeed preserved, but SR violates
the conditions of good rotations; they are not rigid
rotations and they don't appropriately rescale all
the axes that must be rescaled to preserve compati-
bility.
The proof is in the pudding, and the pudding is the
combination of simple tests of the transformations.
We can tell if the transformed data are ratio scale
or interval.
Ratio scale data are like absolute Kelvin. A measure-
ment of zero means there is zero quantity of the
stuff being measured. Ratio scale data support add-
ition, subtraction, multiplication, and division.
The test of a ratio scale is that if one measure
looks like twice as much as another, the stuff
being measured is actually twice as much. With
absolute Kelvin, 100 degrees really is twice the
heat as 50 degrees. 200 degrees really is twice
as much as 100.
Interval scale data are like relative Celsius, which
is why your science teacher wouldn't let you use it
in gas law problems. There is only one mathematical
operation interval scales support, and that has to
be between two measures on the same scale: subtraction.
100 degrees relative (household) Celsius is not twice
as much as 50; we have to convert the data to absolute
Kelvin to tell us what the real ratio of termperatures
is.
However, whether we use absolute Kelvin or relative
Celsius, the difference in the two temperature readings
is the same: 50 degrees.
Thus, if we know the real quantities of the 'stuff'
being measured, we can tell if two measures are on
a ratio scale by seeing if the ratio of the two
measures is the same as the ratio of the known quant-
ities.
If a scale passes the ratio test, the interval scale test
is automatically a pass.
If the scale fails the ratio test, the interval scale
test becomes the next in line.
It isn't just the bare differences on an interval
scale that provides the test, however. Differences
in two interval scale measures are ratio scale, so
it is ratios of two differences that tell the tale.
Let's do some testing, and remember as we do that our
concern is for whether or not the data are messed up,
not with 'reasons', excuses, or avoidance.
------------------------------------------------------
Are we going to take a transformed length and see
whether that length fits ratio or interval scale
definitions?
Of course, not. Interval scale data are ratio after
one measure is subtracted from another. That is the
major reason the SR transforms can be used in science.
Let there be three rods, A, B, C, of length 10, 20, 40,
respectively. These lengths are on a known ratio scale,
our original x-axis, with one end of each rod at the
origin, where x=0, and the other end at the coordinate
that tells us the correct lengths.
Note that these x-values are ratio scale only because
one end of each rod is at x=0. That may remind you of
the correct way to use a ruler or yard/meter-stick:
put the zero end at one end of the thing you are
measuring. Put the one mark there instead of the zero,
and you have interval scale measures.
Let a,b,c be x' at v=.7071c, t=0.
Let A',B',C' be x' at v=.7071c, t=10.
g=sqrt(1-(.7071)^2)=.7071.
A B C a b c A' B' C'
---------------- -------------------- ---------------------
10 20 40 14.14 28.28 56.57 4.14 18.28 46.57
---------------- -------------------- ---------------------
B/A = 2 b/a = 2 B'/A' = 4.42
C/A = 4 c/a = 4 C'/A' = 11.25
C/B = 2 c/b = 2 C'/B' = 2.55
C-A = 10 b-a = 14.14 B'-A' = 14.14
C-A = 30 c-a = 32.52 C'-A' = 42.42
C-B = 20 c-b = 28.28 C'-B' = 28.28
(C-A)/(B-A) = 3 (c-a)/(b-a) = 3 (C'-A')/(B'-A') = 3
(C-B)/(B-A) = 2 (c-b)/(b-a) = 2 (C'-B')/(B'-A') = 2.
The results show that the primed data (a,b,c)
are ratio scale as we'd expect since the vt term
is zero.
The ratios b/a, etc, are the same as the known
ratio scale ratios, B/A, etc.
When vt=0 the data are still ratio scale, but
the rescaling is why the differences (b-a, etc)
are not the same as before transform. The simple
ratios prove the data still ratio, and the ratios
of differences [(c-a)/(b-a), etc] just support
that finding.
When vt<>0, the data (A',B',C') are no longer
ratio scale, which is why the simple ratios now
differ from both the original and vt=0 data.
However, the ratios of differences show us that
the data do satisfy the one mathematical operation
of subtraction, the differences thus being shown
to be ratio scale.
If you do not understand that the above data table
proves that the SR transforms did indeed degrade
the ratio scale to interval scale, please study it
until you understand.
---------------------------------------------------
If we remember that the only effect of gamma=g
is to rescale the data, we realize that the
above results and conclusions also apply to the
galilean transform.
As we said in the introduction of this Subject,
use of the generalized cartesian coordinate form
corrects the interval scale problem. Using this
form for the galilean transformation upgrades the
traditional, incompetent, non-invariant transform
of laws/equations up to invariant (so to speak)
invariance.
To test the results of the use of the generalized
cartesian coordinate form, with (x-x0) instead of
just (x), we can again let the SR version stand
in for both the galilean and SR results.
Here, our unprimed data were with x0=0.
Let a,b,c be x' at v=.7071c, t=0.
Let A',B',C' be x' at v=.7071c, t=10.
g=sqrt(1-(.7071)^2)=.7071.
a'= b'= c'=
A B C x0 (A-x0)' (B-x0)' (C-x0)' x0'
---------------- --------------------------------
10 20 40 0 14.14 28.28 56.57 -10
---------------- --------------------------------
B/A = 2 b'/a' = 2
C/A = 4 c'/a' = 4
C/B = 2 c'/b' = 2
C-A = 10 b'-a' = 14.14
C-A = 30 c'-a' = 42.42
C-B = 20 c'-b' = 28.28
(C-A)/(B-A) = 3 (c'-a')/(b'-a') = 3
(C-B)/(B-A) = 2 (c'-b')/(b'-a') = 2.
The above data table shows us that focusing on (x-x0),
instead of just plain x, will give us ratio scale data
in any equation the transforms are applied to.
Use of the generalized coordinate form verifies the interval
nature of the transforms. Just as one x' subtracted from
another on the same scale is a ratio scale result, just so
does subtracting x0' from every x' create a ratio scale result.
There is absolutely nothing about the SR transform
derivation that says to not use the generalized
coordinate form, absolutely nothing to gain by insisting
- so to speak - on using interval scale data in your
equations. To do so is absolutely absurd.
Doing so is a sufficient cause of the obvious simultaneity
problem of Special Relativity, which is itself the cause
of the absurd Twins Paradox mess.
------------------------------
Subject: 9. The absolute simultaneity SR transforms.
Above we have shown that there is a problem with Einstein's
idea that simultaneity is not absolute across inertial frames.
Here, we add one more demonstration, based on insisting
on use of the generalized cartesian coordinate form in
our transformed equations, as a means of avoiding data
degradation from ratio scale to interval scale.
Using analytic geometry's obvious (x-x0) form, where
x0 is an important 'anchor' or 'centroid' such as a
circle center, we apply the SR transforms, x'=gx-gvt,
and t'=gt-gxv/cc.
(a) (x'-x0')=[ g(x-vt) - g(x0-vt) ] = g(x-x0);
this shows (1) that the transform is thus
a rescaled invariant, and (2) one x transforms
to only one x', regardless of t.
(b) (t'-t0')=[ g(t-vx/cc) - g(t0-vx/cc) ] = g(t-t0);
this shows (1) that the transform is thus
a rescaled invariant, and (2) one t transforms
to only one t', regardless of x.
(c) therefore any pair of points (xa,tc), (xb,tc)
transform to one and only one (xa',tc') and
(xb',tc') pair, which shows that time transformed
intervals do not depend on location and therefore
absolute simultaneity holds.
(d) therefore any pair of points (xc,ta), (xc,tb)
transform to one and only one (xc',ta') and
(xc',tb') pair, which shows that spatial transformed
intervals do not depend on time, and therefore absolute
spatial congruence holds.
------------------------------
Subject: 10. The Relativistic Maxwell absurdity.
When True Believer crackpots are shown the simple
demonstration that the galilean transform on
generalized cartesian coordinates is invariant,
their first defense is usually an incredibly stupid
"x0'=x0, because the coordinate of a circle center,
or point of emission, etc, is a constant and can't
be transformed."
The last defense is "but Maxwell's equations are not
invariant under that coordinate transform." When
asked just what magic occurs in Maxwell that would
prevent the simple algebra
(x'-x0')=[ (x-vt)-(x0-vt) ]=(x-x0)
from working, and when asked them for a demonstration,
they will never do so, however many hundreds of
times their defense is asserted.
The reason may help you understand part of Einstein's
1905 paper in which he gave us his absurd Special
Relativity derivation:
THERE ARE NO COORDINATES IN THE EQUATIONS TO BE TRANSFORMED.
Einstein gave the electric force vector as E=(X,Y,Z)
and the magnetic force vector as B=(L,M,N), where the
force components in the direction of the x axis are
X and L, Y and M are in the y direction, Z and N in
the z direction.
Those values are not, however, coordinates, but values
very much like acceleration values.
BTW, the current fad is that E and B are 'fields', having
been 'force fields' for a while, after being 'forces'.
So, when Einstein says he is applying his coordinate
transforms to the Maxwell form he presented, he is
either delusive or lying.
(a) there are no coordinates in the transform equations
he gives us for the Maxwell transforms, where
B=beta=1/sqrt(1-(v/c)^2):
X'=X. L'=L.
Y'=B(Y-(v/c)N). M'=B(M+(v/c)Z).
Z'=B(Z+(v/c)M). N'=B(N-(v/c)Y).
X is in the same direction as x, but is not a coordinate.
Ditto for L. They are not locations, coordinates on the
x-axis, but force magnitudes in that direction.
Similarly for Y and M and y, Z and N and z.
(b) the v of the "coordinate transforms" are in Maxwell
before any transform is imposed; Einstein's transform
v is the velocity of a coordinate axis, not the velocity
of a particle, which is what was in the equation before
he touched it.
(c) if they were honest Einsteinian transforms, they'd be
incompetent. The direction of the particle's movement is
x, which means it is X and L that are supposed to be
transformed, not Y and M, and Z and N. And when SR does
transform more than one axis, each axis has its own
velocity term; using the v along the x-axis as the v
for a y-axis and z-axis transform is thus trebly absurd:
the axes perpendicular to the motion are not changed
according to SR, the v used is not their v, and the v
is not a transform velocity anyway.
(d) as everyone knows, the effect of E and B are on the
particle's velocity, which is a speed in a particular
direction. Both the speed and direction are changed
by E and B, but v - the speed - is a constant in SR.
As absurd as are the previously demonstrated Einsteinian
blunders, this one transcends error and is an incredible
example of True Believer delusion propagating over decades.
The equations can be put in a coordinate dependent form,
where one or more E or B component is expressed as a
function of location, but internal to those functions
each coordinate may be put in gemeralized coordinate
form and transformed. Invariantly, of course.
-------------------------------------------------------------
The SR crackpots don't know what coordinates are. The
various things they call coordinates include coordin-
nates, but also include a variety of other quantities.
------------------------------------------------------
1. One may express coordinates in a one-axis-at-a-time
manner [like x^2+y^2=r^2] but it is the use of vector
notation that shows us what is going on. In vector
notation the triplet x,y,z [or x1,x2,x3, whatever]
represents the three spatial coordinates, but there
are so-called basis vectors that underlie them. Those
may be called i,j,k. Thus, what we normally treat as
x,y,z is a set of three numbers TIMES a basis vector
each.
2. These e*i, f*j, g*k products can have a lot of meanings.
If e, f, j are distances from the origin of i,j,k then
e*i, f*j, g*k are coordinates: distances in the directions
of i,j,k respectively, from their origin. That makes the
triplet a coordinate vector that we describe as being an
x,y,z triplet; perhaps X=(x,y,z).
The e*i, f*j, g*k products could be directions; take any
of the other vectors described above or below and divide the
e,f,g numbers by the length of the vector [sqrt(e^2+f^2+g^2)].
That gives us a vector of length=1.0, the e,f,g values of
which show us the direction of the original vector. That
makes the triplet a direction vector that we describe as
being an x,y,z triplet; perhaps D=(x,y,z).
The e*i, f*j, g*k products could be velocities; take any
of the unit direction vectors described above and multiply
by a given speed, perhaps v. That gives a vector of length
v in the direction specified. That makes the triplet a
velocity vector that we describe as being an x,y,z triplet;
perhaps V=(x,y,z). Each of the three values, e,f,g, is the
velocity in the direction of i,j,k respectively.
The e*i, f*j, g*k products could be accelerations; take any
of the unit direction vectors described above and multiply
by a given acceleration, perhaps a. That gives a vector of
length a in the direction specified. That makes the triplet
an acceleration vector that we describe as being an x,y,z
triplet; perhaps A=(x,y,z). Each of the three values, e,f,g,
is the acceleration in the direction of i,j,k respectively.
The e*i, f*j, g*k products could be forces (much like accel-
erations); take any of the unit direction vectors described
above and multiply by a given force, perhaps E or B. That
gives a vector of length E or B in the direction specified.
That makes the triplet a force vector that we describe as
being an x,y,z triplet; perhaps E=(x,y,z) or B=(x,y,z). Each
of the three values, e,f,g, is the force in the direction of
i,j,k respectively.
Einstein's - and Maxwell's - E and B are
not coordinate vectors.
============================================================
There is another variety of intellectual befuddlement that
misinforms the idea that Maxwell isn't invariant under the
galilean transform: confusions about velocities.
Velocities With Respect to Coordinate Systems.
-----------------------------------------------
Aaron Bergman supplied the background in a post to a sci.physics.*
newsgroup:
===============================================================
Imagine two wires next to each other with a current I in each.
Now, according to simple E&M, each current generates a magnetic
field and this causes either a repulsion or attraction between
the wires due to the interaction of the magnetic field and the
current. Let's just use the case where the currents are parallel.
Now, suppose you are running at the speed of the current between
the wires. If you simply use a galilean transform, each wire,
having an equal number of protons and electrons is neutral. So,
in this frame, there is no force between the wires. But this is a
contradiction.
================================================================
First of all, the invariance of the galilean transform, (x'-x.c')
=(x-x.c), insures that it is an error to imagine there is any
difference between the data and law in one frame and in another;
the usual, convenient rest frame is the best frame and only frame
required for universal analysis. [Well, (x'<>x, x,c'<>x.c, but
(x'-x.c')=(x-x.c).]
Second, given that you decide unnecessarily to adapt a law to
a moving frame, don't confuse coordinate systems with meaningful
physical objects, like the velocity relative to a coordinate
system instead of relative to a physical body or field.
In other words, what does current velocity with respect to a
coordinate system have to do with physics?
Nothing. Certainly not anything in the example Bergman gave.
What is relevant is not current velocity with respect to a
coordinate system, but current velocity with respect to wires
and/or a medium. The velocity of an imaginary coordinate sys-
tem has absolutely nothing to do with meaningful physical vel-
ocity. You can - if you are insightful enough and don't violate
item (e) - identify a coordinate system and a relevant physical
object, but where some v term in the pre-transformed law is
in use, don't confuse it with the velocity of the coordinate
transform.
Velocities With Respect to ... What?
-----------------------------------------------
Albert Einstein opened his 1905 paper on Special Relativity
with this ancient incompetency:
===============================================================
The equations of the day had a velocity term that was taken
as meaning that moving a magnet near a conductor would create
a current in the conductor, but moving a conductor near a
wire would not. This was belied by fact, of course.
The important velocity quantity is the velocity of the
magnet and conductor with respect to each other, not to
some absolute coordinate frame (as far as we know) and
not to an arbitrary coordinate system.
One possible cause was the idea: "but the equation says the magnet
must be moving wrt the coordinate system" or "... the absolute
rest frame".
There not being anything in the equation(s) to say either of
those, it is amazing that folk will still insist the velocity
term has nothing to do with velocity of the two bodies wrt
each other.
------------------------------
Subject: 11. The Twins Paradox absurdity.
Most of SR demonstrates a symmetry. The contractions and
dilations one oberver supposedly sees for another system,
are exactly what the other system sees for him.
The Twins Paradox says, however, that this symmetry fails.
If the travelling twin left at t=0 and returned at t=100,
then t'=g(t-xv/cc) and t' > t, which would say that the
travelling twin's clock is ticking away faster. The symmetry
would say the traveller sees the stationary clock ticking
away faster than his.
However, the traveller has to change direction, and thus
by magic, as it were, the supposed lack of simultaneity
forces the travelling twins clock to somehow be the ruling
clock.
As we have seen on a number of grounds, the idea that
simultaneity does not hold across inertial frames is
absurd, and the correct use of generalized coordinates,
which preserves ratio scale quality shows it to be
true that simultaneity holds reign.
There is no lack of simultaneity, and there is no
differential aging of such twins.
------------------------------
Subject: 12. The "how does an absurd SR work" non-absurdity.
If you have understood the ratio versus interval scale
discussion, you know a lot of it already.
(a) anytime SR uses a difference of transformed values
it creates ratio scale data out of the degraded interal
scale data. Most of SR does just that in practice. We
have shown that such ratio scale data is 'just' rescaled
galilean data.
(b) as often as not it is E=mc^2 that is what is meant
about SR working. Even if it is true that it is basic
SR - and there are some who say that identity was known
before Einstein - it has nothing directly to do with
the derivation and transform absurdities.
(c) sometimes it is meant that instead of galilean
force, F, being F=ma, it is the relativistic force
equation that is supported daily at every second of
the day at accelerators like CERN. However, F=ma
came from long before accelerators and Maxwell,
and non-relativistic force models exist that at
least come much closer than F=ma.
(d) to show that Einstein's work is absurd in no way
says that his Second Principle is wrong, only that
his implementation is absurd. A correct implementation
may be much closer to T'=T/g than to T'=T, etc. This
would still require differences of the interval data
to be used, unless there is some true, non-distorting
ratio scale transform available.
------------------------------
Subject: 13. The "strange effects of nothing" absurdities.
According to Special Relativity, nothing can have
amazing effects.
There are no coordinate systems in nature; they're 'just'
imaginary. But in SR, they are supposed to have real effects.
One you see being talked about fairly frequently.
Let a charged particle move at velocity v through an
electromagnetic field.
Now, imagine a coordinate system moving at that same velocity.
The velocity of the charged particle is thus zero, they say,
and there is no effect of the electromagnetic field.
They really do say such stupid things, folks.
Einstein started his SR paper in somewhat that way.
Before Maxwell, there was an equation for the effect of
an electric field, and another equation for a magnetic
field. The magnetic one had a velocity term in it, the
electric one didn't.
So, they decided back then, the equations insisted that
if you moved the magnetic near conducting wires there
would be an induced electric current; after all, there
is a velocity term in the magnetic equation.
But, they said, the electric equation equation said there
was no effect if you waved the wires near a magnetic; after
all, there was no velocity term in the electric equation.
In other words, the v in the magnetic field was not a
velocity of a magnet and a wire wrt each other, but
with respect to something that doesn't exist in nature:
a coordinate system.
You will hear it said to this very day by trained SRians,
that Galilean physics says moving the wires will give
you no current.
And they will say that if you transform the Maxwell equations
- with the SR transforms - so that the imaginary coordinate
system is moving at the velocity of the magnet, there is no
induced current.
In other words - that they won't use - if you draw a
coordinate axes system on a piece of paper and put the
wires on it and move the magnet, you'll get a current,
but if you tape the coordinate system to the magnet
and move the magnet, you'll get no current.
That is what SR says.
But if you think about it deeply enough, in terms of the
ratio scale versus interval scale discussion, you'll see
why they have to say such idiotic things.
You see, when you take the generalized form, such as
(x-x0) and transform it, the velocity terms drop out,
or cancel each other arithmetically if you leave the
equation in primed form instead of simplifying it back
to the unprimed form.
But if you don't mind using the degraded interval data
and transform you have only one transform velocity term
in the bag, and so the transform velocity term doesn't
drop out.
And if you already had a velocity term in the equation,
at the same speed, it is true that the algebraic effect
is that there might now be a zero result.
Sure, subtract the velocity of an imaginary velocity
from a real one (perhaps the velocity of a charged
particle or a magnet) and you get a zero result if
the two are the same.
Try telling your mortgage company that you now owe
them nothing because you subtracted an imaginary
payment from the amount you owed them. Hey. If it
works in physics - SCIENCE! - how can a mere finance
company or bank deny your logic?
------------------------------
Subject: 14. The "lasting effects of no effect" absurdity.
You know about length 'contraction': a moving object
is shortened by the fact of its movement, according to
SR, even though you can't tell it is really moving or
not if it isn't accelerating.
Inertial movement is obviously relative. I see something
moving wrt me, and I see you moving wrt me, so you may
or may not see the thing moving wrt you. You will unless
the object and you are moving at the same speed in the
same direction wrt me.
And what speed you see the object moving at determines
how much shorter the thing is while moving.
So, SR says every object has an infinite number of different
lengths all at the one time: one for every possible velocity
it can be seen moving at.
No mathematician would try solving a set of simultaneous
equations including: v=40; v=-20; v=10000000, but SR implies
a universe in which an infinite number of such equations
will work fine.
So, how to get around such absurdities?
Why it's simple. Just claim the effects are only observations,
not real effects.
People do this right here on the Internet in these newsgroups.
The title of this section is:
The "lasting effects of no effect" absurdity.
Let's list some of the supposed, lasting consequences
of the non-real effects:
A travelling twin comes back younger than his stay at
home brother.
A muon coming to earth from space lasts longer than
one in the laboratory.
------------------------------
Subject: 15. The "brag about your absurdities" absurdity.
The Special Relativity transformations terribly screw
up almost every equation known to humankind, and probably
those of every alien species in the universe, as well as
any in heaven and hell.
But Special Relativity makes a virtue of this, proudly
claiming that it is the quantity dx'^2+dy'^2+dz'^2+(icdt')^2
that is invariant.
Even the simplest formulas no longer work on the data
after tranform, for instance the circle formula: x^2+y^2=r^2.
You can find points that fit x'^2+y'^2=r^2, of course; they
just don't correspond to the circle you started with.
"So, the 'repairs' we made to your automobile just made
things worse and destroyed most of what had been working?
So what? It is our ashtray repairs that are world famous."
------------------------------
Subject: 16. The "contraction circus" absurdity.
Just what is it that contracts?
There are three basic possibilities:
(I) The whole universe contracts, parallel to the
line of the moving object's direction.
(II) The whole universe contained in a cylinder centered on
the moving object and extending forwards and rearwards
contracts.
(III) The moving object only contracts.
The really 'cute' one is (II).
============================================================
(III) The moving object only.
Let there be two markers in space at a constant distance
of 10^10 kilometers from each other, as measured by an
observer at rest wrt the markers.
Let a spaceship exist that is measured by the observer as
one kilometer long while it is a rest wrt the observer.
The distance between the markers is thus 10^10 spaceship
lengths.
Let the spaceship depart the observer and eventually pass
one marker at .7071c. The observer sees the spaceship now
as being .5 kilometers in length at t=0, and the moving
clock to be ticking only half as fast as his own.
The spaceship does not see his length as having changed,
and if the distance between the objects didn't also
change, then its perceived distance to the second marker
is now 2*10^10 kilometers, so it takes twice the time
to get to the second marker as one might have supposed,
so according to both the stationary and moving clocks,
the transit time from one marker to the other will be
the same.
QED: if only the object contracts, there is no transit
time difference between the two systems at a given
velocity.
========================================================
(I) The whole universe contracts.
(a) Is the contraction instantaneous throughout the universe?
How could you tell? And what possible difference
could it make? Those are not rhtorical questions.
There would be no way SR could have a meaningful
application, right? If you suggest that time would
not similarly be dilated throughout the universe,
you are suggesting an apparent change in v, for
v is constant in SR only because d/t=d'/t', and
in this case we have no possible d'<>d because
all the universe's measuring sticks contract sim-
ilarly. Similarly? Identically!
(b) Does the contraction propagate through the universe at
the speed of light from the location of the moving object?
Except for questions like "speed of light from any
viewpoint?" this might not be different that the
instantaneous model. Hmm. Or maybe a number of widely
distributed observers in one frame could tell that
something had happened? Again, none of these are
rhetorical questions.
(c) Does the contraction propagate through the universe at
less than the speed of light from the location of the
moving object?
One could see that parts of the universe had contracted.
Your own measuring stick wouldn't contract until after
it had measured the distant contraction.
Whole Universe Summary: who knows what effect could be
eventually discovered; what is knowable is that there would
be no simple(ton) visible contraction.
===========================================================
(II) The whole universe contained in a cylinder centered on
the moving object, and extending forwards and rearward,
contracts.
This is compatible with standard SR; elsewise a transit time
between two markers would show the same elapsed time as for
an observer at rest wrt the markers, as we saw in the dis-
cussion of the 'object only' case.
Let there be a spaceship be at rest between two stars, and
with its axis of incipient motion passing through both stars.
When it accelerates to any appreciable velocity, is it the
center cylinder of the forward star that is snatched from
its guts and hurtles toward the spaceship, or the rearward
star's guts? Or both?
That assumes the center of contraction is at least somewhere
from the rearward star almost to the forward star. If the
center of contraction were somewhere very distant from the
ship, it could be that both star centers and the spaceship
would all be yanked instaneously through the center of one
start to a point that could be light years distant. Unless
the contraction wasn't instantaneous, and then we'd have
some mess indeed, figuring out how much and how far the
contraction had taken effect before the ship once again
changed velocity.
At a simpler level, of course, contraction along the line
of movement implies faster than light transit of information
if the contraction is instantaneous, or at least faster than
light.
In any case, we'd certainly see some calamitous effects were
objects other than light moving at high v anywhere in the
near universe, wouldn't we? If SR were correct.
============================================================
Summary.
============================================================
For our three possibilities in the contraction circus,
(I) The whole universe, parallel to the line of a
moving object's direction contracts, and why
wouldn't time also dilate universally?
(II) The whole universe contained in a cylinder centered on
the moving object and extending forewards and rearwards
contracts, and would yield stellar catastrophes we'd
almost surely have seen by now.
(III) The moving object only contracts, and SR's claim
about transit time differences would be invalid.
The less unlikely possibility seems to be the one where
you not only couldn't tell there had been contraction,
but you'd be darn silly saying there had been.
Then again, that last is the standard SR position, isn't
it? The contractions don't really occur, they're just
observational differences (which you couln't see in the
whole universe case). That's what SRians on these newsgroups
say; and they also say the time differences are real and
lasting, except when they aren't.
------------------------------
Subject: 16. Einstein's anti-simultaneity argument.
Einstein
(a) defined a test for clocks at rest wrt each other
in a stationary system (we'd now say inertial),
to determine that they are synchronized. [At
clock A at time ta send light to clock B which
reflects it at tb to clock A at ta', with observers
at each clock noting the time the clock says at the
three events. If tb-ta=tb-ta' then the clocks are
synchronized.]
(b) had a stationary system thereby synchronize its
clocks.
(c) posited a second inertial - but moving - system
whose clocks at all times and places would show
the first system's times at the immediately
adjacent first system location.
(d) posited the first system running the synchroni-
zation test on the second system clocks; that is, with
a completely non-definition test. With r=distance
between the clocks - per stationary system - he
got tb-ta=r/(c-v) and tb-ta'=r/(c+v).
He concluded that clocks synchronized in one inertial
system cannot satisfy the definitional test for
synchronization in a second inertial frame.
If the second system had indeed run its synchronization
test like the first system had, the times would be
tb-ta=r/c and tb-ta=r/c.
His proof is much like having a stationary pianist
playing a stationary piano and then turning on his
stationary piano stool to play a second piano that
is moving past him, while he stays stationary.
------------------------------
Subject: 17. A straightforward pro-simultaneity argument.
The SR formula for time dilation holds true if SR holds
true; it says that for a fixed location, x, T'=T/(sqrt(cc-vv).
Because his stationary system clocks are synchronized,
the three times in the stationary system clock synchron-
ization are valid times at any fixed location, x, in
the stationary system, and for any such fixed location,
t'=t/sqrt(cc-vv), whether t=tb-ta or t=tb-ta'. This is
to say, equal intervals in one inertial system are nec-
essarily equal intervals in any other.
As shown earlier in this faq, non-simultaneity is an
artifact of poor usage. The generalized coordinate
form (x-x0), etc, of an equation should be used; if
you do so, there is no time difference in t' at
different locations of x, etc.
Simultaneity is absolute.
Eleaticus
!---?---!---?---!---?---!---?---!---?---!---?---!---?---!---?---!---?
! Eleaticus Oren C. Webster ThnkTank@concentric.net ?
! "Anything and everything that requires or encourages systematic ?
! examination of premises, logic, and conclusions" ?
!---?---!---?---!---?---!---?---!---?---!---?---!---?---!---?---!---?