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Invariant Galilean Transformations (FAQ) On All Laws



 
 
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  #1  
Old October 16th 04 posted to sci.physics,sci.physics.relativity,alt.physics,sci.math
Uncle Al
external usenet poster
 
Posts: 17,336
Default Invariant Galilean Transformations (FAQ) On All Laws

Eleaticus wrote:
[snip lies]

Invariant Galilean Transformations (FAQ) On All Laws
(c) Eleaticus/Oren C. Webster

[snip 1300 lines of trolled garbage]

eleaticus, Oren Webster, is a despised and stooopid troll,
http://users.pandora.be/vdmoortel/di...es/Crimes.html
"Several crimes against logic and science" Ha ha ha!

Originally trolled across sci.physics sci.physics.relativity
alt.physics sci.math sci.answers alt.answers news.answers

Psychotic ineducable boring troll Eleaticus,

Internal inconsistencies in SR (meaning inconsistencies of a purely
mathematical logical nature) automatically lead to contradictions in
number theory, itself, and arithmetic, since the mathematics of
Minkowski geometry is equiconsistent with the theory of real numbers
and with arithmetic.

You see yourself this way,
http://www.mazepath.com/uncleal/effete6.jpg
The entire remainder of the planet sees you this way,
http://www.mazepath.com/uncleal/effete3.png

http://www.albinoblacksheep.com/flash/youare.swf
http://www.mazepath.com/uncleal/sunshine.jpg
http://www.you-moron.com/

http://www.apa.org/journals/psp/psp7761121.html
http://insti.physics.sunysb.edu/~siegel/quack.html
http://www.firehead.org/~jessh/film/kubrick/Kubrick-Psycho.html
http://www.naturalchild.com/elliott_barker/prisons.html

Hey, stooopid troll Eleaticus - Do you want EVIDENCE? Each of the 24
GPS satellites carries either four cesium atomic clocks or three
rubidum atomic clocks in orbit, with full relativistic corrections
being applied.

http://math.ucr.edu/home/baez/RelWWW/tests.html
Mathematics of gravitation
http://wugrav.wustl.edu/people/CMW/update98.pdf
http://www.astro.northwestern.edu/AspenW04/Papers/lorimer1.pdf
Equivalence Principle testing
http://arXiv.org/abs/hep-th/0111236
Geometric structure of reality
http://arXiv.org/abs/hep-th/0307140
GR structure, especially Part 4/p. 7
http://relativity.livingreviews.org/Articles/lrr-2001-4/index.html
http://arXiv.org/abs/gr-qc/0311039
http://www.weburbia.demon.co.uk/physics/experiments.html
Experimental constraints on General Relativity.
http://tycho.usno.navy.mil/ptti/ptti2002/paper20.pdf
Nature 425 374 (2003)
http://rattler.cameron.edu/EMIS/journals/LRG/Articles/Volume6/2003-1ashby/index.html
http://www.eftaylor.com/pub/projecta.pdf
http://www.public.asu.edu/~rjjacob/Lecture16.pdf
Relativity in the GPS system
http://arXiv.org/abs/gr-qc/9909014
Phys. Rev. Lett. 92 (2004) 121101
falling light
http://hyperphysics.phy-astr.gsu.edu/hbase/relativ/airtim.html
Hafele-Keating Experiment
http://www.hawaii.edu/suremath/SRtwinParadox.html
http://physics.syr.edu/courses/modules/LIGHTCONE/twins.html
Twin Paradox
Science 303(5661) 1143;1153 (2004)
http://arXiv.org/abs/astro-ph/0401086
http://arxiv.org/abs/astro-ph/0312071
Deeply relativistic neutron star binaries
http://arxiv.org/abs/hep-th/0405160
Black hole evaporation
http://www.npl.washington.edu/eotwash/pdf/prl83-3585.pdf
http://arXiv.org/abs/gr-qc/0301024
Nordtvedt Effect
http://arxiv.org/abs/astro-ph/0403292
http://arXiv.org/abs/astro-ph/0310723
WMAP + Sloane Digital Sky Survey
http://arxiv.org/abs/hep-ph/0404175
Dark matter candidates
http://nedwww.ipac.caltech.edu/level5/March01/Carroll/frames.html
Carroll on what it all means.

NIM A 355 537 (1995)
Physics Letters B 328 103 (1994)
Physical Review Letters 64 1697 (1990)
Physical Review Letters 39 1051 (1977)
Physical Review 135 B1071 (1964)
Physics Letters 12 260 (1964)
Europhysics Letters 56(2) 170-174 (2001)
General Relativity and Gravitation 34(9) 1371 (2002)

http://fourmilab.to/etexts/einstein/specrel/specrel.pdf
http://www.geocities.com/physics_world/sr/ae_1905_error.htm
http://www.physics.gatech.edu/people/faculty/finkelstein/relativity.pdf
http://users.powernet.co.uk/bearsoft/Paper6.pdf
http://users.powernet.co.uk/bearsoft/LPHrel.html
Longitudinal and transverse mass

http://www.navcen.uscg.gov/pubs/gps/gpsuser/gpsuser.pdf
http://www.navcen.uscg.gov/pubs/gps/sigspec/default.htm
http://www.navcen.uscg.gov/pubs/gps/icd200/default.htm
http://www.trimble.com/gps/index.html
http://sirius.chinalake.navy.mil/satpred/
http://www.phys.lsu.edu/mog/mog9/node9.html
http://egtphysics.net/GPS/RelGPS.htm
http://www.schriever.af.mil/gps/Current/current.oa1
http://edu-observatory.org/gps/gps_books.html
http://www-astronomy.mps.ohio-state.edu/~pogge/Ast162/Unit5/gps.html

--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/qz.pdf
Ads
  #2  
Old October 17th 04 posted to sci.physics,sci.physics.relativity,alt.physics,sci.math
David McAnally
external usenet poster
 
Posts: 442
Default Invariant Galilean Transformations (FAQ) On All Laws

Uncle Al writes:

Eleaticus wrote:
[snip lies]

Invariant Galilean Transformations (FAQ) On All Laws
(c) Eleaticus/Oren C. Webster

[snip 1300 lines of trolled garbage]


Eleaticus has explicitly demonstrated what many would have suspected for
ages: that he is completely ignorant of multivariable calculus. He has no
familiarity with, or concept of, the Chain Rule in multivariable calculus.
Take, for example, his much beloved Galilean Transformation:

t' = t,

x' = x - vt,

y' = y,

z' = z.

His refusal to accept that t' must be introduced as a separate variable
presumably springs from an unwillingness to acknowledge that space and
time are best described as a four-dimensional manifold, with four
coordinates, instead of a time evolution of a three-dimensional manifold,
and that the change of coordinate system should be a change of four
coordinates, and not a time-dependent change of three coordinates. This
is particularly vital when it comes to fields over space and time
(electric and magnetic fields for example).

The transformation law for the differential operators under the Galilean
transformation is given by:

d/dt' = d/dt + v d/dx,

d/dx' = d/dx,

d/dy' = d/dy,

d/dz' = d/dz.

This fact alone shows the necessity of introducing a new variable t',
since partial differentiation with respect to t' (constant x', y', z')
is a different operation to partial differentiation with respect to t
(constant x, y, z). The above transformation law is determined by the
Chain Rule:

d/dt' = dt/dt' d/dt + dx/dt' d/dx + dy/dt' d/dy + dz/dt' d/dz,

d/dx' = dt/dx' d/dt + dx/dx' d/dx + dy/dx' d/dy + dz/dx' d/dz,

d/dy' = dt/dy' d/dt + dx/dy' d/dx + dy/dy' d/dy + dz/dy' d/dz,

d/dz' = dt/dz' d/dt + dx/dz' d/dx + dy/dz' d/dy + dz/dz' d/dz.

The presence of the term involving d/dx in the expression for d/dt' is
indicative of the fact that x depends on t' (x', y', z', being held
constant), as can be seen from the fact that the coefficient of d/dx in
the expression for d/dt' is dx/dt'. Because of the now demonstrated fact
that Eleaticus has no formal education in multivariable calculus, he has
managed, somehow, to get it into his head that the presence of the term
involving d/dx in the expression for d/dt' is indicative of t' depending
on x (t, y, z, being held constant). Because of his erroneous idea
Eleaticus cannot get the correct transformation law for the differential
operators under the Galilean Transformation, and he cannot determine the
invariance or otherwise of Maxwell's Equations under the Galilean
Transformation. The first advice to Eleaticus is to learn multivariable
calculus.

Eleaticus should not pretend that he can understand how to determine
invariance or otherwise of Maxwell's Equations under the Galilean
Transformation, or under the Lorentz Transformation, until he has made
sure that he does understand the multivariable calculus which underlies
such considerations. He has yet to prove that he has attained the
proficiency in multivariable calculus which would allow him to make such
determinations.

The homogeneous Maxwell equations are invariant under the Galilean
Transformation, with transformation laws:

E_x' = E_x,

E_y' = E_y - v B_z,

E_z' = E_z + v B_y,

B_x' = B_x,

B_y' = B_y,

B_z' = B_z.

The derivation of these transformation laws was determined using the
transformation laws for the differential operators that I gave above.
These transformation laws have the additional advantage that they
determine the correct transformation for the force law, thus providing
further evidence in favour of the transformation law for the differential
operators, as I gave above.

The inhomogeneous Maxwell equations are also invariant under the Galilean
transformation, with transformation laws:

E_x' = E_x,

E_y' = E_y,

E_z' = E_z,

B_x' = B_x,

B_y' = B_y + v/c^2 E_z,

B_z' = B_z - v/c^2 E_y,

\rho' = \rho,

J_x' = J_x - v \rho,

J_y' = J_y,

J_z' = J_z.

Note the the transformation laws for the charge density and current
density are as they should be under the Galilean transformation.

So we now have that the homogeneous equations are invariant under the
Galilean Transformation, and the inhomogeneous equations are invariant
under the Galilean Transformation, but Maxwell's Equations as a whole are
NOT invariant under the Galilean Transformation, since the transformation
laws required for the EM field for the two cases are inconsistent with
each other. The transformation law for the EM field which makes the
homogeneous equations invariant will not also make the inhomogeneous
equations invariant. The transformation law for the EM field which makes
the inhomogeneous equations invariant will not also make the homogeneous
equations invariant.

On the other hand, all of Maxwell's equations are invariant under the
Lorentz Transformation, with transformation laws:

E_x' = E_x,

E_y' = \gamma (E_y - v B_z),

E_z' = \gamma (E_z + v B_y),

B_x' = B_x,

B_y' = \gamma (B_y + v/c^2 E_z),

B_z' = \gamma (B_z - v/c^2 E_y),

\rho' = \gamma (\rho - v/c^2 J_x),

J_x' = \gamma (J_x - v \rho),

J_y' = J_y,

J_z' = J_z,

where \gamma = 1/sqrt(1 - v^2/c^2).

David

-----
  #3  
Old October 17th 04 posted to sci.physics,sci.physics.relativity,alt.physics,sci.math
Uncle Al
external usenet poster
 
Posts: 17,336
Default Invariant Galilean Transformations (FAQ) On All Laws

David McAnally wrote:

Uncle Al writes:

Eleaticus wrote:
[snip lies]

Invariant Galilean Transformations (FAQ) On All Laws
(c) Eleaticus/Oren C. Webster

[snip 1300 lines of trolled garbage]


Eleaticus has explicitly demonstrated what many would have suspected for
ages: that he is completely ignorant of multivariable calculus. He has no
familiarity with, or concept of, the Chain Rule in multivariable calculus.
Take, for example, his much beloved Galilean Transformation:

t' = t,

x' = x - vt,

y' = y,

z' = z.

His refusal to accept that t' must be introduced as a separate variable
presumably springs from an unwillingness to acknowledge that space and
time are best described as a four-dimensional manifold, with four
coordinates, instead of a time evolution of a three-dimensional manifold,
and that the change of coordinate system should be a change of four
coordinates, and not a time-dependent change of three coordinates. This
is particularly vital when it comes to fields over space and time
(electric and magnetic fields for example).

[snip erudition]

With your permission, I will also ram your exposition down his
stooopid face every time he trolls his crap.

--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/qz.pdf
  #4  
Old October 17th 04 posted to sci.physics,sci.physics.relativity,alt.physics,sci.math
eleaticus
external usenet poster
 
Posts: 913
Default Invariant Galilean Transformations (FAQ) On All Laws


"David McAnally" wrote in message
...

His refusal to accept that t' must be introduced as a separate variable
presumably springs from an unwillingness to acknowledge that space and
time are best described as a four-dimensional manifold, with four
coordinates, instead of a time evolution of a three-dimensional manifold,
and that the change of coordinate system should be a change of four
coordinates, and not a time-dependent change of three coordinates. This
is particularly vital when it comes to fields over space and time
(electric and magnetic fields for example).


The subject in discussion is NOT the SR transforms, but Newtonian, with NO
asshole time transform.

You are like a simpleton (what a surprize) who insists on imposing the rules
of pinochle on bridge. Base you analysis of the play of a hand on the rules
of the game being played.

The transformation law for the differential operators under the Galilean
transformation is given by:

d/dt' = d/dt + v d/dx,

d/dx' = d/dx,

d/dy' = d/dy,

d/dz' = d/dz.

This fact alone shows the necessity of introducing a new variable t',
since partial differentiation with respect to t' (constant x', y', z')
is a different operation to partial differentiation with respect to t
(constant x, y, z). The above transformation law is determined by the
Chain Rule:


Actually, that shows why you impose the fraudulant (en re Newton) time
transform.

If you had even the tiniest trace of honesty (rather than True Believer
sincerity) I's ask: do the work without imposing the idiot
time transform.


d/dt' = dt/dt' d/dt + dx/dt' d/dx + dy/dt' d/dy + dz/dt' d/dz,

d/dx' = dt/dx' d/dt + dx/dx' d/dx + dy/dx' d/dy + dz/dx' d/dz,

d/dy' = dt/dy' d/dt + dx/dy' d/dx + dy/dy' d/dy + dz/dy' d/dz,

d/dz' = dt/dz' d/dt + dx/dz' d/dx + dy/dz' d/dy + dz/dz' d/dz.

The presence of the term involving d/dx in the expression for d/dt' is
indicative of the fact that x depends on t' (x', y', z', being held
constant), as can be seen from the fact that the coefficient of d/dx in
the expression for d/dt' is dx/dt'. Because of the now demonstrated fact
that Eleaticus has no formal education in multivariable calculus, he has
managed, somehow, to get it into his head that the presence of the term
involving d/dx in the expression for d/dt' is indicative of t' depending
on x (t, y, z, being held constant). Because of his erroneous idea
Eleaticus cannot get the correct transformation law for the differential
operators under the Galilean Transformation, and he cannot determine the
invariance or otherwise of Maxwell's Equations under the Galilean
Transformation. The first advice to Eleaticus is to learn multivariable
calculus.

Eleaticus should not pretend that he can understand how to determine
invariance or otherwise of Maxwell's Equations under the Galilean
Transformation, or under the Lorentz Transformation, until he has made
sure that he does understand the multivariable calculus which underlies
such considerations. He has yet to prove that he has attained the
proficiency in multivariable calculus which would allow him to make such
determinations.

The homogeneous Maxwell equations are invariant under the Galilean
Transformation, with transformation laws:

E_x' = E_x,

E_y' = E_y - v B_z,

E_z' = E_z + v B_y,

B_x' = B_x,

B_y' = B_y,

B_z' = B_z.

The derivation of these transformation laws was determined using the
transformation laws for the differential operators that I gave above.
These transformation laws have the additional advantage that they
determine the correct transformation for the force law, thus providing
further evidence in favour of the transformation law for the differential
operators, as I gave above.

The inhomogeneous Maxwell equations are also invariant under the Galilean
transformation, with transformation laws:

E_x' = E_x,

E_y' = E_y,

E_z' = E_z,

B_x' = B_x,

B_y' = B_y + v/c^2 E_z,

B_z' = B_z - v/c^2 E_y,

\rho' = \rho,

J_x' = J_x - v \rho,

J_y' = J_y,

J_z' = J_z.

Note the the transformation laws for the charge density and current
density are as they should be under the Galilean transformation.

So we now have that the homogeneous equations are invariant under the
Galilean Transformation, and the inhomogeneous equations are invariant
under the Galilean Transformation, but Maxwell's Equations as a whole are
NOT invariant under the Galilean Transformation, since the transformation
laws required for the EM field for the two cases are inconsistent with
each other. The transformation law for the EM field which makes the
homogeneous equations invariant will not also make the inhomogeneous
equations invariant. The transformation law for the EM field which makes
the inhomogeneous equations invariant will not also make the homogeneous
equations invariant.

On the other hand, all of Maxwell's equations are invariant under the
Lorentz Transformation, with transformation laws:

E_x' = E_x,

E_y' = \gamma (E_y - v B_z),

E_z' = \gamma (E_z + v B_y),

B_x' = B_x,

B_y' = \gamma (B_y + v/c^2 E_z),

B_z' = \gamma (B_z - v/c^2 E_y),

\rho' = \gamma (\rho - v/c^2 J_x),

J_x' = \gamma (J_x - v \rho),

J_y' = J_y,

J_z' = J_z,

where \gamma = 1/sqrt(1 - v^2/c^2).

David

-----



  #5  
Old October 17th 04 posted to sci.physics,sci.physics.relativity,alt.physics,sci.math
eleaticus
external usenet poster
 
Posts: 913
Default Invariant Galilean Transformations (FAQ) On All Laws


"Uncle Al" wrote in message
...

His refusal to accept that t' must be introduced as a separate variable
presumably springs from an unwillingness to acknowledge that space and
time are best described as a four-dimensional manifold, with four
coordinates, instead of a time evolution of a three-dimensional

manifold,
and that the change of coordinate system should be a change of four
coordinates, and not a time-dependent change of three coordinates. This
is particularly vital when it comes to fields over space and time
(electric and magnetic fields for example).

[snip erudition]


With your permission, I will also ram your exposition down his
stooopid face every time he trolls his crap.


He starts off with the refusal to play by the Newtonian rules, which are
that there is absolute time, not a time transform, and you prove yourself an
absolute - not just relative - asshole by 'ramming' his intellectually
indefensible crap up my asshole?

There is certainly no room up yours what with your penis-shaped head up
there!

eleaticus


  #6  
Old October 17th 04 posted to sci.physics,sci.physics.relativity,alt.physics,sci.math
eleaticus
external usenet poster
 
Posts: 913
Default Invariant Galilean Transformations (FAQ) On All Laws


"David McAnally" wrote in message
...

Eleaticus has explicitly demonstrated what many would have suspected for
ages: that he is completely ignorant of multivariable calculus. He has no
familiarity with, or concept of, the Chain Rule in multivariable calculus.
Take, for example, his much beloved Galilean Transformation:

t' = t,


Mind if I call you Golem? (sp? From Lord of the Rings).

You have become increasingly corrupt.

t=t.

There is NO time transform in my 'beloved' transforms, as you admit below.
It is YOU and other captains of corruption that insist on treating Newton as
if he believed time was not absolute.

x' = x - vt,

y' = y,

z' = z.

His refusal to accept that t' must be introduced as a separate variable
presumably springs from an unwillingness to acknowledge that space and
time are best described as a four-dimensional manifold, with four
coordinates, instead of a time evolution of a three-dimensional manifold,
and that the change of coordinate system should be a change of four
coordinates, and not a time-dependent change of three coordinates. This
is particularly vital when it comes to fields over space and time
(electric and magnetic fields for example).


In conducting Newtonian-theoretical discussion/analyis, you do Newtonian
things.

eleaticus


  #7  
Old October 17th 04 posted to sci.physics,sci.physics.relativity,alt.physics,sci.math
robert j. kolker
external usenet poster
 
Posts: 3,233
Default Invariant Galilean Transformations (FAQ) On All Laws



eleaticus wrote:

"David McAnally" wrote in message
...


Eleaticus has explicitly demonstrated what many would have suspected for
ages: that he is completely ignorant of multivariable calculus. He has no
familiarity with, or concept of, the Chain Rule in multivariable calculus.
Take, for example, his much beloved Galilean Transformation:

t' = t,



Mind if I call you Golem? (sp? From Lord of the Rings).

You have become increasingly corrupt.

t=t.


Do you have the slightest concept of a co-ordinate transformation?

You have one frame of reference in which the co-ordinates are written
unprimed and another frame of reference in which the co-ordinates are
written with primes. What makes the galilean transform what it is, is
the assumption that time is the same in every inertial frame of
reference and that velocities add.

Bob Kolker



  #8  
Old October 17th 04 posted to sci.physics,sci.physics.relativity,alt.physics,sci.math
eleaticus
external usenet poster
 
Posts: 913
Default Invariant Galilean Transformations (FAQ) On All Laws


"David McAnally" wrote in message
...

His refusal to accept that t' must be introduced as a separate variable
presumably springs from an unwillingness to acknowledge that space and
time are best described as a four-dimensional manifold, with four
coordinates, instead of a time evolution of a three-dimensional manifold,
and that the change of coordinate system should be a change of four
coordinates, and not a time-dependent change of three coordinates. This
is particularly vital when it comes to fields over space and time
(electric and magnetic fields for example).


Go against your corrupt form and treat the Newtonian-theoretical transforms
honestly and THEN make consequential claims against them. There is only one
purpose in treating Newtonian basics dishonestly, and that is to apply the
dishonest results as arguments about subsequent issues.

Treat Newtonian-theoretical transforms in Newtonian fashion, that is without
the three corrupt, strawman mal-feasant impositions of anti-Newton material
on Newton.

Do it, you corrupt analoid.

You True Believer cretins can continue to assert untruths about me because
you won't deal honestly with the basics.

eleaticus




The transformation law for the differential operators under the Galilean
transformation is given by:

d/dt' = d/dt + v d/dx,

d/dx' = d/dx,

d/dy' = d/dy,

d/dz' = d/dz.

This fact alone shows the necessity of introducing a new variable t',
since partial differentiation with respect to t' (constant x', y', z')
is a different operation to partial differentiation with respect to t
(constant x, y, z). The above transformation law is determined by the
Chain Rule:

d/dt' = dt/dt' d/dt + dx/dt' d/dx + dy/dt' d/dy + dz/dt' d/dz,

d/dx' = dt/dx' d/dt + dx/dx' d/dx + dy/dx' d/dy + dz/dx' d/dz,

d/dy' = dt/dy' d/dt + dx/dy' d/dx + dy/dy' d/dy + dz/dy' d/dz,

d/dz' = dt/dz' d/dt + dx/dz' d/dx + dy/dz' d/dy + dz/dz' d/dz.

The presence of the term involving d/dx in the expression for d/dt' is
indicative of the fact that x depends on t' (x', y', z', being held
constant), as can be seen from the fact that the coefficient of d/dx in
the expression for d/dt' is dx/dt'. Because of the now demonstrated fact
that Eleaticus has no formal education in multivariable calculus, he has
managed, somehow, to get it into his head that the presence of the term
involving d/dx in the expression for d/dt' is indicative of t' depending
on x (t, y, z, being held constant). Because of his erroneous idea
Eleaticus cannot get the correct transformation law for the differential
operators under the Galilean Transformation, and he cannot determine the
invariance or otherwise of Maxwell's Equations under the Galilean
Transformation. The first advice to Eleaticus is to learn multivariable
calculus.

Eleaticus should not pretend that he can understand how to determine
invariance or otherwise of Maxwell's Equations under the Galilean
Transformation, or under the Lorentz Transformation, until he has made
sure that he does understand the multivariable calculus which underlies
such considerations. He has yet to prove that he has attained the
proficiency in multivariable calculus which would allow him to make such
determinations.

The homogeneous Maxwell equations are invariant under the Galilean
Transformation, with transformation laws:

E_x' = E_x,

E_y' = E_y - v B_z,

E_z' = E_z + v B_y,

B_x' = B_x,

B_y' = B_y,

B_z' = B_z.

The derivation of these transformation laws was determined using the
transformation laws for the differential operators that I gave above.
These transformation laws have the additional advantage that they
determine the correct transformation for the force law, thus providing
further evidence in favour of the transformation law for the differential
operators, as I gave above.

The inhomogeneous Maxwell equations are also invariant under the Galilean
transformation, with transformation laws:

E_x' = E_x,

E_y' = E_y,

E_z' = E_z,

B_x' = B_x,

B_y' = B_y + v/c^2 E_z,

B_z' = B_z - v/c^2 E_y,

\rho' = \rho,

J_x' = J_x - v \rho,

J_y' = J_y,

J_z' = J_z.

Note the the transformation laws for the charge density and current
density are as they should be under the Galilean transformation.

So we now have that the homogeneous equations are invariant under the
Galilean Transformation, and the inhomogeneous equations are invariant
under the Galilean Transformation, but Maxwell's Equations as a whole are
NOT invariant under the Galilean Transformation, since the transformation
laws required for the EM field for the two cases are inconsistent with
each other. The transformation law for the EM field which makes the
homogeneous equations invariant will not also make the inhomogeneous
equations invariant. The transformation law for the EM field which makes
the inhomogeneous equations invariant will not also make the homogeneous
equations invariant.

On the other hand, all of Maxwell's equations are invariant under the
Lorentz Transformation, with transformation laws:

E_x' = E_x,

E_y' = \gamma (E_y - v B_z),

E_z' = \gamma (E_z + v B_y),

B_x' = B_x,

B_y' = \gamma (B_y + v/c^2 E_z),

B_z' = \gamma (B_z - v/c^2 E_y),

\rho' = \gamma (\rho - v/c^2 J_x),

J_x' = \gamma (J_x - v \rho),

J_y' = J_y,

J_z' = J_z,

where \gamma = 1/sqrt(1 - v^2/c^2).

David

-----



  #9  
Old October 17th 04 posted to sci.physics,sci.physics.relativity,alt.physics,sci.math
eleaticus
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Posts: 913
Default Invariant Galilean Transformations (FAQ) On All Laws


"David McAnally" wrote in message
...
The transformation law for the differential operators under the Galilean
transformation is given by:

d/dt' = d/dt + v d/dx,

d/dx' = d/dx,

d/dy' = d/dy,

d/dz' = d/dz.

This fact alone shows the necessity of introducing a new variable t',
since partial differentiation with respect to t' (constant x', y', z')
is a different operation to partial differentiation with respect to t
(constant x, y, z). The above transformation law is determined by the
Chain Rule:


That is circular 'reasoning'. You impose the anti-theoretical (Newtonian,
rememer) time transform and say the result shows you must have the
anti-theoretical time transformed 'variable'.

eleaticus


  #10  
Old October 17th 04 posted to sci.physics,sci.physics.relativity,alt.physics,sci.math
eleaticus
external usenet poster
 
Posts: 913
Default Invariant Galilean Transformations (FAQ) On All Laws


"David McAnally" wrote in message
...

The transformation law for the differential operators under the Galilean
transformation is given by:


d/dt' = d/dt + v d/dx,


No, d/dt = d/dt.

Show us the results when you do not impose the anti-theoretical (Newtonwise,
which is what is under discussion) time transform. t=t.

Come on, McAnal(ly).

Surely YOU can do it.

It is remarkably corrupt for you to continue taking supposed consequences of
honest treatment as reason to not apply honest treatment.

eleaticus


 




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