In SR, the Lorentz factor is given by the equation,

gamma = c / sqrt(c^2 - v^2)

This can be viewed in terms of a right triangle where c is the
hypotenuse, v is one of the other sides, and therefore, sqrt(c^2 - v^2)
is the remaining side.

This means that the Lorentz factor is the ratio of 2 sides of a right
triangle.

This is based on the Pythagorean theorem in Euclidean geometry, which
can be expressed as,

c^2 = a^2 + b^2

Given that the Pythagorean theorem can be expressed in non-Euclidean
geometry, then the Lorentz factor should also be able to be expressed.

Does anyone know if this has been looked into before?
Does anyone know what the equation for the Lorentz factor would be in
the geometry of GR?
Would such an equation give the correct results in GR?

"Golden Boar" wrote in message
oups.com...
In SR, the Lorentz factor is given by the equation,

gamma = c / sqrt(c^2 - v^2)

This can be viewed in terms of a right triangle where c is the
hypotenuse, v is one of the other sides, and therefore, sqrt(c^2 - v^2)
is the remaining side.

This means that the Lorentz factor is the ratio of 2 sides of a right
triangle.

This is based on the Pythagorean theorem in Euclidean geometry, which
can be expressed as,

c^2 = a^2 + b^2

Given that the Pythagorean theorem can be expressed in non-Euclidean
geometry,

The Pythagorean theorem is equivalent to Euclid's 5th whose violation is
what defines non Euclidian geometry.

Bill

then the Lorentz factor should also be able to be expressed.

Does anyone know if this has been looked into before?
Does anyone know what the equation for the Lorentz factor would be in
the geometry of GR?
Would such an equation give the correct results in GR?

Bill Hobba wrote:
"Golden Boar" wrote in message
oups.com...
In SR, the Lorentz factor is given by the equation,

gamma = c / sqrt(c^2 - v^2)

This can be viewed in terms of a right triangle where c is the
hypotenuse, v is one of the other sides, and therefore, sqrt(c^2 - v^2)
is the remaining side.

This means that the Lorentz factor is the ratio of 2 sides of a right
triangle.

This is based on the Pythagorean theorem in Euclidean geometry, which
can be expressed as,

c^2 = a^2 + b^2

Given that the Pythagorean theorem can be expressed in non-Euclidean
geometry,

The Pythagorean theorem is equivalent to Euclid's 5th whose violation is
what defines non Euclidian geometry.

According to wikipedia,
http://en.wikipedia.org/wiki/Pythago...idean_geometry

Pythagorean theorem can be expressed in spherical geometry and
hyperbolic plane geometry, since the Pythagorean theorem is a special
case of the law of cosines.


Bill

then the Lorentz factor should also be able to be expressed.

Does anyone know if this has been looked into before?
Does anyone know what the equation for the Lorentz factor would be in
the geometry of GR?
Would such an equation give the correct results in GR?

Golden Boar wrote:
Bill Hobba wrote:
"Golden Boar" wrote in message
oups.com...
In SR, the Lorentz factor is given by the equation,

gamma = c / sqrt(c^2 - v^2)

This can be viewed in terms of a right triangle where c is the
hypotenuse, v is one of the other sides, and therefore, sqrt(c^2 - v^2)
is the remaining side.

This means that the Lorentz factor is the ratio of 2 sides of a right
triangle.

This is based on the Pythagorean theorem in Euclidean geometry, which
can be expressed as,

c^2 = a^2 + b^2

Given that the Pythagorean theorem can be expressed in non-Euclidean
geometry,

The Pythagorean theorem is equivalent to Euclid's 5th whose violation is
what defines non Euclidian geometry.

According to wikipedia,
http://en.wikipedia.org/wiki/Pythago...idean_geometry

Pythagorean theorem can be expressed in spherical geometry and
hyperbolic plane geometry, since the Pythagorean theorem is a special
case of the law of cosines.

True but irrelevant.

1) Special relativity is a brand of hyperbolic geometry. Go and see if
Pythagoras holds for (t,x,y,z). You are unknowingly only considering
(t,x).

2) The actual geometry of general relativity varies wildly. Like I was
trying to tell Porat, you have no reason to expect any concept of
special relativity to be valid in general relativity. Other than the
local speed of light, however. [I said *LOCAL*, I don't want to hear
any **** about Sagnac from the uneducated].

Think carefully - give me a well-reasoned answer as to why you would
expect the Lorentz factor in GR other than in the case where GR reduces
to SR.

The Lorentz factor is simply a common factor that pops up when
converting between coordinates. You can derive the Lorentz factor from
the Minkowski metric without any assumptions, assuming you have the
metric. Try deriving what the Lorentz factor would be for...the
Schwarzschild metric for example.




Bill

then the Lorentz factor should also be able to be expressed.

Does anyone know if this has been looked into before?
Does anyone know what the equation for the Lorentz factor would be in
the geometry of GR?
Would such an equation give the correct results in GR?

Golden Boar пи�ал(а):

In SR, the Lorentz factor is given by the equation,

gamma = c / sqrt(c^2 - v^2)

This can be viewed in terms of a right triangle where c is the
hypotenuse, v is one of the other sides, and therefore, sqrt(c^2 - v^2)
is the remaining side.

This means that the Lorentz factor is the ratio of 2 sides of a right
triangle.

This is based on the Pythagorean theorem in Euclidean geometry, which
can be expressed as,

c^2 = a^2 + b^2

Given that the Pythagorean theorem can be expressed in non-Euclidean
geometry, then the Lorentz factor should also be able to be expressed.

Does anyone know if this has been looked into before?

The triangle you are considered is the same that lies in the base of
my derivation of Lorentz transformation (it was been already sited
at that group http://vps137.narod.ru/article3a.html). So the gamma
is 1/cos(alpha), where alpha is a tilt angle, a characteristic of
velocity of the body. It may be given as the definition of the
velocity in 4D model proposed.

Does anyone know what the equation for the Lorentz factor would be in
the geometry of GR?
Would such an equation give the correct results in GR?

I hope GR might be further development of 4D model.

Eric Gisse wrote:
Golden Boar wrote:
Bill Hobba wrote:
"Golden Boar" wrote in message
oups.com...
In SR, the Lorentz factor is given by the equation,

gamma = c / sqrt(c^2 - v^2)

This can be viewed in terms of a right triangle where c is the
hypotenuse, v is one of the other sides, and therefore, sqrt(c^2 - v^2)
is the remaining side.

This means that the Lorentz factor is the ratio of 2 sides of a right
triangle.

This is based on the Pythagorean theorem in Euclidean geometry, which
can be expressed as,

c^2 = a^2 + b^2

Given that the Pythagorean theorem can be expressed in non-Euclidean
geometry,

The Pythagorean theorem is equivalent to Euclid's 5th whose violation is
what defines non Euclidian geometry.

According to wikipedia,
http://en.wikipedia.org/wiki/Pythago...idean_geometry

Pythagorean theorem can be expressed in spherical geometry and
hyperbolic plane geometry, since the Pythagorean theorem is a special
case of the law of cosines.

True but irrelevant.

1) Special relativity is a brand of hyperbolic geometry. Go and see if
Pythagoras holds for (t,x,y,z). You are unknowingly only considering
(t,x).

It it works for (t,x) then it works for (t,x,y,z).

Spacial interval
ds^2 = dx_1^2 + dx_2^2 + dx_3^2

Space-time interval
ds^2 = dx_1^2 + dx_2^2 + dx_3^2 + dx_4^2

I don't see what you are objecting to.


2) The actual geometry of general relativity varies wildly. Like I was
trying to tell Porat, you have no reason to expect any concept of
special relativity to be valid in general relativity. Other than the
local speed of light, however. [I said *LOCAL*, I don't want to hear
any **** about Sagnac from the uneducated].

I don't *expect* it to be valid. I'm wondering whether extending the
idea into GR could be acomplished, and if it could would it obtain the
correct results.

And I dont want to hear any **** from someone who thinks 782 is not a
little less than 800, when 800 is a rough estimate.


Think carefully - give me a well-reasoned answer as to why you would
expect the Lorentz factor in GR other than in the case where GR reduces
to SR.

What I mean by the Lorentz factor in GR is the ratio of two sides(or
arcs) of a spherical triangle, which in the case where GR reduces to SR
gives the ratio of two sides of a right triangle, c / sqrt(c^2 - v^2).

It's just a thought.


The Lorentz factor is simply a common factor that pops up when
converting between coordinates. You can derive the Lorentz factor from
the Minkowski metric without any assumptions, assuming you have the
metric. Try deriving what the Lorentz factor would be for...the
Schwarzschild metric for example.

You can derive the Lorentz factor from a right triangle without any
assumptions.





Bill

then the Lorentz factor should also be able to be expressed.

Does anyone know if this has been looked into before?
Does anyone know what the equation for the Lorentz factor would be in
the geometry of GR?
Would such an equation give the correct results in GR?

Golden Boar wrote:
Eric Gisse wrote:
Golden Boar wrote:
Bill Hobba wrote:
"Golden Boar" wrote in message
oups.com...
In SR, the Lorentz factor is given by the equation,

gamma = c / sqrt(c^2 - v^2)

This can be viewed in terms of a right triangle where c is the
hypotenuse, v is one of the other sides, and therefore, sqrt(c^2 - v^2)
is the remaining side.

This means that the Lorentz factor is the ratio of 2 sides of a right
triangle.

This is based on the Pythagorean theorem in Euclidean geometry, which
can be expressed as,

c^2 = a^2 + b^2

Given that the Pythagorean theorem can be expressed in non-Euclidean
geometry,

The Pythagorean theorem is equivalent to Euclid's 5th whose violation is
what defines non Euclidian geometry.

According to wikipedia,
http://en.wikipedia.org/wiki/Pythago...idean_geometry

Pythagorean theorem can be expressed in spherical geometry and
hyperbolic plane geometry, since the Pythagorean theorem is a special
case of the law of cosines.

True but irrelevant.

1) Special relativity is a brand of hyperbolic geometry. Go and see if
Pythagoras holds for (t,x,y,z). You are unknowingly only considering
(t,x).

It it works for (t,x) then it works for (t,x,y,z).

Spacial interval
ds^2 = dx_1^2 + dx_2^2 + dx_3^2

Space-time interval
ds^2 = dx_1^2 + dx_2^2 + dx_3^2 + dx_4^2

The metrics are wrong.


I don't see what you are objecting to.

You don't have a triangle in 4 dimensions.



2) The actual geometry of general relativity varies wildly. Like I was
trying to tell Porat, you have no reason to expect any concept of
special relativity to be valid in general relativity. Other than the
local speed of light, however. [I said *LOCAL*, I don't want to hear
any **** about Sagnac from the uneducated].

I don't *expect* it to be valid. I'm wondering whether extending the
idea into GR could be acomplished, and if it could would it obtain the
correct results.

What is the idea, exactly? Stop putting the Lorentz factor on such a
pedestal, it isn't that special.


And I dont want to hear any **** from someone who thinks 782 is not a
little less than 800, when 800 is a rough estimate.

You give Porat a pass on *how* much stupidity?



Think carefully - give me a well-reasoned answer as to why you would
expect the Lorentz factor in GR other than in the case where GR reduces
to SR.

What I mean by the Lorentz factor in GR is the ratio of two sides(or
arcs) of a spherical triangle, which in the case where GR reduces to SR
gives the ratio of two sides of a right triangle, c / sqrt(c^2 - v^2).

GR works in 4 dimensions, not 2.


It's just a thought.

Which has been brought up by you and shot down HOW MANY TIMES now?



The Lorentz factor is simply a common factor that pops up when
converting between coordinates. You can derive the Lorentz factor from
the Minkowski metric without any assumptions, assuming you have the
metric. Try deriving what the Lorentz factor would be for...the
Schwarzschild metric for example.

You can derive the Lorentz factor from a right triangle without any
assumptions.

It is like Schoenfelch saying he can "derive" the solution to d^2x/dt^2
= 0 by assuming a power series and setting the coefficients to what he
wants them to be. Completely true, even more completely worthless.






Bill

then the Lorentz factor should also be able to be expressed.

Does anyone know if this has been looked into before?
Does anyone know what the equation for the Lorentz factor would be in
the geometry of GR?
Would such an equation give the correct results in GR?

"Golden Boar" wrote in message
ps.com...

Eric Gisse wrote:
Golden Boar wrote:
Bill Hobba wrote:
"Golden Boar" wrote in message
oups.com...
In SR, the Lorentz factor is given by the equation,

gamma = c / sqrt(c^2 - v^2)

This can be viewed in terms of a right triangle where c is the
hypotenuse, v is one of the other sides, and therefore, sqrt(c^2 -
v^2)
is the remaining side.

This means that the Lorentz factor is the ratio of 2 sides of a
right
triangle.

This is based on the Pythagorean theorem in Euclidean geometry,
which
can be expressed as,

c^2 = a^2 + b^2

Given that the Pythagorean theorem can be expressed in
non-Euclidean
geometry,

The Pythagorean theorem is equivalent to Euclid's 5th whose violation
is
what defines non Euclidian geometry.

According to wikipedia,
http://en.wikipedia.org/wiki/Pythago...idean_geometry

Pythagorean theorem can be expressed in spherical geometry and
hyperbolic plane geometry, since the Pythagorean theorem is a special
case of the law of cosines.

True but irrelevant.

1) Special relativity is a brand of hyperbolic geometry. Go and see if
Pythagoras holds for (t,x,y,z). You are unknowingly only considering
(t,x).

It it works for (t,x) then it works for (t,x,y,z).

Spacial interval
ds^2 = dx_1^2 + dx_2^2 + dx_3^2

Space-time interval
ds^2 = dx_1^2 + dx_2^2 + dx_3^2 + dx_4^2

I don't see what you are objecting to.

For one the plus sign in front of dx_4^2 if you want coordinates to be real.
For another in Euclidian geometry that equation applies for macroscopic
distances - not just infinitesimal ones.

Bill



2) The actual geometry of general relativity varies wildly. Like I was
trying to tell Porat, you have no reason to expect any concept of
special relativity to be valid in general relativity. Other than the
local speed of light, however. [I said *LOCAL*, I don't want to hear
any **** about Sagnac from the uneducated].

I don't *expect* it to be valid. I'm wondering whether extending the
idea into GR could be acomplished, and if it could would it obtain the
correct results.

And I dont want to hear any **** from someone who thinks 782 is not a
little less than 800, when 800 is a rough estimate.


Think carefully - give me a well-reasoned answer as to why you would
expect the Lorentz factor in GR other than in the case where GR reduces
to SR.

What I mean by the Lorentz factor in GR is the ratio of two sides(or
arcs) of a spherical triangle, which in the case where GR reduces to SR
gives the ratio of two sides of a right triangle, c / sqrt(c^2 - v^2).

It's just a thought.


The Lorentz factor is simply a common factor that pops up when
converting between coordinates. You can derive the Lorentz factor from
the Minkowski metric without any assumptions, assuming you have the
metric. Try deriving what the Lorentz factor would be for...the
Schwarzschild metric for example.

You can derive the Lorentz factor from a right triangle without any
assumptions.





Bill

then the Lorentz factor should also be able to be expressed.

Does anyone know if this has been looked into before?
Does anyone know what the equation for the Lorentz factor would be
in
the geometry of GR?
Would such an equation give the correct results in GR?

Golden Boar wrote:
In SR, the Lorentz factor is given by the equation,

gamma = c / sqrt(c^2 - v^2)

This can be viewed in terms of a right triangle where c is the
hypotenuse, v is one of the other sides, and therefore, sqrt(c^2 - v^2)
is the remaining side.

This means that the Lorentz factor is the ratio of 2 sides of a right
triangle.

This is based on the Pythagorean theorem in Euclidean geometry, which
can be expressed as,

c^2 = a^2 + b^2

Given that the Pythagorean theorem can be expressed in non-Euclidean
geometry, then the Lorentz factor should also be able to be expressed.

Does anyone know if this has been looked into before?
Does anyone know what the equation for the Lorentz factor would be in
the geometry of GR?
Would such an equation give the correct results in GR?

I think you are confusing geometry and topolgy.
For an example how the Lorentz force can enter into
an inertial system look at equation (7)
http://chaos.fullerton.edu/~jimw/gen...rtia/index.htm

Gravitomagnetic potentials are predicted by Einstein's
formalism but a recent experiment has cast some doubt
about how they are derived.
http://www.esa.int/SPECIALS/GSP/SEM0L6OVGJE_0.html

Release of the Gravity Probe-B analysis, early in 2007 is
expected to shed some light on the issue.
http://einstein.stanford.edu/

A toy model of a plausible inertial mechanism
is descirbed he
http://www.citebase.org/cgi-bin/cita...hysics/0107015
http://www.chem.purdue.edu/gchelp/liquids/inddip.html
http://www.mypage.bluewin.ch/Bizarre/GRAV.htm

The Kouropoulos paper only expresses the Lorentz factors as
freqency or phase shifts so you have to see how the Woodward
paper overlaps... not an easy task, even if you are already well
founded in the relation between radiative and induction phenomena.


A statement from Kouropoulos companion paper:
Similarly, the Lorentz-like forces in [8] allow one to deduce
the torques of precessing gyroscopes by the forces on the mass
currents in the rotor owing to the magnetic effects of the precession.
However, to experience such inertial fields and forces, one
necessarily strays from the free-fall geodesics that justify the
Riemanian connexions often assumed to be approximated in
[2]. Note that the Newtonian paradigm of the PPN approximation
only considers non-geodesic forces, and it is therefore legitimate
to understand the antisymmetry of Fa in [2] as that of a
contorsion tensor.
http://www.mypage.bluewin.ch/Bizarre/MAX.htm

....may well explain the disparity between the Tajamar /
de Matos experiment and the predictions of GR.

Sue...


..

Sue... wrote:
Golden Boar wrote:
In SR, the Lorentz factor is given by the equation,

gamma = c / sqrt(c^2 - v^2)

This can be viewed in terms of a right triangle where c is the
hypotenuse, v is one of the other sides, and therefore, sqrt(c^2 - v^2)
is the remaining side.

This means that the Lorentz factor is the ratio of 2 sides of a right
triangle.

This is based on the Pythagorean theorem in Euclidean geometry, which
can be expressed as,


c^2 = a^2 + b^2

Given that the Pythagorean theorem can be expressed in non-Euclidean
geometry, then the Lorentz factor should also be able to be expressed.

Does anyone know if this has been looked into before?
Does anyone know what the equation for the Lorentz factor would be in
the geometry of GR?
Would such an equation give the correct results in GR?

I think you are confusing geometry and topolgy.
For an example how the Lorentz force can enter into
an inertial system look at equation (7)
http://chaos.fullerton.edu/~jimw/gen...rtia/index.htm

Gravitomagnetic potentials are predicted by Einstein's
formalism but a recent experiment has cast some doubt
about how they are derived.
http://www.esa.int/SPECIALS/GSP/SEM0L6OVGJE_0.html

Release of the Gravity Probe-B analysis, early in 2007 is
expected to shed some light on the issue.
http://einstein.stanford.edu/

A toy model of a plausible inertial mechanism
is descirbed he
http://www.citebase.org/cgi-bin/cita...hysics/0107015
http://www.chem.purdue.edu/gchelp/liquids/inddip.html
http://www.mypage.bluewin.ch/Bizarre/GRAV.htm

The Kouropoulos paper only expresses the Lorentz factors as
freqency or phase shifts so you have to see how the Woodward
paper overlaps... not an easy task, even if you are already well
founded in the relation between radiative and induction phenomena.


A statement from Kouropoulos companion paper:
Similarly, the Lorentz-like forces in [8] allow one to deduce
the torques of precessing gyroscopes by the forces on the mass
currents in the rotor owing to the magnetic effects of the precession.
However, to experience such inertial fields and forces, one
necessarily strays from the free-fall geodesics that justify the
Riemanian connexions often assumed to be approximated in
[2]. Note that the Newtonian paradigm of the PPN approximation
only considers non-geodesic forces, and it is therefore legitimate
to understand the antisymmetry of Fa in [2] as that of a
contorsion tensor.
http://www.mypage.bluewin.ch/Bizarre/MAX.htm

...may well explain the disparity between the Tajamar /
de Matos experiment and the predictions of GR.

Sue...
--------------------------
you are waisting your precious time and energy

gravitation is not caused by curved space-time
it is a property of some basic particles unknownand undiscovered yet
space is nothion and cant have any properties except hostong matter
if it is (imho) against GR so be it
yet th e special relativity is right (imho again )

ATB
Y.Porat
-----------------------


.