Minkowski's reformulation of Special Relativity is characterized

by elegance and symmetry. Can it be generalized?

Many theorists are guided by the belief that the most

general transformations applicable to the laws that govern a

given physical system or interaction, especially those that are

endowed with invariance properties, will have the greatest

probability for focusing light upon more general principles.

With that thought in mind, the author sought a

generalization of the Lorentz Transformations by way of a

straight forward generalization of the ring of complex numbers.

The reader will recall that all fields (including the complex

numbers) are rings. The converse, however, is not necessarily

true. But what is true is the historical fact that Minkowski

was able to reformulate Special Relativity, within the frame-

work of Minkowski Space-Time, by utilizing the properties of

complex numbers. He was thus able to unify space and time in

a most elegant mathematical fashion.

The author has humbly tried to follow the lead of

Minkowski’s treatment of SR (which involves particles

moving with relative constant velocities) in the search

of a set of straight forward invariant transformations for

particles (or frames of reference) that have a constant

relative acceleration with respect to each other. An intro-

duction to these concepts may be found at

http://www.intelrap.com/lt1.html

"Symmetry Observer" wrote in message
...

Minkowski's reformulation of Special Relativity is characterized

by elegance and symmetry. Can it be generalized?

Many theorists are guided by the belief that the most

general transformations applicable to the laws that govern a

given physical system or interaction, especially those that are

endowed with invariance properties, will have the greatest

probability for focusing light upon more general principles.

============================================

Many Catholics are guided by the belief that their tin god's
mother was a virgin when she conceived. That doesn't make them
right and neither are your general transformations no matter how
many crackpots believe in them, ****HEAD.
*plonk*

--
Androcles, proud to be as British as Baldric.
http://www.androcles01.pwp.blueyonde...MagnaCarta.wmv

On Jun 19, 9:39*pm, Symmetry Observer
wrote:
Minkowski's reformulation of Special Relativity is characterized

by elegance and symmetry. Can it be generalized?

* * *Many theorists are guided by the belief that the most

general transformations applicable to the laws that govern a

given physical system or interaction, especially those that are

endowed with invariance properties, will have the greatest

probability for focusing light upon more general principles.

* * * With that thought in mind, the author sought a

generalization of the Lorentz Transformations by way of a

straight forward generalization of the ring of complex numbers.

The reader will recall that all fields (including the complex

numbers) are rings. The converse, however, is not necessarily

true. But what is true is the historical fact that Minkowski

was able to reformulate Special Relativity, within the frame-

work of Minkowski Space-Time, by utilizing the properties of

complex numbers. He was thus able to unify space and time in

a most elegant mathematical fashion.

* * * The author has humbly tried to follow the lead of

Minkowski’s treatment of SR (which involves particles

moving with relative constant velocities) in the search

of a set of straight forward invariant transformations for

particles (or frames of reference) that have a constant

relative acceleration with respect to each other. An intro-

duction to these concepts may be found at

http://www.intelrap.com/lt1.html

xxein: Are you pretending to do physics or just math tricks?

On Jun 19, 8:05*pm, xxein wrote:
On Jun 19, 9:39*pm, Symmetry Observer
wrote:





Minkowski's reformulation of Special Relativity is characterized

by elegance and symmetry. Can it be generalized?

* * *Many theorists are guided by the belief that the most

general transformations applicable to the laws that govern a

given physical system or interaction, especially those that are

endowed with invariance properties, will have the greatest

probability for focusing light upon more general principles.

* * * With that thought in mind, the author sought a

generalization of the Lorentz Transformations by way of a

straight forward generalization of the ring of complex numbers.

The reader will recall that all fields (including the complex

numbers) are rings. The converse, however, is not necessarily

true. But what is true is the historical fact that Minkowski

was able to reformulate Special Relativity, within the frame-

work of Minkowski Space-Time, by utilizing the properties of

complex numbers. He was thus able to unify space and time in

a most elegant mathematical fashion.

* * * The author has humbly tried to follow the lead of

Minkowski’s treatment of SR (which involves particles

moving with relative constant velocities) in the search

of a set of straight forward invariant transformations for

particles (or frames of reference) that have a constant

relative acceleration with respect to each other. An intro-

duction to these concepts may be found at

http://www.intelrap.com/lt1.html

xxein: *Are you pretending to do physics or just math tricks?- Hide quoted text -

- Show quoted text -

That is a good question. And in anticipation of such questions I
coined the phrase “Mathematical Phiction”. Just as many things
that were once in the realm of science fiction are now firmly
based in reality, I want to call attention to certain mathe-
matical conceptualizations, endowed with rich and exotic
symmetry, that one day may have actual physical applications.

Correct me if I am mistaken about the fact that one can use
a Foucault Pendulum to determine the direction and magnitude
of acceleration. If that is the case then it would appear to be
not unreasonable to consider the possibility that invariant
coordinate transformations would be extremely useful in
transforming the laws of nature from an inertial to a
uniformly accelerated non-inertial frame of reference.

General Relativity is a monumental intellectual achieve-
ment. But it apparently does not present a straight forward
set of coordinate transformation equations that explicitly reduce to,
in the important realm of ordinary Newtonian Mechanics , the
equivalent of

X = x – (1/2)at^2

T = t

where the uniform acceleration a is small in comparison with the
acceleration near the surface of the sun or say near the
center of the galaxy.

In the corresponding case of the Lorentz Transformations, they
do indeed reduce to the ordinary Galilean Transformations

X = x-vt

T = t

when v is much smaller than the speed of light.

If someone is aware of a theorem that states that GR is the
one and only one theoretical framework that facilitates a description
of the laws of nature in accelerated frames of reference then please
let me know.

The bottom line is that if one knows his (uniform) accele-
ration (using an accelerometer of some type) with respect
to an inertial frame then for some (even cosmological)
applications it may not be necessary to use GR to calculate
“how matter tells space-time how to curve and how space-
time tells matter how to move”. It may be only necessary to
transform the laws of physics from an inertial frame to
a uniformly accelerated frame by way of a set of invariant
coordinate transformations for uniformly accelerated
motion.

The concepts presented in the author’s preliminary paper may be
generalized to higher orders of motion (non-zero higher order
derivatives of distance with respect to time) in more than
one spatial dimension.


http://www.intelrap.com/lt1.html

On Jun 20, 5:25*pm, Symmetry Observer
wrote:
On Jun 19, wrote:





On Jun 19, 9:39*pm, Symmetry Observer
wrote:

Minkowski's reformulation of Special Relativity is characterized

by elegance and symmetry. Can it be generalized?

* * *Many theorists are guided by the belief that the most

general transformations applicable to the laws that govern a

given physical system or interaction, especially those that are

endowed with invariance properties, will have the greatest

probability for focusing light upon more general principles.

* * * With that thought in mind, the author sought a

generalization of the Lorentz Transformations by way of a

straight forward generalization of the ring of complex numbers.

The reader will recall that all fields (including the complex

numbers) are rings. The converse, however, is not necessarily

true. But what is true is the historical fact that Minkowski

was able to reformulate Special Relativity, within the frame-

work of Minkowski Space-Time, by utilizing the properties of

complex numbers. He was thus able to unify space and time in

a most elegant mathematical fashion.

* * * The author has humbly tried to follow the lead of

Minkowski’s treatment of SR (which involves particles

moving with relative constant velocities) in the search

of a set of straight forward invariant transformations for

particles (or frames of reference) that have a constant

relative acceleration with respect to each other. An intro-

duction to these concepts may be found at

http://www.intelrap.com/lt1.html

xxein: *Are you pretending to do physics or just math tricks?- Hide quoted text -

- Show quoted text -

That is a good question. And in anticipation of such questions I
coined the phrase “Mathematical Phiction”. Just as many things
that were once in the realm of science fiction are now firmly
based in reality, I want to call attention to certain mathe-
matical conceptualizations, endowed with rich and exotic
symmetry, that one day may have actual physical applications.

Correct me if I am mistaken about the fact that one can use
a Foucault Pendulum to determine the direction and magnitude
of acceleration. If that is the case then it would appear to be
not unreasonable to consider the possibility that invariant
coordinate transformations would be extremely useful in
transforming the laws of nature from an inertial to a
uniformly accelerated non-inertial frame of reference.

General Relativity is a monumental intellectual achieve-
ment. But it apparently does not present a straight forward
set of coordinate transformation equations that explicitly reduce to,
in the important realm of ordinary Newtonian Mechanics , the
equivalent of

X = x – (1/2)at^2

T = t

where the uniform acceleration a is small in comparison with the
acceleration near the surface of the sun or say near the
center of the galaxy.

In the corresponding case of the Lorentz Transformations, they
do indeed reduce to the ordinary Galilean Transformations

X = x-vt

T = t

when v is much smaller than the speed of light.

If someone is aware of a theorem that states that GR is the
one and only one theoretical framework that facilitates a description
of the laws of nature in accelerated frames of reference then please
let me know.

The bottom line is that if one knows his (uniform) accele-
ration (using an accelerometer of some type) with respect
to an inertial frame then for some (even cosmological)
applications it may not be necessary to use GR to calculate
“how matter tells space-time how to curve and how space-
time tells matter how to move”. It may be only necessary to
transform the laws of physics from an inertial frame to
a uniformly accelerated frame by way of a set of invariant
coordinate transformations for uniformly accelerated
motion.

The concepts presented in the author’s preliminary paper may be
generalized to higher orders of motion (non-zero higher order
derivatives of distance with respect to time) in more than
one spatial dimension.

http://www.intelrap.com/lt1.html- Hide quoted text -

- Show quoted text -

xxein: The trouble is "the possibility that invariant coordinate
transformations would be extremely useful in transforming the laws of
nature from an inertial to a uniformly accelerated non-inertial frame
of reference." is that the transform has already been set.

Lorentz did it (among others) and then Einstein did it. The
difference was that Einstein added a connection to gravity with GR.
The trouble with that is using FOR's in gravity without knowing how
gravity functions. All he did with GR is paste a math onto a
subjective observation.

At least Lorentz inferred to it being a subjective observation. -This
is what see and measure for a reason apart from the objectivity of the
universe as a whole.- Einstein's mistake was to broil on the
subjective aspect of it.

"It may be only necessary to
transform the laws of physics from an inertial frame to
a uniformly accelerated frame by way of a set of invariant
coordinate transformations for uniformly accelerated
motion." Again you forget (or do not know) that GR does that.

What it doesn't do is 'explain' with a physical logic. It only
attempts to do so with math.

On Jun 20, 3:59*pm, xxein wrote:
On Jun 20, 5:25*pm, Symmetry Observer
wrote:





On Jun 19, wrote:

On Jun 19, 9:39*pm, Symmetry Observer
wrote:

Minkowski's reformulation of Special Relativity is characterized

by elegance and symmetry. Can it be generalized?

* * *Many theorists are guided by the belief that the most

general transformations applicable to the laws that govern a

given physical system or interaction, especially those that are

endowed with invariance properties, will have the greatest

probability for focusing light upon more general principles.

* * * With that thought in mind, the author sought a

generalization of the Lorentz Transformations by way of a

straight forward generalization of the ring of complex numbers.

The reader will recall that all fields (including the complex

numbers) are rings. The converse, however, is not necessarily

true. But what is true is the historical fact that Minkowski

was able to reformulate Special Relativity, within the frame-

work of Minkowski Space-Time, by utilizing the properties of

complex numbers. He was thus able to unify space and time in

a most elegant mathematical fashion.

* * * The author has humbly tried to follow the lead of

Minkowski’s treatment of SR (which involves particles

moving with relative constant velocities) in the search

of a set of straight forward invariant transformations for

particles (or frames of reference) that have a constant

relative acceleration with respect to each other. An intro-

duction to these concepts may be found at

http://www.intelrap.com/lt1.html

xxein: *Are you pretending to do physics or just math tricks?- Hide quoted text -

- Show quoted text -

That is a good question. And in anticipation of such questions I
coined the phrase “Mathematical Phiction”. Just as many things
that were once in the realm of science fiction are now firmly
based in reality, I want to call attention to certain mathe-
matical conceptualizations, endowed with rich and exotic
symmetry, that one day may have actual physical applications.

Correct me if I am mistaken about the fact that one can use
a Foucault Pendulum to determine the direction and magnitude
of acceleration. If that is the case then it would appear to be
not unreasonable to consider the possibility that invariant
coordinate transformations would be extremely useful in
transforming the laws of nature from an inertial to a
uniformly accelerated non-inertial frame of reference.

General Relativity is a monumental intellectual achieve-
ment. But it apparently does not present a straight forward
set of coordinate transformation equations that explicitly reduce to,
in the important realm of ordinary Newtonian Mechanics , the
equivalent of

X = x – (1/2)at^2

T = t

where the uniform acceleration a is small in comparison with the
acceleration near the surface of the sun or say near the
center of the galaxy.

In the corresponding case of the Lorentz Transformations, they
do indeed reduce to the ordinary Galilean Transformations

X = x-vt

T = t

when v is much smaller than the speed of light.

If someone is aware of a theorem that states that GR is the
one and only one theoretical framework that facilitates a description
of the laws of nature in accelerated frames of reference then please
let me know.

The bottom line is that if one knows his (uniform) accele-
ration (using an accelerometer of some type) with respect
to an inertial frame then for some (even cosmological)
applications it may not be necessary to use GR to calculate
“how matter tells space-time how to curve and how space-
time tells matter how to move”. It may be only necessary to
transform the laws of physics from an inertial frame to
a uniformly accelerated frame by way of a set of invariant
coordinate transformations for uniformly accelerated
motion.

The concepts presented in the author’s preliminary paper may be
generalized to higher orders of motion (non-zero higher order
derivatives of distance with respect to time) in more than
one spatial dimension.

http://www.intelrap.com/lt1.html-Hide quoted text -

- Show quoted text -

xxein: *The trouble is "the possibility that invariant coordinate
transformations would be extremely useful in transforming the laws of
nature from an inertial to a uniformly accelerated non-inertial frame
of reference." is that the transform has already been set.

Lorentz did it (among others) and then Einstein did it. *The
difference was that Einstein added a connection to gravity with GR.
The trouble with that is using FOR's in gravity without knowing how
gravity functions. *All he did with GR is paste a math onto a
subjective observation.

At least Lorentz inferred to it being a subjective observation. *-This
is what see and measure for a reason apart from the objectivity of the
universe as a whole.- *Einstein's mistake was to broil on the
subjective aspect of it.

"It may be only necessary to
transform the laws of physics from an inertial frame to
a uniformly accelerated frame by way of a set of invariant
coordinate transformations for uniformly accelerated
motion." *Again you forget (or do not know) that GR does that.

What it doesn't do is 'explain' with a physical logic. *It only
attempts to do so with math.- Hide quoted text -

- Show quoted text -

What are the GR invariant coordinate transformations, for
uniformly accelerated motion, that reduce
simply to

X = x - (1/2)at^2

T = t

in the Newtonian Limit ?