On May 27, 5:59 am, jem <x...@xxx.xxx> wrote:

It is odd though that you'd claim to have derived a result from the "most irreducible axioms possible", without ever explicitly indicating what those axioms are. Can you remedy that, Shooby, by posting a list of your postulates so they can be compared side-by-side with other sets of postulates that have been used to derive the LT?

The common notion of a postulate list is an extremely short list
mathematically independent hypotheses that can be put into a
remarkably succinct form. My derivation of the Lorentz transformation
is based entirely on conceptualizing the toy universe Xi_2, which
consists of two moving lines in one spatial dimension. The current
description of Xi_2 requires approximately 2 & 1/3 pages. I don't know
how to encapsulate the fundamental idea presented there into one
cogent principle at this time. But I do believe that my paper is clear
and should be understandable to bright high school students. I figure
that it is only a matter of time for the assumptions in my derivation
to be neatly translated into the pure language known as mathematical
logic. So for now, do the best you can and just read those 2 & 1/3
pages.

Shubeehttp://www.everythingimportant.org/relativity/special.pdf

On May 27, 5:59 am, jem <x...@xxx.xxx> wrote:

It is odd though that you'd claim to have derived a result from the "most irreducible axioms possible", without ever explicitly indicating what those axioms are. Can you remedy that, Shooby, by posting a list of your postulates so they can be compared side-by-side with other sets of postulates that have been used to derive the LT?

The common notion of a postulate list is an extremely short list
mathematically independent hypotheses that can be put into a
remarkably succinct form. My derivation of the Lorentz transformation
is based entirely on conceptualizing the toy universe Xi_2, which
consists of two moving lines in one spatial dimension. The current
description of Xi_2 requires approximately 2 & 1/3 pages. I don't know
how to encapsulate the fundamental idea presented there into one
cogent principle at this time. But I do believe that my paper is clear
and should be understandable to bright high school students. I figure
that it is only a matter of time for the assumptions in my derivation
to be neatly translated into the pure language known as mathematical
logic. So for now, do the best you can and just read those 2 & 1/3
pages.

Shubee
http://www.everythingimportant.org/relativity/special.pdf

On May 27, 8:25 pm, Tom Roberts <tjroberts...@sbcglobal.net> wrote:

Shubee wrote:

http://www.everythingimportant.org/relativity/special.pdf

I find it quite ridiculous for this paper to emphasize the
"axiomatization of physics" in title, abstract, and the opening page and
a half, and then to completely and utterly omit presenting any axioms at
all. Or even make any discernible progress towards such axioms. This
alone makes this paper useless,

I no longer believe this accusation. I did present the axioms of Xi_3
on page 6. They are exactly what I told you on this thread. I quote:

No, you have merely demonstrated that you can use his PoR without
stating that you did so, and can fool yourself into believing your own
omission.

Where did I use it? I only used the time equations from Xi_2 and the
assumption that my kindergarten time concept is well-defined
mathematically and is frame independent. That's correct. Time can be
defined in a similar manner, point by point, throughout the universe.
This approach permits both linear and nonlinear solutions. I gave a
reference to the nonlinear solution that solves the given problem and
presented all the major details for the linear case. Then I showed
that answer to be equivalent to the Lorentz transformation. The entire
approach of mine is perfectly consistent with an absolute frame of
reference. Therefore, I'm not using anything unnecessary like
Einstein's PoR. Note that I'm not excluding it either but future
editions of my paper will explain the logical possibility that
Einstein's PoR is a mathematical fantasy, i.e., it may be like the
Continuum Hypothesis or its negation. Physicists can use either one of
these two axioms and never reach a contradiction but only one of these
axioms is really true. Likewise, it could be that Einsteinian SR
doesn't even exist in the Hilbert atlas of all possible universes.

And the axioms for Xi_2 also seem sufficiently clear. I think that the
way I've illustrated and explained Xi_2 by letting my axioms unfold
naturally as my derivation progresses, is the best way to communicate
my meaning to high school students. I will work on improving my
presentation of Xi_2.

After eq (30) the dismissal of k<0 is just plain wrong. k<0 corresponds
to the 4d Euclid group, and it is associative. There are reasons to
dismiss it, but they are not given in this paper.

I corrected that mistake today and uploaded the revised paper.

On May 27, 8:25 pm, Tom Roberts <tjroberts...@sbcglobal.net> wrote:

Shubee wrote:

http://www.everythingimportant.org/relativity/special.pdf

I find it quite ridiculous for this paper to emphasize the
"axiomatization of physics" in title, abstract, and the opening page and
a half, and then to completely and utterly omit presenting any axioms at
all. Or even make any discernible progress towards such axioms. This
alone makes this paper useless, but it has numerous other faults as well.

It would be ridiculous if a high school student couldn't understand my
paper or would fail to recognize all my assumptions. My work is a work
in progress. I wouldn't mind adding my axioms at the very end. The
point of the paper is to teach students of high school algebra how to
derive the LT equations as simply as possible, with the fewest
assumptions possible.

The whole point of the "toy universes" appears to be an attempt to
describe uniform rectilinear motion without calling it that.

No. The whole point of Xi_2 is to arrive at equations (1) and (2),
which are nonlinear, new and the basis of my entire derivation. Thanks
for acknowledging that I'm presupposing Newton's first law of motion
and that I've described Newton's first law with nonlinear equations!

The unusual method of defining "time" by coordinates passing each
other is unrelated to common usages of the word,

I wrote that "Little children know intuitively that a tiny arrow that
moves steadily along a continuum of numbers is a clock." Forgive me
for breaking with tradition and for using a kindergarten concept that
is too difficult for physicists to understand.

and the need for an arbitrary and conventional minus sign should
be a BIG RED FLAG that something is amiss.

I thought that I explained that rather carefully. I'll have to write
this down as one of my axioms.

AXIOM 1.
If a clock is running backwards at the same rate that another clock is
moving forward, then a sign change is recommended for one of the
clocks. (Sigh).

Note that "uniform motion" is assumed but not defined (uniform
with respect to what?); there is no description of how such coordinate
frames could be set up or uniformity of motion assured.

Do you really believe that children would have a problem
conceptualizing clock time as an arrow moving steadily along a
continuum of numbers? That's the beauty of my approach. Elapsed time
is proportional to the distance traveled on a number line.

After eq (30) the dismissal of k<0 is just plain wrong. k<0 corresponds
to the 4d Euclid group, and it is associative.

You are confused. My k is defined differently than what you're
expecting. The rotation matrix is automatically excluded in my
approach. The operation defined by equation (30) is not associative
for negative k on real numbers. Ask a mathematician.

There are reasons to
dismiss it, but they are not given in this paper. k=0 is never dismissed
at all, and the possibility is just ignored. Given the historical
significance of k=0 (the Galilei group) this is a major omission.

There is no omission. You just haven't read carefully enough. I wrote:

"To emphasize that k is nonnegative, we write k = 1/c^2. At this
point, the only meaning that I have ascribed to c is that c is a real
number greater than zero. If the case where k=0 needs to be
considered, we may adopt the convention that c=infty in that
instance."

The author appears to be completely ignorant of modern mathematics, or
indeed any math other than elementary algebra (e.g. the labored and
clumsy application of group theory without ever mentioning this fact,

You have already displayed a remarkable amount of pompous arrogance
and the need to obfuscate the simplicity of my kindergarten clock. Now
you belittle me because I use the right level of mathematics for high
school students. Didn't I say they are my intended audience? And what
is the basis of your fantasy? I did not use any group theory in my
derivation. My boast is that group theory, like Einstein's relativity
principle, isn't required to derive the LT.

On May 27, 8:25 pm, Tom Roberts <tjroberts...@sbcglobal.net> wrote:

Shubee wrote:

http://www.everythingimportant.org/relativity/special.pdf

I find it quite ridiculous for this paper to emphasize the
"axiomatization of physics" in title, abstract, and the opening page and
a half, and then to completely and utterly omit presenting any axioms at
all. Or even make any discernible progress towards such axioms. This
alone makes this paper useless, but it has numerous other faults as well.

It would be ridiculous if a high school student couldn't understand my
paper or would fail to recognize all my assumptions. My work is a work
in progress. I wouldn't mind adding my axioms at the very end. The
point of the paper is to teach students of high school algebra how to
derive the LT equations as simply as possible, with the fewest
assumptions possible.

The whole point of the "toy universes" appears to be an attempt to
describe uniform rectilinear motion without calling it that.

No. The whole point of Xi_2 is to arrive at equations (1) and (2),
which are nonlinear, new and the basis of my entire derivation. Thanks
for acknowledging that I'm presupposing Newton's first law of motion
and that I've described Newton's first law with nonlinear equations!

The unusual method of defining "time" by coordinates passing each
other is unrelated to common usages of the word,

I wrote that "Little children know intuitively that a tiny arrow that
moves steadily along a continuum of numbers is a clock." Forgive me
for breaking with tradition and for using a kindergarten concept that
is too difficult for physicists to understand.

and the need for an arbitrary and conventional minus sign should
be a BIG RED FLAG that something is amiss.

I thought that I explained that rather carefully. I'll have to write
this down as one of my axioms.

AXIOM 1.
If a clock is running backwards at the same rate that another clock is
moving forward, then a sign change is recommended for one of the
clocks. (Sigh).

Note that "uniform motion" is assumed but not defined (uniform
with respect to what?); there is no description of how such coordinate
frames could be set up or uniformity of motion assured.

Do you really believe that children would have a problem
conceptualizing clock time as an arrow moving steadily along a
continuum of numbers? That's the beauty of my approach. Elapsed time
is proportional to the distance traveled on a number line.

After eq (30) the dismissal of k<0 is just plain wrong. k<0 corresponds
to the 4d Euclid group, and it is associative.

You are confused. My k is defined differently than what you're
expecting. The rotation matrix is automatically excluded in my
approach. The operation defined by equation (30) is not associative
for negative k on real numbers. Ask a mathematician.

There are reasons to
dismiss it, but they are not given in this paper. k=0 is never dismissed
at all, and the possibility is just ignored. Given the historical
significance of k=0 (the Galilei group) this is a major omission.

There is no omission. You just haven't read carefully enough. I wrote:

"To emphasize that k is nonnegative, we write k = 1/c^2. At this
point, the only meaning that I have ascribed to c is that c is a real
number greater than zero. If the case where k=0 needs to be
considered, we may adopt the convention that c=infty in that
instance."

The author appears to be completely ignorant of modern mathematics, or
indeed any math other than elementary algebra (e.g. the labored and
clumsy application of group theory without ever mentioning this fact,

You have already displayed a remarkable amount of pompous arrogance
and the need to obfuscate the simplicity of my kindergarten clock. Now
you belittle me because I use the right level of mathematics for high
school students. Didn't I say they are my intended audience? And what
is the basis of your fantasy? I did not use any group theory in my
derivation. My boast is that group theory, like Einstein's relativity
principle, isn't required to derive the LT.

On May 27, 8:25 pm, Tom Roberts <tjroberts...@sbcglobal.net> wrote:

Shubee wrote:

http://www.everythingimportant.org/relativity/special.pdf

I find it quite ridiculous for this paper to emphasize the
"axiomatization of physics" in title, abstract, and the opening page and
a half, and then to completely and utterly omit presenting any axioms at
all. Or even make any discernible progress towards such axioms. This
alone makes this paper useless, but it has numerous other faults as well.

It would be ridiculous if a high school student couldn't understand my
paper or would fail to recognize all my assumptions.

in progress. I wouldn't mind adding my axioms at the very end. The
point of the paper is to teach students of high school algebra how to
derive the LT equations as simply as possible, with the fewest
assumptions possible.

The whole point of the "toy universes" appears to be an attempt to
describe uniform rectilinear motion without calling it that.

No. The whole point of Xi_2 is to arrive at equations (1) and (2),
which are nonlinear, new and the basis of my entire derivation. Thanks
for acknowledging that I'm presupposing Newton's first law of motion
and that I've described Newton's first law with nonlinear equations!

The unusual method of defining "time" by coordinates passing each
other is unrelated to common usages of the word,

I wrote that "Little children know intuitively that a tiny arrow that
moves steadily along a continuum of numbers is a clock." Forgive me
for breaking with tradition and for using a kindergarten concept that
is too difficult for physicists to understand.

and the need for an arbitrary and conventional minus sign should
be a BIG RED FLAG that something is amiss.

I thought that I explained that rather carefully. I'll have to write
this down as one of my axioms.

AXIOM 1.
If a clock is running backwards at the same rate that another clock is
moving forward, then a sign change is recommended for one of the
clocks. (Sigh).

Note that "uniform motion" is assumed but not defined (uniform
with respect to what?); there is no description of how such coordinate
frames could be set up or uniformity of motion assured.

Do you really believe that children would have a problem
conceptualizing clock time as an arrow moving steadily along a
continuum of numbers? That's the beauty of my approach. Elapsed time
is proportional to the distance traveled on a number line.

After eq (30) the dismissal of k<0 is just plain wrong. k<0 corresponds
to the 4d Euclid group, and it is associative.

You are confused. My k is defined differently than what you're
expecting. The rotation matrix is automatically excluded in my
approach. The operation defined by equation (30) is not associative
for negative k on real numbers. Ask a mathematician.

There are reasons to
dismiss it, but they are not given in this paper. k=0 is never dismissed
at all, and the possibility is just ignored. Given the historical
significance of k=0 (the Galilei group) this is a major omission.

There is no omission. You just haven't read carefully enough. I wrote:

"To emphasize that k is nonnegative, we write k = 1/c^2. At this
point, the only meaning that I have ascribed to c is that c is a real
number greater than zero. If the case where k=0 needs to be
considered, we may adopt the convention that c=infty in that
instance."

The author appears to be completely ignorant of modern mathematics, or
indeed any math other than elementary algebra (e.g. the labored and
clumsy application of group theory without ever mentioning this fact,

You have already displayed a remarkable amount of pompous arrogance
and the need to obfuscate the simplicity of my kindergarten clock. Now
you belittle me because I use the right level of mathematics for high
school students. Didn't I say they are my intended audience? And what
is the basis of your fantasy? I did not use any group theory in my
derivation. My boast is that group theory, like Einstein's relativity
principle, isn't required to derive the LT.

confusion about the Euclid group,

No. You are confused and thanks for clearly demonstrating that.

the misuse of the standard symbol for
a direct-sum without mention,

I did not misuse oplus and it is used for much more than just a direct
sum. Thanks for giving me a review that's all about style and no
substance.

and the overall tone of presentation
implies the author has never read the technical literature).

My goal wasn't to mimic the technical literature, which is often
bombastic in style.

This whole
paper seems like a "just so" story which could be told using modern
mathematics in far less space and with much more clarity (e.g.
digressions to "ancient times" and attempts at using rational numbers
are not helpful to a modern audience).

I thought that my discussion of how real numbers are constructed set
the tone quite nicely on how simple my derivation really is.

The author is also ignorant of the vocabulary of modern physics (e.g.
repeated misuse of the term "proper"),

If the velocity of an object is v, what is its proper velocity? It's
exactly what I said it is without the unnecessary 4-vector definition.
If I can't use the term proper velocity because its ordinary meaning
applies to 4-vectors, should I replace my misused term "proper
velocity" with "Shubee velocity"?

and the very basics of physics
(the world we inhabit has 3 spatial dimensions, but there is no obvious
way to generalize this construct to 3 spatial dimensions).

There are plenty of derivations of the Lorentz transformation in 1
spatial dimension in the "scientific literature" and I certainly don't
see the need to apologize for something intended for students of high
school algebra.

I have proven that Einstein's relativity postulate isn't necessary

No, you have merely demonstrated that you can use his PoR without
stating that you did so, and can fool yourself into believing your own
omission.

Where did I use it? I only used the time equations from Xi_2 and the
assumption that my kindergarten time concept is well-defined
mathematically and is frame independent. That's correct. Time can be
defined in a similar manner, point by point, throughout the universe.
This approach permits both linear and nonlinear solutions. I gave a
reference to the nonlinear solution that solves the given problem and
presented all the major details for the linear case. Then I showed
that answer to be equivalent to the Lorentz transformation. The entire
approach of mine is perfectly consistent with an absolute frame of
reference. Therefore, I'm not using anything unnecessary like
Einstein's PoR. Note that I'm not excluding it either but future
editions of my paper will explain the logical possibility that
Einstein's PoR is a mathematical fantasy, i.e., it may be like the
Continuum Hypothesis or its negation.

these two axioms and never reach a contradiction but only one of these
axioms is really true.

doesn't even exist in the Hilbert atlas of all possible universes.

Had you made an attempt to enumerate your axioms you would
have learned this.

Hint: how did you select your initial frame, and what
conditions apply to that selection? -- Without the PoR you
need to specify unusual conditions....

You seem truly and honesty baffled by Xi_2.

You obviously don't understand my claim of devising the most
irreducible axioms possible.

Without stating those axioms, you have no valid claim. You'll find you
have actually used A LOT more axioms than you seem to think. You just
did not bother to enumerate them, and thus have deceived yourself.

I agree that I've used many axioms. But now I have enumerated one:

AXIOM 1.
If a clock is running backwards at the same rate that another clock is
moving forward, then a sign change is recommended for one of the
clocks.

This just goes to prove that you wouldn't have recognized this
assumption from reading my paper without me telling you ahead of time
that I'm going to use it.

Unacknowledged assumptions are a difficult problem.
As Bilge pointed out, a major reason Einstein is so
revered today is because he pointed out some important
but unacknowledged axioms that pervaded the physics of
his day, but were not necessary; he showed that without
them he could reconcile two cherished principles that
were previously thought to be irreconcilable.

My derivation of the Lorentz transformation uses axioms that are
logically equivalent to the Lorentz transformation itself, correctly
interpreted.

You GREATLY overestimate you own cleverness. Which is all the more
remarkable because you repeatedly make claims about your "axioms", which
you have never displayed. That's just ridiculous. And sad.

If I had stated all my assumptions in advance, like AXIOM 1, no one
would want to read my paper.

I got a good idea. In the future, I'm going to call AXIOM 1 the "BIG
RED FLAG" axiom in your honor because, to you, it seems like a
difficult concept.

Shubee
http://www.everythingimportant.org/relativity/special.pdf

On May 27, 8:25 pm, Tom Roberts <tjroberts...@sbcglobal.net> wrote:

Shubee wrote:

http://www.everythingimportant.org/relativity/special.pdf

I find it quite ridiculous for this paper to emphasize the
"axiomatization of physics" in title, abstract, and the opening page and
a half, and then to completely and utterly omit presenting any axioms at
all. Or even make any discernible progress towards such axioms.

It would be ridiculous if a high school student couldn't understand my
paper or would fail to recognize all my assumptions.

[...] with the fewest
assumptions possible.

Thanks
for acknowledging that I'm presupposing Newton's first law of motion
and that I've described Newton's first law with nonlinear equations!

I wrote that "Little children know intuitively that a tiny arrow that
moves steadily along a continuum of numbers is a clock."

and the need for an arbitrary and conventional minus sign should
be a BIG RED FLAG that something is amiss.

I thought that I explained that rather carefully. I'll have to write
this down as one of my axioms.
AXIOM 1.
If a clock is running backwards at the same rate that another clock is
moving forward, then a sign change is recommended for one of the
clocks. (Sigh).

Note that "uniform motion" is assumed but not defined (uniform
with respect to what?); there is no description of how such coordinate
frames could be set up or uniformity of motion assured.

Do you really believe that children would have a problem
conceptualizing clock time as an arrow moving steadily along a
continuum of numbers?

That's the beauty of my approach. Elapsed time
is proportional to the distance traveled on a number line.

After eq (30) the dismissal of k<0 is just plain wrong. k<0 corresponds
to the 4d Euclid group, and it is associative.

You are confused. My k is defined differently than what you're
expecting. The rotation matrix is automatically excluded in my
approach.

My boast is that group theory, like Einstein's relativity
principle, isn't required to derive the LT.

If the velocity of an object is v, what is its proper velocity?

and the very basics of physics
(the world we inhabit has 3 spatial dimensions, but there is no obvious
way to generalize this construct to 3 spatial dimensions).

There are plenty of derivations of the Lorentz transformation in 1
spatial dimension in the "scientific literature"

I have proven that Einstein's relativity postulate isn't necessary

No, you have merely demonstrated that you can use his PoR without
stating that you did so, and can fool yourself into believing your own
omission.

Where did I use it?

I only used the time equations from Xi_2 and the
assumption that my kindergarten time concept is well-defined
mathematically and is frame independent.

If I had stated all my assumptions in advance, like AXIOM 1, no one
would want to read my paper.