Einstein: "Guided by empirical data, the investigator rather develops
a system of thought which, in general, is built up logically from a
small number of fundamental assumptions, the so-called axioms."

What Einstein describes is an axiomatic system which, by definition,
can be presented as a sequence of propositions with the axioms at the
beginning followed by theorems (deduced propositions), where each
theorem is accompanied by an explicit authentication of the exact
deductive path leading to it. In other words, the path from the axioms
to a particular proposition (theorem) can be disintegrated into steps
each of which has the form

a,b,... - c

and can undergo the scrutiny of both critics and sycophants (secretly
in the latter case).

Perhaps, after 100 years of intensive begging the question, it is time
for relativists to perform this important operation. Let me suggest a
possible beginning:

Axiom (1) Principle of relativity
Axiom (2) Constancy of speed of light
1,2 (3) Time dilation in BOTH inertial frames
........(4)........................

The derivation is set out as a sequence of numbered lines (1), (2),
(3) etc. The fact that line (3) was obtained from (1) and (2) as
premises is shown by writing 1,2 to the left of the line number (3).

According to Einstein, the sequence eventually leads to

p,q,... (r) A clock in a non-rotating system undergoes time
CONTRACTION relative to a clock on the periphery of a rotating disc.

x,y,... (z) Two clocks placed at different gravitational potentials
will go at different rates in accordance with v=v_0(1+phi/c^2).

Now relativists should present all the steps leading to the above two
propositions and eventually replace p,q,r,x,y,z with real numbers.
They will fail because both (r) and (z) are just Einstein's
"intuitions", not theorems. Still some truth will be revealed and
truth should be valued in science shouldn't it.

Pentcho Valev

Pentcho Valev wrote:
Einstein: "Guided by empirical data, the investigator rather develops
a system of thought which, in general, is built up logically from a
small number of fundamental assumptions, the so-called axioms."

What Einstein describes is an axiomatic system which, by definition,
can be presented as a sequence of propositions with the axioms at the
beginning followed by theorems (deduced propositions), where each
theorem is accompanied by an explicit authentication of the exact
deductive path leading to it. In other words, the path from the axioms
to a particular proposition (theorem) can be disintegrated into steps
each of which has the form

a,b,... - c

and can undergo the scrutiny of both critics and sycophants (secretly
in the latter case).

Perhaps, after 100 years of intensive begging the question, it is time
for relativists to perform this important operation. Let me suggest a
possible beginning:

Axiom (1) Principle of relativity
Axiom (2) Constancy of speed of light
1,2 (3) Time dilation in BOTH inertial frames
.......(4)........................

The derivation is set out as a sequence of numbered lines (1), (2),
(3) etc. The fact that line (3) was obtained from (1) and (2) as
premises is shown by writing 1,2 to the left of the line number (3).

According to Einstein, the sequence eventually leads to

p,q,... (r) A clock in a non-rotating system undergoes time
CONTRACTION relative to a clock on the periphery of a rotating disc.

x,y,... (z) Two clocks placed at different gravitational potentials
will go at different rates in accordance with v=v_0(1+phi/c^2).

Now relativists should present all the steps leading to the above two
propositions and eventually replace p,q,r,x,y,z with real numbers.
They will fail because both (r) and (z) are just Einstein's
"intuitions", not theorems. Still some truth will be revealed and
truth should be valued in science shouldn't it.

Pentcho Valev

Actually, the problem with SR begins much earlier than at (r) and (z).
Take a look at the parallel thread "Download a new book on
quantum mechanics and relativity". I repeatedly ask relativists there to
prove statement (3) from axioms (1) and (2). They can certainly do that
for simple "light clock" (postulate (2) is very handy in this case),
but they cannot do it for a
clock of arbitrary design for which axiom (2) is of no help.
So, in order to get special relativity, Minkowski space-time, etc.
one should introduce somewhere in this axiomatic system an additional
postulate

(?) Lorentz transformations are valid for all systems independent on
their composition and interactions.

Another (correct) approach is to skip this postulate (which turns out to
be wrong at closer inspection) and derive transformations
of observables from solution of dynamical problem. That's what
the "new book on quantum mechanics and relativity" is about.

Eugene.

"Eugene Stefanovich" wrote in message
...
|
|
| Pentcho Valev wrote:
| Einstein: "Guided by empirical data, the investigator rather develops
| a system of thought which, in general, is built up logically from a
| small number of fundamental assumptions, the so-called axioms."
|
| What Einstein describes is an axiomatic system which, by definition,
| can be presented as a sequence of propositions with the axioms at the
| beginning followed by theorems (deduced propositions), where each
| theorem is accompanied by an explicit authentication of the exact
| deductive path leading to it. In other words, the path from the axioms
| to a particular proposition (theorem) can be disintegrated into steps
| each of which has the form
|
| a,b,... - c
|
| and can undergo the scrutiny of both critics and sycophants (secretly
| in the latter case).
|
| Perhaps, after 100 years of intensive begging the question, it is time
| for relativists to perform this important operation. Let me suggest a
| possible beginning:
|
| Axiom (1) Principle of relativity
| Axiom (2) Constancy of speed of light
| 1,2 (3) Time dilation in BOTH inertial frames
| .......(4)........................
|
| The derivation is set out as a sequence of numbered lines (1), (2),
| (3) etc. The fact that line (3) was obtained from (1) and (2) as
| premises is shown by writing 1,2 to the left of the line number (3).
|
| According to Einstein, the sequence eventually leads to
|
| p,q,... (r) A clock in a non-rotating system undergoes time
| CONTRACTION relative to a clock on the periphery of a rotating disc.
|
| x,y,... (z) Two clocks placed at different gravitational potentials
| will go at different rates in accordance with v=v_0(1+phi/c^2).
|
| Now relativists should present all the steps leading to the above two
| propositions and eventually replace p,q,r,x,y,z with real numbers.
| They will fail because both (r) and (z) are just Einstein's
| "intuitions", not theorems. Still some truth will be revealed and
| truth should be valued in science shouldn't it.
|
| Pentcho Valev
|
| Actually, the problem with SR begins much earlier than at (r) and (z).
| Take a look at the parallel thread "Download a new book on
| quantum mechanics and relativity". I repeatedly ask relativists there to
| prove statement (3) from axioms (1) and (2). They can certainly do that
| for simple "light clock" (postulate (2) is very handy in this case),
| but they cannot do it for a
| clock of arbitrary design for which axiom (2) is of no help.
| So, in order to get special relativity, Minkowski space-time, etc.
| one should introduce somewhere in this axiomatic system an additional
| postulate
|
| (?) Lorentz transformations are valid for all systems independent on
| their composition and interactions.

LOL!!
"It follows, further, that the velocity of light c cannot be altered by
composition with a velocity less than that of light. For this case we obtain
V = (c+w)/(1+w/c) = c."- Einstein.

½[tau(0,0,0,t)+tau(0,0,0,t+x'/V+x'/V)] = tau(x',0,0,t+x'/V)



|
| Another (correct) approach is to skip this postulate (which turns out to
| be wrong at closer inspection) and derive transformations
| of observables from solution of dynamical problem.
LOL!!

"But the ray moves relatively to the initial point of k,
when measured in the stationary system, with the velocity c-v..." - Einstein

½[tau(0,0,0,t)+tau(0,0,0,t+x'/(c-v)+x'/(c+v))] = tau(x',0,0,t+x'/(c-v))


That's what
| the "new book on quantum mechanics and relativity" is about.
|
| Eugene.

That's what "Eugene is so smart, he can switch sides any time he likes" is
about.
Androcles.

"Pentcho Valev" wrote in message
om...
Einstein: "Guided by empirical data, the investigator rather develops
a system of thought which, in general, is built up logically from a
small number of fundamental assumptions, the so-called axioms."

What Einstein describes is an axiomatic system which, by definition,
can be presented as a sequence of propositions with the axioms at the
beginning followed by theorems (deduced propositions), where each
theorem is accompanied by an explicit authentication of the exact
deductive path leading to it. In other words, the path from the axioms
to a particular proposition (theorem) can be disintegrated into steps
each of which has the form

a,b,... - c

and can undergo the scrutiny of both critics and sycophants (secretly
in the latter case).

Perhaps, after 100 years of intensive begging the question, it is time
for relativists to perform this important operation.

Perhaps after posting your drivel for as long as you have it is time to
admit that since SR is as consistent as Euclidian geometry you are barking
up the wrong tree.

Bill

Let me suggest a
possible beginning:

Axiom (1) Principle of relativity
Axiom (2) Constancy of speed of light
1,2 (3) Time dilation in BOTH inertial frames
.......(4)........................

The derivation is set out as a sequence of numbered lines (1), (2),
(3) etc. The fact that line (3) was obtained from (1) and (2) as
premises is shown by writing 1,2 to the left of the line number (3).

According to Einstein, the sequence eventually leads to

p,q,... (r) A clock in a non-rotating system undergoes time
CONTRACTION relative to a clock on the periphery of a rotating disc.

x,y,... (z) Two clocks placed at different gravitational potentials
will go at different rates in accordance with v=v_0(1+phi/c^2).

Now relativists should present all the steps leading to the above two
propositions and eventually replace p,q,r,x,y,z with real numbers.
They will fail because both (r) and (z) are just Einstein's
"intuitions", not theorems. Still some truth will be revealed and
truth should be valued in science shouldn't it.

Pentcho Valev

Androcles wrote:


That's what "Eugene is so smart, he can switch sides any time he likes" is
about.
Androcles.



What do you mean "switch sides"? You probably noticed that I posted a
book. So I staked out my claim. I took my side and I am going to stick
to it.

Eugene.

"Eugene Stefanovich" wrote in message
...
|
|
| Androcles wrote:
|
|
| That's what "Eugene is so smart, he can switch sides any time he likes"
is
| about.
| Androcles.
|
|
|
| What do you mean "switch sides"?

I'd point it out to you, but you snipped everything you agreed to.


| You probably noticed that I posted a
| book.

Oh? Where? I must have missed it. I certainly didn't notice it.


| So I staked out my claim. I took my side and I am going to stick
| to it.
|
| Eugene.

What claim are you talking about?
Androcles

Pentcho Valev wrote:

Einstein: "Guided by empirical data, the investigator rather develops
a system of thought which, in general, is built up logically from a
small number of fundamental assumptions, the so-called axioms."

What Einstein describes is an axiomatic system which, by definition,
can be presented as a sequence of propositions with the axioms at the
beginning followed by theorems (deduced propositions), where each
theorem is accompanied by an explicit authentication of the exact
deductive path leading to it. In other words, the path from the axioms
to a particular proposition (theorem) can be disintegrated into steps
each of which has the form

With one big Addition. There is a way of mapping a subset of the formal
theorems of the system in to predictive assertions about the world which
can actually be tested.

Anyone can write a formal axiomatic system. Few can develop systems with
with a general applicablity to a wide range of phenomena, and make
testable predictions which are actuall corroberated by experiment and
which are not falsified by experiment.

THAT is the difference between abstract formal systems and honest to God
physicsics.

Rudolph Carnap and his buddies from the Wien Kreisse tried for years to
-usefully- formalize physics. They failed. Subsequently it is been tried
and to no avail. A well crafted non-formal physical theory that works
will do just fine. Formalization will not add a smidgin of emperical
truth to any theory about the world.

Bob Kolker

Bill Hobba wrote:


Perhaps after posting your drivel for as long as you have it is time to
admit that since SR is as consistent as Euclidian geometry you are barking
up the wrong tree.

Bill, my lad, your short and to the point expostulations are a breath of
fresh air. Bravo!

Bob Kolker

Eugene Stefanovich wrote:

What do you mean "switch sides"? You probably noticed that I posted a
book. So I staked out my claim. I took my side and I am going to stick
to it.


Has your book been reviewed by competent physicists or mathematicians?
If so please give references indicating who reviewed it and what they
had to say about it.

Bob Kolker

"Pentcho Valev" wrote in message om...
Einstein: "Guided by empirical data, the investigator rather develops
a system of thought which, in general, is built up logically from a
small number of fundamental assumptions, the so-called axioms."

What Einstein describes is an axiomatic system which, by definition,
can be presented as a sequence of propositions with the axioms at the
beginning followed by theorems (deduced propositions), where each
theorem is accompanied by an explicit authentication of the exact
deductive path leading to it. In other words, the path from the axioms
to a particular proposition (theorem) can be disintegrated into steps
each of which has the form

a,b,... - c

and can undergo the scrutiny of both critics and sycophants (secretly
in the latter case).

Perhaps, after 100 years of intensive begging the question, it is time
for relativists to perform this important operation. Let me suggest a
possible beginning:

Axiom (1) Principle of relativity
Axiom (2) Constancy of speed of light
1,2 (3) Time dilation in BOTH inertial frames
.......(4)........................

The derivation is set out as a sequence of numbered lines (1), (2),
(3) etc. The fact that line (3) was obtained from (1) and (2) as
premises is shown by writing 1,2 to the left of the line number (3).

According to Einstein, the sequence eventually leads to

p,q,... (r) A clock in a non-rotating system undergoes time
CONTRACTION relative to a clock on the periphery of a rotating disc.

x,y,... (z) Two clocks placed at different gravitational potentials
will go at different rates in accordance with v=v_0(1+phi/c^2).

Now relativists should present all the steps leading to the above two
propositions and eventually replace p,q,r,x,y,z with real numbers.
They will fail because both (r) and (z) are just Einstein's
"intuitions", not theorems. Still some truth will be revealed and
truth should be valued in science shouldn't it.

Pentcho Valev

Pentcho forgot to mention something: *definitions*.

Dirk Vdm