On Apr 29, 8:29�pm, Bryan Olson wrote:
rbwinn wrote:
Bryan Olson wrote:
rbwinn wrote:
Look, after ten or twelve times of trying to get a scientist to admit
that two clocks running at different rates cannot be represented by
the equation t'=t, I think that this basic principle has been
emphasized enough.
There's no question that the same variable cannot represent two
non-equal quantities. The problem is that you claim to use the
Galilean transform, then you contradict the Galilean transform.

I understand what you are saying. �You are a
respected scientist and Party member,
You must have me confused with someone else.

Spoken like a scientist. �Only a scientist could claim that I am
contradicting the Galilean transformation equations by using them.

Spoken like a true kook. It's not the using and no one said it was.

Exactly how am I contradicting the Galilean transformation equations?

You say devices to measure time at rest in S' will find it to be
something other than t'.
The earth rotates on its axis the same number of times in S' as it
does in S. The Sun rotates on its axis the same number of times in S'
as it does in S. The planets revolve around the sun the same number
of times in S' as they do in S. So how is t' different in S' than in
S?
Robert B. Winn

rbwinn wrote:
Bryan Olson wrote:
rbwinn wrote:
Bryan Olson wrote:
rbwinn wrote:
Look, after ten or twelve times of trying to get a scientist to admit
that two clocks running at different rates cannot be represented by
the equation t'=t, I think that this basic principle has been
emphasized enough.
There's no question that the same variable cannot represent two
non-equal quantities. The problem is that you claim to use the
Galilean transform, then you contradict the Galilean transform.
I understand what you are saying. �You are a
respected scientist and Party member,
You must have me confused with someone else.

Spoken like a scientist. �Only a scientist could claim that I am
contradicting the Galilean transformation equations by using them.
Spoken like a true kook. It's not the using and no one said it was.

Exactly how am I contradicting the Galilean transformation equations?

You say devices to measure time at rest in S' will find it to be
something other than t'.

The earth rotates on its axis the same number of times in S' as it
does in S. The Sun rotates on its axis the same number of times in S'
as it does in S. The planets revolve around the sun the same number
of times in S' as they do in S. So how is t' different in S' than in
S?

Robert, *you* came up with n' for time measured in S', and *your* n'
does not equal t in general. "How" time is different between frames
is an interesting question (which has a well-established answer that
many of us have tried to explain in this newsgroup), but you
contradict Galileo's theory regardless of that issue.

Contradicting Galileo's transform makes sense. His theory turns out
not to hold when |v| is a significant fraction of the speed of light.

Accepting Galileo's transform can also make sense. Considering the
objects we encounter, "v c" holds with few exceptions. Galileo
never had the chance to observe the phenomena that motivated
development of the Lorentz transform and special relativity.

What makes no sense is to do both simultaneously. To assert that
time measured in S' will be n', while also holding that time in S'
is t'=t, makes sense if and only if n'=t'=t in general. Robert, in
your system n' does not equal t' in general.


--
--Bryan

On Apr 29, 8:29�pm, Bryan Olson wrote:
rbwinn wrote:
Bryan Olson wrote:
rbwinn wrote:
Look, after ten or twelve times of trying to get a scientist to admit
that two clocks running at different rates cannot be represented by
the equation t'=t, I think that this basic principle has been
emphasized enough.
There's no question that the same variable cannot represent two
non-equal quantities. The problem is that you claim to use the
Galilean transform, then you contradict the Galilean transform.

I understand what you are saying. �You are a
respected scientist and Party member,
You must have me confused with someone else.

Spoken like a scientist. �Only a scientist could claim that I am
contradicting the Galilean transformation equations by using them.

Spoken like a true kook. It's not the using and no one said it was.

Exactly how am I contradicting the Galilean transformation equations?

You say devices to measure time at rest in S' will find it to be
something other than t'.

No, Bryan, the earth rotates the same number of degrees whether
observed fro S or S', the sun rotates the same number of degrees
whether observed from S or S'. You do have this cesium clock running
slower in S' than an identical clock in S. If a clock is running
slower or faster, it can still be used with the Galilean
transformation equations. You just have to determine the rate of the
clock compared to t'.
Robert B. Winn

On Apr 30, 8:10Â*pm, Bryan Olson wrote:
rbwinn wrote:
Bryan Olson wrote:
rbwinn wrote:
Bryan Olson wrote:
rbwinn wrote:
Look, after ten or twelve times of trying to get a scientist to admit
that two clocks running at different rates cannot be represented by
the equation t'=t, I think that this basic principle has been
emphasized enough.
There's no question that the same variable cannot represent two
non-equal quantities. The problem is that you claim to use the
Galilean transform, then you contradict the Galilean transform.
I understand what you are saying. �You are a
respected scientist and Party member,
You must have me confused with someone else.
Spoken like a scientist. �Only a scientist could claim that I am
contradicting the Galilean transformation equations by using them.
Spoken like a true kook. It's not the using and no one said it was.

Exactly how am I contradicting the Galilean transformation equations?
You say devices to measure time at rest in S' will find it to be
something other than t'.
The earth rotates on its axis the same number of times in S' as it
does in S. Â*The Sun rotates on its axis the same number of times in S'
as it does in S. Â*The planets revolve around the sun the same number
of times in S' as they do in S. Â*So how is t' different in S' than in
S?

Robert, *you* came up with n' for time measured in S', and *your* n'
does not equal t in general. "How" time is different between frames
is an interesting question (which has a well-established answer that
many of us have tried to explain in this newsgroup), but you
contradict Galileo's theory regardless of that issue.

Contradicting Galileo's transform makes sense. His theory turns out
not to hold when |v| is a significant fraction of the speed of light.

Accepting Galileo's transform can also make sense. Considering the
objects we encounter, "v c" holds with few exceptions. Galileo
never had the chance to observe the phenomena that motivated
development of the Lorentz transform and special relativity.

What makes no sense is to do both simultaneously. To assert that
time measured in S' will be n', while also holding that time in S'
is t'=t, makes sense if and only if n'=t'=t in general. Robert, in
your system n' does not equal t' in general.

No, Bryan, scientists say that a cesium clock in S' is running slower
than an identical clock in S. That means that it cannot be called t'
in the Galilean transformation equations. Sorry, you would have to
use a clock that is showing exactly the same time as a cesium clock in
S. If you do not have a clock like that and are too lazy to construct
one the way Eric Gisse and PD are, you might want to look at the
cesium clock in S. That shows what a t' clock in S' would show. As
for the slower clock in S', you will have to call the time on that
clock by some other variable than t' if you want to use the Galilean
transformation equations. This is really a moot point at this
particular time, because I am fairly sure that there are no scientists
who want to used the Galilean transformation equations. Just go ahead
and use the Lorentz equations if that is what you want to do.
Robert B. Winn

rbwinn wrote:
On Apr 30, 8:10 pm, Bryan Olson wrote:
rbwinn wrote:
Bryan Olson wrote:
rbwinn wrote:
Bryan Olson wrote:
rbwinn wrote:
Look, after ten or twelve times of trying to get a scientist to admit
that two clocks running at different rates cannot be represented by
the equation t'=t, I think that this basic principle has been
emphasized enough.
There's no question that the same variable cannot represent two
non-equal quantities. The problem is that you claim to use the
Galilean transform, then you contradict the Galilean transform.
I understand what you are saying. �You are a
respected scientist and Party member,
You must have me confused with someone else.
Spoken like a scientist. �Only a scientist could claim that I am
contradicting the Galilean transformation equations by using them.
Spoken like a true kook. It's not the using and no one said it was.
Exactly how am I contradicting the Galilean transformation equations?
You say devices to measure time at rest in S' will find it to be
something other than t'.
The earth rotates on its axis the same number of times in S' as it
does in S. The Sun rotates on its axis the same number of times in S'
as it does in S. The planets revolve around the sun the same number
of times in S' as they do in S. So how is t' different in S' than in
S?
Robert, *you* came up with n' for time measured in S', and *your* n'
does not equal t in general. "How" time is different between frames
is an interesting question (which has a well-established answer that
many of us have tried to explain in this newsgroup), but you
contradict Galileo's theory regardless of that issue.

Contradicting Galileo's transform makes sense. His theory turns out
not to hold when |v| is a significant fraction of the speed of light.

Accepting Galileo's transform can also make sense. Considering the
objects we encounter, "v c" holds with few exceptions. Galileo
never had the chance to observe the phenomena that motivated
development of the Lorentz transform and special relativity.

What makes no sense is to do both simultaneously. To assert that
time measured in S' will be n', while also holding that time in S'
is t'=t, makes sense if and only if n'=t'=t in general. Robert, in
your system n' does not equal t' in general.

No, Bryan, scientists say that a cesium clock in S' is running slower
than an identical clock in S. That means that it cannot be called t'
in the Galilean transformation equations.

Calling it something else doesn't change the fact that time measured
in S' is not equal to t.

Sorry, you would have to
use a clock that is showing exactly the same time as a cesium clock in
S. If you do not have a clock like that and are too lazy to construct
one the way Eric Gisse and PD are, you might want to look at the
cesium clock in S. That shows what a t' clock in S' would show. As
for the slower clock in S', you will have to call the time on that
clock by some other variable than t' if you want to use the Galilean
transformation equations. This is really a moot point at this
particular time, because I am fairly sure that there are no scientists
who want to used the Galilean transformation equations. Just go ahead
and use the Lorentz equations if that is what you want to do.

The choice is not arbitrary. We want to get things right.


--
--Bryan

On May 1, 2:53Â*am, Bryan Olson wrote:
rbwinn wrote:
On Apr 30, 8:10 pm, Bryan Olson wrote:
rbwinn wrote:
Bryan Olson wrote:
rbwinn wrote:
Bryan Olson wrote:
rbwinn wrote:
Look, after ten or twelve times of trying to get a scientist to admit
that two clocks running at different rates cannot be represented by
the equation t'=t, I think that this basic principle has been
emphasized enough.
There's no question that the same variable cannot represent two
non-equal quantities. The problem is that you claim to use the
Galilean transform, then you contradict the Galilean transform.
I understand what you are saying. �You are a
respected scientist and Party member,
You must have me confused with someone else.
Spoken like a scientist. �Only a scientist could claim that I am
contradicting the Galilean transformation equations by using them.
Spoken like a true kook. It's not the using and no one said it was.
Exactly how am I contradicting the Galilean transformation equations?
You say devices to measure time at rest in S' will find it to be
something other than t'.
The earth rotates on its axis the same number of times in S' as it
does in S. Â*The Sun rotates on its axis the same number of times in S'
as it does in S. Â*The planets revolve around the sun the same number
of times in S' as they do in S. Â*So how is t' different in S' than in
S?
Robert, *you* came up with n' for time measured in S', and *your* n'
does not equal t in general. "How" time is different between frames
is an interesting question (which has a well-established answer that
many of us have tried to explain in this newsgroup), but you
contradict Galileo's theory regardless of that issue.

Contradicting Galileo's transform makes sense. His theory turns out
not to hold when |v| is a significant fraction of the speed of light.

Accepting Galileo's transform can also make sense. Considering the
objects we encounter, "v c" holds with few exceptions. Galileo
never had the chance to observe the phenomena that motivated
development of the Lorentz transform and special relativity.

What makes no sense is to do both simultaneously. To assert that
time measured in S' will be n', while also holding that time in S'
is t'=t, makes sense if and only if n'=t'=t in general. Robert, in
your system n' does not equal t' in general.

No, Bryan, scientists say that a cesium clock in S' is running slower
than an identical clock in S. That means that it cannot be called t'
in the Galilean transformation equations.

Calling it something else doesn't change the fact that time measured
in S' is not equal to t.

Sorry, you would have to
use a clock that is showing exactly the same time as a cesium clock in
S. Â*If you do not have a clock like that and are too lazy to construct
one the way Eric Gisse and PD are, you might want to look at the
cesium clock in S. Â*That shows what a t' clock in S' would show. Â*As
for the slower clock in S', you will have to call the time on that
clock by some other variable than t' if you want to use the Galilean
transformation equations. Â*This is really a moot point at this
particular time, because I am fairly sure that there are no scientists
who want to used the Galilean transformation equations. Â*Just go ahead
and use the Lorentz equations if that is what you want to do.

The choice is not arbitrary. We want to get things right.

Well, the Lorentz equations will give you a fairly close approximation
of the time on the cesium clock in S'. It will be accurate enough to
do anything that scientists of this particular time are going to do.
Robert B. Winn

On Apr 27, 8:52 pm, Koobee Wublee wrote:
On Apr 27, 10:39 am, JanPB, the film critic wrote:

On Apr 27, 8:58 am, Koobee Wublee wrote:
“Was Einstein a fake?” asked John Farrell.

Einstein was a nitwit, a plagiarist, and a liar. You can consider him
a fake I suppose.

Detailed responses to your claims (which are FAPP false) were posted
many times on this NG already.

This is a wishful thinking on your part. It is OK to fantasize, but
it is not if you cannot tell what your fantasy is and what is not.
shrug

For those unfamiliar with Koobee - he is a crank of the "technical
mumbo-jumbo" variety.

So, a special crank of some sort that you are so scared sh*tless.
shrug

Unlike those who got stuck early on some
elementary algebra or calculus issue, he got stuck at a bit higher
level: basic differential geometry.

Another interpretation which is the correct one is that Koobee Wublee
has surpassed beyond differential geometry. After he has pointed out
the problem associated with what is commonly believed, you remained
confused. You have no ability to comprehend even the basic stuff.
shrug

Because of that he can easily
generate reams of technical nonsense which "looks" reasonable to a
layman.

Boy, you are really insulting the ‘layman’, Mr. film critic.

Answering this sort of thing takes time so people who do know
this stuff usually don't bother.

As I said, keeping silent is a very good strategy to prolong the
nonsense in SR and GR. shrug

After all, it makes no difference.

Well, if you keep silent, you would not be embarrassed by Koobee
Wublee that seems to be the tail-between-the-legs approach favored by
Professors Carlip and Roberts. shrug

You write complete nonsense, as usual. Not worth responding to.

--
Jan Bielawski

On May 1, 7:42 pm, JanPB wrote:
On Apr 27, 8:52 pm, Koobee Wublee wrote:

Well, if you keep silent, you would not be embarrassed by Koobee
Wublee that seems to be the tail-between-the-legs approach favored by
Professors Carlip and Roberts. shrug

You write complete nonsense, as usual. Not worth responding to.

Sometime ago, you promised to look through the mathematics I have
posted on GR. In doing so, you were gun-ho about pointing out errors
within. Well, it has been over a year. The mathematics I have
presented is actually very simple. You must have choked on seeing the
nonsense manifested by the beauty of mathematics in GR. Why don’t you
just accept it and stop torment yourself? It took me a few weeks of
denial to finally accept the nonsense in what I was taught. It was a
great relief after I have finally accepted the nonsense in what I was
taught. You are taking it much harder than I did. It has been
several years for you, and your internal struggle is eating you away
in which I fully understand. However, this is science that we are
discussing and not the integrity of your mental health. The brief
Koobee Wublee’s summarization of GR is once again presented as follows
for your pleasure. Please enjoy one more time, and don’t ever
complain about Koobee Wublee ever not reaching out and helping out
that queer of England.

* * * * General Theory of Relativity (GR) * * * *

The development of GR first diverged from Newtonian physics around the
middle of the nineteenth century, when Riemann wrote down the
relationship of an actual displacement segment to how an observer
observes this same displacement segment.

ds^2 = g_ij dq^i dq^j

Where

** ds = Invariant geometry in displacement
** g_ij = Elements of the metric
** dg^i = Observer’s choice of coordinate system
** i, j = 1, 2, 3 (3 spatial dimensions)

The shortest distance through the actual space (invariant geometry)
can now be computed using the calculus of variations. This was
exactly how Christoffel did it in the famous geodesic equations.

d^2q^n/ds^2 + g^nk (@g_ik/@q^j + @g_jk/@q^i - @g_ij/@q^k) @q^i/@s @q^j/
@s / 2 = 0

Where

** i, j, k, n = 1, 2, 3
** @ = Partial derivative operator

The quantities called the connection coefficients in the geodesic
equations become the Christoffel symbols of the second kind below.

Y^n_ij = g^nk (@g_ik/@q^j + @g_jk/@q^i - @g_ij/@q^k) / 2

Where

** d^2q^n/ds^2 + Y^n_ij @q^i/@s @q^j/@s = 0

However, due to the symmetry in the metric, there is at least another
way of presenting the geodesic equations.

d^2q^n/ds^2 + g^nk (@g_ik/@q^j - @g_ij/@q^k / 2) @q^i/@s @q^j/@s = 0

In doing so, the connection coefficients are very different from the
Christoffel symbols of the second kind.

Z^n_ij = g^nk @g_ik/@q^j - @g_ij/@q^k / 2

Where

** d^2q^n/ds^2 + Z^n_ij @q^i/@s @q^j/@s = 0

About a decade before the transition of the nineteenth and the
twentieth centuries, Ricci defined the covariant derivative based on
the geodesic equations and the connection coefficients. However,
Ricci did not know there is another set of connection coefficients
that are equally valid to describe the geodesic equations as the
Christoffel symbols of the second kind.

DX^n/Ds = dX^n/ds + Y^n_ij dq^i/ds X^j

Where

** DX^n/DS = Covariant derivative on X, a vector

The idea is to allow the covariant derivative of (X = dq^n/ds) to be
null in accordance with the geodesic equations. However,
mathematically there exists another operator that can achieve the
exact same thing.

EX^n/Es = dX^n/ds + Z^n_ij dq^i/ds X^j

Where

** EX^n/ES = Another operator on X, a vector

Ricci went on to derive (invent) the Riemann tensor which just like
the metric is merely a matrix. The derivation takes us through the
null geodesic variations.

R^n_ikj = @Y^n_ij/@q^k - @Y^n_ik/@q^j + Y^n_kl Y^l_jk – Y^n_jl Y^l_ik

Or

R^n_ikj = @Y^n_ij/@q^k - @Y^n_ik/@q^j + Y^n_jl Y^l_ik – Y^n_jl Y^l_ik

Ricci, however, only discovered the first tensor above while the
second one is also very mathematically valid in accordance with the
method of null geodesic variations. Ricci’s student Levi-Civita then
invented the Ricci tensor based on the Riemann tensor derived by Ricci
(the first equation above).

R_ij = @Y^k_ij/@q^k - @Y^k_ik/@q^j + Y^k_kl Y^l_ij – Y^k_jl Y^l_ik

Where

** R_ij = R^k_ikj

The Ricci scalar follows as described below.

R = g^ij R_ij

Where

** g^ij = inverse of the matrix g_ij the metric

After the introduction of the Lorentz transformation, the Goettingen
group of physicists including Minkowski, Hilbert, Schwarzschild, and
Klein extended Riemann’s description of curved space into a four-
dimensional spacetime.

ds^2 = g_ij dq^i dq^j

Where

** ds = Invariant geometry in spacetime
** g_ij = Elements of the metric
** dg^i = Observer’s choice of coordinate system
** i, j = 0, 1, 2, 3 (1 temporal and 3 spatial dimensions)

In 1915, Hilbert finally invented the following Lagrangian which does
not even satisfy as a Lagrangian according to the variations of
calculus.

L = (H R + p c^2) sqrt(-det(g^ij))

Where

** L = Hilbert's Lagragian
** R = Ricci scalar
** p = density of matter
** det() = determinant of the matrix as operand
** H = a constant

Hilbert then went on to take the partial derivative of this Lagrangian
with respect to each element of the metric represented by g^ij and
setting it to zero.

@L/@g^ij = H sqrt(-det(g^ij)) @R/@g^ij - H R @det(g^ij)/@g^ij / sqrt(-
det(g^ij)) / 2 - p c^2 @det(g^ij)/@g^ij / sqrt(-det(g^ij)) / 2 = 0

Where (mathematical identity)

** @R/@g^ij = R_ij
** @det(g^ij)/@g^ij = g_ij det(g^ij)

The result is the set of Einstein field equations.

R_ij - R g_ij / 2 = c^2 p g_ij / H / 2

Or

G_ij = T_ij

Where

** G_ij = R_ij - R g_ij / 2
** T_ij = c^2 p g_ij / H / 2

Einstein played no role. His rediscovery of the equivalence principle
also finds no role in the derivation. The derivation of GR is totally
based on mathematical nonsense.

Very soon after the introduction of the field equations, Schwarzschild
discovered the following static and spherically symmetric solution
(metric).

ds^2 = c^2 (1 – R / (r^3 + R^3)^(1/3)) dt^2 – r^4 dr^2 / (r^3 + R^3) /
((r^3 + R^3)^(1/3) – R) – (r^3 + R^3)^(2/3) dO^2

Where

** R = G M / c^2
** dO^2 = cos^2Phi dTheta^2 + dPhi^2

There are actually an infinite number of solutions (metric) to the
field equations using the same set of coordinate system. The most
popular one was derived by Hilbert in 1916 now called the
Schwarzschild metric.

ds^2 = c^2 (1 – 2 R / r) dt^2 – dr^2 / (1 – 2 R / r) – r^2 dO^2

Notice Schwarzschild’s original solution does not manifest black holes
but Schwarzschild metric does. The following solution also as simple
as the Schwarzschild metric does not manifest black holes as well.

ds^2 = c^2 dt^2 / ( 1 + 2 R / r) – (1 + 2 R / r) dr^2 – (r + R)^2 dO^2

Although not all the static and spherically symmetric solutions
degenerate to Newtonian law of gravity, all these three metrics above
do. This means the universe must be expanding and finally collapsing
back to itself. After observing the universe to be static, Einstein
correctly identified the field equations and Newtonian law of gravity
as not fit this observation. He cleverly introduced (pull out of his
*ss) a negative mass density to counter the attraction of gravity.
The reason is very simple. Positive mass manifests attraction in
gravity; negative mass manifests repulsion in gravity. In order to
hide the embarrassment of introducing negative mass in vacuum, he
again cleverly called this quantity as the Cosmological constant. The
development of GR at this stage is a total joke, but the nonsense did
not end here. Friedman, Lemaitre, Robertson, and Walker discovered a
non-static but spherically symmetric solution to the field equations
called the Friedman-Lemaitre-Robertson-Walker (FLRW) metric.

ds^2 = c^2 dt^2 – a^2 (dr^2 / (1 – r^2 / R^2) + r^2 dO^2)

Where

** a = Function of t only
** R = Constant

This means two of the field equations are

** (da/dt)^2 / a^2 + c^2 / R^2 / a^2 = 8 pi G p / 3
** 2 d^2a/dt^2 / a + (da/dt)^2 / a^2 + c^2 / R^2 / a^2 = 8 pi G p

We can very easily solve these differential equations.

If R^2 = 0,

** a^2 = c^2 cosh^2(w(t+T)) / (w^2 R^2)
** p = 3 w^2 / (4 pi G)

If R^2 0,

** a^2 = - c^2 cos^2(w(t+T)) / (w^2 R^2)
** p = - 3 w^2 / (4 pi G)

Where

** w, T = Integration constants

The density of the universe, p, must always remain constant. This
means the universe must be static as observed back then. Even with
the introduction of the Cosmological constant, the basic form of the
solution above remains the same. The Cosmological becomes totally
useless. The introduction of the Cosmological constant is the only
blunder in Einstein’s contribution in GR.

There are two problems with this FLRW metric.

** There is no solution combining the Schwarzschild metric and the
FLRW metric. This means the FLRW metric does not satisfy the
Newtonian law of gravity. Gravity is not caused by a curvature in
spacetime in general but only the gravitational time dilation.

** When Lemaitre first then Hubble discovered the red shift of
distant galaxies, there is no remedy for the FLRW metric to satisfy
this observation even with the Cosmological constant.

There are so many problems with GR right from the start. The most
basic is even more embarrassing. Any diligent grade school children
can identify the mathematical relationship below.

Given that

A = B C

If (A = constant and B != 0), then (C = A / B).

This blunder came as early as during Ricci’s time when the Riemann
tensor which is merely a matrix was incorrectly identified as a tensor
which means invariance to any coordinate transformation. Similarly,
the metric is merely a matrix. Ricci deified the metric into a
tensor. Mathematically, this can easily be proven wrong.

We have two different geometries described by the same coordinate
system with two different metrics.

** ds^2 = [g] * [dq^2] = g_ij dq^i dq^j
** ds'^2 = [g'] * [dq^2] = g'_ij dq^i dq^j

Where

** ds^2 = Geometry #1
** ds'^2 = Geometry #2
** [g] = Metric #1
** [g'] = Metric #2
** [dq^2] = Coordinate system, same
** * = Dot/inner product of two matrices

Or we have the same geometry described below by different metrics and
different coordinate systems. One example involves the linearly
rectangular and the spherically symmetric polar coordinate systems.

** ds^2 = [g] * [dq^2] = [g']* [dq'^2]
** ds^2 = g_ij dq^i dq^j = g'_ab dq'^a dq'^b

The geometry, ds^2, must be invariant due to obvious reason. The
choice of coordinate system, d[q^2], is observer dependent. This can
only mean the metric, [g], must also be observer dependent. The
metric, the Riemann, and the Ricci tensors cannot be tensors after
all. All solutions to the field equations must be unique and
independent of each one where all solutions must reference to the same
choice of coordinate system in describing vastly different invariant
geometries. What good is the set of field equations that can generate
an infinite numbers of solutions to describe infinitely different and
independent universes? What good is the set of field equations that
can either generate a solution that manifests black holes and also
ones that don’t?


* * * * Malicious Troll McCullough’s Stupid Question * * * *

The static and spherically symmetric solutions to the field equations
in general take one such form below.

ds^2 = c^2 dt^2 / (1 + K / R) – (1 + K / R) (dR/dr)^2 dr^2 – (R + K)^2
dO^2

Where

** R(r) = Function of r
** dO^2 = cos^2(Phi) dTheta^2 + dPhi^2
** K = Integration constant
** dr, dTheta, dPhi = Choiced coordinate system

Only if the following is true, you get the Schwarzschild metric.

** R = r - K

Where

** K = 2 G M / c^2

If the following is true, you get Schwarzschild’s original solution
which does not manifest any black holes.

** R = (r^3 + K^3)^(1/3) - K

If the following is true, you get another solution just as simple as
the Schwarzschild metric but without manifestation of black holes.

** R = r

If the following is true, you get a constantly expanding universe that
also obeys the Schwarzschild metric --- a trait that even the FLRW
metric fails to do so.

** R = r / (1 + r^2 / K / L)

Where

** L = Cosmic constant

If the following is true, you get an accelerated expanding universe.

** R = r / (1 + r^2 / K / L + r^3 / K / L / N)

Where

** L, N = Cosmic constants

Each of these solutions is uniquely independent of the others.
Claiming these solutions being the same is utter nonsense --- a
misunderstanding on your part of failure to understand the metric is
not a tensor but merely a matrix. In addition, the last two metrics
prove the Birkhoff’s theorem wrong.

On May 1, 11:56*pm, Koobee Wublee wrote:
On May 1, 7:42 pm, JanPB wrote:

On Apr 27, 8:52 pm, Koobee Wublee wrote:
Well, if you keep silent, you would not be embarrassed by Koobee
Wublee that seems to be the tail-between-the-legs approach favored by
Professors Carlip and Roberts. *shrug

You write complete nonsense, as usual. Not worth responding to.

Sometime ago, you promised to look through the mathematics I have
posted on GR. *In doing so, you were gun-ho about pointing out errors
within. *Well, it has been over a year.

Unfortunately, this proves nothing (besides my having not as much time
to post to this NG as I had thought).

It's really quite simple:

1. In general, it's easy to make false claims with bogus technical
terminology,
2. In general, it's a lot of work to dissect such claims and expose
them for what they are (namely, baloney). The technical complication
of the argument makes it irrelevant to 99.9% of the population anyway
- most of them will make their judgment based on common sense which
obviously concludes that the probablity you are right is
infinitesimal. The remaining 0.1% already knows your claims are
nonsense from start to finish.

--
Jan Bielawski

On May 2, 2:36 pm, JanPB wrote:
On May 1, 11:56 pm, Koobee Wublee wrote:

Sometime ago, you promised to look through the mathematics I have
posted on GR. In doing so, you were gun-ho about pointing out errors
within. Well, it has been over a year.

It's really quite simple:

1. In general, it's easy to make false claims with bogus technical
terminology,

Yes, but what I have presented was GR pre-1958, and it is an actual
account of mathematical history. shrug

2. In general, it's a lot of work to dissect such claims and expose
them for what they are (namely, baloney). The technical complication
of the argument makes it irrelevant to 99.9% of the population anyway
- most of them will make their judgment based on common sense which
obviously concludes that the probablity you are right is
infinitesimal. The remaining 0.1% already knows your claims are
nonsense from start to finish.

Therefore, your promise is worth nothing. shrug

What I have presented is the reason why Einstein never received that
Nobel Prize in GR as everyone thinks he should deserve. In fact,
there is nothing the Einstein had contributed. Your idol is a nitwit,
a plagiarist, and a liar. shrug

Well, here is once again for you enjoyment. Upon request, I have SR
as well.

* * * * General Theory of Relativity (GR) * * * *

The development of GR first diverged from Newtonian physics around the
middle of the nineteenth century, when Riemann wrote down the
relationship of an actual displacement segment to how an observer
observes this same displacement segment.

ds^2 = g_ij dq^i dq^j

Where

** ds = Invariant geometry in displacement
** g_ij = Elements of the metric
** dg^i = Observer’s choice of coordinate system
** i, j = 1, 2, 3 (3 spatial dimensions)

The shortest distance through the actual space (invariant geometry)
can now be computed using the calculus of variations. This was
exactly how Christoffel did it in the famous geodesic equations.

d^2q^n/ds^2 + g^nk (@g_ik/@q^j + @g_jk/@q^i - @g_ij/@q^k) @q^i/@s @q^j/
@s / 2 = 0

Where

** i, j, k, n = 1, 2, 3
** @ = Partial derivative operator

The quantities called the connection coefficients in the geodesic
equations become the Christoffel symbols of the second kind below.

Y^n_ij = g^nk (@g_ik/@q^j + @g_jk/@q^i - @g_ij/@q^k) / 2

Where

** d^2q^n/ds^2 + Y^n_ij @q^i/@s @q^j/@s = 0

However, due to the symmetry in the metric, there is at least another
way of presenting the geodesic equations.

d^2q^n/ds^2 + g^nk (@g_ik/@q^j - @g_ij/@q^k / 2) @q^i/@s @q^j/@s = 0

In doing so, the connection coefficients are very different from the
Christoffel symbols of the second kind.

Z^n_ij = g^nk @g_ik/@q^j - @g_ij/@q^k / 2

Where

** d^2q^n/ds^2 + Z^n_ij @q^i/@s @q^j/@s = 0

About a decade before the transition of the nineteenth and the
twentieth centuries, Ricci defined the covariant derivative based on
the geodesic equations and the connection coefficients. However,
Ricci did not know there is another set of connection coefficients
that are equally valid to describe the geodesic equations as the
Christoffel symbols of the second kind.

DX^n/Ds = dX^n/ds + Y^n_ij dq^i/ds X^j

Where

** DX^n/DS = Covariant derivative on X, a vector

The idea is to allow the covariant derivative of (X = dq^n/ds) to be
null in accordance with the geodesic equations. However,
mathematically there exists another operator that can achieve the
exact same thing.

EX^n/Es = dX^n/ds + Z^n_ij dq^i/ds X^j

Where

** EX^n/ES = Another operator on X, a vector

Ricci went on to derive (invent) the Riemann tensor which just like
the metric is merely a matrix. The derivation takes us through the
null geodesic variations.

R^n_ikj = @Y^n_ij/@q^k - @Y^n_ik/@q^j + Y^n_kl Y^l_jk – Y^n_jl Y^l_ik

Or

R^n_ikj = @Y^n_ij/@q^k - @Y^n_ik/@q^j + Y^n_jl Y^l_ik – Y^n_jl Y^l_ik

Ricci, however, only discovered the first tensor above while the
second one is also very mathematically valid in accordance with the
method of null geodesic variations. Ricci’s student Levi-Civita then
invented the Ricci tensor based on the Riemann tensor derived by Ricci
(the first equation above).

R_ij = @Y^k_ij/@q^k - @Y^k_ik/@q^j + Y^k_kl Y^l_ij – Y^k_jl Y^l_ik

Where

** R_ij = R^k_ikj

The Ricci scalar follows as described below.

R = g^ij R_ij

Where

** g^ij = inverse of the matrix g_ij the metric

After the introduction of the Lorentz transformation, the Goettingen
group of physicists including Minkowski, Hilbert, Schwarzschild, and
Klein extended Riemann’s description of curved space into a four-
dimensional spacetime.

ds^2 = g_ij dq^i dq^j

Where

** ds = Invariant geometry in spacetime
** g_ij = Elements of the metric
** dg^i = Observer’s choice of coordinate system
** i, j = 0, 1, 2, 3 (1 temporal and 3 spatial dimensions)

In 1915, Hilbert finally invented the following Lagrangian which does
not even satisfy as a Lagrangian according to the variations of
calculus.

L = (H R + p c^2) sqrt(-det(g^ij))

Where

** L = Hilbert's Lagragian
** R = Ricci scalar
** p = density of matter
** det() = determinant of the matrix as operand
** H = a constant

Hilbert then went on to take the partial derivative of this Lagrangian
with respect to each element of the metric represented by g^ij and
setting it to zero.

@L/@g^ij = H sqrt(-det(g^ij)) @R/@g^ij - H R @det(g^ij)/@g^ij / sqrt(-
det(g^ij)) / 2 - p c^2 @det(g^ij)/@g^ij / sqrt(-det(g^ij)) / 2 = 0

Where (mathematical identity)

** @R/@g^ij = R_ij
** @det(g^ij)/@g^ij = g_ij det(g^ij)

The result is the set of Einstein field equations.

R_ij - R g_ij / 2 = c^2 p g_ij / H / 2

Or

G_ij = T_ij

Where

** G_ij = R_ij - R g_ij / 2
** T_ij = c^2 p g_ij / H / 2

Einstein played no role. His rediscovery of the equivalence principle
also finds no role in the derivation. The derivation of GR is totally
based on mathematical nonsense.

Very soon after the introduction of the field equations, Schwarzschild
discovered the following static and spherically symmetric solution
(metric).

ds^2 = c^2 (1 – R / (r^3 + R^3)^(1/3)) dt^2 – r^4 dr^2 / (r^3 + R^3) /
((r^3 + R^3)^(1/3) – R) – (r^3 + R^3)^(2/3) dO^2

Where

** R = G M / c^2
** dO^2 = cos^2Phi dTheta^2 + dPhi^2

There are actually an infinite number of solutions (metric) to the
field equations using the same set of coordinate system. The most
popular one was derived by Hilbert in 1916 now called the
Schwarzschild metric.

ds^2 = c^2 (1 – 2 R / r) dt^2 – dr^2 / (1 – 2 R / r) – r^2 dO^2

Notice Schwarzschild’s original solution does not manifest black holes
but Schwarzschild metric does. The following solution also as simple
as the Schwarzschild metric does not manifest black holes as well.

ds^2 = c^2 dt^2 / ( 1 + 2 R / r) – (1 + 2 R / r) dr^2 – (r + R)^2 dO^2

Although not all the static and spherically symmetric solutions
degenerate to Newtonian law of gravity, all these three metrics above
do. This means the universe must be expanding and finally collapsing
back to itself. After observing the universe to be static, Einstein
correctly identified the field equations and Newtonian law of gravity
as not fit this observation. He cleverly introduced (pull out of his
*ss) a negative mass density to counter the attraction of gravity.
The reason is very simple. Positive mass manifests attraction in
gravity; negative mass manifests repulsion in gravity. In order to
hide the embarrassment of introducing negative mass in vacuum, he
again cleverly called this quantity as the Cosmological constant. The
development of GR at this stage is a total joke, but the nonsense did
not end here. Friedman, Lemaitre, Robertson, and Walker discovered a
non-static but spherically symmetric solution to the field equations
called the Friedman-Lemaitre-Robertson-Walker (FLRW) metric.

ds^2 = c^2 dt^2 – a^2 (dr^2 / (1 – r^2 / R^2) + r^2 dO^2)

Where

** a = Function of t only
** R = Constant

This means two of the field equations are

** (da/dt)^2 / a^2 + c^2 / R^2 / a^2 = 8 pi G p / 3
** 2 d^2a/dt^2 / a + (da/dt)^2 / a^2 + c^2 / R^2 / a^2 = 8 pi G p

We can very easily solve these differential equations.

If R^2 = 0,

** a^2 = c^2 cosh^2(w(t+T)) / (w^2 R^2)
** p = 3 w^2 / (4 pi G)

If R^2 0,

** a^2 = - c^2 cos^2(w(t+T)) / (w^2 R^2)
** p = - 3 w^2 / (4 pi G)

Where

** w, T = Integration constants

The density of the universe, p, must always remain constant. This
means the universe must be static as observed back then. Even with
the introduction of the Cosmological constant, the basic form of the
solution above remains the same. The Cosmological becomes totally
useless. The introduction of the Cosmological constant is the only
blunder in Einstein’s contribution in GR.

There are two problems with this FLRW metric.

** There is no solution combining the Schwarzschild metric and the
FLRW metric. This means the FLRW metric does not satisfy the
Newtonian law of gravity. Gravity is not caused by a curvature in
spacetime in general but only the gravitational time dilation.

** When Lemaitre first then Hubble discovered the red shift of
distant galaxies, there is no remedy for the FLRW metric to satisfy
this observation even with the Cosmological constant.

There are so many problems with GR right from the start. The most
basic is even more embarrassing. Any diligent grade school children
can identify the mathematical relationship below.

Given that

A = B C

If (A = constant and B != 0), then (C = A / B).

This blunder came as early as during Ricci’s time when the Riemann
tensor which is merely a matrix was incorrectly identified as a tensor
which means invariance to any coordinate transformation. Similarly,
the metric is merely a matrix. Ricci deified the metric into a
tensor. Mathematically, this can easily be proven wrong.

We have two different geometries described by the same coordinate
system with two different metrics.

** ds^2 = [g] * [dq^2] = g_ij dq^i dq^j
** ds'^2 = [g'] * [dq^2] = g'_ij dq^i dq^j

Where

** ds^2 = Geometry #1
** ds'^2 = Geometry #2
** [g] = Metric #1
** [g'] = Metric #2
** [dq^2] = Coordinate system, same
** * = Dot/inner product of two matrices

Or we have the same geometry described below by different metrics and
different coordinate systems. One example involves the linearly
rectangular and the spherically symmetric polar coordinate systems.

** ds^2 = [g] * [dq^2] = [g']* [dq'^2]
** ds^2 = g_ij dq^i dq^j = g'_ab dq'^a dq'^b

The geometry, ds^2, must be invariant due to obvious reason. The
choice of coordinate system, d[q^2], is observer dependent. This can
only mean the metric, [g], must also be observer dependent. The
metric, the Riemann, and the Ricci tensors cannot be tensors after
all. All solutions to the field equations must be unique and
independent of each one where all solutions must reference to the same
choice of coordinate system in describing vastly different invariant
geometries. What good is the set of field equations that can generate
an infinite numbers of solutions to describe infinitely different and
independent universes? What good is the set of field equations that
can either generate a solution that manifests black holes and also
ones that don’t?


* * * * Malicious Troll McCullough’s Stupid Question * * * *

The static and spherically symmetric solutions to the field equations
in general take one such form below.

ds^2 = c^2 dt^2 / (1 + K / R) – (1 + K / R) (dR/dr)^2 dr^2 – (R + K)^2
dO^2

Where

** R(r) = Function of r
** dO^2 = cos^2(Phi) dTheta^2 + dPhi^2
** K = Integration constant
** dr, dTheta, dPhi = Choiced coordinate system

Only if the following is true, you get the Schwarzschild metric.

** R = r - K

Where

** K = 2 G M / c^2

If the following is true, you get Schwarzschild’s original solution
which does not manifest any black holes.

** R = (r^3 + K^3)^(1/3) - K

If the following is true, you get another solution just as simple as
the Schwarzschild metric but without manifestation of black holes.

** R = r

If the following is true, you get a constantly expanding universe that
also obeys the Schwarzschild metric --- a trait that even the FLRW
metric fails to do so.

** R = r / (1 + r^2 / K / L)

Where

** L = Cosmic constant

If the following is true, you get an accelerated expanding universe.

** R = r / (1 + r^2 / K / L + r^3 / K / L / N)

Where

** L, N = Cosmic constants

Each of these solutions is uniquely independent of the others.
Claiming these solutions being the same is utter nonsense --- a
misunderstanding on your part of failure to understand the metric is
not a tensor but merely a matrix. In addition, the last two metrics
prove the Birkhoff’s theorem wrong.