FAQFAQ   SearchSearch   MemberlistMemberlist   UsergroupsUsergroups 
 ProfileProfile   PreferencesPreferences   Log in to check your private messagesLog in to check your private messages   Log inLog in 
Forum index » Science and Technology » Physics » Relativity
A Flaw of General Relativity, a New Metric and Cosmological Implications
Post new topic   Reply to topic Page 1 of 4 [56 Posts] View previous topic :: View next topic
Goto page:  1, 2, 3, 4 Next
Author Message
Sue...
science forum Guru


Joined: 08 May 2005
Posts: 2684

PostPosted: Sat Jul 08, 2006 9:09 am    Post subject: Re: A Flaw of General Relativity, a New Metric and Cosmological Implications Reply with quote

Zanket wrote:
Quote:
A Flaw of General Relativity, a New Metric and Cosmological Implications



http://zanket.home.att.net/



Abstract: General relativity is shown to be inconsistent. A new metric for
Schwarzschild geometry is derived and shown to be confirmed by all
experimental tests of the Schwarzschild metric. (Those tests compose the
vast majority of experimental tests of general relativity.) The predictions
of the new metric and the Schwarzschild metric diverge as gravity
strengthens. Black holes are not predicted by the new metric. The
cosmological implications show that gravity alone can explain away the
flatness and horizon problems and cause the universe to seemingly accelerate
in its expansion.



Serious discussion appreciated, especially from those who attack the paper
directly.



For the babies: Yes, I know I'm a crackpot for challenging general
relativity, a proven fact. And yes I know that "experimental confirmation"
in no way implies empirical evidence.

Most real world clocks (Mossbauer, Cesium ) respond gravitationally
as we would predict for any oscillating mass. The elements loose
energy to a planet by following curved rather than straight paths.

The Schwarzschild solution, somewhat carelessly treats this
effect as a change in time rather than energy. The error is
demonstrated in the difference in the interpretations of the
Pound-Rebka and later Pound-Snider experiments.

http://www.citebase.org/cgi-bin/citations?id=oai:arXiv.org:physics/9907017

The Kankek paper is too extensive for a hobbyist as myself to
attack or support but the cause of the interpretive errors
certainly warrants further illumination. I reserve my toughest
skepticism for any cosmlogical extrapolatons which can't rigoursly
show they are not founded on the misinterpretation of Pound-Rebka.

The Kankek paper might be a little more concise
and less theoretical by focusing on the errors that can result
when time is interchanged for energy.

Sue...
Back to top
Bilge
science forum Guru


Joined: 30 Apr 2005
Posts: 2816

PostPosted: Sat Jul 08, 2006 10:31 am    Post subject: Re: A Flaw of General Relativity, a New Metric and Cosmological Implications Reply with quote

Zanket:
Quote:
A Flaw of General Relativity, a New Metric and Cosmological Implications



http://zanket.home.att.net/



Abstract: General relativity is shown to be inconsistent.

Try again. Your argument is based on your misunderstanding
of general relativity and/or black koles. General relativity is
not invalidated by your misunderstanding of it.

[...]
Quote:

For the babies: Yes, I know I'm a crackpot for challenging general
relativity, a proven fact. And yes I know that "experimental confirmation"
in no way implies empirical evidence.

No, the reason that you are a crackpot is that you insist that general
relativity be defined by your own misunderstanding of general relativity
used as a strawman. You can find lots of articles in the physics literature,
written by non-crackpots who question general relativity.

By the way, what is it that makes you nutcases such religious
zealots for a galilean spacetime? It's just geometry. Do you
realize your entire crusade amounts to a jihad over euclid's
fifth postulate? Sheeesh...
Back to top
dda1
science forum Guru


Joined: 06 Feb 2006
Posts: 762

PostPosted: Sat Jul 08, 2006 2:03 pm    Post subject: Re: A Flaw of General Relativity, a New Metric and Cosmological Implications Reply with quote

Zanket wrote:
<snipped>

You were told to f*** off the Bad Astronomy Forum. Now you are being
told to f*** off from this forum. So: f*** off.
Back to top
brian a m stuckless
science forum Guru


Joined: 31 Aug 2005
Posts: 2024

PostPosted: Sat Jul 08, 2006 3:45 pm    Post subject: Re: A Flaw of General Relativity, a New Metric and Cosmological Implications Reply with quote

Quote:
The proper time is the elapsaed time along a world line
as measured by a clock traversing that world line.
$$

$$ And ONLY that clock is at THAT point-in-time AT ONCE, dimwit.
$$ [This, WHY any GR-"clock" & "various TiME" are GR-oxyMORONs].
-=-SNiP-=-
Quote:
Your concept of ``real time'' must obviously be different from the
rest of us who use the standard timepieces manufactured on this
planet as a measure of time. [There ARE various GR-"time-ZONEs".]
-=-
Anyone who follows your explanation will certainly not understand
the lorentz transforms. [Likewise for ANY COHERENT "explanation".]

Lorentz Transform violates the Principle of Simultaneity.

There is no such thing as the ``Principle of Simultaneity.''
Simultaneity in relativity is _defined_ by the poincare transforms
(of which the lorentz transforms are a [albeit, previously-DECLARED
by yourself, Bilge, to be UN-reachable via-POiNCARE ..duh] subset).
-=-
SR is actually the study of inertial reference frames -=- -=-

$$ REST (inertial) frames are *BARYCENTER-centred* ..NOT Galilean;
$$ M1 & m1 in Newton's G*M1*m1, are *moving* REST-mass magnitudes.
$$ M1 has acceleration to barycentre; m1 has another acceleration.
$$ There is NO COHERENT way to see M1 & m1 .. EACH from the OTHER.
$$ [The Newton context here is a three-dimensional SPACE in TiME].
$$ [There is NO COHERENT way to see m1, from M1 ..mathematically].
$$ [There is NO COHERENT way to see M1, from m1 ..mathematically].

Quote:
The hyperbolic Lagrangian remains invariant under Lorentz
transformations, which are actually hyperbolic rotations.

$$ But, are *NOT* "invarient" in the REST frame of the BARYCENTRE.

Quote:
What is hyperbolic Lagrangian?
A lagrangian extremized by a metric for a hyperolic space.

$$ Define (explain) "extremized" in BOTH near-&-far-field context?

$$ General Universal Equation-of-State System (GUESS iSS) ANALYSiS:
$$ Classical OLD Lagrangian: || The Classical OLD Hamiltonian:
$$ L = H - 2*eP || H = L + 2*eP
$$ = eK - eP || = eK + eP
$$ = eK - Potential; || = eK + Potential (energy) eP;
$$ in GUESS = eK - Volt*A*sec || = eK + eM ..as per ADDENDUM;
$$ = eK - eV ..energy || = L + Gibb's eG .. " " "
$$ = eM - Helmholtz eF || = eK + iNTRiNSiC REST eM " " "
$$ = E - Gibb's eG. || = GUESS iSS ENTHALPY energy E.
$$
$ COMPLETELY combines all CHEMiSTRY equations-of-state, COHERENTLY.

Sue... wrote:
Quote:

Zanket wrote:
A Flaw of General Relativity, a New Metric and Cosmological Implications



http://zanket.home.att.net/



Abstract: General relativity is shown to be inconsistent. A new metric for
Schwarzschild geometry is derived and shown to be confirmed by all
experimental tests of the Schwarzschild metric. (Those tests compose the
vast majority of experimental tests of general relativity.) The predictions
of the new metric and the Schwarzschild metric diverge as gravity
strengthens. Black holes are not predicted by the new metric. The
cosmological implications show that gravity alone can explain away the
flatness and horizon problems and cause the universe to seemingly accelerate
in its expansion.



Serious discussion appreciated, especially from those who attack the paper
directly.



For the babies: Yes, I know I'm a crackpot for challenging general
relativity, a proven fact. And yes I know that "experimental confirmation"
in no way implies empirical evidence.

Most real world clocks (Mossbauer, Cesium ) respond gravitationally
as we would predict for any oscillating mass. The elements loose
energy to a planet by following curved rather than straight paths.

The Schwarzschild solution, somewhat carelessly treats this
effect as a change in time rather than energy. The error is
demonstrated in the difference in the interpretations of the
Pound-Rebka and later Pound-Snider experiments.

http://www.citebase.org/cgi-bin/citations?id=oai:arXiv.org:physics/9907017

The Kankek paper is too extensive for a hobbyist as myself to
attack or support but the cause of the interpretive errors
certainly warrants further illumination. I reserve my toughest
skepticism for any cosmlogical extrapolatons which can't rigoursly
show they are not founded on the misinterpretation of Pound-Rebka.

The Kankek paper might be a little more concise
and less theoretical by focusing on the errors that can result
when time is interchanged for energy.

Sue...
Back to top
Zanket
science forum beginner


Joined: 08 Jul 2006
Posts: 21

PostPosted: Sun Jul 09, 2006 6:37 am    Post subject: Re: A Flaw of General Relativity, a New Metric and Cosmological Implications Reply with quote

I assume you can't find an actual problem.

"Bilge" <dubious@radioactivex.lebesque-al.net> wrote in message
news:slrneav6d7.2tl.dubious@radioactivex.lebesque-al.net...
Quote:
Zanket:
A Flaw of General Relativity, a New Metric and Cosmological Implications



http://zanket.home.att.net/



Abstract: General relativity is shown to be inconsistent.

Try again. Your argument is based on your misunderstanding
of general relativity and/or black koles. General relativity is
not invalidated by your misunderstanding of it.

[...]

For the babies: Yes, I know I'm a crackpot for challenging general
relativity, a proven fact. And yes I know that "experimental
confirmation"
in no way implies empirical evidence.

No, the reason that you are a crackpot is that you insist that general
relativity be defined by your own misunderstanding of general relativity
used as a strawman. You can find lots of articles in the physics
literature,
written by non-crackpots who question general relativity.

By the way, what is it that makes you nutcases such religious
zealots for a galilean spacetime? It's just geometry. Do you
realize your entire crusade amounts to a jihad over euclid's
fifth postulate? Sheeesh...

Back to top
Zanket
science forum beginner


Joined: 08 Jul 2006
Posts: 21

PostPosted: Sun Jul 09, 2006 6:50 am    Post subject: Re: A Flaw of General Relativity, a New Metric and Cosmological Implications Reply with quote

Oh now you hurt my feelings.

"dda1" <rangeravenger@yahoo.com> wrote in message
news:1152367409.601841.94350@m79g2000cwm.googlegroups.com...
Quote:

Zanket wrote:
snipped

You were told to f*** off the Bad Astronomy Forum. Now you are being
told to f*** off from this forum. So: f*** off.
Back to top
Sue...
science forum Guru


Joined: 08 May 2005
Posts: 2684

PostPosted: Sun Jul 09, 2006 9:21 am    Post subject: Re: A Flaw of General Relativity, a New Metric and Cosmological Implications Reply with quote

brian a m stuckless wrote:
Quote:
The proper time is the elapsaed time along a world line
as measured by a clock traversing that world line.
$$
$$ And ONLY that clock is at THAT point-in-time AT ONCE, dimwit.
$$ [This, WHY any GR-"clock" & "various TiME" are GR-oxyMORONs].
-=-SNiP-=-
Your concept of ``real time'' must obviously be different from the
rest of us who use the standard timepieces manufactured on this
planet as a measure of time. [There ARE various GR-"time-ZONEs".]
-=-
Anyone who follows your explanation will certainly not understand
the lorentz transforms. [Likewise for ANY COHERENT "explanation".]

Lorentz Transform violates the Principle of Simultaneity.

There is no such thing as the ``Principle of Simultaneity.''
Simultaneity in relativity is _defined_ by the poincare transforms
(of which the lorentz transforms are a [albeit, previously-DECLARED
by yourself, Bilge, to be UN-reachable via-POiNCARE ..duh] subset).
-=-
SR is actually the study of inertial reference frames -=- -=-

$$ REST (inertial) frames are *BARYCENTER-centred* ..NOT Galilean;
$$ M1 & m1 in Newton's G*M1*m1, are *moving* REST-mass magnitudes.
$$ M1 has acceleration to barycentre; m1 has another acceleration.
$$ There is NO COHERENT way to see M1 & m1 .. EACH from the OTHER.
$$ [The Newton context here is a three-dimensional SPACE in TiME].
$$ [There is NO COHERENT way to see m1, from M1 ..mathematically].
$$ [There is NO COHERENT way to see M1, from m1 ..mathematically].

Brian,
Bob and Ted and Carol and Alice stole half the decryption key
that surely came by separate post but Vav der Pol oscillators
are one way to model what is 'seen' between M1 and m1.
http://www.cmp.caltech.edu/~mcc/Chaos_Course/Lesson3/Demos.html

Sue...

Quote:

The hyperbolic Lagrangian remains invariant under Lorentz
transformations, which are actually hyperbolic rotations.

$$ But, are *NOT* "invarient" in the REST frame of the BARYCENTRE.

What is hyperbolic Lagrangian?
A lagrangian extremized by a metric for a hyperolic space.

$$ Define (explain) "extremized" in BOTH near-&-far-field context?

$$ General Universal Equation-of-State System (GUESS iSS) ANALYSiS:
$$ Classical OLD Lagrangian: || The Classical OLD Hamiltonian:
$$ L = H - 2*eP || H = L + 2*eP
$$ = eK - eP || = eK + eP
$$ = eK - Potential; || = eK + Potential (energy) eP;
$$ in GUESS = eK - Volt*A*sec || = eK + eM ..as per ADDENDUM;
$$ = eK - eV ..energy || = L + Gibb's eG .. " " "
$$ = eM - Helmholtz eF || = eK + iNTRiNSiC REST eM " " "
$$ = E - Gibb's eG. || = GUESS iSS ENTHALPY energy E.
$$
$ COMPLETELY combines all CHEMiSTRY equations-of-state, COHERENTLY.

Sue... wrote:

Zanket wrote:
A Flaw of General Relativity, a New Metric and Cosmological Implications



http://zanket.home.att.net/



Abstract: General relativity is shown to be inconsistent. A new metric for
Schwarzschild geometry is derived and shown to be confirmed by all
experimental tests of the Schwarzschild metric. (Those tests compose the
vast majority of experimental tests of general relativity.) The predictions
of the new metric and the Schwarzschild metric diverge as gravity
strengthens. Black holes are not predicted by the new metric. The
cosmological implications show that gravity alone can explain away the
flatness and horizon problems and cause the universe to seemingly accelerate
in its expansion.



Serious discussion appreciated, especially from those who attack the paper
directly.



For the babies: Yes, I know I'm a crackpot for challenging general
relativity, a proven fact. And yes I know that "experimental confirmation"
in no way implies empirical evidence.

Most real world clocks (Mossbauer, Cesium ) respond gravitationally
as we would predict for any oscillating mass. The elements loose
energy to a planet by following curved rather than straight paths.

The Schwarzschild solution, somewhat carelessly treats this
effect as a change in time rather than energy. The error is
demonstrated in the difference in the interpretations of the
Pound-Rebka and later Pound-Snider experiments.

http://www.citebase.org/cgi-bin/citations?id=oai:arXiv.org:physics/9907017

The Kankek paper is too extensive for a hobbyist as myself to
attack or support but the cause of the interpretive errors
certainly warrants further illumination. I reserve my toughest
skepticism for any cosmlogical extrapolatons which can't rigoursly
show they are not founded on the misinterpretation of Pound-Rebka.

The Kankek paper might be a little more concise
and less theoretical by focusing on the errors that can result
when time is interchanged for energy.

Sue...
Back to top
dda1
science forum Guru


Joined: 06 Feb 2006
Posts: 762

PostPosted: Sun Jul 09, 2006 4:19 pm    Post subject: Re: A Flaw of General Relativity, a New Metric and Cosmological Implications Reply with quote

Zanket wrote:
Quote:
Oh now you hurt my feelings.
rest snipped


Ok, go back where you came from :your mother's ass.
Back to top
Zanket
science forum beginner


Joined: 08 Jul 2006
Posts: 21

PostPosted: Sun Jul 09, 2006 7:03 pm    Post subject: Re: A Flaw of General Relativity, a New Metric and Cosmological Implications Reply with quote

Now I'm crying.

"dda1" <rangeravenger@yahoo.com> wrote in message
news:1152461977.549990.237020@75g2000cwc.googlegroups.com...
Quote:

Zanket wrote:
Oh now you hurt my feelings.
rest snipped

Ok, go back where you came from :your mother's ass.
Back to top
dda1
science forum Guru


Joined: 06 Feb 2006
Posts: 762

PostPosted: Mon Jul 10, 2006 1:09 am    Post subject: Zanket - a Motherfucking IDIOT Reply with quote

Zanket wrote:
Quote:
Now I'm crying.

"dda1" <rangeravenger@yahoo.com> wrote in message
news:1152461977.549990.237020@75g2000cwc.googlegroups.com...

Zanket wrote:
Oh now you hurt my feelings.
rest snipped

Ok, go back where you came from :your mother's ass.


You've been told you are a fUCKING IDIOT multiple times here:

http://www.physicsforums.com/search.php?searchid=421230

So, there , you are a Mother Fucking IDIOT.
Back to top
koobee.wublee@gmail.com
science forum Guru Wannabe


Joined: 01 Feb 2006
Posts: 141

PostPosted: Mon Jul 10, 2006 3:27 am    Post subject: Re: A Flaw of General Relativity, a New Metric and Cosmological Implications Reply with quote

Zanket wrote:
Quote:
A Flaw of General Relativity, a New Metric and Cosmological Implications


"Zanket" <zanket@gmail.com> wrote in message

news:urJrg.339953$Fs1.306945@bgtnsc05-news.ops.worldnet.att.net...

Quote:
A Flaw of General Relativity, a New Metric and Cosmological Implications

http://zanket.home.att.net/

Abstract: General relativity is shown to be inconsistent. A new metric for
Schwarzschild geometry is derived and shown to be confirmed by all
experimental tests of the Schwarzschild metric. (Those tests compose the
vast majority of experimental tests of general relativity.) The predictions
of the new metric and the Schwarzschild metric diverge as gravity
strengthens. Black holes are not predicted by the new metric. The
cosmological implications show that gravity alone can explain away the
flatness and horizon problems and cause the universe to seemingly accelerate
in its expansion.

The escape velocity in General Relativity consists of more complicated
usage of the metric than your model presents. That means the metric
does not have a direct impact on the escape velocity. Since your
simple conjecture is based on the escape velocity, you have to prove
how the metric (which there are sixteen elements) is a function of the
escape velocity.

Your metric also has a chance of being a valid one. However, you have
to modify Newtonian law of gravity to

F = - G M m / r^2 + k3 / r^3 + k4 / r^4...

Of course, under normal circumstances, the 2nd term and beyond are very
small compared to the first one.
Back to top
Tom Roberts
science forum Guru


Joined: 24 Mar 2005
Posts: 1399

PostPosted: Mon Jul 10, 2006 4:31 am    Post subject: Re: A Flaw of General Relativity, a New Metric and Cosmological Implications Reply with quote

Zanket wrote:
Quote:
A Flaw of General Relativity, a New Metric and Cosmological
Implications http://zanket.home.att.net/

The flaw is in your assumptions, and lack of recognizing what
assumptions you are actually making, not in GR.

I'll discuss the exterior Schwarzschild solution in GR, using the usual
radial variable r. I'll use the usual definition and call it a black hole.


Your article says:
Quote:
Section 1 shows that directly measured free-fall velocity approaches
a limit of c in a uniform gravitational field. This limit applies
everywhere since a gravitational field is everywhere uniform locally.
Then the directly measured free-fall velocity of an object falling
freely from rest at infinity approaches a limit of c. This was
inferred by means general relativity allows. In general relativity,
above an event horizon of a black hole, an object falling freely from
rest at infinity passes each altitude at a directly measured
velocity equal to the escape velocity there (3). If this velocity
approached a limit of c then so would escape velocity, in which case
escape velocity would always be less than c and then there would be
no black holes. But general relativity predicts black holes. Then
the theory is inconsistent.

You are implicitly assuming a single coordinate system can be used from
infinity all the way in to r=0. And you assume that this coordinate
system can be used to measure meaningful velocities with a limit of c as
predicted by SR. This is a blatantly false assumption, because the
manifold is curved. It is indeed true that at each point along the
falling object's path you can find LOCAL coordinates with that property,
but there is no such SINGLE coordinate system throughout, as you
implicitly assumed. See below for how to do this.

Let me discuss this particular statement there in more detail:
Quote:
If this velocity approached a limit of c then so would escape
velocity, in which case escape velocity would always be less than c
and then there would be no black holes.

Consider an object infalling from r=infinity. At every point along its
trajectory one can construct a LOCAL inertial frame by using standard
clocks and rulers, holding them at rest relative to the black hole, and
releasing them into freefall just as the infalling object arrives (one
must pre-arrange to set the clocks so they will be synchronized
immediately after the frame is released). Consider this construction at
points at successively smaller values of r -- in the limit as r->2M, the
speed of the infalling object measured by these successive inertial
frames will approach c.

So indeed, in the above sense the limit of the velocity of an infalling
object is indeed c. You are correct, and the speed of that infalling
object is the escape velocity from the point it is measured. Note that
this limit of c is reached as r->2M, and there _IS_ a black hole
present. <shrug>


In Section 3 you say:
Quote:
an object falling freely from rest at infinity passes each altitude
at a directly measured velocity equal to the escape velocity there,
in which case section 2 shows that escape velocity must approach a
limit of c (unity) as r tends to zero.

But your section 2 is quoted in its entirety above (except some dialog),
and it does not support this claim at all. Indeed, the limit of c is
reached at r=2M, not r=0, and that is fully consistent with the a priori
requirement that infalling velocity = escape velocity.

You are implicitly assuming that the object can escape from any point
with r>0 (and therefore must have speed <c relative to any
locally-inertial frame). But you have no basis for this assumption, and
did not even mention it at all. In fact, in GR for the Schwarzschild
spacetime, a timelike object cannot escape from any point with r<2M --
this is not an assumption, but is a _conclusion_ based on the geometry
of the manifold.


Quote:
It has long been known that general relativity predicts its own
demise by predicting central singularities where its equations fail
and where it is incompatible with quantum mechanics. Then it should
not be a surprise that the theory is flawed.

Yes. But these flaws are quite different from the flaws in your
argument. Note that all other physical theories have such singularities
and unphysical solutions, so this is not at all unique to GR. GR's
incompatibility with QM is far more serious, but your argument does not
touch upon it at all.


Your argument is based on basic misunderstandings, no more.


Tom Roberts
Back to top
Tom Roberts
science forum Guru


Joined: 24 Mar 2005
Posts: 1399

PostPosted: Mon Jul 10, 2006 4:40 am    Post subject: Re: A Flaw of General Relativity, a New Metric and Cosmological Implications Reply with quote

Koobee Wublee wrote:
Quote:
The escape velocity in General Relativity consists of more complicated
usage of the metric than your model presents.

He is discussing the Schwarzschild spacetime, which is _STATIC_. For a
static manifold, his usage of escape velocity is correct: the velocity
of an infalling test particle released from rest at infinity is equal in
magnitude to the escape velocity, at every point of its trajectory.

Additional caveats are needed for situations less symmetric
than Schw. spacetime.


Quote:
That means the metric
does not have a direct impact on the escape velocity.

For this particular static situation, his construction is valid. In
general, one must integrate the metric out to infinity to determine the
escape velocity for a given path (in general the escape velocity from a
given point depends on the path taken).


Tom Roberts
Back to top
Zanket
science forum beginner


Joined: 08 Jul 2006
Posts: 21

PostPosted: Mon Jul 10, 2006 5:12 am    Post subject: Re: Zanket - a Motherfucking IDIOT Reply with quote

Now I'm upset.

"dda1" <rangeravenger@yahoo.com> wrote in message
news:1152493767.676948.307750@35g2000cwc.googlegroups.com...
Quote:

Zanket wrote:
Now I'm crying.

"dda1" <rangeravenger@yahoo.com> wrote in message
news:1152461977.549990.237020@75g2000cwc.googlegroups.com...

Zanket wrote:
Oh now you hurt my feelings.
rest snipped

Ok, go back where you came from :your mother's ass.


You've been told you are a fUCKING IDIOT multiple times here:

http://www.physicsforums.com/search.php?searchid=421230

So, there , you are a Mother Fucking IDIOT.
Back to top
koobee.wublee@gmail.com
science forum Guru Wannabe


Joined: 01 Feb 2006
Posts: 141

PostPosted: Mon Jul 10, 2006 5:31 am    Post subject: Re: A Flaw of General Relativity, a New Metric and Cosmological Implications Reply with quote

"Tom Roberts" <tjroberts137@sbcglobal.net> wrote in message
news:ISksg.63446$fb2.25790@newssvr27.news.prodigy.net...

Quote:
Koobee Wublee wrote:
The escape velocity in General Relativity consists of more complicated
usage of the metric than your model presents.

He is discussing the Schwarzschild spacetime, which is _STATIC_. For a
static manifold, his usage of escape velocity is correct: the velocity
of an infalling test particle released from rest at infinity is equal in
magnitude to the escape velocity, at every point of its trajectory.

The Euler Lagrange equation associated with s, the spacetime itself,
yields

E^2 / (m^2 c^4) = (1 - 2 U) / (1 - (dr/dt)^2 / (1 - 2 U)^2 / c^2 + ...)

Where

** U = G M / r / c^2

Thus, the escape velocity at the normalized pontential, U, is achieve
through the following.

E^2 / (m^2 c^4) <= (1 - 2 U) / (1 - v^2 / (1 - 2 U)^2 / c^2)

Where

** v = escape velocity

Solving for v, we get

v >= c (1 - 2 U) sqrt(1 - (m^2 / c^4 / E^2) (1 - 2 U))

In a Newtonian world, we have

** 1 >> 2 U
** E ~= m^2 c^4

Thus, we have the escape velocity identified as

v = c sqrt(2 U) = sqrt(2 G M / r)

Therefore, Mr. Zanket's escape velocity for GR is grossly simplified.
Escape velocity is the result of the metric involved; the metric is not
the result of the escape velocity.

Quote:
Additional caveats are needed for situations less symmetric
than Schw. spacetime.

That means the metric
does not have a direct impact on the escape velocity.

For this particular static situation, his construction is valid. In
general, one must integrate the metric out to infinity to determine the
escape velocity for a given path (in general the escape velocity from a
given point depends on the path taken).

To use generic terms, we have the following diagonized spacetime.

ds^2 = c^2 g_00 dt^2 - g_11 dr^2 + ...

The Euler-Lagrange Equation associated with s yields

E^2 / (m^2 c^4) = g_00 / (1 - g_11 (dr/dt)^2 / g_00 + ...)

In which, the escape velocity should then be

v = c sqrt(g_00 / g_11) sqrt(1 - (m^2 / c^4 / E^2) (1 - g_00))

Mr. Zanket's mistake is using the Newtonian escape velocity which is
not valid under the Schwarzschild metric.
Back to top
Google

Back to top
Display posts from previous:   
Post new topic   Reply to topic Page 1 of 4 [56 Posts] Goto page:  1, 2, 3, 4 Next
View previous topic :: View next topic
The time now is Mon Mar 17, 2014 4:21 am | All times are GMT
Forum index » Science and Technology » Physics » Relativity
Jump to:  

Similar Topics
Topic Author Forum Replies Last Post
No new posts "Another Rebuff to General Relativity By Cosmological Obs... Tde Physics 0 Thu Jul 20, 2006 5:11 pm
No new posts "Another Rebuff to General Relativity By Cosmological Obs... Tde New Theories 0 Thu Jul 20, 2006 5:11 pm
No new posts "Another Rebuff to General Relativity By Cosmological Obs... Tde Particle 0 Thu Jul 20, 2006 5:11 pm
No new posts "Another Rebuff to General Relativity By Cosmological Obs... Tde Relativity 0 Thu Jul 20, 2006 5:11 pm
No new posts FLAW in the classical Wagner approach using in SOFC tom_miya@ballade.plala.or Electrochem 0 Mon Jul 17, 2006 5:48 pm

Copyright © 2004-2005 DeniX Solutions SRL
Other DeniX Solutions sites: Electronics forum |  Medicine forum |  Unix/Linux blog |  Unix/Linux documentation |  Unix/Linux forums  |  send newsletters
 


Powered by phpBB © 2001, 2005 phpBB Group
[ Time: 0.0945s ][ Queries: 16 (0.0452s) ][ GZIP on - Debug on ]