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koobee.wublee@gmail.com
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Joined: 01 Feb 2006
Posts: 141

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

"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.
koobee.wublee@gmail.com
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Joined: 01 Feb 2006
Posts: 141

Posted: Mon Jul 10, 2006 5:42 am    Post subject: Re: A Flaw of General Relativity, a New Metric and Cosmological Implications

"Tom Roberts" <tjroberts137@sbcglobal.net> wrote in message
news:XKksg.63443\$fb2.30315@newssvr27.news.prodigy.net...

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

what you have said.

Mr. Zandet made one more assumption/postulate than GR where GR is piled
on several more of its own. Therefore, the validity of Mr. Zandet's
presentation of his metric is highly questionable. Since GR only makes
one fewer assumption/postulate than Mr. Zandet did, what does that
tells you with GR?
Zanket
science forum beginner

Joined: 08 Jul 2006
Posts: 21

Posted: Mon Jul 10, 2006 6:37 am    Post subject: Re: A Flaw of General Relativity, a New Metric and Cosmological Implications

Hi Tom,

 Quote: You are implicitly assuming a single coordinate system can be used from infinity all the way in to r=0.

No, look carefully; the analysis in section 2 is wholly above an event
horizon. The flaw can be shown between any two altitudes above an event
horizon.

 Quote: 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.

The speed approaches c, but does not approach a limit of c, and that's a
huge difference. Rather, the speed approaches a limit of infinity just like
escape velocity does as r tends to zero. Look at eq. 4 in fig. 2. Above an
event horizon, eq. 4 is Einstein's equation for the speed to which you
refer. What limit does it approach as r tends to zero? It approaches
infinity.

 Quote: 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>

At and below an event horizon all objects must fall, establishing the limit
to which you refer. But that limit is a different animal than the limit the
speed approaches above an event horizon, which is infinity. Section 2 uses
the latter limit to show a flaw of GR; the former limit is immaterial to
that.

 Quote: 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.

As noted above, you're misusing your limits. There are two limits involved.
When the applicable one is used, the claim is supported.

 Quote: 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.

The comment you quoted is just saying that we already know the theory is
flawed in one way, so it should not be a surprise that it is flawed in
another way.

"Tom Roberts" <tjroberts137@sbcglobal.net> wrote in message
news:XKksg.63443\$fb2.30315@newssvr27.news.prodigy.net...
 Quote: Zanket wrote: 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: 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: 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. 0 (and therefore must have speed
Bilge
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Joined: 30 Apr 2005
Posts: 2816

Posted: Mon Jul 10, 2006 7:13 am    Post subject: Re: A Flaw of General Relativity, a New Metric and Cosmological Implications

Zanket:
 Quote: I assume you can't find an actual problem.

Assume whatever you want. You are arguing against your own
misrepresentation of general relativity.

 Quote: "Bilge" wrote in message news:slrneav6d7.2tl.dubious@radioactivex.lebesque-al.net... 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...
Sorcerer1
science forum Guru

Joined: 09 Jun 2006
Posts: 410

 Posted: Mon Jul 10, 2006 10:41 am    Post subject: Re: A Flaw of General Relativity, a New Metric and Cosmological Implications "Tom Roberts" wrote in message news:XKksg.63443\$fb2.30315@newssvr27.news.prodigy.net... | Zanket wrote: | > 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. This is PHYSICS, not math or logic, and "proof" is completely irrelevant. -- Humpty Roberts. Androcles.
Dirk Van de moortel
science forum Guru

Joined: 01 May 2005
Posts: 3019

Posted: Mon Jul 10, 2006 10:58 am    Post subject: Re: A Flaw of General Relativity, a New Metric and Cosmological Implications

"Koobee Wublee" <koobee.wublee@gmail.com> wrote in message news:1152510153.277694.104560@s13g2000cwa.googlegroups.com...
 Quote: "Tom Roberts" wrote in message news:XKksg.63443\$fb2.30315@newssvr27.news.prodigy.net... The flaw is in your assumptions, and lack of recognizing what assumptions you are actually making, not in GR. [...] If I have interpreted your comments correctly, allow me to summarize what you have said. Mr. Zandet made one more assumption/postulate than GR where GR is piled on several more of its own. Therefore, the validity of Mr. Zandet's presentation of his metric is highly questionable. Since GR only makes one fewer assumption/postulate than Mr. Zandet did, what does that tells you with GR?

If you can't even properly read the string "Zanket", how would
you expect to have correctly interpreted Tom's comments?

Dirk Vdm
Sorcerer1
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Joined: 09 Jun 2006
Posts: 410

 Posted: Mon Jul 10, 2006 11:29 am    Post subject: Re: A Flaw of General Relativity, a New Metric and Cosmological Implications "Dirk Van de moortel" wrote in message news:jpqsg.528975\$bn7.12748973@phobos.telenet-ops.be... [anip] This is PHYSICS, not math or logic, and "proof" is completely irrelevant. -- Humpty Roberts, co-author of relativity FAQs. Never mind the math, check the physics. -- Dork Van de merde, local village idiot. Androcles.
science forum Guru Wannabe

Joined: 11 Sep 2005
Posts: 290

Posted: Mon Jul 10, 2006 12:43 pm    Post subject: Re: A Flaw of General Relativity, a New Metric and Cosmological Implications

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

Sue, your often referenced paper is a masterpiece of sophistry:

arXiv: physics/ 9907017 v2 27 Jul 1999

ON THE INTERPRETATION OF THE REDSHIFT IN A STATIC GRAVITATIONAL FIELD
L.B. OKUN and K.G. SELIVANOV
ITEP, Moscow, 117218, Russia
e-mail: okun@heron.itep.ru, selivano@heron.itep.ru
and
V.L. TELEGDI
EP Division, CERN, CH - 1211 Geneva 23
e-mail: valentine.telegdi@cern.ch

For instance,

Excerpt:

"Alongside the experiments [3]-[7] special measurements of the
dependence of the atomic clock rate on the altitude were done directly
In these experiments a clock which had spent many hours at high
altitude was brought back to the laboratory and compared with its
"earthly twin". The latter, once corrected for various
background effects, lagged behind by Delta T = (gh/c^2)T,
where T is the duration of the flight at height h , g the gravitational
acceleration,
and c the speed of light.

[8] J. Haefele and R. Keating, "Around the world atomic clocks:
predicted relativistic gains,"
Science 177, 166-167 (1972); "Around the world relativistic clocks:
observed relativistic time gains," ibid., 168-170."

My comment:

Only experiments where clocks are brought back to Earth can support
the view that the flying clocks ticked faster than the ground clocks.
Till now, this has been done only once, it was the H&K experiment,
but "An analysis of the real data shows that no credence can be
given to the conclusions of Hafele and Keating.", see
http://www.cartesio-episteme.net/H&KPaper.htm .

Excerpt:

"Consider from such an elevator falling with the acceleration g
a photon of frequency Omega which is emitted upwards by an atom at
rest on the surface of the earth and which is expected to be
absorbed by an identical atom fixed at height h . The frequency of
light is not affected by any gravitational field in a freely falling
elevator: it keeps the frequency with which it was emitted.
Assume that at the moment of emission (t = 0) the elevator had zero
velocity. At the time t = h/c , when the photon reaches the absorbing
atom, the latter will have velocity v = gh/c directed upwards in
the elevator frame. As a result the frequency of the photon, as seen
by the absorbing atom, will be shifted by the linear Doppler effect
by v/c = gh/c^2 towards the red, that is
delta Omega / Omega = -gh/c^2.
<...>
Obviously, in the elevator frame there is no room for the
interpretation
of the redshift in terms of a photon losing its energy as it climbs
out of the gravitational well."

And elsewhere in the paper:

"Near the earth's surface (at h = r -R « R ) it is legitimate
to approximate phi linearly. <...>
(The linear approximation Eq. (2) is valid for the description of
experiments [8, 9]. It is obvious, however, that for the high flying
rockets [7] (h ~ 10^4 km), it is not adequate and the newtonian
potential should be used, but this is not essential for the dilemma
"clocks versus photons" which is the subject of this paper.)".

My comment:

The authors used v = gt and t = h/c to get v = gh/c and eventually
a shift -gh/c^2 from the linear Doppler effect, the same shift as the
one obtained with "a photon losing its energy as it climbs out of
the gravitational well".

Notice that the "Doppler shift" is observed in the elevator frame,
and the "potential energy" shift is observed in the Earth frame.

But one should notice that the authors used what they called the
"linear approximation", claiming that using the Newtonian potential
is not essential for the "dilemma clocks vs photons".

This is wrong. If they had used g = GM/(R*(R+h)) instead of linearly
g = GM/R^2, their demonstration "in favor of clocks", using v = gt and
the Doppler effect, would have been a failure.

Conclusively, the authors' claim (see abstract) that the approach
in terms of an energy loss of a photon as it overcomes the
gravitational attraction of the massive body is misleading is not
justified, on the contrary.

Marcel Luttgens

 Quote: 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...
science forum Guru Wannabe

Joined: 11 Sep 2005
Posts: 290

Posted: Mon Jul 10, 2006 2:16 pm    Post subject: Re: A Flaw of General Relativity, a New Metric and Cosmological Implications

 Quote: 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 Sue, your often referenced paper is a masterpiece of sophistry: arXiv: physics/ 9907017 v2 27 Jul 1999 ON THE INTERPRETATION OF THE REDSHIFT IN A STATIC GRAVITATIONAL FIELD L.B. OKUN and K.G. SELIVANOV ITEP, Moscow, 117218, Russia e-mail: okun@heron.itep.ru, selivano@heron.itep.ru and V.L. TELEGDI EP Division, CERN, CH - 1211 Geneva 23 e-mail: valentine.telegdi@cern.ch For instance, Excerpt: "Alongside the experiments [3]-[7] special measurements of the dependence of the atomic clock rate on the altitude were done directly by using airplanes [8], [9] (see also reviews [10]). In these experiments a clock which had spent many hours at high altitude was brought back to the laboratory and compared with its "earthly twin". The latter, once corrected for various background effects, lagged behind by Delta T = (gh/c^2)T, where T is the duration of the flight at height h , g the gravitational acceleration, and c the speed of light. [8] J. Haefele and R. Keating, "Around the world atomic clocks: predicted relativistic gains," Science 177, 166-167 (1972); "Around the world relativistic clocks: observed relativistic time gains," ibid., 168-170." My comment: Only experiments where clocks are brought back to Earth can support the view that the flying clocks ticked faster than the ground clocks. Till now, this has been done only once, it was the H&K experiment, but "An analysis of the real data shows that no credence can be given to the conclusions of Hafele and Keating.", see http://www.cartesio-episteme.net/H&KPaper.htm . Excerpt: "Consider from such an elevator falling with the acceleration g a photon of frequency Omega which is emitted upwards by an atom at rest on the surface of the earth and which is expected to be absorbed by an identical atom fixed at height h . The frequency of light is not affected by any gravitational field in a freely falling elevator: it keeps the frequency with which it was emitted. Assume that at the moment of emission (t = 0) the elevator had zero velocity. At the time t = h/c , when the photon reaches the absorbing atom, the latter will have velocity v = gh/c directed upwards in the elevator frame. As a result the frequency of the photon, as seen by the absorbing atom, will be shifted by the linear Doppler effect by v/c = gh/c^2 towards the red, that is delta Omega / Omega = -gh/c^2. ... Obviously, in the elevator frame there is no room for the interpretation of the redshift in terms of a photon losing its energy as it climbs out of the gravitational well." And elsewhere in the paper: "Near the earth's surface (at h = r -R « R ) it is legitimate to approximate phi linearly. <... (The linear approximation Eq. (2) is valid for the description of experiments [8, 9]. It is obvious, however, that for the high flying rockets [7] (h ~ 10^4 km), it is not adequate and the newtonian potential should be used, but this is not essential for the dilemma "clocks versus photons" which is the subject of this paper.)". My comment: The authors used v = gt and t = h/c to get v = gh/c and eventually a shift -gh/c^2 from the linear Doppler effect, the same shift as the one obtained with "a photon losing its energy as it climbs out of the gravitational well". Notice that the "Doppler shift" is observed in the elevator frame, and the "potential energy" shift is observed in the Earth frame. But one should notice that the authors used what they called the "linear approximation", claiming that using the Newtonian potential is not essential for the "dilemma clocks vs photons". This is wrong. If they had used g = GM/(R*(R+h)) instead of linearly g = GM/R^2, their demonstration "in favor of clocks", using v = gt and the Doppler effect, would have been a failure. Conclusively, the authors' claim (see abstract) that the approach in terms of an energy loss of a photon as it overcomes the gravitational attraction of the massive body is misleading is not justified, on the contrary. Marcel Luttgens

I claimed:

"This is wrong. If they had used g = GM/(R*(R+h)) instead of linearly
g = GM/R^2, their demonstration "in favor of clocks", using v = gt and
the Doppler effect, would have been a failure."

Sorry, the authors would have obtained in the elevator frame a shift of

-(GM/c^2) * (h/R*(R+h)), which is right.

Anyhow, in the Earth frame, the same shift is obtained, but which
is explained by the relativistic mass and the loss of potential
energy of the photon.

Marcel Luttgens

 Quote: 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...
Zanket
science forum beginner

Joined: 08 Jul 2006
Posts: 21

Posted: Mon Jul 10, 2006 5:53 pm    Post subject: Re: A Flaw of General Relativity, a New Metric and Cosmological Implications

Yes master.

 Quote: Zanket: I assume you can't find an actual problem. Assume whatever you want. You are arguing against your own misrepresentation of general relativity. "Bilge" wrote in message news:slrneav6d7.2tl.dubious@radioactivex.lebesque-al.net... 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...
Zanket
science forum beginner

Joined: 08 Jul 2006
Posts: 21

Posted: Tue Jul 11, 2006 12:25 pm    Post subject: Re: A Flaw of General Relativity, a New Metric and Cosmological Implications

Tom,

Reader: At and below an event horizon, the directly measured velocity of an
object is always less than c. So directly measured free-fall velocity *does*
approach a limit of c.

Author: That puts the cart before the horse. If the velocity approached a
limit of c then so would escape velocity, and then there would be no event
horizons.

 Quote: 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.

Reader: Special relativity does not apply to curved spacetime.

Author: It is used only in flat spacetime.

"Tom Roberts" <tjroberts137@sbcglobal.net> wrote in message
news:XKksg.63443\$fb2.30315@newssvr27.news.prodigy.net...
 Quote: Zanket wrote: 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: 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: 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. 0 (and therefore must have speed
Zanket
science forum beginner

Joined: 08 Jul 2006
Posts: 21

Posted: Tue Jul 11, 2006 12:37 pm    Post subject: Re: A Flaw of General Relativity, a New Metric and Cosmological Implications

 Quote: Mr. Zanket's mistake is using the Newtonian escape velocity which is not valid under the Schwarzschild metric.

For Schwarzschild geometry Einstein shares Newton's escape velocity
equation, eq. 4. Only their interpretations of it differ.

"Koobee Wublee" <koobee.wublee@gmail.com> wrote in message
 Quote: "Tom Roberts" wrote in message news:ISksg.63446\$fb2.25790@newssvr27.news.prodigy.net... 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. 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.
Tom Roberts
science forum Guru

Joined: 24 Mar 2005
Posts: 1399

Posted: Wed Jul 12, 2006 12:53 am    Post subject: Re: A Flaw of General Relativity, a New Metric and Cosmological Implications

Zanket wrote:
 Quote: Tom Roberts said: You are implicitly assuming a single coordinate system can be used from infinity all the way in to r=0. No, look carefully; the analysis in section 2 is wholly above an event horizon. The flaw can be shown between any two altitudes above an event horizon.

No, your whole point is as r->0.

 Quote: 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. The speed approaches c, but does not approach a limit of c, and that's a huge difference.

Sure that is a limit -- you cannot actually evaluate anything in these
coordinate _at_ r=2M, you can only approach r=2M from above. That's what
a limit is. <shrug>

 Quote: Rather, the speed approaches a limit of infinity just like escape velocity does as r tends to zero.

Nonsense. The limit r->0 DOES NOT EXIST because these coordinates are
invalid for r<=2M. <shrug>

 Quote: At and below an event horizon all objects must fall, establishing the limit to which you refer. But that limit is a different animal than the limit the speed approaches above an event horizon, which is infinity. Section 2 uses the latter limit to show a flaw of GR; the former limit is immaterial to that.

Your section 2 does no such thing. It _assumes_ that r=0 can be
approached, when in fact it cannot.

Tom Roberts
Tom Roberts
science forum Guru

Joined: 24 Mar 2005
Posts: 1399

Posted: Wed Jul 12, 2006 12:58 am    Post subject: Re: A Flaw of General Relativity, a New Metric and Cosmological Implications

Zanket wrote:
 Quote: Reader: At and below an event horizon, the directly measured velocity of an object is always less than c. So directly measured free-fall velocity *does* approach a limit of c. Author: That puts the cart before the horse. If the velocity approached a limit of c then so would escape velocity, and then there would be no event horizons.

You are quite confused, and have completely hidden the frames relative
to which your velocities are measured. Outside the horizon my earlier
construction can be used to measure the infalling object's speed
relative to a local inertial frame at rest relative to the black hole.
As I said before, such measurements _DO_ approach a limit of c as r->2M
(for an object released from rest at r=infinity).

For r<=2M that construction simply cannot be done because there are no
such frames.

Because your statements here have hidden important details they are just
plain wrong. As is your conclusion -- there _IS_ an event horizon. <shrug>

Tom Roberts
Zanket
science forum beginner

Joined: 08 Jul 2006
Posts: 21

Posted: Wed Jul 12, 2006 11:26 am    Post subject: Re: A Flaw of General Relativity, a New Metric and Cosmological Implications

You are putting the cart before the horse below. I'll address that in your
other post to avoid duplication.

"Tom Roberts" <tjroberts137@sbcglobal.net> wrote in message
news:MJXsg.63698\$Lm5.22007@newssvr12.news.prodigy.com...
 Quote: Zanket wrote: Tom Roberts said: You are implicitly assuming a single coordinate system can be used from infinity all the way in to r=0. No, look carefully; the analysis in section 2 is wholly above an event horizon. The flaw can be shown between any two altitudes above an event horizon. No, your whole point is as r->0. 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. The speed approaches c, but does not approach a limit of c, and that's a huge difference. Sure that is a limit -- you cannot actually evaluate anything in these coordinate _at_ r=2M, you can only approach r=2M from above. That's what a limit is. 0 DOES NOT EXIST because these coordinates are invalid for r<=2M.

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