# Thread: Invited (peer) review of article(s) by Otto Rössler

1. Originally Posted by Trooper
BTW, how in hell can he be a jack of all trades? In regards to his publications, I don't understand how university affiliation works? Why would they allow this?
The wonderful world of tenure or prestige. Josephson is known for being wacko in his work, so much so he's banned from posting on ArXiv, despite having a Nobel Prize. Of course anyone who sees his last few papers there before being banned can see the ridiculous nature of his work. Paranormal stuff and string theory? How can he not see it as nonsense? And yet he's got a professorship position at Trinity College, Cambridge and works at the Cavendish labs in Cambridge. He's taking up a position someone capable of proper work could use but then his salary is a drop in the ocean for somewhere like Cambridge and having a Nobel Prize winner on the books counts for something.

Most of the time tenure isn't a problem, someone who does enough good work to get tenure is likely to be the sort of person who continues to do good work even when they are practically unfireable (short of committing a crime). A few abuse it though, much to the annoyance of postdocs fighting for the scraps left over once the funding budget has been bled dry.

There's a move away from such "Job for life" attitudes of days gone by. It's never been an official thing in the UK but it has always been next to impossible to fire a full academic (postdocs and postgrads are shuffled every 3~5 years anyway, they just don't get a new position). Given the massive cut in funding for the sciences there's more of a drive to make sure people earn their positions, no more "Work hard for 10 years, got a lecturing job and then **** the university!" some people did. This is a good thing to prevent elderly professors doing bugger all for 2 decades but it's due to the general decline in available positions

I'm occasionally poking Professor Rossler over on the lifeboat website. It's not terribly respectful to call him Mr Rossler or Otto but then he has less working experience with GR than even me. If he were talking about chemistry or dynamical systems I would give him the respect due in those areas. Talking about his Gothic R theorem (supposition more like) doesn't really grant him such respect.

2. Geodesics of flat space-time in Rindler coordinates (continued)
Starting with $ds^2 = -\frac{k^2}{c^2} x^2 dt^2 + dx^2 + dy^2 + dz^2$
We computed the Riemann tensor as zero and thus the physics of these coordinates are those of flat-space time.
Then we wrote down the geodesic equations which describe parametrized curves that are natural to the geometry. $\ddot{t} + 2 x^{\tiny -1} \dot{x} \dot{t} = 0, \; \ddot{x} + k^{\tiny 2} c^{\tiny -2} x \dot{t}^{\tiny 2}, \; \ddot{y} = \ddot{z} = 0$.
Solving those equations can be frustrating (especially if you are working off sloppy notes that transposed x and t and played fast and loose with minus signs), but at the end of the day we are rewarded with three sets of solutions, depending on the sign of $b = \dot{x}^{\tiny 2} - k^{\tiny 2} c^{\tiny -2} x^{\tiny 2} \dot{t}^{\tiny 2}$.

$
\begin{array}{r | c | c | c} \hline \\ \hline \\ & b < 0 & b = 0 & b > 0 \\ \hline
\\ t & t_0 + \frac{c}{k} \tanh^{\tiny -1} \left( - u_0 ( \lambda - \lambda_0 ) \right) & t_0 \pm \frac{c}{2k} \ln \left( u_0 ( \lambda - \lambda_0 ) \right) & t_0 + \frac{c}{k} \coth^{\tiny -1} \left( u_0 ( \lambda - \lambda_0 ) \right)
\\ x & x_0 \sqrt{1 - u_0^2 ( \lambda - \lambda_0 )^2 } & x_0 \sqrt{u_0 ( \lambda - \lambda_0 ) } & x_0 \sqrt{u_0^2 ( \lambda - \lambda_0 )^2 -1}
\\ y & y_0 + \dot{y} ( \lambda - \lambda_0 ) & y_0 + \dot{y} ( \lambda - \lambda_0 ) & y_0 + \dot{y} ( \lambda - \lambda_0 )
\\ z & z_0 + \dot{z} ( \lambda - \lambda_0 ) & z_0 + \dot{z} ( \lambda - \lambda_0 ) & z_0 + \dot{z} ( \lambda - \lambda_0 )
\\ \frac{ds^2}{d\lambda^2} & - x_0^2 u_0^2 + \dot{y}^2 + \dot{z}^2 & \dot{y}^2 + \dot{z}^2 & x_0^2 u_0^2 + \dot{y}^2 + \dot{z}^2
\\ \dot{t}x^2 & - \frac{c}{k} x_0^2 u_0 & \pm \frac{c}{2k} x_0^2 u_0 & - \frac{c}{k} x_0^2 u_0
\\ \ddot{x}x^3 & - x_0^4 u_0^2 & - \frac{1}{4} x_0^4 u_0^2 & - x_0^4 u_0^2
\\ x \sinh \frac{k}{c} t & x_0 \sinh \frac{k t_0}{c} - x_0 u_0 \cosh \frac{k t_0}{c} (\lambda - \lambda_0) & \mp \frac{x_0}{2} e^{\tiny \mp \frac{k t_0}{c}} \pm \frac{x_0 u_0}{2} e^{\tiny \pm \frac{k t_0}{c}} (\lambda - \lambda_0) & x_0 \cosh \frac{k t_0}{c} + x_0 u_0 \sinh \frac{k t_0}{c} (\lambda - \lambda_0)
\\ x \cosh \frac{k}{c} t & x_0 \cosh \frac{k t_0}{c} - x_0 u_0 \sinh \frac{k t_0}{c} (\lambda - \lambda_0) & \frac{x_0}{2} e^{\tiny \mp \frac{k t_0}{c}} + \frac{x_0 u_0}{2} e^{\tiny \pm \frac{k t_0}{c}} (\lambda - \lambda_0) & x_0 \sinh \frac{k t_0}{c} + x_0 u_0 \cosh \frac{k t_0}{c} (\lambda - \lambda_0)
\\ \hline
\\ T_0 & \frac{x_0}{c} \sinh \frac{k t_0}{c} & \mp \frac{x_0}{2 c} e^{\tiny \mp \frac{k t_0}{c}} & \frac{x_0}{c} \cosh \frac{k t_0}{c}
\\ \dot{T} & - \frac{x_0 u_0}{c} \cosh \frac{k t_0}{c} & \pm \frac{x_0 u_0}{2 c} e^{\tiny \pm \frac{k t_0}{c}} & \frac{x_0 u_0}{c} \sinh \frac{k t_0}{c}
\\ X_0 & x_0 \cosh \frac{k t_0}{c} & \frac{x_0}{2} e^{\tiny \mp \frac{k t_0}{c}} & x_0 \sinh \frac{k t_0}{c}
\\ \dot{X} & - x_0 u_0 \sinh \frac{k t_0}{c} & \frac{x_0 u_0}{2} e^{\tiny \pm \frac{k t_0}{c}} & x_0 u_0 \cosh \frac{k t_0}{c}
\\ -c^2\dot{T}^2 + \dot{X}^2 + \dot{Y}^2 + \dot{Z}^2 & - x_0^2 u_0^2 + \dot{y}^2 + \dot{z}^2 & \dot{y}^2 + \dot{z}^2 & x_0^2 u_0^2 + \dot{y}^2 + \dot{z}^2
\\ \frac{\dot{X}}{\dot{T}} & c \tanh \frac{k t_0}{c} & \pm c & c \coth \frac{k t_0}{c}
\end{array}$

h/t http://en.wikipedia.org/wiki/Rindler_coordinates for the cannonical transformation to Lorentzian coordinates.

3. Status
Much progress has been made learning the tools of General Relativity. The more I learn, the more obvious it appears that Rössler has not been doing physics or even geometry.

To-do
I need to move some work from http://www.sciforums.com/showthread.php?114537 here and wrap up the Rindler coordinate exercise with some physics.
I also need to go back and explain that General Relativity is a physical theory about geometry and if you start re-defining distance you make a shambles of geometry.
References
• [MTW1973] CS Misner, KS Thorne, JA Wheeler, Gravitation (New York: Freeman 1973)
• [Wald1984] RM Wald, General Relativity (Chicago: Chicago University Press 1984)
• [Rössler1997] OE Rössler, C. Giannetti, "Cession, twin of action (La cesión: hermana gemela de la acción)" In: Arte en la era electronica: Perspectivas de una nueva estética (ed. by C. Giannetti), (Barcelona: Associación de Cultura Temporánia L’Angelot, and Goethe-Institut Barcelona 1997), p.124. [Not located in print]
• [Rössler2005] OE Rössler, H. Kuypers, "The scale change of Einstein’s equivalence principle." Chaos, Solitons and Fractals, 25 897-899 (2005) http://www.sciencedirect.com/science...60077904007805
• [FN2005] J Foster and JD Nightingale A Short Course in General Relativity, 3rd edition (New York: Springer-Verlag 2005) [I don't own this volume]
• [Rössler2007] OE Rössler, "Abraham-like return to constant c in general relativity: gothic-R theorem demonstrated in Schwarzschild metric." Paper allegedly accepted for publication in Chaos, Solitons and Fractals.
• [Rössler2007b] OE Rössler, "Abraham-Solution to Schwarzschild Metric Implies That CERN Miniblack Holes Pose a Planetary Risk" http://www.wissensnavigator.ch/docum...IBLACKHOLE.pdf
• [Rössler2007b2] OE Rössler "Abraham-like return to constant c in general relativity: “ℜ-theorem“ demonstrated in Schwarzschild metric" http://www.wissensnavigator.ch/docum...IBLACKHOLE.pdf
• [Nicolai2008] H Nicolai, "Comments from Prof. Dr. Hermann Nicolai, Director, Max Planck-Institut für Gravitationsphysik (Albert-Einstein-Institut) Potsdam, Germany on speculations raised by Professor Otto Roessler about the production of black holes at the LHC." http://environmental-impact.web.cern...Comment-en.pdf
• [GN2008a] D Giulini, H Nicolai, "Zu den Ausfuhrungen O.E. Rösslers" http://www.ketweb.de/stellungnahmen/...co_Giulini.pdf
• [GN2008b] D Giulini, H Nicolai, "On the arguments of O.E. Rössler" http://environmental-impact.web.cern...Comment-en.pdf
• [Bruhn2008] GW Bruhn, "Commentary on two papers by O.E. Roessler on black holes" http://www.mathematik.tu-darmstadt.d...slerPaper.html
• [Ich2008] "Entfernungen in der Schwarzschildmetrik (Distances in the Schwarzschild metric)" http://www.achtphasen.net/miniblackh...warzschild.pdf
• [Rössler2008] OE Rössler, "Abraham-like return to constant c in general relativity: gothic-R theorem demonstrated in Schwarzschild metric." http://lhc-concern.info/wp-content/u...llpreprint.pdf
• [Rössler2008b] OE Rössler, "Added in proof: reception, erratum, confirmation" http://www.wissensnavigator.com/docu...d-in-proof.pdf
• [Rössler2008c]OE Rössler, "Abraham-solution to Schwarzschild metric implies that CERN miniblack holes pose a planetary risk." In: Vernetzte Wissenschaften: Crosslinks in Natural and Social Sciences (ed. by P.J. Plath and E.C. Haß), (Berlin: Logos Verlag 2008) pp. 263-270. [Not located in print]
• [Rössler2009] OE Rössler, "Abraham-like return to constant c in general relativity: “ℜ-theorem“ demonstrated in Schwarzschild metric." revised draft at http://www.wissensnavigator.com/documents/Chaos.pdf
• [Rössler2010] OE Rössler, D Fröhlich "The weight of the Ur-Kilogram" http://www.achtphasen.net/index.php/...10/12/11/p1890
• [Rössler2012] OE Rossler, "Einstein's equivalence principle has three further implications besides affecting time: T-L-M-Ch theorem (“Telemach”)" African Journal of Mathematics and Computer Science Research 5(3), pp. 44-47, (9 February, 2012) http://www.academicjournals.org/AJMC...eb/Rossler.pdf

4. Originally Posted by rpenner
If we replace the radial coordinate $r = \frac{G M}{c^2} + r_1 + \frac{G^2 M^2}{4 c^4 r_1} = \left( 1 + \frac{G M}{2 c^2 r_1} \right)^2 r_1 ; \quad r_1 = \frac{r - \frac{GM}{c^2} + \sqrt{r^2- \frac{2 GM r}{c^2}}}{2}$ then we get
$c^2 {d \tau}^{2} = \frac{\left(1 - \frac{G M}{2 c^2 r_1} \right)^2}{\left(1 + \frac{G M}{2 c^2 r_1} \right)^2} c^2 dt^2 - \left(1+\frac{G M}{2 c^2 r_1}\right)^4 \left( dr_1^2 + r_1^2 d\Omega^2 \right)$
And so the anisotropic coordinate speed of light in terms of $r_1$ is
$\frac{\left(1 - \frac{G M}{2 c^2 r_1} \right)}{\left(1 + \frac{G M}{2 c^2 r_1} \right)^3} c$ which goes to zero at $r_1 = \frac{GM}{2 c^2}$ that corresponds to $r = \frac{2 GM}{c^2}$.
Originally Posted by Aethelwulf
Sorry... but how is this true... I followed everything up to this point.
Obviously not, so I have provided additional context.

The Schwarzschild coordinates are for a geometry with metric $c^2 {d \tau}^2 = \left(1 - \frac{2 G M}{c^2 r} \right) c^2 {dt}^2 - \left(1 - \frac{2 G M}{c^2 r} \right)^{\tiny -1} {dr}^2 - r^2 {d \Omega}^2$. This suffers a cosmetic defect which Rössler should have addressed if he were self-consistent and speaking authoritatively on General Relativity, in that the coordinate speed of light is numerically different in different directions.
$0 = \left. c^2 {d \tau}^2 \right| _{\tiny d\Omega = 0} = \left(1 - \frac{2 G M}{c^2 r} \right) c^2 {dt}^2 - \left(1 - \frac{2 G M}{c^2 r} \right)^{\tiny -1} {dr}^2 \quad \Rightarrow \quad \left| \frac{dr}{dt} \right| = \left( 1 - \frac{2 G M}{c^2 r} \right) c \\ 0 = \left. c^2 {d \tau}^2 \right| _{\tiny dr = 0} = \left(1 - \frac{2 G M}{c^2 r} \right) c^2 {dt}^2 - r^2 {d \Omega}^2 \quad \Rightarrow \quad \left| \frac{r d\Omega}{dt} \right| = \sqrt{1 - \frac{2 G M}{c^2 r}} c$

So if we substitute $r = \left( 1 + \frac{G M}{2 c^2 r_1} \right)^2 r_1$, this leads to $dr = \left( 1 + \frac{G M}{2 c^2 r_1} \right)\left( 1 - \frac{G M}{2 c^2 r_1} \right) d r_1$, $1 - \frac{2 G M}{c^2 r} = \frac{\left( 1 - \frac{G M}{2 c^2 r_1} \right)^2}{\left( 1 + \frac{G M}{2 c^2 r_1} \right)^2}$, and therefore:
$c^2 {d \tau}^2 = \frac{\left( 1 - \frac{G M}{2 c^2 r_1} \right)^2}{\left( 1 + \frac{G M}{2 c^2 r_1} \right)^2} c^2 {dt}^2 - \frac{\left( 1 + \frac{G M}{2 c^2 r_1} \right)^2}{\left( 1 - \frac{G M}{2 c^2 r_1} \right)^2} \left( 1 + \frac{G M}{2 c^2 r_1} \right)^2 \left( 1 - \frac{G M}{2 c^2 r_1} \right)^2 {d r_1}^2 - \left( 1 + \frac{G M}{2 c^2 r_1} \right)^4 r_1^2 {d \Omega}^2 \\ = \frac{\left( 1 - \frac{G M}{2 c^2 r_1} \right)^2}{\left( 1 + \frac{G M}{2 c^2 r_1} \right)^2} c^2 {dt}^2 - \left( 1 + \frac{G M}{2 c^2 r_1} \right)^4 {d r_1}^2 - \left( 1 + \frac{G M}{2 c^2 r_1} \right)^4 r_1^2 {d \Omega}^2$
So in these new coordinates (for the same geometry) we see that the coordinates have the property that the numerical speed of light (at a certain point) is the same in every direction:
$0 = \left. c^2 {d \tau}^2 \right| _{\tiny d\Omega = 0} = \frac{\left( 1 - \frac{G M}{2 c^2 r_1} \right)^2}{\left( 1 + \frac{G M}{2 c^2 r_1} \right)^2} c^2 {dt}^2 - \left( 1 + \frac{G M}{2 c^2 r_1} \right)^4 {d r_1}^2 \quad \Rightarrow \quad \left| \frac{dr_1}{dt} \right| = \frac{1 - \frac{G M}{2 c^2 r_1}}{\left( 1 + \frac{G M}{2 c^2 r_1} \right)^3} c \\ 0 = \left. c^2 {d \tau}^2 \right| _{\tiny dr_1 = 0} = \frac{\left( 1 - \frac{G M}{2 c^2 r_1} \right)^2}{\left( 1 + \frac{G M}{2 c^2 r_1} \right)^2} c^2 {dt}^2 - \left( 1 + \frac{G M}{2 c^2 r_1} \right)^4 r_1^2 {d \Omega}^2 \quad \Rightarrow \quad \left| \frac{r_1 d\Omega}{dt} \right| = \frac{1 - \frac{G M}{2 c^2 r_1}}{\left( 1 + \frac{G M}{2 c^2 r_1} \right)^3} c$

So after following all of that, are we really to believe that you didn't follow $\left. \frac{r - \frac{GM}{c^2} + \sqrt{r^2- \frac{2 GM r}{c^2}}}{2} \right|_{\tiny r = \frac{2 G M}{c^2}} = \frac{G M}{2 c^2}$ or $\left. \frac{1 - \frac{G M}{2 c^2 r_1}}{\left( 1 + \frac{G M}{2 c^2 r_1} \right)^3} c \right|_{\tiny r_1 = \frac{G M}{2 c^2}} = 0$ ?

Originally Posted by Aethelwulf
I am missing something?
Correct.

Originally Posted by Aethelwulf
Also, your factor of 2 is in the wrong place.
Incorrect.

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