User talk:Pervect

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Hi. (Take the normal long winded welcome as read).

I have moved Pervect:Example/Sandbox to User:Pervect/Example/Sandbox - naming conventions. -- RHaworth 22:21, 9 August 2006 (UTC)

1 COM frame
2 Photon mass
3 Hi, I see you've met the local fauna
4 Line breaks
5 original research
6 Carl Brannen at Physicsforum
- 6.1 Privacy policy at Physics Forum
7 Physics Forums - could use your help
8 Please e-mail me
9 LUFE Matrix and unit conversion
10 Bell's_spaceship_paradox
11 Greetings!

[edit] COM frame

I understand your attachment to this concept but I hope you will have the honesty to admit that it is neither practical , nor is it realistic. Theoretically you can always find a frame for which $Σ p = 0$ but you will need to perform all your calculations in that inconvenient fram and transform the results into your lab frame. This may not be easy nor is it always possible: think about a single photon system for example. Ati3414 17:32, 10 August 2006 (UTC)

[edit] Photon mass

Sorry, you cannot say that the photon mass is E/c^2. This simply gives a lot of ammunition to dozens of crackpots . Especially coming from you, who argued very adeptly that there is no such thing as relativistic mass (correctly) and especially in light of the many experiments that constrain the photon ONLY "mass" to about 6*10^-17 eV which is about 17 orders of magnitude smaller than the 3eV you would get by applying m=E/c^2. So, please do not undelete my correction to your entry. Ati3414 17:40, 10 August 2006 (UTC)

[edit] Hi, I see you've met the local fauna

Ati3414 simply does not want to believe that systems of photons have mass other than relativistic mass (which is naturally an obsolete term as we all agree). Many of us have tried to tell him that photons and kinetic energy add rest mass and invariant mass to systems, and that therefore systems of photons and such HAVE mass (albeit as a system property, not one that attaches to individual photons, even though each photon adds to it). He cannot accept this. He will argue with you till the cows come home. I urge you not to waste your time at this until you read the TALK section of photon. It's all been said to him and it does not penetrate. I see you understand GR, so you may wish to simply tell him a real physicist's views. He does not accept the Baez and Carlip FAQs on the mass of boxes of photons and such, choosing to believe he is correct and the physicists are wrong. So you see how it is. S B H arris 05:17, 11 August 2006 (UTC)

Hi yourself. I'm still learning the ropes here at Wiki. I usually hang out at Physics Forums, but

I'm branching out a bit.

We'll see how this thing goes with Ati3141 - I don't want to start any wars (especially being new),

but I've got strong (negative) views about sloppy physics. I guess we'll just have to wait and see.

Pervect 09:08, 11 August 2006 (UTC)

Hi, Pervect, FWIW I think you've been doing a good job over at Physics Forums! I'd consider participating myself (see the "sticky" pointing to Relativity on the World Wide Web for a website I created when I was a graduate student, which is now unmaintained :-/ by John Baez), but unfortunately I can't seem to find a privacy policy and information about who operates the PF website.

Too bad you weren't here last year, when a few of us (too few) tried to start up WikiProject GTR, which was eventually abandoned in part because we never did drum up enough support from Wikipedians who have mastered this interesting subject. Hope you and Ed Schaefer have forgiven each other for that regretable misunderstanding concerning gtr as an effective field theory!---CH 02:51, 7 September 2006 (UTC)

Thanks for the compliment. I know that the owner of PF is Greg Bernhardt, and I understand that he started PF as a high school project. I assume he's in college now, but I don't know this for a fact. I don't know about their privacy policy, but, I've started a thread asking about it, we'll see what sort of replies we get. The thread is http://www.physicsforums.com/showthread.php?t=131209

Greg also appears to be on sitepoint, see http://www.sitepoint.com/article/super-moderator-guide

I was a little miffed at Ed Schaefer after the second, unrelated revert on a really minor issue (the date issue). It seems to me that he's a bit trigger happy on the 'revert' button. It appears to me that the situation is straightened out now, at least my edits aren't being reverted, and nobody is yelling and screaming, so everything must be OK :-). Pervect 18:45, 8 September 2006 (UTC)

Yes, I think so. There are so many gtr-know-nothings here (and everywhere else on the Net) that inevitably one adopts the default assumption that a newbie is unlikely to know as much as Ed does :-/ This is unfortunate but probably unavoidable, so I am glad that you have taken it in your stride.

I am kinda hoping you'll like WikiProject GTR enough to express interest in trying to rejuvenate this WikiProject. Although without at least a dozen devoted cruft patrollers and sufficiently many highly knowledgeable enthusiasts able to create good new content, this is probably unworkable.

I am following the physicsforums thread. It is quite impressive that the site was started by a high school student! But nonetheless very strange that it has no privacy policy; he should really hire a lawyer and create a good (perhaps boilerplate) policy.---CH 20:13, 9 September 2006 (UTC)

[edit] Line breaks

Regarding your edits to talk:black hole, please be aware that you don't have to hit "enter" after every line. In fact, this ends up messing up your comment's formatting when viewed in most browsers. To avoid this, just hit return twice for paragraph breaks, and don't use it at all inside paragraphs. --Christopher Thomas 16:39, 12 August 2006 (UTC)

[edit] original research

Thank you for your help at equivalence principle. However, do be advised that this kind of stuff is fairly common, and is why I was so quick to revert your edits on general relativity.

As for the GR page itself, I am willing to work with you on it. In general (no pun intended) I prefer to work with other editors, but a significant shift in emphasis like that needs to be considered. Just give this a little time and track the discussion there. I find the idea that this effective field theory business is "cut and dried" to be hard to swallow, but as an area of active study and consideration it apprears to be quite worthy of some kind of somewhat supportive mention. --EMS | Talk 19:56, 28 August 2006 (UTC)

[edit] Carl Brannen at Physicsforum

First: a quick remark about the privacy policy question. I can't discuss all of my concerns in public, but one thing I would like to know is where the money to run the site is coming from. If there is no clear answer, I'd be concerned that the money might be coming from selling data on forum users to marketing firms, for example. And who has laptops containing the user database which they might leave in their car, which might be broken into? In any case, the Wikipedia privacy policy would be an obvious model for chroot to examine :-/

While I was checking in over at Physicsforum, the threads started by Carl Brannen caught my eye. Since I've solved the EFE thousands of times, and have studied the Schwarzschild solution alone in about one hundred different charts, I can offer him some advice based upon my experience and knowledge of the vast literature on exact solutions of the EFE.

Question: what's with this "poll" business? We surely don't settle questions of applied mathematics by taking a vote!

Question: what is Carl really trying to do? I have the impression that in the end he is trying to write a nifty applet that anyone can use over the web to compute and visualize a geodesic in the Schwarzschild vacuum. Indeed, that would be a fun project for a Java programmer with a background in applied mathematics. I just hope he knows that the Kerr geodesics are considered to be well known, so this is certainly not an open problem! On the other hand, if he is really interested in understanding how gtr differs from Newtonian gravitation, studying just one (highly symmetric) solution is not the best way of gaining insight into this question. Much better to follow the textbooks and study weak field general relativity for isolated sources (e.g. written in terms of a multipole expansion). Indeed, if this his interest, he should use PPN formalism to compare relativistic gravitation theories such as Brans-Dicke with gtr (this is not as straightforward as some textbooks suggest, BTW, a caveat which is well known in the literature).

Question: does he seek the geodesics as parameterized curves or only as trajectories? Is he perhaps interested only in null geodesics? The answer can suggest different charts as being more or less suitable. For example, if he seeks only the trajectories of null geodesics, he should know about the Fermat metric introduced by Frankel.

Here I'll assume he seeks parameterized geodesic curves, and only for the Schwarzschild and Kerr vacuums.

Question: what is a "Cartesian chart"? By definition, no chart in a curved spacetime can have vanishing Christoffel coefficients, i.e. in any chart, some geodesics must not appear as coordinate lines. However various other properties we might associate with Cartesian charts in euclidean space might be realizable.

Let me focus for a minute on the much easier case of the Schwarzschild geodesics.

Perhaps by "Cartesian" he means "no coordinate singularity at the origin"? Here, the slices $T = T 0$ in the ingoing Painleve chart

$ds^2=-(1-2 m/r) \, dT^2 + 2 \, \sqrt{2 m/r} \, dT \, dr + dr^2 + r^2 \, d\Omega^2$

$d\Omega^2 = d\theta^2 + \sin(\theta)^2 \, d\phi^2$

$-\infty < T < \infty, \; 0 < r < \infty, \; 0 < \theta < \pi/2, \; -\pi < \phi < \pi$

are locally isometric to E³, but $r = 0$ corresponds to the future curvature singularity so must be deleted. Still, the fact that the spatial hyperslices (they are everywhere orthogonal to the world lines of the infalling Lemaitre observers, who fall in "from rest at $r = \infty$ ") are locally flat makes this chart very suitable for visualizing the physical experience of infalling observers. Carl is correct in claiming that the obvious transformation

$x = r \sin(\theta) \cos(\phi), \; y = r \sin(\theta) \, \sin(\phi), \; z = r \cos(\theta)$

brings the above chart into the form

$ds^2 = -(1-2 m/r) \, dT^2 + 2 \, \sqrt{\frac{2m}{r}} \, dT \, dr + dx^2 + dy^2 + dz^2$

$r = \sqrt{x^2 + y^2 + z^2}, \; -\infty < t,x,y,z < \infty, \; x^2 + y^2 + z^2 \neq 0$

which is well suited to low level programming. But all forty algebraically independent Christoffel coefficients are nonvanishing (and not particularly pretty) for this chart, so this is not a very good chart for numerically solving the geodesic equation, but once solutions are found in another chart, they can be transformed into this one, which is indeed well suited for visualizations.

We can transform any of the standard frame fields from the standard Painleve chart using the above transformation, but they won't be aligned with $\partial_x, \; \partial_y , \; \partial_z$ and won't look very nice. However, we can easily rotate to "align the spatial vectors" in the frame with these coordinate vectors. For example, the "Cartesian adapted frame" for the Lemaitre observers is

$\vec{e}_0 = \partial_T - \sqrt{2 m/r} \; \left( \frac{x}{r} \, \partial_x + \frac{y}{r} \, \partial_y + \frac{z}{r} \, \partial_z \right), \; \vec{e}_1 = \partial_x, \; \vec{e}_2 = \partial_y, \; \vec{e}_3 = \partial_z,$

which has the dual coframe field

$\sigma^0 = -dT, \; \sigma^1 = dx + \sqrt{2m/r^3} \, x \, dT, \; \sigma^2 = dy + \sqrt{2m/r^3} \, y \, dT, \; \sigma^3 = dz + \sqrt{2m/r^3} \, z \, dT$

$r=\sqrt{x^2 + y^2 + z^2}, \; dr = \frac{ x \, dx + y \, dy + z \, dz}{r}$

In terms of the coframe field, the metric tensor is

$g = -\sigma^0 \otimes \sigma^0 + \sigma^1 \otimes \sigma^1 + \sigma^2 \otimes \sigma^2 + \sigma^3 \otimes \sigma^3$

i.e. we are dealing with what MTW call an orthonormal basis of covector fields (and the dual basis of vector fields). Here, the integral curves of the vector field $\vec{e}_0$ are indeed the world lines of the infalling Lemaitre observers. So this is a nonspinning inertial frame which is about as "Cartesian" as you can ever hope to see in a curved spacetime.

Perhaps by "cartesian" he means that all the Christoffel coefficients should be, if not zero, then at worst rational functions of the coordinates? Such rational charts are realizable. Indeed, a standard chart (the rational prolate spheroidal Weyl canonical chart) is:

$ds^2 = -\exp (2 u) \, dt^2 + \exp (-2 u) \, \left( \exp (2 v) \, \left( \frac{x^2-y^2}{x^2-1} \; dx^2 + \frac{x^2-y^2}{1-y^2} \, dy^2 \right) \right.$

$\left. + (x^2-1) \, (1-y^2) \, d\phi^2 \right)$

$u=\log \sqrt{(x+1)/(x-1)}, \; v=\log\sqrt{(x^2-1)/(x^2-y^2)}$

This chart is only valid in the exterior region; the horizon appears as a "rod" $- 1 < y < 1, x = 1$ lying on the symmetry axis, assuming that the surfaces $x = x 0$ are plotted as nested prolate spheroids. In this chart, the geodesic equation has coefficients which are rational in the coordinates. In the equatorial plane $y = 0$ they simplify to

$\ddot{t} + \frac{2}{x^2-1} \, \dot{t} \, \dot{x} = 0$

$\ddot{x} + \frac{x-1}{m^2 \, (x+1)^3} \, \dot{t}^2 - \frac{1}{x^2-1} \, \dot{x}^2 - (x^2-1) \, \dot{\phi}^2 = 0$

$\ddot{\phi} + \frac{2}{x+1} \, \dot{x} \, \dot{\phi} = 0$

and we immediately obtain the first integrals

$\dot{t} = E \, \frac{x+1}{x-1}, \; \dot{\phi} = \frac{L}{(x+1)^2}$

and then we reduce the problem to a second order nonlinear ODE in x. The solution can be expressed as an integral, but for Carl's purposes it is better to obtain a numerical solution x(s) and then plug in to find the other variables (or to solve the full system given initial conditions). Here, the first integrals can be used to check that the numerical solutions do maintain constant values to within some tolerance. Then we can transform to exterior Schwarzschild and then to regular Painleve and the "Cartesian" Painleve chart given above in order to plot and visualize the results (in the exterior region, anyway).

There are also nice charts for the interior region, although matching up numerical solutions across the horizon could be a bit tricky. (Truth to tell, numerical solutions in the original and awful Painleve chart aren't too bad, so this isn't a serious problem.) Carl should be aware of the duality between certain colliding plane wave solutions and the "shallow interior" of various black hole solutions including Kerr (and thus Schwarzschild). In particular, it turns out that a simple example from the Gowdy family of vacuum solutions is locally isometric to the shallow interior of the Schwarzschild vacuum:

$ds^2 = -\frac{2}{\sqrt{p+q}} \, dp \, dq + (p+q) \; (dx^2 + dy^2)$

$-1/2 < p,q < 1/2, \; -\infty < x,y < \infty$

This has nice (not quite rational) geodesic equation. Alternatively, the full interior region is covered by a chart in LTB form (similar to the LTB dust solutions). These are written by introducing metric functions which must obey constraints. More generally, introducing auxilliary variables (with constraints) can assist in finding numerical solutions.

Carl should also be aware of extensive work on ultraboosts. It turns out that the gravitational field outside any isolated object (the vacuum exterior of any axially symmetric asympotically flat solution) looks like an axisymmetric gravitational pp-wave if you boost the object. The geodesic equations of such ultraboosts are particularly simple, but it is no easy task to "invert" to obtain the geodesics in the original asymptotically flat axisymmetric vacuum solution, since forming the ultraboost involves a fairly tricky limiting process (there have recently been significant simplications in this limit process, however). Since this stuff involves Dirac deltas, it gets us into the difficult question of what is admissable as a "solution" to the EFE (the concensus is that the answer depends upon context, but whatever works in a given situation is generally deemed acceptable).

As for Kerr, this all gets much more complicated. The Doran chart is indeed an impressive achievement for the techniques of geometric algebra (this is merely a not very widely used formalism for working with structures like Clifford algebras, by the way; it is not a theory of physics!), but unfortunately the hyperslices orthogonal to the world lines of the Doran observers (who are analogous to the Lemaitre observers) are not locally flat (except in the special case of nonrotating Kerr objects, i.e. the Schwarzschild case), so the Doran chart is not neccessarily very well suited to visualization. Still, Carl should know that the Kerr geodesics are well known, since, quite remarkably, Brandon Carter found that the geodesic equations of the Kerr vacuum happen to be completely integrable. This doesn't mean that new analytical simplifications or nifty numerical integration schemes might not still be found. To the contarary, I have worked with dozens of charts for the Kerr and am often surprised by unexpected virtues or flaws.

Another thing Carl might want to be aware of: a problem of current research interest involves giving closed form solutions of the equations of motion for spinning test particles, say in the Kerr vacuum. In gtr, spinning test particles should experience extremely tiny spin-spin forces (genuine forces yielding nonzero path curvatures, i.e. a spinning test particle's world line is forced off a geodesic path) when moving through the gravitational field near a massive spinning object such as the Earth. These forces are far too tiny to be measurable in solar system experiments, or even (AFAIK) in known astronomical systems which are currently being observed, so this problem is currently mostly of theoretical interest. Keyword: the Dixon-Papapetrou equations replace the usual geodesic equations in this problem. ---CH 04:36, 11 September 2006 (UTC)

As far as where Carl is coming from, it's hard for me to say. You might look at the previous thread

http://www.physicsforums.com/showthread.php?t=126996

I'd be interested if you concur with my solutions in http://www.physicsforums.com/showpost.php?p=1046874&postcount=17 also 18,19, 21

I do not really understand Carl's fixation with using what he calls "Cartesian" coordinates. I felt that I said everything that I had to say to Carl that was useful in that previous thread, including recommending a more sensible coordinate choice (more sensible = less Christoffel symbols) so I eventually stopped following the thread.

The best place to hold this discussion would probably be PF, if your privacy concerns can be satisfied, somehow. Pervect 21:22, 11 September 2006 (UTC)

I assume that getting a good official privacy policy will take some time. Another question: do any sysops at PF run around with the user database in a laptop? (I hope not!). AFAIK, Wikipedia has a record of good security, despite being one of the most visiable sites in the world.

I did see the previous thread. It seems that Brannen was interested not in reducing the number of independent Christoffel coefficients but in concocting a chart which is as close as possible to euclidean experience. If so, the Cartesian form of the Painleve chart is a good choice for displaying plots of geodesics, but probably not a good choice for finding numerical solutions, much less analytical ones.

As for the Painleve geodesics, I have verified my own computations with GRTensorII running under a recent edition of Maple. For the geodesic equations, I find 5 + 5 + 2 + 2 = 14 nonvanishing coefficients for the first order derivatives:

$\ddot{T} + \sqrt{\frac{2 m^3}{r^5}} \, \dot{T}^2 + \frac{2 m}{r^2} \, \dot{T} \, \dot{r} + \frac{1}{2} \sqrt{\frac{2 m}{r^3}} \, \dot{r}^2 - \sqrt{2 m r} \, \left( \dot{\theta}^2 + \sin(\theta)^2 \, \dot{\phi}^2 \right) = 0$

$\ddot{r} + \frac{m}{r^2} \left( 1- \frac{2 m}{r} \right) \, \dot{T}^2 - 2 \, \sqrt{\frac{2 m^3}{r^5}} \, \dot{T} \, \dot{r} - \frac{m}{r^2} \, \dot{r}^2 - (r-2 m) \, \left( \dot{\theta}^2 + \sin(\theta)^2 \, \dot{\phi}^2 \right) = 0$

$\ddot{\theta} + \frac{2}{r} \, \dot{r} \, \dot{\theta} - \sin(\theta) \, \cos(\theta) \, \dot{\phi}^2 = 0$

$\ddot{\phi} + 2 \left( \frac{1}{r} \, \dot{r} + \cot(\theta) \, \dot{\theta} \right) \, \dot{\phi} = 0$

where overdots denote derivatives with respect to an affine parameter. If you read off the geodesic Lagrangian from the line element and apply the Euler-Lagrange equations, you should obtain the same result. GRTensorII (only available for Maple) is far more useful than GRTensorM, by the way. If you are still you student and haven't bought a student edition of Maple, you should do so without delay! It is a very good idea to use both Maple and Mathematica in order to check results, since these are developed largely independently (and both have of course bugs known and unknown). Note that Maple has some conversion tools which can help to convert Mathematica code to Maple code.

In the equatorial plane, we immediately obtain a first integral $\dot{\phi} = L/r^2$ , which reduces the geodesic equations to a coupled system of a second order equation for $\dot{r}$ and a first order equation for $\dot{T}$ .

In your post, is your τ my T (proper time lapse for Lemaitre observers, also coordinate time for Painleve chart) and my λ (affine parameter, especially proper time along a curve) your t? Are you restricting to the equatorial plane θ = &pi&/2? Are you perhaps just looking for the stable circular orbits?---CH 03:12, 14 September 2006 (UTC)

Should I post a link to PF pointing Carl to your comments, here? I'm not sure my wiki talk page is the best place to hold an conversation. The obvious best place would be PF, but if your privacy concerns can't be met, perhaps there is an alternative?? Pervect 21:22, 11 September 2006 (UTC)

I agree your user page is not the best place. If Carl wants to respond, I can create a "Physics Forum" subpage in my own user space. ---CH 03:12, 14 September 2006 (UTC)

In my post (#20 for the Painleve metric) I was indeed restricting θ to π/2, however my tau was the affine parameter lambda, which was eliminated from the equations, and t was T, the coordinate time for the Lemaitre observer.

Substituting theta=pi/2 into your equations yields sin(theta)=1, cos(theta)=0, and makes all the derivatives of theta vanish, giving the geodesic equations I started with.

The goal as I understood it was to solve for the differential equations as functions of r, phi, and t, and eliminate all references to lambda. If we write r(t(lambda)), it's easy to see that r can be considered as a function both of t and of lambda "at will". Interpreting r as a function of t, we have in my notation vr = dr/dt and ar = d^2 r /dt^2. The same can be said for phi. Interpreting r as a function of lambda, we have in my notation rdot = dr/dlambda, and rdotdot = d^2r / d lambda^2. The chain rule says that dr/dlambda = dr/dt * dt/dlambda, which in my notation is rdot = vr * tdot, where tdot = dt/dlambda. The rest more or less follows, I think, from the post, especially the maple code in http://www.physicsforums.com/showpost.php?p=1046889&postcount=18 once you know what I used for variable names.

I'm using GrTensorII (with Maple) and unfortunately I don't own Mathematica to be able to run double checks. Carl is using Maxima, I believe.

I'll take your comments as implied permission to post a link to this webpage in PF, so that Carl can read your input directly, and get in touch with you if he's interested in talking with you further. I assume he can drop a note on your user talk page - if he can't, he is welcome to drop a note here to make arrangements as to how to get in touch.

BTW, I think that PF may be a much smaller operation than you (CH) are envisioning, and that we may see very fast action on a privacy policy. Pervect 05:49, 14 September 2006 (UTC)

Sure, go ahead and post the link. Eliminating the parameter λ: that is what I meant by finding the "trajectory", as opposed to solving the original geodesic equations (which results in affine parametrized geodesics). Very glad to hear you are using GRTensorII with Maple! Both are fine products and a lot of fun.---CH 08:43, 14 September 2006 (UTC)

[edit] Privacy policy at Physics Forum

FYI - I just checked and noticed that the PF privacy policy was up. Pervect 16:45, 16 September 2006 (UTC)

Good, I am looking into it. BTW, re the question about "deflection of light at high speeds": talking about "frame" like that without elaboration tends to foster confusion with "boosting" in str and also fosters confusion between "frame field" and "coordinate transformation". Most authors are careless on both points but this doesn't help students! Also, the poster might be interested in Aichelburg-Sexl ultraboost, about an exact vacuum solution (if you allow impulsive components in the curvature tensor) which is obtained by a limiting process from the Schwarzschild vacuum, and which models a Schwarzschild object whizzing by an observer at very nearly the speed of light. The most important point to make is that in such a situation, the gravitational field closely resembles that of a certain axisymmetric pp wave. That is, the encounter is very brief, so the curvature mostly concentrated near a certain "planar" wavefront, and within that wavefront the curvature (tidal forces) fall off more slowly with distance than r^-3, which is the Coulomb scaling appropriate for observers moving slowly wrt an isolated massive object.---CH 20:50, 21 September 2006 (UTC)

Uh oh, SelfAdjoint wrote in the thread "Linear Momentum in GR": "A hyperbolic space would be an example [of an asymptotically flat spacetime]. It has a region of maximum curvature and as you move farther and farther from that region the curvature gradually tends toward zero.". Whatever he meant, he can't have been talking about Hⁿ or even something like the de Sitter lambdavacuum (which has constant curvature)! ---CH 20:59, 21 September 2006 (UTC)

Hmm... I can't seem to find the privacy policy! ---CH 21:02, 21 September 2006 (UTC)

The privacy policy is stickied at http://www.physicsforums.com/showthread.php?t=131804

I'm not sure what SA had in mind with that post either. Check out the privacy policy - if it's satisfactory, you can ask him :-) Pervect 09:03, 22 September 2006 (UTC)

[edit] Physics Forums - could use your help

http://www.physicsforums.com/showthread.php?t=135384

discussing the concept of "gravitational potential" in General Relativity. I think the problems with the thread will be obvious if you read the thread :-(.

Don't know if you're satisfied with the privacy policy there, or have the time, but I thought I'd ask for some help. Pervect 03:04, 9 October 2006 (UTC)

Hi, Pervect, sorry, I thought I'd gotten back to you about that. I like the proposed privacy policy, but he needs to establish it permanently by creating a prominent permanent link on the main page, and he needs to clarify the issue of who maintains the site, at least by giving his name and his lawyer's address or whatever, before I would feel comfortable in participating. You should wikimail me (give me several days to respond) so that I can express in private two other remaining concerns.

When I get a chance I'll take a look at that specific thread and comment here.---CH 03:16, 9 October 2006 (UTC)

[edit] Please e-mail me

I have an e-mail from Chris Hillman to forward to you. --EMS | Talk 06:21, 22 November 2006 (UTC)

I have forwarded it to the e-address that you gave me. Thanks. --EMS | Talk 19:37, 23 November 2006 (UTC)

[edit] LUFE Matrix and unit conversion

I recently added unidimensional version of LUFE Matrix to Geometrized unit system article talk, and too documenting reference to less simplified original duodimensional LUFE Matrix. I too recently converted second into meter, kilogram, second, ampere, kelvin, mole and candela, by using cross-consistent converting formulas that too retains cross-consistency in converting between meter, kilogram, second, ampere, kelvin, mole and candela, finally obtaining cross-consistent results by using formulas from discussions linked below to perform this conversion task, that was performed directly from second and second-derivations into these units as follows:

from second to one power to meter
from second to one power to kilogram
from second to one power to second
from second to zero power to ampere
from second to minus one power to kelvin
from second to zero power to mole
from second to zero power to candela

by performing these tasks as is stated here:

http://en.wikipedia.org/wiki/Talk:Geometrized_unit_system#Unit_conversion
http://www.physicsforums.com/showthread.php?t=149595 (thread closed and locked by admin)
http://www.scienceforums.net/forum/showthread.php?t=24751 (thread closed and locked by admin)

Finally our discussion about septenary geometrized units was crowned by releasing by me principles and creation process of such system in article placed here: http://www.internet-encyclopedia.org/index.php/Septimalisation But I need your help in verification of ampere, mole and candela-related stuff, and too complete set of geometrization factors, that is stated further in Wikipedia talk related to geometrized unit system article placed here: [1]. I propose include these factors after verification into main article. Wikinger 15:15, 16 April 2007 (UTC)

Someone already added them to article after verification. 83.5.50.45 19:39, 21 April 2007 (UTC)

[edit] Bell's_spaceship_paradox

Hi it looks like the last one to tag Bell's_spaceship_paradox with NPOV was you. If so, please either motivate why you still have that opinion or remove the tag; and if not, could you ask the last one who did so ask this?

Thanks, Harald88 15:11, 17 June 2007 (UTC)

[edit] Greetings!

Hi, P,

Haven't heard from you in quite some time; drop me an email (or a PM at PF) if you get a chance, I'd like to catch up! (Or did you quit both PF and WP?) ---CH (talk) 01:42, 4 June 2008 (UTC)