“I do not understand the Telemach theorem but I feel it is too simple to be possibly correct; yet please, do not mention my name.” ‘t Hooft and Hawking join-in in the loud silence.

Hereby the existence of a highly sophisticated version of Telemach, found independently by a high-ranking academic, is kept from the media. It is known to CERN and would take years to discuss. I therefore support his continuing on outside the limelight.

Dear, venerable CERN: Please, make a 4-week pause immediately to give Telemach a chance to be put to rest. Nothing would make his father and the planet more happy. I publicly offer a bet to Stephen Hawking that he will not succeed in this task. If I lose I shall write a preface to his next book.

P.S. I briefly append Telemach again:

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Einstein’s Equivalence Principle Has Three Further Implications Besides Affecting Time: T-L-M-Ch Theorem (“Telemach”)

Otto E. Rossler

Institute for Physical and Theoretical Chemistry, University of Tubingen, Auf der Morgenstelle A, 72076 Tubingen, F.R.G.

Abstract

General relativity is notoriously difficult to interpret. A “return to the mothers” is proposed to better understand the gothic-R theorem of the Schwarzschild metric of general relativity. It is shown that the new finding is already implicit in Einstein’s equivalence principle of 1907 and hence in special relativity (with acceleration included). The TeLeMaCh theorem, named onomatopoetically after Telemachus, is bound to transform metrology if correct.

(March 31, 2011)

1. Introduction

Recently it was shown that the Schwarzschild metric of general relativity admits at least one further canonical observable, the so-called gothic-R distance [1]. In terms of this distance, the speed of light c is globally constant. Is this result only a new mathematically allowed physical interpretation, or does it have deeper “ontological” significance?

A convenient way to find out is to pass over to an even more fundamental level of description. The “equivalence principle” between kinematic and gravitational acceleration, which still belongs to special relativity, is the oldest and in a sense most powerful element of general relativity since everything grew out of this “happiest thought of my life” as Einstein used to call it.

A famous “ontological” implication of the equivalence principle is the slower ticking rate of clocks at the rear end of a long constantly accelerating train or rocketship. It was deduced by Einstein in a chain of heuristic mental steps. The latter involved light-pulse emitting clocks and light-pulse detecting devices in a mentally pictured scenario comprising long hollow cylinders releasable into free fall sporting hooks and vertical slits in their sides to allow one to put in clocks and sensors at different height levels before or after release into free fall, cf. [2].

More than a half-century later, Wolfgang Rindler [3] succeeded in graphically retrieving all pertinent results of Einstein’s in the famous Rindler metric. The latter describes a long collection of simultaneously ignited infinitesimally short rocketships, or rather hollow rocket-rings, that stay together spontaneously owing to a careful choice of their systematically differing constant accelerations. The most concise description of the resulting 2-D space-time diagram, with its “scrollable” simultaneity axes that all pass through one point, can be found in Wald’s 1984 otherwise algebra-oriented book “General Relativity” [4, p. 151]. For an independent re-discovery, see John S. Bell’s intriguing paper [5].

2. The Secret Power of the Equivalence Principle

Clocks at the end of a long constantly accelerating rocketship in outer space have elongated ticking intervals when their light pulses arrive at the rocket’s tip, because the latter has in the meantime acquired a well-defined positive velocity compared to the point of origin of the light pulses, as Einstein found out in 1907. The resulting special-relativistic redshift at first sight appears to be a mere observational effect: “in reality” the clocks in question ought to tick at their normal rate (but they don’t).

We know how it is with Einstein’s deceptively simple gedanken experiments: He has a knack for following them up to a breaking point where something “impossible” occurs. Remember his previous observation of an apparent clock slowdown of a constant-speed departing twin clock which, while with constant speed returning, has an equally accelerated pulse rate, considered in his seminal founding paper of special relativity of two years before: When the twin clock with its elongated-appearing ticking intervals is turned around and comes back with its equally reduced-appearing ticking intervals, everyone would have bet that the net effect must be zero once the two clocks are re-united as physical twins. But to everyone’s surprise, a net effect (a manifest age difference) remains: the “ontological mehrwert” of Einstein’s.

Here with the constantly accelerating rocketship, the same thing occurs: A clock that is carefully lowered from the tip to the slower-appearing rear-end of the accelerating long rocketship will, after having been hauled back up, again fail to be as old as its stationary twin at the tip [6, p.18]. This proves that the clocks “downstairs” indeed are ontologically slower-ticking there. Note that the philosophical term “ontological” is utterly unfamiliar outside Einsteinian physics.

3. Three Added Implications of the Equivalence Principle

Everything that has been said so far is well known. If the clocks are genuinely slower-ticking downstairs rather than just looking slower from above: how about the existence of further ontological implications at the rear end of the rocketship? This suspicion is justified as it turns out. Einstein first found out – as described – that

T_tail = T_tip *(1+z), (1)

where z+1 is the local gravitational redshift factor that applies in the Rindler metric (Einstein called it 1+Phi/c^2, Phi being the gravitational potential [7]).

With Einstein’s result put into this simple form, one is immediately led to expect a spatial corollary: If all temporal wavelengths T are increased, the very same thing is bound to hold true for the spatial wavelengths L of the same light waves:

L_tail = L_tip *(1+z), (2)

and so by implication for all local lengths since everything appears normal locally as mentioned. Formally this conclusion follows from the constancy of the speed of light c (since L/T = c implies L = cT for light waves). If T is locally counterfactually increased by Eq.(1) as we saw, L must be equally increased in Eq.(2) if c is constant.

Although this is correct and we are here still in the realm of special relativity with its absolutely constant c despite the presence of acceleration, the conclusion just drawn is possibly premature since c is believed to be non-constant in general relativity (only “locally constant”). Therefore it is “safer” to first proceed to M and then from there back to L.

M, the mass of a particle that is locally at rest, is necessarily reduced by the very factor by which T is increased,

M_tail = M_tip /(1+z). (3)

This follows from the fact that all locally normal-appearing photons by Eq.(1) have a proportionally decreased frequency f, and hence have a proportionally reduced energy (by Planck’s law E = h f). They have so much less mass-energy by Einstein’s E = mc^2. If all locally generated photons have so much less mass at the rocketship’s tail in a counterfactual manner, necessarily all other masses – by virtue of their being locally inter-transformable into photons (like positronium)in principle – are reduced by the same factor. Hence Eq.(3) is valid.

From the M of Eq.(3), the L of Eq.(2) can now be retrieved as announced via the Bohr radius formula of quantum mechanics: a_0 = h/(m_e*c*2pi*alpha), where m_e is the mass of the electron and alpha the dimensionless fine structure constant. But if the radius of the hydrogen atom is increased in proportion to 1/m_e, wirh m_e varying in accord with Eq.(3), then the size of all objects scales linearly with (1+z) and so does space itself. This was the content of Eq.(2) above.

With Eqs.(1−3) we have arrived at the following abbreviated new law valid in the equivalence principle: “T-L-M.” Einstein’s old finding of T thus has acquired two corollaries of equal standing, L and M for short. What about the third candidate, Ch for charge?

If mass is counterfactually reduced locally and if charge stands in a fixed ratio to mass locally, then charge is bound to be counterfactually reduced in proportion for every class of charged particles. This follows – to give only one example – from the fact that locally, two “511 keV” photons still suffice to produce a positronium atom, consisting of a locally normal-appearing electron and a locally normal-appearing positron. Since both these particles have a reduced mass content by Eq.(3) as we saw, they must also have a proportionally reduced charge content, if all laws of nature are to remain intact locally. This latter condition is guaranteed by Einstein’s principle of “general covariance” which states that the laws of nature are the same in every locally free-falling inertial system. Note that a freshly released free-falling particle (like our positronium atom) is still locally at rest. Therefore, charge is reduced in proportion to the stationary mass,

Ch_tail = Ch_tip /(1+z). (4)

The herewith obtained “completed gravitational redshift law of Einstein” comprises 4 individual equations of equal importance. The new law can be condensed into four letters, T,L,M,Ch. Since the very same consonants pertain to a famous personality of mythological history, Ulysses’s son Telemach (or Telemachus), the 4-letter result can be called the “Telemach theorem.”

To witness, the gravitational redshift (1+z) on the surface of a neutron star is of order of magnitude 2. And the gravitational redshift on the surface (“horizon” in Rindler’s terminology) of a black hole is infinite. By virtue of Telemach, objects on the surface of a neutron star must be visibly enlarged in the vertical direction by a factor of about two [8], which may be measurable. At the same time, the distance toward and from the horizon of a black hole has become infinite (as the corresponding light travel time is already well-known to be [6, p. 20]). Obviously, no known physical phenomenon contradicts the new result which can be tested further empirically.

4. Discussion

Two points need to be discussed. First: Is the Telemach result derived in the equivalence principle robust enough to carry over to the Schwarzschild metric and from there on to all of general relativity? Second: Is the result acceptable in principle from the point of view of modern physics and especially the science of metrology?

The first point is easy to answer. All arguments used above carry over to the Schwarzschild metric. The L of Eq.(2) is nothing but the “poor man’s version” of the gothic-R theorem of the Schwarzschild metric [1]. Conversely, the Schwarzschild metric would have a hard time if the “gothic-R” did not fit the “L” of the more basic theory of the equivalence principle.

Before we come to the testable second point announced, a brief digression into the literature is on line. As noted in ref. [1], similar propositions (sub-vectors of T,L,M,Ch as it were) are not unfamiliar. An analog of L was quite often conjectured to hold true in general relativity. For example, an engineer of the Global Positioning System who – in distrust of Einstein – had built-in a special switch in case Einstein’s predictions were to prove true, later wrote a paper [9] to come to grips with his own surprise; in one formula (his Eq.9 for the “local rest mass energy”), he comes close to Eq.(3) above. More recently, George W. Cox wrote an autodidactic paper arriving, in the present terminology, at T, L and M [10]; he also is the first scientist to explicitly support Ch (personal communication 2010). And professor Richard J. Cook arrived very elegantly at T,L,M (including these symbols) in general relativity [11], correctly invoking a variation in the gravitational constant G by (z+1)^2, but leaving Ch unscathed. Ch proves to be the real crux of the present return to the roots of Einstein’s theory. A discussion with members of the Albert-Einstein Institute in early 2009 made it clear that validity of the Gausss-Stokes theorem of electrostatics [4, p. 432] is put at stake by any change in Ch. So is the Reissner-Nordström metric which no general relativist would easily sacrifice. But this is not all. A change in L alone is bad enough already; for it apparently implies invalidity of the famous Kerr metric and certain cosmological solutions of the Einstein equation. Thus the above theory – while implicit in the equivalence principle and the Schwarzschild metric as the heart of general relativity – is by no means an easy-to-absorb implication of general relativity. This fact can explain some of the resistance the gothic-R theorem encountered when first proposed.

The announced second point is even more important because it makes the connection to measurement. Just as Newton’s universal second (the ” Ur-second” so to speak) was toppled by Einstein’s revolutionary finding of the gravity-dependent “local second” T of Eq.(1), so the famous “Ur-meter” adhered-to up until now is toppled by the gravity-dependent “local meter” L of Eq.(2). The same holds true for the “Ur-kilogram” which with the M of Eq.(3) has now has become different on the moon (much as its once taken-for-granted universal weight had been dethroned by Newton’s law). And the “Ur-charge” Ch (of an electron) now ceases to be universally valid by Eq.(4). The whole to be measured-out cosmos thus acquires a new face if Einstein’s happiest thought (Eq.1) has been correctly elaborated in Eqs.(2−4) above.

In return for this drawback (if it is one), four quantized physical variables arise, three of them new: Besides (i) “Kilogram times Second,” Leibniz’s later famous “action,” there are now:

(ii) “Kilogram times Meter” (“cession” [12]),

(iii) “Coulomb times Second,” and

(iv) “Coulomb times Meter” [13].

The explanation of (ii) is that time and space (Second and Meter) scale in strict parallelism (by Eqs.1,2). The explanation of (iii) and (iv) is that rest mass and charge (Kilogram and Coulomb) scale in strict parallelism (by Eqs.3,4). The quantization laws (iii) and (iv) have no names as of yet (“pulsion”?, “gression”?); they come in several particle-type specific varieties each [12]. Note also that while both G and epsilon_o (and with it mu_o) cease to be fundamental constants as a consequence of L,M,Ch, their ratio (more specifically, the square root of the product of G and epsilon_o) becomes a new fundamental constant of nature which may be named “G_o,”

(v) G_o = 2.4308 *10^(−11) C/kg,

as is straightforward to check by inserting the currently accepted values for G and epsilon_o. A particle-class specific splitting of (v) may or may not have to be reckoned with. Many experiments testing the derived results (ii-v) can be devised. Foreign new technological applications come into sight.

To conclude, a minor revolution in physics was tentatively proposed. The skepticism shown by some members of the experimental profession up until now can be hoped to be overcome with Eqs.(2−4) above. The gothic-R theorem may cease to be controversial. The author would be grateful if a currently running prestigious experiment the fundamentals of which are affected by the above results could be interrupted until the above findings have either been falsified or taken into regard. For it appears that dangers – even apocalyptic ones – cannot be excluded in the wake of the Telemach theorem. Owing to Telemach’s youthful and exotic character, it still appears possible that all of the above is “absolute nonsense” as a colleague who has since changed his mind once publicly called the gothic-R theorem. Einstein in the dusk of his life came to doubt everything he had done, the atomic bomb being the obvious reason. Now his results could for once have an opposite (globe-saving) effect. Timely criticism by the community is invited.

I thank Eric Penrose for discussions and Peter Plath for stimulation. For J.O.R.

References

[1] O.E. Rossler, Abraham-like return to constant c in general relativity: gothic-R theorem demonstrated in Schwarzschild metric (2007; 2009). On:

http://www.wissensnavigator.com/documents/Chaos.pdf

(Remark: Bernhard Umlauf kindly showed that Eq.9 of ref. [1] contains a calculation error, with the following phrase: “the numerator of the fraction under the natural logarithm must read r_0^(1/2)+(r_0-2m)^(1÷2) and the denominator analogously must read r_i^(1/2)+(r_i-2m)^(1÷2).” Note that this correction leaves the text of ref. [1] unchanged.)

[2] A. Pais, “Subtle is the Lord …,” Oxford: Oxford University Press 1982, pp. 180–181.

[3] W. Rindler, Counterexample to the Lenz-Schiff argument, Am. J. Phys. 36, 540–544 (1968).

[4] R.M. Wald, “General Relativity,” Chicago: University of Chicago Press 1984.

[5] J.S. Bell, How to teach special relativity, Progress in Scientific Culture 1, (2) 1976. Reprinted in: J.S. Bell, “Speakable and Unspeakable in Quantum Mechanics,” Cambridge: Cambridge University Press (1984), pp. 67–80.

[6] V.P. Frolov and I.D. Novikov, “Black Hole Physics: Basic Concepts and New Developments,” Dordrecht: Kluwer Academic Publishers 1998.

[7] A. Einstein, On the relativity principle and the conclusions drawn from it (in German), in: “Jahrbuch der Radioaktivität und Elektronik,” Vol. 4, pp. 411–484 (1907), Eq.(30a), p. 479; English translation in: The Collected Papers of Albert Einstein, Volume 2, The Swiss Years: Writings, 1900–1909, pp. 252–311, p. 306. Princeton: Princeton University Press 1989.

[8] H. Kuypers, Atoms in the gravitational field: Hints at a change of mass and size (in German). PhD dissertation, submitted September 2005 to the university of Tubingen, faculty for chemistry and pharmacy.

[9] R.R. Hatch, Modified Lorentz ether theory, Infinite Energy 39, 14–23 (2001).

[10] G.W. Cox, The complete theory of quantum gravity (2009). On:

http://lhc-concern.info/wp-content/uploads/2009/10/quantumfieldtheory31.pdf

[11] R.J. Cook, Gravitational space dilation (2009). On: http://arxiv.org/PS_cache/arxiv/pdf/0902/0902.2811v1.pdf

[12] O.E. Rossler and C. Giannetti, Cession, twin of action (La cesión: hermana gemela de la acción). In: “Arte en la era electronica” (ed. by C. Giannetti), Barcelona: Associación de Cultura Temporánia L’Angelot, and Goethe-Institut Barcelona 1997, p.124.

[13] O.E. Rossler and D. Fröhlich, The weight of the Ur-Kilogram (2010). On http://www.achtphasen.net/index.php/plasmaether/2010/12/11/p1890

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Paper submitted to “Einstein-online” (previous version, no answer) and “African Journal of Mathematics” (acceptance pending).