Dear young Physicists and Architects: Please, picture a frictionless Wheel that is lowered reversibly in Gravity

Otto E. Rossler

Faculty of Mathematics and Science, University of Tübingen, 72076 Tübingen, Germany

Abstract

The accepted wisdom in physics is that only mathematical (in the sense of algebraic) arguments are sufficient to arrive at reliable results on which the rest of physics can be based. However, this view is too narrow. Symmetry arguments and spatial representation are even more powerful in their native state. Eventually, everything can be brought into algebraic form. But sometimes, a century passes by during which everyone got led astray by prematurely formalized thinking. Specifically, several new features of gravitation follow from Emmy Noether’s rotational symmetry theorem if the latter is applied to a prototype situation. The main implication, c-global, is good for a revolution in physics after more than a century. A survival error is exposed that can only be appreciated by the “parallel guild” of architects. Can you help the physicists so as to avoid the error in time?
Keywords: Architecture as parallel physics; the power of symmetry; rotating wheel; Noether’s intuition; early Einstein rehabilitated; micro black holes; global c; final catastrophe avoided; CERN’s safety report; Gianotti’s unique task. (May 20, 2015)’’’’’’

Introduction

A fundamental finding implicit in Noether’s method is described. The rotating frictionless wheel is introduced as a sentinel in gravitation, and a cryptic word defined – Lomrr. The main implication is a new size change implicit in nature which in turn implies global constancy of the speed of light in the vacuum: c-global. Finally, a 76 years old false interpretation of a mathematical result will be corrected. And an almost-incurred global catastrophe is exposed which can be averted at the last minute if the one or the other reader understands the crisis well enough to help avert the danger.

A new fundamental Paradigm

When you, my dear reader, join me in the following “picturing job” you will come very close to Einstein’s heart. At the same time you will see that he still lacked one specific sentinel in 1907 and 1915: Noether’s ultra-hard intuitive result of 1917. Therefore the centenary of Einstein’s opus maximum this year will be followed by a similar celebration of Noether’s kindred result in two years’ time from now.
I first solicit your help to kindly improve on the following fundamental finding: “Noether’s Theorem plus Einstein Equivalence Principle yields c-global.” This finding transforms physics if true. I have 5 steps to offer, the sixth depends on your initiative.
(i) What is at stake is a revolution in physics based on an improved version of the Einstein equivalence principle. Here an inconsistency was reluctantly accepted by Einstein in 1907 in the absence of Noether’s theorem. This inconsistency can be removed. Einstein felt forced to arrive at the embarrassing conclusion that the speed of light c in the vacuum is reduced downstairs in a constantly accelerating long rocketship in outer space even though the ship is described by special relativity with its inherent globally constant c. This drawback encountered in the equivalence principle in 1907 made Einstein fall silent on gravitation for 3 and 1/2 years and impaired progress on general relativity. Two years after the final version of the latter theory came Emmy Noether’s 1917 result of “global conservation of angular momentum in nature.” This finding – like energy conservation – possesses an overriding power. It is based on a fundamental symmetry of nature – rotation symmetry – and can be visualized geometrico-dynamically:
Take a frictionless bicycle wheel suspended from its hub and lower it and pull it back up again in gravity.
Everything is pre-specified if this simple sentinel is pictured in the mind. Firstly, the rotation rate of this “clock” must go down reversibly like that of any other clock that is hauled down due to Einstein’s gravitational clock slowdown. Secondly, since angular momentum is conserved in the process, the two other components of angular momentum besides rotation rate (mass and radius) cannot both remain unchanged downstairs. It becomes a rewarding pastime to figure out what is bound to occur in this Galilean gedanken experiment.
(ii) The conserved angular momentum obeys a simple formula when the wheel has a constant horizontal or vertical orientation. The one-liner that applies is given as Eq. (8.32) in Tipler’s weighty textbook, for example, but Madame du Chatelet could already have written it down in the 18th century:

L = ω m r^2 ………………………………….….….….….….….….….….….….….….….….….………………………………….. (1)

Since this expression is amazingly hard to remember by heart, the dialect word L’hombre (Spanish for “man”) can be helpful as a mnemonic aid. L is the conserved angular momentum, omega ω is the rotation rate, m is the mass and r the radius of our horizontally rotating frictionless bicycle wheel – Lomrr.
If ω is halved (as approximately valid on the surface of a neutron star with its close-to-unity gravitational redshift and hence halved time rate): What about m and r, the two other components of the wheel’s conserved L down there?
I propose that m is halved and r is doubled. The halved mass is the key. It follows from the halved frequency (and hence energy) of any photon emitted on the surface of a neutron star. These photons look non-reduced in their frequency locally and remain locally transformable into mass-bearing particles in accordance with the laws of quantum mechanics (its creation and annihilation operators). Thus if a sufficiently sturdy PET scan (working on the basis of positronium annihilation) could be lowered onto the neutron star without getting smashed, it would still work properly there. The normal-appearing half-mass atoms down there automatically possess a doubled Bohr radius (and hence size) according to the universal laws of quantum mechanics. Both facts taken together yield L’ = ½ ω ½ m (2r)^2 = L , in conformity with Eq.(1).
This result of a doubled radius r of the halved-rotation-speed wheel downstairs is at first sight at variance with a well-known fact implicit in the theory which underlies Einstein’s constantly accelerating Apollo-like rocketship in outer space: special relativity. The latter theory requires that light rays that connect points on a stationary solid object with the same points when the object is moving away at constant orientation and speed, travel along parallel lines (“railway tracks principle”). Special relativity thus demands that the doubled radius of the horizontally rotating wheel valid far downstairs be optically masked when viewed from above. (This can be understood in turn by looking at the interior of a transversally receding light clock.) Thus our wheel looks non-enlarged from above even though its radius r has doubled!
(iii) To confirm this interactively, let your Noether wheel for once rotate vertically rather than horizontally. Then the doubled radius will remain optically masked in the horizontal direction but not so in the vertical direction: You now get a 2:1 vertical ellipse on the neutron star when looking down on the rotating wheel fromfar above with a super telescope.
The optical contraction of all horizontal directions downstairs implies that when you look down from far above, a transversally moving light ray will be seen to “creep” at half speed on the surface of the Neutron star. This is what Einstein found in essence in 1907. Thus everything appears to be consistent.
But: does light really “creep” down there? We just realized that the answer is no. For the distance travelled downstairs is doubled compared to above as the optically compressed wheel teaches. Hence c remains constant in spite of its apparent creeping. This new information was unavailable in 1907 owing to the absence of the Noether-wheel.
The newly retrieved global constancy of c in the equivalence principle comes not really as a surprise because the equivalence principle is based on special relativity with its constant c in the first place. The at the time irreparable inconsistency explains why Einstein fell silent on gravitation for years after having been forced to conclude that c is non-constant in the constant–c equivalence principle. It would take this catastrophe more than a century to be healed.
(iv) The retrieved globally constant c has an important implication: The vertical distance down to the surface of the neutron star (or down to the bottom of a very long rocketship) has increased in proportion to the observed redshift. Thus the groove in the “cloth of spacetime” has deepened. Hence the famous empirical Shapiro-time-delay, discovered half a century later, gets complemented by a matching new Shapiro space dilation.
More spectacularly, the globally constant c implies that the spatial distance all the way down to the “horizon” (surface) of a black hole becomes as infinite from above – as infinite as the temporal distance for light that is going down or coming up has always been known to be since Oppenheimer and Snyder’s paper on black holes of 1939.
Hence black holes are never finished in finite outer time due to the infinite distance of the horizon from the outside world. At this point I hear you ask: But is it not a well-known fact that an astronaut can fall onto (and into) a stellar black hole in finite wristwatch time as Oppenheimer and Snyder also showed (and as we all could witness in Kip Thorne’s carefully researched science fiction blockbuster movie Interstellar)?
(v) The answer is a final point: All clocks of an in-falling astronaut get infinitely slowed eventually so that infinitely much outer time has elapsed on her or his arrival down there – provided that the universe will still exist by then (and that no larger black hole has come across to re-direct all in-falling trajectories).
Note that our lowered wheel’s rotation rate ω like that of any other clock becomes zero on the horizon while simultaneously its radius r becomes infinite in an invisible-from-above manner. Hereby the tangential velocity of the wheel’s rim surprisingly stays invariant as the wheel’s radius grows and eventually approaches infinity (Sanayei effect). Hence the speed of light c surprisingly is not the only globally invariant speed in nature.

Four Conclusions

The Noether wheel teaches us several new things: First, there exists no Hawking radiation by virtue of the infinite distance of the horizon found valid from without. Hence nothing can disappear behind the horizon in finite outer waiting time as Hawking assumed.
Second, general relativity needs to be re-scaled so that it ceases to mask the global-c constraint. The Noether wheel thus implies that a new, simpler-looking re-scaled “global-c version of general relativity” exists. General relativity thereby loses its up to this day valid incompatibility with quantum mechanics, so that the holy grail of unification materializes as a consequence of Eq.(1). A bonanza for young physicists and self-assured architects is in the making. The new physically realistic transform of the Einstein equation is a promised land.
Third, the standard claim that angular momentum is conserved in general relativity in its present form is put in doubt by the Noether wheel because the latter brings in a previously lacking, in the limit unbounded size change. If the old theory with its non-global c indeed conserved angular momentum directly, then this has been a lucky coincidence.
Fourth, there is a footnote to add to the described bonanza: The recaptured c-global forms a non-ignorable argument in favor of the renewal of a 7 years old safety report: the “LSAG” report of the famous LHC-experiment near Geneva. The latter experiment is among other goals designed to produce miniature black holes down on earth. But the Noether wheel’s implied c-global shows that black holes cannot Hawking evaporate as mentioned. The miniature black holes hoped-for will rather grow exponentially inside earth, in accordance with the results of a conference paper published in 2008 with the International Institute for Advanced Studies in Systems Research and Cybernetics titled “A rational and moral and spiritual dilemma” which is also on the web.

Hope for Help from the young Generation

The last-mentioned “dark implication” of the Noether wheel is the reason why (in parallel to the present publication in the proceedings of the Institute) I herewith publicly address you – the young generation – also directly here on Lifeboat todate because time is so pressing. You may have heard that CERN has announced to in two weeks’ time from now double its in the history of the universe unprecedented center-of-mass collision energy on a first celestial body – earth – in the hope to create Hawking-evaporating black holes on it. But as we saw, such pre-Noetherian collision experiments are now scientifically outdated notwithstanding the prestige of Stephen Hawking.
The plan to continue is not merely a waste of taxpayers’ money. In light of the Noether-wheel based result of c-global, any attempt at producing miniature black holes down on earth must be considered an “attack against humankind” because any resident micro black hole is bound to grow exponentially inside earth.
Are you, the youngest and therefore most open-minded citizens of our planet, able and willing to provide any help according to your own judgment? That is, can you perhaps come up with an idea how to persuade CERN to kindly respond to the Noether-based critique of the announced doubling of their unprecedented symmetric collision energy?
CERN has decided to non-renew their 7 years old LSAG Safety Report before starting. Everyone automatically has a full understanding for the fact that it is humanly impossible to respond quickly to surprise new evidence – like an iceberg named Noether being headed on a collision course – when you are the captain of an only slowly maneuverable ocean liner. Therefore, my question to you: Do you have any idea how the spotted iceberg can be brought to the attention of the captain on the bridge in time?
There is a female captain-elect to take office next year. Would it make sense to try and contact her? To the present author she does not reply. But perhaps she can – within the frame of her binding duties – spot a remaining legal way to respond to your kind request: possibly by calling on her own for a “brief thinking pause to evaluate a Noetherian result” before the announced start of collisions in June gets its final okay from the bridge?
To conclude, by systematically inspecting a frictionless wheel used as our sentinel, we have arrived at an unusual result: that the speed of light c is a global constant in gravitation. And that, for this reason, black holes possess radically new properties. A “super application” turned up in this way in which the whole physics community proved to have gone astray for a century. And so with a vengeance: even the short-term survival of planet earth appears to be put in jeopardy by the spotted formal error (loss of c-global) maintained for a century. A scientific error can assume the rank of a survival error. Or to put it positively: Emmy Noether can save us all.

Explanatory Appendix: It is not the Mathematics – it is the Visualization which went astray

It is a strange experience to realize that so far, no one in physics appears able to understand the main teaching of the Noether wheel in gravitation: The well-known infinite temporal distance which the horizon of a black hole possesses from the outer universe since Oppenheimer and Snyder 1939 (excepting the wristwatch of the in-falling astronaut) implies logically that the horizon of a black hole does not even exist before an infinite time has passed by in the outside universe. This in principle well-known fact is only made more palpable by the new infinite spatial distance revealed by the Noether wheel.
But even the old infinite temporal distance of the horizon of a black hole does already reveal a disquieting historical fact: Up to this day, every educated physicist thinks and readily explains with heavyweight arguments that the “frozen appearance from the outside” of the in-falling astronaut only masks what has already happened down there before: Namely, that the horizon has formed and that objects and information have disappeared for good behind it and that the “singularity” is a physical reality inside.
Everyone in physics “knows” this for many decades – although the mathematics says the opposite as we saw. Thus it is only the visualization that went astray. What everyone falsely believes in is that the two time scales valid for an outside observer and for an in-falling observer, respectively, would possess equal rights. During the two-day in-falling time registered on the wristwatch of an in-falling astronaut, who appears frozen in time to us on the outside, indeed his target black hole including horizon and singularity will have fully formed when he arrives. However so only if the whole universe has not been wiped-out trillions of years in the future from now – before that arrival.
You probably see my point but are perhaps not convinced: Is it true that the generally held view of the finished horizon can really not be legitimately upheld? After all, this view is tested by the consensus of a century!
Let me explain it all with a look at a simple quantitative drawing to be found in a famous textbook (Figure 25.5 on page 667 of the “bible” in the field titled Gravitation written by my late friend John Wheeler together with Charles Misner and Kip Thorne in 1973). The figure is so simple it can be described in words. It shows the time axis plotted to the right and the traditional distance valid away from the center of the black hole plotted upwards. The curve of the astronaut falling-in describes a Galilean half parabola that is flat at first and becomes steeper and steeper to soon reach the horizon of the black hole and continue on downwards to hit the singularity at the bottom after approximately two days of astronaut time. The same Figure also shows the same in-falling event from the outside perspective. Here, the astronaut’s path first hugs the former parabola from above, but then gently disengages itself to remain aloof and eventually approach the horizon’s height level asymptotically on the right in an almost horizontal line that never quite reaches the horizon in finite time.
Everyone in the field is happy with this interpretation for 76 years (and with this printed Figure for 42 years). But it is totally misleading by its failing to make a connection between the two touch-down events which are identical. To see this, I encourage you to enter the mirror-symmetric return trajectory of the astronaut into the picture in the two cases. To this end you only need to assume that the horizon harbors an un-damped trampoline as is admissible in principle. The latter catapults the astronaut right back upwards again on a symmetric return trajectory. He then will be right back after another two days’ wristwatch time. This mirror-symmetric return trajectory thus ends after 4 days – still on the far left of the Figure once you have entered it. So much for the lower curve. How about the upper curve? It, too, acquires a mirror image. This mirror image requires that you first copy the whole Figure onto transparent sheet, then turn the latter over and glue it symmetrically onto the original one on the right. Then in the middle we have the dotted points twice which represent infinity in time. Hence in the outside world the astronaut returns after “twice infinity in time”! The crew waiting on the circulating satellite from which the astronaut departed will according to this picture wait in vain on the fourth day and the say after and forever.
For some reason, no one in physics has ever drawn this completed picture before. So the “freezing” is indeed not something that represents an unrealistic projection phenomenon valid in the outside world while “in reality,” the astronaut arrives on the horizon soon (as everyone in the scientific community believes). It rather is the other way round: the astronaut herself is frozen!
When she returns as young as she is, an infinity of time has passed in the outside world. The movie Interstellar, filmed under the scientific supervision of Kip Thorne (second author on the mentioned gravitation bible), did a wonderful job in showing the gravitational time slow-down affecting an astronaut at finite depths down the funnel: He returned young to meet his beloved little daughter saying good bye to him on her old-age death bed. The movie then only forgot to keep up with this for the extremal case of hitting the horizon and coming back, as the “wormhole” paradigm of the script implies.
The movie strictly follows all textbooks and curricula. Thus a whole profession has overlooked the obvious for three generations. The theory of black holes, founded by Schwarzschild a century ago, thus contains an error. But it is not a mathematical error: it is “only” an error of common sense judgment. And it is a potentially fatal error at that. Unless someone can convince Professor Gianotti to kindly persuade her colleague Professor Heuer on the bridge to permit a renewal of the 7 years old Safety Report LSAG before the doubled-energy collisions scheduled for June 2015 are given their final okay, the doubled-energy experiment will be based on an error of logical judgment rated “unforgivable to a school boy.” Now it might cause a global survival error.
Forgive me for having bothered you with a cut-and-paste job. There indeed never existed a more prolonged and more embarrassing logical mistake made collectively in the history of science. Only architects – “parallel physicists” spared the traditional brainwash – can fully understand the predicament laid open above. It is only they who can explain it to the world. The scholastic phase of the medieval period was also marked by quantitative results like “How many angels, exactly, do fit onto a needle’s tip?” We therefore can speak of the scholastic phase of theoretical physics in our own time. Emmy Noether’s modesty put an end to the male assertiveness.
I predict that Professor Gianotti will reply graciously to you if you take a female mathematician’s methods seriously enough to write a letter to her begging to win some time before the doubled-cosmic record collisions start – so as to allow for a discussion of the Noether wheel’s implications. I for one apologize here to her for every too harsh word I ever said against CERN. I hope she will graciously grant you this birthday present for me on my 75th birthday, today.

Acknowlegments

Paper to be published by the International Institute for Advanced Studies in Systems Research and Cybernetics. I thank Frank Kuske, Anton Traum and Guido Göhler for encouragement, György Darvas, Wolfgang Müller-Schauenburg and Kostas Kokkotas for discussions, and Greg Andonian and George Lasker of the International Institute for their kind invitation. For J.O.R.