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.

But if so, it means the end of earth soon. This frequently published result is contradicted by no one in physics. The lobby just bets on the media remaining quiet.

It is ironic that so many physicists take their children hostage. This is because the media do not ask them why they are not afraid. For then they would start to stutter and their children would begin to ask questions. Even Stephen Hawking could no longer afford to skirt the issue.

The ultimate reason, of course, is Einstein. He alone can help. The “happiest thought of my life,” as he always said, has a further consequence (c-global). Ask your teachers about it. You will learn they have no idea. This is at the root of the problem: irrational dogmatism. Worse to date than in the middle ages because the consequences do not hurt a minority of women: this time around everyone is the victim.

The poor witches on the stakes probably foresaw it all since no one else had a closer look at the nature of human society. So only in Auschwitz later on, after the doors were closed. Please, do change your attitude, poor consensus-based society without a heart: Why not show the world that you love your children, my dear physicist colleagues? Do stand the trial that you are under in the face of a watching globe!

In June it might already be too late. So please, forgive me the urgency of my tone. Old men sometimes behave like this if no one is able to find the so vitally needed counter-information. None of my colleagues who unlike my friends John Wheeler and Bryce DeWitt are still alive dares say a word. If I were younger, I would probably understand their cowardice.

On the other hand, you see: It is normal that scientists do not care about the results of others. Max Planck said that it takes 30 years. Problem is only that we do not have those 30 years for once.

Why NOT have the UN or a single good journalist of high standing investigate? It costs nothing, after all.

And if a danger is infinite, taking it easy is somehow not justified, right?

by Otto E. Rossler, Faculty of Mathematics and Science, University of Tübingen, 72076 Tübingen, Germany

When you are doing this picturing job, you will directly get close to Einstein’s heart. He only did not yet have this special sentinel available in 1907. Noether’s ultra-hard result of 1917 came 2 years in the wake of Einstein’s opus maximum that is being celebrated this year.

I need your kind help to improve on the following finding: “Noether’s Theorem + Einstein Equivalence Principle = c-global.” I have 5 steps to offer so far, the sixth would be your initiative.

(i) If true, this result amounts to a revolution in physics. For it removes an inconsistency that was reluctantly accepted by Einstein in 1907 in the absence of Noether’s theorem: the embarrassing conclusion that c is reduced downstairs in a constantly accelerating long rocketship in outer space described by special relativity. This drawback found in the equivalenve principle let Einstein fall silent on gravitation for 3 ½ years and retarded progress on general relativity afterwards. Two years in the latter’s wake came Emmy Noether’s “global conservation of angular momentum in nature.” Her formal result can be visualized geometrically:

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” will go down reversibly like that of any other clock that is hauled downwards. Secondly, since angular momentum is conserved, the other two components besides rotation rate (mass and radius) cannot go both unchanged. It becomes a rewarding game to figure out what is bound to happen in this simple gedanken experiment.

(ii) The conserved angular momentum obeys a simple formula if the wheel has a constant horizontal (or vertical) orientation which orientation will be automatically preserved. The one-liner is given as Eq. (8.32) in Tipler’s big textbook, for example, but Madame du Chatelet could already have written it down in the 18th century:

L = ω m r^2

Since this expression is hard to remember by heart, the dialect word L’hombre (Spanish for “man”) can be helpful as a bridge. L is the conserved angular momentum, ω is the rotation rate, m the mass and r the radius of our horizontally rotating frictionless bicycle wheel.

If ω is halved (as is approximately valid on the surface of a neutron star with its almost unit-redshift): what about m and r , the two other components of the 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 down there. These photons look non-reduced in their frequency locally. They remain locally transformable as usual into massive particles in accordance with quantum mechanics’ creation and annihilation operators. Thus if a sufficiently sturdy PET scan could be lowered onto the neutron star, it would still work there. The locally normal-appearing half-mass atoms possess a doubled Bohr radius (and hence size) according to the laws of quantum mechanics. Both facts, taken together, yield L’ = ½ ω ½ m (2r)^2 = L , in conformity with the above equation.

But this result of a doubled radius r of the halved-rotation-speed wheel downstairs, is ostensibly at variance with a well-known fact implicit in the theory which underlies the constantly accelerating Einstein rocketship: special relativity. The latter requires that light rays that connect points on a stationary solid object with the same points on the same object while the latter is moving away at constant orientation, travel along parallel lines. This railway tracks principle of special relativity demands that the doubled radius of the horizontally rotating wheel found valid downstairs must be optically masked when viewed from above. So our wheel indeed looks non-enlarged from above even though its radius r has doubled!

(iii) To check on this, let your Noether wheel for once rotate vertically rather than horizontall. 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 wheel from above.

The optical contraction of all horizontal directions, valid downstairs on our wheel, implies that when you look down from above, transversally moving light will be seen to “creep” at half speed on the surface of the Neutron star. This is what Einstein effectively found in 1907. Thus everything appears to be consistent.

But: does light really “creep” down there? We see that the answer is no. For the distance travelled downstairs is doubled compared to above as the optically compressed wheel teaches us. 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 since the equivalence principle is based on special relativity with its constant c. This fact explains why Einstein fell silent on gravitation for more thanthree years after feeling forced to conclude that c is non-constant in the equivalence principle.

(iv) The retrieved globally constant c has an important implication: The vertical distance to the surface of the neutron star has increased. That is, the indentation into the curved “cloth of spacetime” has deepened. In other words, the famous empirical Shapiro-time-delay is complemented by a matching new Shapiro space dilation.

The stronger the gravitational pull, the deeper the trough. Therefore, the new globally constant c implies that the distance down to the “horizon” (surface) of a black hole is as infinite from above as the temporal distance for light going down or coming up is known to be since Oppenheimer and Snyder’s 1939 paper.

Hence black holes are never finished in finite outer time! 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 time, as Oppenheimer and Snyder showed and as we all could witness in Kip Thorne’s carefully researched science fiction blockbuster movie Interstellar?

(v) The answer is a final Noetherian point: all clocks of the falling astronaut get infinitely slowed eventually, so that infinitely much outer time has elapsed on her to be hoped-for arrival down there, provided the universe will still exist by then. As to our lowered wheel, its rotation rate becomes zero on the horizon while the tangential velocity of the rim stays invariant as the wheel’s diameter approaches — invisibly-to-above — infinity (Sanayei effect).

My dear readers: what did we learn from points (i) to (v)? The Noether wheel teaches us several new things:

First, there exists no Hawking radiation by virtue of the new infinite distance of the horizon valid from without.

Second, general relativity must be re-scaled so that it no longer masks the global–c constraint. The Noether wheel thus entails that a new simpler-appearing, re-scaled version of general relativity exists – predictably without any remaining incompatibility with quantum mechanics. The holy grail of unification is therefore within reach: a bonanza for young physicists in the making.

Third, the often heard claim that angular momentum were conserved in general relativity in its present form is falsified by the example of the Noether wheel because the latter brings-in a previously lacking, in the limit of the horizon unbounded, size change as an intrinsic element of the theory.

Am I allowed to add a Footnote to this bonanza?

The recaptured c–global forms an apparently non-ignorable argument in favor of the renewal of a 7 years old safety report: specifically the so-called “LSAG” of the famous LHC–experiment near Geneva. The latter experiment is apart from its other goals designed with the aim in mind to produce miniature black holes down on earth. The Noether wheel’s c–global implies as we saw that black holes cannot Hawking evaporate since nothing can disappear behind a not yet existing horizon. The miniature black holes will rather grow exponentially inside earth in accord with a conference paper published in 2008.

This “dark implication” of the Noether wheel is the reason why I so publicly address you – the young generation – on Lifeboat today: because time is pressing. You may know that CERN has announced to double its (unprecedented in the history of the universe) almost stationary center-of-mass collision energy on a privileged celestial body (earth) in the hope to create Hawking-evaporating black holes on it. As we saw, such pre-Noetherian collision experiments are now scientifically outdated.

Not only a blemish, though: In light of the above Noether-wheel based result of c-global, any attempt at producing miniature black holes down on earth constitutes a “crime against humanity” if you understand what I mean. Are you – the youngest and therefore most open-minded citizens of our planet – able to provide help according to your own judgment? That is, can you perhaps think of a good idea how to persuade CERN to kindly respond to the Noether-based criticism of their announced doubling of their symmetric collision energy? CERN announced to start symmetric collisions in early June. And it in addition decided to non-renew its 7 years old — pre-Noetherian — Safety Report. Every person of course readily understands that it is humanly impossible to respond quickly to surprise evidence (like that of an iceberg named Noether being headed on a collision course) when you are the captain of an only slowly maneuverable ocean liner. Hence my question to you, dear young readers: Do you have any idea how the spotted iceberg can be brought to the attention of the captain?

I have a constructive proposal in mind: There is a female captain elected to take office next year. Would it make sense to try and contact her? Perhaps she sees – besides her being duty-bound – a way to call for a “brief thinking pause devoted to evaluating a formal Noetherian result” before the announced start of collisions in June gets its final okay? Who amongst you would support this kind request?

The retrieved global constancy of c in the equivalence principle implies that the vertical distance to the surface of the neutron star has increased compared to the traditional view: the indentation into the “cloth” of spacetime has become deeper.

The stronger the gravitational acceleration, the deeper the trough. The new globally constant-c result due to Noether implies that the spatial distance right down to the “horizon” (surface) of a black hole has become infinite. This novel spatial distance valid from the outside corresponds with the well-known infinite temporal distance valid from the outside for light sent down to, or coming up from, the horizon (Oppenheimer and Snyder, 1939).

So black holes are never finished in finite outer time. But I hear you ask: Is it not quite well known that one can fall-in onto a large black hole in finite astronaut time? Yes, this is correct.

How come? This is the last Noetherian point: The on-board clocks of the astronaut are infinitely slowed. Also our rotating wheel comes to a virtual standstill of its rotation on the horizon (the tangential velocity of the wheel staying invariant in reality while the wheel’s diameter invisibly approaches infinity).

So the Noether wheel teaches us that there is no Hawking radiation. And that general relativity can be re-scaled so that it no longer masks the new c-global constraint. Noether’s genius thus implies that a whole new simpler version of general relativity exists – predictably without any remaining incompatibility to quantum mechanics: a bonanza for young physicists.

c-global forms a no longer ignorable reason to renew the 7 years old Safety Report LSAG of the LHC experiment in Geneva which, in light of Noether’s result, will now with a certain probability produce miniature black holes that can only grow exponentially inside matter.

Dear young generation: I publish this “call to you in 4 parts” on Lifeboat.com before CERN can start to double their in the universe unheard-of center-of-mass collision energies on one celestial body – yours – in the no longer valid hope to create Hawking-evaporating black holes down on earth.

Such pre-Noetherian experiments are scientifically outdated by now and will, if endangering the planet as the Noeterian result implies, in addition constitute a crime against humanity if attempted. Can you help me persuade CERN to kindly reply to this objective criticism of what they have announced to do – before starting to “shoot sharp” in June as still officially planned?

To see what happens, let your Noether wheel rotate about a horizontal axis (that is, rotate vertically). Then the doubled radius will still be optically masked in the horizontal direction, but not so in the vertical direction. Hence you get a 2:1 vertical ellipse.

The optical contraction in the horizontal directions, found to be valid downstairs using the Noether wheel, implies that light will be seen to “creep” downstairs at halved speed when watched from above. This is what Einstein already found in 1907. So everything is fine.

But: does light really creep down there? The answer is no. For the distance travelled is doubled compared to above.

The conserved angular momentum L obeys a simple formula for a constant vertical (or else horizontal) rotation axis of the wheel:

L = ω m r^2

Since this expression is hard to remember by heart, the word “L’hombre” can help even though it is not high-Spanish. ω is the rotation rate, m the mass and r the radius of Noether’s frictionlessly rotating bicycle wheel.

If ω is halved (as on the surface of a neutron star), what about m and r , the other two components of the conserved L ?

You guess it: m is halved and r doubled. How come? The halved mass follows from the halved frequency and hence energy of the photons produced down there. They are locally transformable into particles with mass, via quantum mechanics’ creation and annihilation operators. The resulting half-mass atoms have a doubled Bohr radius: so r is doubled if ω is halved.

But does this doubled size of the wheel rotating downstairs at halved speed not contradict the fact, implicit in the theory which underlies the accelerating Einstein rocketship (special relativity), that light has to travel up and down along straight vertical lines?

The latter fact indeed remains in charge. It thereby entails that the doubled radius of the horizontally rotating wheel must be optically masked when viewed from above. So the wheel looks non-enlarged horizontally when viewed from above – even though its radius r is doubled.

This simple insight amounts to a revolution in physics. It resolves an inconsistency accepted by Einstein in the absence of Noether’s theorem in 1907: that c were reduced downstairs in a constantly accelerating long rocketship in outer space.

Noether allows you to see what happens. She discovered “global conservation of angular momentum in nature” as is well known in 1916.

Take a frictionless bicycle wheel that is suspended from its hub, and lower it and then pull it back up again. What happens if angular momentum is constant all the time as she showed?

Answer: The rotation rate of this “clock” must go down reversibly like that of any other clock. But since angular momentum is conserved (Noether), the other two components in angular momentum besides rotation rate (i.e. mass and radius) cannot both remain unchanged.

This is a wonderful new result enabled by Emmy Noether.

I have simple thinking in mind – like visualizing a rotating wheel suspended from its hub without friction so it can be pulled up and down easily.

You can trust that angular momentum remains constant (nature has a knack for that). But the wheel is also a clock. So if you lower it, it must go slower down there and become faster again when retrieved. It thus makes for a beautiful mental plaything (a “hot” one as the young people would say). Angular momentum can be called “L’hombre” (a macho word which is not quite right in Spanish). Can you feel L’hombre in your hand while moving up and down your toy in your mind?

The word “L’hombre” allows one to remember “L = ω mr^2 ” for angular momentum L in one’s mind forever. Omega (or ω) is the rotation rate, m the mass of the wheel’s rim (with a virtually weightless hub for simplicity), and r is the radius. So the wheel is now transparent to us like glass, right? What happens if ω is halved for simplicity as on a neutron star?

Either m must be doubled, or else r must be increased by square-root 2, or both m and r must have changed somehow in a compatible manner. How about m halved and r doubled?

The latter option is the correct one. How can one be sure? Because of quantum mechanics, of all things. Light coming from below has half the frequency and energy when ω is halved. But photon energy and particle masses are locally inter-convertible. So all masses downstairs are halved since photon energy is halved. Hence L’ = ½ ω ½ m (2r)2 = L. High-noon L’hombre has won.

This is what the wheel told us. But: People know from special relativity that the transversal size of departing objects (at the bottom in our case) does not change. Fortunately, optical distortions are allowed. Hence the horizontal doubling of r that is implicit in L’hombre is real albeit masked from above. This implies that the constant speed of light c appears to be halved optically when watched from above even though it is not reduced. This halving was predicted by Einstein in 1907. So the present Noetherian picture – since Emmy Noether discovered the power of angular-momentum conservation in 1916 – is correct.

Unfortunarely, the L’hombre result retrieved by our letting the wheel go down and then up again in our minds lies so deep in the foundations of nature that its consequences cut very deep, too. It, for example, follows from this macho phantasy that certain experiments that still got planned before L’hombre was applied to our wheel need to be postponed: until the consequences of L’hombre on them have been investigated thoroughly. Otherwise those consequences could cause a big – nasty – surprise because L’hombre is so strong after his having sprung from a female phantasy.

I need not mention which experiment I have in mind that is presently being prepared under a communication curtain regarding its safety. L’hombre is ready to pull the false garment away.