Kurt Gödel, Rotating Universes, and Hubble Tension

    Kurt Gödel (1906-1978) was an eccentric but brilliant mathematical prodigy. He was born on April 28, 1906 in the city of Brno of the Austro-Hungarian Empire, which is now the second-largest city in the Czech Republic.  At the University of Vienna as a young mathematician he became famous for proving the existence of mathematical statements that are true but unprovable (Gödel’s Incompleteness Theorem, 1931). In 1940, having escaped the Nazi takeover of Austria, Gödel and his wife Adele took the Trans-Siberian Railway all the way to the Pacific, sailed from Japan to San Francisco, crossed the USA by train, and joined Albert Einstein at Princeton’s Institute for Advanced Studies.

    Under Einstein’s influence, Gödel became fascinated with the cosmological applications of general relativity (GR) to describe exotic universes. In 1948 he used Einstein’s field equations to prove that time travel is possible within GR, or at least possible in a rotating universe with a negative cosmological constant.

    When he reached the age of 71 years, Gödel unfortunately developed a paranoid delusion that enemies were trying to poison his food. He refused any meals not prepared by his wife Adele. When she had a stroke and was hospitalized, he stopped eating altogether. On January 14, 1978, he died of starvation.

    Gödel’s time-travel solution to Einstein’s field equations of general relativity postulates a universe that is slowly rotating, that is stabilized against outward centrifugal force by the attractive force from a negative cosmological constant (ours is positive), and that, because of the rotation, has outer regions containing objects that move with superluminal tangential velocities relative to a central observer. (Note: in GR the speed of light is only the local speed limit; distant objects may have superluminal radial and tangential velocities relative to a local observer.) Gödel showed that this scenario makes it possible for a space traveler who visits these outer regions and returns to arrive in his own past, constructing a closed time-like loop and therefore engaging in time travel.

    Of course, this scenario is not actually an achievable time-travel scheme because (a) Gödel’s hypothetical universe is not the one we believe that we live in, and (b) the time traveling observer would require a net travel duration that is a sizable fraction of the age of the universe. Gödel’s solution has remained an interesting innovation in the annals of general relativity and until recently has been considered to be only an odd mathematical outlier.

    Now, curiously enough, Gödel’s rotating universe has found a new use and is undergoing renewed scrutiny. As readers of these AV columns may be aware, progress in observational cosmology has produced a problem called the Hubble Tension. Today's ΛCDM Standard Model of Cosmology, which explains the vast majority of the available cosmological observations, tells us that the universe contains about 5% normal matter, 25% cold dark matter, and 70% dark energy, that it started from the Big Bang about 13.6 billion years ago, underwent a brief period of exponential inflation, and ever since has been expanding at a nearly constant rate.

    A recent publication by Hungarian cosmologists Szigeti, Szapudi, Barna, and Barnafoldi (SSBB) has revived a version of Gödel’s rotating universe in an effort to explain the Hubble Tension. Essentially all astronomical objects (asteroids, planets, stars, galaxies, …) are observed to have some amount of rotation. SSBB postulates that the Big Bang left our universe itself with a net rotational angular momentum, so that it is now a rotating object.

    As the universe has expanded, this angular momentum has remained constant. As a spinning ice skater or ballerina rotates more slowly when her arms are extended than when they are drawn in, the angular rotation rate of the universe has slowed as it has expanded. SSBB showed that the apparent Hubble expansion rate of the universe, as represented by H₀, is inversely affected by the rate of rotation. They calculate from the conflicting Hubble values that the universe now has a rotation rate of about 2×10⁻⁶ radians/Myr (Myr = million years), while at the time that the cosmic microwave background was released the universe had a rotation rate of about 3.54 radians/Myr. This resolves the Hubble Tension problem, because the falling rate of rotation produces an increasing Hubble “constant”.

    Curiously, the highest possible rotation rate that today’s universe could have to avoid peripheral objects at the horizon with superluminal tangential velocities (thereby enabling Gödel’s closed time-like loops and time travel) is also about 2×10⁻⁶ radians/Myr. Is the remarkable correspondence of these two rotation rates just a coincidence, or is this the Hand of Nature in action?

    So SSBB has demonstrated that adding rotation to ΛCDM makes the Hubble constant age dependent in a natural way that explains the Hubble Tension. However, as the authors pointed out, the ΛCDM model has become today’s standard model because there is an entire intertwined network of observations, confirmations, and successful numerical models supporting it. It is not clear if (or by how much) the introduction of rotation of the universe into ΛCDM will disrupt its remarkable agreement.

    This work clearly raises some questions. One that might be asked is: If our universe is indeed rotating, does that mean that time travel is possible? No. Even if, as SSBB suggests, the universe is rotating, it is not rotating fast enough to meet Gödel’s necessary conditions for time travel.

    Another question is: How did the Big Bang supply the initial angular momentum, and why wasn’t it zero, as spatial symmetry should require? There is no easy answer to this question. However, speculating cosmologists, concerned with the other asymmetries in our universe (matter dominance over antimatter and a definite arrow of time), have postulated that perhaps the Big Bang produced twin universes, and that as compensation the other universe has dominate antimatter and a time flow in the other direction. So perhaps that anti-twin universe also rotates in the other direction, conserving overall angular momentum.

    Although I have published two papers in the area of astrophysics, my own area of expertise in physics is far away from this kind of cosmology and I am not fluent in general relativity, but I have a question about a rotating universe. It seems to me that if our universe is rotating, there must be an axis of rotation that makes space somewhat asymmetrical. In the direction perpendicular to that rotation axis, stars and galaxies near the universe’s visible horizon should have near-lightspeed tangential velocities, while similar stars and galaxies close to the rotation axis should have almost no tangential velocity. I would think that this would produce observable differences (transverse Doppler effect?) between off-axis and on-axis objects, both now and in the era when the cosmic microwave background was released and the rotation speed was much larger. Yet as far as I know, there is no observational evidence for such directional asymmetries in the very distant objects.

In any case, this old/new concept of giving the universe an angular rotation has been brought into the stage-center spotlight, and it will be examined by astrophysicists in much more detail in the near future. Watch this column for developments.

    Ley died of a heart attack in 1969, just before he was scheduled to go to NASA-Houston to be in the control room when Apollo 11 made the first Moon Landing. The NYT article included a many reader comments, some suggesting that Ley’s ashes should be transported to the Moon and perhaps scattered in the back side lunar crater that bears his name.

    When I was a teenager in the late 1940s, I read many science articles by Willy Ley in Astounding (now Analog). I was an avid ASF subscriber and reader, and I was also an amateur physics experimenter. Along with my investigations with iron filings and magnets and gold foil electrometers and Tesla coils and Wilson cloud chambers, I figured out how to wind a magnetic solenoidal coil with the shape of a Möbius Strip. As you may know, the Möbius Strip is a peculiar twisted cylinder with the topological property of having only one edge instead of two. In my Möbius winding scheme, a wire went into the center of the coil and wound progressively along the coil’s outer edge on both sides.

    I thought that since there was only one edge, it should do something interesting when I ran an electric current through it, but it didn't. So, I took a picture of it and sent it to Willy Ley at Astounding, asking why it didn't produce one magnetic pole instead of two, since it only had only one edge.

    To my amazement, Ley replied with a long letter, exposing me for the first time to the ideas behind Maxwell's Equations and explaining why my weird coil had to have two magnetic poles. Although I was only about 14, I went to the Houston Public Library to find, and with considerable difficulty, to read some books discussing Maxwell’s Equations. It was an important step on the path that led me to get a PhD in experimental nuclear physics, to become a physics professor at an excellent university, and to write this column. Willy, I owe you a lot, and I wish that I could have thanked you in person. I hope that you posthumously make it to the Moon.

John G. Cramer's 2016 nonfiction book describing his transactional interpretation of quantum mechanics, The Quantum Handshake - Entanglement, Nonlocality, and Transactions, (Springer, January-2016) is available online as a hardcover or eBook at:
        http://www.springer.com/gp/book/9783319246406 or https://www.amazon.com/dp/3319246402 .

SF Novels:  John's 1^st hard SF novel Twistor is available online at: https://www.amazon.com/Twistor-John-Cramer/dp/048680450X.   His 2^nd and 3^rd novels, Einstein's Bridge and its new sequel Fermi's Question, are now available as eBooks from Baen Books at: https://www.baen.com/einstein-s-bridge.html and https://www.baen.com/fermi-s-question.html .

Alternate View Columns Online: Electronic reprints of 238 or more of "The Alternate View" columns written by John G. Cramer and previously published in Analog are currently available online at:  http://www.npl.washington.edu/av .

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