Constructing the Gödel universe (original) (raw)
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Visualizing some ideas about Godel-type rotating universes
2008
Some kinds of physical theories describe what our universe looks like. Other kinds of physical theories describe instead what the universe could be like independently of the properties of the actual universe. This second kind aims for the "basic laws of physics" in some sense which we will not make precise here (but cf. e.g. Malament [25,). The present paper belongs to the second kind. Moreover, it is even more abstract than this, namely it aims for visualizing or grasping some mathematical or logical aspects of what the universe could be like.
2023
This paper concerns the dispute about space, time, and motion, about whether space, time, and motion are absolute or relative. This paper focuses on one aspect of the dispute by investigating a kind of motion, the rotation of galaxies with respect to the inertial frame. In rotating universes, distant galaxies rotate with respect to the inertial frame. Our universe does not rotate. Nonetheless, rotating universes throw light on our own, or so this paper argues. First, the paper presents historical evidence of the fundamental theoretical use of the rotating solution in physics. Second, the paper identifies three consequences for time and the causal order.
The Cosmological Rotation Reversal and the Gödel-Brahe model: the Modifications of the Gödel Metric
The General Relativistic Gödel-Brahe model visualizes the universe rotating with angular velocity 2π radians/day-around a stationary earth. The wave function of this model of universe ψ U niv , has two chiral states-clockwise and anti clockwise. Due to instabilities in the electromagnetic fields, the wave function can tunnel between the two states. Gödel-Rindler model with a heigth varying acceleration gives the gravitational field of the earth. Gödel-Obukhov model with a sinusoidally varying scale factor gives the yearly north-south motion of the sun. Gödel-Randall-Sundram model with an angular velocity varying with height, gives the yearly rotation of sun with respect to the back ground of the fixed stars. Confinement of light rays due to rotation in the Gödel universe, coupled with an appropriate mapping, generates the illusion of sphericity over a flat earth-with half of earth lit by sun light and the other half in darkness. Finally a metric combining all these properties is given. Discussion of further work is given, namely-(1) Origin of earth's magnetic field due to a charged Gödel universe-with a relation to the Van Allen radiation belt, (2) Geomagnetic reversals due to reversals of cosmological rotation, (3) Caismir energy in the charged Gödel type universe and the energy density required for the Gödel-Brahe model and (4) Behaviour of Causality in Gödel universe and the Einstein-Podolsky-Rosen (EPR) paradox.
The new conceptions of the universe. Circular flow of matter: the formation, growth, disintegration. Rotation within the universe as the basic event.
The Gödel Universe: A Practical Travel Guide
We study the Gödel universe through worldlines associated with motion at constant speed and constant acceleration orthogonal to the instantaneous velocity (WSAs). We show that these worldlines can be used to access every region-both spatial and temporal-of the space-time. We capture the insights they accord in a series of sketches, which extend significantly the Hawking and Ellis picture of the Gödel universe.
Use of Godel Universe to Construct A New topology
A new example of (2 + 1)-dimensional Zollfrei metric, with the topology R 2 × S 1 , is presented. This metric is readily obtained from the celebrated (3 + 1)dimensional rotating Gödel universe G 3,1 . This is because G 3,1 has the interesting property that, the light rays which are confined to move on the plane perpendicular to the rotation axis, return to their origin after a time period T = 2π ω [ √ 2 − 1] -where ω is the angular velocity of the universe. Hence by -the topological identification of pairs of points on the time coordinate, seperated by the time interval T . and droping the flat x 3 coordinate -which is directed along the rotation axis; one obtains the (2 + 1)-dimensional Zollfrei metric with the R 2 × S 1 topology.
On Becoming, Cosmic Time and Rotating Universes
Time, Reality & Experience, 2002
In the literature on the compatibility between the time of our experience and the time of physics, the special theory of relativity has enjoyed central stage. By bringing into the discussion the general theory of relativity, I suggest a new analysis of the misunderstood notion of becoming, developed from hints in Gödel's published and unpublished arguments for the ideality of time. I claim that recent endorsements of such arguments, based on Gödel's own "rotating" solution to Einstein's field equation, fail: once understood in the right way, becoming can be shown to be both mind-independent and compatible with spacetime physics. Being a needed tertium quid between views of time traditionally regarded as in conflict, such a new approach to becoming should also help to dissolve a crucial aspect of the century-old debate between the so-called A and B theories of time.
The Problem of Gravity: Spacetime, Rotating Universes, and a Theory of Everything
The problem of gravity is one that has plagued the best minds from Newton to Einstein. The reason that gravity has eluded these giants is a general misconception of the nature of gravity as a force. This work-in-progress attempts to reframe the argument of gravity as a fundamental force, and instead view it as a manifestation of the photon, which it will be argued is the fundamental element in the universe, out of which creation springs forth.
Geodesic time travel in Gödel's universe
Revista Mexicana De Fisica E, 2016
This work is an introduction at a beginning graduate or advanced undergraduate level to Kurt Godel's foray into cosmology. After an elementary introduction to the basics of Einstein's theory of gravitation, we simply present the Godel's solution and the geodesic equations associated with it. This equations are then explicitly solved obtaining its full set of temporal geodesics. Armed with such explicit expressions, the geodesic time-travelling possibilities of Godel's universe are discussed. We search for their time-like closed geodesics that, following Godel's analysis, other people has imagined as possible routes for time-travel. We next exhibit that such time-travelling possibility do not exist in his model universe. This is done in the most straightforward way possible, framing the discussion as to serve as a simple example for students of General Relativity