*A First Course in General Relativity*.

Here a few thoughts stimulated by this book.

Apologies in advance for your having to think this through.

It is a (tacit or explicit) axiom of modern physics that only sensuous data received in the present exist; "sensuous" here includes all that an observer-subject can sense with the aid of apparatuses such as microscopes, vibrating membranes in microphones, telescopes, radio-telescopes, gravitational interferometers, etc. etc.

For relativity physics, all observations are relative to the observer-subject in its respective reference frame receiving signals in the form of electromagnetic (including, in particular, the visible colour spectrum) or gravitational waves, which all move at the absolute speed of light, c = 300,000 km/s, either in a straight line (special relativity) or on a curved line (general relativity). The motion of such waves is the absolute motion. All scientific observation is relative to and solely dependent upon receiving such e-m and gravitational waves. The

**ang**

**els**of modern physics are photons and gravitons which, at their specific, differentiated frequencies, carry information. Gravitation itself is equivalent to the curvature of four-dimensional space-time in co-ordinates (x. y, z, t). The specific way in which these four co-ordinates are related to each other in the metric of the Riemann tensor, R, determines whether the space-time in question is either flat or curved. If R=0 everywhere, the space-time is flat.

For modern physics, it is solely by virtue of the e-m and gravitational signals an observer-subject receives that the observer can 'see' or 'hear' the universe. Such signals bear energy, i.e. are pure potential and actual motion, that is registered by the recipient medium, such as the eye's retina, AS

**difference**, i.e.

**information**. Because these signals only reach an observer at the speed of light, looking out into the universe is looking back in linear time, t, which, in relativity theory, for convenience, is not measured in seconds, but in metres, that is, the metres travelled by light in a given time interval. By convention and for ease of mathematical manipulation, the speed of light c is set equal to 1. Hence modern physics both mathematizes and spatializes time entirely.

First it was optical telescopes, starting with Galileo's, that enabled scientists to see further out into the universe than the naked eye is capable of. The light signals carried the information necessary to see better. Optical telescopes got better and better, with larger and larger lenses and ever improved resolutions allowing ever finer differentiation to be seen in the light-messages. Starting after WWII, telescopes receiving radio, gamma rays, x-rays, etc. entered the fray, enabling e-m radiation also outside the visible, optical spectrum to be received and hence 'seen'. These radiation signals (spectrometry) allowed completely new phenomena in the sky to be observed for the first time, which in turn greatly modified the theoretical models (i.e. equations) developed to understand the information-signals received. Phenomena such as black holes, quasars, pulsars, neutron stars were now 'visible' for the scientific observer-subject via the signal data received and their often very laborious analysis, which has become a major branch of modern physics.

E-m radiation received from the sky is itself subject to disturbance by other e-m radiation from other sources. The further the e-m radiation has travelled to the observer, the more it has been corrupted by this noise from having to pass through and by other matter with its own e-m radiation. It cannot get through so-called 'decoupled' plasma-matter at all, which supposedly predominated in the young universe. By using multiple observers and analyzing very large amounts of data ('messages'), the noise can be filtered out to get to the underlying 'core' message. Everything depends, of course, on the sensitivity of the receiver-apparatuses. The signals received carry energy which activates the sensors in the receiver apparatus with a certain amplitude. The more sensitive the apparatus (e.g. radio telescope), the further the observer can 'see' or 'hear' into the universe.

Gravitational waves were detected directly for the very first time in 2015 by the LIGO interferometers in the U.S. These waves are extremely hard to detect, for their energy is low, which means low amplitude which has to be sorted out from the various sources of noise (extraneous information), principally seismic noise from vibrations at low frequencies, thermal noise from heat sources at middle frequencies, shot noise from quantum effects at higher frequencies. On the other hand, gravitational waves are not affected by the intervening matter like e-m radiation is, enabling better 'hearing' further back in linear time. With the advance from the Earth-based LIGO interferometers to the space-based LISA interferometers within the next couple of years, cosmologists hope the improved sensitivity to be able to detect the less-noisy gravitational signals coming from further back in the universe's linear time. Thus they hope to 'hear' the young universe, to 'see' its highly energetic state with its relativistic velocities close to the speed of light. Such relativistic velocities cannot be achieved on Earth even with the most powerful particle accelerators (the Large Hadron Collider at CERN). Do the equations worked out by physicists to capture the motion of matter continue to hold up for the very young, compact universe with its highly energetic (high-temperature) matter moving close to the absolute speed of light? The cosmologists are still waiting from the differentiating message from long ago.

Cosmology itself rests on the observation that on the very, very large scale, beyond that of galaxies and even clusters of galaxies, the universe is homogeneous in every direction and also isotropic, i.e. it is moving outward in all directions from any given observation-point at all, either accelearting or decelerating. These observations have led modern cosmology to postulate the expanding universe. From this postulation and the observation of the expansion velocity, assumed uniform, it's easy to calculate backwards to the time zero when the universe was just a dot. This is the event of the Big Bang at around 14 billion years ago. As a dot, however, ultimately-small Planck dimensions are attained and quantum dynamics with quantum indeterminacy come into play. To date there is no unified theory of gravity (curved space-time) and quantum dynamics, not for want of trying. Einstein spent the later part of life in vain trying to formulate mathematically a unified quantum-gravity theory. What a bummer! Undaunted, cosmologists aim nevertheless to get closer and closer to the Big Bang event by receiving especially relatively noiseless gravitational signals from further and further out, i.e. back in time.

Astoundingly, the universe for the modern cosmologist is an evenly expanding sphere from ANY observation point at all in the universe. This conception, remarkably enough, corresponds to Greek cosmological conceptions with their emphasis on circles and spheres when accounting for the observed motions in the sky and the structure of the cosmos.

But there is at least one major difference. In

*Timaios*, Plato casts a cosmos consisting not merely of matter in motion, as modern physics does, but of "bodies" (_s

__o__mat

__o__n_

*Tim*. 34b2) "encapsulated" (_periekalypsen_ 34b4) by the

**psyche**(_psychae_). The psyche for the Greeks is the principle of life, i.e. of self-movement. All that is living is capable of, has the

**power**of self-movement. The cosmic psyche embraces the bodies of the cosmos, endowing them with self-movement in the sky. The cosmic movement of bodies is governed by the psyche as its "despot and ruler" (_despotin kai arxousan_ 34c6). Plato then differentiates this psychically encapsulated and governed cosmos by mixing unchangeable being and changeable becoming to form indivisible sameness (_tau'ton_35a4) and divisible difference (_heteron_35a4). The realm of difference is then differentiated further into seven according to arithmetic proportions. The realm of the same is forced into a "circuit of the same and similar" (_tautou kai homoiou periphorai_ 36d1), the realm of difference is split into "seven unequal circles" (_hepta kuklous anisous_ 36d2).

The thoughtful part of the all-encapsulating psyche, _nous_ or mind, ensures that the cosmos is ordered according to arithmetically rational proportions. One does not have to wonder, then, that Werner Heisenberg, the famous German mathematical physicist who first developed the matrix formulation of quantum mechanics, along with the unsettling quantum indeterminacy for the movement of dynamic states, took a strong orientation in his work precisely from Plato's

*Timaios*(cf. his autobiography,

*Der Teil und das Ganze*). In his mathematical quantum theory, Heisenberg followed above all principles of symmetry and simplicity, the main 'aesthetic' criteria in mathematics. And if you delve into Einsteinian general relativity theory, you'll also find that the challenging mathematical language he especially developed for it (tensor mathematics), which aims at maximizing compact brevity through symmetries built into the notation, reduces in the end to wondrously simple-looking equations.

In contrast to modern relativity physics, the cosmic psyche and its mind is not reliant on receiving messages from the absolute motion of electro-magnetic and gravitational radiation. Its _nous_ (reason) is all-encompassing, enabling it to 'see' the entire cosmos in its arithmetic structure, as furthered developed in

*Timaios.*Thus does the cosmos presence rationally for the mind.

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