On Infinity and Creation (Seven Discussions)

 

Featuring Richard Dawkins, Lawrence Krauss, Arthur C. Clarke, Carl Sagan, Stephen Hawking, Roger Penrose, Carlo Rovelli, Helen Czerski, Adrian W. Moore, John D. Barrow, and H. Peter Aleff.

 

'Something from Nothing' A narrow understanding of reality plus a limited knowledge of the history of ideas can make idiots out of otherwise really bright people. A conversation with Richard Dawkins & Lawrence Krauss. youtu.be/q0mljE9K-gY via @YouTube #RichardDawkins #LawrenceKrauss #SomethingFromNothing #Atheism #Cosmology #Physics

 

‘God, the Universe, and Everything Else’ (1988). A discussion (52 minutes) with Arthur C. Clarke, Carl Sagan, and Stephen Hawking. Moderated by Magnus Magnusson. #God #Religion #Spirituality #Science #Physics #Mathematics #Infinity #Mandelbrotset #Time https://www.youtube.com/watch?v=HKQQAv5svkk

 

‘Why Did Our Universe Begin?’ (Roger Penrose) A short discussion which shows the limitations of trying to understand creation purely on the basis of mathematics and physics, and a great deal of inference. #Infinity #BigBang #Creation #Entropy #RogerPenrose #Universe https://www.youtube.com/watch?v=ypjZF6Pdrws

 

Physics in all its glory (BBC ‘Start the Week’, first broadcast November 9, 2020) Nobel Laureate Sir Roger Penrose joins Carlo Rovelli and Helen Czerski to discuss black holes and ocean currents with Andrew Marr. https://www.bbc.co.uk/programmes/m000p6dl #Physics #Cosmology #Creation #BlackHoles #Size #CarloRovelli #RogerPenrose #HelenCzerski

 

Evading the Infinite: a Review of Adrian Moore’s radio series, 'A History of the Infinite', broadcast by the BBC in 2016. #Infinite #Infinity #philosophy #Reality #Mathematics #Being #SetTheory #Plato #Aristotle #Plotinus #Neoplatonism #Hilbert https://shrineinthesea.blogspot.com/2017/10/obscured-by-clouds-critical-review-of.html

 

Continued Fractions Professor John Barrow (Gresham College lecture) https://www.youtube.com/watch?v=zCFF1l7NzVQ transcript and downloadable versions of the lecture are available from the Gresham College website: http://www.gresham.ac.uk/

 

The Egyptian Shen Ring. Discussed at Peter Aleff's 'Recovered Science' site. An Egyptian exercise in abstract and philosophical thought. #Shen #Egypt #Abstraction #Philosophy #Transcendentalism #Infinity #Nun #Atum #Creation #Numbers #HPeterAleff http://www.recoveredscience.com/const104shenring1.htm

The Plenum and Physics (Writing to George Shiber)

[This text is from The Double Nature of Reality, which will be published at some later point. Two other texts are also included which formed part of a correspondence with George Shiber in 2016]

Dear George,

It occurs to me that I might have bowled you a bit of a googly with my opening gambit. So I’m going to explain a bit more of where I think I’m going with that gambit, why the route is worth pursuing, and how we are likely to end up talking physics.

As I suggested, there isn’t much we can say about the initial state of physical reality at a notional time of its emergence, if the various parameters of what can be said of it don’t have any existence. That’s the problem physics has when it is looking for causes and mechanisms.

However it is possible to talk about the initial state of reality in terms of logical argument, which is how it was done in antiquity. That’s why I chose to start the discussion from that point of view. They were familiar with talking about reality in terms of extreme states: does it exist? What is it? Is it one or two? If it is two is reality other than itself? Is reality complete in itself? Is physical existence a copy based on the pattern of reality itself? If it is a copy, has the nature of reality itself been compromised?

Whatever the initial conditions might have been, we can say that those conditions are at the edge of physical existence. Which is not to suggest that they actually occupy some kind of space at the edge of physical existence. Just that, since the initial conditions don’t participate in the conditions of our physical existence (extension, vectors, time, etc), then these conditions will, to us, appear to be something which we can find at the extremes of physical existence.

This is the root of the idea of the telos. It is about beginnings and endings – how things start and finish. When what is ultimately real is considered in this way, it is susceptible to logical analysis, and an idea of a prime mover beyond the properties of the telos itself is not required.

A discussion of this conception of the telos should be untarnished by the general deprecation of teleological argument in any kind of scientific analysis. We aren’t looking for purpose. But we are looking for the beginning, and how things might have unfolded from that beginning. The concept of the telos as a plenum, a pleroma undefined by the kind of parameters we find in our physical existence, as opposed to the idea that physical existence  just appeared ex nihilo, can be discussed. Nothing as absence is very hard to discuss, except in the context of its opposite. In fact it cannot reasonably be conceived without that context.

The discussion of Aristotle places his laws of thought into a wider context. The laws represent tools in the Greek dialectical armoury. So do the techniques used by Plato. But they are quite different and produce different kinds of argument and result in different conclusions. They belong to the same armoury (a discussion for another time). It is possible to understand some things with Plato’s approach which would not be possible with a rigorous application of Aristotle’s laws of thought. It isn’t the case that one logical approach is correct, and the other not. But they are appropriate to different contexts.

A plenum can be understood as identical with itself, and so, in that sense, can be thought of as consistent with the first of the laws of thought. But its properties, as understood from the point of view of physical reality, cannot be self-consistent, since it is beyond definition in physical terms. So the plenum must have a paradoxical aspect (literally meaning it is beyond human understanding), and therefore must breach the other two laws of thought (it can be one thing or its opposite; and it may also be neither one thing or its opposite).

There are several ways we can go from here. One is to take the view that physical reality represents a partial view of the plenum. Or can be understood as an assemblage of partial views of the plenum. It contains consistencies and regularities, but at a granular level (particularly), it behaves with apparent inconsistency, being best understood in terms of probability. That is how the plenum is, or at least the best way it can be understood by us. It isn’t one thing or the other. But occasionally its granularity looks like one thing or the other. And sometimes both at the same time. We can describe what is going on in terms of probabilities, which is how physics handles it, but it is not understood except in terms of mathematical description. The idea of the plenum, as established through a purely logical analysis, gives us insight into how the universe is actually operating.

It could be argued that physical reality behaves as it does at the quantum level because, for all practical purposes, the plenum has no size. So, at the quantum level, we are looking more closely at the nature of the plenum as it is, or rather as it must, on account of its nature, look to us.

Quantum entanglement might have a similar basis, on the ground that what is happening is actually happening in the plenum, rather than in physical space. Despite it having no size, it must necessarily be (in a sense) distributed throughout space and time.

You see where I’m going. So, in addition to talking about initial cosmological conditions, we could, on the basis of this notion of the plenum, talk about Bell’s Theorem; Einstein, Podolsky, Rosen; and Klein-Kaluza. We could also talk about how and why Maxwell’s equations can be derived from Klein-Kaluza, and why the maths of Klein-Kaluza has two states.

Best, Thomas

(Fall, 2016)

Physics and the Origins of the Universe (III)

This is the third in the series of posts on Physics and the Origins of the Universe, and contains a discussion of the Kaluza-Klein hypothesis, which is a hypothesis which brings Einstein's field equations together with Maxwell's equations for Electrodynamics. Its proposition, that there are five dimensions of space and time, not four, and that it is hard to characterise the fifth spatial dimension in terms of size, may point to the presence of a plenum beneath physical reality. 

The Plenum and its Properties (II)

How many dimensions are there? It depends on what you are doing and how many you need to describe and understand physical reality. The number will change according to what phenomenon is being explored.

We are accustomed to thinking that, for most of recorded history, the human race has made do with three dimensions of space, plus time, in order to make sense of the world. If we treat time as a dimension, that gives us four dimensions. Three separate dimensions in which things can exist, and in which they can move. And whether these things are motionless or moving, they are also moving through time, at the same rate, irrespective of whether they are travelling left or right, backwards or forwards, or up or down.

In fact four dimensions is an inadequate number to explain how the world of physical reality actually works, and how its component parts fit together. For the most part, our understanding of what physically exists is described in scalar and vector terms within four dimensions, because that seems to work. Most of the time. Unless you are working in Fermilab or CERN, where their descriptions of physical reality concern the quantum level of physical reality, and things are more complicated there. But even at the anthropic scale, sometimes four dimensions can be found wanting. A description is not an explanation, and some things are therefore not explained.

I will borrow a little from the Wikipedia article on the Kaluza-Klein theory, which has been described as a unified theory of gravitation and electromagnetism built around the idea of a fifth dimension beyond the standard four of space and time. The article describes how this five dimensional theory was developed, and breaks it down into three steps.

The original hypothesis came from Theodor Kaluza, who sent his results to Einstein in 1919,^[1] and published them in 1921. Kaluza's theory was a purely classical extension of general relativity to five dimensions. The five-dimensional metric has 15 components. Ten components are identified with the four-dimensional spacetime metric, four components with the electromagnetic vector potential, and one component with an unidentified scalar field.

This extension to five dimensions for Einstein’s equations yields

 …the four-dimensional Einstein field equations, the Maxwell equations for the electromagnetic field, and an equation for the scalar field.

Now that is pretty interesting, and it is surprising that physicists were not falling over themselves at the time to understand the mechanics of this mathematical description which tied electromagnetic vector potential with Space and Time.

It would be intriguing to know what was in Theodor Kaluza’s mind when he came up with this five dimensional model, which involved an unidentified scalar field.  His model involved a hypothesis which is described as the ‘cylinder condition’, which means that

 that no component of the five-dimensional metric depends on the fifth dimension. Without this assumption, the field equations of five-dimensional relativity are enormously more complex.

In other words, the five dimensional model of physical reality has two potential states – one of which results in impossibly difficult field equations. The cylinder condition is the other state for the model, which results in relatively simple and intelligible equations.

The article suggests that

 standard four-dimensional physics seems to manifest the cylinder condition.

Which may be the case, or it may be that there is a fundamental problem with the five dimensional model, and that it is a conception which doesn’t reflect physical reality. Kaluza

… set the scalar field equal to a constant, in which case standard general relativity and electrodynamics are recovered identically.

Meaning that Kaluza knew how the equations should turn out, and he knew how to characterise the unknown scalar field in order for the equations to turn out correctly.

The second step in the development of Kaluza’s theory was a quantum interpretation, supplied by Oskar Klein in 1926. This to enable the theory to

accord with the then-recent discoveries of Heisenberg and Schrödinger. Klein introduced the hypothesis that the fifth dimension was curled up and microscopic, [my emphasis] to explain the cylinder condition. Klein also calculated a scale for the fifth dimension based on the quantum of charge.

The third step happened in the 1940s, when the classical theory was completed, and the

full field equations including the scalar field were obtained by three independent research groups

The introduction to the article concludes by saying that even under the cylinder condition the full Kaluza equations are quite complex, and that

The complete Kaluza equations were evaluated using tensor algebra software in 2015

Here is a section from the main body of the Wikipedia page. I can understand the concepts involved, but I’m not remotely competent to evaluate the equations.  I’ve left the links to the Wikipedia references intact. [this version of the document presents the Wikipedia text as graphics, so the links are not functional. The original article is at: https://en.wikipedia.org/wiki/Kaluza-Klein_theory]

I’ll pick out some parts of the text -

So far, this decomposition is quite general and all terms are dimensionless. Kaluza then applies the machinery of standard general relativity to this metric. The field equations are obtained from five-dimensional Einstein equations, and the equations of motion are obtained from the five-dimensional geodesic hypothesis. The resulting field equations provide both the equations of general relativity and of electrodynamics; the equations of motion provide the four-dimensional geodesic equation and the Lorentz force law, and one finds that electric charge is identified with motion in the fifth dimension.

It has been an objection to the original Kaluza hypothesis to invoke the fifth dimension only to negate its dynamics. But Thiry argued that the interpretation of the Lorentz force law in terms of a 5-dimensional geodesic mitigates strongly for a fifth dimension irrespective of the cylinder condition. Most authors have therefore employed the cylinder condition in deriving the field equations.

…It shows that the electromagnetic field is a source for the scalar field. Note that the scalar field cannot be set to a constant without constraining the electromagnetic field. The earlier treatments by Kaluza and Klein did not have an adequate description of the scalar field, and did not realize the implied constraint on the electromagnetic field by assuming the scalar field to be constant.

In the Kaluza theory, the gravitational constant can be understood as an electromagnetic coupling constant in the metric. There is also a stress-energy tensor for the scalar field. The scalar field behaves like a variable gravitational constant, in terms of modulating the coupling of electromagnetic stress energy to spacetime curvature. The sign of phi in the metric is fixed by correspondence with 4D theory so that electromagnetic energy densities are positive. This turns out to imply that the 5th coordinate is spacelike in its signature in the metric.

***

So what are we actually looking at with this five dimensional model of physical reality? The theory unifies Einstein’s field equations, and Maxwell’s equations, and does appear to be describing physical reality, even if there are problematic aspects to it.

The fifth dimension is invoked, and then dismissed as a functional component in the model, which reduces it to a dimension on a par with the other four. But it is very small, and may be rolled up. It is practical to treat it as if it is on a par with the other dimensions, which is what physicists generally do. But ignoring the complexity the model may have beyond the cylinder condition – one of the two states of the model - doesn’t mean that it does not have this complexity, and that the fifth dimension does not have an important role in how the physical world functions.

It is possible that what has been identified in the course of the development of the theory is in fact the plenum, and not simply another dimension on a par with the other four.

Thomas Yaeger, 22 February 2016.