“The Asymmetry of Being” – A reflection on The End of Time by Julian Barbour (1999) and the wider importance of (mainly) Leibnizian ideas in modern physics.

Posted by | peter | 18.12.12 | No Comments

In this evocative book Barbour proposes a speculative physics of the All - and inspired by hidden elements within Einstein’s equations (first hinted at by Dirac: “This result has led me to doubt how fundamental the four dimensional requirement in physics is” (pg2)) proposes that the next revolution in physics is that: reality is timeless. From here, and drawing on the history of thought surrounding and leading up to the relativity revolution – Leibniz, Mach and others – Barbour sketches out an alternative framework of physics. Rather than being embedded in an absolute Newtonian space and time, he argues that reality is instead a vast configuration space of all the possible states of the universe called “Platonia”.
Platonia is a timeless landscape of Escher-like proportions; vast with an incomprehensible amount of dimensions – corresponding to the degrees of freedom of all the particles in the universe considered as a system (see fig1 below – pg56). The landscape borders nothingness and opens up from an apex point called Alpha from which it unfolds infinitely. Its infinite plain is composed of infinite points, like grains of sand, each one represents the entire state of the universe at a particular instant of time, what Barbour calls a “NOW'. Each NOW corresponds to the position of everything in the universe at one moment, and all this information is reduced to a solitary point in state space – they are “worlds unto themselves” (pg45). And these are strewn amongst countless others in this gigantic configuration space. What we think of as history equates to paths in Platonia – but in reality these are not joined up threads since each world is a complete picture at one distinct NOW. The paths comprised of these distinct and separate NOWs only begin after the alpha or apex of the configuration space – beyond this there is nothing. Alpha marks the edge of possibility – the point or region of possibility at which all particles in the universe coincide in their positions (pg42). Beyond this there is no possible other configurations and hence nothingness. Barbour calls this the “asymmetry of being” (pg320) since Platonia unfolds from this region into all other possible configurations and this unfolding is infinite since “there is no limit to the size or complexity of things that can exist […there is…] no omega” (pg46).
Barbour uses a toy universe he calls “Triangle land” to pedagogically explain the difference between the standard Newtonian way of doing physics and his proposed physics of the All. Triangle land is the configuration space of a three particle system (with each snapshot of the whole system corresponding to a triangle of a particular shape). Standard Newtonian ways of viewing this system would be to treat each particle as different and show the system like so (apologises for the shocking diagram – see pg84 for much better versions)…
Here, time is represented by the vertical axis, whereas the horizontal axes represent the positions of the three particles, A, B, and C, in space. The thick solid lines represent the worldlines of the three particles respectively. The thin lines represent the triangular shapes traced out by the system as the whole (three have been highlighted: 1, 2, and 3).
Barbour follows a Leibnizian and Machian approach to space and time and wants to eliminate the idea of a necessary external container or framework. Instead, space must be thought of as the totality of the positions of all things. As such, rather than tracing out all the individual worldlines, Triangle land is the configuration space of all possible triangle shapes formed by the particles taken together. I have recreated Barbour’s visualisation of this below (see pg73, 77, and 85 for the originals) – again apologises for the roughness.
This diagram corresponds to the entire topological space of all possible triangles that could be formed by the three particle toy universe. Instead, of an external absolute space, space is entirely composed of the relative positions of the particles, and the triangle-shapes that these relations form. The three boundaries equate to triangles where the angles have become zero (so that all the particles are on one line), the dotted lines represent isosceles triangle state systems and the centre point is an equilateral triangle. Each point in the above diagram corresponds to a triangle formed by the three particles A, B, and C (i.e. one of the states labelled 1, 2, and 3 in Fig2). I have traced out what the history of the system as a whole (as a series of triangles) as the S-shaped path of in the shape space of Triangle land – please note this is there for demonstrative purposes only and does not correspond to the history of Fig2. For proper correspondence please see the originals on the pages cited above.
            Barbour states that Platonia is one of two key concepts in the book (pg208). And we can understand it as a vastly more complicated configuration space than the three particle shape space of triangle land that I have briefly described. To give us an insight into quite how much more stupendously vast, Barbour states that the configuration space of a cloud chamber is 3 x 1027 (3 degrees of freedom for 1027 particles – see pg290 for more details). The other key concept is a static quantum mechanical wave equation of the entire universe (henceforth ψ). Barbour draws on the work of Born, Schrodinger, the Wheeler-DeWitt equation and Everett’s Many Worlds Interpretation to elaborate how this will work practically, but ultimately admits that he cannot back this up with equations and he has to stick to speculation. The way ψ works is colourfully imagined as a mist that covers the rugged landscape of Platonia and determines which possible states of the entire universe are realised by the intensity of the mist at these various points. This corresponds to a probability distribution which is affected by the landscape of Platonia itself – like one of Stuart Kauffman’s fitness landscapes in reverse: imagine water poured onto a ragged landscape, it will pool in the deeper ravines and avoid the higher plateaus. Thus, in Platonia, these ravines, or attractors, which are highly ordered special structures (such as this instant NOW in which you are experiencing and reading this sentence) cause themselves to be more probable than other states. This quality is extremely important since Platonia, as the configuration space of all possible worlds, contains vastly more state spaces that are highly unordered than those that are. The difference is unimaginable – states that relate to universes with order are equivalent to a vanishingly small candle in abyssal darkness where order is either rare or non-existent. If it were not for this selective pressure or mechanism orchestrated by the very structure of Platonia of itself, then no higher order structure would be realised considering the gigantic probability gulf favouring chaos.
            In this respect, Barbour follows both Kauffman and Penrose in stating that there must be some mechanism for realising order when chaos seems so much more probable. Penrose has focused on the extremely unlikely initial conditions of the universe and he calculates this as the perplexingly astronomical 1010100 (see either The Emperor’s New Mind ch.7 “How special was the Big Bang?” or The Road to Reality ch27.13). Stewart and Cohen, in an interview for Collapse, have criticised this calculation for the anthropic tendencies it leads to; they state that there are other viable initial conditions with subsequently different physical outcomes – but this does not overly detract from the central point that chaos vastly outweighs order in the scheme of Platonia. Furthermore, since we are following Barbour’s exposition, it is the fact that the universe itself is fine tuning – by having each point in configuration space, or each grain of sand, resonate with each other (pg255) – and this avoids any unnecessary fideism. I.e. the parts resonate with each other in the probability distribution and this draws ψ towards the richer structure creating a “perfect, circle-closing rational explanation for all the relative probabilities” – the paths through Platonia that equate to our universe (ibid). This is similar to the work of Kauffman, along with Smolin, who also explore the notion that the universe is able self-organise itself (see Investigations ch10 for more details). At this juncture, I would like to make two observations: 1. Fideism and possibility of science; 2. Leibnizian roots.
1. On the subject of fideism, fine-tuning and the possibility of science; it is noteworthy that J.H. Spencer has recently written about the necessity of having faith in the rationality of the universe in order that scientific investigation is possible (The Eternal Law 2012, pg17). This, and other similar arguments, about the limits of reason and having ultimately needing to have faith in reason were succinctly paraphrased by a Christian I once spoke to at a wedding: “reason can take you 95% of the way, but the last bit has to be faith”. This last statement is perhaps a rather extreme version of this view, but it captures the sentiment well and also expresses what I think undermines scientific activity. The undermining arises from the fact that science can dig and dig away at enquiring into nature, but ultimately it must have faith. Kant, in the introduction to The Critique of Judgement called this “the principle of purposiveness”: scientific investigation is possible insofar as the universe has been made amenable to its investigation. Now, this seems a reasonable postulate: nature is systematic and unified, and the incredible success of science, especially physics and its use of mathematical beauty in the discovery of the laws of nature, definitely testify to something wonderful going on in nature. But, this does not mean that nature is rational for us. This view falls right into an anthropic and narrow minded way of thinking. It models our way of thinking and then naively projects it onto reality. Furthermore, as a principle, it relies on a  non-sequitur between [a] “judgement of nature is possible” to [b] “nature is purposive for our judgement”. We can deny statement [b] without violating any principles of logic and this reduces a degree of fideism attached to this issue. But furthermore, we do not even have to accept statement [a] in its brute form. Now, at this juncture J.H. Spencer would classify this line of thought as insane, and I assume he would put me in with Smolin when he says that “he really should know better” (2012 pg18) for even considering this line of enquiry. But this rather harsh and derogatory critique relies on two mistakes. Firstly, J. D. Mcfarland (Kant’s Concept of Teleology, 1970 see especially pg86-87) identifies that the principle of purposiveness can be split into two versions: 

Strong – the affirmation that nature is amenable to judgement and is purposive in this respect.

Weak – the non-rejection that judgement of, or the applying logic to, nature is possible.

From this we can see that the strong version need not be affirmed as a condition for the possibility of science – i.e. it is not necessary to applying logic to affirm that it can be applied to nature; instead, it is only necessary that a similar assumption not be denied before attempting to apply logic to nature. McFarland gives a pertinent example to clarify this:

“Someone could say, ‘I am going to see whether I can systematise this body of data’, without positively assuming that it can be systematised, although he could not sensibly make the attempt while denying the truth of the statement.”   

As such, the principle of purposiveness does not equate to a necessary principle and is merely regulative for science insofar as it is a tacit background non-rejection of the principle that science is actually possible.
            Secondly, to use the language of I.H. Grant, science is an ungrounded and an ungrounding activity. It has no definitive roots. This can best be seen by the fact that there is no actual scientific method. There is only a loose set of principles and observations and guesses and rules of thumb and a good measure of awe and scepticism (as Carl Sagan would say). This rickety raft has no real absolute foundations, and this is reflected in the negative usage of a reflective principle that McFarland devises, rather than a fideistic and anthropic standard reading. The latter is homely, the former accepts the abyssal nature at the foundations of our knowledge and does not try to shore it up with faith. Rather it continues to dig, not knowing what it will find. Maybe the laws of nature aren’t necessary, let’s test it and find out. Experiment ultimately determines science. And this view cannot be immediately overhauled by stating that if the laws of nature aren't necessary then they’d be changing all the time (Spencer 2012 pg19). Quentin Meillassoux calls this “frequentialist implication” (After Finitude, 2008 pg94):

“If the laws of nature could actually change without reason – i.e. if they were not necessary – they would frequently change for no reason.”

Following Vernes, Meillassoux identifies that the link between a lack of necessity and a frequency of change is based upon “probabilistic reasoning” and this leads to a fallacy we can call “meta-stability”. Let us suppose the probability of the laws of nature remaining unchanged without reason is analogous to one side on a million sided dice. From this it would appear that the odds of the same event succeeding another with regularity becomes infinitesimally small and therefore that we have ceded the argument to J. H. Spencer and others. But this analogy requires, for its repetition, that the situational framework (in this example, the number of dice sides) remains stable/constant so that the event has an equal chance each time. But this begs the question of stability that we are trying to answer because it places it within a meta-stable framework. Probabilistic reasoning requires a meta-stability within which to ask the question of stability and if this removed in any attempt of refutation it occurs at another level (e.g. a meta-meta-stability). It therefore not only begs the question but also leads to an infinite regress. This suggest that chance is perhaps an inadequate way of thinking about a universe without permanent laws – and also without laws governing this impermanence as well.
Unfortunately, although Meillassoux raises this argument, as well as others, in defence of non-necessary laws of nature, they are of a negative nature since they only deflect prima facie rejections against the notion. To make his case convincingly, a positive case must be made for contingent laws of nature. As yet, he has not done so.
We shall leave this issue at this juncture since I am ambivalent as to whether there are eternal laws or not for nature. My central concern is to prevent fideism from undermining science as a free and sceptical attitude. And, despite my objections to emphasis J.H. Spencer places on faith, I think his recent book examining the Platonic foundations of quantum mechanics and modern physics is fantastic and a must read for anyone interested in philosophy and the nature of reality.  
2. The second main thread I wish to draw is that all these modern considerations have a common philosophical origin in Leibniz – Barbour explicitly states his influence through a series of excellent quotes which he says best captures the spirit of Leibnizian philosophy (if not the exact letter). Barbour interprets Leibniz’s “best of all possible worlds” as maximal variety with the most possible order – he has written a number of other papers on this very issue (some co-authored with Smolin) – so that best equates to order. And considering that the majority of the “monstrously multidimensional configuration space” of Platonia is chaos (pg289-291), order – or what Barbour calls “rich structure” – can definitely be considered the best for its curious and special nature (since it is not chaos). Barbour adds that our anthropocentric and evolved familiarity with this specialness blinds us from its rarity (pg289). He writes that of the all the possibles, which must be, since Platonia is the configuration space of everything that is logically possible, “we are answers to the question what of can be maximally sensitive to the totality of what is possible” (pg325). And the instant, the NOW that we experience is expressible through a combination of Leibniz’s Monadology and the Pythagorean notion of the music of the spheres: “You are the music of the spheres heard from a particular vantage point that is you” (pg326). This beautiful sentiment is all the more important considering that Barbour sees “Leibnizian ideas [as the] only genuine alternative to Cartesian-Newtonian materialism” (pg240) because of [a] its emphasis on structure and [b] the Principle of the identity of indiscernibles (henceforth PII). These two considerations are both intriguing, since [a] an emphasis on structure has recently been proposed by J. Worrall (Structural Realism: The Best of Both Worlds, 1989) as a way of solving the impasse between the problem of theory change and the no miracles argument in the realism/anti-realism debate. This view, which Worrall calls Structural Realism avoids the problem of ontological discontinuity caused by paradigm shifts by placing the emphasis on the structural content of theories – in which there is a definite accumulation of knowledge. How Worrall’s view is cashed out is still a matter of debate: either as a neo-Kantian epistemic limitation view or as an ontological view that borders on Platonism and Pythagorean thinking (the physicist Max Tegmark is the most explicit in acknowledging this). Either way, Leibniz’s views and thoughts are bound to helpful or as Barbour puts it “suggestive” for this line of thinking. And this can be seen straight away by considering [b].
The role of PII has been found somewhat wanting at the level of the quantum particle. In a seminal paper, S. French and M. Redhead (Quantum Physics and the Identity of Indiscernibles, 1988) demonstrate that quantum particles defy PII. Various other thinkers have attempted to resolve this problem with various other identity principles but this has just further complicated matters (see S. French and J. Ladyman In Defence of Ontic Structural Realism, 2011 pg29 for a good short overview of this) and ultimately leads some to propose that our metaphysical categories should be reconceptualised. On this view, it is not that PII is wrong, but rather that it doesn’t apply to quantum particles. But if it doesn’t apply to quantum particles, does it apply to our universe at all? I believe that the answer is yes, each of the points in Platonia is a different possible configuration of the whole universe, as such, each possible state of the universe as a whole satisfies PII and it holds at a cosmological scale. I find this truly fascinating. It means that every moment, every instant, is truly astonishing and special in a way that our anthropocentric everydayness – to follow Heidegger – hides. I think an excerpt from Rilke’s Ninth Elegy best captures the sentiments that Barbour’s Platonia evokes for me:

“Once for each thing.  Just once; no more.  And we too,
just once.  And never again.  But to have been
this once, completely, even if only once:
to have been at one with the earth, seems beyond undoing.”

Although I have repeatedly derided anthropocentric thinking throughout this essay, I am aware that how we conceive of the universe affects us. My immediate thoughts on the subject of ethics and existentialism turn to Nietzsche's "eternal return" thought experiment and Camus discussion of how we must imagine a defiant Sisyphus happy. Barbour uses the epilogue to tackle some prima facie reflections on the notion that there is no time, only a vast and unending scattering of possible worlds of which we experiencing one of the vanishingly rare ordered ones:
Firstly, everything is eternal and yet nothing moves. What we think of as the past is just a different possible world. Therefore, the me that writes this sentence NOW, is in a different possible world to the me that will re-read and edit it.
Secondly, Barbour’s version of the many worlds theory has a profound effect on causality. Causality has been under serious challenge since Hume, and although he has in certain ways been rebutted, it has never successfully been put in the clear. In the many worlds interpretation, debates about freedom seem to go by the by, since you (or at least versions of you) do all possible things that could conceivably happen – including the extremely unlikely and incredibly unpleasant event of you turning spontaneously into an oversized duck (additionally, S. Harri’s notion of a “moral landscape” of all possible moral worlds – from heaven to hell – are intrinsically contained within Platonia by its very nature). This does through a huge spanner in the works for identity theories of human beings. Furthermore, causation cannot be said to manifest itself in the way that we have evolved to of expect it to. If time is an illusion, then so is motion, and subsequently so is any straightforward notion of causation. Again Leibniz helps us to consider this problem. Each possible state of the entire universe envisioned as a point in Platonia, or as a grain of sand on incredibly vast beach is separate from all the others, they are each a totality, and contain everything they need and are. This matches onto Leibniz’s notion of a monad. Barbour argues that between these monadic-like grains of sand, or NOWS there is

“…a timeless beauty contest to win the highest probability. The ability of each NOW to ‘resonate’ with the other NOWS is what counts. Its chance to exist is determined by what it is in itself. The structure of things is the determining power [i.e. causality] in a timeless world.” (pg325)

The notion of reality as a dynamical structure also ties in with the ontological interpretation of structural realism mentioned above.
            Thirdly, and finally, Penrose has objected to the many world interpretation by asking why it is that we only see one universe and we don’t see the multiverse. Barbour’s Leibnizian answer to this is that we are the universe as seen from a particular: “We are all part of one another, and we are each just the totality of things seen from our own viewpoint” (pg329). 'Trapped', seems the wrong word, perhaps ‘Frozen’ is better, but that is what we are, and a god’s eye view of Platonia would be able to see not a series, but a cloud or bifurcating tubes of similar (near in state space) versions of us at each separate possible world forming paths across this misty landscape. An evolution explanation suffices to some extent – perception is not about seeing reality as it really is, it is about seeing nature insofar as it useful for survival. But since what is is dependent upon how it resonates with everything else this means that the evolved framework of perception must contain this totality: that which is in sense but cannot itself be sensed - “that by which the given is given” to quote Deleuze (Difference and Repetition, 1994). So in a way we are aware of the vastness of reality beyond our parochial view – and although we may struggle to comprehend or think about it rationally – mathematics has allowed us to explore this and thus we can have a speculative physics of the all.   


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