A Monetary Drain due to Excess Liquidity. Why is the RBI Playing Along

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And so we thought demonetization was not a success. Let me begin with the Socratic irony to assume that it was indeed a success, albeit not in arresting black money for sure. Yes, the tax net has widened and the cruelty of smashing down the informal sector to smithereens to be replaceable with a formal economy, more in the manner of sucking the former into the latter has been achieved. As far as terror funding is concerned, it is anybody’s guess and so let them be with their imaginations. What none can deny is the surge in deposits and liquidity in the wake of demonetization. But, what one has been consciously, or through an ideological-driven standpoint denying is the fact that demonetization clubbed with the governmental red carpet for foreign direct investment has been an utter failure to attract money into the country. And the reason attributed for the same has been a dip in the economy as a result of the idiosyncratic decision of November 8 added with the conjuring acts of mathematics and statistics in tweaking base years to let go off the reality behind a depleting GDP and project the country as the fastest growing emerging economy in the world. The irony I started off with is defeated here, for none of the claims that the government propaganda machine churns out on the assembly line are in fact anywhere near the truth. But, thats what a propaganda is supposed to doing, else why even call it that, or even call for a successful governance and so on and on (sorry for the Žižekian interjections here).

Assuming the irony still has traces and isn’t vanquished, it is time to move on and look into the effects of what calls for a financial reality-check. Abruptly going vertically through the tiers here, it is recently been talked about in the corridors of financial power that the Reserve Bank of India (RBI) is all set to drain close to 1.5 lakh crore in excess liquidity from the financial system as surging foreign investments forces the central bank to absorb the dollar inflows and sell rupees to cap gains in the local currency. This is really interesting, for the narrative or the discourse is again symptomatic of what the government wants us to believe, and so believe we shall, or shall we? After this brief stopover, chugging off again…Foreign investments into debt and shares have reached a net $31 billion this year, compared with $2.7 billion in sales last year, due to factors including India’s low inflation and improving economic growth. This is not merely a leap, but a leap of faith, in this case numerically. Yes, India is suffering from low inflation, but it ain’t deflation, but rather disinflation. There is a method to this maddening reason, if one needs to counter what gets prime time economic news in the media or passes on as Chinese Whispers amongst activists hell-bent on proving the futility of the governmental narrative. There is nothing wrong in the procedure as long as this hell-bent-ness is cooked in proper proportions of reason. But, why call it disinflation and not deflation? A sharp drop in inflation below the Reserve Bank of India’s (RBI’s) 4% target has been driven by only two items – pulses and vegetables. the consumer price index (CPI), excluding pulses and vegetables, rose at the rate of 3.8% in July, much higher than the official headline figure of 2.4% inflation for the month. The re-calculated CPI is based on adjusted weights after excluding pulses and vegetables from the basket of goods and services. The two farm items – pulses and vegetables – have a combined weight of only 8.4% in the consumer price index (CPI) basket. However, they have wielded disproportionate influence over the headline inflation number for more than a year now owing to the sharp volatility in their prices. So, how does it all add up? Prices of pulses and vegetables have fallen significantly this year owing to increased supply amid a normal monsoon last year, as noted by the Economic Survey. The high prices of pulses in the year before and the government’s promises of more effective procurement may have encouraged farmers to produce more last year, resulting in a glut. Demonetisation may have added to farmers’ woes by turning farm markets into buyers’ markets. Thus, there does not seem to be any imminent threat of deflation in India. A more apt characterization of the recent trends in prices may be ‘disinflation’ (a fall in the inflation rate) rather than deflation (falling prices) given that overall inflation, excluding pulses and vegetables, is close to the RBI target of 4%. On the topicality of improving economic growth in the country, this is the bone of contention either weakening or otherwise depending on how the marrow is key up.

Moving on…The strong inflows have sent the rupee up nearly 7 per cent against the dollar and forced the RBI to buy more than $10 billion in spot market and $10 billion in forwards this year – which has meant an equivalent infusion in rupees. Those rupee sales have added liquidity into a financial system already flush with cash after a ban on higher-denomination currency in November sparked a surge in bank deposits. Average daily liquidity has risen to around Rs 3 lakh crore, well above the RBI’s goal of around Rs 1 lakh crore, according to traders. That will force the RBI to step up debt sales to remove liquidity and avoid any inflationary impact. Traders estimate the RBI will need to drain Rs 1 lakh crore to Rs 1.4 lakh crore ($15.7 billion to $22 billion) after taking into account factors such as festival-related consumer spending that naturally reduce cash in the system. How the RBI drains the cash will thus become an impact factor for bond traders, who have benefitted from a rally in debt markets. The RBI has already drained about Rs 1 lakh crore via one-year bills under a special market stabilisation scheme (MSS), as well as Rs 30,000 crore in longer debt through open market sales. MSS (Market Stabilisation Scheme) securities are issued with the objective of providing the RBI with a stock of securities with which it can intervene in the market for managing liquidity. These securities are issued not to meet the government’s expenditure. The MSS scheme was launched in April 2004 to strengthen the RBI’s ability to conduct exchange rate and monetary management. The bills/bonds issued under MSS have all the attributes of the existing treasury bills and dated securities. These securities will be issued by way of auctions to be conducted by the RBI. The timing of issuance, amount and tenure of such securities will be decided by the RBI. The securities issued under the MSS scheme are matched by an equivalent cash balance held by the government with the RBI. As a result, their issuance will have a negligible impact on the fiscal deficit of the government. It is hoped that the procedure would continue, noting staggered sales in bills, combined with daily reverse repo operations and some long-end sales, would be easily absorbable in markets. The most disruptive fashion would be stepping up open market sales, which tend to focus on longer-ended debt. That may send yields higher and blunt the impact of the central bank’s 25 basis point rate cut in August. The RBI does not provide a timetable of its special debt sales for the year. and if the RBI drains the cash largely through MSS bonds then markets wont get too much impacted. This brings us to close in proving the success story of demonetization as a false beacon, in that with a surge in liquidity, the impact on the market would be negligible if MSS are resorted to culminating in establishing the fact that demonetization clubbed with red-carpeted FDI has had absolutely no nexus in the influx of dollars and thus any propaganda of this resulting as a success story of demonetization is to be seen as purely rhetoric. QED.

Where Hegel Was, There Deconstruction Shall Be: The Dialectical Calculus Between Lukács and Laclau & Mouffe. Thought of the Day 81.0

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Lukács would be the condensation of everything that is deemed politically regressive about the social theory of “the rationalist ‘dictatorship’ of Enlightenment” (Ernesto Laclau New Reflections on the Revolution of Our Time), of just about everything that the new social logic of postmodern culture brings into crisis. In this context – which is theoretically and politically hostile to the concept of totality – Laclau and Mouffe’s recasting of the Gramscian concept of hegemony is designed to avoid the Lukácsian conception of society as an “expressive totality”. For Lukács, a single principle is “expressed” in all social phenomena, so that every aspect of the social formation is integrated into a closed system that connects the forces and social relations of production to politics and the juridical apparatus, cultural forms and class-consciousness. By contrast, Laclau and Mouffe insist that the social field is an incomplete totality consisting of a multitude of transitory hegemonic “epicentres” and characterised by a plurality of competing discourses. The proliferation of democratic forms of struggle by the new social movements is thereby integrated into a pluralistic conception of the social field that emphasises the negativity and dispersion underlying all social identities. “Radical and plural democracy,” Laclau and Mouffe contend, represents a translation of socialist strategy into the detotalising paradigm of postmodern culture.

For Lukács, the objective of a new conception of praxis is to establish the dialectical unity of theory and practice, so as to demonstrate that the proletariat, as the operator of a transparent praxis, is the identical subject-object of the historical process. The subject of history is therefore the creator of the contents of the social totality, and to the extent that this subject attains self-reflexivity, it is also the conscious generator of social forms. This enables Lukács to emphasise the revolutionary character of class conscious as coextensive with revolutionary action. Laclau and Mouffe’s concept of discursive practice has the same effect – with this difference, that Laclau and Mouffe deny that discursive practices can become wholly transparent to social agents (Ernesto Laclau, Chantal Mouffe Hegemony and Socialist Strategy Towards a Radical Democratic Politics). By reinscribing the concept of praxis within a deconstruction of Marxism, Laclau and Mouffe theorise a new concept of discursive practice that “must pierce the entire material density of the multifarious institutions” upon which it operates, since it has as its objective a decisive break with the material/mental dichotomy. “Rejection of the thought/reality dichotomy,” they propose, “must go together with a re-thinking and interpenetration of the categories which have up until now been considered exclusive of one another”.

Critically, this means a fusion of the hitherto distinct categories of (subjective) discourse and (objective) structure in the concept of “hegemonic articulation”. This theoretical intervention is simultaneously a decisive political advance, because it now becomes clear that, for instance, “the equivalence constituted through communist enumeration [of the alliance partners within a bid for political hegemony] is not the discursive expression of a real movement constituted outside of discourse; on the contrary, this enumerative discourse is a real force which contributes to the moulding and constitution of social relations”. In other words, the opposition between theory and practice, discursive practice and structural conditions, is resolved by the new theory of hegemonic articulation. The operator of these discursive practices – the new agent of social transformation – is at once the instigator of social relations and the formulator of discourses on the social.

The most significant difference between Lukács and Laclau and Mouffe is their respective evaluations of Hegelian dialectics. Where, for Lukács, a return to dialectical philosophy held out the prospect of a renewal of Marxian social theory, for Laclau and Mouffe it is “dialectical necessity” that constitutes the major obstacle to a radical postmodern politics. Laclau and Mouffe’s fundamental objection to dialectics is to the substitution of a logically necessary sequence for the contingency of the historical process. They applaud the dialectical dissolution of fixity but deplore the supposed inversion of contingency into necessity and the imposition of a teleology of reconciliation. Hegel’s work, therefore, “appears as located in a watershed between two epochs” and is evaluated as “ambiguous” rather than simply pernicious. On the one hand, Laclau and Mouffe reject the Hegelian notion that “history and society … have a rational and intelligible structure”. This is regarded as an Enlightenment conception fundamentally incompatible with the postmodern emphasis on contingency, finitude and historicity. On the other hand, however, “this synthesis contains all the seeds of its own dissolution, as the rationality of history can only be affirmed at the price of introducing contradiction into the field of reason”. Once the impossibility of including contradiction within rationality is asserted, it then becomes clear that the “logical” transitions between historical “stages” are secured contingently:

It is precisely here that Hegel’s modernity lies: for him, identity is never positive and closed in itself but is constituted as transition, relation, difference. If, however, Hegel’s logical relations become contingent transitions, the connections between them cannot be fixed as moments of an underlying or sutured totality. This means that they are articulations.

This is not a rejection of Hegel but a re-interpretation. Interpreted in this light, Hegel’s “logical” relations are the language games that frame social practices – rather than formally rational structures deducible a priori – and their “transitions” are only the contingent connections created by political articulations. In opposition to the logically necessary sequence of closed totalities, Laclau and Mouffe insist on a historically contingent series of open discursive formations. Resolutely contesting the category of the totality, Laclau and Mouffe declare that:

The incomplete character of every totality leads us to abandon, as a terrain of analysis, the premise of “society” as a sutured and self-defined totality. “Society” is not a valid object of discourse.

So where Lukács once declared that “the category of the totality is the bearer of the principle of revolution in science”, Laclau and Mouffe now announce, by contrast, that totality is an illusion because “‘society’ as a unitary and intelligible object which grounds its own partial processes is an impossibility”. Where Hegel was, there deconstruction shall be – or so it would seem.

Hypersurfaces

Let (S, CS) and (M, CM) be manifolds of dimension k and n, respectively, with 1 ≤ k ≤ n. A smooth map : S → M is said to be an imbedding if it satisfies the following three conditions.

(I1) Ψ is injective.

(I2) At all points p in S, the associated (push-forward) linear map (Ψp) : Sp → MΨ(p) is injective.

(I3) ∀ open sets O1 in S, Ψ[O1] = [S] ∩ O2 for some open set O2 in M. (Equivalently, the inverse map Ψ−1 : Ψ[S] → S is continuous with respect to the relative topology on [S].)

Several comments about the definition are in order. First, given any point p in S, (I2) implies that (Ψp)[Sp] is a k-dimensional subspace of MΨ(p). So the condition cannot be satisfied unless k ≤ n. Second, the three conditions are independent of one another. For example, the smooth map Ψ : R → R2 defined by (s) = (cos(s), sin(s)) satisfies (I2) and (I3) but is not injective. It wraps R round and round in a circle. On the other hand, the smooth map : R → R defined by (s) = s3 satisfies (I1) and (I3) but is not an imbedding because (Ψ0) : R0 → R0 is not injective. (Here R0 is the tangent space to the manifold R at the point 0). Finally, a smooth map : S → M can satisfy (I1) and (I2) but still have an image that “bunches up on itself.” It is precisely this possibility that is ruled out by condition (I3). Consider, for example, a map : R → R2 whose image consists of part of the image of the curve y = sin(1/x) smoothly joined to the segment {(0, y) : y < 1}, as in the figure below. It satisfies conditions (I1) and (I2) but is not an imbedding because we can find an open interval O1 in R such that given any open set O2 in R2, Ψ[O1] ≠ O2 ∩ Ψ[R].

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Suppose(S, CS) and (M, CM) are manifolds with S ⊆ M. We say that (S, CS) is an imbedded submanifold of (M, CM) if the identity map id: S → M is an imbedding. If, in addition, k = n − 1 (where k and n are the dimensions of the two manifolds), we say that (S, CS) is a hypersurface in (M, CM). Let (S, CS) be a k-dimensional imbedded submanifold of the n-dimensional manifold (M, CM), and let p be a point in S. We need to distinguish two senses in which one can speak of “tensors at p.” There are tensors over the vector space Sp (call them S-tensors at p) and ones over the vector space Mp (call them M-tensors at p). So, for example, an S-vector ξ ̃a at p makes assignments to maps of the form f ̃: O ̃ → R where O ̃ is a subset of S that is open in the topology induced by CS, and f ̃ is smooth relative to CS. In contrast, an M-vector ξa at p makes assignments to maps of the form f : O → R where O is a subset of M that is open in the topology induced by CM, and f is smooth relative to CM. Our first task is to consider the relation between S-tensors at p and M-tensors there.

Let us say that ξa ∈ (Mp)a is tangent to S if ξa ∈ (idp)[(Sp)a]. (This makes sense. We know that (idp)[(Sp)a] is a k-dimensional subspace of (Mp)a; ξa either belongs to that subspace or it does not.) Let us further say that ηa in (Mp)a is normal to S if ηaξa =0 ∀ ξa ∈ (Mp)a that are tangent to S. Each of these classes of vectors has a natural vector space structure. The space of vectors ξa ∈ (Mp)a tangent to S has dimension k. The space of co-vectors ηa ∈ (Mp)a normal to S has dimension (n − k).

Hegelian Marxism of Lukács: Philosophy as Systematization of Ideology and Politics as Manipulation of Ideology. Thought of the Day 80.0

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In the Hegelian Marxism of Lukács, for instance, the historicist problematic begins from the relativisation of theory, whereby that it is claimed that historical materialism is the “perspective” and “worldview” of the revolutionary class and that, in general, theory (philosophy) is only the coherent systematisation of the ideological worldview of a social group. No distinction of kind exists between theory and ideology, opening the path for the foundational character of ideology, expressed through the Lukácsian claim that the ideological consciousness of a historical subject is the expression of objective relations, and that, correlatively, this historical subject (the proletariat) alienates-expresses a free society by means of a transparent grasp of social processes. The society, as an expression of a single structure of social relations (where the commodity form and reified consciousness are theoretical equivalents) is an expressive totality, so that politics and ideology can be directly deduced from philosophical relations. According to Lukács’ directly Hegelian conception, the historical subject is the unified proletariat, which, as the “creator of the totality of [social] contents”, makes history according to its conception of the world, and thus functions as an identical subject-object of history. The identical subject-object and the transparency of praxis therefore form the telos of the historical process. Lukács reduces the multiplicity of social practices operative within the social formation to the model of an individual “making history,” through the externalisation of an intellectual conception of the world. Lukács therefore arrives at the final element of the historicist problematic, namely, a theorisation of social practice on the model of individual praxis, presented as the historical action of a “collective individual”. This structure of claims is vulnerable to philosophical deconstruction (Gasché) and leads to individualist political conclusions (Althusser).

In the light of the Gramscian provenance of postmarxism, it is important to note that while the explicit target of Althusser’s critique was the Hegelian totality, Althusser is equally critical of the aleatory posture of Gramsci’s “absolute historicism,” regarding it as exemplary of the impasse of radicalised historicism (Reading Capital). Althusser argues that Gramsci preserves the philosophical structure of historicism exemplified by Lukács and so the criticism of “expressive totality,” or spiritual holism, also applies to Gramsci. According to Gramsci, “the philosophy of praxis is absolute ‘historicism,’ the absolute secularisation and earthiness of thought, an absolute humanism of history”. Gramsci’s is an “absolute” historicism because it subjects the “absolute knowledge” supposed to be possible at the Hegelian “end of history” to historicisation-relativisation: instead of absolute knowledge, every truly universal worldview becomes merely the epochal totalisation of the present. Consequently, Gramsci rejects the conception that a social agent might aspire to “absolute knowledge” by adopting the “perspective of totality”. If anything, this exacerbates the problems of historicism by bringing the inherent relativism of the position to the surface. Ideology, conceptualised as the worldview of a historical subject (revolutionary proletariat, hegemonic alliance), forms the foundation of the social field, because in the historicist lens a social system is cemented by the ideology of the dominant group. Philosophy (and by extension, theory) represents only the systematisation of ideology into a coherent doctrine, while politics is based on ideological manipulation as its necessary precondition. Thus, for historicism, every “theoretical” intervention is immediately a political act, and correlatively, theory becomes the direct servant of ideology.

Historicism. Thought of the Day 79.0

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Historicism is a relativist hermeneutics, which postulates the incommensurability of historical epochs or cultural formations and therefore denies the possibility of a general history or trans-cultural universals. Best described as “a critical movement insisting on the prime importance of historical context” to the interpretation of texts, actions and institutions, historicism emerges in reaction against both philosophical rationalism and scientific theory (Paul Hamilton – Historicism). According to Paul Hamilton’s general introduction:

Anti-Enlightenment historicism develops a characteristically double focus. Firstly, it is concerned to situate any statement – philosophical, historical, aesthetic, or whatever – in its historical context. Secondly, it typically doubles back on itself to explore the extent to which any historical enterprise inevitably reflects the interests and bias of the period in which it was written … [and] it is equally suspicious of its own partisanship.

It is sometimes supposed that a strategy of socio-historical contextualisation represents the alpha and omega of materialist analysis – e.g. Jameson’s celebrated claim (Fredric Jameson – The Political Unconscious) that “always historicise” is the imperative of historical materialism. On the contrary, that although necessary, contextualisation alone is radically insufficient. This strategy of historical contextualisation, suffers from three serious defects. The historicist problematic depends upon the reduction of every phenomenal field to an immanent network of differential relations and the consequent evacuation of the category of cause from its theoretical armoury (Joan Copjec-Read My Desire: Lacan against the Historicists). It is therefore unable to theorise the hierarchy of effective causes within an overdetermined phenomenon and must necessarily reduce to a descriptive list, progressively renouncing explanation for interpretation. Secondly, lacking a theoretical explanation of the unequal factors overdetermining a phenomenon, historicism necessarily flattens the causal network surrounding its object into a homogeneous field of co-equal components. As a consequence, historicism’s description of the social structure or historical sequence gravitates in the direction of a simple totality, where everything can be directly connected to everything else. Thirdly, the self-reflexive turn to historical inscription of the researcher’s position of enunciation into the contextual field results, on these assumptions, in a gesture of relativisation that cannot stop short of relativism. The familiar performative contradictions of relativism then ensure that historicism must support itself through an explicit or implicit appeal to a neutral metalinguistic framework, which typically takes the form of a historical master narrative or essentialist conception of the social totality. The final result of the historicist turn, therefore, is that this “materialist” analysis is in actuality a form of spiritual holism.

Historicism relies upon a variant of what Althusser called “expressive causality,” which acts through “the primacy of the whole as an essence of which the parts are no more than the phenomenal expressions” (Althusser & Balibar – Reading Capital). Expressive causality postulates an essential principle whose epiphenomenal expressions are microcosms of the whole. Whether this expressive totality is social or historical is a contingent question of theoretical preference. When the social field is regarded as an expressive totality, the institutional structures of a historical epoch – economy, politics, law, culture, philosophy and so on – are viewed as externalisations of an essential principle that is manifest in the apparent complexity of these phenomena. When the historical process is considered to be an expressive totality, a historical master narrative operates to guarantee that the successive historical epochs represent the unfolding of a single essential principle. Formally speaking, the problem with expressive (also known as “organic” and “spiritual”) totalities is that they postulate a homology between all the phenomena of the social totality, so that the social practices characteristic of the distinct structural instances of the complex whole of the social formation are regarded as secretly “the same”.

Something Out of Almost Nothing. Drunken Risibility.

Kant’s first antinomy makes the error of the excluded third option, i.e. it is not impossible that the universe could have both a beginning and an eternal past. If some kind of metaphysical realism is true, including an observer-independent and relational time, then a solution of the antinomy is conceivable. It is based on the distinction between a microscopic and a macroscopic time scale. Only the latter is characterized by an asymmetry of nature under a reversal of time, i.e. the property of having a global (coarse-grained) evolution – an arrow of time – or many arrows, if they are independent from each other. Thus, the macroscopic scale is by definition temporally directed – otherwise it would not exist.

On the microscopic scale, however, only local, statistically distributed events without dynamical trends, i.e. a global time-evolution or an increase of entropy density, exist. This is the case if one or both of the following conditions are satisfied: First, if the system is in thermodynamic equilibrium (e.g. there is degeneracy). And/or second, if the system is in an extremely simple ground state or meta-stable state. (Meta-stable states have a local, but not a global minimum in their potential landscape and, hence, they can decay; ground states might also change due to quantum uncertainty, i.e. due to local tunneling events.) Some still speculative theories of quantum gravity permit the assumption of such a global, macroscopically time-less ground state (e.g. quantum or string vacuum, spin networks, twistors). Due to accidental fluctuations, which exceed a certain threshold value, universes can emerge out of that state. Due to some also speculative physical mechanism (like cosmic inflation) they acquire – and, thus, are characterized by – directed non-equilibrium dynamics, specific initial conditions, and, hence, an arrow of time.

It is a matter of debate whether such an arrow of time is

1) irreducible, i.e. an essential property of time,

2) governed by some unknown fundamental and not only phenomenological law,

3) the effect of specific initial conditions or

4) of consciousness (if time is in some sense subjective), or

5) even an illusion.

Many physicists favour special initial conditions, though there is no consensus about their nature and form. But in the context at issue it is sufficient to note that such a macroscopic global time-direction is the main ingredient of Kant’s first antinomy, for the question is whether this arrow has a beginning or not.

Time’s arrow is inevitably subjective, ontologically irreducible, fundamental and not only a kind of illusion, thus if some form of metaphysical idealism for instance is true, then physical cosmology about a time before time is mistaken or quite irrelevant. However, if we do not want to neglect an observer-independent physical reality and adopt solipsism or other forms of idealism – and there are strong arguments in favor of some form of metaphysical realism -, Kant’s rejection seems hasty. Furthermore, if a Kantian is not willing to give up some kind of metaphysical realism, namely the belief in a “Ding an sich“, a thing in itself – and some philosophers actually insisted that this is superfluous: the German idealists, for instance -, he has to admit that time is a subjective illusion or that there is a dualism between an objective timeless world and a subjective arrow of time. Contrary to Kant’s thoughts: There are reasons to believe that it is possible, at least conceptually, that time has both a beginning – in the macroscopic sense with an arrow – and is eternal – in the microscopic notion of a steady state with statistical fluctuations.

Is there also some physical support for this proposal?

Surprisingly, quantum cosmology offers a possibility that the arrow has a beginning and that it nevertheless emerged out of an eternal state without any macroscopic time-direction. (Note that there are some parallels to a theistic conception of the creation of the world here, e.g. in the Augustinian tradition which claims that time together with the universe emerged out of a time-less God; but such a cosmological argument is quite controversial, especially in a modern form.) So this possible overcoming of the first antinomy is not only a philosophical conceivability but is already motivated by modern physics. At least some scenarios of quantum cosmology, quantum geometry/loop quantum gravity, and string cosmology can be interpreted as examples for such a local beginning of our macroscopic time out of a state with microscopic time, but with an eternal, global macroscopic timelessness.

To put it in a more general, but abstract framework and get a sketchy illustration, consider the figure.

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Physical dynamics can be described using “potential landscapes” of fields. For simplicity, here only the variable potential (or energy density) of a single field is shown. To illustrate the dynamics, one can imagine a ball moving along the potential landscape. Depressions stand for states which are stable, at least temporarily. Due to quantum effects, the ball can “jump over” or “tunnel through” the hills. The deepest depression represents the ground state.

In the common theories the state of the universe – the product of all its matter and energy fields, roughly speaking – evolves out of a metastable “false vacuum” into a “true vacuum” which has a state of lower energy (potential). There might exist many (perhaps even infinitely many) true vacua which would correspond to universes with different constants or laws of nature. It is more plausible to start with a ground state which is the minimum of what physically can exist. According to this view an absolute nothingness is impossible. There is something rather than nothing because something cannot come out of absolutely nothing, and something does obviously exist. Thus, something can only change, and this change might be described with physical laws. Hence, the ground state is almost “nothing”, but can become thoroughly “something”. Possibly, our universe – and, independent from this, many others, probably most of them having different physical properties – arose from such a phase transition out of a quasi atemporal quantum vacuum (and, perhaps, got disconnected completely). Tunneling back might be prevented by the exponential expansion of this brand new space. Because of this cosmic inflation the universe not only became gigantic but simultaneously the potential hill broadened enormously and got (almost) impassable. This preserves the universe from relapsing into its non-existence. On the other hand, if there is no physical mechanism to prevent the tunneling-back or makes it at least very improbable, respectively, there is still another option: If infinitely many universes originated, some of them could be long-lived only for statistical reasons. But this possibility is less predictive and therefore an inferior kind of explanation for not tunneling back.

Another crucial question remains even if universes could come into being out of fluctuations of (or in) a primitive substrate, i.e. some patterns of superposition of fields with local overdensities of energy: Is spacetime part of this primordial stuff or is it also a product of it? Or, more specifically: Does such a primordial quantum vacuum have a semi-classical spacetime structure or is it made up of more fundamental entities? Unique-universe accounts, especially the modified Eddington models – the soft bang/emergent universe – presuppose some kind of semi-classical spacetime. The same is true for some multiverse accounts describing our universe, where Minkowski space, a tiny closed, finite space or the infinite de Sitter space is assumed. The same goes for string theory inspired models like the pre-big bang account, because string and M- theory is still formulated in a background-dependent way, i.e. requires the existence of a semi-classical spacetime. A different approach is the assumption of “building-blocks” of spacetime, a kind of pregeometry also the twistor approach of Roger Penrose, and the cellular automata approach of Stephen Wolfram. The most elaborated accounts in this line of reasoning are quantum geometry (loop quantum gravity). Here, “atoms of space and time” are underlying everything.

Though the question whether semiclassical spacetime is fundamental or not is crucial, an answer might be nevertheless neutral with respect of the micro-/macrotime distinction. In both kinds of quantum vacuum accounts the macroscopic time scale is not present. And the microscopic time scale in some respect has to be there, because fluctuations represent change (or are manifestations of change). This change, reversible and relationally conceived, does not occur “within” microtime but constitutes it. Out of a total stasis nothing new and different can emerge, because an uncertainty principle – fundamental for all quantum fluctuations – would not be realized. In an almost, but not completely static quantum vacuum however, macroscopically nothing changes either, but there are microscopic fluctuations.

The pseudo-beginning of our universe (and probably infinitely many others) is a viable alternative both to initial and past-eternal cosmologies and philosophically very significant. Note that this kind of solution bears some resemblance to a possibility of avoiding the spatial part of Kant’s first antinomy, i.e. his claimed proof of both an infinite space without limits and a finite, limited space: The theory of general relativity describes what was considered logically inconceivable before, namely that there could be universes with finite, but unlimited space, i.e. this part of the antinomy also makes the error of the excluded third option. This offers a middle course between the Scylla of a mysterious, secularized creatio ex nihilo, and the Charybdis of an equally inexplicable eternity of the world.

In this context it is also possible to defuse some explanatory problems of the origin of “something” (or “everything”) out of “nothing” as well as a – merely assumable, but never provable – eternal cosmos or even an infinitely often recurring universe. But that does not offer a final explanation or a sufficient reason, and it cannot eliminate the ultimate contingency of the world.

Conformal Factor. Metric Part 3.

Part 1 and Part 2.

Suppose gab is a metric on a manifold M, ∇ is the derivative operator on M compatible with gab, and Rabcd is associated with ∇. Then Rabcd (= gam Rmbcd) satisfies the following conditions.

(1) Rab(cd) = 0.

(2) Ra[bcd] = 0.

(3) R(ab)cd = 0.

(4) Rabcd = Rcdab.

Conditions (1) and (2) follow directly from clauses (2) and (3) of proposition, which goes like

Suppose ∇ is a derivative operator on the manifold M. Then the curvature tensor field Rabcd associated with ∇ satisfies the following conditions:

(1) For all smooth tensor fields αa1…arb1 …bs on M,

2∇[cd] αa1…arb1 …bs = αa1…arnb2…bs Rnb1cd +…+ αa1…arb1…bs-1n Rnbscd – αna2…arb1…bs Ra1ncd -…- αa1…ar-1nb1…bs Rarncd.

(2) Rab(cd) = 0.

(3) Ra[bcd] = 0.

(4) ∇[mRa|b|cd (Bianchi’s identity).

And by clause (1) of that proposition, we have, since ∇agbc = 0,

0 = 2∇[cd]gab = gnbRnacd + ganRnbcd = Rbacd + Rabcd.

That gives us (3). So it will suffice for us to show that clauses (1) – (3) jointly imply (4). Note first that

0 = Rabcd + Radbc + Racdb

= Rabcd − Rdabc − Racbd.

(The first equality follows from (2), and the second from (1) and (3).) So anti-symmetrization over (a, b, c) yields

0 = R[abc]d −Rd[abc] −R[acb]d.

The second term is 0 by clause (2) again, and R[abc]d = −R[acb]d. So we have an intermediate result:

R[abc]d = 0 —– (1)

Now consider the octahedron in the figure below.

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Using conditions (1) – (3) and equation (1), one can see that the sum of the terms corresponding to each triangular face vanishes. For example, the shaded face determines the sum

Rabcd + Rbdca + Radbc = −Rabdc − Rbdac − Rdabc = −3R[abd]c = 0

So if we add the sums corresponding to the four upper faces, and subtract the sums corresponding to the four lower faces, we get (since “equatorial” terms cancel),

4Rabcd −4Rcdab = 0

This gives us (4).

We say that two metrics gab and g′ab on a manifold M are projectively equivalent if their respective associated derivative operators are projectively equivalent – i.e., if their associated derivative operators admit the same geodesics up to reparametrization. We say that they are conformally equivalent if there is a map : M → R such that

g′ab = Ω2gab

is called a conformal factor. (If such a map exists, it must be smooth and non-vanishing since both gab and g′ab are.) Notice that if gab and g′ab are conformally equivalent, then, given any point p and any vectors ξa and ηa at p, they agree on the ratio of their assignments to the two; i.e.,

(g′ab ξa ξa)/(gab ηaηb) =  (gab ξa ξb)/(g′ab ηaηb)

(if the denominators are non-zero).

If two metrics are conformally equivalent with conformal factor, then the connecting tensor field Cabc that links their associated derivative operators can be expressed as a function of Ω.

Charlottesville

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The whole debacle illustrates several major problems with the non-mainstream Right. They are:

1) Lack of a moral compass which allows malign elements to infiltrate the group.
2) High T, Low IQ membership which favours unthinking intuitive action.
3) A lack of an understanding of what it means to be Right.
4) A lack of an understanding of what we are up against.

Still, the events represent a strategic victory for the Dissident Right. And by Dissident Right, it is as Gottfried originally envisaged it. A Right that was built upon the traditions and identity of the West minus the modernistic ideologies trying to infiltrate it. The Charlottesville debacle seems to have pushed enough people to disavow themselves from the Natsocs which makes me think that future infiltration by them will be neutralised. They are now persona non grata. The Social Pathologist dissects it.

Unique Derivative Operator: Reparametrization. Metric Part 2.

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Moving on from first part.

Suppose ∇ is a derivative operator, and gab is a metric, on the manifold M. Then ∇ is compatible with gab iff ∇a gbc = 0.

Suppose γ is an arbitrary smooth curve with tangent field ξa and λa is an arbitrary smooth field on γ satisfying ξnnλa = 0. Then

ξnn(gabλaλb) = gabλaξnnλb + gabλbξnnλa + λaλbξnngab

= λaλbξnngab

Suppose first that ∇ngab = 0. Then it follows immediately that ξnngabλaλb = 0. So ∇ is compatible with gab. Suppose next that ∇ is compatible with gab. Then ∀ choices of γ and λa (satisfying ξnnλa =0), we have λaλbξnngab = 0. Since the choice of λa (at any particular point) is arbitrary and gab is symmetric, it follows that ξnngab = 0. But this must be true for arbitrary ξa (at any particular point), and so we have ∇ngab = 0.

Note that the condition of compatibility is also equivalent to ∇agbc = 0. Hence,

0 = gbnaδcn = gbna(gnrgrc) = gbngnragrc + gbngrcagnr

= δbragrc + gbngrcagnr = ∇agbc + gbngrcagnr.

So if ∇agbc = 0,it follows immediately that ∇agbc = 0. Conversely, if ∇agbc =0, then gbngrcagnr = 0. And therefore,

0 = gpbgscgbngrcagnr = δnpδrsagnr = ∇agps

The basic fact about compatible derivative operators is the following.

Suppose gab is a metric on the manifold M. Then there is a unique derivative operator on M that is compatible with gab.

It turns out that if a manifold admits a metric, then it necessarily satisfies the countable cover condition. And then it guarantees the existence of a derivative operator.) We do prove that if M admits a derivative operator ∇, then it admits exactly one ∇′ that is compatible with gab.

Every derivative operator ∇′ on M can be realized as ∇′ = (∇, Cabc), where Cabc is a smooth, symmetric field on M. Now

∇′agbc = ∇agbc + gnc Cnab + gbn Cnac = ∇agbc + Ccab + Cbac. So ∇′ will be compatible with gab (i.e., ∇′agbc = 0) iff

agbc = −Ccab − Cbac —– (1)

Thus it suffices for us to prove that there exists a unique smooth, symmetric field Cabc on M satisfying equation (1). To do so, we write equation (1) twice more after permuting the indices:

cgab = −Cbca − Cacb,

bgac = −Ccba − Cabc

If we subtract these two from the first equation, and use the fact that Cabc is symmetric in (b, c), we get

Cabc = 1/2 (∇agbc − ∇bgac − ∇cgab) —– (2)

and, therefore,

Cabc = 1/2 gan (∇ngbc − ∇bgnc − ∇cgnb) —– (3)

This establishes uniqueness. But clearly the field Cabc defined by equation (3) is smooth, symmetric, and satisfies equation (1). So we have existence as well.

In the case of positive definite metrics, there is another way to capture the significance of compatibility of derivative operators with metrics. Suppose the metric gab on M is positive definite and γ : [s1, s2] → M is a smooth curve on M. We associate with γ a length

|γ| = ∫s1s2 gabξaξb ds,

where ξa is the tangent field to γ. This assigned length is invariant under reparametrization. For suppose σ : [t1, t2] → [s1, s2] is a diffeomorphism we shall write s = σ(t) and ξ′a is the tangent field of γ′ = γ ◦ σ : [t1, t2] → M. Then

ξ′a = ξads/dt

We may as well require that the reparametrization preserve the orientation of the original curve – i.e., require that σ (t1) = s1 and σ (t2) = s2. In this case, ds/dt > 0 everywhere. (Only small changes are needed if we allow the reparametrization to reverse the orientation of the curve. In that case, ds/dt < 0 everywhere.) It

follows that

|γ’| = ∫t1t2 (gabξ′aξ′b)1/2 dt = ∫t1t2 (gabξaξb)1/2 ds/dt

= ∫s1s2 (gabξaξb)1/2 ds = |γ|

Let us say that γ : I → M is a curve from p to q if I is of the form [s1, s2], p = γ(s1), and q = γ(s2). In this (positive definite) case, we take the distance from p to q to be

d(p,q)=g.l.b. |γ|:γ is a smooth curve from p to q.

Further, we say that a curve γ : I → M is minimal if, for all s ∈ I, ∃ an ε > 0 such that, for all s1, s2 ∈ I with s1 ≤ s ≤ s2, if s2 − s1 < ε and if γ′ = γ|[s1, s2] (the restriction of γ to [s1, s2]), then |γ′| = d(γ(s1), γ(s2)) . Intuitively, minimal curves are “locally shortest curves.” Certainly they need not be “shortest curves” outright. (Consider, for example, two points on the “equator” of a two-sphere that are not antipodal to one another. An equatorial curve running from one to the other the “long way” qualifies as a minimal curve.)

One can characterize the unique derivative operator compatible with a positive definite metric gab in terms of the latter’s associated minimal curves. But in doing so, one has to pay attention to parametrization.

Let us say that a smooth curve γ : I → M with tangent field ξa is parametrized by arc length if ∀ ξa, gabξaξb = 1. In this case, if I = [s1, s2], then

|γ| = ∫s1s2 (gabξaξb)1/2 ds = ∫s1s2 1.ds = s2 – s1

Any non-trivial smooth curve can always be reparametrized by arc length.

Metric. Part 1.

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A (semi-Riemannian) metric on a manifold M is a smooth field gab on M that is symmetric and invertible; i.e., there exists an (inverse) field gbc on M such that gabgbc = δac.

The inverse field gbc of a metric gab is symmetric and unique. It is symmetric since

gcb = gnb δnc = gnb(gnm gmc) = (gmn gnb)gmc = δmb gmc = gbc

(Here we use the symmetry of gnm for the third equality.) It is unique because if g′bc is also an inverse field, then

g′bc = g′nc δnb = g′nc(gnm gmb) = (gmn g′nc) gmb = δmc gmb = gcb = gbc

(Here again we use the symmetry of gnm for the third equality; and we use the symmetry of gcb for the final equality.) The inverse field gbc of a metric gab is smooth. This follows, essentially, because given any invertible square matrix A (over R), the components of the inverse matrix A−1 depend smoothly on the components of A.

The requirement that a metric be invertible can be given a second formulation. Indeed, given any field gab on the manifold M (not necessarily symmetric and not necessarily smooth), the following conditions are equivalent.

(1) There is a tensor field gbc on M such that gabgbc = δac.

(2) ∀ p in M, and all vectors ξa at p, if gabξa = 0, then ξa =0.

(When the conditions obtain, we say that gab is non-degenerate.) To see this, assume first that (1) holds. Then given any vector ξa at any point p, if gab ξa = 0, it follows that ξc = δac ξa = gbc gab ξa = 0. Conversely, suppose that (2) holds. Then at any point p, the map from (Mp)a to (Mp)b defined by ξa → gab ξa is an injective linear map. Since (Mp)a and (Mp)b have the same dimension, it must be surjective as well. So the map must have an inverse gbc defined by gbc(gab ξa) = ξc or gbc gab = δac.

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In the presence of a metric gab, it is customary to adopt a notation convention for “lowering and raising indices.” Consider first the case of vectors. Given a contravariant vector ξa at some point, we write gab ξa as ξb; and given a covariant vector ηb, we write gbc ηb as ηc. The notation is evidently consistent in the sense that first lowering and then raising the index of a vector (or vice versa) leaves the vector intact.

One would like to extend this notational convention to tensors with more complex index structure. But now one confronts a problem. Given a tensor αcab at a point, for example, how should we write gmc αcab? As αmab? Or as αamb? Or as αabm? In general, these three tensors will not be equal. To get around the problem, we introduce a new convention. In any context where we may want to lower or raise indices, we shall write indices, whether contravariant or covariant, in a particular sequence. So, for example, we shall write αabc or αacb or αcab. (These tensors may be equal – they belong to the same vector space – but they need not be.) Clearly this convention solves our problem. We write gmc αabc as αabm; gmc αacb as αamb; and so forth. No ambiguity arises. (And it is still the case that if we first lower an index on a tensor and then raise it (or vice versa), the result is to leave the tensor intact.)

We claimed in the preceding paragraph that the tensors αabc and αacb (at some point) need not be equal. Here is an example. Suppose ξ1a, ξ2a, … , ξna is a basis for the tangent space at a point p. Further suppose αabc = ξia ξjb ξkc at the point. Then αacb = ξia ξjc ξkb. Hence, lowering indices, we have αabc =ξia ξjb ξkc but αacb =ξia ξjc ξib at p. These two will not be equal unless j = k.

We have reserved special notation for two tensor fields: the index substiution field δba and the Riemann curvature field Rabcd (associated with some derivative operator). Our convention will be to write these as δab and Rabcd – i.e., with contravariant indices before covariant ones. As it turns out, the order does not matter in the case of the first since δab = δba. (It does matter with the second.) To verify the equality, it suffices to observe that the two fields have the same action on an arbitrary field αb:

δbaαb = (gbngamδnmb = gbnganαb = gbngnaαb = δabαb

Now suppose gab is a metric on the n-dimensional manifold M and p is a point in M. Then there exists an m, with 0 ≤ m ≤ n, and a basis ξ1a, ξ2a,…, ξna for the tangent space at p such that

gabξia ξib = +1 if 1≤i≤m

gabξiaξib = −1 if m<i≤n

gabξiaξjb = 0 if i ≠ j

Such a basis is called orthonormal. Orthonormal bases at p are not unique, but all have the same associated number m. We call the pair (m, n − m) the signature of gab at p. (The existence of orthonormal bases and the invariance of the associated number m are basic facts of linear algebraic life.) A simple continuity argument shows that any connected manifold must have the same signature at each point. We shall henceforth restrict attention to connected manifolds and refer simply to the “signature of gab

A metric with signature (n, 0) is said to be positive definite. With signature (0, n), it is said to be negative definite. With any other signature it is said to be indefinite. A Lorentzian metric is a metric with signature (1, n − 1). The mathematics of relativity theory is, to some degree, just a chapter in the theory of four-dimensional manifolds with Lorentzian metrics.

Suppose gab has signature (m, n − m), and ξ1a, ξ2a, . . . , ξna is an orthonormal basis at a point. Further, suppose μa and νa are vectors there. If

μa = ∑ni=1 μi ξia and νa = ∑ni=1 νi ξia, then it follows from the linearity of gab that

gabμa νb = μ1ν1 +…+ μmνm − μ(m+1)ν(m+1) −…−μnνn.

In the special case where the metric is positive definite, this comes to

gabμaνb = μ1ν1 +…+ μnνn

And where it is Lorentzian,

gab μaνb = μ1ν1 − μ2ν2 −…− μnνn

Metrics and derivative operators are not just independent objects, but, in a quite natural sense, a metric determines a unique derivative operator.

Suppose gab and ∇ are both defined on the manifold M. Further suppose

γ : I → M is a smooth curve on M with tangent field ξa and λa is a smooth field on γ. Both ∇ and gab determine a criterion of “constancy” for λa. λa is constant with respect to ∇ if ξnnλa = 0 and is constant with respect to gab if gab λa λb is constant along γ – i.e., if ξnn (gab λa λb = 0. It seems natural to consider pairs gab and ∇ for which the first condition of constancy implies the second. Let us say that ∇ is compatible with gab if, for all γ and λa as above, λa is constant w.r.t. gab whenever it is constant with respect to ∇.