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.

“approximandum,” will not be General Theory of Relativity, but only its vacuum sector of spacetimes of topology Σ × R, or quantum gravity as a fecund ground for metaphysician. Note Quote.

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In string theory as well as in Loop Quantum Gravity, and in other approaches to quantum gravity, indications are coalescing that not only time, but also space is no longer a fundamental entity, but merely an “emergent” phenomenon that arises from the basic physics. In the language of physics, spacetime theories such as GTR are “effective” theories and spacetime itself is “emergent”. However, unlike the notion that temperature is emergent, the idea that the universe is not in space and time arguably shocks our very idea of physical existence as profoundly as any scientific revolution ever did. It is not even clear whether we can coherently formulate a physical theory in the absence of space and time. Space disappears in LQG insofar as the physical structures it describes bear little, if any, resemblance to the spatial geometries found in GTR. These structures are discrete and not continuous as classical spacetimes are. They represent the fundamental constitution of our universe that correspond, somehow, to chunks of physical space and thus give rise – in a way yet to be elucidated – to the spatial geometries we find in GTR. The conceptual problem of coming to grasp how to do physics in the absence of an underlying spatio-temporal stage on which the physics can play out is closely tied to the technical difficulty of mathematically relating LQG back to GTR. Physicists have yet to fully understand how classical spacetimes emerge from the fundamental non-spatio-temporal structure of LQG, and philosophers are only just starting to study its conceptual foundations and the implications of quantum gravity in general and of the disappearance of space-time in particular. Even though the mathematical heavy-lifting will fall to the physicists, there is a role for philosophers here in exploring and mapping the landscape of conceptual possibilites, bringing to bear the immense philosophical literature in emergence and reduction which offers a variegated conceptual toolbox.

To understand how classical spacetime re-emerges from the fundamental quantum structure involves what the physicists call “taking the classical limit.” In a sense, relating the spin network states of LQG back to the spacetimes of GTR is a reversal of the quantization procedure employed to formulate the quantum theory in the first place. Thus, while the quantization can be thought of as the “context of discovery,” finding the classical limit that relates the quantum theory of gravity to GTR should be considered the “context of (partial) justification.” It should be emphasized that understanding how (classical) spacetime re-emerges by retrieving GTR as a low-energy limit of a more fundamental theory is not only important to “save the appearances” and to accommodate common sense – although it matters in these respects as well, but must also be considered a methodologically central part of the enterprise of quantum gravity. If it cannot be shown that GTR is indeed related to LQG in some mathematically well-understood way as the approximately correct theory when energies are sufficiently low or, equivalently, when scales are sufficiently large, then LQG cannot explain why GTR has been empirically as successful as it has been. But a successful theory can only be legitimately supplanted if the successor theory not only makes novel predictions or offers deeper explanations, but is also able to replicate the empirical success of the theory it seeks to replace.

Ultimately, of course, the full analysis will depend on the full articulation of the theory. But focusing on the kinematical level, and thus avoiding having to fully deal with the problem of time, lets apply the concepts to the problem of the emergence of full spacetime, rather than just time. Chris Isham and Butterfield identify three types of reductive relations between theories: definitional extension, supervenience, and emergence, of which only the last has any chance of working in the case at hand. For Butterfield and Isham, a theory T1 emerges from another theory T2 just in case there exists either a limiting or an approximating procedure to relate the two theories (or a combination of the two). A limiting procedure is taking the mathematical limit of some physically relevant parameters, in general in a particular order, of the underlying theory in order to arrive at the emergent theory. A limiting procedure won’t work, at least not by itself, due to technical problems concerning the maximal loop density as well as to what essentially amounts to the measurement problem familiar from non-relativistic quantum physics.

An approximating procedure designates the process of either neglecting some physical magni- tudes, and justifying such neglect, or selecting a proper subset of states in the state space of the approximating theory, and justifying such selection, or both, in order to arrive at a theory whose values of physical quantities remain sufficiently close to those of the theory to be approximated. Note that the “approximandum,” the theory to be approximated, in our case will not be GTR, but only its vacuum sector of spacetimes of topology Σ × R. One of the central questions will be how the selection of states will be justified. Such a justification would be had if we could identify a mechanism that “drives the system” to the right kind of states. Any attempt to finding such a mechanism will foist a host of issues known from the traditional problem of relating quantum to classical mechanics upon us. A candidate mechanism, here and there, is some form of “decoherence,” even though that standardly involves an “environment” with which the system at stake can interact. But the system of interest in our case is, of course, the universe, which makes it hard to see how there could be any outside environment with which the system could interact. The challenge then is to conceptualize decoherence is a way to circumvents this problem.

Once it is understood how classical space and time disappear in canonical quantum gravity and how they might be seen to re-emerge from the fundamental, non-spatiotemporal structure, the way in which classicality emerges from the quantum theory of gravity does not radically differ from the way it is believed to arise in ordinary quantum mechanics. The project of pursuing such an understanding is of relevance and interest for at least two reasons. First, important foundational questions concerning the interpretation of, and the relation between, theories are addressed, which can lead to conceptual clarification of the foundations of physics. Such conceptual progress may well prove to be the decisive stepping stone to a full quantum theory of gravity. Second, quantum gravity is a fertile ground for any metaphysician as it will inevitably yield implications for specifically philosophical, and particularly metaphysical, issues concerning the nature of space and time.

Mapping Fields. Quantum Field Gravity. Note Quote.

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Introducing a helpful taxonomic scheme, Chris Isham proposed to divide the many approaches to formulating a full, i.e. not semi-classical, quantum theory of gravity into four broad types of approaches: first, those quantizing GR; second, those “general-relativizing” quantum physics; third, construct a conventional quantum theory including gravity and regard GR as its low-energy limit; and fourth, consider both GR and conventional quantum theories of matter as low-energy limits of a radically novel fundamental theory.

The first family of strategies starts out from classical GR and seek to apply, in a mathematically rigorous and physically principled way, a “quantization” procedure, i.e. a recipe for cooking up a quantum theory from a classical theory such as GR. Of course, quantization proceeds, metaphysically speaking, backwards in that it starts out from the dubious classical theory – which is found to be deficient and hence in need of replacement – and tries to erect the sound building of a quantum theory of gravity on its ruin. But it should be understood, just like Wittgenstein’s ladder, as a methodologically promising means to an end. Quantization procedures have successfully been applied elsewhere in physics and produced, among others, important theories such as quantum electrodynamics.

The first family consists of two genera, the now mostly defunct covariant ansatz (Defunct because covariant quantizations of GR are not perturbatively renormalizable, a flaw usually considered fatal. This is not to say, however, that covariant techniques don’t play a role in contemporary quantum gravity.) and the vigorous canonical quantization approach. A canonical quantization requires that the theory to be quantized is expressed in a particular formalism, the so-called constrained Hamiltonian formalism. Loop quantum gravity (LQG) is the most prominent representative of this camp, but there are other approaches.

Secondly, there is to date no promising avenue to gaining a full quantum theory of gravity by “general-relativizing” quantum (field) theories, i.e. by employing techniques that permit the full incorporation of the lessons of GR into a quantum theory. The only existing representative of this approach consists of attempts to formulate a quantum field theory on a curved rather than the usual flat background spacetime. The general idea of this approach is to incorporate, in some local sense, GR’s principle of general covariance. It is important to note that, however, that the background spacetime, curved though it may be, is in no way dynamic. In other words, it cannot be interpreted, as it can in GR, to interact with the matter fields.

The third group also takes quantum physics as its vantage point, but instead of directly incorporating the lessons of GR, attempts to extend quantum physics with means as conventional as possible in order to include gravity. GR, it is hoped, will then drop out of the resulting theory in its low-energy limit. By far the most promising member of this family is string theory, which, however, goes well beyond conventional quantum field theory, both methodologically and in terms of ambition. Despite its extending the assumed boundaries of the family, string theory still takes conventional quantum field theory as its vantage point, both historically and systematically, and does not attempt to build a novel theory of quantum gravity dissociated from “old” physics. Again, there are other approaches in this family, such as topological quantum field theory, but none of them musters substantial support among physicists.

The fourth and final group of the Ishamian taxonomy is most aptly characterized by its iconoclastic attitude. For the heterodox approaches of this type, no known physics serves as starting point; rather, radically novel perspectives are considered in an attempt to formulate a quantum theory of gravity ab initio.

All these approaches have their attractions and hence their following. But all of them also have their deficiencies. To list them comprehensively would go well beyond the present endeavour. Apart from the two major challenges for LQG, a major problem common to all of them is their complete lack of a real connection to observations or experiments. Either the theory is too flexible so as to be able to accommodate almost any empirical data, such as string theory’s predictions of supersymmetric particles which have been constantly revised in light of particle detectors’ failures to find them at the predicted energies or as string theory’s embarras de richesses, the now notorious “landscape problem” of choosing among 10500 different models. Or the connection between the mostly understood data and the theories is highly tenuous and controversial, such as the issue of how and whether data narrowly confining possible violations of Lorentz symmetry relate to theories of quantum gravity predicting or assuming a discrete spacetime structure that is believed to violate, or at least modify, the Lorentz symmetry so well confirmed at larger scales. Or the predictions made by the theories are only testable in experimental regimes so far removed from present technological capacities, such as the predictions of LQG that spacetime is discrete at the Planck level at a quintillion (1018) times the energy scales probed by the Large Hadron Collider at CERN. Or simply no one remotely has a clue as to how the theory might connect to the empirical, such as is the case for the inchoate approaches of the fourth group like causal set theory.

Loop Quantum Gravity and Nature of Reality. Briefer.

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To some “loop quantum gravity is an attempt to define a quantization of gravity paying special attention to the conceptual lessons of general relativity”, while to others it does not have to be about the quantization of gravity but should be “at least conceivable that such a theory marries a classical understanding of gravity with a quantum understanding of matter”

The term ‘loop’ comes from the solution written for every line closed on itself on the proposed structure of quanta’s interactions. John Archibald Wheeler was one of the pioneers in constructing a representation of space which had a granular structure on a very small scale. Together with Bryce DeWitt they produced a mathematical formula known as Wheeler-DeWitt equation, “an equation which should determine the probability of one or another curved space”. The starting point was spacetime of general relativity having “loop-like states”. Having a quantum approach to gravity on closed loops, which are threads of the Faraday lines of the quantum field, constitutes a gravitational field which looks like a spiderweb. A solution could be written for every line closed on itself. Moreover, every line determining a solution of the Wheeler-DeWitt equation describes one of the threads of the spiderweb created by Faraday force lines of the quantum field which are the threads with which the space is woven. The physical Hilbert space as the space of all quantum states of the theory solves all the constraints and thus ought to be considered as the physical states. This implies that the physical Hilbert space of Loop Quantum Gravity is not yet known. The larger space of states which satisfy the first two families of constraints is often termed the kinematical Hilbert space. The one constraint that has so far resisted resolution is the Hamiltonian constraint equation with the seemingly simple form Hˆ|ψ⟩ = 0, the Wheeler-DeWitt equation, where Hˆ is the Hamiltonian operator usually interpreted to generate the dynamical evolution and |ψ⟩ is a quantum state in the kinematical Hilbert space. Of course, the Hamiltonian operator Hˆ is a complicated function(al) of the basic operators corresponding to the basic canonical variables. In fact, the very functional form of Hˆ is debated as several inequivalent candidates are on the table. Insofar as the physical Hilbert space has thus not yet been constructed, Loop Quantum Gravity remains incomplete.

Space, then, is defined based on the nodes on this spiderweb, which is called a spin network, and time, which already lost its fundamental status with special and general relativity, vanishes from the picture of the universe altogether.

Loop quantum gravity combines the dynamic spacetime approach of general relativity with quanta nature of gravity fields. Accordingly, space that bends and stretches are made up of very small particles which are called quanta of space. If one had eyes capable zooming into the space and seeing magnetic fields and quanta, then, by observing the space, one would first witness the quantum field, and then would end up seeing quanta which are extremely small and granular.