:: xx century philosophy on space·time
:: recommended links and bibliography





:: xx century philosophy on space·time


: hegel

Although idealism doesn't mathematically deal with the notion of time, it is reasonable to think that as long as it tries to bridge the gap between subject and object, between the I and Nature [thus arriving at the notion of Spirit, the Absolute, a conceptual I], the notion of time becomes no longer a formal a priori frame nor a perpetual becoming.

In fact, time for Hegel is the I=I principle; it is pure self·consciousness. Hegelian analysis is related to Aristotelian as it stresses the inseparatibility of space and time. But as a whole, time only appears as the atemporal unfolding of the Idea, in such a way that temporality is merely the epiphany of the Idea or the Spirit.


: martin heidegger

Heidegger's philosophy is focused on the issue of temporality. In his work Being and Time, he tries to explain the relation between both concepts, but focuses mainly on the analysis of the relation between the being·there and time. He distinguishes a traditional notion of time [an a priori frame where events unfold in succesion] from the ontological notion of temporality, which far from being conceived as a priori, derives from the being·there's structure. According to Heidegger, it is senseless to differentiate a before, from a now and an after. Since Death is the most common outcome of existence, he'll denominate each referential moment of the being·there [present, past and future] as «ecstasy».


: wittgenstein

It seems that we don't really know what space is, so maybe we shouldn't have the right to name it. | Wittgenstein

Firstly, we must point out that when Wittgenstein wonders what space·time is, the object of his question isn't space·time itself but the grammar of the word space·time. When someone asks himself what space is, he compulsively searches "for a meaning, a sense, and when he doesn't find it he assumes that what he's looking for must be an ethereal thing.” That is to say, if you're going to talk about time do so only within certain context: “I don't have time to read your gibberish" for instance. And only thus, your listener will be able to grasp what you mean when you use the word “time”.

What about space? Well, same thing, you can only conceive it within certain linguistic context, as when you say “There isn't much space here to waste with such gibberish”. Only by being exposed to these kinds of approximations we can familiarise ourselves with the terms "time" and "space". Of course, nobody teaches you in which contexts you can use these terms nor how.

So... what the hell is space for Wittgenstein, then? To express what space is we always apply terms like "extension", "interval", "length", etc. Any of these terms would require a 100 page essay itself. So summing up, we shouldn't search for any object or thing called "space" because "space" isn't usually applied to any material or substantial thing.

And as for time, he writes: “The philosopher asks himself: Is time the same thing as the events that take place in it? or is it the position of the clock-hand? And if it is replied that none of these is time itself, then the question arises ‘What then is time?’ And now one seeks some definition, e.g. ‘Time is the form of what happens’, ‘Time is the possibility of change’, etc., whereas the simple truth is that just this whole loose and complex pattern of speaking provides the true meaning of the word ‘time’ and that there is nothing else to be done other than describe the complete grammar of this word.”

Metaphysics may lead us in the search for something hidden, something substantial behind the term “space”, but “philosophy simply puts everything before us, and neither explains nor deduces anything. Since everything lies open to view there is nothing to explain.”


: presentism and eternalism

Everything past is unreal, everything future is unreal, everything imagined, absent, mental... is unreal... Ultimately real is only the present moment of physical efficiency. | Stcherbatsky

Presentism is the belief that there are no past nor future. Time is the order of various realities and at a specified moment, some things exist and some don't. This is the only reality we can conceive and we cannot say, for instance, that "Homer exists right now". Presentism is consistent with Galilean relativity, in which time is independent of space, but it's probably inconsistent with Lorentzian/Einsteinian relativity.

Saint Augustine proposed that the present is a knife edge between the past and the future and could not contain any extended period of time. This seems evident because, if the present is extended, it must have separate parts - but these must be simultaneous if they are truly part of the present. According to early philosophers time cannot be both past and simultaneously present, so it is not extended. Contrary to Saint Augustine, some philosophers [like William James] propose that conscious experience is extended in time. Other famous presentist philosophers are J. M. E. McTaggart [who wrote “The unreality of Time”] and various Buddhist philosophers of the Hindu tradition like Stcherbatsky.

Eternalism, on the other hand, builds on the standard method of modeling time as a dimension in physics, to give time a similar ontology to that of space. This would mean that time is just another dimension, that future events are "already there" [that is "Homer exists now!"], and that there is no objective flow of time. It is sometimes referred to as the "Block Time" or "Block Universe" theory due to its description of space·time as an unchanging four·dimensional "block", as opposed to the common·sense view of the world as a three·dimensional space modulated by the passage of time. Eternalism has become a very useful philosophy for phenomenological dialectics. The Swedish philosophers Alexander Bard and Jan Söderqvist have proposed the dialectic relation between eternalism and presentism as the foundation of paradoxical philosophy. In their work entitled “The Global Empire” [2003], they affirm that this philosophy is the best way to describe a contemporary understanding of the chaos·order dialectics in relation to perception, bearing in mind the implications of Heisenberg's Uncertainty principle.

Eternalism [Pali: sasatavada] related to Buddhism is the doctrine of the "eternal becoming" or eternal lives, "one life after the other" within the Samsara wheel. Buddhism, however, rejects eternalism and nihilism based on the notion that when a phenomenological object is analysed in its constituent parts, no eternal independent parts can be found. This notion is shared by the Vedanta and Neoplatonism, where the "eternal becoming" is a heresy and responds to the spirit's weakness identified to matter and the perpetual reincarnation into another form.


: endurantism and perdurantism

Endurantism is a theory of persistence and identity. According to the endurantist view material objects are persisting three·dimensional individuals wholly present at every moment of their existence. A perdurantist believes instead that objects have distinct temporal parts which exist as a continuous reality. The use of "endure" and "perdure" to distinguish two ways in which an object can be thought to persist can be traced to Lewis (1986). However, contemporary debate has demonstrated the difficulties in defining both terms.

For instance, Ted Sider's work in 2001 suggests that, although endurantist objects can have temoral parts, it is more exact to define perdurantism as the theory that defends the notion that the objects have temporal parts at any given moment of its existence. In 1996 Zimmerman opposed this idea because many perdurantists believe that time is divisible and that for each interval of time there is a sub·interval. Anyway, the debate remains open.
Perdurantists split into two groups:

· the “worm theorists”, who argue that a persistent object is composed of various temporal parts besides the spatial ones. All persistent objects are therefore four·dimensional worms extending in space·time.

· the Stage Theory argues that you only exist at an instantaneous moment in time. But as there are other temporal parts in other moments to which you're somehow related [like when you say "ah, when I was little…”], those moments are equally true, because you are intrinsically related to a temporal part that constituted the YOU that you were when you were little...


: conventionalism

Conventionalism states that all issues relative to space and time are determined by convention. As there are many non·euclidean geometries equally valid when it comes to describing the phenomenology of space, the "true" one will have to be determined by convention.

This perspective was updated to include Hans Reichenbach's ideas on relativistic physics. Reichenbach's conventionalism focuses on the idea of a coordinative definition. This has two main characteristics:

· it determines length units using certain phyisical objects [simply because we cannot make out an object's length without measuring it]. So we must chose a physical object, like the Standard Metre kept at the Bureau International des Poids et Mesures or Cadmium's wavelength, for instance, to determine our length unit.

· although we can supposedly prove the length correspondence of two rulers when they are next to each other, we can know nothing about their lengths when they are far apart. This impossibility eliminates our chances to determine the length correspondence between two distant objects. "Length correspondence" must be determined, therefore, by definition.

The geometry of space·time is determined according to a coordinative definition stating that "light travels equal distances in equal times”.


: temporalism | bergson, dilthey, husserl

Temporalism stirred last century's philosophy when it provided a new way to understand Time. Bergson criticises positivists' notion of psychic phenomena and explains how they either avoid the notion of time or reduce it to a kind of space, studying the states of consciousness as if they were external facts. For Bergson, duration encompasses the succession of conscious states in an immeasurable flow, and real time therefore is the experience of duration as apprehended by intuition, time perceived as indivisible. He is led to a theory of mind·body relations, opposing the preference of the separate operations of instinct and intellect. Bergson differentiates a spatialised time [physical time as studied by science] from an authentic time [the duration of consciousness]. Scientific time is always homogeneous, isotropic and reversible, whereas time as perceived by intuition is heterogeneous and irreversible, is pure novelty.

Dilthey conceives time as history: life is a reality that you cannot separate from history or interpret according to other categories such as substance, subject, etc. To explain events "from the outside" you need to introduce an implicated time to the narrative, because narration usually searches for structured forms of time. It implies not only a recoil from the notion of Time as a frame from which you can order, analyse and explain facts, but also that time was not set a priori or added a posteriori, it emerges from life itself as a historical event.

Also reacting against positivism, Husserl searches for the absolute keystone of philosophy within the conscious mind. He doesn't apply a natural science of consciousness but a phenomenology of consciousness, that is to say: an analysis, a description of phenomena impressing on the conscious mind [the "lived experiences"]. With this notion he will emphasise, very much like Bergson, the distinction of a physical time from a phenomenological time. Physical time doesn't determine a causistical order for the "lived experiences" as if they were instants of time: "lived experiences" are Temporality. And always inseparable, they constitute the flow of what's been lived [the real duration]. Temporality cannot be conceived without the conscious mind.


: symmetry | invariance and covariance principles

Under certain transformations, aspects of a system remain "unchanged" according to a particular observation. A symmetry of a physical system is a physical or mathematical feature of the system [observed or intrinsic] that is preserved under some change. The transformations may be continuous [such as rotation of a circle] or discrete [like the reflection of a bilaterally symmetric figure, or rotation of a regular polygon]. Continuous and discrete transformations give rise to corresponding types of symmetries. Symmetries are frequently amenable to mathematic formulation and can be exploited to simplify many problems.

Invariance is specified mathematically by transformations that leave some quantity unchanged. This idea can apply to basic real·world observations. For example, temperature may be constant throughout a room. Since the temperature is independent of position within the room, the temperature is invariant under a shift in the measurer's position. Similarly, a uniform sphere rotated about its center will appear exactly as it did before the rotation. The sphere is said to exhibit spherical symmetry. A rotation about any axis of the sphere will preserve how the sphere "looks". Invariance can also be applied to symmetries in forces.

Michael Friedman points out the distinction between invariance by mathematical transformation and covariance by transformation. Invariance or symmetry applies to objects; that is, the symmetry of space·time theory determines which objects' properties are invariable or absolute and which are variable or dynamic. Covariance applies to theory formulation and determines the range of coordinate systems where the laws of physics will still apply.

Many powerful theories in physics are described by Lagrangians [a function that summarizes the dynamics of the system] which are invariant under certain symmetry transformation groups. When they are invariant under a transformation identically performed at every point in the space in which the physical processes occur, they are said to have a global symmetry.

In a gauge theory the requirement of global transformations is relaxed such that the Lagrangian is required to have merely local symmetry. The importance of gauge theories for physics stems from the tremendous success of the mathematical formalism in providing a unified framework to describe the quantum field theories of electromagnetism, the weak force and the strong force. This theory, known as the Standard Model, accurately describes experimental predictions regarding three of the four fundamental forces of nature. Modern theories like string theory, as well as some formulations of general relativity, are, in one way or another, gauge theories.


: cyclic time vs. the arrow of time

The arrow of time is a term initially created by Eddington to define the directional aspect of time, proving that all phenomena take place in a certain order that flows from the past to the future. This aspect is tightly related to the linear notion of time and its one·dimensionality [distinguishing it from three·dimensional space].

Historically, the notion of an irreversible direction of time is quite recent, as in antiquity predominated the idea of a circular time related to the tidal cycles, the solstices and the four seasons. The individual experience of growth and death was placed within this cyclic·time frame to consider the possibility of a return. But judeo·christian tradition, influenced by the notion of a creation and an end of times and the irreversibility of Christ's passion, death and resurrection, believes in a linear time conceived as a flow from the past to the future. This linear time sets the basis for concepts like progress and evolution.

However, in all physics equations, time can be understood as a reversible magnitude: the time symmetry of physics equations is preserved [except for the weird K meson: its disintegration seems to be aware of the direction of time]. But the second principle of thermodynamics [which Bergson considers “the most metaphysical law of physics”], pointing out that the entropy increases in isolated systems, provides a criteria to determine the temporal orientation. For example, if you smash a statue into hundreds of fragments, the entropy has increased [the system has lower energy, is more "disordered"]. Well, experience shows us that the statue will NEVER be restored spontaneously. But according to Boltzmann's interpretation, this is so not because it is absolutely impossible but because it is highly improbable. The increase in entropy allows us to distinguish a past from a future. This notion is known as the "thermodynamic arrow of time”.

By studying systems far from equilibrium, some authors have stressed the essentially irreversability of time. But like Prigogine, for instance, they focus on biological systems, so they deal mainly with notions like evolution, complexity, increase of information, etc.] where the irreversibility of time seems to rule. In this context we also find studies on chaos and complexity, which explain the surge of self-organised phenomena from apparently structureless systems.

Psychologically, the arrow of time is established by arguing that we have memories of our past, but not of our future. This line of reasoning is known as the “psychological arrow of time”.

Contemporary cosmology states that the universe is expanding and this determines a "cosmological arrow of time". According to Stephen Hawking, the three arrows of time go together, they keep the same direction and are related to the anthropic principle. But according to Roger Penrose, only through the unification of general relativity and quantum mechanics we will finally understand what the arrow of time really is.


: relativism | mach, lorentz and einstein

Mach's principle is a theory about the nature of non·inertial forces stated for the first time by Ernst Mach in 1893. It affirms that the inertia of a body is determined in relation to all other bodies in the universe. Contrary to what sir Isaac Newton proposed in 1689, for Mach there is no absolute space, and he used the same thought-experiment presented by Newton himself to prove it [featuring a bucket full of water suspended from a fixed point in empty space; one of the most beautiful scientific debates ever, press here for more info].

Mach's principle influenced Albert Einstein when he was working on his General Theory of Relativity [although this principle doesn't have any precise mathematical formulation and constitutes no substantial part of Einstein's theory].

The Special Theory of Relativity relies on the idea that the laws of physics are the same for all observers in uniform motion, no matter the frame of reference. That is, there is no privileged inertial reference system as Newton believed. An ideal observer is a geometrical point in space·time placed at the vortex of a "lightcone" observing the events as they extend in time as well as in space. Thus, observers in different states of motion may disagree with the idea of simultaneity.

Lorentz contraction is the effect of temporal dilation, length contraction and the increase of inertial mass of a body or particle when it approaches speeds near to the speed of light. It was originally introduced by Lorentz as a way to explain the lack of positive results of the Michelson·Morley experiment [no matter how hard they tried, they couldn't measure the supposed changes in the speed of light when they travelled towards the light-source or receeded from it]. Lorentz contraction is defined by the following expression:



is the where L0 is the proper length (the length of the object in its rest frame), L1 is the length observed by an observer moving at speed V, and C is the speed of light. Note that in this equation it is assumed that the object is parallel with its line of movement. An observer at rest viewing an object travelling at the speed of light would observe the length of the object in the direction of motion as zero. Among other reasons, this suggests that objects with mass cannot travel at the speed of light.

In his General Theory of Relativity, Einstein states that an inertial frame of reference is the frame following a geodesic of space·time, and that if an object moves in any other direction, there must be a force acting on it. Using the notions of curved space proposed by mathematicians like Riemann, he determines that the curvature of space·time is created by the presence of matter, and that its tension [deformation] is proportional to the mass of the object. Therefore, gravitational acceleration could be defined as the geometrical property of space·time.

Even though Einstein denied the possibility of absolute simultaneity, he continued considering time as an order in succession. When considering time like a physical magnitude from the perspective of classical physics, time appeared like a reversible magnitude. That is why he affirmed that from the point of view of physics, "time is just an illusion”.


: geometrodynamics | John Wheeler

In the early 60's, the American physicist John Wheeler extended Einstein's work to build a more complete theory of the world based only in the geometry of empty space·time. His goal was to explain the existence of particles and forces in terms of geometrical structures. Thus, Wheeler's geometrodynamic model determines that, for example, an electrically charged particle is actually a kind of portal into a tiny tunnel communicating one point in space with another; something like a spatial bridge in another dimension. The end of the tunnel is the same particle but with the opposite electric charge. Thus, both ends of a "Wheeler hole" could be an electron·positron pair.

What xix century scientists called electric "lines of force" were contained within the charged particles; but for Wheeler these lines stretch along the tunnel to emerge on the other side.

Geometrodynamics is very charming, but it never worked completely. Wheeler himself wrote that its most evident failure was that it couldn't explain the spin 1/2 in general and to the neutrino in particular. Actually, the failure of geometrodynamics is said to be due to its restriction to four dimensions.

Wheeler believes that the ultimate solution will emerge from quantum physics and waits for the day when we will finally understand that the quantum is the fundamental constituent of reality.

It looks like that day has come.


: quantum space·time | what are time and space made of?

Quantum mechanics teaches us that the physics of the microscopic world's fundamental ingredient is the fact that energy isn't transferred in a continuous flux but in certain "bundles", quanta, indivisible portions of energy. One of the most attractive theories in the last years consists of supposing that at very high energy levels [very much like the state of the universe very little after it was originated at the big·bang] space·time itself stops being a continuum and manifests a granular or discrete structure. Thus it is postulated the existence of space·time quanta, minimal bundles of longitude, surface, volume and time. To gain an intuition on its dimensions, suffices to say that the "quantum" volume would be as tiny compared to an atomic nucleus as the volume of that a nucleus compared to a cubic metre of capacity.

One of the current research trends [where Ángel Ballesteros and Francisco Javier Herranz at the University of Burgos work] consists on studying how to DICRETIZAR spatial relativity in such a way that the granular structure be only visible in very small longitude scales and we recuperate the ordinary relativity theory in ordinary conditions. There are many possible "quantifications" of space·time and each one of these new models can be understood as a "theory of double relativity” in which, besides the speed of light there is a second fundamental constant: the typical length of granular structure of space·time itself.

The structure of what's infinitesimally small has consequences directly observable in the macroscopic world. Light wouldn't propagate the same way in a quantum space·time as it would in a continuum, and this effect could even be measured in the near future: it is hoped that GLAST satellite will be able to experimentally detect traces of this discretisation of space·time.


: superstrings and m-theory

M-Theory is a master theory that unifies the five superstring theories and is the result of the work of many theoreticians [including Chris Hull, Paul Townsend, Ashoke Sen, Jared Farris, Michael Duff and John H. Schwarz]. Taking each superstring theory as a different aspect of the same underlying theory, Witten proposed his M-Theory, still incomplete, but applicable to many situations.

Before these unifying theory, it was considered that superstrings were the fundamental constituents of the universe, but M-Theory adds another fundamental ingredient: the membrane [or brane]. A membrane is an object that may have different dimensions [from 0 to 9], thus being 0-brane = 1 dot. The inclusion of membranes doesn't contradict superstring theories because these didn't even took it into account.

In 1995 Joseph Polchinski discovered that in certain situations the loose ends of strings cannot move with total freedom, as they are stuck to certain regions of space. Polchinski reasoned that if the extremes of the open strings are restricted to move within the region of space they occupy, then that same space must be occupied by a membrane and demonstrated that this kind of sticky membranes may exert certain tension fixing the loose points of the strings and holding them within the region of space they occupy. But not all strings have loose ends and are confined to membranes. The gravitons are closed in loops and are completely free to move from membrane to membrane [which, by the way, makes them unique]. Researches speculate that this is reason why nor even the study of the weak force, the strong force and the electromagnetic force can indicate the possibility of extra dimensions, as the force carrier particles have loose ends and are therefore confined to inhabit the membranes].

Because of all this, experimentation with gravitation constitutes by many nowadays the only way of demonstrating the existence of extra spatial dimensions.


: the beautiful theory | a holographic universe?

The theoretical results related to the entropy of black holes lead us to conclude that the Universe may be a huge hologram. | Jacob D. Bekenstein

The absolute limits of information in certain region of space have been deduced from the study of the properties of black holes. Bearing in mind that those limits depend on the matter·energy contained within that space it is amazing that a limit can be deduced without even knowing [with absolute certainty] the ultimate constituent of matter. The key is in the entropy, defined in 1877 by Ludwig Boltzmann as the number of microscopic states in wich the particles composing a chunk of inert matter may be arranged, in such a way that it keeps on looking as the same chunk of matter from a macroscopic point of view.

When mathematician Claude E. Shannon searched for a way to quantify the information contained within a message, logics led him to a formula that looked very much like Boltzmann's. Later it was observed that thermodynamic and Shannon's entropies were conceptually equivalent.

It was also believed that when matter fell into a black hole, its entropy would also disappear, but Demetrious Christodoulou and Stephen W. Hawking demonstrated that in the process of fusion of two black holes, the total area of their even horizons would never decrease. From these studies and the later discovery of the fact that black holes emit radiation, it was determined that the entropy of a black hole is exactly a fourth part of the area of the event horizon measured in Plank areas [10 –66 squared centimetres]. It is as if entropy, as a unit of information, were written over the event horizon in such a manner that each bit [each 0 or 1 of the digital codification] corresponded to 4 areas of Planck.

This amazing result has a natural explanation if the holographic principle proposed in 1993 by Nobel awarded Gerard ‘t Hooft [University of Utrech] and elaborated by Leonard Susskind were true. About this theory, the Argentinean Juan Maldacena [Harvard University] asserts that: “The force of gravity and one of the spatial dimensions may proceed from the peculiar interactions between particles and fields existing in a space with less dimensions”.

A three·dimensional description of the law of gravity would be equivalent to the holographic description without gravity and in two dimensions, in a way that certain calculation pretty touch in one description may be trivial in the other. Despite their radical differences, both theories may equally describe everything we perceive in space·time and any piece of information we could gather about the universe's mechanics.

A hologram is a two·dimensional object which encodes all information described by a three·dimensional image. Our three·dimensional universe may be coded on a surface containing it, like some kind of huge hologram. The experiments of particle physics at high levels of energy, according to Juan Maldacena and his frontier theory, may have found signals of the validity of this principle [!].

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:: links and recommended bibliography

· A Wittgensteinian dissolution of the Question of Space
· The dynamic unity of reality
· El tiempo en la filosofía del siglo XX
· Agujeros Negros, Cuerdas y Gravedad Cuántica por Juan Maldacena
· Viajes a través del Tiempo
· Banks, T., W. Fischer, S. H. Shenker, L. Suskind. M-Theory as a Mtrix Model: A conjecture.
· Ballard, Kaith Emerson. Leibniz's theory of space and time
· Camacho, Isaac. Presentismo: Una defensa de la enseñanza de la ciencia
· Davies, Paul. Superfuerza
· Einstein, Albert. Teorías Especial y General de la Relatividad
· Euclides. Los Elementos
· Green, Brian. El universo elegante.
· Green, Brian. The Fabric of the Cosmos
· Gribbin, John. In search for the edge of time
· Hawking, Stephen. Historia del Tiempo. Del Big Bang a los Agujeros Negros. 1992.
· Kaku, Michio. Teoría-M, la madre de todas las supercuerdas
· Khamara, Edward J.: Space, Time, and Theology in the Leibniz-Newton Controversy


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