Phenomenology of Space and Time

Today, talks about multiple dimensions and all sorts of exotic spaces do not stir a slightest inner discomfort. We grow accustomed to mathematical abstractions that must replace the simple naive idea of space and as simple feeling of time. Well, let physicists develop theoretical toys. A philosopher is made to never believe in formal banalities, especially when they violate the trivial evidence of our senses. However far from promoting the ancient 3D vision as an absolute dogma for the entire universe, we still need some intuitive consistency, a common base for minute distinctions. That is why it might be useful (at least for a few freaks) to temporarily abandon mathematical monsters for a typically physical (or rather natural scientific) approach, starting from a couple of qualitative observations that could outline the scope of admissible formalizations.

Both scientific and popular literature produce a persistent impression of an epidemic term confusion. If a physical something bears the same name as a mathematical object, this does not mean that physics and mathematics have become one science. Physical space has as little in common with mathematical spaces, as hot dogs have nothing to do with canine attractiveness. In science, we rarely invent terminology from scratch. Any science grows from vague everyday experiences that get gradually sorted out to form an abstract categorization, with the traditional names of most categories hinting to the science's history. When the development of a science gives birth to a new notion, we first try to find an appropriate (that is, intuitively appealing) name from the common language, and if this fails, one might take a random word, or invent a neologism. In any case, it is the matter of borrowing, and different sciences may borrow the same words for different reasons. In particular, both mathematical and physical notions of space go back to the same practical idea, but their identification would be of the same vulgar sort as taking apes for the ancestors of the humanity (or the other way round).

In a way, the mathematical notion of a space is originally a generalization of a physical idea related to our common experience of motion. However, as soon as it becomes a formal structure, it can accept any kind of geometry, topology etc., unlike the physical space that incorporates these partial characterizations in a syncretic manner, as the aspects of the whole that cannot be detached from each other and arbitrarily combined. On the next level, physics takes the idea of a formal space from mathematics and substitutes the original physical notion for an abstract structure serving as an a priori framework for further research. Nobody cares any longer for objective study of space, nor for its objective difference from time. In effect, this leads to a loss of specificity: physical space becomes indistinguishable from any other feature, since anything at all can be digitalized and thus put in a formal mathematical space. Numbers do not stink. First, we represent some physical entity with a mathematical construct; then we forget about physics and declare that our approximate representations are the physical reality itself, and there is nothing else to study.

A similar recurrent fallacy is also haunting mathematics, which is often deemed to be the science of mere designations, virtually identical to its language. However, even very young children know that the word 'chocolate' is not quite as tasty as a real brick of chocolate and every adult perfectly knows that talking of money is far from actually possessing it.

Still, there is a remarkable divergence between physics and mathematics that probably could explain their fundamental role in the hierarchy of science in general. Somehow, mathematics did not yet usurped the physical notion of time, which remains very important in physics, albeit abandoned by many physicists trying to match the mathematical standards of rigor in their essentially non-rigorous science. Mathematics and physics are therefore the principal representatives of two complementary paradigms in science: the static and the dynamic, a structure and a system. Mathematics describes how the world is made; physics tells us how it goes. There is a third as universal paradigm, a hierarchy (meaning that, in addition to mere being and going, thins also grow and develop), but it has not yet been culturally associated with any particular science.

Paradoxically, where there is a single science, there is no science at all. New knowledge comes in comparison; nothing to compare means nothing to learn. That is, trying to reduce all sciences to mathematics (or any other universal foundation) is undermining the very idea of science. Paying too much attention to commonality, we neglect differences, which, indeed, constitute the content of knowledge as such. There is nothing exciting in demonstrating how mathematical physics can be, or in saying that chemical reactions are based on the physical properties of atoms and molecules; it is much more interesting (and challenging) to show which aspects of physics make it different from mathematics, or to observe the principal difference of chemistry from physics, of biology from chemistry, of psychology from physics and physiology. And that is exactly the purpose of phenomenology, to outline an object area before and in spite of any formalizations. It is only in this way that we can indicate the real scope of an abstract theory, and thus the possible alternatives, the promising (from both scientific and practical perspective) directions of research.

As soon as one has acknowledged the importance of a phenomenal view, the problem of space and time can be critically reassessed. Of course, all such assessments are very selective, never pretending to any exhaustiveness; on the other hand, compete science is dead science. To come to a physical picture of the world, we must put together many individual pictures and let them interact, to produce a higher-level integrity. This is the physical way of doing things.

So, here is a sample outlook. In the following, the words 'space' and 'time' refer to physical space and physical time respectively, unless a different meaning is explicitly specified.

1.  Space and time refer to the motion of material bodies.

Any physical system is primarily a number of material things interacting with each other. That is, to remain in the domain of physics, we must consider any objects as outer to the subject, regardless of how they may participate in human activity. Of course, many physical things we deal with have been made by humans; however, in physics, we do not speak of their origin, we describe their motion as independent of the creator and the observer, assuming that the same behavior will occur whenever a similar physical system comes to existence, regardless of whether humans constitute a part of the system's environment or not. We intentionally exclude any subjective elements reducing them to the conditions of motion and constraints. A physical effect observed in humans or animals must as well be observable without humans nor animals (that is, we can always find natural systems exhibiting that kind of behavior, or develop a technology to produce the same effect in an automated way). For example, if some features of brain operation seem to be due to the presence of a new physical force, the same force must be found outside any brains, acting in an objective way. Otherwise, we can only conclude that the already known physical forces sum up to produce the impression of a new force, as if it existed in the brain. Similarly, in atomic physics, we describe holes in atomic shells as independent particles interacting with electrons, thought, in fact, there are no real particles, and the observable picture can also be obtained considering electron correlations (which, however, may be much less elegant).

There are other ideas of space and time that do not directly involve any physical motion. Thus, psychological space and time are different from physical space-time, though, of course, any psychology is only possible as a superstructure of some physical motion. Similarly, some space- or time-like features can be discussed in history, in logic, or in computing, but their relation to physical space and time may be very distant and obscure.

2.  Space and time are objective.

Referring to objective motion, they are themselves independent of any human interference. When physical bodies move unobserved, they remain the same bodies, and the spatial and temporal characteristics of their motion are preserved. There is no physical motion beyond space and time. Consequently, a physical description of space and time must allow their natural existence, deriving any observable features from nature, and not the other way round.

3.  Space and time are determined by the character of motion.

Strictly speaking, this character just manifests itself as space and time. The traditional picture of something moving in space and time is but metaphorical. The objectivity of space and time is of a different kind than the objectivity of material bodies and their motion. Space and time do not exist as separate entities; they merely are the objective aspects of material motion.

However, physical motion may have aspects that do not directly correspond to its spatial and temporal character (and this poses the problem of additional specification). A particular study may focus on such secondary features, but this does not entirely remove space and time from physics, which provide the necessary background to further consideration. Thus, describing an isolated physical system as a whole, we do not need the details of its inner motion or its spatial position (which is formally expressed as the homogeneity and isotropy of space). Similarly, in the case of stationary motion, we do not need to track minor changes, rather observing an overall pattern; any attempts to delve into the process of its formation would introduce a certain degree of non-stationarity.

4.  Space and time are complementary as the aspects of motion.

That is, first of all, they are different, and even opposite, though impossible without each other. When it comes to measurement, we may evaluate spatial dimensions using time, or express time in the units of space; this does not mean that spatial and temporal phenomena are physically identical. The very possibility of such interchangeability is determined by the character of motion.

To compare, in mechanics, there is a well-known duality between coordinates and momenta; in a potential field, one can describe motion using either configuration representation or, equivalently, a momentum-space picture. This does not make coordinates and momenta physically the same. In general, any measurement at all will express one physical feature in terms of another. Still, the target system is different from the instrument. The width of a computer screen can be measured using a ruler; but you can hardly make the ruler display this text. Similarly, this text's lifetime is quite limited, but it does not live in the clock.

The separation of space and time is yet another physical problem distinguishing physics from its mathematical slang. This is an absolute requirement for any physical system, which would not otherwise be completely defined. Any relativity refers to the possible formal representations, but never to space and time as such. That is, for any physical system, spatial and temporal characteristics of motion can (but do not need to) be compared to the dynamics of another physical system (a frame of reference), and the result will naturally be different for different reference frames. But the original motion does not depend on the way of its expression, and, in particular, its space and time exist before any measurement, as the objective properties of the system. This means, in particular, that, to correctly reproduce the physical picture, one cannot take just any frame of reference at all; the structure of the frame must be compatible with the objective character of motion. For example, one can speak about the physical equivalence of all the frames of reference that move slower than light relative to each other; any faster-than-light frames are incompatible with such "local" dynamics (which does not mean that there are no other kinds of dynamics that would require a "non-local" frame).

5.  Space and time do not always refer to physical states and events.

For an outer observer (a different physical system), the motion of any physical system looks like a stream of physical events changing the system's state. However, this picture will vary from one observer to the next. In particular, the same object can participate in human activity in many ways, requiring an appropriate physical description in each case. Some of such descriptions may include spatial and temporal characteristics of motion, some others won't. For example, a balloon traveler needs to control the temperature and pressure of the gas inside the bag, while a land observer will mostly track the spatial displacement of the balloon as a whole; the two observers will be interested in different kinds of physical events, though both may consider, say, the height of the fly as practically important. Of course, the presence of humans is of no physical relevance. For a photon emitted by an atom, it does not matter, where exactly the parent atom resides; on the contrary, for a free electron, its distance from an ion or atom is of crucial importance, since it determines the character of interaction.

Formally, the possible states of a physical system are often considered to belong to an abstract configuration space, so that any physical process could be pictured as a transition from one configuration to another (sometimes graphically illustrated using a drawing or a 3D model). Though this closely resembles the common vision of space, there is a significant difference. An abstract configuration space can be of any nature; its dimensionality, geometry and topology only reflect the character of the physical interactions involved. Thus, in atomic physics, the configuration space of a helium atom is a complex infinite-dimensional structure, including both discrete and continuous domains; the elements of this space (physical states) could be roughly described as complex-valued (or operator-valued) distributions over an inner Euclidean space, which binds the physical description to the ordinary space-time; however, the inner space does not correspond to any observable displacements, and the inner time (the sequencing of events in the configuration space) has little to do with "macroscopic" time (applicable to the atom as a whole). Though some theoreticians tend to treat configuration space and time as the only physical reality, this approach does not seem too productive in clarifying the nature of physical space-time. Dismissing the problem is not the best way to cope with it.

Sometimes, spatial relations are included in the physical state; in other cases they stay somewhere in the background. Similarly, physical events can be either "real" (that is, occurring in physical time) or "virtual" (of no relevance to the outer behavior of the physical system). In any case, the representation of physical motion with a chain of state changes (events) is relative, and the same motion could be pictured with many different sequences of events, which, in particular, will produce alternative physical theories.

6.  Space and time assume physical interaction but do not entirely depend on it.

Though space and time express the character of motion, they do that in a very general and fundamental way. Yes, matter certainly influences the properties of space and time. But this is not what most physicists usually mean. General relativity is a bright guess; but we still need to guess what we have really guessed. Equations of motion describe the structure of configuration space, carving out an intricate manifold from the complete body of possibilities. But this does not necessarily influence physical space and time. Indeed, at least within the "standard model", all the physical interactions seem to merely form a kind of superstructure over space and time; they introduce symmetries and constraints that determine the properties of the corresponding interactions, without touching the spatiotemporal background. In particular, special relativity is an expression of the symmetries pertaining to electromagnetic filed, while general relativity is a formal representations of the local symmetries of gravitation. Those who have not yet refused to trust physical (rather than mathematical) intuition will admit that the very idea of space and time comes before any dynamics, as a premise, and not an implication. To bind spatial coordinates and time into the relativistic interval, we first need something to bind. To discuss connectivity and curvature, we need something to connect or curve. In the most sophisticated physical theories, one could still find a hidden substrate of plain space and time (similarly, any abstruse mathematical reasoning goes back to the fundamental primitives like points and junctions).

In other words, space and time represent a kind of relations between material bodies other than physical interaction; somehow, this is related to the very comparison of different things and processes (in philosophy we speak about the types of reflection). A specific interaction obviously assumes a particular way of putting it all together. But there are many interactions possible within the same reflective framework; on the other hand, without being aware of what we thus presume, an entirely different conceptual (and physical) base only could be found by a pure fluke.

7.  Space means identity. Time means distinction.

Basically, the idea of space includes simultaneity. Space is what can be taken at the same time. Conversely, time is what happens in the same spatial point. That is, spatial relations connect different things, thus making them equivalent, belonging to the same class (a moment of time). Time makes the same thing differ from itself (this is what we call development).

In a formal approach, this difference disappears, since one can always treat a many-dimensional space as a series of "slices" with effectively lowered dimensionality. In the Euclidean space, a cube can be pictured as an infinity of squares piled on top of each other. This may produce the impression of time, as the points of each square certainly belong to the same equivalence class, represented by the "height" coordinate. However, such a formalism is implicitly based on the idea of motion, actually producing the different layers of the cube by changing the spatial position of a single square with time. Consequently, the time-like behavior of spatial dimensions is a secondary effect, a projection of spatial displacement into space, which hides (folds) the temporal side of motion, but does not eliminate it, merely making it virtual. Spatial forms spanned by motion are not yet real bodies; they could be compared with the traces of motion on a long-exposition photograph. The very possibility to mentally decompose a real thing into a number of lower-dimensionality layers presumes the existence of higher dimensions, to give room for that particular kind of motion. The complete integration of time with space in modern theoretical physics is therefore an illusion, or, in the formal aspect, a logical fallacy.

The relativity of space and time is usually explained by the observation that, in two frames of reference moving relative to each other, the meaning of "the same point" appears to be different. This formally leads to relative simultaneity, and hence the entanglement of space and time is accepted as a fundamental physical fact. This argument is logically deficient. Indeed, it implicitly assumes the physical comparability of the two frames, that is, the existence of common physical events. Such a common event is supposed to occur in a single spatial point at a definite time, though the numerical representation of this occurrence (spatial coordinates and time value) may vary from one reference frame to another. But a spatial point in one frame does not correspond to a point in another; rather, it corresponds to a trajectory (or a density). A physical event in one frame does not correspond to an event in another; rather, it must be related to a process (or a probability). Consequently, formal coordinate transforms simply mapping one space-time onto another have nothing to do with the comparison of the physical dynamics. To be honest, we need to map trajectories to single points (folding) and single points to trajectories (unfolding). In the hierarchical approach, this is described as conversion of hierarchies.

Any point-to-point transforms are only applicable when there is a common space-time, however differently represented in each reference frame. Physical motion is understood as developing in the same space, and temporal sequencing is the same in all the frames. Any differences are of a purely quantitative nature, while the overall physical picture remains intact. This imposes very strong restrictions on the character of interactions in such a system, cutting any attempts to go beyond such a "truncated" reality.

8.  Space and time are prior to measurement; interactions produce scales.

Physical motion is objective; it is the same regardless of whether somebody detects it or does any measurements. Of course, we can influence the behavior of some physical systems; but this only means that a wider system must be considered, including the physical effects of human activity. The overall character of physical motion, as described by space and time, is therefore indifferent to any outer (that is, non-destructive) interactions. However, even very small influences may slightly modify the state of the physical system, without influencing the mode of motion. Observing such "infinitesimal" reactions, we can judge about the structure of the system and, in particular, about its space and time.

A detailed study of the effects caused by a standard probing interaction is available for the area very far from physics, namely, the theory of pitch scale formation in music. An admixture of a small local perturbation is shown to result in a global scale allowing to compare distant elements of the whole. The homogeneity of the original system (that is, the possibility of reproducing the same structures in respect to any element) makes this scale quasi-discrete, that is, consisting of a number of separate zones representing the detectable values of relative distance. The number and widths of the zones depend on the selectivity of the probing interaction. Moreover, each scale allows a number of subscales, which do not necessarily coincide with the subsets of the base scale. This hierarchical structure is not arbitrary; it is entirely defined by the properties of the base scale ("embedded" in it).

Though the details depend on the kind of the system, the qualitative picture of scale formation is the same, and one could judge (however metaphorically) about physical space and time in the same lines as about musical pitch.

First of all, we infer that scales are not inherent in the observable system; they are an "artefact" of the mode of observation. However, the possible structures are objective, and, as soon as the type of probe has been fixed, we can only "tune" our perception to one of the available levels. A different kind of probing interaction will produce a different range of allowed scales, possibly incompatible with the others. That is, to define a class of comparable frames of reference, we need to specify the reference interaction common to all the members of the class. In relativistic physics, this role is played be weak electromagnetic fields; the constancy of the speed of light is, in this context, not a physical fact, but rather a specification of a class of physical phenomena we are going to involve.

Further, each scale allows different levels of detail within the same spatiotemporal background. The typical times and lengths may vary; however, the hierarchy of the qualitatively different pictures is not arbitrary, as it is entirely determined by the adopted scale. From a higher-level perspective, any lower-level motion cannot be resolved, and the corresponding physical events happen in the same point at the same time. This justifies the formal method of the traditional relativistic physics as one of the possible levels of description. In addition, we clarify some notions of quantum physics picturing the observable macroscopic structure as the effect of inner (virtual) motion.

Finally, in any given scale, with all its embedded hierarchy, we cannot resolve any details at all; there are areas where the current scale is no longer adequate, and we'll need different notions of space and time.

9.  Space and time refer to relations between bodies as well as to individual bodies.

Connecting different material bodies, space manifests itself as distance; as a feature of a single body, space becomes its size. Similarly, two events can be separated by a definite time interval; alternatively, any single event has a definite duration. The distinction and mutual determination of inner and outer definiteness is one of the difficult problems in philosophy and logic. However, physically, it is obvious that the size of a body can be measured by the distances between its ultimate parts, while the duration of an event corresponds to the interval from its beginning to its end. Conversely, the distances between different bodies determine the size of a many-body system and the time interval between two events determines the duration of the complex event comprising the both. In other words, there is a hierarchy of bodies and events, and the external relations of the lower level get folded in the inner characteristics of the higher. Folding and unfolding this hierarchy is not a mere mental exercise; in physics, one needs a technological solution allowing to practically regroup things whenever needed. If you cannot (at least virtually) bind two things together by some physical interaction, you have no right to speak of a compound system. On these grounds, the promoters of the close-coupling technique in the physics of atomic collisions deny the physical meaningfulness of autoionizing states in atoms and ions, since the resonances observed in inelastic scattering can be described on the lower level, as transitions in the spectral continuum. On the contrary, in high-energy physics, any resonance is treated as an effect of virtual particle formation, a true physical event.

When several material bodies form a compound system, and several events are included in a higher-level event, different combinations are possible. The traditional duality of parallel and sequential composition is, possibly, the most obvious. Thus, a star and its planets form a system with the size much greater than the sizes of the components, while the electronic and ionic components of interstellar plasma occupy exactly the same space. Similarly, a displacement along the X-axis can be followed by a displacement in the Y-direction or, alternatively, the two evens may happen simultaneously, in parallel. The possibility of decomposition is determined by the character of interactions involved, that is, by the structure of the system's space-time. For instance, to round a city block you have to sequentially pass the two rows of buildings, unless you know a short cut across the courtyards. An example of a less trivial combination can be provided by the multiplexing techniques in computer networks. In general, there is a hierarchy of complementary routes, and the actual choice depends on the system's history.

However, there is yet another possible manifestation of space and time closely related to scale formation. Under certain conditions, physical bodies and events can be characterized in an absolute way by their spatial or temporal positions. To build such a coordinate system, we need to select a few reference bodies or processes, assuming that their spatial and temporal characteristics are stable in the relevant range. The practical implementation of such a rigid construction is not a trivial task; in most cases, we only hope that our choice is sound enough; a variety of industrial applications is to justify it or demand a critical reassessment.

Every particular selection of reference bodies and events determines a frame of reference. As indicated, different frames are not necessarily comparable; the equivalence of reference frames can only be established in a local manner, for a limited range of physical systems.

10.  Space and time can be embodied in physical dynamics.

In philosophy, we find that every individual thing can be made by giving a specific form to some material. Physicists represent the material aspect of the Universe by the notions like mass or energy, while the reflective (ideal) aspect includes, in particular, space and time. However, from the philosophical standpoint, the very distinction of material and form is relative: forms can become matter, and matter can manifest itself as a kind of reflection. Indeed, if there are a few things, each being a unity of material and form, we can use them to make a new thing; in this compound thing, the original things will play the role of material, and hence their form (the ideal aspect, a mere relation between material bodies) must be somehow convertible in higher-level matter. There is no absolute material, and no abstract forms. That is, the motion of material bodies can itself become a material body.

For a modern physicist, this seems to be an almost trivial statement. However, matter is not necessarily represented by mass, and some future theories may need a different (possibly more structured) representation. Still, we can be sure that a similar structure will be discovered in space and time, leading to an extended principle of duality. On the other hand, today, we merely postulate the equivalence of energy and mass, without trying to trace its physical origin. A formal convertibility is not enough. We need to discover the physical mechanism establishing this equivalence and thus indicate its limits and the ways of extension. That is, in the present state, the presence of physical dualities can be considered as a formulation of a problem rather than an answer, and their physical justification is yet to be found.

Just for a hint, let us recall that time becomes dual to energy in the context of some oscillatory motion; the higher is the frequency of oscillation, the greater is the corresponding energy. When there are several levels of motion, with very different characteristic times, the motion of the lower level is hidden from the higher-level observer, and its effect will only contribute to the internal energy (mass) of the higher-level bodies. It seems like oscillatory (repetitive, recurrent) movement is physically more fundamental than the trivial inertial motion, and, quite probably, the world of the future physics will be more like a hierarchy of reproduction cycles rather than a box-like space and monotonic time. This agrees with the general philosophical idea that there is only one all-comprising world; there is nothing else; hence, whatever exists, or whatever happens, can only be one of the possible modes of the world's self-reproduction.