Some philosophical reflections on the implications of relativity theory for the nature of ontology.
Measuring the Temporal
Maxwell's
equations were accepted by scientists as reflections or embodiments of certain aspects of
the invariance inherent in the character of the laws governing natural phenomena. If one
treated time as an absolute, Maxwell's equations produced variable results as one moved
from one frame of reference to another.
Thus, if one
wanted to retain these equations, then, one had to make adjustments in the manner in which
one methodologically approached the issue of time. Einstein did this by requiring the
temporal component of a coordinate system to be subject to the same translation process as
the three spatial components of that same coordinate system.
One of the
mistakes which may have been made in classical mechanics is that the measurement of
time was considered to be absolute in the same way that time itself was considered an
absolute. Measurement is affected by a variety of forces operative in a given framework
(and time is but one such dimensional force), whereas time's ontology is not necessarily
affected by such things at all.
In other
words, the structural character of the ontology of time may be such that it permits a
range of possible dialectics between itself and various modes of measurement which may
engage it. While the mode of measurement will be sensitive to a variety of forces that
will affect its capacity to get an accurate reading of the character of time, the
dimension of time is not affected by any of these forces. As such, although time acts
upon, and shapes, whatever engages it, time may not, in turn, be affected by the activity
or character of any of the entities or forces that it engages. In this sense, ontological
time (as opposed to measured time) could be said to have perfect elasticity, since no
matter how it is engaged or by what it is engaged, ontological time retains its original
structure without displacement affects ensuing from such engagement.
In any
event, part of Einstein's revolution was to draw our attention to the extent to which the
measurement of time is extremely sensitive, under certain circumstances, to the effects of
motion, gravitational fields, and so on. Nonetheless, as indicated earlier, nothing which
Einstein said could be considered to carry any necessary entailments with respect to the
ontology of time itself.1
The
scientists from Galileo onward, up to the time of Einstein, made a mistake when they
assumed that because the ontology of time is everywhere the same, therefore, the measurement
of time must everywhere be the same. They failed to properly understand the relation
of methodology to ontology.
For
instance, they failed to understand that the hermeneutical engagement of time, as
expressed in terms of some mode of measurement, constitutes an operationalizing of the
temporal dimension and comes to be used as an index for such hermeneutical engagement.
This index of measurement is dependent on the state of motion, or on the state of the
conditions of gravitation, in which the measurement index is embedded. In other words, the
scientists from Galileo up to the time of Einstein failed to understand that the
measurement of time is relative to the frame of reference in which the measurement takes
place since the latter is affected by the conditions and forces which prevail locally
within that frame of reference.
Since the
time of Einstein, there also has been an erroneous assumption which has been made. This
faulty assumption is the reverse of the mistake by Galileo, Newton and others.
Whereas
Galileo, et. al., had mistakenly assumed that because the ontology of time is everywhere
the same, then, therefore, the measurement of time must everywhere be the same, Einstein,
and subsequent generations, have mistakenly assumed that because the measurement of time
will vary from framework to framework, therefore, the structural character or the
ontology of time also will vary from framework to framework. This need not be the
case.
The ontology
of time may be independent of one's mode of measurement. However, the mode of measurement
is not independent of the structural character of the ontology of time since the latter
establishes the parameters within which any given mode of temporal measurement must
operate.
The
confusion between the measurement of time and the ontology of time carries over into
another issue of some importance to the theory of relativity - namely, the problem of
simultaneity. In a sense, this problem is really only a variation on the measurement issue
discussed previously. As a result, there is a failure to keep a clear distinction between
the measurement of simultaneity and the idea of absolute simultaneity, in and of itself.
When one
says the word "now", the instant required to say that word exists simultaneously
everywhere in the universe. This is an intuitive example of absolute simultaneity.
However, once one undertakes to measure the instant in question and to attempt to compare
the measurements taken, then, one encounters all the problems of simultaneity about which
Einstein talked and wrote.
If one treats changes in the ratio of constraints and degrees of freedom as evidence of the presence of one or more forces, then, several questions which need to be asked are these: first, how does a force bring about a change in the ratio of constraints and degrees of freedom? Secondly, what is the relationship between a force and a field?
These questions will not be answered in their entirety within the context of the present essay. What is being offered here is more like pointing in a certain direction and identifying a few of the components. It is an unfinished sketch to which an increasing amount of detail can be added over time as new data and understanding become available.
Part of the answer to the foregoing questions concerns the idea of an order-field. An order-field is generated through the dialectic of a set of dimensions. The structural character of these dimensions is an expression of a spectrum of various ratios of constraints and degrees of freedom which have been established by the underlying order-field. This underlying order-field induces different aspects of the spectrum of ratios to engage one another.
The ensuing engagement generates a further spectrum of ratios which give expression to the character of the dialectic between, or among, different dimensions. This dialectic of dimensions generates, in turn, a further spectrum of ratios of constraints and degrees of freedom which give expression to point-structures, in neighborhoods, and latticeworks on different levels of scale.
At the heart of any field theory - whether it be rooted in Faraday's idea of a force, or in Maxwell's model of a mechanical ether, or in the geometry of Einstein's general theory of relativity - is an antagonism to the concept of Newton's idea of action-at-a distance. Field theories are all predicated on the principle that the dynamics of the field, the dialectical activity of the field, is a function of contiguous events. Field theories differ from one another in the manner in which they attempt to account for the structural character of the contiguous relationship among various aspects of the field and how effects are propagated through the field by means of such contiguity.
Consequently, an order-field constitutes a field due to the way that the underlying order has contact, in some sense, with, or is contiguous with, each aspect of the fundamental dimensions which have been established. The order-field also gives expression to field properties in the way it has contact with the dialectic which it induces these basic dimensions, and from which emerge various point-structures, neighborhoods, and latticeworks. All of this contact is accomplished through the spectrum of ratios of constraints and degrees of freedom out of which dimensionality and dialectical activity initially arise.
Thus, the order-field is present at each and every point of these spectrums, on whatever level of scale one cares to consider - from the microcosmic to the macrocosmic. This presence manifests itself as a field which organizes, arranges, shapes, directs, orients and generates all structures and structuring activity.
These structures and structuring activities are waveform manifestations of the way the order-field gives expression to itself as a result of operating on itself. So, the order-field is more akin to the contiguous character of Faraday's notion of a force field, than it is to either, the action-at-a-distance field concept of Newton, or the bifurcated matter/field concept of Maxwell.
Nevertheless, the order-field being proposed here is different from Faraday's notion of a force field. From the perspective of the theory being put forth in this essay, the idea of a force is itself an index of the presence of an order-field, manifesting itself in a form which results in a change in a given ration of constraints and degrees of freedom.
Consequently, as such, force is not the basic constituent of the universe as it is for Faraday. Force is, instead, itself a manifestation of something more fundamental - namely, order. The structural character of any given force is a function of the ratio, or set of ratios, of constraints and degrees of freedom which have been arranged through the presence of order.
The 'range of a force' is described by the series of point-structures, neighborhoods, or latticeworks whose altered character can be traced to the presence of a capability for bringing about a transformation in the ratio(s) of constraints and degrees of freedom of the observed kind. The path of a force is described by the vectoral or tensoral series of point-structures, neighborhoods, or latticeworks whose alteration in ratio character can be traced to the primary epicenter(s) of intensity of the force's presence, as opposed to secondary, after-shock effects which occur away from the primary points of field intensity. The structural character of either the range of a force or the path of a force need not be simple or linear in nature.
The notion of an order-field provides a potential means for any given point of time/space to be in "contact" with any other point of time/space by means of the dialectic of phase relationships through which the ratios of constraints and degrees of freedom are given expression. However, these junctions of contact are not necessarily physical in character.
Furthermore, the dialectic connecting various neighborhoods does not need to be construed in terms that require the transmission of physical signals between points which are spatially separated. The points of contact are manifestations of the dialectic of dimensions which have been set in motion by the underlying order-field. Thus, 'points' may be in non-physical contact on the level of the order-field, and this contact may manifest itself on the level of scale of physical events as simultaneous events between, or among, physical points separated by spatial distances.
Methodologically, one may not be able to demonstrate the simultaneity of such events because of the sorts of problems pointed out by Einstein concerning the measurement of simultaneity in relation to points that are physically separated. Nonetheless, ontologically, the events may be simultaneous expressions of certain facets of an underlying order-field. Consequently, viewed from such a perspective, the ontological character of an order-field underwrites the simultaneity of events, not the mode of measurement.
On a given level of scale, a particular ratio of constraints and degrees of freedom expresses itself as a point-structure. A group of related ratios manifest themselves as a structural neighborhood.
In the hermeneutical context, neighborhoods tend to build-up (e.g. through learning and memory) around points of phenomenological engagement to which attention is directed and identifying reference is made. Indeed, attention and identifying reference mark the beachhead landing of the hermeneutical operator with respect to various aspects of the phenomenology of the experiential field. Whether - and, if so, to what extent - a neighborhood will bind the hermeneutical operator or whether the hermeneutical operator will remain relatively unbound will be a function of the dialectical engagement between (or among) the hermeneutical operator and a given neighborhood or neighborhoods.
Hermeneutical point-structures are not geometric points. In other words, they are not necessarily ‘spatial’ or simple in character. Consequently, unlike geometric points, hermeneutical point-structures cannot necessarily be construed as lacking an internal structure.
A point-structure is a ratio of constraints and degrees of freedom which give expression, when taken all together, to a form that can have multiple facets and themes. This suggests a potential for complexity of structural character.
A further flavor of complexity comes from the fact that what is a point-structure on one level of scale, may, on another level of scale, give rise to a neighborhood of point-structures or even a variety of latticeworks. As such, point-structures have the capacity to manifest fractal-like properties when engaged on different levels of scale.
Latticeworks are the result of a collection of neighborhoods which are held together by a set of phase relationships. These phase relationships establish identifiable patterns of focal activity, as well as identifiable patterns of horizonal boundaries, within which the collection of neighborhoods interact with one another.
Ratios of constraints and degrees of freedom are related to one another by means of phase relationships. More precisely, ratios are linked to one another by a spectrum of constraints and degrees of freedom that establish parameters within which phase quanta are exchanged between interacting ratios. Phase quanta are discrete arrangements of constraints and degrees of freedom that are drawn from the spectrum of arrangements which are possible in a given context of interacting point-structures, neighborhoods, and/or latticeworks established through a given order-field.
At any given time, if two point-structures or neighborhoods or latticeworks are linked to one another, the structural character of the link is an expression of one aspect of the spectrum of ratios which is generated by the underlying dialectic of dimensions. When such a link manifests itself, this is known as a phase quanta exchange, and this exchange gives expression to a state known as a phase relationship.
Thus, the phase relationship state encompasses the following sequence of activity. (a) It begins with first engagement of specific ratios; (b) proceeds through phase quanta exchanges; (c) includes the alteration of the ratio character of the point structures, neighborhoods and/or latticeworks involved in the engagement process; and, (d) ends with the disengagement of previously interacting ratios.
Both the process of phase quanta exchange, as well as the state of phase relationship in which that exchange is embedded, are subject to the influence of differential, vectoral pressure components. Sometimes the structural character of the way these vectoral pressure components interact is complex.
When this is the case, the dialectic of components gives expression to tensor components which constitute a source of stresses capable of simultaneously pushing, pulling, twisting and stretching any given phase quanta exchange or phase relationship state. This is comparable to the manner in which Faraday's lines of force could be subjected to a variety of stresses and pressures within the electromagnetic field.
The order-field is continuous in the sense that a relay race is continuous. In other words, despite the presence of discrete elements (i.e., the runners for the different teams competing in the race), these elements are organized or arranged in such a way that one or more of the runners is always running throughout the race, although not all the runners will be running at any given instant during the course of the race.
The integrity of the continuity of the race is preserved because of the way the runners, taken as discrete elements, are ordered within the context of the rules which govern the running of the race. The primary characteristic of this ordering is that there should be an overlapping of one discrete element with another discrete element at different points of the race. This is the region within which the baton is passed on from one runner to the next.
Similarly, an order-field is continuous because the spectrum of ratios on any given level of scale will always be giving expression to one or more particular instances of the ratios which form that spectrum. Moreover, there is an overlapping of events which occurs between the expression of one ratio and a subsequent expression of another ratio drawn from the same spectrum.
This region of overlap is contained either in the phase relationship which links the two ratios which are being expressed, or it is contained in the mere contiguity of the events. In either case, as one ratio, for whatever reason, ceases manifesting itself, other ratios spontaneously will manifest themselves, or be induced to do so, even though there may be no causal link between or among such contiguous events, and all of this is traceable to the modes of manifestation being expressed through the order-field.
From the perspective of field theory, the laws describing the fundamental character of physical phenomena will be expressed in terms of a set of field variables, fv. Each observer will map these field variables in a continuous fashion by means of a coordinate system which gives representational expression to three spatial components and one temporal component. However, each observer may use a different set of words or hermeneutical functions (of which mathematics is but one modality) to describe such space-time coordinate systems.
Irrespective of what labels may be assigned to the coordinate system in each frame of reference, the principle of relativity requires that the physical laws which are derived by various observers in relative motion with respect to one another must, nonetheless, be in one-to-one correspondence with each other. However, until one has devised a means of translating from the coordinate language of one frame of reference to the coordinate language of another frame of reference, one is in no position to establish whether or not the physical laws deduced in the different frameworks which are in relative motion to one another are capable of being placed in one-to-one correspondence.
On the other hand, if one is successful in generating a set of translations that: (a) allow one to move from one framework to another in a way that conforms to the invariant structural character of the physical laws of nature, and (b) is independent of the state of motion of any given observer relative to the state of motion of any other observer, then, such a set of translations is known as a continuous transformation group.56 If one has a set of homeomorphic analog mapping latticeworks which preserve the invariance or symmetry of the laws of understanding independently of the state of dialectical engagement of any given hermeneutical observer with respect to some given event or phenomenon, such a set constitutes a continuous hermeneutical group. The methodology of special relativity theory may, in fact, be a special limiting case of the more general principle of hermeneutical relativity which is directed toward establishing invariance of structural character in the context of dialectical engagement of ontology by a number of different observational frameworks and their concomitant systems of measurement.
One encounters the social community of knowers and interpreters in the context of the continuous hermeneutical transformation group. This occurs in the following way.
In order for the invariance or symmetry of a given law of understanding to be preserved, one must establish congruence with that which makes phenomena of such structural character possible. The fact that various hermeneutical latticeworks of different observers are analogs of one another is not sufficient.
They must all preserve symmetry through generating congruence functions in relation to the structural character of the phenomenon to which all observers are making identifying reference. Only in this context of each hermeneutical framework having established defensible congruence functions with respect to some aspect of the structural character of reality would there be significance in being able to demonstrate that these different frameworks are analogs for one another.
At the same time, through the dialectic between, or among, different hermeneutical frameworks, members of the community can work toward uncovering facets of invariance in different aspects of the structural character of reality or ontology. In this sense, the hermeneutical activity of the community considered as a whole takes on the form of a hermeneutical operator which engages the point-structure products which are generated by individuals through the activity of their own hermeneutical operator.
In other words, the hermeneutical activity of the community as a whole forms a latticework in which the hermeneutical activity of individuals forms complex point-structures or neighborhoods (in the case of a number of people whose hermeneutical positions are similar but not entirely the same) within that community latticework. Thus, the hermeneutical activity of the community is an expression of the hermeneutical operator considered from a different level of scale than that of the individual.
Consequently, all of the basic components which are inherent in the individual's hermeneutical operator, also are inherent in the community run hermeneutical operator. Furthermore, just as one finds different kinds of attractors on the individual level of scale, one also finds various kinds of attractors on the community level of scale.
When one speaks of the invariance or symmetry of a law of understanding, it is important to understand that one is not talking about an abstract structure which is divorced from a concrete context. While invariant laws must be independent of the idiosyncrasies which may characterize the hermeneutical framework of any particular observer, such laws are not independent from the structural character of the aspect of ontology which is giving expression to this sort of invariance. Indeed, only when the hermeneutical framework of a given observer merges horizons with a certain aspect of ontology by means of congruence functions, could one say that the individual has grasped something - on a given level of scale - of the invariant structural character of that to which identifying reference is being made.
In the classical tradition of physics, the idea of a physical material or substance was something which could be assigned a determinate, usually unique, location in space and time. Moreover, this idea usually included an array of properties- the array varying with different substances- which gave expression to various facets of the character of the substance in question.
In addition, whatever array of properties might be associated with a given substance, the traditional view held that, in general (although there were exceptions to this) such properties would be conserved as the substance is exposed to, or moves through, a variety of changes across time and space. Finally, by following the transitions undergone by a given substance or set of substances, classical scientists believed the character of causal relationships could be detected from which one could deduce universal laws, such as the laws of motion governing physical substances or materials.
Einstein rejected an essential portion of the classical idea of substance which has been outlined above. For example, Einstein argued that one cannot make any unique assignment of properties - such as mass, length, velocity, time, causality or simultaneity - to any aspect of a field.
Instead, in accordance with the transformation equations which Einstein had derived, not only will one be required to assign different values to such properties in different frameworks, one also will not be able to identify any of these assignments as being the 'true' or 'real' one. Indeed, according to Einstein, one's methodology does not permit one to do anything but treat all of the values as being equally real or true.
While Einstein did not accept the idea of substance in the traditional sense, neither did he believe that the assignment of values could be made arbitrarily. In fact, once one makes an assignment of a value in some given frame of reference, all of the other values for that frame of reference can be determined by means of the transformation equations.
Because, as indicated previously, none of these assignments or determinations really can be said to be rooted in some substance in the field, what was being described was an event. This event could be observed to be characterized by a different set of property values in different frames of reference.
Consequently, Einstein had substituted the idea of: events with variable properties which, nonetheless, conformed to invariant laws of nature, for the classical idea of: a substance whose properties were conserved across time and space and which was subject to laws of causality. In short, with Einstein's special theory of relativity, physics became an exploration into the realm of invariance, which had no room for the notion of a physics rooted in the fixed identity of some conserved substance.
There is a difference, however, between: our methodological incapacity to establish the uniqueness of the properties of matter and the field, and saying that there is no uniqueness of the ontological properties of matter and the field. In a sense, the relativity principle sacrificed the issue of uniqueness of property value on the altar of invariance.
In other words, apparently, Einstein had to pay a price for having a methodological means of establishing invariance in the laws of nature amongst a group of referential frames exhibiting differential values of time, mass, length, simultaneity, and so on, with respect to one-and-the-same event. That price was to lose any chance of determining an ontologically unique set of property values in relation to that event.
More specifically, local conditions include the way one's methodology engages the universal laws that are given expression through the manner in which physical phenomena unfold under a particular set of circumstances in a given locality of space time. Thus, such issues as causality, force, energy distribution, substance, and so on, will manifest themselves as a function of the manner in which the field properties of the methodology of special relativity theory engage localized aspects of ontology.
The field properties of the methodology of special relativity theory also are given expression in the so-called Lorentz transformations which permit one to take the values that have been measured in the context of a given inertial framework and translate those values into the context of some other inertial frame of reference. In essence, the transformation equations represent nothing more than a transfer of the field properties of the methodology of the special theory of relativity from one inertial framework to another. In fact, such transformation equations ensure that the special theory of relativity remains a field theory in as much as the values which are to be assigned to the various physical properties of a given inertial framework will always be a continuous reflection of the local conditions which prevail with respect to that inertial framework.
In a sense, the methodological flavor which characterizes Einstein's special theory of relativity serves to lay the groundwork for the kind of field theory which is encompassed by Einstein's later, general theory of relativity. In other words, the field concept of the general theory of relativity also is rooted in methodological considerations - namely, the geometry of space-time. This means the phenomenon of gravitation is reduced to being a function of the methodological means (i.e., geometry) which Einstein chose to use in order to give operational expression to certain universal laws of relationship among different bodies of the physical universe.
Moreover, as required by the general idea of the field concept, one can measure the gravitational effect on any given point of space by taking into consideration the geometric properties which manifest themselves in the local region of the point. Consequently, gravitation, when expressed as a function of the geometric properties which prevail with respect to a given set of conditions in a given region of space-time, transmits its 'influence' in accordance with the characteristics of field theory - namely, on a localized, point-by-point basis.
Although there are obvious differences between the methodological character of the field properties of Einstein's special theory of relativity and the field properties of his general theory of relativity, there is an underlying, thematic sameness to them. Essentially, this commonality or unity lies in the fact that Einstein's idea of a field in each case is solidly embedded in the properties of the methodology used to operationalize and give representational expression to certain aspects of ontology. Said in another way, the underlying thematic sameness of the two theories of relativity lies in the way Einstein makes field properties in each theory a function of methodology, rather than ontology.
One is able to describe what occurs from one point to the next of space-time in the special theory of relativity, by taking into account the effects of relative motion on measurement and/or using an appropriate set of transformation equations which permit one to translate the values generated by the measurement process in one framework into the values which will be generated by the measurement process in another framework. In the general theory of relativity, one is able to describe what occurs from one point to another in space-time by taking into account the effects of the structural character of the geometry which manifests itself in the context of a methodological engagement of gravitational phenomena in a given locality.
In the special theory of relativity, one is not able to establish, or know, the nature of reality in and of itself. One only can interact with reality through the frames of the methodological glasses one uses to engage that reality.
Therefore, although the character of the relativistic lenses of the special theory permits one to see the universality of physical laws in all frameworks, they prevent one from seeing just what it is that is being governed in such a law-like way. From Einstein's perspective, all that one sees are the values generated by the methodology of special relativity.
Similarly, in the general theory of relativity, one is not able to make contact with reality in and of itself. Again, one's vision is limited to the structural character of the frames of the methodological glasses one uses to engage reality. Therefore, although the character of the relativistic lenses of the general theory of relativity permits one to see that the law of gravitation is universally applicable in all frameworks, one does not know why space-time has the geometry it does, or what it is that is capable of warping space to generate geometric characteristics of the kind that are observed in various cases.
One sees there is a correlation among geometry, mass and gravitational phenomena, but one does not know what it is that sustains this correlation. To say that gravitation is geometry, does not account for how space comes to have the geometry it does, nor does it account for why mass should be proportional to geometric properties.
Consequently, the methodological strategy which Einstein used in the special theory of relativity to develop his notion of a field had laid the groundwork for his doing the same sort of thing when it came to the development of the field concept in the context of the general theory of relativity. Moreover, by rooting the field concept in methodology, each theory of relativity was able to permit one to describe certain universal properties and behaviors which are manifested in the context of localized frameworks, while, simultaneously, limiting one’s understanding of the underlying reality which made universal properties and behaviors of such structural character possible.
1.) There are several experimental findings which often are cited to justify an ontological interpretation of Einstein's special theory of relativity. One such finding concerns the manner in which two atomic clocks that were synchronized initially, subsequently yielded differences of measurement in the passage of time relative to one another after one of the clocks had been transported by jet while the other remained stationary on the ground. Supposedly, this experiment showed that as one approached (even in a modest fashion) the speed of light, time slowed down, since the clock on the moving jet plane indicated that less time had passed than did the stationary clock on the ground.
Another experimental finding involves the manner in which the decay-rate of certain accelerated particles is slowed down relative to the decay rate of these same sort of particles at lesser velocities. Again, the tendency has been to suppose this demonstrates that the structural character of the ontology of time is capable of being affected as velocities approach the speed of light.
Neither of these experimental findings, however, undermines the position being expressed in this essay. For example, although an atomic clock is a highly precise mode of measurement, it is, nonetheless, a measuring device.
As such, it is susceptible to being affected by the conditions of gravitation, velocity and so on that surround it and to which it is subjected. The atomic clock experiment proves only that the mode of measurement was affected by conditions of jet transport and says absolutely nothing about the ontology of time being affected.
Thus, on the one hand, the experiment is perfectly consistent with what Einstein's special theory of relativity would predict. On the other hand, it offers no evidence to contradict what is being advocated in the present chapter concerning the relationship between methodology and ontology in relation to the temporal dimension.
The same sort of result follows from the particle decay experiment. The rate of decay of a particle constitutes a special kind of measuring device. The fact this decay rate can be speeded up or slowed down merely means that it shares a property in common with other clock devices - namely, that its mode of measurement is affected by the physical conditions to which it is exposed.
Gravitational fields and velocity affect the rate at which the internal structure of the particle unfolds across time. Gravitational fields and velocity affect the manner in which the phase relationships governing the rate of decay phenomenon manifest themselves.
However, neither gravitational fields nor velocity has any effect whatsoever on the structural character of the ontology of time. What is affected is the methodological engagement of time. Return to Essay