Time in Quantum Mechanics
Time in Quantum Mechanics
Time in Quantum Mechanics
Let's consider here different aspects of time in non-relativistic quantum theory.
The main observation is that there are two different mathematical objects to describe the two notion of time:
Present Time
We have an absolute time variable t used in the Schroedinger equation:
This notion of time has some interesting properties:
• The time t is predefined and always certain (not uncertain).
• The time t does not depend on the physical situation.
• The time t is not measurable (there is no predefined self-adjoint operator related with t).
• The time t defines the causality in QM.
This shows that it is the realization of the concept of present time in QM.
Time Measurement
To measure time we have to use some self-adjoint operator T with
Because H is positive, this relation cannot be exact. So, exact time measurement not possible. We can define only some uncertain time measurement using a symmetric (but not self-adjoint) operator T or some self-adjoint operator A with
That means, it is connected not only with the uncertainty of energy measurement by the uncertainty relation
but even in principle does not allow an exact measurement of time.
Moreover, this operator depends on the concrete physical situation, because this situation will be described by the Schrödinger operator H - a remarkable distinction to the operator of coordinate measurement. And, last not least, there is no default procedure to define some A for a given operator H.
As the uncertainty, as the dependence on the physical situation are additional indicators that this is the realization of the concept of time measurement.
The Concept of Present Time
I introduce here the notion of present time instead of absolute time because I want to point to the metaphysical contents of this notion instead of the concrete mathematical realization.
We can distinguish three types of events - future, present and past events. There is an obvious qualitative distinction between these types of events. In a complete theory, this distinction has to be described.
There is no a-priori argument for an assumption that this present time may be measured in any way. Thus, it is necessary to distinguish two concepts of time - present time and time measurement.
On the other hand, present time is deeply connected with causality. Indeed, an event A may be the cause of B at some moment A is in the past and B in future.
Two Aspects of Time
What is time? This is a very old philosophical question. There are very different aspects of this notion. We don't want to describe them all, and we don't want to find here the universal solution.
But we want to distinguish here two aspects of time - present time and time measurement. Our point is not to describe them completely, but simply to clarify that there is a difference between them, and that an equivalence between them is a nontrivial assumption. Other aspects like causality, biological or conscious time or the relation to entropy we do not consider here in detail. Questions related with space we consider separately.
The standard point of view does not distinguish clearly these two aspects of time. If, as I assume, these two aspects of time have to be described by different mathematical notions in quantum gravity, this may be one of the reasons for the failure of previous attempts to unify GR and QM.
At first, let's define the two aspects of time we want to consider here. Later we will see how they are "implemented" in different theories ( NM, GR, QM, QG, PG).
Measured Time
The first notion of time describes the result of time measurement by clocks. This concept we denote in the following measured time.
Time measurement is discussed in almost every introduction into general relativity, and there is no reason to repeat it. Remark only that the existence of such a unique "measured time" is a nontrivial physical result or assumption of general relativity. In principle, there may be worlds with different sorts of clocks so that each sort of clock shows a different time.
Present Time
The other concept describes the subdivision of events into future, presence and past. Let's denote this concept present time. It associates that this time is always present, independend of every measurement, and that it allows to define presence (together with future and past). It is not connected with the special realization of present time in classical mechanics, by an absolute time coordinate (even if I have no idea for another realization).
In the last time, also other things related with time have been discussed, like the relation of increasing entropy and the time arrow. I do not discuss these things here, personally I think that entropy is something secondary, a consequence of termodynamics, and not related with this fundamental distinction between future and past we have named here present time.
Discussion
At first, remark that these two notions describe different parts of the reality. The difference between future and past is some objective property of our real world, not an abstract idea of some people. Time measurement with clocks is another, very different part of the reality. A connection between these two things is not obvious. It may be only an assumption of a special physical theory or a result of experiments. The principal possibility that they may be different is easy to understand.
Newtonian Mechanics
In classical mechanics the absolute time variable t can be used as for measured, as for present time. So, the distinction of the two different time concepts is not necessary from mathematical point of view. But also in this theory it seems natural to make a difference between these two notions and to remark that this identification is a non-trivial physical assumption of the theory. It is interesting to remark that Newton has really done this.
Classical Quantum Mechanics
In the case of non-relativistic quantum theory, the situation is even more interesting. Looking carefully, we find that our two notions of time will be realized by different concepts in the quantum theory!
1. We have an absolute time variable t used in the Schroedinger equation:
This time is uniquely defined, independend of the physical situation and not measurable. It defines the quantum causality.
2. To measure time we have to use some self-adjoint operator T with
Because H is positive, this relation cannot be exact. So, exact time measurement is even not possible. This operator depends also on the concrete physical situation and is not predefined like the time itself or the coordinate measurement.
General Relativity
Let's consider now relativistic theory. In the ideology of special and general relativity, only time measurement by clocks defined by
will be considered.
But, nonetheless, some rudimental parts of the concept of present time have survived even in general relativity.
Another point of view is that present time is something outside the theory, something like God, life or conciousness. The formal reason not to consider present time is that there is no measurement procedure to detect absolute contemporaneity of events.
Quantum Gravity
I think, this consideration of present and measured time gives some evidence that also in Quantum Gravity above concepts have to be realized, present time as a generalization of the absolute time of quantum mechanics and measured time as a unification of the path-dependent time measurement of general relativity and the uncertain time measurement in quantum mechanics.
To follow this scheme, we have to introduce present time into GR too. This is done in our variant of the GR named here post-relativistic gravity (PG). This theory is considered as an intermediate step between GR and QG which realizes above concepts of time in a different way.
The Concept of Time Measurement
A time measurement is defined by some class of clocks.
Thus, time measurement has the following properties:
• There may be some uncertainty - at least the error of measurement, but in the case of a quantum clock there will be some other, more principal uncertainty.
• The time measured by clocks may depend on the physical situation. Indeed, there is no guarantee that the clock is not influenced by some field in the neighbourhood of the clock.
• It may depend on the path of the clock, not only on the begin and end point.
Causality
In PG, we define causality in the following way:
Between two events e_1 and e_2 with coordinates (x_1,t_1) resp. (x_2,t_2) there may be a causal connection (e_1 is cause of e_2) if t_1 < t_2.
To refer to this definition of causality instead of relativistic causality I use the notions absolute or classical causality.
This notion of causality is not relativistic invariant. Different PG-solutions with the same underlying GR-solution are considered as physically different.
Wave Function Reduction
This concept of causality coinsides with that of classical QM.
Especially, we have no problem with considering wave function reduction by measurement as causal.
Relation to Relativistic Causality
Instead of the harmonic condition, there is no predefined relation between the time t and the gravitational field g_ij. Especially there is no condition that the surfaces t=const have to be space-like. Situations with an (at least partially) time-like surface t=const are possible.
At a first look, it seems meaningful, even necessary, to assume that the surfaces t=const have to be space-like.
But to realize this, we have to prove that if such a condition if fulfilled for the initial values it will be fulfilled forever. But this seems to be false.
Moreover, following the general "path integral" ideology, through quantization we have to consider alternatives which are not solutions of the classical equations.
On the other hand, the role of g_ij in PG is reduced to define the velocity of some physical processes (like clocks), and it has nothing to do with causality. Thus, the assumption that t=const is not space-like does not lead to great difficulties.
Let's consider this situation in detail. In such a situation there may be time-like paths so that t is not a monoton function on it. But it is easy to interpret these trajectories in our causality using antiparticles. The part with decreasing t has to be interpreted as an antiparticle, the extremal points of t as points with pair creation resp. annihilation.
http://www.berlinet.de/schmelzer/PG/timeQM.html
Emergent Phenomena OF Time in Quantum Mechanics
Koichiro Matsuno
Department of BioEngineering
Nagaoka University of Technology
Nagaoka 940-2188, Japan
Abstract
Despite the fact that quantum mechanics does not totally dismiss the possibility that time could serve as an operator carrying some agential capacity, time in the usual practice of quantum mechanics is taken to be a parameter instead of an operator. An alternative to render time to be an operator or an agency in the realm of quantum mechanics is found in appreciating the local act of preparing boundary conditions explicitly. The act of preparing boundary conditions is inseparable from another local act of measuring part of the boundary conditions since the preparation assumes identification of the participants. Both preparation and measurement are forms of interaction of material origin. Preparation-measurement complex constitutes a unique form of dynamics in the sense that what has been prepared can subsequently be measured and what has been measured can participate in subsequent preparation. Although time as a parameter in quantum mechanics is synonymous with complete preparation of boundary conditions to whatever extent in a manner of being totally independent of the act of measurement, preparation-measurement complex through local acts undermines time as a parameter. Instead, time as an operator or an agency comes up. What is specific to quantum mechanics is the occurrence of quantum entanglement intertwining the preparation-measurement complex. Unless both acts of preparation and measurement are rigid enough to eliminate room for internal determination on the part of local participants, quantum entanglement can make it possible to put those local participants as much as possible under a common non-local umbrella of quantum coherence. This is nothing but an actual embodiment of time as an agency. Quantum entanglement as an intrinsic material capacity of organization extending non-locally, potentially without limits, is tailored by another agency called time. Actual emergent phenomena of material origin in the empirical domain are due to the interplay between two agencies, quantum entanglement and time.
1 Introduction
Time is taken to be a fundamental attribute of any dynamics. Nonetheless, it remains as a perpetual enigma. A major difficulty with the notion of time rests upon the ambivalence in whether time is of itself dynamic or something else is dynamic in time. In this regard, contemporary physics serves as a witness to the impasse surrounding the issue of time. Many practitioners share with Davies (1974) the view:
“Present day physics makes no provision whatever for a flowing time, or for a moving present moment. ... Eddington has written that the acquisition of information about time occurs at two levels: through our sense organs in a fashion consistent with laboratory physics, and in addition through the back door of our minds. It is from the latter source that we derive the customary notion that time moves.”
This view on time is in fact traced back to Kantian notion of time as an a priori category for our consistent perception of the outside world as paraphrased in Newton’s own words (Newton, 1687):
“Absolute, true and mathematical time, of itself, and from its own nature, flows equably without relation to anything external.”
Newtonian absolute time that is declared to flow uniformly in space in a globally synchronous manner has already incorporated into itself a very specific form of dynamics on how time could move. Any dynamics in Newtonian absolute time is nested and grounded upon the one-level deeper dynamics of time facilitating its uniform flow in a globally synchronous manner. Curiously enough, however, Newtonian absolute time prohibits us from asking how it could attain the uniform global synchronism in the first place, while taking it for granted. This prohibition of asking the likelihood of globally synchronous time is even more reinforced in special and general relativity, despite admitting the absence of any means for a simultaneous communication over a distance, by imposing the articulated scheme of global synchronism; the Lorentz transformation for special and the covariance for general relativity. Globally synchronous time remains intact even in relativity.
Globally synchronous time is thus absolute and non-relational as dispensing with any material means for accomplishing the global synchronism. Nonetheless, when it is conferred upon empirical phenomena of material origin, globally synchronous time is seen unidirectional and irreversible in its flow. Empirical unidirectionality of the flow of time is associated with those temporal asymmetries in the decay of the neutral K meson, measurement in quantum mechanics, irreversible thermodynamics or the second law, expanding radiation and no contraction, development and evolution in biology, learning and memory in psychology, cosmic evolution in the Big-Bang cosmology, and domination of black holes over white holes (e.g., Davies, 1974). The apparent unidirectionality of time in the empirical domain is unquestionably relational in that globally synchronous time is related to material phenomena in one way or another. In particular, we humans who have been evolutionary latecomers in the empirical domain on the planet earth are responsible for coining globally synchronous time. This anthropic aspect of coming to terms with globally synchronous time now invokes a convoluted reflection upon whether the time itself might be intrinsically relational instead of being absolute contrary to Newton’s original claim, because the Kantian justification of absolute time as an a priori category for us humans is anthropocentric. Anthropocentric time is fundamentally relational to what we humans are.
Relational aspect latent in what one calls globally synchronous time is already implicit in general relativity. The presence of closed timelike curves in the realm of general relativity discovered by Gödel (1949) suggests that unless globally synchronous time is constrained internally, the forward causation along a closed timelike curve would come to destroy the causation itself when it returned to the younger stage while rounding the closed curve in the forward direction. That is the grandfather paradox, referring to the scenario that, for instance, a boy travels into the past and shoots his grandfather at a time before he became father, ending up with no such boy traveling into the past in the first place (Earman, 1995). Although this paradox may look almost nothing but a science fiction, it is quite pedagogical in pointing out the possibility that globally synchronous time conceived in general relativity as a self-contained theoretical framework could not remain internally consistent in itself. General relativity may require some additional constraints in order to remain consistent even in its theory alone. Globally synchronous time in general relativity can be relational in observing the global self-consistency at the same time.The likelihood of globally synchronous time being relational is thus both empirical and theoretical. We shall first examine a relational underpinning of globally synchronous time in the empirical domain, because an empirical discourse can minimize intrusion of theoretical artifacts.
2 Global Synchronism
At issue is whether the global synchronism could remain irreducible in itself. In order to examine this problem further, one cannot take a global perspective for granted any more. Global stance makes the Cartesian split between subject and object inevitable, and lets the descriptive object remain globally immutable. Such an immutability of the global object is, however, strictly of methodological origin thanks to the convention that the descriptive subject may be entitled to make an access to the descriptive object from its outside without disturbing it even to the slightest degree. Needless to say, unless global consistency of a descriptive object is guaranteed, no descriptive enterprise could be sanctioned (even including the present article). This observation comes to urge us to explore a possibility of grounding the global stance and the accompanying Cartesian split on a much deeper level, if any.
A likely candidate for facilitating a global consistency and description is the presence of a record of finished events as a time capsule (Matsuno, 1989, 1996; Barbour, 1994). For instance, a fossilized rock to a paleontologist looks like a record of finished events frozen in a time capsule. The fossilized rock remains immutable as it is. What concerns the paleontologist is to figure out a consistent description of what those fossilized rocks combined together are all about. The split between the paleontologist and the fossilized rocks is guaranteed because the latter are there in their own right irrespective of whether the former is present on the scene. The split between an onlooker and a time capsule does not require the Cartesian split, though both may look similar. The similarity is, however, superficial. The time-capsule split from the onlooker is not methodological, but intrinsic to the notion of the time capsule itself in that nobody who found time capsules is allowed to forge them. Although the Cartesian split forces the subject to separate itself from the object for the sake of its own sustenance whatever the object may be, the time-capsule split from the onlooker begs the time capsule to allow the onlooker to move around. The time-capsule split makes the presence of an object a principal cause for the participation of a descriptive subject, while the Cartesian split lets the subject be the sole cause for establishing the presence of an invariant object.
At this point, it should be emphasized that the time-capsule split from the onlooker does not necessarily imply that the onlooker could satisfactorily describe what the time capsule is all about. Only the competent paleontologist can do that. The descriptive burden within the time-capsule split is on the descriptive subject, in sharp contrast to the Cartesian case in which a complete immunization of the descriptive subject to whatever object is methodologically guaranteed. Even if the description completed in the scheme of the time-capsule split may look similar to that obtained in the descriptive scheme of the Cartesian split, the difference will be substantial. Those descriptive subjects who failed in coming up with a consistent description over a whole array of time capsules are not allowed to participate in the completed description. In contrast, no such failure is approved of by any of Cartesian subjects.
The situation is totally upside down. If one starts from the Cartesian split, the global descriptive consistency of the object will have to be respected at all cost. No one is allowed to question how such a global descriptive consistency could be guaranteed. Otherwise, the Cartesian split would fail. If how the global descriptive consistency could come into being becomes a matter of concern, on the other hand, the Cartesian split is methodologically incompetent for the task. An alternative can be the time-capsule split from the onlooker, because the presence of an object suggests only a possibility of attaining its globally consistent description. What is required is how to read out the available time capsules in a mutually consistent manner, and no more. Extrapolation of the fossil record into the future is strictly prohibited. Nonetheless, one can cope with how the globally consistent description could come into being while admitting successive alternation of the participating descriptive stances and subjects. This viewpoint may provide us with a likelihood for reading out any relational aspect latent in globally synchronous time, because the latter is unquestionably embodied in any time capsules available at the present moment insofar as they can eventually be deciphered in a mutually consistent manner.
3 Local Asynchronism
Globally synchronous time latent in a globally consistent description resides in the contrast between the presence of an invariant object to be described and the act of describing the object in terms of linear linguistic strings. The activity of forming, tracing, and processing a sequence of linear strings in globally synchronous time is destined to preserve the invariant nature of the object. Uniform progression of processing linear strings while maintaining the descriptive object invariant is certainly consistent with the linear progression of globally synchronous time whose global synchronism comes to guarantee the presence of the global object completely separated from the descriptive subject. However, those descriptive activities yielding a globally consistent description in the effect without presupposing any privileged global perspective in the beginning cannot proceed in globally synchronous time. When there is no privileged global perspective to begin with, the resulting description would be at most a consequence of the interplay among the participating local perspectives. Time associated with each local perspective is also local. Each local time is asynchronous, and there is no a priori mechanism for their synchronization. Only those local times that could succeed in synchronizing among themselves would come to survive in the consequent global description that is also accompanied with its a posteriori globally synchronous time. Unless it is forcibly taken to be irreducible in itself, globally synchronous time can be seen as a consequence of the interplay among locally asynchronous times that are equated with possible local perspectives of description internal to the object to be described globally only in the effect.
Locally asynchronous time internal to each local perspective of description is both transitory and contingent, but still goes ahead of globally synchronous one. Internal descriptions unique to local perspectives precede external description of an invariant object in a global perspective. Each internal description provides the context which others of the similar nature would consult, and at the same time constantly keeps modifying its own context so as to be incorporated into a globally consistent description in the effect. Those internal descriptions that would eventually fail in participating in the finished global description are constantly wiped out. Locally asynchronous times are thus seen as relational components upholding globally synchronous time via intermediaries of internal description of a local character.
The relational characteristic latent in the globally synchronous time deciphered in terms of locally asynchronous ones is, however, more than just the matter of description. It is also dynamic in itself as an object of description. The activity of internal description unique to each local perspective manifests the capacity of awareness in that perspective. Awareness as a fundamental attribute of measurement suggests that measurement internal to material bodies of whatever kind may also be associated with their locally asynchronous times (Matsuno, 1989, 1996). That measurement internal to material bodies, or internal measurement in short, is rendered to be an object of description again makes both internal measurement and internal description indistinguishable. Locally asynchronous time is intrinsic to internal measurement as much as to any internal description in a local perspective. This is consonant at least methodologically with globally synchronous time in global dynamics, in which a globally consistent description of the dynamics yields time no other than that of being globally synchronized. The difference in the descriptive stance is, however, significant.
In particular, the local-to-global transformation in any dynamics described in globally synchronous time is just a matter of integration. Any local dynamic laws parameterized in globally synchronous time such as those expressed in differential equations of local field variables are taken to yield a global description through their integration. This likelihood of integration rests in the premise of taking a globally synchronous time for granted from the very beginning. Time in the global dynamics is not dynamic, but simply a parameter in the dynamics. In contrast, the local-to-global transformation in locally asynchronous time is dynamic in letting time itself be involved in the dynamic motion for generating a globally synchronous time. Time in internal measurement is dynamic in locally moving and being moved by others. Such capacity is primary to locally asynchronous time, whereas no agency in globally synchronous time.
Asking absoluteness of globally synchronous time could be metaphysical at the best. Unless such metaphysical stipulations are imposed forcibly, time remains relational and accordingly locally asynchronous. Relational capacity latent in globally synchronous time can be envisaged only if one views it from the perspective of locally asynchronous time. This points to a practical problem of how to synchronize two separate clocks, a time-honored enigma first perceived by Gottfried Wilhelm von Leibniz (Leydesdorff, 1994). He proposed only three alternatives for the solution; through a material means, through an intervention of immaterial agency, or due to the internal precision of each clock. Although Leibniz was in favor of the third alternative, the actual solution remains far from its completion. A major difficulty with the notion of a clock is in its proclaimed global synchronization without being equipped with the actual material underpinning. Any clock presumes its global synchronization. A remedy for the present malaise is appraisal of locally asynchronous time by letting both globally synchronous time and clocks conceived there be a consequence of the dynamic time that is local.
Describing any dynamics is an activity relating time to something else. Recognition of locally asynchronous time makes time itself relationally nested. Time capsules frozen in fossilized rocks when read out in a mutually consistent manner, are certainly the carrier of globally synchronous time, and the nested remnant of locally asynchronous time will be wiped out after the successful deciphering. However, there are also living fossils as evidenced in living organisms. What makes living fossils distinct from fossils in rocks is in the activity of making time capsules. In addition to time frozen in time capsules, there is also time making time capsules. It is time in the time capsule in the making that makes time intrinsically dynamic.
4 Dynamic Time
Relationship between interaction and time is convoluted. If one takes time to be completely independent of whatever interaction of material origin as with Newtonian absolute time, any dynamic aspect of time would have to be immaterial and of an imposed character. This immaterial time, when applied to interaction of material origin, would inevitably come to associate the latter with a certain immaterial implication. For instance, even Newton himself reluctantly admitted that the imposition of absolute time would have to come to terms with action at a distance in spite of the observation that instantaneous propagation of action over a distance would remain neither mechanistic nor physical (Leibniz, 1966, p. 371 in a letter to Bernouilli in 1698). On the other hand, if one takes time to be intrinsically related to interaction of material origin in one way or another, the dynamic nature of such time would certainly assume its own material dynamics. At the least, our time experience in this empirical world is upheld materialistically. The dynamics of such time mediated by interactions of material origin thus takes the form of a dynamics of time in time since interaction has been taken to relate to time. Nonetheless, dynamics of time in time sounds quite self-reflexive, not to mention its likely fate of being called a misnomer.
An essence of the dynamics of time in time will be seen in a simple example of synchronizing clocks among three or more than three people (Leibniz, 1966, p.272). Suppose that your time read out of your watch and my time read out of mine interact conversationally. The effect of the synchronization of the two, when recognized by the third party, in turn initiates another synchronization between the watch of the latter and, say, mine. Likewise, when you come to recognize the synchronization between that third party and myself, further synchronization of watches between yourself and either the third party or myself would follow (Matsuno, 1998a). Once a synchronization of watches between an arbitrary pair out of three or more people gets started, successive synchronization propagates among the people indefinitely. Time is thus seen as the sticky web of the timing experiences among the people carrying their watches.
We shall now examine how material time could be envisioned in the framework of material dynamics, since time inherent to our empirical world is exclusively materialistic. For this purpose, we require a certain reference against which the intended dynamics of time in time could be figured out. The candidate we shall try is our linguistic institution itself in view of the fact that any likely discourse of the dynamics has to be practiced in our languages.
5 Grammatical Constraints on Temporality of Interaction
A most fundamental reference to any dynamic aspect of interaction is descriptively intended in the present progressive mode (Matsuno, 1998a). Interaction materializes in the mutual process of action and reaction in progress more than anything else. Take, for instance, two molecules that are colliding with each other. Any empirical observation of the colliding molecules presumes the presence of an observer who can describe the molecular collision in progress. The object of this description is necessarily in the present progressive mode. It is subsequently transferred into the past progressive mode with the description of the ongoing interaction. The descriptive transference from the present progressive to the past progressive tense requires a timing of interaction to be frozen in the record in the sense that interactions in the past progressive tense remain invariant in the record. The timing of the crossing from variable to invariable interactions is a temporal activity of descriptive origin. Although one may say that any changes in interaction materialize in the mode of the present progressive tense, their descriptive comprehension always takes place in the past progressive. This is due to the simple fact that speaking and comprehending the speaking cannot simultaneously be accomplished by the same speaking subject (Pattee, 1977). Insofar as one wishes to comprehend interactions descriptively, the capacity of timing the crossing from the present progressive to the past progressive tense has to be taken for granted, otherwise no changes in interaction could be comprehended (Salthe, 1993).
When two hydrogen molecules and one oxygen molecule react and make two water molecules, one may expect that the chemical reaction process could be described in the mode of the present progressive tense. But, what we actually comprehend is through the description in the past progressive tense. The chemical reaction in progress could be extremely fast and completed almost in the order of several femto seconds. Our linguistic comprehension of such a fast reaction process however does not proceed at that fast rate in real time. Only as referring to the reaction already frozen in the record, can one figure out what was going on. The record remains unchanged even if significant changes are described there. Those changes depicted in the invariant record is, however, not the direct property of the record, but an outcome of the very nature of the interaction in progress. Even if the temporality of the present progressive tense is not directly accessible descriptively, that of the past progressive does remain descriptively invariant in the record and thus accessible to its descriptive comprehension. Consequently, interaction turns out to have the capacity of crossing two temporalities, the present progressive and the past progressive tenses. Unless this capacity is available, one cannot descriptively identify what interaction is all about (Matsuno, 1998b).
The nature of time associated with interaction having the capacity of crossing two different tenses is seen in timing of crossing between the two temporalities. Time as the capacity of timing interactions is already latent in the occurrence of interactions. Insofar as it is taken to be descriptively accessible, interaction comes to associate with itself the temporal capacity of crossing from the present progressive to the past progressive tense.
One more temporal characteristic of interaction is seen in the reverse concatenation from the past progressive to the present progressive tense. When the present progressive mode is transferred into the past progressive one, the generative capacity of interaction is necessarily lost because of the frozen nature of the latter in the record. In order to envision the recovery of the generative capacity, it has to be noted that interaction in progress carries with itself the variable capacity that was forcibly eliminated in the transference into the past progressive mode. Transference of interaction into the past progressive tense has to be supplemented by the temporal capacity to sustain interactions, the latter of which is of necessity left behind the transferred past progressive mode. The reverse concatenation from the past to the present progressive mode leads to and is saved by time as the capacity to sustain interactions (Matsuno, 1989; Gunji, 1995). When two hydrogen molecules and one oxygen molecule react and make two water molecules, the energy released from the molecular binding process has to be dissipated toward the outside, otherwise no stable water molecules could be available in the end. This energy dissipation in turn facilitates to sustain interactions for forming water molecules and impart to the latter a temporally irreversible character (Brooks and Wiley, 1988). Time as the capacity to sustain interactions is at the least linguistically embodied in the transference from the past progressive mode to the present progressive.
Both the capacities of timing and to sustain interactions, which are attributed to time, are however not metrical. If we are interested in time as a measure instead of a capacity of doing something as is most often the case, it will also be required to elucidate the linguistic foundation otherwise we would lose the ground upon which time as a measure could descriptively be referred to. Precisely at this point, the role of the descriptive mode in the present perfect tense is focused. Once interactions in progress are transferred into the ones already completed and perfected, the descriptive transference from the present progressive to the present perfect tense comes to the surface. The present perfect tense is as a matter of fact a very special case of the past progressive tense in that the movement referred to is already completed, whereas the movement referred to in the past progressive tense could remain yet to be completed. Water molecules in their excited states, that were being formed from two hydrogen molecules reacting with one oxygen molecule, have not perfected their interactions.
In contrast, water molecules in their ground states can sustain their interaction configuration as invariant unless disturbed externally. This observation yields that the reverse concatenation from the present perfect to the present progressive tense is also a special case of the one from the past to the present progressive while maintaining completed interactions invariant. Time as the capacity to sustain interactions, when applied to the special reverse concatenation from the present perfect to the present progressive tense, leads itself to time as a measure of the duration of invariant interactions. Our linguistic practice of crossing temporalities from the present perfect to the present progressive tense provides us with the capability of associating the duration of invariant interactions with its measure. That is time as a measure.
Compared to time as the capacities of timing and to sustain interactions, time as a measure of the duration of invariant interactions can be neither agential nor causative anymore. Nonetheless, the greatest advantage of having time as a measure of the duration of invariant interactions is to guarantee and to enable us to see the global consistency of any movement in progress with its context at any moment. The presence of completed interactions is contextual, while the duration of completed interactions is individualistic in each component movement. The global consistency consequential upon the acceptance of time as a measure maintains a complete synchronization between the two processes of contextualization and individualization. Neither one of the two can serve as a causative factor to the other once time as a measure is adopted. Complete synchronization between contextualization and individualization should certainly be sought in any description of interactions because the description does presume that any individual statement has to conform to its context.
Time as a measure undoubtedly serves as a means of establishing such a global synchronization. This association of time with global contextual synchronization, however, raises a serious question of whether the adoption of time as a measure could be the sole means to guarantee the descriptive consistency of any movement in progress, though this scheme has historically been overwhelming in exercising its influence. Our observation of time as a measure simply as a derivative from time as the capacities of timing and to sustain interactions may suggest to us one more possibility of coming to terms with a descriptive consistency even if starting from time as an agency. The issue is how to relate the past to the present progressive tense in a mutually consistent manner. This is the place where the role of the present tense comes to be focused.
6 Contextualization through the Present Tense
Time as the capacity of timing interactions associated with crossing from the present progressive to the past progressive tense is contextual in accomplishing the descriptive consistency in the latter. As the same time, time as the capacity to sustain interactions associated with the reverse concatenation from the past progressive to the present progressive tense is individualistic in driving each movement in the latter. These two capacities are integrated into time as an agency, which is in turn embodied in the present tense. This is due to our linguistic convention enabling us to let any statement in the present tense migrate into arbitrary temporalities. For instance, once we accept such a statement made in the present tense that two molecules collide with each other, the transference of the temporality into such as “are colliding”, “were colliding” or “have collided” could naturally be conceivable. The descriptive mode in the present tense guarantees a consistent transference into either the past progressive or the present progressive tense while maintaining its own descriptive consistency. Time in the present as the capacities for crossing between the past progressive and the present progressive tense in either direction certainly satisfies the condition of fulfilling its temporality in the present tense.
Time in the present tense serves as a principle of global consistency as much as the whole discourse in the present tense could be globally consistent descriptively. Nonetheless, the global consistency that time in the present tense implies is local in its own making since any activities latent in time as the principle of global consistency are concretized in the individualistic progressive mode. The present progressive mode by itself does not assume any contextual organization. Only when it is transferred into the past progressive mode, our linguistic stipulation enables us to come to terms with a contextualization of the progressive mode. This contextualization is descriptively accessible in the past progressive tense because doing and describing the doing are descriptively completely separated there. On the other hand, the associated individualization carrying the past progressive forward to the present progressive tense cannot descriptively be accessible because of the incommensurability between doing and describing the doing on the spot, but cannot be denied.
The effect of preceding individualization is descriptively approachable only through the subsequent contextualization (Küppers, 1992). However, there could always be an artifact enabling us to approach the individualization process descriptively. If one can devise such a scheme that any individualization may uniquely determine its subsequent contextualization in advance, the descriptive identifiability of contextualization could also apply to the individualization. A supreme example of this type of descriptive artifacts is seen in the transference from the present perfect to the present tense. The presence of completed and invariant interaction configuration to the global extent reinforces any local participant to be completely consistent with the whole body. Complete synchronization between individualization and contextualization renders the individualization descriptively accessible. In fact, mechanistic causality based upon efficient causation driving the past progressive forward to the present progressive tense uniquely could descriptively be sanctioned only when the synchronization is guaranteed in advance. Otherwise, time as an agency descriptively identifies its activity only in the process of contextualization. The associated intrinsic impossibility in identifying the process of individualization is strictly descriptive in its origin in view of the fact that one cannot do both doing and describing the doing at the same time. Time in the present tense is and has to be necessarily indefinite in its implication. The indefiniteness is not due to the absence of individualization, but to the absence of its independence from the preceding contextualization.
Time as the principle of contextualization is unquestionably materialistic in its operation because of its constant reference to interactions of material origin as demonstrated in quantum entanglement (Schulman, 1997). It is both formal and final in exercising its own causation. Time in the present tense is formally causative in letting the preceding context drive the subsequent contextualization. In addition, it is also finally causative in letting each individual participant as a derivative of the preceding contextualization move toward the subsequent contextualization. Time as a material cause being responsible for material contextualization thus come to precipitate both formal and final causes. Unless it is limited to a measure of the duration of invariant interactions, time can be seen internally causative in letting the material cause preside over both formal and final causes.
7 Quantum Mechanics of Time
Time is multifarious. What is at the least required of clarifying the sturdy issue of time is to identify the condition upon which time is inevitably employed and practiced. Insofar as it is noted that any dynamic movement first materializes itself in the present progressive mode, its descriptive stipulation has to be invoked. The incommensuarability between doing and describing the doing on the spot, however, renders the direct descriptive reference of the movement in progress to the present progressive mode unattainable. Above all, time is a descriptive device to approach the present progressive mode. If it is possible to approach the present progressive through the present perfect mode, time as a measure of the duration of completed and invariant interactions could be sanctioned. Physical sciences have based themselves exclusively upon time as a measure, even including their relativistic cousins. However, once one takes the historical perspective toward physical sciences as practiced in cosmology or in evolutionary biology, the agential capacity of time would also have to be focused. Descriptive prerequisite for appreciating the agential capacity of time is to give second thought to the time-honored practice of letting time be a measure of the duration.
One more candidate for accommodating time into our linguistic institution is to perceive it as the capacity to sustain interactions as the agency crossing from the past progressive to the present progressive mode. Although this observation has severely been under-represented in the common practice of sciences, it squarely faces the linguistic stipulation prohibiting occurrence of both doing and describing the doing on the one and the same ground. The outcome is time as the capacity to sustain the activities of doing. Appraisal of time as an agency is however accomplished only by dismissing the likelihood of direct descriptive access to the present progressive mode. Despite the extraordinary influence of letting time be a measure of the duration in conformity to the tradition of situational logic, our linguistic practice legitimately saves in time itself the capacity to move itself in the form of situational agency. Quantum mechanics certainly carries such a situational agency in the form of measuremet.
Measurement internal to implementing whatever interactions in quantum mechanics is intrinsically local in the sense that there is no physical means for completing the global measurement instantaneously. Every interaction to be met in the unitary transformation in quantum mechanics has to be a construct of internal measurement that is strictly local. The present difference between internal measurement and the unitary transformation is in fact more than just being physical. The difference is even linguistic in a more significant manner. Internal measurement addressing the dynamics of measurement internal to arbitrary material bodies is unique in its present progressive mode compared to the unitary dynamics in quantum mechanics. Although it can yield the unitary transformation in progress, the unitary dynamics rests upon an invariant characteristic specified in the present tense as embodied in Hamilton’s principle of mechanics. In contrast, internal measurement or measurement dynamics of material origin founds itself upon the present progressive mode that is necessarily local. An invariant characteristic on the global scale, if any, can be salvaged only in the present perfect mode when it has been registered as an irrevocable record. The issue of measurement in quantum mechanics thus urges us to see how material movements including biological ones manifesting themselves in the present progressive mode could be vindicated and how they could be described, whether in the present or in the present perfect tense, or whatever else for this matter.
Measurement is about the process of sending and receiving material signals of a local character. Since those signals to be exchanged have recourse to material resources, measurement internal to material bodies has to fulfill at the least the condition of resource limitation as in the form of the conservation of energy or energy flow continuity. At the same time, interactions implemented by internal measurement set the further conditions for how subsequent internal measurement would proceed. The present local nature of interactions based upon internal measurement now imparts upon these interactions also a temporally asymmetric character such that the global invariant of interactions, if any, is consequential upon the occurrence of internal measurement rather than the other way around. Material interactions due to the exchanging of material signals of a local character are thus constantly in the process of fulfilling the global condition of the conservation of energy, among others, from within. One then observes that material interactions grounded upon internal measurement are internally cohesive in exercising the capacity of pulling material signals of a local character for the sake of fulfilling the conservation of energy on the global scale. Although pushing is a mode of interaction forced by the context external to the object to be pushed, the activity of pulling is internally caused from within due to the fact that any material signal to be exchanged in the process of internal measurement is pulled and absorbed by one party of the interacting bodies without being forced to do so externally.
Cohesive interactions based upon internal measurement is strictly local in its origin. Their actualization is constantly in the present progressive mode in that there are many cohesive agencies each of which is exercising its own capacity locally without having prior global coordination with all of the others of a similar nature. This exhibits a marked contrast to electrostatic interactions, that are cohesive between two of oppositely charged particles, conceived within the framework of the unitary dynamics of quantum mechanics. Electrostatic interactions in the unitary dynamics are describable in the present tense as in the form of the unitary transformation of a state vector in the Hilbert space and are not agential anymore as letting every charged particle move in the manner of being pushed by the definite boundary conditions the dynamics takes for granted. The agential activity of pulling unique to cohesive interactions upon internal measurement survives exclusively in the present progressive mode. This observation necessarily implies that the agential capacity latent in the cohesive interactions could totally be dismissed if the descriptive artifact sticking to the present tense is maintained at all costs. No dynamics prescribed in the present tense is agential because what has descriptively been specified in the present tense remains invaraint as it is at any present moment. The present dismissal of agential activity is however merely descriptive in its origin. Once a descriptive artifact sticking to the present tense is lifted, material dynamics can reveal the agential capacity on the very material grounds. The descriptive vehicle for appreciating such an agential capacity is found within the present progressive mode.
At issue is the nature of the linguistic artifact to be adopted in any case as facing dynamic movements proceeding in the material world. If dynamics in the present tense as with the unitary dynamics of quantum mechanics is attempted, there would be no room for agential activities to survive within the dynamics. On the other hand, dynamics in the present progressive tense as with internal measurement is the case, it will be the rule to observe agential activities to be exercised.
Comparing these two modes of describing dynamics, one comes to recognize that the present progressive tense is too loose and too weak to come up with a definitive description because of the involvement of plural active agents, while the present tense monopolized by a single agent identified as the descriptive author is too restrictive to allow in itself the room of agential capacity to emerge from within from the outset. A more pressing issue will be to supplement the dynamics in the present progressive mode, if ever possible, by something else that can avoid imposing an unnecessary and unjustifiable artifact of descriptive origin, such as the one encountered in the present tense, as much as possible. One candidate for satisfying this role will be observations made in the present perfect tense, since the events in the perfect tense can remain frozen in the record as they were while keeping a legitimate distance from the action in progress on the scene.
Quantum entanglement is in fact identifiable in the record registered in the present perfect tense, while measurement in the present progressive mode is constantly holding multi-agential character of time at the same time. Emergent phenomenon of material origin turns out to be a convoluted interplay between quantum entanglement in the present perfect tense perceivable even by a single agency identified as an impartial observer and multi-agential measurements in the present progressive mode.
