The Concept of Event-Driven Time

Sergey K. Aityan Lincoln University, 401 15th Street, Oakland, California 94612, USA

Abstract: The most fascinating feature of time is that there is no time at all. This study introduces the concept of event-driven time. Time is considered a count of changes or events that set up a local “clock” in each system. With such an approach, every system runs its own local time. Time does not exist without changes in the system. As two systems interact, they generate a sequence of interaction events that are being added to the internal pool of events in each system. Any observation is made with the local time of the observer system and this fact changes the observer’s local time by adding observation events to the observer’s time count. Local time in any finite and closed system is finite and obeys the saturation principle due to limitations of the event counting capacity of the system. Traditional continuous time is a convenient approximation for the enormous number of events occurring in our world that set up our local “clock”. The event-based approach does not conflict with modern physics but proposes a new view of the fundamental notion of time and brings us one step closer to understanding the world in which we live. The greatest mystery of the notion of time is that there is no time at all.

Key words: Time, nature of time, event-time, quantum time

INTRODUCTION speed of light (the group speed) is an invariant constant that cannot be exceeded. Time is the most fascinating feature of matter. The Relativity and quantum mechanics have opened a concept of time has always been a cornerstone of all new page in human understanding of space-time and theories in physics and other disciplines of natural matter. Both approaches are dealing more accurately sciences. In the past, people thought of time as a with the concept of an observer and its impact on the universal outside clock ticking independently of matter observation. In his study on the uncertainty principle, and space, just tracking all processes in the universe. Heisenberg wrote “I believe that the existence of the Isaac Newton in his Principia, Newton, 1687 (Newton classical ‘path’ can be pregnantly formulated as and Reviewer, 1999) wrote,- “absolute, true and follows: The ‘path’ comes into existence only when we mathematical time, of itself and from its own nature, observe it” (Heisenberg, 1927). The essence of this flows equably without relation to anything external.” approach implies that the observer changes the Later, as the theory of relativity (Einstein, 2004) observable system by getting into an observation emerged, the concept of time has become more closely interaction with the observable system. tied to matter and space. One of two fundamental The Big Bang theory states that the universe and postulates of relativity is based on the Lorentz space-time originated with a huge explosion about transformation and declares the invariance of the speed fourteen (some estimates may vary) billion years ago as of light in a vacuum. It states that in vacuum, light propagates with respect to any inertial frame and in all an expanding ball of fire that keeps expanding. Some directions with the universal speed c and this speed is more recent studies extend the concept of the Big Bang constant of nature. As a conclusion derived from this to the Self-Reproducing Inflationary Universe (Linde postulate, it became evident that time runs differently 1994) where “the early universe came through the stage at high speeds of motion of matter (Einstein, 2004) as of inflation, exponentially rapid expansion in a kind of well as at gravitational extremes (Hawking, 1998; unstable vacuum-like state (a state with large energy 2001). These results have turned the notion of the density, but without elementary particles). Vacuum-like universal clock into a new concept of local clocks state in inflationary theory usually is associated with a being a part of space-time. However, the postulate of scalar field, which is often called ‘the inflation field.’ the invariance of the speed of light does not reveal the The stage of inflation can be very short, but the fundamental mechanisms that would explain why the universe within this time becomes exponentially large”.

© 2011 Sergey K. Aityan. This open access article is distributed under a Creative Commons Attribution (CC-BY) 3.0 license which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly credited. DOI: 10.3844/pisp.2011.40.49 Phy. Intl. 2 (2): 40-49, 2011

For thousands of years human beings have been Thus, events in the observable system are referred learning how to measure time, but we are yet far away to events in the reference system (observer). However, from a clear understanding of what make time run. the question arises, what kind of events must be What makes time run slowly in matter and space at referenced. We refer the registered events in the near-light speeds and near gravitational extremes and observable system to the measurable events in the how does time run differently in condensed matter reference system. For example, as we observe a versus in “light” matter and space? Was there a process, we register observable events in the process- beginning of time? Will there be an end? Though say, steps of the process we are able to register-and significant progress has been made in modern physics refer them to the time measuring events in the in understanding space-time, the internal structure of observation system as a count of periods between the time and the fundamental mechanisms that bring time events in the observable system-say, clock measuring and matter together have yet to be discovered. events-which we consider the accuracy of the clock. To answer these questions first we have to understand what time is. The mystery of time has The notion of time: Let’s try to analyze time as a constantly puzzled researchers and some of them have measure of the evolution of matter and space. To avoid already made various attempts to understand its internal any possible confusion, let’s consider time as a structure and the mechanisms that make it flow measurable quantity used to specify the order in which (Barbour, 2001, 1994; Brout, 1987; Green, 2005; Don events occur in the system. Time periods are being and William, 1983; Smolin, 1991; Zeh, 1999). Does measured by the number of events which precede or time exists on its own, is it a part of space, or does time follow. Thus, for time to run it needs events to occur not exist at all (Barbour 2001; 1994; Don and William, Aityan, 2002. 1983; Stenger, 2000). This study is an attempt to get inside the internal Timeless system: Imagine system S α in which no structure of space-time and matter and try to uncover events are happening. The state of such a system stays the possible origin and mechanisms that make time run. unchanged and no time is running inside the system. For time to exist in the system at least one event must Time as a sequence of events: take place, otherwise the system has no time at all. The The concept of time: It would be a mistake to try to hypothetical system defined above has no grounds for understand time by using the notion of time itself. So, having internal time because it shows no evolution or what can we do if every theory in physics that describes changes. The system stays “dead” awaiting for events motion of matter uses time as a parameter? Let’s try to to launch its time mechanism. set apart the notion of time and see how the concept of time can be derived from the notion of matter and its Time between the same events from different transformations. By no means am I trying to remove observation views: Assume an observer from our time from matter and space, rather, just making an world (system S A)-where time is running in its natural attempt to understand its nature and dynamics. course-has managed to make two observations of another system, S B, at two different points in time of our world (S ), t and t . Taking into account that no Events and the count of changes: We mention time to A 1 2 observation can be made without interaction and that refer to the changes in the observable system by interaction generates events, a number of events must mapping the appropriate events in the observable be generated by that observation. For the sake of system to some reference events in the reference simplicity, assume that every observation generates a system. For example, by saying that a tree grew by one single event. Let’s call it an “observation event.” Thus meter last year, we refer to the changes in height of the from the perspective of our world, the time elapsed tree as one full circle of the earth around the sun. between these two observations is equal to t 2 - t1; that Likewise, if we say that the distance between two can be a second, day, month, year or any other period of buildings has not changed during the last week, we time from the perspective of system SA. Assume that refer to no changes in the distance between two only a single event separates these two observations in buildings as seven full rotations of earth around its axis. system S B, or in other words, just a single bit or If we say that a process takes 8.5 sec we refer to all quantum of time has elapsed in SB between two registered events in the process as the reference events observation events in SA. in the time registration device, say, one tenth of a second is a reference event that can be registered by the Time in different systems: The above example time counting device. illustrates that time driven by events runs 41 Phy. Intl. 2 (2): 40-49, 2011

fundamentally differently in different systems. This conclusion is completely in synch with the space-time

concept contemplated in the theory of relativity. However, there is a conceptual difference between Fig. 1: An event these two approaches. While relativity just ascertains the fact of different time scales in different systems move at different speeds, event-based time describes

the internal mechanism that makes time run differently. This mechanism is responsible for time itself and for Fig. 2: Sequential events the differences in the clocks in different systems. Time Any two events in a system can be ordered by “<”. in each system is being generated by the events in that For example, eα< e α means that eα preceded system, while near-light speeds or super-gravitational k,k1+ k + 2,k + 3 k,k+ 1 event eα , but other events may occur between them. forces could be just one of the factors causing k+ 2,k + 3 variations in the occurrence of events that generate The distance between any two close events shown different courses of time in different systems. in Fig. 2 has no meaning, no value and cannot be For a more general example, let’s consider an measured within the system itself. The fact that some interaction between two quasi-independent systems, S α distance, either equal or different, is shown between the and S β, which engages a much smaller number of events in Fig. 2 is just for illustrative purposes. Every events than the number of events occurring within each event is a single quantum of time. The time, α α system in the course of interaction between the systems. t(eαk,k + 1 ,e k +−+ N 1,k N ) , that elapsed in system Sα between α α If the number of internal events, T α and T β, between two events ek,k+ 1 and ek+ N − 1,k + N by definition is a count of the consecutive interactions between systems S α and S β is sequential events that occurred between the former different, say T α>T β, then the internal time that elapsed mentioned events, i.e. Eq. 1:

between such interactions in S is T which is a longer α α α α α = ek+ N − 1,k + N t(eαk,k + 1 ,e k +−+ N 1,k N )T α (1) time than the internal time T β that elapsed in S β between ek,k+ 1 the same interactions. α ek+ N − 1,k + N where, T α is a count of the sequential events that Definitions of event and time: Let’s assume that there is ek,k+ 1 α α no time at all. Matter exists and is permanently changing occurred between events ek,k+ 1 and ek+ N − 1,k + N which is its state. Let’s call the change of state an event. α equal to N in the example shown in Fig. 2. Event ekm is a single transition between two states α α Observation path: Consider system Sα and all s and s of system S α with no intermediate states k m events occurring in the system. For the sake of between sα and sα . An illustration of an event is k m simplicity, we presume that all events are measurable shown in Fig. 1. α by their energy level and we will use notation ek for Time in system Sα is a running count of events that α e . Let’s mark the events we want to track or observe occur in the system. Thus time is just the count of k,k+ 1 events as shown in Fig. 2. Events can be ordered by in system S α as an observer. We call such events only the “next/previous” relationship that constitutes a observation events. The observation events marked by crosses in Fig. 3 constitute the observation path: sequence of events. We will use sign “ < ” to show the “next/previous” relationship. For example, αα α α Ωα(i,i + K) = (O ,O +++ ,O ,...,O ) eα e α eα eα i i1 i2 iK k,k1+< k1,k + + 2 means that event k+ 1,k + 2 is next to k,k+ 1 or, α α The observation path measures time between the vice versa, event ek,k+ 1 is previous to ek+ 1,k + 2 . Let’s call observations, thus t (Oα ,O α ) is the time between such “neighboring” events close events. In other words, αi i + 1 α α there are no other events between close events, at least observation Oi and Oi+ 1 . In the example given in Fig. within the current accuracy of measurement. It may 3, the time in the observation path runs as follows: happen that as we increase the precision of event registration, more events will be registered in the α α = tα (O,Oi i + 1 ) 3 system and some previously deemed close events α α t(O ,O )= 4 (2) will no longer be close. Thus the notion of close αi1 + i2 + α α = events is subject to the precision of measurement. t(OαiK1 +− ,O iK + ) 1 42 Phy. Intl. 2 (2): 40-49, 2011

Thus one can count specific time intervals between observation events in system S α and these periods of time are defined by the events in the system.

Time saturation: Every finite and closed system has a finite number of possible states and hence a finite number of possible events. This leads to the conclusion that such a system may exhaust its time counting Fig. 3: Observation events capability and consequently must reset its internal time.

Timeless systems: Consider an elementary system that has only one possible state, implying that no events may occur in the system. Such a system has no time at all. For instance, a photon may stay in its current state Fig. 4: System S β until the photon is absorbed by some other system. Emission of the photon and its absorption are the only events in the photon’s life.

The notion of speed: The notion of speed elaborates changes in geometric space per time. Both geometric space and time space (events) have a discrete nature and thus speed represents changes of the position in geometric space per discrete time interval these changes Fig. 5: Completely compatible systems S α and S β take place: Completely compatible systems can share their time = = ⊗ α α and the time in a combined system, SSαβ S α S β , is ∆xα (O ,O ) = i i+ 1 vα α α (3) a superposition of times in system S and system S . t (O ,O ) α β αi i + 1 Thus time measured in the observation path of the combined system S runs as Eq. 4: α α α ∆ α where, v is speed, x (Oi ,O i+ 1 ) is a change of the αβ αβ α α = tαβ (Oi ,O i + 1 ) 6 position in geometric space and tα (Oi ,O i + 1 ) is the time αβ αβ α α = tαβ (Oi1 + ,O i2 + ) 5 (4) interval between observations Oi and Oi+ 1 . Time α α αβ αβ tαβ (O +− ,O + )= 3 interval tα (Oi ,O i + 1 ) represents the minimum time iK1 iK between two close observation events because there are α α In contrast to the time specific to S only that runs as no observations between observations O and O . One α i i+ 1 Eq. 5: of the conclusions of the notion of speed given above is α α = that the commonly accepted definition of speed as tα (Oi ,O i + 1 ) 3 α α dx∆ x α α t(O ,O )= 4 (5) = = ∆ < αi1 + i2 + v lim is no longer valid at t t(O,Oαi i + 1 ) ∆t → 0 ∆ α α = dt t t(OαiK1 +− ,O iK + ) 1 and must be replaced with the definition given in Eq. 3. as shown in Eq. 2. For the time between systems S α and Local time in subsystems: Sβ to be shared, every event in the combined system Completely compatible systems: Two systems are must be observable from both subsystems. completely compatible by time if their combined events can be ordered into a single sequence of events. Parallel (Non-Compatible) systems: Two systems, S α and S β, are parallel (non-compatible) by time if none of According to the definition above, two systems, S α the events of system S α can be ordered as and S β, are completely compatible by time if the “next/previous” with any of the events in system S β and “next/previous” order can be set to all their combined vice versa. events. In other words, both systems constitute a single As follows from the definition of parallel systems, system in terms of time. Assume that system S α shown time in parallel systems cannot be tied up to one in Fig. 3 is combined with system S β shown in Fig. 4 to another due to the incompatibility of their events order. = ⊗ define a new joint system S Sα S β as shown in Fig. 5. The events in parallel systems cannot be cross-ordered. 43 Phy. Intl. 2 (2): 40-49, 2011

Fig. 6: Orthogonal systems S α and S β Fig. 7: Time in two systems For example, if no other information in available, systems S α and S β shown in Fig. 3 and 4 are parallel. Systems S α and S β share two common states, αβ αβ However, as soon as an observer identifies both parallel sm and sn . These common states may occur as a result systems the observer itself becomes a link between the of interaction between S and S β . Suppose observation systems through the observation events that makes the α Oα eα Oα initially parallel systems no longer parallel. We will events in system S α are 1 , which is k+ 1 and 2 , which α come back to analyze this phenomenon later. is ek+ 5 . Similarly, suppose observation events in system In parallel systems there is no way to say which β β β β Sβ are O , which is e and O , which is e . With no one of two events in different systems occurred earlier 1 i+ 1 2 i+ 3 or later than the other one. other interactions between the systems they have only α α two cross-time reference points each: O and O for S α Orthogonal (Partially Compatible) systems: Two 1 2 and Oβ and Oβ for S . This means that the following systems are orthogonal (partially compatible by time) if 1 2 β the systems are not completely compatible by time but cross-order of events can be established: at least one event of one of the systems can be ordered eαβ e ande αβ e forS→ S as “next/previous” with at least one of the events of the k1++> i2 k5 ++ > i4 αβ other system. An example of orthogonal systems is shown β in Fig. 6. Both systems share a common state, sa , that and β βα βα allows for a “next/previous” order between event ei+ 2 of → ei> e k2+ ande i3 ++ > e k6 forS βα S α system S β and event ek+ 2 of system S α as well as α β where, “ →” denotes the direction of view. Thus from between event e + of system S α and event e + of k 1 i 3 α α α α the perspective of S α, four events {e+ ,e + ,e + ,e + } system S β. Though time in systems S α and S β are k2 k3 k4 k5 basically incompatible, the history of both systems can occurred between the measurements, while from the β β β perspective of S β, only two events {e+ ,e + } occurred be compared with reference to event e3 i.e. can be i2 i3 β referred to the common state sa that belongs to both S between the same reference points, i.e.: α and S β as a reference point. Such “intersection” creates t (Oα ,O α )= 4 a common point of reference in the history of the α 1 2 (6) β β = systems incompatible by time. Though it is impossible tβ (O,O1 2 ) 2 α β to say which event, for example em or en , occurred earlier or later than the other, one can easily say that Eq. 6 explicitly shows that time is running β α differently in S and S β and different counts of time event en in S β follows event ek in S α. Thus in α orthogonal systems some events from different systems elapsed between two mutual observations. There are no can be ordered by time while some events cannot. other time references between these two systems. For example, it is impossible to set any order between α β Time viewed from different systems: Consider two events ek+ 3 and ei+ 2 . subsystems, Sa and Sβ, that interact only by two observation events, i.e., they share two common states Time absorption: As two systems interact, they add as shown in Fig. 7. interaction events on top of their internal events and 44 Phy. Intl. 2 (2): 40-49, 2011

hence increase the number of events in each system. Thus every interaction between two systems adds up to the time count in each of them. One can say that each of the interacting systems observes the other if the system is capable of counting time. Consider two independent

systems, S α and S β and some time intervals in those systems Eq. 7:

α α α = ek 2 tα (ek1 ,e k2 ) T α ek1 (7) β β β = em 2 t(eβ m1 ,e m2 ) T β em1

Assume that interaction between systems S α and S β αβ αβ has generated additional events {en1 , ... ,e n2 } between events eα and eα in S and additional events Fig. 8: Observation of two systems k1 k2 α βα βα β β {er1 , ... ,e r2 } between events em1 and em2 in Sβ. As a Observing time in two systems: Imagine two result, the time count in both systems has changed to absolutely identical but separate and not interacting Eq. 8: systems, S α and S β, that go through the sequence of events as shown in Fig. 8.

~ αα αα αβαβ α αβ ek2e n2 t(e,eα )= t(e,e ) + t(e ,e ) =+ Tα T αβ Assume that the sequence of events in system S α: k1k2α k1k2 α n1 n2 e e k1 n1 (8) α α α α ~ {ek1+ ,e k2 + ,e k3 + ,e k4 + } is identical to the sequence of ββ ββ βαβα β βα em2 e r2 t(eβ ,e )= t(e ,e ) + t(e ,e ) =+ Tβ T βα β β β β m1m2β m1m2 β r1 r2 e e m1 r1 events in system S β: {ek1+ ,e k2 + ,e k3 + ,e k4 + } . It implies that the internal time in system S from the view of system Let’s call this phenomenon time absorption. It is α S runs identically to the internal time in system S β clear that with more interaction between these systems, α from the view of system S β Eq. 9: more time is being added to both of them. αααα= ββββ = t(eα++++k1k2k3k4 ,e ,e ,e ) t(e β++++ k1k2k3k4 ,e ,e ,e ) 4 (9) Observation and observer:

Observation, observer and existence: Anything we know about our world must be observed otherwise we For the sake of simplicity, let’s assume that every have no chance to know about it. For example, if an event in S α and S β results in the emission of a particle, entire other world exists somewhere in the universe- say, a photon that can be observed by system S 0. Each even close to us-but we are unable to interact with it, time for S α and S β from system S 0 runs differently for then it does not exist for us until we find a way to Sα and S β: interact with that other world and observe it. By observation we mean more than just explicit αα α α α = = t(eOk1k2k3k4++++ ,e ,e ,e ) t(e On3 + ,...,e n9 + ) 7 observation, i.e., an observation made directly by our ββ β β β (10) t(e ,e ,e ,e )= t(e ,...,e ) = 11 senses. Some observations are implicit; for example, O k1k2++++ k3k4 O n1 + n11 + humans do not explicitly observe the chemical content of food they eat but the chemical content Furthermore, every event in S α is registered with impacts the human metabolism and finally the human every other event in observer S 0, i.e., the observation body. In this study, observation refers to a general shows the same time periods between the events meaning of interaction without differentiating observed in S α while the time periods observed between explicit and implicit observation. events in S β are different in S 0. The time periods We understand the observer as a system that is able between the events in S observed by S run as (2, 2, 2) to interact with the observable system and does so by α 0 while the time between the events in S β observed by S explicit or implicit observation. 0 run as (3, 4, 3). Though the major focus of this study is on the observation of time, the concept of observation and Thus two identical systems, S α and S β, that have observer can be applied to any other types of identical local internal times may be observed with observation. This concept is completely in line with the different times by the observer. The scale of processes concept of observation and observer commonly occurring in two identical systems may also be skewed accepted in modern physics. by the fact of observation. 45 Phy. Intl. 2 (2): 40-49, 2011

Impact of observations on the local time in systems: Every observation adds up events in both the observer system and the observable system. In the macro world, the number of observation events is negligibly smaller than the number of bulk (internal) events in every system. Therefore, in the macro world we never register any impact of the observation on time. However, if the number of bulk events in the observer system is comparable or greater than the number of observation events generated by the observation, then the impact of Fig. 9: Back tracking along the time thread by view from Now the observation must start playing a significant role in the flow of time. β βα em2 e r2 Tβ<< T βα e e (15) Consider two systems, S α and S β, where S β is an m1 r1 observer and S α is an observable system. Fundamentally, there is no difference between an observer and an Leads to: observable system because both systems are observing ~ ββ βαβα ββ β ≈ >> each other as they interact. In the present example we have t(em1m2 ,e ) t(eβ r1 ,e r2 ) t(e β m1m2 ,e ) (16) identified the observer and the observable system just for convenience, so all further considerations are also This implies that the time course in observer Sβ applicable in the opposite direction. was dramatically changed due to the observation.

Weak impact observations: Assume that the number Normal observations: The fact that in our normal day- of internal bulk events in observer Sβ is much higher to-day observations we do not register the impact of than the number of observation events in the observer. each observation on time just implies that the number of In this case, Eq. 11 shows the differences in time, bulk events in our world is much higher than the similar to Eq. 10: observation events we are registering. As we start coming

β βα to extreme areas where the number of observation events e e m2>> r2 Tβ T βα (11) becomes comparable with or higher than the number of em1 e r1 bulk events, we most likely start registering an impact of that leads to Eq. 12: the observations on the system clock.

~ ββ ββ Multidimensionality of time: t(eβ ,e )≈ t(e ,e ) (12) m1 m2β m1 m2 Virtual time threads: At any particular moment (event eα ) in system S , events can be tracked back to This implies virtually no changes in the time t α course of the observer generated by the observation. past events along the time thread that led to the current state of the system as shown in Fig. 9. In other words, Equal impact observations: Assume that the number the system itself knows its history. However, an of internal bulk events in observer Sβ is comparable observer is capable of knowing the history of system S α with the number of observation events in the observer. only to the degree of observation events that link S α In this case, as with Eq.10 and 13: with the observer. If an observer places himself at one of the past states of system S α and tries to predict the β βα em2 e r2 Tβ≈ T βα (13) next event, he will face multiple possibilities due to the em1 e r1 uncertainty or probabilistic nature of the events in the that leads to Eq. 14-16: system as shown in Fig. 10. α Thus from the perspective of Now a, event et− N is a ~ ββ ββ βαβα ββ β = + ≈ certain event that was a member of the time thread t(em1m2 ,e ) t(eβ m1m2 ,e ) t(e β r1 ,e r2 ) 2t(e β m1m2 ,e ) (14) leading to Now α. On the other hand, from the α This implies that the time duration in the observer perspective of event et− N , several different threads is about to double due to the observation. <α, β, γ, …> have chances to be realized and thread <α> leading to Now α is just one of them. For the Strong impact observations: Assume that the number observer located at Now a, all other threads < β, γ,…> of internal bulk events in observer S β is much less than except thread < α> shown in Fig. 10 can be considered the number of observation events in the observer. In virtual threads, i.e., the threads that were possible but this case, as with Eq.10: not realized from the perspective of Now α. 46 Phy. Intl. 2 (2): 40-49, 2011

in the time threads cannot be compared or ordered with future events in the other threads unless these threads will intersect in the future. Assuming that our universe goes through an infinitely large number of events that originate an infinite number of virtual time threads, one can conclude that time has an infinite number of dimensions. Thus every state of matter in our universe opens a possibility for multiple virtual events that create virtual time threads. Then, every virtual time thread may split into multiple time threads at every further event. In a finite system the number of virtual threads is large but finite, while in an infinite system the power of the set of all virtual threads is infinite {2 ⁿ} which makes it

uncountable or continuum. Fig. 10: Dual view at the causality thread As long as disorder increases as the universe evolves, it creates more and more virtual threads and hence dimensions of time.

The past and the future: As mentioned above in a discussion on virtual time threads, all past events (or previous events) on the time thread viewed back from a position on a time thread, such as Now α, have occurred with certainty while future events are yet uncertain. This makes a substantial difference between the past and the future. One can say that the past is a sequence

of events that have been realized while the future is a Fig. 11: Multiplicity of virtual threads possibility of events that may occur. Thus any current observation point is a break point between the past and All these threads define orthogonal systems because the future, which have quite a different nature. they are not completely compatible by time but have at I would like to avoid creating a wrong impression α least a common reference at et− N . that the future cannot be predicted by the application of α In general, the virtual threads originated from et− N this theory. Any observable process is a sequence of are shown in Fig. 11 which illustrates multiplicity of observation events as shown in Fig. 3. These virtual threads. Virtual thread < α> is shown in Fig. 11 in observation events are a small subset of the other bold lines. Let’s call the virtual threads virtual worlds. events, referred to as bulk events, happening in the To summarize the different perspectives from different universe. Thus in predicting a future under the positions of the observer on thread < α>, one must note assumption that the chosen observation events have a that from the perspective of Now event eα is a negligible impact on the bulk events in a system, we α t− N can consider the bulk events to be the main time definite ancestor of Now while any Now is a α X< X =αβγ ,,... > generating events that set up a reference “clock” for the α virtual descendant of event et− N from the perspective of observation events in the process as discussed above in event eα . this study. It is clear that such clocks are basically t− N measuring different counts of time depending on the process, environment, points of reference and specific Dimensions of time: Every virtual time thread conditions of matter. If a process significantly impacts the represents a new dimension of time. The time in a bulk events in a system by significantly changing the virtual time thread is not compatible with the time in number of bulk events, then setting up a reference “clock” any other virtual time thread except for the common in the system may become a more complicated task. point of reference or points of reference represented by The implication is that such local clocks can be the common event or events in the past from which different for different systems, subsystems and these threads were originated. It implies that all virtual observations and that there is no universal clock for time threads that originated from any event have this many reasons, at the very least because there is no common “time” point of reference, while future events universal observer. 47 Phy. Intl. 2 (2): 40-49, 2011

The arrow of time: As noted by Stephen Hawking, originates and runs. Though all of us have already been “Disorder increases with time because we measure accustomed to the discrete (quantum) nature of matter time in the direction in which disorder increases” and space in modern physics, we still keep considering (Hawking, 1998). time to be a continuous and scalar parameter. The The event-based approach defines arrow of time as approach taken in this study makes time a the “next/previous” relationship between the events in multidimensional component of the multidimensional each virtual time thread. However, there is no such space and matter. The greatest mystery of the notion of notion as an arrow of time between different time threads time is that there is no time at all. It is a derivative for the events that cannot be ordered into the concept of the motion of matter. Matter creates time in its “next/previous” relationship. It is quite possible that time evolution as a measure of changes in matter and space. may not be obeying a straight arrow of time between This concept of time is believed to provide a new orthogonal and partially orthogonal time threads. angle of viewing space-time as a unified entity. It is For the finite and closed systems, the arrow of time expected to find experimental proofs of the theory in may reset as time in the system saturates and that brings astronomy and cosmology, in elementary particles and the system to some previous and pre-existed state. Such at low temperatures where the number of bulk events an effect may change or reverse the arrow of time within starts deviating from what we have in our normal the same virtual time thread. With an interaction between world. For example, a reflection in a cold mirror at a different time threads, such effects may occur even low temperature is expected to show some red shift without saturation of time in any specific time thread. unlike the same reflection at higher temperatures. Time originated in the universe at the Big Bang, Transition to the continuous time: To extend the but it runs differently in different systems in the definition of time given in this study to the world where universe and even differently at different stages of the we belong, one can say that most measurements we evolution of the universe. It is quite possible that time make represent the observation paths upon a sequence at the early stages of the universe ran differently from of an enormous number of other events occurring in the time in our days and what from today’s view would be system that set up the “clock” for the system. Let’s call a split fraction of a second just after the Big Bang these other events “bulk events”. These bulk events would be billions of years from a point of view closer make us believe in the existence of the “universal to the time of the Big Bang. clock” ticking with no regard to the processes we The event-based theory of time presented in this measure. However, as soon as we start pushing the study is believed to be just the first step in a envelope to the extreme, a more accurate understanding comprehensive study in this area. There are still many and interpretation of the notion of time must replace questions to be answered and more detailed theory to be such a traditional understanding of time. developed in line with the concepts of this study. It Though time is measured as a count of events and would be interesting to learn more about the interaction has an inherently discrete nature, actually, time can be of matter, space and time and its dependence on energy. treated as a continuous parameter in large systems due As long as disorder increases as the universe evolves, to an enormously large number of diverse bulk events the concept of entropy of time should be considered per every measurement. The transition from a discrete with regard to the arrow of time and to a continuous description is typical for physics and multidimensionality of time. It is very important to other sciences, for instance, the transition from show how event-based time describes the fundamental quantum mechanics to classical mechanics or the laws of physics. It is quite possible that the postulate of application of the continuous approach to population invariance of speed of light in a vacuum in the relativity dynamics even though the population consists of a and uncertainty principle in quantum mechanics are discrete number of individuals. Thus continuous time is based on the quantum (event-based) nature of time. It just a convenient approximation for the fundamentally would not be surprising if universal constants in physics discrete (quantum) time. In this regard, we have to be become no longer constants but a reflection of the ready to find out that even continuous time runs current state of matter and space. All these and many differently in different systems under much broader other questions will be addressed in our future research. conditions than has been defined by relativity effects. The greatest mystery of the notion of time is that there is no time at all! CONCLUSION ACKNOWLEDGMENT This study has addressed the nature and structure of time as an immanent count of the evolution of matter I greatly appreciate extremely helpful and and space. The main focus was on the foundations of challenging discussions with and comments by the event-based theory of time that explains how time Professor Octavian Ksenzhek (Ukrainian 48 Phy. Intl. 2 (2): 40-49, 2011

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