Valentin Koulikov (Verizon Business)

Published in physic.philica.com

Abstract
A new approach is hereby suggested to the unification of quantum and relativity principles. It is shown that the assumption of all of the physical processes going back in time leads us to a new clear and unified interpretation of fundamental phenomena of quantum and relativity physics: quantum probability and uncertainty, real and virtual quanta, quantum identity, entanglement, existence of fundamental speed, timelike and spacelike intervals, bosons and fermions, etc. A clear understanding of the meaning and interconnection of the concepts of time, space, energy, observation and information could be reached within this approach. The fundamental equations of quantum and general relativity physics are derived from subject-object local dynamic symmetry (local observation) based on the approach.

Article body

1.      Introduction

While going on the long way of human knowledge it is very useful from time to time to stop and to look around carefully. It seems that the moment has come to seriously reconsider one extremely long-lived and powerful "taboo" in physical science.  Let us take a fresh and unbiased look at the principle of causality.

Questions on the boundaries and possible non-universality of the famous principle have been asked long before, see among many famous Gödel articles [1]  on the matter of CTC (Closed Timelike Curves or simply time loops), works of Thorne et al [2] and even the early work on two-directional time of Wheeler and Feynman [3]. Yet no one has ever considered the possibility that the principle could be wrong as it is, fundamentally. It is true that in classic terms of causality quantum mechanics seemingly breaks the principle, for example in such concepts as virtual quanta and the processes "within Heisenberg uncertainties" but, once again, it was never considered as "real causality breaking". In the case of time loops (CTC) in general relativity, causality breaking was never considered local and in quantum mechanics it was always considered both probabilistic and non-observable.

An intriguing question remains though, what if there is no causality at all whatsoever? What exactly would happen if all events in the "classic", non-quantum universe are allowed to go back and forth in time? Interestingly enough, one without bias would find that most things would seem to go exactly the same way they are going in reality, except that many fundamentally unexplained  physical features of the universe (now taken "for granted", like "energy", etc.) would acquire extremely plain and natural explanations.

One can remind himself that the very "fabric" of General Relativity (GR) space-time is made from local "elementary events", that is from elementary "changes", located in space and time.  These events are "observable" in the way that they could be "observed" by "observer", which in general could be any other event (detector), changed by interaction with the "causally preceding event".

Let us assume now that each and every event in the universe can go "back in time" or, in other words, let us look at each "elementary event" as at an actual "elementary loop in time" (do not mix this elementary infinitesimal loop, representing a single space-time "point" with Closed Timelike Curves, which consist of many points). What does this possibly mean?

Fundamentally going back in classic local time means that all of the things are "restored" exactly to the way they used to be "before".  For an elementary event it means that the whole observable change of this particular event "consists of" is "rolled back" to its original state.  To put it plainly, after the loop is done, no changes and no event "occurred" to any (local) observer.  In other words, an elementary loop in time, by itself and as a whole, cannot be observed by classic observer - in principle. And what can be observed instead?

The first "half of the loop", of course, representing an actual elementary change which means that the event "is observed". Then, after the loop is finished and "started over again", the original event (half of the loop) will be effectively "duplicated" in a way, very familiar to those who read science fiction novels about travelers in time. A loop in time means duplication, or mathematically speaking, a recursive fundamental operation (like recursive "+1") where all the fundamental units are identical, indistinguishable from each other. Except the event itself, duplication is the only change observable after the loop is done and by definition of information  there is no way to distinguish one elementary event from its own double.

Now, what "lay in between" these classic duplicates?  The second "unobservable half" of the loop, the half where the event actually went back in time. This "antitime" interval between the identical events cannot be considered as "time" interval, because there is no change observed. To the classic observer these two events occurred "simultaneously", or in other words, the only event was a duplication itself.  This means that an "antitime" interval between duplicate events actually could be interpreted as an entity that we are used to term as  "space". As we will see, space in our approach, serves actually as a memory storage of the past (processed) events.

What we have here? Obviously, after just a few elementary loops, considering that all duplicates are identical, our universe will be growing exponentially, being started from single elementary loop, which gives us a classic qualitative example of the inflation stage of universe evolution. All the events in such a universe are fundamentally identical twins of the first loop, so if an observer wants to get a definitive answer to the question which one event of many it is observing right now, the answer could not be given. Among other things it means that any process of physical numeration of elementary events, as a process of assigning space coordinates to the events in any particular physical reference frame would be fundamentally probabilistic. For example any attempt to trace any particular observable event chain like "particle movement" has to take into consideration that "space position" could be assigned to the particle in a probabilistic way only.  On the other hand, time coordinates would be based on the chain of observable and distinguishable changes (bits of information), which could be ordered and numerated easily.

It is easy to see that the behavior of these elementary loop-events is very much similar to what we have with quanta in quantum mechanics. It is needed to stress though that we remain in a strictly classic physical realm now.  The only assumption we have made is that we allowed classic elementary events to go back in time. This assumption quickly leads us to the universe actually very different from the classic universe of General Relativity. In Einstein theory we have a set of elementary events with almost predetermined ordering and numeration. It looks like that "by definition" each and every event in the universe can get a unique set of numbers that we call coordinates. Now we can see that it may be not the case at all. General Relativity by itself does not prohibit events to go back in time, all it does is that it distinguishes timelike events (intervals) from the spacelike.  Now we see that the events divided by spacelike intervals may be indistinguishable from each other, identical. There is no way for an observer to assign a unique set of space coordinates to any event. That gives us a totally new picture of a classically probabilistic universe. As we will see, going further this way we will come to a picture that is almost indistinguishable from what we have in quantum theory, but based on classic assumptions.  It is easy to see that Bell's theorem [4] is not applicable to our case when causality is broken, so entanglement phenomenae gets here its natural interpretation. Entangled events are actually one and the same classic event here. Thus this approach looks like an ideal way to unify quantum and relativity principles in a smooth way.

Before going further to the mathematical side let us make some significant notes.

First of all it cannot pass unnoticed that this approach is much about information in its fundamental interconnection with space and time. The very fact that going back in time cannot be observed locally is a direct consequence of the nature of information as it is. Because there is no change in "antitime"(space), there is no information. No information means no observation. (probably that's why the space (vacuum) looks that "empty".) So a theory based on essential local non-causality has to be a theory of information, a theory of symmetry/interaction between object and subject. Even more, as we will see, information appears to be a universal invariant of this fundamental symmetry.  There has been a lot of effort recently to include information into the very foundation of physics [5, 6, 10-12] and this particular approach is definitely going the same direction.

Second, all elementary events (quanta) in such a universe are identical not only to each other, but also to the very first (primary) event, being the universe itself. This means that all the observable scales and all observable sizes of "identical" events are relative in such a universe. In the very same way the relations like "inside" and "outside" become relative too.  All quanta are "inside" the universe - and the universe is "inside" each and every quanta, as well as it is "outside" them. Corresponding relative sizes are derived from particular space-time relations of the quanta such as "perspective", and fractal "self-similarity", etc.

Third, the existence of such identical events forming the very fabric of space-time actually means the existence of fundamental "maximum speed" of observable chain of events, which are able to carry information (speed of movement). As one could see, maximum observable speed in the chain of events is an amount of elementary space intervals which are "overcome" within certain amount of elementary time intervals (elementary changes, bits). If there are no space intervals (timelike curve in the rest frame) there is nothing to "overcome" and speed is null.  If there are no time intervals (spacelike curve in the rest frame) there is nothing to observe (no changes at all), so speed is null also.  Therefore there has to be a maximum speed somewhere in between.

Fourth, elementary events-quanta would be seen in two basic forms, corresponding to timelike and spacelike intervals, which are natural to term as  fermions and bosons.  Fermions are directly observable events, that correspond to actual changes that could be ordered in time.  Quite opposite, bosons could be observed in an indirect way only, by the change-interaction of fermion pairs, in the same way as identical twins are observed in the time loop (simultaneously). Therefore bosons could not be ordered. It could be shown that well-known statistics of fermions and bosons are derived directly from this fundamental fact.

And fifth, because of the fact that all elementary events-quanta are formed in "generations", sequential loops, an observer (detector) at the same time could observe quanta from all different generations.  Despite the fact that their observed location is unpredictably probabilistic, the influence of any particular quanta onto other quanta will be significantly related to its actual generation, which could be found out by ordering. After all, "later" generations are formed from the "earlier" ones. This "perspective in time" will create a hierarchy among events-quanta, identical in almost everything except the level of their relative influence on each other. Again, this fact is very much illustrated in science fiction novels about almighty travelers in time. What the authors of such novels have really missed was that this level of influence on each other was the most natural way of explaining one extremely well-known and famous but still totally unexplained physical phenomenon usually termed as "energy". According to our approach whenever people use energy they actually use an influence through time.

As a result one gets a classic physical realm picture of an essentially fractal and probabilistic observable universe. Phenomena of time and space with 3 dimensions both (corresponding to past, present and future tenses in time) get their clear explanation.  This universe resembles in many details the Everett's quantum universe [9] with the significant exception that instead of multiple universes we have just a single universe. In space of it all of the previous "time loop results" are "stored" like in a memory. In an observed single history of the single universe many probable "histories" are actually created in the many "moments of observation" by physically existing but locally non-observable interaction between the events-quanta via "back in time".  The observable universe significantly depends on how we, among the other detector quanta look at it. One may be confused now by a resemblance to the Copenhagen interpretation and we have to remember that we are coming directly from the classic (but non-causal) picture of the universe without any additional probabilistic or any other assumptions.

This fundamental objective relativity of observation may be named the observation relativity principle  - and this principle opens a real possibility of an actual unification of quantum and relativity principles on a single base of non-causal universe.

2.      Fundamental object-subject symmetry. Space and time.

To follow the suggested approach we have to introduce some abstract model of elementary interaction between an abstract object as a sender of information and an abstract subject or observer as the information recipient. As a model of an elementary event this interaction will therefore effectively become a starting point and further, a "template" for all of the identical elementary events making up the very fabric of space-time.  Generally speaking, almost any piece of physical matter could be an object and also a subject in such an interaction.  Even more, one and the same object can also be a subject, self-acting on itself, being effectively an observer of itself. This suggests a certain level of recursion, of course, or in other words, non-linearity of the physical matter as it is - but it is easy to see that a recursion of this kind was inherently there at the very moment we introduced a loop in time or non-causality.

One can say that there exists a fundamental local dynamic symmetry between object and subject. This symmetry represents information as an invariant of this symmetry. Information is the only feature that is common between an abstract object and a subject, the only feature that is conserved in the transformation of object into subject. Symmetry transformation of an object into a subject describes therefore a process of transmitting information from object to subject. During the process the roles between object and subject may be exchanged many times, so both the object and the subject act here also as information carriers or material signs, representing and containing information.

We can see that the only stable, invariant or, in other words, "most observable" part of this dynamic process is information itself.  One may say that information is the only "survivor" in this process of "survival of the fittest". Information is observed not as it is but always in the form of some material signal. Its invariant nature means that, to put it simply, the "ability to survive" in the universe is much higher for the information than for anything else. By the classic definition of Claude Shannon, information means some change in object that really changes the state of a subject,  if there is no change there is no information. If some object contains absolutely no information at all it would not be observed at all, and by all means should be considered a "survival loser" in the subject frame of reference. Because there should always be some subject in the process of observation, one may conclude as well that an unobservable object "does not exist at all". This will be true only for the subject's particular local frame of reference, of course.

The easiest algebraic way to describe such an interaction has been suggested in my early work [13] (also in [14]) where this process was interpreted in terms of finite groups and abstract linguistics. Due to its obviously controversial matter  (at the time of writing) it still remains unpublished, so it would be helpful to partly reproduce it here. In this approach, an elementary event is defined as a (local) symmetry between subject and object, where the actual coordinates in space and time are derived from the count of such identical events (number of time loops) in ordered (time) or unordered (space) fashion.

Elementary events are represented by finite group operators. At the very beginning, when an object is indistinguishable from a subject (meaning they are the one) there is no change, no information whatsoever and nothing is observed.  This kind of a "primary event" or "the universe before the Big Bang" may be considered as a physical "vacuum event" or "Big Unknown".  Let us denote the vacuum event by symbol  .  This operator, as a single object, forms a finite group of one element, namely, the unit of the group . The cyclic group    has a very simple "algebra": . One can assume that there is no "time flow" at this stage, because there is absolutely no way to observe any difference between degenerated objects/subjects, transformed by cyclic group elements where . A vacuum event could be considered also as a state of "absolute symmetry", because it looks like an absolute Unknown or Nothing, and no transformation by can disturb its undistinguished state.

Things become different with the first actual change. From the very moment of nonlinear self-acting , vacuum-vacuum interacting when a vacuum event is actually observed by itself, the absolute symmetry of the Unknown is destroyed, broken, creating new symmetry, symmetry  between  known (differentiated, changed) and unknown (integrated, unchanged). 

Taking into consideration that operators represent here an actual physical interaction between object and subject (even when they are one and the same), this kind of "original observation" can occur with any level of nonlinearity in the real universe, even if nonlinearity is infinitesimally small. Self-observation in this case may occur after any amount of operations  "doing almost nothing", like until it overcomes the threshold of observation. Before that, nothing happens to the observer, even time does not flow, because there are no changes whatsoever.  But when it is done and the primary symmetry is broken, we get some new element for new group of symmetry - and time makes its first step.

Now we have a group of order 2 with the group unit as a symbol of unknown, unobserved and - the sign of "all that is observed". Let us redesignate elements to and, correspondingly, so the group becomes . Due to finite group properties this group is cyclic, with being a generator of the group: . What happened is effective group unit nonlinear "doubling", where the group unit is "divided" into two elements, opposite to each other in the sense that each is an inverse operator of another . We may look at this process of duplication as at an abstract fractal generation step, similar to the producing of "second harmonic" with doubled frequency, that is well-known in physics of nonlinear processes.

The sign , actually represents a single material sign (process), differentiated from  "unknown" itself, sign which accumulates now all the knowledge about previously "nothing", "unknown". As a material sign it represents a single existing "observational device", or a single subject we currently have.

To transform the "unknown" into the "known", to   we must multiply by :  . The operator , combining operator with equality operator ,  we designate as a regular pair, a translation vector  .  It is the sign of information reception, the sign of "answer" or "observation". The inverse vector   appears to be the same as   in this group, so the sign of "question" coincides with the sign of "answer". Thus, the     operator is the operator of projecting vacuum upon the basis (frame of reference device) , having   as a projection.  On the other hand we can consider it as a projecting operator with basis and projection .  We can say that this is an operator of cognition. The cognition here is a non-interrupting exchange of roles, played by and , where the continuous multiplication by  represents the time flow. While    describes a process resulting in change, i.e. something observable,  inversed process   results in undisturbed state and therefore cannot be observed. The subject is getting only "answers" here and with its "questions" being non-observable the operator looks like a "passive" one.

The process of self-action and gaining information by observation continues. Due to nonlinearity this material process at some point may be considered a sign of itself once again, differentiated from  and . We can redesignate it as .  Now we have a new group of order 3: . Due to the properties of finite groups, is an inverse element to in this group, so an "answer"   as     and "question"    as   are different signs now. However, we can distinguish from each other only the opposite directions of the information flow, and because of the continuous role exchange by the operator action of   we  have   and ,  that  is  to  say,  the answer  is the question  from  the partner's point of view and vice versa.

Our group time cycle is the following:

                        (1)                                                    

The basis designating operator , as a group generator, is a sign creation operator, with  being a sign destruction, or a "sign usage" operator  (we can see here, that the sign is used as a real material device, as a tool).  These operators together form the "life" of the sign, its birth and death . Using vector designations we have for   operator:

- translation from present to  past ;

- translation from future to  present;         (2)

- translation from past to future;

Here we must remember that for the sign (subject!) itself (in his own "rest" reference frame) its birth is in the past, its death is in the future, and in the present we have only.  We can now make some natural redesignations, so:

                                                                                                      (3)

where the formal unit designates the complete time/life cycle, and the sign "minus" means the inverted time sequence. Natural multiplication rules for these vectors (the second starts where the first ends) lead to well-known quaternion algebra with as imaginary units:

(4)

One may look at the real unit as at a complete time circle (time loop), and a discrete analogue of  topological charge. Therefore the count of the time units here is the count of cycles, the count of topological charges. This count allows us to define natural addition/subtraction operations. Thus,

is a double count of the time cycles, started from unit  :

In general, for example, we have this for cycles count of unit:

  ( )     (5)  

   We can see now, that the time/count starting point ( or , may be) is of great importance.  Using wave analogy, we may call it the phase of the discrete "time wave". (Here discrete formal signs designate the time flow, which may be or may not be discrete  in reality). Due to cyclic group properties there is  the degeneration, or the total identity of units/cycles.  So, the  number of cycles is just a formal number here.  One may put it in different words by saying that the number of cycles is just probable. Degenerated cycles are absolutely independent and we may formally combine all cycles with all possible phases in a quaternion:

,  where - integer numbers  (6)

Time count, as we have already mentioned, is the exchange (transformation, change) of signs, reference systems, personal roles ( like you vs. me ) of  the  subject,  too.  The difference between  the  inverse operators becomes very important in this context.  Thus,  the sign creation operator:

  when considered as a basis  vector, makes a projection of the whole time cycle vector (  to be , the inverse of ( ) .  This  operator  is  the sign destruction operator,  being  an object creating  (transforming) operator at the same time. So, ( ) transforms the subject (observation device) and - the object (the well-known  passive and  active forms  of  any  operator). They form the time cycle  unit  vector  altogether.  Taking  a widely  used concept of co- and contravariant components, we may redesignate basis vectors as:

,

  (7)

Thus, the  full   number  of  time  cycles  (  full topological charge) one can calculate as a scalar  product of two ( co- and contravariant ) vectors (quaternions) :

   (8)

 where tilde ~ marks quaternion  conjugation:

We see, that this material cognition process forms in material  signs  elementary conceptions of time flow and time "grammatical" tenses: past, present, future, combined in topological charge, complete time cycle. To describe this process even more, let us introduce new isomorphic representation of  our cyclic groups,  a multiplicative groups of discrete abstract numbers.

At first, one may  notice that the transition  from  one finite group  to  a  group  of the next order always occurs with the formal multiplying unit of the group (cycle)  by  -  group generator (cycle lengthening). In vector designation it appears to be multiplied by , or by in quaternion group representation. We have, actually,

                  - 1st transition         (9)  

In multiplicative representation of cycle transformation it looks like this:

(10)

                  For 2nd transition we have, correspondingly:

     (11)

As a transition from cycle to   cycle, we have in vector designations a new sign for operator playing the role of group to group transition operator: , according to group of order 3. So, in multiplicative representation:

(12)

where we designate naturally: .

Going further on this way, lets multiply this unit cycle by a new imaginary unit ,  , which commutates with any other operator.

The new cycle is the following, where we use the identity:

(13)

where:              

One can see, that:

and may be represented [10, 11] as

(14)                                                

These operators form a complex quaternion (biquaternion) finite  algebra,  where   plays  the  role  of a commutative imaginary unit.  Taking into consideration account cycles, started from all types of basis operators, we define a biquaternion:

      (15)    

where:  - integer numbers.

We have  to  understand  now,  what is the meaning of new real units: .  Semantically, they were created by forming an operator, inversed to the time cycle operator. Easy to see that this antitime, "time destruction" operator we should interpret as a memory operator. It corresponds to non-causal action, which may be  unobservable as it is locally but it "leaves" observable elementary identical events-signs (loops) separated by spacelike intervals as a memory of past events in time.

Mathematically, the biquaternion algebra corresponds to well-known space-time transformations  (Lorentz  boosts and space rotations). Thus, the time count flow leads to the cyclic acceleration/braking movement and rotation in space. The latter is known as a quantum spin [22]. We can see now, that form  the  local vector basis in space (local frame  of reference), while describe "the dimensions of time" - the basis "grammatical" tenses.

Fundamental space-time symmetry here exists due to the symmetry destruction operator, imaginary unit , being one of the  representations  of  the group  generator .  It is well-known in physics as a duality operator, which appears to describe one of the most fundamental relations in our approach [20, 21, 23, 24].

3.      Quantum equations. Continuous and discrete.

Because of the element chain degeneration in finite groups,  our  space-time has a set of undistinguished elementary events "distributed" both in time and in space. We may say,  that  there is  only  one single space-time event, or many absolutely  undifferentiated (probable) events. We have a sort of quantum events condensate - in a classic realm of physics. One may remind oneself that this event identity is a strict consequence of non-causality and the nature of information, the result of the fact that space (antitime) interval cannot be observed locally as a real change.

Up to this time we did not even discuss whether space-time was discrete or continuous.  The duality operator and  its inversed , being the transformations from time to space and vice versa, introduce  the    difference "discrete/continuous" for the first time. One can see though, that the identity of the complete space-time cycles is of two different types. They are  closely connected with the two types of reference devices existing  in  the space-time  duality  group  (where is   the generator).  Thus,  multiplicative  "real" unit ,  taken as a basis vector,  forms  the  cycle  in a multiplicative chain  of  almost  degenerated, non-ordered bosonic type:

         (16)                                       

where:

When we want to start from another basis vector, to  take another cycle wave phase, namely , we must take into account, that on the very next step the self-acting of the imaginary unit   will generate  new  anticommutative quaternion units:

, just as it has happened with imaginary   and .  The cycle chain will be as follows:

         (17)     

where: 

It is easy to see,  that this one chain (space-time path, history,  world line) is  streamlined,  ordered.  In fact, the frame of reference,  the device with   as a basis vector is of anticommutative, fermionic type.

Thus, the choice of basis observational device shows us either the discrete or the continuous side of the universe. This kind of symmetry is well-known under the name "supersymmetry" [7, 8],  so the duality operator  becomes the supersymmetry operator at the same time

The space-time cycle operator designates the elementary portion  of  movement (acceleration-braking) with rotation (spin) in space-time [21].  This translation vector in both physical and linguistic meanings, this  space-time topological charge, (which one may also term as instanton because of its finite action value) we may call an informational quantum, informon.  The count of informons is  the  quantitative count of bits, the elementary units of information. To get the information, by  definition,  is  to  make  a  choice  between absolutely identical  objects,  introducing some order into undifferentiated chaos [17-19]. The superspin operator  of  duality   plays this very role.

By informon  producing destroys the bosonic chaos, deleting antiinformon, which may be called entropon. And vice versa, the creation  of  chaos  quantum  entropon  is  the informon's destruction. Fermionic time order represents here a well-known observed property, time causality.  On the other hand bosonic space chaos, or observable cycle identity is the main cause of "quantum" probability. The cause of such a fundamental fact one may see in that the observed sign of a bosonic space-time cycle is not the sign of real translation,  real shift,  (which implies real change) but is the sign of translation  chance,  only.  Informon superspace-time does not need any "quantization", it is "quantum" from the time of its birth.

Due to degeneration (indistinguishable identity) of all possible cycles (for all  our  finite  groups),  we have a lot of chains for one and the same translation biquaternion :

(18)

(i.e. any quaternion unit in chain will work)              

All these chains are of equal possibility, consequently - of equal  probability, so we have to consider some average chain, or the average between all possible chains-histories (well-known path or   history  integrating). This  averaged biquaternion   shows the density of chances to  form  one  or another basis  frame  sign.  The conjugated  biquaternion shows the chance density of the frame  sign  destructing,  or the device operation, action. Their multiplication  is the density of probability to register (to observe) the quantum by  this  particular device. Thus "registering" or "observing" always  means  both "objective" change, sign creating and "subjective" device operating, while observing this sign. The former is observable change, the latter is directly unobservable influence of the subject "back" on the object.

To  shift  the  informon  in space-time we must multiply the biquaternion by any chain unit,  simply by , for example. We may consider this  shift  as effectively  infinitesimal,  because,  as we have seen, one and the same reality may be observed as discrete or  continuous.  So,  to describe this shift in general we may use the differential shift operator (which one knows under the name of momentum operator     (h = 1 )), taken  in the rest frame of reference. Thus, due to equality of these operators action, we have:

(19)                                       

where: 

Here we have taken for  (proper time) the count of pure time cycles ( combined  - cycles) without any tense differentiation, such as it is taken in common use of time coordinate.  The simple way to take into  consideration  an  arbitrary laboratory frame   of   reference   lay  in  introducing  (new self-acting!) a new formal unit . This leads to the creation of new imaginary units:

 anticommutative with and . The new cycle is:

(20)

where:

,

,

Using these units ( of Dirac matrices algebra), we  have  in a laboratory frame:

   (21)                                     

This is the biquaternion form of Dirac equation for the quantum of unit mass, where coordinates mean the numbers of cycles in different dimensions:

(or:   )

correspondingly. Time dimensions (tenses) are not taken into account,  so we have only one time dimension here .

Taking into  consideration  the multiple topological charge   sort of a number of "internal" cycles in a single  proper-time  cycle),  we  get Dirac equation for a massive quantum [19, 20]:

  (22)                                                

Introducing particle rest mass m as a multiple topological charge may seem to be phenomenological at the moment, but it finds its justification in the concept of physical energy which we discuss below.

4.      Field equations. Concept of physical energy.

To derive the  space-time  equations  we  must  define  a covariant (gauge) derivative, which is  the same shift operator, but with the local  basis  frame  transformation taken  into consideration:

  (23)

Here the  vector-biquaternions   describe the informon field  (curved space-time) - the  informational  interaction  between informons, between two local basis frames (devices, subjects).  When the  informon  field  is  present  (in  informon/fermion  or entropon/boson forms), the particle equations becomes [20] :

            (24) 

where:

Recalling that all   are the supersymmetry  operators, which transform  space  to time (or boson to fermion) we may describe the  complete  space-time  cycle  of  informon  movement (discrete single unit or  infinitesimal  -  no difference) as two translations, two shifts, inversed to each other:

(25) 

where tilde ~ means the sign change in all .

This symmetry  between  two  shift   forms   (timelike   and spacelike)   is   the  same  dual  space-time  supersymmetry, represented here as Dirac operator . Taking into consideration the obvious invariance of the space-time shift to the double-dual transformation, we can write:

  (26)

This equation may be considered as a fundamental space-time  equation.  It may be shown that it leads to double-self-dual curvature tensor. The main solutions of such equations are very similar to "empty spacetime" solutions of Einstein equations : well-known space-time  instantons [23] (Kerr and Schwarzschild metrics,  for example) that are, by definition, finite-action solutions.  We can say now that such instantons describe the  space-time  structure  of  informons (elementary events) that are  finite both in space and in time (cyclical). In other words, according to this approach, such instanton solutions describe substantial back-and-forth-in-time events (quanta) with antitime action hidden behind the horizons.

It is easy to see that such a space-time of multiple instantons will look like an essentially granular structure.  These "granules" (topological charges) are separated by different kinds of  horizons, which are hiding from observers (i.e. from each others) their "back-in-time" internal regions (where time become space and vice versa). Such a structure with substantial space-time curvatures on the micro scale will be impossible to cover by the regular non-stochastic coordinate map.  Therefore the usage of such geometrical measures as metric   would be possible only on the base of observational probability.

Let us remind ourselves now that in the perspective of classic General Relativity all that we discussed up to this moment is considered an empty space-time. It is true though that space-time instantons (that correspond to our loops in time) represent some kind of objects which we presume to be material and to be representing physical particles. But without a concept of physical energy there is no way to understand what relation it all has to physical reality. A conceptual solution could be found in realizing the simple fact that our loops create the fractal structure of elementary events in which some of the events actually precede the others (i.e. events are ordered). 

An obvious but not easily understood fact of non-causality is that all of these events-ancestors could be actually observed in space as simultaneous and are absolutely identical to their events-descendants.  Identical in everything except the very fact that one of them is "formed" from others. There are events of different generations. We dealing here with non-local effects of non-causality now.  One cannot observe direct local influence back in time, but it could be observed as non-local influence instead. 

What happens when events of different generations interact with each other? "Interaction" in our terms means the change of the local frame when one elementary event is transformed to the neighboring one which is described by the gauge field  .   It is easy to see that because of the fractal branching (duplication), the earlier an actual event is (relatively further in time loops count from the "point" of observation), the bigger is the local frame change it can cause. To put it simply, plain number of loops in time has a multiplying effect on any particular change, representing actual influence. In this context "bigger influence" means a stronger   field. We get relative differences in the  event interaction field and therefore may introduce a concept of physical energy to describe these differences.

Thus physical energy (and matter, like rest mass that we introduced  in particle equation) is taken here as a relative measure of potential influence of elementary events over one another through loops in  time (through topological charge).  According to this approach the observable phenomenae of physical energy is the main and fundamental non-local effect of non-causality. Not only everything that we observe in space is all in the past, but also all of the observable effects that we have are caused by the past. Using physical energy actually means using physical particles that travel through time. Space is a true dynamic memory of events and all that happens is retrieved from this memory by its own means.

5.      Observation relativity. Events ordering and wave propagation.

All that we saw until this moment was based on the local "cognition" symmetry object-subject. It is easy to see that in a particular chain of elementary events, the object and subject are exchanging their roles constantly.  Which one at any particular "moment" is considered an object and which is a subject depends on the local frame of reference.  This means that observability is actually relative and depends on this choice too. When we are talking about ourselves as experimenters it is a simple task to find out where is the subject, but it is not that easy in the realm of elementary events.

Let us take a close look at the ordered chain of such events.  They are almost identical except the fact that one of them was chosen as a subject (the ultimate end subject here belongs to a brain cell of the human experimenter).  Once the choice of the end subject is made,  the knowledge of "who is who" immediately propagates through the whole chain, making some parts of the chain observable and some not.  Therefore it effectively implies the direction of observable time flow (causality) in the chain.  Correspondingly the opposite direction (antitime, non-causality) becomes unobservable. This kind of "propagation" process is well-known under the name of spontaneous symmetry breaking.

One can see that such symmetry breaking can happen only in the chain that is prepared to be ordered (ordered in the mathematical sense).  In the real physical world of initially unordered events any choice of the event for a subject means some kind of change for this event.  Change implies ordering between the subject of our choice and any elementary event that happens to interact with the subject.  Then this event in its own turn takes a role of a subject and so on.  Induced by an initial change, the ordering process propagates towards both directions, one of which becomes a direction of observable causality and the other (non-causal) may be called direction of cognition.

It could be shown that these types of propagation lead to phenomena known in quantum theory as wave propagation and wave decoherence, correspondingly. 

One may add that so called "virtual" quanta and events corresponding to the "uncertainties principle"  do really exist in this approach but they belong to the relative realm of locally unobservable.  As it was already mentioned in introduction,  this approach demands an existence of fundamental maximum speed of observable propagation or "particle movement".  If there are no elementary space units to "overcome" the speed is zero. The same is true for the case where there are no elementary time units, where there are no changes and hence there is nothing to observe. Maximum speed divides space-time into two realms of timelike and spacelike paths, which corresponds in our approach to the realms of time and space correspondingly. "Virtual" quanta are mostly the quanta moving "faster" then maximum speed (spacelike paths), which means they are locally unobservable.  This corresponds to the term "event horizon", which is well-known in relativity theory.

Less obvious but it still may be shown that the fact that events "within quantum uncertainties"  actually correspond to the same "event horizon" phenomenae. Even from the very process of time loops chaining used here to derive the Dirac particle equation, one can see that going "within uncertainties" means going "inside the time loop".  This is obviously "impossible" which means that the process cannot be observed locally.  And what could be observed instead?  To understand this we should consider new phenomenae that may be termed as "scale perspective".

Well-known phenomenae of visual size perspective (angle size of an object decrease with the distance) follows here from the simple space geometry, where distance is measured by the number count of loops.  Much more interesting scale perspective arrives with the fact that elementary events under observation becomes actually ordered.  It should be mentioned explicitly that observation does not mean here an actual observation by some real or imaginary human. Anthropic principle [15] is implicitly here, but not that straightforward. It means instead that observable events are "observed" or "detected" by some other events they interact with. Those events (detectors) "feel others" by interaction, they "play the role" of subjects and that is all to it. Thus the universe becomes ordered by "observing itself" step by step, generation by generation.

Ordering means that in the way of space perception some of  the  later events increasingly become, to the observer spatially smaller and placed inside others - in the same sense how, as we saw before, the events preceding others in the time perception "acquired" bigger energy.  Actually both are direct consequences of events fractal self-similar structure. Energy in time corresponds to scale in space. Ordering means progressive scaling. The simple way of seeing it is to realize that the very first (primary) elementary event (universe) remains absolutely identical to elementary events (quanta) that we observe today. What is different are the observed scale and space relations outside- inside  which directly correspond to the time relations before-after.

One more point should be stressed: while fermions, representing "time change" could be ordered directly, bosons as "space quanta" do not represent any observable change and thus could not be ordered directly.  They still could be ordered indirectly instead, as some kind of  "vacancies" in the sea of ordered fermions. In the real world it means that even when some bosons in the form of "vacancies" are observed "inside" some volume, there is no way to know if they are really inside it or not. The answer is always a probabilistic one.

What has been said is absolutely enough to understand why there exist such well-known phenomena as quantum bose- and fermi-statistics. The exponential character of statistical distribution is a "birth mark"  of a fractal  (geometric progression in time and space) structure. The difference between bose- and fermi- follows from different commutational behavior of bosons as spacelike events and fermions as timelike events. And the temperature is a usual relative measure of the ratio of the chaotic energy to the regular energy.

6.      Experimental consequences. Paradoxes. Space and time travel.

There are many experimentally observable consequences of this approach that could be suggested to approve or disapprove it. But the most intriguing and obvious is the possibility of real time travel for macro objects - which is explicitly opened by this approach.  This possibility is opened by the trivial fact that one can consider establishing  a real classic material frame of reference (experimental device) based on some objects that are currently  seen as essentially "quantum". Needless to say that the up-to-date "official" quantum theory interpretations explicitly prohibit the existence and/or usage of such reference frames/devices. 

Quite opposite to the existing theories allowing loops in time [1-3], the characteristic constant of the time loops here is Plank's constant ?, not fundamental Plank's length or gravitational constant, which are substantially smaller.  Actual experiments on time travel according to this approach could be conceived and planned right now, today.

Does this actually mean that the famous loop time-travel paradoxes actually exist? Surprisingly, not at all.  The very formulation of such paradoxes is based on the logic of an ordered chain of events, but as we have seen, ordering could be done only for events that exist ("survived","observed") already.  In the possible opposite (paradox) outcome of event destruction by its own means ("killing its own ancestor") an event disappears from existence causing the complete reordering of events and the restructuring of the whole observable picture. According to what has been said here, such a restructuring would be interpreted as an ordinary  result of simple energy usage. Time travel could be considered simply as a nice interface to change the current state of events.

The first choice object for such an experiment in time-travel should obviously be a massive amount of mutually entangled quantum particles like Bose-Einstein condensates (BEC) or quantum liquids and crystals like superfluid He⁴. Particles there behave like a single quantum object but according to this particular approach they really are one classic object. An experimental macro device to be sent in time could  be modeled out of the condensate itself as its small but complex excitation pattern -a material hologram of the device "written" onto the condensate as a carrier wave.  In this way the whole system condensate-device would be essentially "quantum", but the structure and operation of such an experimental device would remain "classic".  It is similar to the well-known situation in quantum superfluids like  He⁴ where superfluid  actually "plays the role" of  a "normal component" (non-superfluid) too. A quantum condensate wave works here as a real carrier, modulated by a material signal of excitation.

Interestingly enough that the field equations (26) solution for such a condensate would still represent a single instanton ( like the Schwarzschild metric or non-gravitational "black hole"). It means that any small excitation of it could be interpreted as a small object "falling" onto the "black hole".  The passing of the event horizon by such an object could  mean a beginning of its trip through time in some analog of the "wormhole" effect.  The same wormhole effect could also be used to travel in space with the effective speed of close to or even higher than the speed of light.

As for the experiments on real time or space travel of macro objects like people, etc. one would probably need something like a dineutron (pair of coupled neutrons or cooper-pair) condensate which could in principle carry a real complex macro object without disturbing its internal functionality in a form of quantum excitation hologram.  For now it may seem like a pure speculation but  creating the superdense neutron-pair condensate in the lab would definitely be possible in the not so distant future.

One of intriguing observable consequences of this possibility is an obvious stage of  widely spread everyday life usage of such space travel portable technology for every civilization just a little more technically advanced then ours [16]. Resulting from such usage is the significant slowing of the  time flow rate of the civilization as a whole, giving a clear explanation to today's famous fenomenae of "cosmic silence", to the well-known "Fermi paradox".  The time flow rate slowing factor for such an advanced civilization depends on how much of the galaxy space is actually held under control by that civilization and has been estimated to be as significant as 10^-4 - 10^-6 [16].  Such a huge time tempo slowing factor makes any communication with all sufficiently advanced civilizations impossible until we reach a certain stage of development.

7.      Conclusions

In spite of some equations derived here, this paper should be considered mostly a conceptual one.  Many of the results are just mentioned in passing and definitely need much more accuracy and mathematical effort. The author is completely aware of the fact that the suggested approach is highly controversial and would probably become a subject of sharp criticism. Nevertheless the possibilities opened within this approach and the contours of a new science paradigm that is brought by it are so obviously and clearly overwhelming that it would definitely be a shame not to take it into some serious consideration.

The questions which this approach plainly promises to answer are of the most intriguing in modern science: what is quantum, what is space-time, what is energy, why causality, why quantum probability, why quantum identity, why fundamental speed, why bosons and fermions,  is time travel possible and many more.  The author hopes that the publication of this paper will trigger an open and fruitful discussion on the fundamental principles of modern physics and will serve the development of scientific thought.

The author gratefully acknowledges the many useful and stimulating conversations with my dear friends and colleagues  S.Elkin and D.Gavrilov.

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The full citation for this Article is: Koulikov, V. (2009). Time loops and the unification of quantum and relativity principles. PHILICA.COM Article number 177.