The Recombination Principle: The decision and perception (recognition) process as cause and consequence of multiple recombinations, happening from moment to moment
Preliminary note and hint for reading
(NewInfo) is an elementary entry. Especially for readers with mathematical entry knowledge there are precise formulations of the introducing arguments and building up on this quantitative considerations to the nature of proper time(TimePerception). However, it isn't necessary to understand all details at once. Additionally, during first reading the lot of footnotes may be skipped. The table of contents offers a concise outline, also look at the by (***)marked locations within the text[1]. A concise formulary is separately accessible.
{InformationDef} The word "information" resp. "information quantity" plays an important role and is sometimes interpreted variously. Therefore it's emphasized, that here the word "information" is used in the standard sense of technical literature (information theory) [lish1] [2].
1 Infinity resp. infinite diversity is permanently emerging (because of differentiation and decision) and not a priori existing as constant entity (completed in past)
{RealInfinityGrowsWithTime}[3] At the beginning of the 21-th century the (obvious[4]) understanding of the infinite resp. infinite diversity as something, which permanently is emerging together with time (TimeConformApproach) due to differentiations and decisions[5], which cannot be classified as something a priori (i.e. before present in past as completed totality) existing, was still unusual. Basis of mathematical physics were the axioms of traditional set theory[6] which start out of (a priori) existence of infinite sets resp. infinite diversity. But if something exists in the physical meaning, it's already past and thus fixated and naturally restricted (cf. a. [liro]).
To avoid misunderstandings: Of course I don't think, that's all. There is everywhere and always the prerequisite for every distinction, (distinguishable) time and decision. This exceeds the limits of every possible perception and imagination, i.e. it is really unlimited resp. infinite {RealInfinity}[7].
1.1 A large number, which is much smaller than ...
It seems that the term "infinity" often is underestimated, therefore this chapter:
Let g: INo →IN denote a function on the natural numbers. We define for n ∈ INo :
The function g is extremely increasingly increasing. Already g(1) by far exceeds human imagination and all physically measurable proportions. The number oops is much … much greater. Nevertheless also oops (and oops_oops[8] etc.) is vanishing small when compared to "infinity" (like all other fixed resp. time independent numbers).
In calculus one works with intervall lengths smaller than 1/oops. It is clear that so small intervals (e.g. in SI units) do not exist[9]. The consideraton of this fact and of the resulting combinatorics in mathematical physics could be the start of substantial progress (RGraphTheoreticalResearch) .
2 To the usage of infinite sets in mathematical physics
Unlike the infinite the (within finite time) measurable (as information perceptible[10]) reality, which is the physical reality, is just characterized by being finite. Particularly it's information content is finite.
Concerning the physically existing reality (resp. physical reality) a scientific consensus should be possible. Even Hilbert comes to the following result ( [lihi] p.165, translated from german):
"Now we have established the finiteness of the reality in two directions: to the infinite small and to the infinite large."
Every physical measuring needs a finite, different from zero measurement time and provides information (cf. a. InfoConcrete) in form of the choice of a measurement result from all possible measurement results. If infinitely many (different) measurement results would be possible, the choice[11] of a measurement result could deliver infinite information (an infinite information quantity [InformationDef]). But the results of physical measurings (of finite[12] duration) never deliver an infinite quantity of information. Therefore the set of all possible measurement results a priori is finite[13].
This (natural) fact has been mentioned in literature already long time ago (cf. e.g. [lipe] p. 195). Nevertheless even in quantum physics analytical models and derived concepts (exponential functions, operators with continuous spectra...) are still usual. - May be that many people (also scientists) cling on the model of continuous reality (as something which already exists) not only because of the macroscopic impression but also because they think that "continuum" is necessary for freedom of decision - because it's subdivisible infinitely often. I think there can be a bridge: Future as the subdivisible together with freedom of decision along proper time as primary axiom, and finer and finer approximation of continuum as consequence - so fine subdivision not a priori, but in the course of time as result of decisions. The order (Order) is important.
In physical reality steps towards infinity cannot be done independently of time; they are coupled with a growing time coordinate.
In the physical reality only a finite information quantity can be processed within a finite (proper) time[14] interval. For mathematical models whose representation requires a processing of an infinite quantity of information, for example irrational numbers, no (exact) equivalent exists in the physical reality. So mathematical calculations, which have an equivalent in physical reality, can only be rational combinations of rational numbers. Conclusions arise from this for the foundations of mathematical physics.
2.1 The perceptible (physical) reality as that, what is (exactly) conceivable within finite time
Deduced[15] analytic functions like
etc. are frequently used for description of physical (natural) processes. The question arises for a fundamental explanation of the fact, that those functions can be used to make approximative prediction of physical measurement results (that is a limited forecast of perception resp. future). Such explanations should[16] base on as simple as possible axioms.
It is now started out from the assumption, that those axioms permit only a finite number of elementary combinations per time unit, in which an elementary combination {ElementaryCombination} is defined as basic calculating operation, i.e. as addition resp. subtraction or multiplication resp. division of integer quantities resp. numbers. This assumption seems to be justified, because such elementary combinations are within finite time exactly conceivable (comprehensible), at least in the potential sense, for example by counting. That's important, because something, which is perceptible, is also conceivable at least in the potential sense.
There are common mathematic models, e.g. numbers, which aren't conceivable within finite time and therefore aren't perceptible (sometime, in some representation, in complete exactness[17]). Therefore these models deviate from perceptible reality[18] after some time and in principle are unsuitable for an exact elementary approach to it[19], even if these models deliver and further will deliver good approximative results.
Of course also
mathematical partial models can be very helpful {helpful} (especially for approximative[20] calculations) and are thus fully
justified[21], for example in case of to macroscopic particle numbers greater 10^26 and
still much larger number of combinations n per proper time unit (ProperTimeUnit)… We only should guard against over interpretation[22] of our models of thought because
they are not equivalent to reality(AnalysisAtBestApproximative). Particularly, if we forget the
simplifications contained in our model, we would block[23] a "thinking beyond the
model". This problem of course also affects my mathematic suggestions.
Also here occasionally approximative considerations are used (as bridging) e.g.
the use of the
At first the following preceding chapter should clarify the mentioned difficulties of current models: They orient themselves too little to our fundamental decision and perception process. Particularly the natural sequence(Order) of the combinations which are (in the large and in the small measure) cause and result of our decisions and perceptions (resp. measurings) isn't taken into account in these models.
For example the axiom of choice (on which basic analytical concepts build up) postulates a priori the existence of infinitely many decisions - from the physical point of view a contradiction in terms, because "a priori" means "before presence" resp. "in past", but physical (measured) past is finite.
3 Model concepts like infinite continuous sets, Hilbert spaces and the axiom of choice permit the disregard of the natural (temporal) order
In mathematical physics analytical approaches and concepts (i.e. approaches and concepts of analysis) are quite common, and with that also the usage of continuous, a priori infinite sets. Most important examples for those sets are the complex and real numbers. They form a metric space equipped with the absolute value norm. Hilbert[24] spaces play a central role in quantum physics. Important quality of these metric Hausdorff-spaces is the completeness i.e. any Cauchy sequence converges towards a limiting value which is contained in the space. This is problematic if used for description of nature, because for the exact description of the limiting value of a Cauchy sequence it's mostly[25] necessary to carry out (isolatedly, before any interaction with the surroundings[26]) an infinite set of approximation steps, if one allows respectively only elementary combinations [ElementaryCombination]. This implicitly means (uncoupled from the natural order[27](Order)) an infinite number of decisions[28] (application of the axiom of choice[29][limy]), therefore the processing or production of an infinite large quantity of information[30], which isn't possible under natural conditions within in finite time[31] (at finite availability of free energy (FreeEnergy)).
So from the retrospective point of view the appearance of quantum phenomena in the physical reality [PhysicalReality] would have been predicable (cf. a. [NoAnticipation]): Confirmed is not only the fundamental limitation of the quantity of information, which is perceptible within finite proper time, it also becomes clear, that basic analytic concepts (i.e. continuous sets of numbers) are models, which deviate from reality{AnalysisAtBestApproximative}.[32]
3.1 In principle restricted validity of the used models
It isn't a miracle therefore that mathematical models which are based on the completeness of the underlying metric spaces only can be restrictedly valid for the description of actual natural events[33]. The problem quite similarly also lie in other models which also require the axiom of choice (often indirectly and hidden)[34] or which start out in some other way of the infinite (of infinite diversity) as something which already exists as completed entity [RealInfinityGrowsWithTime].
Specially at calculation models, whose validation is not guaranteed because of missing or only indirect experimental possibilities, there is a strong[35] likelihood that the sequence of calculation steps (implicitly connected to decisions and perceptions[36] within the restricted model) differs from the natural order(Order) of the combinations connected to decisions[37] and perceptions. So nonsensical calculation results are the consequence. The difficulties lying in these results are (more or less) known by many insiders and also should be evident in publications[38].
3.2 Task: Finite approach to the existing, physical reality
If our considerations should not be superficial, the mentioned problem is fundamental and severe. Therefore we have to accept, that a mathematical approach, which is faithful to physical reality, also is finite (finite according to http://arXiv.org/abs/quant-ph/0108121 ). There are two possibilities for the method on the way to this approach:
1. We continue to work with the usual mathematical models, which presuppose a priori existence of infinite sets and the axiom of choice, and hope, that sometime the infinities can be in a way reduced, so that the resulting approach finally is finite.
2. We start with plausible approaches, which don't presuppose a priori infinite sets (which are finite from the beginning and so also discrete). This implies that we have to consider initially minimal sets of possibilities for experimental results which are created and enlarged in the course of time (inclusive order). In the borderline case "t_total to infinite" this process should lead to current physics (and more) - a start from the other side to meet in the middle (again).
As far as I know up to the beginning of the 21st century only the first of both possibilities is considered in literature[39]. Due to the diversity of publications it's difficult for me to estimate, how far the in 1. mentioned hope for complete reduction of all infinities is legitimate, but I got the strong impression that lopsided much intellectual capacity is invested in this possibility. It is questionable, whether this is efficient - the method "explore and hope for reduce" allows many wanderings.
Without guideline there are (too) many possibilities{TooManyPossibilities}. Already today there are many special subjects (and special-purpose languages) so that an increasing hindrance of communication is the consequence. Due to the nature of the matter substantial progress on a way to an exact[40](and therefore also finite) approach probably only is possible, if at this research is done without the axiom of choice, continuous number sets and all from it derived model concepts, even if it is difficult[41] at first.
This is one of the reasons for this which caused me to try the 2nd possibility. At this it's comprehensible to work on the principle that the finiteness is reflected in the fact, that the number of combinations (mapped on elementary arithmetic steps) leading from a decision (to measure) to a perception (of a measurement result) is finite, exactly if measuring time is finite. This is the case in the approach discussed below[RecombinationCountFinite], in which the progress of proper time is related to a meeting of (own) pattern with (formerly separated) counter pattern(TimePerception).
3.3 Finite approach by combinatorial inspection of information paths
No doubt, the way of the information from our decisions to our perceptions depends on a physical law. Because of the shown problems this law can not be of analytical and therefore continuous (for example geometric[42]) nature. Primarily it must be a discrete, combinatorial law[43]. Of course in case of a macroscopic measuring many combinations happen, so that the borderline case of the continuous, geometric appearance results.
Abbreviated prehistory: About 1992 I
noticed, that we could only recognize codes, for which we have the counter code
(the decoding code). So before every measurement we have to send away something
from us like an "anti pattern" or "test pattern"
(later I recognized that this action lays in our decision for the measurement)
and the change of the returning pattern (relatively to the original) contains
the information of the measurement result. I studied the probabilities for
return of the test pattern and noticed, that they correspond to the coefficients
of the
One important progress connected with this approach is, that it gives first insight in the (of course finite) ways of information from decision (to measurement) to perception (of measurement result) and that it contains only finitely many arithmetic steps - from start in the present center until return to the center. There is no a priori necessity[44] of analytic models [which implicitly uncouple[45] physical reality from consciousness, which hide the connection between our frames of reference and so can lead to a wrong and restricted philosophy [EgoismIsStupid].
The next chapter should give insight into the nature, way and sequence of the combinations, which are connected to our decision and perception process and make first mathematical suggestions, of course only as far as I could get ideas of it. I hope you then will understand why I have named these combinations "recombinations". I have approached the topic in a similar way in thoughts like the next chapter is written.
4 Geometric appearance as (statistical) result of a discrete combinatorial law
First a recall: We should not forget that all geometrical appearances like "location" and "direction" are only possible, if rest mass exists, i.e. if there is an asymmetrical appearance of matter and antimatter relatively to our present frame of reference {AsymmetryAsPreconditionOfGeo}(***).
4.1 No isolatedly definable metric units, no "smallest particles" resp. "building blocks" of matter
It is already known that the concept "(smallest) particle" is only a model idea which doesn't correspond (exactly) to reality. Of course it's understandable that use of this model concept is frequently made: It is easy to imagine matter as composition of smallest particles or "building blocks”[46] (with firm, absolute sizes) and helpful for calculations. But it isn't consequent to be left with this model (or the mathematically equivalent wave model[47]).
4.2 Special functions as dimensionless conversion factors
When we try to free ourselves from this model idea, first of all the question after the basis of metric[48] sizes arises: What is small, what is big? It is known that measurement results regarding this are dependent on the observer's "point" of view. In this context the functions
play both in geometry and in the physics an important role, e.g. QV(v/c) [49] as factor for relativistic time dilation or QW(v/c) as factor for length contraction (cf. a.[GyroscopeModel]). These functions contain only an approximative approach but they after all are used for calculations which don't start out of absolute scales but of a non-linear[50] connection of the sizes of the observer system and watched system.
4.2.1 Discrete considerations to nonlinear relativistic relations can lead to a bridging from relativity theory to quantum physics
{BridgesToRel} Relativity theory (problematically) presupposes continuous geometry and the frequently used functions QV and QW lead to irrational results. The following discrete considerations (e.g. to finite series expansions of QV and QW, cf. (TaylorQV), (TimeDilation) and (TaylorQW)) avoid this from the beginning and at the same time offer approaches for a bridging from relativity theory to quantum physics.
4.3 Correlation (of sizes) and flow of information
Correlation implies flow of information and this is necessary for every observation (to and for finished perception also back[51](FinishedPerception)) The conservation laws (Cons0Sum)show that calculation is exact in the end {ConservationLawsImplyExactness}.
(To be new the transmitted new information component should lie in (physical) quantities, which are temporarily solved from this connection (correlation coefficient resp. scalar product is 0, geometrically: orthogonal). Probably therefore the individual flow of the information must change the direction[52]{DirectionChanges} at every new observation.)
As generally known, information (initially) is transmitted by photons[53]. These information packets move to the following target point[FollowingMeeting] (where the are absorbed) with light speed and no information exchange is possible in between(otherwise we would regard the "in between” as following target, [WayTimeConstantTillNextMeeting]. Especially in elementary consideration at the moment of the start we don't know, which of two elementary directions[54], which spin the photon will choose resp. which possibility is predestined (by an earlier decision). In abbreviated formulation[55]: We don't have information about the destination of the photon or its next decision.
4.4 Combinatorial considerations to the ways of information (Q0-triangle) (***)
We come to the {combinatorics} now {InformationPath}:
The elementary information unit is a bit which means the information about the choice for one of two possible alternatives. Let us assume that we have no information about the next decision resp. the next direction. No direction is preferred in the beginning {DecisionFreedom}. Thus both alternatives have equal probability p=(1-p)=1/2. Now, each of these possibilities again is starting point for a new decision etc... The so emerging probabilities for the different ramification possibilities resp. recombination points have a symmetrical binomial distribution (cf. [lifa] p. 245-281, [ligr] p. 153-256, also[56][lied] p. 3). We will call the totality of recombination points subsequently "Q0-triangle"[57] :
n k-> -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9
¯
0 1' *1/1
1 1 1 *1/2
2 1 2' 1 *1/4
3 1 3 3 1 *1/8
4 1 4 6' 4 1 *1/16
5 1 5 10 10 5 1 *1/32
6 1 6 15 20' 15 6 1 *1/64
7 1 7 21 35 35 21 7 1 *1/128
8 1 8 28 56 70' 56 28 8 1 *1/256
9 1 9 36 84 126 126 84 36 9 1 *1/512
...
The probabilities in the vertical symmetry axis of the triangle are indicated by " ' ". These are the probabilities of meeting events{CentralMeeting}in the center, the "central meeting probabilities” and dependent on the row number n. We shall call them Q0Z (n) and obtain
The resulting table for Q0Z(n) is
On the other hand
the
Remember that QV(x) is the factor of relativistic time dilation in case x=v/c {TimeDilation} (cf. e.g. [lifl] p. 26 and 27).
4.5 The middle column as the vertical symmetry axis, the column of the central meeting probabilities of pattern and counter-pattern
{CounterPattern}The
(vertical) sum[59] of the
"central meeting probabilities" (probabilities for return)
corresponds (because[60] of 4p(1-p)= x^2) to the
4.5.1 Correlation of decision resp. perception (orthogonality as information theoretical concept)
If 0 < x < 1, then we have a correspondence to the case that the probability p of a step to the right differs from the probability of a step to the left, i.e. p is unequal 1/2. This means that we here already have more or less information about the next decision there i.e. already more or less information exchange[61] has been possible between here and there. The proper times[62] of here and there are not orthogonal, i.e. the "correlation coefficient[63] of decision resp. perception" isn't zero, but has a parallel, common component [CommonComponent]. Because of inertia this is valid along a series[64] of steps, in which proper time here seems to run QV(x) times faster then there [TimeDilation], where the factor QV(x) is equivalent to the sum of the own central meeting probabilities[PerceptionInCenter].
4.5.2 Proper time proportional to the sum of the central meeting probabilities; input is descended from former output
In analogous way also from our own (lokal, individual) point of view the central meeting probabilities correspond to the probabilities (per double step n->n+2) that the information resp. pattern, which had been temporarily separated[65] (in form of free energy[FreeEnergy]) by our decisions from us resp. the information starting from us returns to us and is perceived[66] by us again in recombined[67] form. This can be understood indicating, that with our temporal perception{TimePerception}, with each proper time progress necessarily the re-union[68] of our own (lokal, individual) pattern and counter-pattern[69][CounterPattern](which has been separated from us by our former decisions) is connected – that in the end exactly that pattern is perceptible for us, which is descended from us[70] (separated by our own former decisions[71]) [OwnPerception], whereby (outside of present consciousness) in between more or less many recombinations happened[72](***){PTimePropSumQ0}.
May be, that on the second look much of this conclusion is obvious without much arithmetic, already due to the constancy of the light or information speed relatively to us personally.
So the formulae indicate, that all information[73], which we now receive (input) is descended from information, which we formerly have sent (output), and, of course, that also future input will be consequence of former output (***).
4.5.2.1 In the two-dimensional model the total number of steps resp. central meeting points is proportional to t^2
{NPropT2} If we define
then holds
So if we start out from the assumption that (in case of no reference system change, two-dimensional model) the sum the central meeting probabilities Q0Z (return probabilities) is proportional to proper time t, then (for large n) the step resp. row number n increases proportionally to the square of proper time.
4.5.2.2 (Proper time without reference system changes; row number n and distance covered during constant acceleration )
Preliminary note: At last this approach seemed to me less relevant than the one of (small) correlation (GravitationBecauseOfCorrelation).
We know that the length of the distance covered during constant acceleration is proportional to t^2. This may remind to the proportionality of the row number n to t^2 in (NPropT2). Also gravitation conveys the impression of constant acceleration, at "constant" distance (and missing centrifugal force). But the classification of a distance as "constant" is dependent on the own length scale, and with the row number n also squarely the row length and with that the own length scale can increase {DynamicLengthScale}. Of course more exact considerations should take into account also the distance dependence. The probability for way there and way back between recombination points is the greater, the smaller the relative distance between them.)
4.5.3 In case x=E0/E the symmetry center k=0 corresponds to v=0
{xAsE0divEandkAsMomentum}Above(TimeDilation)we set x=v/c and recognized QV(x) as proportionality factor of the relativistic time dilation. But the interpretation possibilities are by no means exhausted. If for example we understand x as quotient E0/E of rest energy and total energy and P as absolute momentum, then because of [QWasExpectationValue]we get
{Ppropkdivn} We see that the momentum is proportional to the expectation value of k/n. So the symmetry center k=0 of the distributions (vgl. (Q0Triangle) und (Q1Triangle)) can be related not only to the case P=mc resp. P=mc but also the case P=0 resp. v=0 (Low Temperature Physics).
4.5.3.1 At this the mean value of k/n is proportional to the quotient wave number/frequency of matter waves
The wave number K of matter waves is
and their angular frequency
.
So in the case x = E0/E because of [Ppropkdivn] follows
.
4.6 The introduced model (Q0-triangle) needs additions
The presented model, which works with the Q0-triangle, surely is incomplete (and also too flat, cf. a. [NotFlat])), questions like "From where comes the source in the start?" cannot be answered so. A modified Q0-triangle shall be introduced now, in which the central meeting probabilities are "flowing out" and therefore in the actual system for the present cannot be sources any more (by the fact that they are put on 0).
They then could flow out to another (orthogonal) direction and come back after[74] and after. Symmetry considerations (attention of conservation laws) can give first hints, where and how this happens. If for example something flows out in the center (concerning both sides exactly symmetrically) then the total effect of the returning must also concern both sides in symmetric way (e.g. output in k=0 <-> input in k=0 or symmetrically round k=0; generally the number of drains isn't necessarily equal to the number of sources. Multiple points (PerceptionOfMultiplicity) of in flow and of out flow (also "back flow"[75]) are possible per proper time unit (ProperTimeUnit).).
4.7 Directed flow of information, centrally "flowing out" probabilities: Q1-triangle
The following "Q1-triangle" bases on the assumption, that during measure resp. perception process all of the central meeting probabilities[76] is taken away, so that they can't be sources (for superposition, interference) in the same triangle any longer (directed flow of information).
So they get incompatible with each other: The definition of incompatibly can be formulated miscellaneously, e.g.:
1. Incompatibly of two events means that they cannot happen[77] simultaneous.
2. Events not appearing at the same time are incompatible with each other if the first excludes the following.
The second definition applies to our case: If a single quantum is "flown out" centrally in the previous row, it cannot flow out in the next but one row again {DistinguishableOrder}.
4.7.1 Orthogonal change of direction in recombination points (multidimensional approach); Separation (of inside/outside, past/future) due to perception (of something separable), due to differentiation
The more central probabilities "flow out" (are set to 0) with increasing row number n, the more disconnected become left and right side of the triangle. Therefore a so described perception resp. measurement {QuantumPhysicalObservation}causes (quantifiable) separation (***) resp. separability (according to the perception[78]), which a decision makes possible in turn, in this model between the left and the right[79], in multidimensional[80] approach perhaps also between "inside" and "outside"[81] or past and future [IOtime]. Geometrical concepts like orthogonality are portable to [information] theoretical concepts, cf.(orthogonal)
If one provides the probabilities in the normal Q0-triangle on the left side with negative[82] sign (cf. [ProbabilityAmplitude]), the following "Q1-triangle" results. It is a modified Q0-triangle with central probabilities[83] set to 0:
n k-> -9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9
¯
0 ±1 *1/1
1 1 -1 *1/2
2 1 0 -1 *1/4
3 1 1 -1 -1 *1/8
4 1 2 0 -2 -1 *1/16
5 1 3 2 -2 -3 -1 *1/32
6 1 4 5 0 -5 -4 -1 *1/64
7 1 5 9 5 -5 -9 -5 -1 *1/128
8 1 6 14 14 0 -14 -14 -6 -1 *1/256
9 1 7 20 28 14 -14 -28 -20 -7 -1 *1/512
...
4.7.2 Quantitative considerations, symmetries
It is obvious that the amounts of the probabilities decrease (centrally they are flowing out[84]).
For even n the sum of all probabilities in row n equals the central meeting probability Q0Z(n) of the normal Q0-triangle, the sum of all squares of them equals Q0Z(2n). The simple sum yields 0, what matches the conservation laws well {Q1RowSumIs0}.
4.7.3 Differentiation of the Q0-triangle, solutions of the quantum mechanical oscillator, Hermite polynomials
One can arithmetically regard this Q1-triangle as discrete differentiation [DiscreteDiff] of the Q0-triangle along k, the horizontal direction. So the removing (perceiving) of the Q0Z results in a differentiation along the horizontal direction (difference left-right, d/dk). Perception surely also means differentiation along time axis (difference future-past, vertical, d/dn) and the correspondence [TimeSpaceCorrInMiddle] of vertical and horizontal differentiation in the middle is remarkable.
The graph of a multiple (discretely) differentiated Q0 function yields an continuous seeming wave-like picture after a larger number of recombinations [wavelike].There is a far-reaching analogy between those multiple discretely differentiated functions and the solutions of the quantum mechanical harmonic oscillator: By multiple discrete differentiation construction of orthogonal systems is possible, analogous to the Hermite polynomials [HermPolDiscrete]. At this the Hermite polynomials [HermPol] are (except sign) special cases of pre-factors resulting from multiple differentiation in the analytic borderline case. There are further considerations possible concerning integration and differentiation. Some can be found in the download files.
4.7.4 Possible further (open) combination possibilities
Particularly demanding: How can several triangles[85] be combined in different (how much?) directions(NotFlat)? At this the system must remain {open}[86](***). Do multiple application of the Maxwell-equations give partial hints? How can the recombination points (in symmetric way) be connected, to get broad analogies to the physical measure-, distinction and decision process (cf. [PauliMatrices][87])? Which recombination points are (dependent on observer location) differentiable in time[88], which one differentiable in localization, which seem to be an unit (cf. [ElementaryCoordinates])?
4.7.4.1 Strength of interactions
If there is a physical interaction between two systems, there is a way between them over more or less many recombination points. The shorter the passage, the more probable it is in the average (per proper time unit(ProperTimeUnit)), the stronger it appears. For example the strong interaction probably goes over only relatively few recombination points. This also permits more symmetries. The weak interaction however probably needs more recombinations, so that this complex connection hasn't left-right symmetry any longer [DecisionFunnelBorder]. It needs more time, from which the possibility for a comparison with past left-right definition arises.
4.7.5 Neg. sum of central "outflowing probabilities" multiplied by the sum of the central meeting probabilities yields 1
For every even row number n>0 let be the number |Q2Z(n)|=-Q2Z (n) the "outflowing probability", i.e. the probability for flowing out[89] centrally. Q2Z(n) is equivalent to the 1nd (discrete) derivative of Q1(n,k) in k=0 along k, i.e. Q2Z(n) = (Q1(n-1,1)-Q1(n-1,-1))/2; so Q2Z(n) is in k=0 the 2nd derivative of Q0(n,k) along k. It holds:
The resulting table for Q2Z(n) is
On the other hand the
The coefficients of
the
A discrete differentiation (DiscreteDiff), here along (proper) time is clearly dependent on the relation subject/object.
4.7.6 QW (x) corresponds to the expectation value of |k/n|
In case of equal probabilities of steps to the right and to the left no direction of coordinate k (cf. (Q0Triangle)(Q1Triangle)) is preferred and the expectation value <k/n> of k/n is zero. <k/n> is equal to the difference of the probability p of a step to the right and (1-p) of a step to the right, i.e. <k/n> = p-(1-p)=2p-1. Because of x^2=4p(1-p) [xAndp] from this results {QWasExpectationValue}
4.7.7 An information theoretical interpretation of the Planck effect quantum h
{hAsConstantProduct}We know, that the Planck effect quantum can be
understood as product t*E of proper time t (of a measurement) and the energy
uncertainty E (of the measurement result). Proper time resp. measuring time is
proportional to the function QV(x) resp. to the sum of the return probabilities
in the Q0-triangle(PTimePropSumQ0). The partial sum of
the
4.8 Many (arithmetical) coherences
Due to the shown coherences of course it is reasonable to examine finite partial sums of the taylor series expansions of QV(x) resp. QW(x) more exactly, also in the case of imaginary[91] x, |x|=1 and even for |x|>1 . The corresponding "probabilities" for steps to the right or to the left wouldn't be limited within the real interval [0,1] any more[92] because of 4p(1-p)=x^2.
The mean vertical reach (1st order momentum) of |Q2Z(n)| from row n=1 on up to the outflow is equivalent to the sum of the Q0Z(n) from row n=2 on (cf. [DefQ2Z]), i.e. the mean reach from row n=0 on is equivalent to the sum of the Q0Z(n) from row n=0 on and therefore approximates QV(x). At more detailed occupation with the topic many coherences stand out (cf. [DeviationQ1Equal1], the formulary in wqm or the concise formulary). A more exact definition of concepts like "simultaneity" resp. "concomitance", a more exact analysis of the process of new creation[93] of information and the process of copying[94] (also parallelizing) information would be necessary. The formation of scalar products (Scalarproduct) in horizontal and vertical (and even sloping) direction in the triangle could serve as bridging to the common mathematical framework of quantum physics[95]. Because of the underlying recombination principle and for study of different branching resp. connection possibilities in the triangle the consultation of specialists in [combinatorics] and graph theory [RGraphTheoreticalResearch] can be helpful (perhaps even of geneticists or in the field of the genetics active mathematicians).
4.8.1 The mean deviation in the Q1-triangle is constant
{DeviationQ1Equal1}An example of arithmetical coherences:
In
connection with the
also the
Here the summation goes over both horizontal halves, the impulse was decomposed in time * force. The time ET was interpreted as a not sub-divisible unit, as elementary time between the beginning and end of the summation (the integral) and the force as current probability for flowing out, as probability for leaving within the time ET the relative[96] location with maximum impulse (with maximal speed v=c).
(A possible bridging to quantum
physics: One could consider the Compton effect (***), (the interaction of a photon with
matter; I also think of the generalized
The Plancksche effect quantum hq still was interpreted here quite graphically (as product of physical quantities). [A priori] An information theoretical interpretation is more consistent, though (hAsConstantProduct)[lish1]. One also can understand hq as energy * time and so as information * proper time. On the average much Information can be given [give] resp. transferred only along short time intervals, little information along longer intervals. Of course at this has to be considered, that the conversion factor for energy * time to information * proper time isn't a constant but a function, dependent on the extent of branching depth and on renormalization .
4.8.2 Q1 as finite difference of Q0
The exact formula of the Q1 function is:
Let be n a natural number, k an integer with absolute value smaller or equal n, and p a number contained in the interval [0,1]. If we define
and
then holds
The Q1-triangle results from a superposition of two Q0-triangles with opposite sign, starting in position n=1, k=±1 after multiplication by 1/2. Addition of both means a discrete differentiation {DiscreteDiff}[99] along k. The formula then arises from the difference quotient with minimal dk, i.e. dk=2:
(Q0 (n, k + 2) - Q0 (n, k)) / 2 = Q1 (n + 1, k + 1) .
Analogously one can make m-th order (discrete) differentiation by using row n=m of the Q0-triangle, equipped with along k respectively alternating sign, as starting row[100](BinCoeffDiffMatrix). The initial zigzag of the accompanying function graph flattens in the following rows to m+1 continuous seeming waves {wavelike}. Discrete alternating state functions can also cause wave-like phenomenons (probability distributions), if the initial situation (e.g. the binomial distributed discrete analogue of "phase angle"[PhaseAngle]) is not sharp. The superposition of many rows with even (or odd) row number n and alternating sign respectively yields a wave-like picture.
Still to mention is, that a second order discrete differentiation (finite difference) along k means[101] a first order discrete differentiation (finite difference) along n:
A connection to the (***) Schrödinger equation {Schroedinger} seems reasonable.
Remarkable is the correspondence of vertical and horizontal differentiation in the middle{TimeSpaceCorrInMiddle}:
Q1(n+1,1) = Q0(n+2,0) - Q0(n,0) = (Q0(n,2) - Q0(n,0)) / 2
The middle (the vertical symmetry axis k=0) represents the relativistic borderline case[VisCinMiddle] - also in the common theory arise equal rights of time and location coordinates in the relativistic borderline case.
5 Bridges to current concepts of quantum physics
5.1 Probabilities and probability amplitudes
{ProbabilityAmplitude}[liba][libo][lifi][liko][lipa] In quantum physics usually one talks about complex valued probability amplitudes, the corresponding probabilities are calculated secondarily from the square of the absolute amount, i.e. from the scalar product with the corresponding complex conjugated probability amplitudes. Just also the central meeting probabilities Q0Z(n) (resp. |Q2Z(n)|) correspond to such a scalar product. In the presented example (cf. Scalarproduct) real probability amplitudes are used - even if the currently used probability amplitudes are complex, their scalar product has to be real, if measurable. As bridge to current concepts one also could e.g. identify the absolute value of Q0(n, k) resp. Q1(n, k) as amount of a probability amplitude, whose phase angle is varying with n and k (cf. RowSumAsWave). It has to be remarked here that in context of discrete considerations the phase angle{PhaseAngle} cannot be calculated (exactly) and so doesn't have an equivalent in the reality. The (continuous) trigonometric functions and of course also the (complex valued) exponential function are approximative. However, exact discrete representations[102][DiscreteRepresetations]are possible, which don't imply infinite series expansions.
5.2 Example of a (discrete) scalar product
{Scalarproduct}: In discrete considerations [like] of course integrals have to be replaced by finite sums[103]. Particularly important sums are scalar products. In the compendium of formulas wqm several dependencies are described for different possibilities of scalar product formation in the Q0-triangle. Also in the Q1-triangle there are such. An particularly obvious example, which allows remarkable simplifications[104](***), is listed here. For m smaller or less n holds:
For example one gets for m=n=3 {ScalarproductExample}
The list of the accompanying recombination points in the graph for the ways from A to B is:
n k-> -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6
¯
0 A *1/1
1 1 -1 *1/2
2 1 0 -1 *1/4
3 1 1 -1 -1 *1/8
4 1 2 0 -2 -1 *1/16
5 1 3 2 -2 -3 -1 *1/32
6 1 4 5 B -5 -4 -1 *1/64
Every way from A to B contains an only finite sequence of recombination points{FiniteRecombinationSequence}. Abbreviated said it can be subdivided into a (Dirac) "ket" part (e.g. from A to row n=3) and a remaining "bra" part. The recombination points on the ways from A to B are marked by underlining. A simultaneous perception of row 3 (with all way possibilities coming from the decision in A, cf.{DecisionCenter}) is at the earliest {earliest} in the center (k = 0) of row 6 = 3+3 possible, i.e. after new not perceived branchings[105] already have arisen again (in not underlined recombination points). The system remains [open], though for every (also arbitrarily great) n the simultaneous perception of row n always is possible from row 2n on (an analogous argumentation is possible for the Q0-triangle). From row 2n on for every way to a point in row n also a corresponding way back exists, which is necessary for finished perception {FinishedPerception}.
Perhaps the spread of row n resp. 2n is cause of the in principle unsharpness of perception (the very last past) - the mean deviation in the Q1-triangle is constant like the Planck effect quantum hq (DeviationQ1Equal1), and the scalar product can correspond to the integration over one period. Sharpness however can exist concerning the origin (point n=0, k=0) of this distribution (completed past).
If for a system in A because of the initial decision resp. differentiation there a special way is predestined, for example a way over point 1', a probability gradient [ProbabilityGradient] arises relative to the distribution listed here, which could result in a relative force (working on this system, to and back again).
Point A determines the origin and also the coordinates of point B in the center {DeterminedReturnInCenter}. This leads to manifestation of conservation laws and to a partial determination of the experimental result. So in the above example the second half of the graph can be regarded as a converging "funnel" for the ways caused by the decision for this experiment in A {FunnelOfDecision}.
5.3 Deduce of Heisenberg's uncertainty (indeterminateness) relation using Q0(n,k) as discrete state function (***)
It will be shown shortly, how Heisenberg's uncertainty relation results, if Q0(n,k) is used as state function and k is identified with the location coordinate x. At first we introduce the variances of the location x and the impulse p
in which the dash marks the quantum mechanical expectation value. We can always transform the coordinates so that we get
.
Then we may assume
.
If y is the not normalized state function of a quantum mechanical system, one defines (cf. [liha] p. 434)
If we replace y by the discrete function Q0 (n, k) (cf. [DefQ0]) and k by x, we get, if we use the same notation for analytical and discrete differentiation
Because of
we get
which had to be shown.
Here it's worth mentioning, that the discrete scalar product
disappears in case of odd l. Particularly consecutive derivatives are orthogonal resp. [uncorrelated].
5.3.1 Interpretation: Operator works on all way possibilities
Under con-attention of the discussion to the discrete scalar product the following qualitative interpretation is possible: The operator (multiplication by x, discrete differentiation) works in all points of row n on all ways from point k=0 of row 0 of the last perception to point k=0 in row 2n of the current perception. All way possibilities[106] have to be taken into account {AllPossibleWays}: The more exact the measuring resp. the finer the differentiation, the greater is n (,the smaller is the renormalization factor in the denominator), the more way possibilities exist, the greater is the variance of the complementary quantity in line 2n.
5.3.2 Perceptible equivalent of information
{InfoConcrete}The following interpretation is possible: As mentioned the location coordinate x was identified with the horizontal coordinate k in the Q0-triangle (cf. [LocationXasK]). Remembering the discrete [Schroedinger]equation the vertical coordinate n can be identified with the time coordinate. The distribution of the probability amplitude valid in row n is a function of the variable k and can be understood as state function over which a discrete scalar product is formed. At perception in row 2n (cf.[FinishedPerception]) the won information resp. the measurement result (for example the location) lies in the result of the scalar product over row n.
5.4 Information theoretical interpretation with simple example
We can represent reality conform information units as choices of an element from a finite set M, as choice functions on this set - after distinction of the elements of M is possible and so freedom for new information (which needs separated resp. free energy (FreeEnergy)). Suppose M has 2m+1 elements which represent the possible values of a discrete variable. We choose in our example m=3 and M={-6, -4, -2, 0, 2, 4 6}
(The elements may represent e.g. multiples of the half effect quantum hq/2).
Now let's look at the information of the choice of one element of M. We can represent this information by a choice function f(M), whose result is a vector
f(M)=(k_6, k_4, k_2, k0, k2, k4, k6)
whose components k.. are binary variables with possible values 0 or 1. Exactly one[107] of these components is equal to 1, which means, that the corresponding element of M is selected resp. "true"; the other components are equal to 0. For example f(M)={0, 0, 0, 1, 0, 0, 0} would mean: "Element 0 is selected" resp. "Element 0 is true".
Because in this case the information concerning the choice within the set M is complete (the remaining indefiniteness resp. entropy concerning this choice is zero), M cannot contain all variables of physical reality and therefore the function f(M) can only provide a partial description of reality. There must be at least one additional free variable after the moment of perception resp. measurement of f(M) - a complementary variable. For the meaning of "after" and the together with time increasing number of possibilities see (RGraphTheoreticalResearch).
The creation of the set M has to be done step by step, beginning with an minimal initial set M0, e.g. with M0={0}. If creation of M and choice of an element is done very often, a probability distribution of the possible results arises. For symmetry reasons we can assume a binomial distribution of the probabilities around the initial element "0". So we get the probability distribution
p(k)="Probability, that element k of M is true"
of the result vectors f(M) of the above experiment, e.g. p(k)=Q0(6,k). We can regard p(k) as one of the first functions within a sequence of exact discrete state functions, which can be approximated by the currently usual continuous state functions in case of very large M. It can be easily shown (ScalarproductExample), that one can understand the values p(k) also as scalar products of probability amplitudes or (later) as probability amplitudes (from which scalar products are formed after progress of proper time). Even if the probability amplitudes are complex, their scalar product is real, if measurable.
5.4.1 Example for an operator on a discrete state function
Now an example for an operator on p: (discrete) differentiation. We make a discrete resp. finite difference along k. In our case |M|=7, there are 7 possibilities for kÎM:
-6 , -4 , 2 , 0 , 2 , 4 , 6 , and
1/64, 6/64, 15/64, 20/64, 15/64, 6/64, 1/64
are the corresponding values of p(k)=Q0(6,k). The sum of these is 1, so we can set p(k)=0 for kÏM. Now let's call the Operator for discrete differentiation D; it maps the function p to Dp:
Dp(k):=(p(k+1)-p(k-1))/2 .
So we get
Dp(k)=1/128, 5/128, 9/128, 5/128, -5/128, -9/128, -5/128, -1/128 for
k = -7 , -5 , -3 , -1 , 1 , 3 , 5 , 7,
otherwise Dp(k)=0. We notice, that these are the values of Q1(7,k), cf. (DiscreteDiff). They aren't any longer probabilities in the ordinary meaning, but can be probability amplitudes after normalization (ProbabilityAmplitude).
5.4.2 Remark: Results of physical experiments as vectors
In the mentioned example we can interpret f(M) as sharp special case of the result vector of a physical experiment. Usually the result is not sharp - then similarly the experimental result can be represented by an probability weighted result vector pf(M) with index k, e.g. pf(M)=(1, 6, 15, 20, 15, 6, 1)/64. That's equivalent to representation as state function p(k) and can facilitate the combinatorial understanding in case of small |M|. If we "artificially" increase the dimension of pf(M) by adding zeros we can represent an operator as square matrix even if it increases |M|. Example for pf(M) and operator D as finite difference "along index" in form of a matrix, completed in suitable way with zeros:
¦ 0 1 0 0 0 0 0 0 0 0 0 0 0 0 -1 ¦ ¦ 0 ¦ ¦ 1 ¦
¦ -1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 ¦ ¦ 1 ¦ ¦ 0 ¦
¦ 0 -1 0 1 0 0 0 0 0 0 0 0 0 0 0 ¦ ¦ 0 ¦ ¦ 5 ¦
¦ 0 0 -1 0 1 0 0 0 0 0 0 0 0 0 0 ¦ ¦ 6 ¦ ¦ 0 ¦
¦ 0 0 0 -1 0 1 0 0 0 0 0 0 0 0 0 ¦ ¦ 0 ¦ ¦ 9 ¦
¦ 0 0 0 0 -1 0 1 0 0 0 0 0 0 0 0 ¦ ¦ 15 ¦ ¦ 0 ¦
¦ 0 0 0 0 0 -1 0 1 0 0 0 0 0 0 0 ¦ 1 ¦ 0 ¦ 1 ¦ 5 ¦ 1
Dpf(M) = ¦ 0 0 0 0 0 0 -1 0 1 0 0 0 0 0 0 ¦·——— • ¦ 20 ¦·———— = ¦ 0 ¦·—————
¦ 0 0 0 0 0 0 0 -1 0 1 0 0 0 0 0 ¦ 2 ¦ 0 ¦ 64 ¦ -5 ¦ 128
¦ 0 0 0 0 0 0 0 0 -1 0 1 0 0 0 0 ¦ ¦ 15 ¦ ¦ 0 ¦
¦ 0 0 0 0 0 0 0 0 0 -1 0 1 0 0 0 ¦ ¦ 0 ¦ ¦ -9 ¦
¦ 0 0 0 0 0 0 0 0 0 0 -1 0 1 0 0 ¦ ¦ 6 ¦ ¦ 0 ¦
¦ 0 0 0 0 0 0 0 0 0 0 0 -1 0 1 0 ¦ ¦ 0 ¦ ¦ -5 ¦
¦ 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 1 ¦ ¦ 1 ¦ ¦ 0 ¦
¦ 1 0 0 0 0 0 0 0 0 0 0 0 0 -1 0 ¦ ¦ 0 ¦ ¦ -1 ¦
Similarly to [BinomialCoeffMatrix] also multiple powers of above matrix exhibit binomial coefficients [BinCoeffDiffMatrix].
5.5 Combinatorial considerations to entangled quantum mechanical states
Measurement is only possible when time advances. Due to our considerations to perception of time (TimePerception) we can assign each progress of proper time to the reunion of two ways within some symmetry center, a reunion which is necessarily connected with emission and absorption of free energy (photons) on rest mass. In the simplest case the symmetry center has only one dimension s (e.g. spin)[108] less that the (discrete) global surrounding space (the "global lattice"). Then after start (i.e. decision resp. separation) of the ways there is for each way-point (s,...) a corresponding (anti-)symmetric point (-s,...) "on the other side" and absorption resp. emission of energy occurs exactly in s=0.
There is a remarkable parallel to the ways of particles with entangled state: These may be spatially separated in between times, but on the ways of both particles until measurement no energy exchange with surrounding is possible, i.e. s<>0 from beginning of separation, and sign of s cannot change until measurement. If we measure that s was greater 0 for one incoming particle, we know that s>0 has been true since separation (i.e. during a more or less long period of time), i.e. we gain information. We also know, that s<0 since separation must have been true for the other particle because in between crossing of s=0 is not possible for particles with entangled state or - in another formulation - due to conservation of s. So we can interpret the measurement results on entangled states as a consequence of
(anti-)symmetric behavior from start until first return
to a symmetry center. The word "first" signals, that in between times the objects with entangled state are separated from the symmetry center, i.e. in between times there is no information exchange (resp. absorption or emission of free energy on rest mass, resp. crossing of s=0). From this point of view entangled states are special cases, which are (due to missing energy exchange with rest mass in between times) simple enough, that symmetry becomes clear (symmetry around s=0, around a symmetry center, in which absorption and emission of free energy occurs).
Of course nature is not restricted to such simple cases. If there is exchange of energy with rest mass in between times, e.g. in row n0, in this moment all ways of the exchanged energy quanta (photons) pass the symmetry center s=0 of the row. Descended states can be represented as a product [of the form å(amplitudes of ways to n0, s=0) * å(amplitudes of ways starting from n0, s=0)]] and therefore aren't entangled.
If in between times, until reunion, exchange of energy (crossing of s=0) is possible with systems, which are at the moment separated from the measuring device (rest mass), (combinatorics) becomes more difficult, but study of these more complicated ways can become necessary to gain deeper insight.
5.6 Discrete representations
Analytical functions with infinite power series expansion cannot have an equivalent in physical reality. But rational discrete representations of them are often possible, i.e. representations which are rational functions and which have a discrete but arbitrarily fine subdivided range of values.
5.6.1 Discrete representation of sine, cosine, rotations
Two-dimensional rotations can be represented as multiplication by rotation matrices and as multiplication by complex numbers. We choose for reasons of better clearness latter possibility, i.e. we represent the rotation with assumed[109] angle w as multiplication by a complex number with amount 1 and phase angle w. To consider probability amplitudes (instead of the resulting probabilities), we define in generalization of (Q0Pvar)
from which
and the following distribution results:
n k-> -4 -3 -2 -1 0 1 2 3 4
¯
0 1
1 s c
2 ss sc cc
3 sss 3ssc 3scc ccc
4 ssss 4sssc 6sscc 4sccc cccc
...
The (horizontal) sum over row n just corresponds to the binomial expansion of (s+c)^n. So if we set[110]
s := i sin(w) und
c := cos(w)
this sum simply corresponds to (i sin(w)+cos(w))^n = e^(inw) = i sin(nw)+cos(nw), i.e. to the complex number with amount 1 and phase angle nw. The smallerïwï, the finer is the gradation of the realizable rotations. In detail we get {RowSumAsWave}
and the components can be separated by addition resp. subtraction of the corresponding row of the (for symmetry reasons existing) triangle with opposite phase angle{GetComp}. One receives for instance
For deduction of this representation only simple arguments are necessary, nevertheless it is unusual. Remarkable is the separation of the cases of even or uneven line numbers following in natural way from this (in analogy to the natural separation of the spin cases of Bosons and Fermions) and the now obvious possibility for summation also in vertical direction of the triangle.
In the case ï4scï=ï2sin(2w)ï=1 and therefore wÎ{mp/2 ±p/12 ï m integer} the central amounts ïQ0SC(2n,0,s,c)ï just correspond to the central meeting (CentralMeeting) probabilities Q0Z(2n)=Q0(2n,0), in the case ï2sin(2w)ï<1 and therefore wÎ{]mp/2-p/12, mp/2+p/12[ ï m integer} the vertical sum
converges absolutely, otherwise (for n->¥) there is no upper bound for ïQ0SC(2n,0,s,c)ï. So there is convergence just if W is within a 30 degrees broad interval around the coordinate axes, a third of all possible angles.
In quantum mechanics a state with determined energy E is associated with the wave function
,
with [RowSumAsWave] (and TimePerception) it is fair to assume in first approximation
and for example Eµw und nµt .
5.6.2 Discrete representation of the exponential function
If we choose[111] s=sinh(w) und c=cosh(w), the sum over row n ([Q0SCTriangle]) corresponds to the binomial expansion of (sinh(w)+cosh(w))^n = e^(nw) and we get
The (assumed) number w can be complex(ProbabilityAmplitude). We can get the functions sinh and cosh analogously to[GetComp]. With that multiple Lorentz transformations can be chained in a clear way (cf. e.g. [limi] p. 67-68 and [lifl] p. 24-27).
5.6.3 Discrete representations of matrix exponential functions (SU(N)...)
Analogously to the normal exponential function we can construct discrete representations of matrix exponential functions by choosing s and c as matrices (e.g. matrices from SU(n) groups with numbers from Q+iQ). If the matrices commute, we get for example[112] the matrix exponential function (cf. e.g. [lime2] p.113-115 or [liwa] p. 228). If not, nevertheless a clear discrete representation can be possible, e.g. like in case of the Pauli matrices (PauliMatrices). So discrete considerations can facilitate a deeper understanding.
5.7 Pauli matrices, quantal bits
{PauliMatrices}The three Pauli matrices are frequently used in quantum physics. Together with the 2x2 identity matrix I they are defined by
When making a symmetrical binomial distribution[Q0Triangle], per step to the right or to the left a multiplication by the accompanying probability 1/2 is done. Instead of this for
we can multiply by
per step to the right and by
per step to the left. From this results because of
a "zoomed Q0-triangle":
n k-> -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8
¯
0 1' *I
1 1 1 *s/Ö2
2 1 0 1 *I/2
3 1 1 1 1 *s/(2Ö2)
4 1 0 2' 0 1 *I/4
5 1 1 2 2 1 1 *s/(4Ö2)
6 1 0 3 0 3 0 1 *I/8
7 1 1 3 3 3 3 1 1 *s/(8Ö2)
8 1 0 4 0 6' 0 4 0 1 *I/16
...
At this s symbolizes one of the Pauli matrices respectively.
In the general one can also multiply these by the sine and cosine of an angle different fromp/4 and an asymmetrical "zoomed" triangle results. Multiplication by pre-factors whose square sum is smaller resp. greater than 1 yields exponential decrease resp. increase of the row sum in case of increasing row number n. Further modifications are possible, if instead of the hermitean Pauli matrices pseudo-hermitean or real matrices are used, from which easily different types of so-called "quantal bits" (qubits) could be derived ([ligre] p. 17). The interpretation of this might succeed best by those readers who have profound familiarity in the application and meaning of these matrices and who remember the remarks to the Q0-triangle (e.g. those to the central meeting events, proper time unit, cf. CentralMeeting,ProperTimeUnit).
Note: In the above "zoomed Q0-triangle" the occurrence of irrational numbers like 1/2 is problematic. But we can avoid these numbers by further modification with introduction of alternating pairs of multipliers, e.g. 1/2, -1/2 followed by 1, 1 according to the natural sequence of decision and perception.
5.8 (Lie algebras)
5.8.1 Cartan matrices
The rows (columns) of the m-th powers of some important Cartan matrices correspond to the 2m-th rows of the binomial coefficients. For better clearness at first an excerpt from Hazewinkel's Encyclopaedia of Mathematics ([liha2], article to "Lie algebra, semi-simple") and then an example:
... Simple Lie algebras that correspond to root systems of types A-D are said to be classical and have the following form.
Type An, n>=1. g=sl(n+1,k), the algebra of linear transformations of the space k^(n+1) with trace 0; dim g=n(n+2).
Type Bn, n>=2. g=so(2n+1,k), the algebra of linear transformations of the space k^(2n+1) that are skew-symmetric with respect to a given non-singular symmetric bilinear form...
...
The Cartan matrix of a semi-simple Lie algebra over an algebraically closed field also determines this algebra uniquely up to an isomorphism. The Cartan matrices of the simple Lie algebras have the following form:
| 2 -1 0 ... 0 |
| -1 2 -1 ... 0 |
An:= | 0 -1 2 ... 0 |
| . . . ... . |
| 0 0 0 ... -1 |
| 0 0 0 ... 2 |
Bn:= ...
...
For example in case the exponent m=3 and the matrix
| 2 -1 0 0 0 0 0 |
| -1 2 -1 0 0 0 0 |
| 0 -1 2 -1 0 0 0 |
A6 := | 0 0 -1 2 -1 0 0 |
| 0 0 0 -1 2 -1 0 |
| 0 0 0 0 -1 2 -1 |
| 0 0 0 0 0 -1 2 |
we get {BinomialCoeffMatrix}
| 14 -14 6 -1 0 0 0 |
| -14 20 -15 6 -1 0 0 |
m 3 | 6 -15 20 -15 6 -1 0 |
A6 = A6 = | -1 6 -15 20 -15 6 -1 |
| 0 -1 6 -15 20 -15 6 |
| 0 0 -1 6 -15 20 -14 |
| 0 0 0 -1 6 -14 14 |
and we recognize the absolute values of the numbers in the rows resp. columns again in row 6 = 2m = 2*3 of the Pascal triangle (enumeration of the rows beginning with 0 like in the Q0Triangle).
6 Bridges to theory of relativity
6.1 Bridges to special relativity
The connections to special relativity theory are clear [BridgesToRel].
6.2 Bridges to general relativity
Due to the difficult experimental testability here much is speculative [StrongFieldExtrapolationErr][CosmoExtrapolationErr]. Nevertheless the experiments show (statistical) proportionality of gravitating and inertial mass, so the following thoughts are worth an outline:
6.2.1 Gravitation as result of (small) correlation
{GravitationBecauseOfCorrelation}In the quantum mechanics probabilities result from scalar products (ScalarProduct). We can transfer this concept to gravitation. Here in simplified way the first step is outlined: Let be n very great and
proportional to the probability of interaction, with positive resp. negative sign depending on attractive or repulsive interaction. Due to symmetry we can assume (in first approximation, no charge) that a2k und b2k are positive and negative in equal frequency, so that the sum on the right hand side of above equation disappears and only ng2/r2 remains.
6.2.1.1 Gravitating mass
We can identify k and g with radial integer coordinates which are proportional to the distance to the symmetry center of a global distribution[113] and g with the initial value (offset) in the starting point of our present reference system (which is the maximal perceptible distribution). This starting point lies outside the center as a result of an initial decision, e.g. on one side(OneSide) with g>0, and n can be understood as proportional to the gravitating mass. If we furthermore assume, that the frequency of this scalar product (per proper time) is proportional to the second interacting mass N, we receive the desired result, namely a total interaction proportional to Nng2/r2.
6.2.1.2 Inertial mass
Let dp be a change of momentum. We can understand k also as coordinate in the momentum [xAsE0divEandkAsMomentum]space and dkµdp as number of steps to one side corresponding to dp. With that the accompanying speed change dv results from
and dv is proportional to 1/n, i.e. n is proportional to the inertial mass.
6.2.2 (Dynamic length scale)
Preliminary note: At last this approach seemed to me less relevant than the one of (small) correlation [GravitationBecauseOfCorrelation].
The own lengths and time scale is apparently constant, the probabilities of the recombination points however aren't. Very simple model concepts[DynamicLengthScale] lead to an square increase of row number (and length scale) in comparison with proper time. At more detailed treatment of the topic the with falling relative distance increasing probability of interaction between recombination points also has to be taken into account.
7 Recommended graph theoretical research
{RGraphTheoreticalResearch} Of course progress of proper time is connected with every moment of perception (of information). Only an approach {TimeConformApproach}, in which the number of possibilities of experimental results grows together with the duration of the observed experiment, i.e. together with time, can be adequate (ETmGreatEnough). Our considerations [InformationPath] (RealInfinityGrowsWithTime) suggest a graph theoretical description of the ways of information, in which the progress of proper time physically is connected with pairs of emission/absorption of photons on rest mass [PhotonEmissionAbsorptionAsTimeUnit], mathematically with subsequent "central meeting events" (CentralMeeting), events in the center (the vertical symmetry axis) of a Q0-triangle (Q0Triangle) or some (e.g. differentiated, multidimensional) modification of it. Such an extending, directed graph {DirectedGraph} automatically contains the more possible ways and free variables, the more steps are done within it.
7.1 Widely ramified graph - nonlocal seeming effects
The graph can also disclose (anti-)symmetries which start from the (decision (PrimaryDecision) in the) central beginning of it (of the corresponding experiment), which give evidence of conservation laws in it, which hold up to the (perception in the) central end of it ((CentralMeeting) of the corresponding experiment). So effects on opposite sides of the graph are at last (anti-)correlated, even if it is widely ramified and seems to be not local.
7.2 General guidelines for reality conform algorithms
Again: It is important to realize that in physical nature the number of distinguishable possibilities of experimental results is finite at given time (http://arXiv.org/abs/quant-ph/0108121) and is increasing only together with time. Furthermore physical laws are by definition stable, i.e. they are valid iteratively at every time. Therefore nature conform algorithms must be iterative in time [TimeConformApproach] and must operate on discrete spaces resp. numerical lattices (wqps1.pdf), starting with a finite number of different (lattice) quantities and producing an increasing number of new quantities during their iteration. Furthermore the results of http://arXiv.org/abs/quant-ph/0207045 suggest that these algorithms should generate branching loops {BranchingLoops}, i.e. iteratively in the course of time (iteratively after a finite number of iterations of the algorithm) the quantities should have effect on quantities at other new (lattice) coordinates[114] which in turn later have effect backwards.
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9 Addendum
9.1 Maxwell equations
{Maxwell} Since in recombination points changes of direction [DirectionChanges] happen, which are in case of p=1/2 [orthogonal] from local point of view, on the other hand magnetic and electric fields pass into each other[115] locally[116] orthogonal, a combinatorial, multiple application of the Maxwell equations should be very interesting (***). It admittedly is difficult to keep track after multiple discrete differentiation (DiscreteDiff) under consideration of the numbers of the order possibilities, also of the vector potential of the magnetic field (combinatorial computer simulation? [lipo1], cf. also wq2). But this chapter is expandable.
9.1.1 Anti-symmetry of the combinatorial ways through magnetic dipole
There are electric charges, i.e. outflows and inflows of an electric field also can be perceived for themselves, after each other resp. temporally separated. That's not so in case of a magnetic field. Magnetic sources resp. charges (monopolies) weren't found till now[117], so let's now[118] start out from the assumption that there aren't any magnetic charges, i.e. that the poles of a magnet are locally, but not temporally separable. Then the combinatorial ways which go through the (locally separate) poles of a magnet should together (locally simultaneously) and anti-symmetrically flow into resp. out of the observer's point of view, relative to his local time direction. Due to a possible change of the local time direction no contradiction arises to the assignment of matter (Matter) und anti matter (Antimatter). The measurement result is namely dependent on the observer's point of view which is connected narrowly with the way of the measuring. Also remember that the common concept "point of view" of the observer is but clear but not precise since the point concept doesn't suffice for the description of the observer's "point" of view [ObserverViewPoint]. Subsequently a possibility of the change of the combination sequence in case of magnetic field measuring is mentioned.
9.1.2 Characteristic of temporally differentiated perception
The perception simultaneous in a point P1 can contain several events which are separated locally. From another point P2 seen the information ways starting out from these events may arrive subsequently, i.e. the same can be distinguishable (discretely differentiable) once in time[119], once in location, although the physics is equivalent. Such equivalences are expressed among other things[120] in physical equations. There are many such equations which assign (multiple) locally differentiated perception (measuring) to temporally differentiated perception. Due to their combinatorial information content the Maxwell equations are particularly interesting. They show e.g. that temporally varying charge (electrical current) plus a temporally varying electric field is equivalent with a magnetic rotational field. Since there aren't any magnetic sources, all magnetic fields are rotational fields i.e. every (simultaneous) magnetic field is equivalent to the temporal change of something. In this case therefore the combinatorial ways must start out from two subsequent events and flow in the observer's point of view together (locally simultaneously) and anti-symmetrically[121] (resp. symmetrically flow in and out). So it's reasonable to assume the time direction of the magnetic field measuring as orthogonal to the time direction of electric field measuring. The following outline with the first three rows of a triangle should illustrate the consideration:
n0k0
n1k-1 n1k1
n2k-2 n2k0 n2k2
The points n0k0 and n2k2 subsequent central meetings, i.e. temporally separable resp. discretely differentiable (regarding the vertical as time axis). They are anti symmetric to n1k-1 and n1k1. We can for example n1k1 to an observer point of view of the magnetic field measuring{DecentralMeetings} and understand the way n0k0 to n1k1 an inflow and the way n1k1 to n2k0 as outflow. If n0k0 and n2k0 should seem locally simultaneous we have to assume a time direction orthogonal to the vertical axis, for example horizontal to the right for the one who measures the magnetic field in n1k1 (with e.g. n0k0 as North Pole, n2k0 as South Pole). Together with this time direction one can understand n1k1 locally as central meeting, in which the magnetic field is perceived.
The advantage of this consideration it, that it explains the missing of magnetic monopolies, in addition is compatible with the assignment of matter Matter and antimatter Antimatter to right and left side of a primary triangle. However, it's still speculative and unsecured. If there is more security, then of course it's reasonable to carry out further combinations with the help of the Maxwell equations, also under consideration of the [Poynting] vector.
9.1.3 First steps beyond the flat model
{NotFlat}From the changes of direction which are connected with the Maxwell equations we can win clues to supplement the flat Q0-triangle with further dimensions. We know that the electric field corresponds to the differentiation of an electrical potential. Of course here we make discrete considerations. In the Q0-triangle or the Q1-triangle every decision is the choice between two alternatives, which we at first called "step to the right" resp. "step to the left ".
Now every decision is the choice between two orthogonal directions of discrete differentiation of the potential which are furthermore orthogonal to the incoming direction (the direction between last and actual recombination point). If for example the z-axis is the incoming direction, a decision now is the choice between a derivative of the potential either along the x-axis or along the y-axis. A little sketch to this:
QÄ
n0k0
/ \
y x
/ \
n2k-2 <- Ä= -z- n1k-1 n1k1 -z- =Q -> n2k2
\ /
x y
\ /
n2k0
Here the symbols QÄ represent the positive resp. negative z-direction, orthogonal to the drawing plane, the direction from n0k0 to n1k1 represents d/dx as well as the direction from n1k-1 to n2k0, the direction from n0k0 to n1k-1 represents d/dy, as well as the direction from n1k1 to n2k0. Due to the necessary orthogonality the direction from n1k-1 to n2k-2 resp. n1k2 to n2k2 now is anti-parallel or parallel to the z-axis; to take this into account by way of a hint, in the mentioned sketch the points n2k-2 resp. n2k2 are moved a little up, compared with the usual triangle.
If for example in n0k0 we decide to make a step to n1k1, we decide in favor of discrete differentiation of the potential along x, and such differentiation corresponds to the electric field E(x) along x. If we now step from n1k1 to n2k0, we differentiate along y, i.e. the electric field E(x) is differentiated along y: d/dy E(x). The stepping sequence from n0k0 over n1k-1 to n2k0 analogously yields the derivative of the electric field E(y) along x: d/dx E(y). If we now assume a sign inversion left and right of the vertical center (like in the Q1-triangle), so in n2k0 so we have
d/dx E(y) – d/dy E(x)
what just corresponds to the z-coordinate of the
rotation
of E. That,
which starts out of n0k0 and doesn't arrive in n2k0, exactly arrives in n2k-2
and n2k2, it just contains the difference of n0k0 and n2k0 [122]. It is the discrete resp. finite difference along the
row number n, i.e. a differentiation along time direction of something (whose
the physical phenomenon is dependent on the observer point of view), if we
identify the direction of increasing row number with the time direction. Also
the Maxwell equations say 
. A
differentiation along time direction is found here, too. For example is valid
d/dx E(y) – d/dy E(x) = d/dt B(z) .
The mentioned sketch shows that the respectively last step to n2k-2 resp. n2k2 also means a differentiation along the z-axis[123]. If we still consider that the in n2k-2 and n2k2 yielding quantities mean a discrete differentiation (of the vertical center) along n, in which we have identified increasing n with the time direction, so the correspondence with the Maxwell equations is conspicuous (***).
The considerations surely must be made more precisely, but then it would be also interesting to look at further branchings, using the Maxwell equations repeatedly. Now this has been done, with interesting result:
9.1.4 A discrete approach to the vacuum Maxwell equations and the fine structure constant
Discretization of the Maxwell equations is usually carried out in the context of computer simulations (FDTD). However, for the purpose of simplification (after von Neumann Analysis, to avoid divergence), a direct implementation is not done, but application of additional presumptions[124].
We also carried out a discretization of the Maxwell equations and Software implementation, but for in principle reasons we have done this directly, in symmetrical way and simultaneous (central differences, simultaneous and symmetrical realization of the equations at every time step). Interesting is the delayed manner of the divergence, as well as the initial development in dependence of the propagation (resp. coupling) of the fields, particularly if the squares of the propagators correspond to the fine structure constant
.
Also according to the experimental results this constant quantifies the coupling of the electromagnetic fields, and so of course (***) it is associated with the Maxwell equations. Therefore wqpm1.pdf, which contains a more detailed description, is a reasonable mathematical approach to the fine structure constant.
In contrast to that the following relation to the neutron and electron mass is very speculative. I mention it only to illustrate an example for further considerations to the topic.
Equations (16) of the above mentioned paper show that the field components branch[125] from every location into the same and 4 new locations per step from t to t+1. So the probability for branching into a new location (and field component) is |4p|, and the probability for n subsequent new branchings is |4p|^n. [126] If we assume p=±Öa and n=7 (the latter seems very arbitrary), the probability is (4Öa)^7=1/1838,65991 . This number is near to the quotient Mass_electron / Mass_neutron = 1/1838,68364 (Codata values of May 2004 [licodata] ).
9.2 Initial elementary considerations
9.2.1 Construction of an axiomatic system
No {a priori} existence of analytical models[127] is presumed. (***)
When we speak of renormalization {AxiomP1} , we already mentioned the (essential) axiom, which means "we are here" or:
The probability of our presence and of our present perception is 1 {ProbabilityOnePerPresence}
or
The probability of our consciousness is 1 .
This perhaps seems to be trivial at first sight, however, it isn't trivial due to the properties of consciousness resp. life. The following chapter deals with one essential property:
9.2.2 Creation of new information by decision for an order within time-unsharpness (indefiniteness) (***)
{NewInfo} Due to the lot of information which has already arisen from life, we know that life can create information. Since any information transfer is connected to a transfer of free energy, this means that life or our consciousness can send out (separate) from itself positive (free) energy temporarily in the context of the energy-time-unsharpness (give information[128]), if it decides so. Due to conservation of energy this is connected to emergence of negative (bound) energy somewhere else, for example in form of any negative potential which can be noticeable e.g. as electric field[129] or gravitational field and at last as force[130] resp. acceleration. Important is the sequence order: Because we can only perceive free (resp. positive) energy, we as conscious units must (cf. a. [consciousness])
1. at first {give}[131] information resp. send out free (i.e. for the surroundings available, positive) energy {FreeEnergy} (means for us decision, own contribution, effort[132], work {Work}, lack of information), thereby going into lower potential level[133] necessarily due to conservation of energy so that somewhere else free energy is available relatively to us, which is
2. then perceptible by us.[134]
So essential steps to get new information are:
1a. at first subdivision [Subdivision] of an unit[135] (of presence resp. us) into at first two[136] parts, differentiation and taking a
1b. primary decision (PrimaryDecision) for one part [OneSide]. In this part we then are temporarily localized, in the other the free energy which has been sent out by us at first.[137]
2. Perception of this free energy[138] (as present) from the other part in recombined shape and sequence {InfoBack}.
The primary decision yields information coming from us, the information about the temporal order {Order} of the parts or (equivalent) the own localization within the subdivision. We can receive now information from the surroundings (since we are localized on lower potential level). Its quantity is increased because of diversification (Diversification) due to coincidental recombination, said more exactly because of lively recombination of the free energy on the way back[139]. The multiplied information might be represented in division and permutation (along proper time) of the returning free energy.[140]
Due to the conservation laws we must (or want to) go into the other part later (so to speak we shall be decided into this part, having decision liberty in way at determined aim [FunnelOfDecision] – At last we cannot contradict ourselves.). Therefore the information about the initial order might be lost[141] or difficult to find {UncertaintyOfOrder} within the much greater quantity of information received in between.
It is tried in the following chapter to outline the initial sequence of the recombinations, which are connected to our decisions:
9.2.3 Possible initial situation in the Q1-triangle (attempt to make an initial outline)
{StartQ1} Let be k the column number, that is the integral index of the horizontal position within a row, in which k = 0 in the row center, k < 0 on the left of this, k > 0 on the right of this (k makes double-steps, there is no k = 0 in rows with odd numbers n, 2 is divisor of n+k). A (surely still correction requiring) outline of a description of the possible initial situation in the Q1-triangle follows:
In row n=0, k=0 [SymmetryCenter] a primary decision[142]{PrimaryDecision}, an experiment to get new information, a decision within us is done[143]. "After"[144] that one side {OneSide}, right or left to column k=0 in the triangle (Matter) (Antimatter), beginning in n=1, k=1 or n=1, k=-1, is our new localization. Due to the initial symmetry it would have come to the same, if we would have decided in favor of the other side[145]. It is questionable, whether this primary decision is perceivable in usual way. Here the word subdivision[146]{Subdivision} (distinction, differentiation[147]) probably meets better. Only due to this initial subdivision a complete decision in the ordinary sense, which selects one of two (different) possibilities, can be done:
In row n=1, k=1 {n1k1} (without restriction of generality we chose k=1) we take a definitive decision resp. we make the initial (imperfect) subdivision to a completed, perfect[148] decision for which there are 2 possibilities:
In row n=2 exists a distinguishable (differentiable) situation:
k=2 means no further perception - a situation, which exists also in the following rows in the border (k=±n) respectively. Is necessary always somewhere, that new information can emerge from "decisions out of the belly" - in the reality however probably at many places: The two dimensional model is too flat, at multidimensional considerations the border would be an enlarging and complex area[149].
k=0 means progress of proper time and (conscious) perception of a part of the in n=0 not chosen alternative as new present (1/2 of n=1, k=-1), and a part (1/2) of the chosen alternative (n=1, k=1) becomes past[150] - this part is proportional to the past proper time, proportional to the sum the negative central outflow probabilities Q2Z(n) resp. QW(x) (***).
So in row n=2 a part of the present not chosen in n=0 becomes own present (the part becomes more and more complete with increasing n.) Therefore that, which we would have measured, if we would have had the other alternative (the alternative of our environment) as present time in n=0, is not perceptibly and/or presently, but potential future, perceptibly in following rows after return to the middle (the vertical column of the central outflow probabilities, marked with ´) with increasing probability. The sum of the |Q2Z(2n)| over n, starting from row 2n=2, goes against 1.
Since for the present (in n=0) always only a part[151] of the not chosen, free alternative is perceived (and therefore flowing out, therefore becoming fixated past with delay), in between remains enough decision liberty for new information, without contradictions to us (to the information existing in us, to our past and present). So by deciding ourselves we simultaneously create separated (for our present) unknown areas and therefore liberty for further decisions(DecisionFreedom) and new way possibilities. Later we can perceive (represent) also these areas again after such magnification and diversification {Diversification}, step-by-step in small portions. This is quantifiable by the number of way possibilities which lead back to the (common) presence (center column).Interesting is , that this number of remained way possibilities gains with growing row number n{IncreasingWayCount} also in the Q1-triangle (the Q0-triangle differentiated in horizontal direction), in which the center column k=0 is taken away [The number of way possibilities to row 2n of the Q1-triangle is for great n approximately 4^n/Ö(pn) ]. So decision liberty resp. (increasingly growing) possibility for gaining information remains despite perception, if the perception is done after delay (after n=2) {DelayedPerception}; even potentiation is possible, the more, the bigger delay is[152].
(Probably a similar argumentation also can serve as objective proof, that it's nearsighted or even stupid to tear everything (information, safety) back to himself, that voluntary renunciation automatically is worth it and even necessary for a (more extensive) future. Such acceptance of temporary information gaps resp. delayed feedback also requires confidence {ConfidenceNecessary}because it means the renunciation of unnecessary[153] (hindering) control. So confidence is part of every decision - and lack of confidence means a lack of initiative in form of missing ability to release[154]. The magnitude of information which we already can perceive shows that confidence is not only necessary but also well-founded [ConfidenceWellFounded].)
The liberty connected to information gaps[155] is a chance for new information(for ideas[Idea], for more richness in details between start and aim). Just if there is enough confidence, the period "in between" without full information don't need to be a hard slog. Understood correctly (if easily possible for all together), it of course also can (should) mean fun[156] - the possibility for the immediate fast-forward key would contradict the life.
9.2.3.1 Past
By implication (sure) past is defined as information which is no longer changeable. Then we can copy it and measure it repeatedly in the physical reality. But by perception of information we change the physical reality. So something new (the information created by a new decision) is only then (sure) past, if its perception is carried out after delay[DelayedPerception], late enough, that the number of the way possibilities starting out from the decision increase more quickly[IncreasingWayCount]than the number of the ways which lead back to a (consuming) measurement resp. perception.
9.2.4 Creation of free energy and proper time (by a decision) as basic prerequisite for information transfer - a quantitative consideration
The close connection between (creation of) free energy(FreeEnergy), proper time and (creation of) information can also be shown by quantum physical argumentation:
9.2.4.1 Transferable information quantity in dependence of available free energy, time and number of information channels
{ETmGreatEnough} Free energy is necessary for information transfer. Every information transmission means the transfer of free energy from a transmitter to a receiver. A short quantum physical consideration can give more quantitative details. Let's denote by E the available free energy, by T the total available proper time, by m the maximal number of parallelly available information channels (systems with rest mass like atoms, which can emit and absorb free energy). We show a minimum of the product ETm necessary for transmission of a given quantity of information:
At elementary level information is transferred by photons which are emitted and absorbed, simultaneously at most one photon per information channel. We assume the best case, that the probabilities of absorption and non absorption are the same (maximal information capacity of the code; cf. [lifa] p. 61), that all information channels are distinguishable, entirely used and all photons have the same minimal energy, so that absorption of them is possible just within time T. Let's denote by j the number of photons, which can be absorbed by every information channel during this time. The maximal time for emission resp. absorption of a photon is t:=T/j, i.e. the minimal energy of the photon is (hq)/t=j(hq)/T, in which (hq) is the effect quantum. With that maximal l:=jm photons can be transferred, in which jm j(hq)/T £ E . In the best case jm j(hq)/T=E, from which follows (jm)^2=l^2=ETm/(hq). Since there isn't an a priori preferential treatment of absorption or non absorption and the distinction of smaller energy differences than u:=(hq)/t isn't possible during time t, we can gain at most 1 bit information in the receiver per photon with energy u. This means, that even in case of usage of photons with minimal energy u at most Ö(ETm/(hq)) bits can be transferred, and the transfer of n bits is only possible in case of ETm ³ (hq)n^2.
The square of n is interesting. Is ETm/(hq) a square number? E and T may be proportional because of simultaneous determination by our decision (PtimePdecision), but I haven't engrossed this.
9.2.5 Potential for information acquisition and information creation as essential feature of consciousness
{consciousness} Consciousness isn't static but a (time-dependent) process. This shows already the fact that it (the accompanying asymmetry(OneSide)) can be maintained only for finite time, then a complete change (FullReferenceFrameChange) of the reference system is necessary (e.g. dreams). Conscious knowledge implies the ability to active remember, therefore also decision liberty is part of consciousness. It can also decide to new ways, and these decisions influence the environment (e.g. the EEG) and so show themselves as new information. Only after I have written about information creation by (our) decisions, I noticed an interesting "definition"[157] of consciousness in [ligre] on p. 203: There consciousness is "defined" (described) as a synthesis of information acquisition (hence perception resp. measurement) and information creation (hence decision with accompanying expression of will) (of course a complete description isn't possible). There is written literally:
· ”Consciousness is a synthesis of awareness and volition”
· ”Awareness is the acquisition of information”
· ”Volition is the creation of new information”
So the approach there is similar to the one here. Here in addition further details are given, also to the primary order (decision resp. information acquisition before perception resp. information giving), to proper time (connection of proper time progress with central meeting events (TimePerception)(ProperTimeUnit)), to concrete physically measurable equivalents (assignment of decision resp. information giving to allocation of free energy(FreeEnergy)).
With this approach also is suggested, that the first possibility for the complete perception of all results of a decision again lays in the in the location resp. center of gravity of the decision [DecisionCenter]. That's quite natural because everybody is the first who becomes aware of the own (at first mental) decisions resp. thoughts. Everybody is the fastest resp. first in the individual local system {MaxLocalFrequency}.
9.2.5.1 Consciousness in computersystems???
Let's use the term computersystem for any fault-free working computer with software. A computersystem can be (exactly) copied because it is working completely determined, without place for own free decisions or chance in it. But that's also the reason that it cannot create new information. Information quantity is well defined. Assume a computer system S1 with given input data creates x Bit information during the time interval dt. There might be an exact copy S2 of S1 at another location, starting with the same input data and working at the same time (parallelly). So S1 and S2 are equal computersystems and because of assumption S2 also creates x Bit information during the time interval dt. We know, that S1 and S2 are doing exactly the same calculations, so they come to the same result and therefore together produce as much information like one of them, namely x Bit during the time interval dt. So x+x=x from which follows x=0. No new information has been created. Computer systems therefore cannot create new information[158], in contrast to consciousness[ConApproach].
Shortly: Because computersystems are working in a determined way, they can be copied, but for the same reason they cannot make own free decisions and so cannot create new information. So there is no place for consciousness in computersystems.
Also without usage of (ConApproach) this is immediately plausible: Consciousness has the ability to think, i.e. the ability to choose thoughts, i.e. the ability to make decisions. Because computer systems cannot do this, there is no place in them for (free) thoughts and therefore also no place for consciousness.
(We know, that every computersystem can only exist for a finite time. No computer can work fault-free infinitely long.)
To avoid many misunderstandings connected with the concept "determinism", I suggest the following definition:
9.2.5.2 Definition of determinism resp. "determined development"
{determinism} A development Q in System B is determined (deterministic) relatively to System A,
(a) if Q has a result (which means that Q is completed after finite time) and
(b) if in System A is the full (1:1) Information about the result of Q already before completion of Q in System B, i.e. if there is early enough a stabile pattern in System A, which can be mapped 1:1 to the full pattern of the result of Q in B (perfect correlation) after completion of the development Q (roughly said: "if A is faster and/or earlier.").
If the development Q has no end, or if there is no system A which fulfills (b), the development Q is not determined.
We cannot neglect the fact, that we need time and energy for information transfer (EtmGreatEnough) and therefore for constructing equivalents of observable results. It is worth mentioning, that according to this definition the process of calculating an exact (1:1) representation of an irrational number (starting from 1) is not determined (deterministic), because this needs infinite time and energy. The calculation is never completed, the result never exists.
9.3 The concept "probability" in relation to the measuring proper time
The measuring proper time is defined in dependence to the respective arrangement as the proper time interval of the beginning of a measuring up to the perception of the measurement result, that is the time of a decision (to measuring) up to the accompanying perception. The concept "probability" implicitly is connected to this, because the total probability of all possible measurement results only after the variable measuring proper time is 1.
9.3.1 The proper time unit
We mentioned [TimePerception], that proper time progress is connected to central meeting events [CentralMeeting]. Now we can define the proper time unit {ProperTimeUnit} as the shortest possible proper time interval, as the time interval mathematically lying between two subsequent own central meetings[159] (physically lying e.g. between emission and absorption of a photon {PhotonEmissionAbsorptionAsTimeUnit} . The probability of these meetings differs from system to system, it depends also on the energy of the photon, therefore different systems have different proper time units).
Longer time intervals arise from joining of such central meeting events resp. proper time units. A finer subdivision of proper time isn't possible[160]. The experimental results also confirm this. For example in the double slit experiment all way possibilities are equal not only with regard to location but also with regard to time. So it turns out, that we cannot say that the passage of the slits is done "before" absorption at the detector (possibility of the destruction and reconstruction of interference) - after emission the way of the photon together with the event of absorption is one unified moment of simultaneity. So causality violation is impossible. For example think of astronomical observations of the light of far away objects, e.g. quasars, which passes a gravitation lens (e.g. a big galaxy). By the manner, in which the astronomers register the photons of the quasar, they are able to determine, whether the photon has taken both ways round the gravitation lens or only one way "billions of years ago". The photon just doesn't has taken this or that way "billions of years ago" and then was absorbed, instead of this after emission the complete way of the photon together with the moment of absorption is equal in time, since no other central meetings (e.g. absorption) occur in between {WayTimeConstantTillNextMeeting} - quantum phenomena aren't determined until the moment at which they are measured.
The mentioned axiom [ProbabilityOnePerPresence] then shortly means "one (central) meeting per proper time unit". Hereby the central meeting probability Q0Z(2n), which is valid for a current row number 2n, becomes renormalizated to 1. At this has to be noticed, that for the probabilities within the Q1-triangle (FormulaQ1) and for the horizontal scalar product of the Q0(n,2k) is valid:
The formula permits several interpretation possibilities. One is mentioned:
With the renormalization of Q0Z(2n) also the altogether probability of perception from an multitude of outer (not central but by us caused) meetings totals 1, in the gyroscope model (GyrocospeModel) one would say "the probability of the reception of one (recombined) light pulse per emission totals 1" [OneOutOneIn].
So the frequency concept can be a reality near expansion of the probability concept, which is related more clearly to proper time and also permits results greater than 1.
9.3.2 Unity of consciousness and necessity of non-contradiction
Unity and uniqueness of consciousness (the conscious presence) are connected to the unity and uniqueness of every proper time unit resp. of every recombination point. The singular position relatively to the origin indicates the uniqueness of every recombination point, the indivisibility of this point indicates its unity. Non-contradiction means that the unit of the consciousness holds. This requires a more exact explanation:
The concept of information stands before the concept of contradiction, with contradiction we mean "contradictory information" in which the simultaneity is important. Important quality of information is
(1) temporary constancy.
Since with every central meeting, i.e. with every even row number a growth of proper time is connected, (sure, exact) information has to be assigned to the rows with uneven row number n.
Further essential quality of information is
(2) assignment to the past
because we have (sure) information only about the past, i.e. sure information comes of recombination points from rows with smaller row number than the current row number[161]. Concretely this information can lie in the value of k, which was true in row n.
If we localize ourselves for example in row n=2, k=0, we can assign sure information only to row n=1, for example the statement "we were in row n=1 in point k=1" (and not in k=-1), i.e. "k=1 is true. We cannot say, we were in point k=1 and k=-1 simultaneously, the separation of the two points would contradict the unity of consciousness. With the previous decision in n=0, k=0 we had to decide for exactly one value of k=1 or k=-1 and both possibilities are respectively unique.
Possible analogy: Only a single fermion can have one and the same state. This also fits to the assignment of fermions [Fermions] to rows with uneven row number.
9.3.2.1 To the principle of the excluded third
Here still a remark to the principle of the excluded third and possible unnecessary misunderstandings which are connected with it:
We look again at (exactly) one (simultaneous) row n, which contains information (therefore n odd, n smaller than current row number), so is valid either "we were in k=1" resp. "k=1 is true" or "we weren't in k=1" resp. "k=1 isn't true". So the principle of the excluded third is valid in case of simultaneity in past; the past up to the fixed row n is finite, its construction already is completed and so proved also from intuitionistic point of view{IntuitN3}. Without simultaneity in past this principle isn't assured. For example from view of row n=2 we can say "k=-1 isn't true" (in row n=1) and "k=1 isn't true" (in row n=3 due to our decision just taken). Essential is the time coordinate which grows because of our decisions. This coordinate isn't negligible.
9.4 No alternative to primary (initial) symmetry
Physical laws are either not valid or they are valid in all coordinate systems, i.e. everywhere and at every time. So we have to assume a total sum equivalent to 0 and therefore symmetry with regard to physical quantities[162], to which conservation laws apply {Cons0Sum}[163] [Q1RowSumIs0]. Well, 0= -0, i.e. 0 is symmetric in itself, so necessarily there is an initial, primary symmetry[164].
On the way of a central meeting (CentralMeeting)to the next always also decentral meetings[DecentralMeetings] happen, which can cause asymmetric perception. But our asymmetric perception also is result of our own last start point outside[165] the primary (initial) symmetry center (AsymmetryAsPreconditionOfGeo) {AsymPosToAim}. This makes it so difficult for us human beings to recognize the primary symmetry {FullPrimarySymmetry}. Our starting point again results from prior decisions. So these cause with temporarily asymmetric perception also (physical) facts, which are the more generally (e.g. parity violation in b-decay, CP-violation) valid, the greater priority of the causing decision is.
Besides the special role of the central meeting probabilities also the experimental results of quantum physics indicate the fundamental symmetry of nature. We for example know in case of symmetric "annihilation" of matter and antimatter into two photons alone by measuring or perception the state of one photon also the simultaneous state of the other, even if it seems to be separated in location. So if we measure one side, we measure also the other side, what information theoretically means unification of both sides (e.g. of row 3 in the [ScalarproductExample] ) because of a perception in the a symmetry center (point B [166] in the center of row 6 in the ScalarproductExample.
9.4.1 Presence as center of the horizontal ("left-right") symmetry
TheScalarproductExample also shows the nature of the symmetry. Point B forms the symmetry center between right and left half of row 6, but only row 3 is completely accessible there as presence. The horizontal symmetry between left and right side besides B most likely has to be interpreted purely information theoretically, i.e. |k| quantifies (as minimal number of required elementary decisions) the length of the (not necessarily straight) information way to the center. The information of the two sides is equivalent, even synchronized due to the symmetry (however only perceptible from row 12 on).
9.4.2 No vertical ("before"-"afterward") symmetry, no conservation but increase of information quantity
The in B (ScalarproductExample) present row 3 forms the center of gravity of rows 0 to 6 only with regard to the sum of the probabilities. There isn't vertical symmetry [DirectedGraph], the future (n > 3) is of course different from the past (n < 3). The greater n, the greater the path length is (with regard to the number of the decisions), the more way possibilities to and back exist. Therefore every way contains the more information, the greater n is. There isn't a conservation of information quantity, an increase of (per proper time unit (ProperTimeUnit) perceptible) information quantity is possible.
9.4.2.1 Vertically reflected scalar product (point symmetry?)
In the ScalarproductExample one can in case of fixed sum s:=m+n sum vertically (cf. [skahove]). Also valid is
.
Summation before scalar product formation also has interesting results, for example
.
Regarding possible physical interpretation I had only vague, too speculative ideas till now.
9.5 Elementary particles as defined constellations relative to the origin - asymmetry as precondition of all geometrical appearances
{ElementaryCoordinates} A hierarchical constellation of (decisions making) systems is a reasonable assumption [hierarchical]. One may identify elementary "particles" with defined (coordinate sets of) recombination points within defined triangles. There is a lot of free variables. One could for example assign matter {Matter} to branching possibilities[167] going out from the right side of the primary triangle, antimatter {Antimatter} analogous to those from the left, for photons one could assume the (vertical) center column k=0 {PhotonColumn}(***), as (only asymmetrically [AsymmetryAsPreconditionOfGeo] from one side visible) "location" of photon absorption {PhotonAbsorption}. Within subordinate triangles which are starting out of the superordinated triangle respectively orthogonal[168] one could assume for bosons (horizontal) rows with even row number, for fermions[169]{Fermions} rows with uneven row number (n/2 as total angular momentum, k/2 as angular momentum component orthogonal triangle). It has to be considered that single "particles" can have several degrees of freedom (e.g. polarization), so that a point can certainly play a special role (e.g. as center) in the description, but the relation of several points (especially start, destination point[170]) must be taken into account. A couple of initial considerations to this are also found in wq3. Special states of particles e.g. quantum numbers of atom electrons might correspond to the branching possibilities within further subordinate triangles. Also the periodic table of the elements could give hints to this.
9.6 Thoughts to extreme astrophysical extrapolations
To avoid misunderstandings: I don't want to ban speculations - these can be helpful or even necessary for progress. Also simplifications and analytical models can be useful to get an entrance. But their overestimation or even confusion with reality leads to errors, therefore I decided for this chapter.
9.6.1 Extrapolation of approximative models leads to errors
{ExtrAstroPhys}It is quite difficult to get free from the familiar lokal geometrical view and e.g. to turn the consideration way inside out. But the geometric approach uses analytical and therefore approximative models [AnalysisAtBestApproximative]. Therefore extensive extrapolation of the geometrical appearance (which is only a secondary consequence of rest mass (AsymmetryAsPreconditionOfGeo)) leads to a wrong imagination. For example one speaks of the (by implication absolute, "rigid, frozen") diameter[171] of the border (horizon) of black holes. On the other hand one speaks about gravitational lenses: In the proximity of black holes light beams are turning into the hole. What is (our impression of) the diameter of the hole particularly if it is very heavy (visible universe) and it's border is close to us or if we are even in the border (to another hole)? What's real in the decisive (***) situation in the border between two holes? Here we make a decision on which hole forms the future of our proper time coordinate (starting from present, from the current recombination point). Isn't just here[172] an exact calculation necessary again?
If we want to use common formulas: Are masses still almost constant, if there is a great[173] potential difference? Are for example radiation losses adequately taken into account? Do higher degree derivations along special directions become great relevance? There are many open questions. So the probability of great mistakes grows towards 1, if one calculates too far using approximative (analytical) methods.
Analytical models allow usage of infinite sequences of numbers, functions, operators, etc., independently of any time coordinate. This separation (of time) is not realistic (RealInfinityGrowsWithTime). We should not make (like in frequently used cosmological theories) an isolated extreme extrapolation of a single aspect into areas far away from the experimentally checkable, particularly if this extrapolation leads to a dead end[174]. I think, that similar to the big bang model also the model of a point-like, isolated black hole with spherical[175] gravitational field is so simplified that the danger of misunderstandings is great. One remember that all experimental tests of general relativity theory exclusively refer to very weak gravitational fields ([lifl] S. 178) {StrongFieldExtrapolationErr}. I frequently won the impression that models which describe a (restricted) part of reality, are confused with reality, particularly from laymen (and everybody is layman almost everywhere). This is problematic because the consequences can be unnecessarily restricted views of the world and restricted philosophies (EgoismIsStupid).
Evidently the usual geometric approach leads to errors in the end. Of course in astrophysics also relativistic calculations are carried out, but these (4D) geometric analytic approaches also are approximative[176]. Naturally particularly at observations of far away objects with partially very indirect interpretation possibility of measuring results there is a large probability, that the measurement result also is influenced in relevant way by factors, which remained unconsidered in often heavily checkable, on the current state of knowledge based interpretations. This can lead to extreme distorted results. Caution is appropriate especially at extreme results whose physics is hardly known because there is no experimental possibility for verification. It would be helpful, if the widespread[177] publications exhibit the difficulties joined with the models clearly enough and uncoded: then it's easier for a broad readership to find aimed suggestions for improvements and we altogether can advance better. Of course many astrophysical considerations are valuable, even if they contain gaps. The approved four-dimensional approaches give interesting hints.
9.6.2 Perhaps discrete extrapolation can give hints
Astrophysical observations can be also helpful to close gaps in other branches of physics. For example basal appearances like the electron mass are unexplained. In a discrete model units of rest-mass can represent possibilities for start and return of information paths (of photons). The finite and discrete distribution of rest mass coordinates and states determines the finite and discrete set of possible results of all physical experiments (with finite duration) (DeterminedReturnInCenter).
It would be surprising, if globally[178] seen the long-standing creation of rest mass (the long-standing separation of matter (Matter) and antimatter (Antimatter)) is restricted to a unique moment of time. Because the total sum of energy should remain 0 (Cons0sum), consideration of gravitation potential is essential. Astrophysics has best expertise for this subject.
Cosmology always requires extrapolations and is more ore less speculative[179]. There has been much overestimation of several models, often they are at best a relocation[180] of explanation, but there are also many scientists who don't forget the limitations of the models and do their best to recognize global relationships. Of course this earns respect, even if it is more or less speculative - due to missing information there is simply no other choice. There are also secure results, e.g. we got clues about the huge dimensions of the visible universe, and we know that we can see only a (very small) part.
9.7 No contradictions because of (simultaneous) perception of multiplicity
Each sort of elementary particles, atoms, etc. appears repeatedly in our time frame. In the strict sense the (repeated) completely identical behavior of congeneric particles can be explained only by the fact, that their appearance emerges from the (repeated) application of the same sequence of steps within a fundamental (combinatorial) law.
{PerceptionOfMultiplicity} Here a crude outline to the topic multiplicity and consistency:
As before, QW(x) and QV(x) are defined by
We now study a symmetric arrangement (a simplified, flat "gyroscope model” {GyroscopeModel}): Two relatively small transmitter-receivers spin around a very heavy black hole between them, located in the center of gravity (point concept simplified). The centrifugal force compensates the gravity, therefore each of them forms roughly an inertial frame (since each is relatively small). Each moves with speed v/c:=x (about as quickly as in the border of a nucleon) relatively to the other and (after one has begun[181]) sends out a light pulse to everywhere (he "expressed himself") as soon as he has received a light pulse[182] (from the "other").
Due to the symmetry of the arrangement each says about the other: "the other sends only QW(x) times as often to me as I to everywhere send, and I receive only QW(x) times as often as the other to everywhere[183] sends (because of time dilation). So each would have the impression, that from the other only (QW(x))^2 times as many spectral shifted[184] light pulses come back as he to everywhere sends out. How can this be compatible with the fact, that by definition each sends once per reception?
The contradiction dissolves, if one imagines, that each sees 1/QW(x))^2=(QV(x))^2 copies of the other simultaneously (per proper time unit (ProperTimeUnit)) or successively[185]. So he receives altogether just as many light pulses, as he sends out {OneOutOneIn}and can say nevertheless, that each copy sends only (QW(x))^2 times as often.
with
(The last
limit value results, if we insert the
Therefore each sees 1/(QW(x))^2=(QV(x))^2 resp. approximately pn/2 copies of the "other", which is as much, as on a quadrant with radius n (or on a circle with radius n/4) has place. The circle is the two-dimensional[186] approximative area of the simultaneously perceptible (***). It's also interesting that the black hole can have the effect of a gravitation lens and so can cause (for n-> ¥) the impression of a circular distribution of the light pulses coming back, because the light beams from the transmitter to the receiver don't run "straight" (the hole stands in the way) but "bend around"[187] the hole and therefore lay rotation symmetric around the "straight" connecting line through the hole between the two.[188]
(Interesting can also be to think about the minimum number of (independent) decisions necessary to realize the mentioned two-dimensional arrangement from a unit or a "point". Is it in the 2D-model two and therefore one per model dimension)?
Because n is integral, implicitly the mentioned analogy of (QV(x))^2=1/(QW(x))^2 and np/2 raises the question, what shall be valid in the case of inter-results on the left side. Conceivable would be a bridging to quantum physics, e.g. in the form that in the case of inter-results the left side is unstable and transmission/reception of energy results up to next integer level.
Similar, more consistent considerations could lead further. Of course the geometrical model can give hints, but it's secondary, at last one must leave it.
In the end all statements should alone base on primary axioms of our decision and perception process. It would already be remarkable, if we succeed always better.
To demand for more may be too much because it is probably in principle impossible for us human beings to recognize[189] these bases exactly and completely (again).
Recognition (perception) in everyday life is incomplete. It refers to patterns from parts of our lokal past or to associated (partially copied) patterns. A complete perception would also include ourselves as perceiving human beings and therefore is impossible for us.
9.8 Some supplementary philosophical aspects
9.8.1 At important considerations more consequence is necessary
It is necessary, to deepen important things with high priority, to tidy up and systematize them. At important considerations more consequence[190] is necessary. We can help ourselves mutually in doing this.
9.8.2 Uncertainty (lack of information or free energy) multiplied by proper time[191]
This is an elementary cost concept {ETcosts}. At this lack of information is closely connected with lack of free energy [FreeEnergyAndInformation].
Long "dry spells" are not attractive. There is the trend to decisions, which yield with great probability a maximum (of "security" back from the center)[192].
It is a fundamental drive of our consciousness to keep these costs as little as possible. During lack of information[193] we don't want to make decisions. However, this is necessary (ConfidenceNecessary) for advancement. We should choose an effective way, which alltogether is as harmless as possible.
9.8.3 After recombination the own given information pattern returns
{OwnPerception} I am occasionally also surprised, in how far-reaching way this rule applies, particularly at longer-term consideration. Experiences from everyday life seem to confirm that it concerns all decisions and so already starts with thinking (inside us).
The clear correlation between inner and outer information resp. emotion is obvious in every dream, it is the consequence of the primary conjoint starting point and of the following secondary moments of information exchange. Also in the awake state the correlation is more strongly than at first sight visible[194], even if the conjoint origin lies farther away in the past. We meet ourselves - in various faces and ways, at last (in progress of time) ever in a symmetry center(Cons0Sum).
9.8.4 Free energy and responsibility
Obviously free energy is necessary for life[195]. Energy is free (FreeEnergy) (i.e. freely available) if its (back-) ways are (like a reliably fulfilling promise) calculable and determinable (there is enough time {FreeEnergyAndTime} to measure its preferred ways, and, using this information {FreeEnergyAndInformation}, to determine them repeatedly e.g. by a switch in a DC electric circuit). We can use this for example to copy our information and to make it available to several (by energy resp. potential barriers separated) reference systems simultaneously. Because we have these possibilities, we are also responsible. Prerequisite that these possibilities (power over free energy, our body and our sphere of influence) are given to us is confidence that we use them reasonably {FreeEnergyNeedsConfidence}.
9.8.5 Faster than (Darwin
From quantum physics we have learned (cf. e.g.[AllPossibleWays]), that also the possible influences the ways of nature. Just the possible is that, which is fast detected by parallel foresight within many small units,
(i.e. by quick extrapolation the local[196] inner (partial) models or maps[197] of reality[198], for preselection),
faster than it could be done alone by a "global experiment". By combination of the "global large-scale experiment" with many parallel running (approximative) local experiments in thoughts optimization can be done very fast.
Only a small (consistent) portion of the thought experiments' results becomes conscious[199] as information. If this information is new relatively to the outer surroundings, we often call it idea{Idea}.
9.8.5.1 In the long run the good memory is decisive
The concept "only the strongest will survive" may be correct for the short term within a restricted frame (in case of restricted definition of "survival"). In the long run thoughts are decisive, because they initiate all decisions. They are dominated by that which we freely like to remember. At this we don't like to remember contradictory things, we like the [truth] (because only truth contains usable information).
9.8.5.2 Objective reasons for confidence
{ConfidenceWellFounded} Perceiving the great quantity of information already created we see that in the long run the altogether non-contradictory (the truth, and the number of observable bits per proper time unit (ProperTimeUnit)) dominates over the contradictory, and increases, even if interim temporarily painful steps backwards are possible.
Determined by a primary decision (PrimaryDecision) in a new direction, {truth} has the greatest branching depth (RGraphTheoreticalResearch) and therefore cannot be eliminated.
9.8.5.3 Inevitability of conscious existence
It is improbable, that our conscious existence was only possible due to the (long) chain of past coincidental events which led to our birth, already due to the (from initial view) statistical improbability of our pedigree. Rather it is reasonable to assume that our consciousness also would exist (in other form), if there wasn't this pedigree (but another)(ProbabilityOnePerPresence). Therefore we don't need to ask whether it proceeds after a change of the reference frame(FullReferenceFrameChange), but how it proceeds[200]. This "how" contains information which is again result of decisions - which are influenced by memory.
Briefly said: It proceeds, and memory significantly controls, how it proceeds.
9.8.5.4 Perfect equitableness
At first perfect equitableness seems to be farfetched, simply because the own fate is influenced by decisions of others, which appear to lie outside the own sphere of influence. This is correct however only for short-term considerations. In the long run even the concept "own" becomes undefined, furthermore we do not know, how far the current "own" has been formerly involved in decisions, which influence the current decisions of "others". Taking into account the volatileness of the current definition of "own" in the long run summary considerations should become decisive, whereby temporarily even "many" later individuals can bear responsibility (and so have to expect consequences) for the decision of one earlier. The exact observation of the conservation laws indicates that in the long run equitableness (Cons0Sum) becomes more and more perfect for "everyone" (and for "all together").
9.8.6 Cause and consequence – hen and egg
{RemarkToHeadline} Initially one can say that recombinations are the caused by a primary decision (PrimaryDecision). But subsequently decisions are also consequence of recombinations (of recognition resp. perception connected with them). Because of separation which is caused by decisions (differentiations) then a definition of location is possible. As human beings we are already separated resp. located. So every moment there is exactly one local (individual, inner) reality resp. presence for each of us, depending on our localized (individual) point of view[201]. That’s quite usual, it's everyday occurrence. Our inner realities are separated according to our decisions[202]. Because of vast speed of light the macroscopic outer reality seems to permit an location independent definition of outer time direction[203] and therefore an location independent definition[204] of "before" and "afterwards". But the fact, that speed of light is finite, is enough that as long as[205] the observed systems are separated (by a potential barrier, locally) there is no location independent possibility to define "before" and "afterwards" exactly. In the end that's enough to avoid contradictions (because we know, that small causes/results can mean great results/causes at another time)[206].
9.8.7 No exact anticipation of future
{NoAnticipation} The following argumentation is not new, it's repeated here only because of some references to the other text:
The classical physical models (before introduction of quantum physics) theoretically would have permitted the exact calculation of future measuring results. But (theoretical) models which permit an exact anticipation of the future are from the beginning unsuitable for elementary (exact) descriptions of natural occurrences because this anticipation doesn't happen in nature. If this would be possible, there wouldn't exist any liberty. One can also say conversely: Since we can predict the approximative (short-term) future, restraints (basic conditions) exist for our freedom.
Inertia (and therefore even gravitation) plays an important role in the mediation of elementary decisions, for instance decisions between "spin positive" and "spin negative" (At the moment we don't need more exact definitions.). One should not be disturbed about different orders of magnitude - the elapsed time between decision and perception implies a (depending on duration of time, more exactly said depending on number of elementary times or recombinations in between, more or less large) lot of (way)possibilities and therefore small probabilities per possibility, so that a great renormalization factor [Renormalization] results. (Some considerations to this topic (special role of the third power) also can be found in the download files. If you are interested, please search for (***) particularly, as usual)
By the fact that we (as most future observer in our own individual, local system) determine definite destination points by localization of our counter pattern [LocalizationOfCounterpattern] due to our decisions(FunnelOfDecision) allowing in between only free choice of way [FreeChoiceOfWay], somewhere else restraints of freedom[207] arise, which affect a moment later also us personally - as soon as our decision becomes irreversible also for us because of our interaction with surroundings.
Important destination points of our life are already decided (predetermined), primary decisions (PrimaryDecision) specify not only the constellation of our birth, they also cause the obvious[208] disposition and flows, which lead to a significant hindrance or preferential treatment of certain way directions.
9.8.8 Quantity of the own long-term effect
It is clear that the own decisions are the more directive to surroundings, the more non-contradictory they are. The non-contradictory part[209] magnifies itself in the long run[210](Diversification), and many things, also symmetry considerations (cf. [OwnDecisiveContribution]), signal particularly, that we together should avoid contradictions within ourselves[211] to the greatest possible extent, if we want to have durable effect.
This implies also consistency (along time coordinate) and therefore[reliability].
9.8.8.1 Long-term importance of the "own" non-contradictory contribution (despite huge differences of the orders of magnitude)
Faced with the huge size differences of different reference systems already within the visible universe the short-term size of the own sphere of influence is not very important, more important however is a durable orientation to the right guideline(give), that it leads our decisions consistently and permanently.
Also this can be justified more exactly: We know that the conservation laws are fulfilled perfectly in the end (the long-term approach is essential here). Since therefore the total sum of all conserved quantities is 0 (Cons0Sum), the overall non-contradictory part of the "own" effect is at last decisive in the "own"[212] frame of reference. Therefore it is so important that our decisions altogether follow the "right algorithm" [GiveBeforeReceive].
So on average the number of new possibilities and the quantity of new non contradictory information per common proper time (ProperTimeUnit) can grow permanently [RealInfinity].
9.8.9 Perception in favor of the prettier alternative
We know that every perception is connected with a finite sequence of decisions(FiniteRecombinationSequence). We can influence them the more, the greater the natural room for interpretation of the truth is. Often in case of doubt there is the possibility to choose the prettier alternative, without fooling oneself, for example at estimation of the thoughts of other human beings. If we use this with best knowledge and conscience, we create a new even prettier (and also more detailed) truth.
9.8.9.1 We can be valuable
One often hears phrases like as "everybody only thinks of himself" etc..
In this way we cannot proceed. It surely would be wrong to regard mankind as "varmint" who plunders earth[EnvProt]. Instead of this we as complex creatures have the possibility to create a rich common memory which is valuable (which doesn't contradict the surroundings and which starts out from own effort[213]), so we can be very valuable.
9.8.10 Good reasons for gratitude
There are good reasons to be grateful. One of them:
We have reason to be grateful for the great diversity which we perceive, and for the large effort(Work) which has been necessary to create this diversity.
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, then
