Robert P. Turner (independent researcher, Lancaster University)
Published in psycho.philica.com Abstract Two axioms of Special Relativity (that increasing spatial speed up to light speed dilates time until it stops, and contracts trajectory length down to a point) are combined with the Doctrine of Reciprocal Transference (a philosophical doctrine used by Descartes in the seventeenth century, the logic of which is beyond compelling). Rolled up dimensions are then seen to be dual aspects of familiar dimensions at light speed to each other. The dual aspect of light as point photon and extended wave is thus demonstrated to have a larger context in dual space and dual time. Other things also fall out naturally including the post Big Bang concept of space inflation as photons collide to make sub luminal entities and the pre Big Bang concept “before” time. Article body
Introduction By Special Relativity a dynamic trajectory length contracts with increased spatial speed down to a point at light speed when measured from the static frame it moves through, so a light wave is a point photon in the material rest frame whereas it is an extended light wave measured in the photon’s rest frame. By Special Relativity, time dilates with increased speed until at light speed it is static, so a photon represents a static point of time just as a charge point represents a static point in its electrostatic space. Thus a photon traces a point of time through space and a charge point traces a point of space through time. Redefining space as electrostatic space defines a charge point as static in its own electrostatic rest frame whilst moving in collective charge’s space. Reciprocal transference equates material motion through space with space flow (contra direction) through material so that Special Relativity time dilation, trajectory length contraction can be restated that increasing space flow decreases time flow and trajectory length (by equal factors) to give an invariant length / time ratio (in accord with a condition of mutual transference that any contra flow has a mutual approach / separation speed), a space, time invariant interval in any space rest frame, which becomes [(r + ct) (r  ct) = 0] at light speed. By the seventeenth century Doctrine of Reciprocal Transference, a vibrating charge point and its emitted photon are in mutual separation at light speed, and it is an arbitrary choice to define the charge as static with the photon separating at light speed or the photon as static with the charge point separating at light speed, the two trajectories being mutual and opposite. By considering charge in general to be approximately static in a material rest frame (compared to the speed of light) it is possible to make an arbitrary choice of static space with light speed photons or static time with light speed charge points. Transposing time and space is equivalent to transposing photons (time points) and charge (space points) and is therefore just as valid as transposing space and material (or different inertial rest frames), and when the Doctrine of Reciprocal Transference defines two points separating, it allows the arbitrary choice of which point is static and which dynamic with an alternate choice transposing the time point from dynamic to static along with the space point from static to dynamic (or vice versa).Thus when Special Relativity defines time as static at light speed space, the Doctrine of Reciprocal Transference makes equally valid the transposition that time flows at light speed in static space. This requires measurement of time flow in static space to be equated with measurement of spatial flow in static time, a transposition which inverts space and time as well as direction, which gives [ ct / r =  r / ct ] which is equivalent to [(r + ict) (r – ict) = 0], complex conjugates analogous to Quantum Mechanics. That the choice of rest frame is arbitrary means that both choices are equally valid requiring dual attributes of particulate as well as wavelike behaviour. Thus whilst a light wave appears as a point photon in the material rest frame it retains its wavelike nature. When another condition of Special Relativity, trajectory length contraction to a point at light speed, is included as its dynamic aspect in the chosen rest frame, then dynamic time is a collapsed aspect of time (now) in static space whilst inflated in static time, dual aspects of time analogous to the dual aspects of point photon and inflated light wave, also collapsed space in static time being dual to inflated static space. Space contraction at increased speed has its counterpart of space inflation at decreased speed, thus space inflates after Big Bang as a consequence of measurement in a slower spatial rest frame as photons collide to slow space. In other words by redefining space as electro static space it approximates (when compared to light emissions which move rapidly relative to material movement) the rest frame for the material it connects together and a point of charge coexists with a set point of space. Photons are the quantum aspect of light waves and time is the rest frame for photons because Special Relativity requires time to stop at light speed, so that an individual photon coexists with a unique set point of time. These two fixed points are not fixed relative to each other, being set in different rest frames which move at light speed relative to each other and therefore have an interface one to the other. This provides two parallel universes, static space with dynamic photons and static time with static light waves and dynamic charge points. Both are valid and exhibit particulate quantum properties alongside wave interference properties, expressed in Quantum Mechanics with complex conjugates understood in reciprocal transference to be two fields in mutual transference at light speed. Essential Reciprocal Transference The essence of seventeenth century Descartes definition of motion is only the action of separating (assumed to include closing). When point A (or its extension AB) separates from point C (or its extension CD) the concept from A is that C moves and the concept from C is that A moves (in the opposite direction). So it is an arbitrary decision whether to say that extension AB is in motion and its neighborhood CD at rest, or vice versa. Thus a body separating with its neighbourhood is in reciprocal transference with it and, because of the Doctrine of the Reciprocity of Transference, whenever a point is in motion then so is its neighbourhood, but in the opposite direction (this being the consequence of the juxtaposition from rest frame A to rest frame C). From this we see that time flow is motion closing/separating time with/from space and its consequent reciprocal transference which from charge adjoined to space points includes photons adjoined to time points inbound from the (spatially distant) future to now at the charge point and outbound to the (spatially distant) past, being the reciprocal transference of the charge point’s now moving along a time parameter line from past to future (this being the opposite direction). Essential Special Relativity It is a condition of Special Relativity that trajectory length contracts as spatial speed increases until it is a point at light speed, also that time dilates as spatial speed increases until it is static at spatial light speed. Recall that space includes the electrostatic component of the material rest frame, and that it is not an inert background void. Given that an atom is almost entirely space anyway (in that a nucleus occupies the tiniest fraction of it and even this contains internal space) then when a rod contracts it is essentially its internal space contracting. According to Special Relativity, a rod contracts along its trajectory length as its speed increases. So does the space it occupies. So does the space it does not occupy! Treat space as a physical medium, and when a photon flows through a rod of space in one direction then by the Doctrine of the Reciprocity of Transference the rod of space also flows (in the opposite direction) through the photon, thereby length contracting along its light speed trajectory to a point, given Special Relativity’s length contraction condition. Therefore space is a rolled up dimension in static time (that is in the photon rest frame, given Special Relativity’s time dilation condition that time stops for a photon). These two axioms (that time dilates, and trajectory length contracts with increased spatial speed) of Special Relativity can be rephrased as one axiom with the premise that time duration as measured by an atomic clock has two components, the number of beats of its caesium atoms (i.e. recorded time) and the interval length (ct) between adjoining beats (which can then represent a fixed number of quanta, being proportional to the phase length between quanta). Time dilation requires a moving clock to dilate the interval between beats and thereby to record fewer beats than a static clock, so the interval length inflates between beats as spatial motion increases and as time slows. If slower time inflates the interval length between beats then faster time contracts it. The conflated axiom then becomes: increased spatial speed contracts spatial trajectory length and increased temporal speed contracts time’s quantum interval length, with the proviso that increasing spatial speed decreases temporal speed and vice versa, the dynamic aspect being collapsed at light speed. Thus reciprocal transference at the interface of space with time is a quantum confinement due to Special Relativity length contraction. Because space time has an interface of dimensions incident at light speed, a Special Relativity factor is introduced infinitely enhancing electromagnetic field strength in the transverse plain whilst voiding it in the trajectory of the mutual reciprocal transference. Confinement of magnetic loops and electric radials to the transverse plain of the photon reciprocal transference with charge at their point of contact due to the infinite enhancement in that plain alone as required of such light speed encounters by Special Relativity, is a natural context for string theory. That a rolled up dimension is a light speed aspect to its static dual aspect is an essential requirement. Dimensions have Dual Aspects By the Doctrine of Reciprocal Transference, the material rest frame with light speed time has a counterpart static time with light speed space. The premise to this argument defines a photon as a set point in its own temporal rest frame and a charge point as a set point in its own spatial rest frame. If time stops at light speed as required by Special Relativity, then time stops for a photon, so that a photon occupies a unique set point of time (of emission from a vibrating charge). Thus the photon and a set point of time coexist, are cojoined. That time stops for a photon means that the photon traces its time point through space, thus different points of time pass different points of space and vice versa. If a stellar photon transits a million light years to reach my telescope, then so does the set point of time it adheres to. Thus time flows (with its photon hosts) through space, at light speed. If space has shape (in particular, trajectory length) as required by General Relativity, and if trajectory length contracts to a point at light speed as required by Special Relativity, then space collapses to a rolled up dimension in static time. Also if time is defined as a phase length, ct, being the transit length of a photon through time, t, and if trajectory length contracts to a point at light speed as required by Special Relativity, then time also collapses to a rolled up dimension (a charge’s now) in static space; and (by reciprocity of transference) this spatial charge point flows through time, at light speed. If a photon and its emitting (or absorbing) charge are in reciprocal transference, then time (a time point being static with its associated photon) also is in reciprocal transference with charge and, by extension, space. Thus one point and its extension in reciprocal transference at light speed with another has dual aspects from the effects of contraction in accord with Special Relativity in that a point’s extension is an extended aspect to other points at rest with it (in its own rest frame) whereas it has a collapsed aspect to points in another frame with respect to which it is at light speed. A consequence of Reciprocal Transference is that the choice of rest frame is arbitrary so that the effect of Special Relativity due to the choice of static frame with extended aspect is dual to its collapsed aspect in the same sense that light is simultaneously both point photon and extended wave (i.e. both aspects coexist, only one being apparent). Quantum time A photon is the quantum aspect of a light wave, individual and particulate. According to Special Relativity time stops for a photon, therefore a photon occupies a unique set point of time. When an observer at A emits a photon to reflect back from B and reabsorb at A, this set point of time creates three separate events at three separate observations of time, t_{emit }t_{reflect} t_{absorb} in spite of being the same time point. This paradox requires time to have more than one aspect. The observed difference in time for the same point of time is an aspect of spatial distance between A to B or B to A, but not between A to A where the photon is reabsorbed at the same place. This aspect requires that a point of time can reappear to an observer’s sense of now. Thus it is the sense of now which is a continual sequence whereas points of time are individual quanta which come together at now to form a coherent sequence, so that now is seen to be an interacting spatial point such as a charge point, moving through time with analogous symmetry of a photon being a time point moving through space. When we perceive now flowing along a time parameter from past to future this is equivalent to time’s influence flowing through an egocentric now at time’s interface with charge from future to past, flowing like photons incoming from a distant source and outgoing to a distant sink. Thus a point of time has no universally absolute value at now (because now is individual to each spatial charge point and synchronizes with distant now future (+ r/c) also past (r/c)) and acquires its relative value as it slots arriving influence (e.g. other photons) into sequence as they interact with the associated charge. In this respect an unattached time point has a particulate nature, available to enter a time line sequence more than once, if reflected back in for instance. This allows comparison with the twin paradox that a space travelling twin can return to find his static twin more aged than himself. In this case the photon is a space traveller and the charge point static. On emission, reflection and reabsorption the photon has not aged at all, whereas the charge point has aged twice r/c. Conclusion Minkowski coordinates are replaced by two separate rest frames in reciprocal lightspeed transference thereby presenting an interface which confines interaction to the transverse plain of the trajectory. When the length contracting and time dilating axioms of Special Relativity are represented in this context then dual aspects emerge which explain the dual aspects of light and give a natural context for duration prior to Big Bang and the start of time flow at Big Bang when there was no material and energy was in photon form so space flowed at lightspeed through static time. To create time flow space has to slow by collision of photons whereby space slows with the creation of X particles. To maintain the light speed reciprocal transference of space and time, when space flow slows then time flow commences, increasing as space flow decreases. Thus material creation slows space which (because space was collapsed in static time) causes space inflation, an essential element of the Big Bang story of cooling into the present phase as X particles decay to material fermions such as quarks and leptons leading to more familiar material. Even so, time flows in our material rest frame, not withstanding that it remains static in a light rest frame, anywhere in time including Big Bang, this being a dual aspect of dynamic time in static space and static time with dynamic space. In Quantum Mechanics, the Schroedinger equation relates the first power of total energy to the second power of momentum, which relates a first time derivative to a second space derivative necessitating the complex wave function. Associating light waves and time introduces phase, which Quantum Mechanics describes with complex conjugates reminiscent of fundamental space, time reciprocal transference. Reciprocal transference implies that the space length, r, transfers through the time length, ct, with velocity r / ct coincident with the time length transfer through the space length with opposite and inverse velocity. Thus [r / ct =  ct / r] alternately [(r + ict)(r – ict) = 0] which are the complex conjugates associated with this transference. This link with Quantum Mechanics is based on the wave nature inherent in photon and (after de Broglie) particles, for which the Schroedinger equation can only be solved for bound particles using particular discreet values of energy resonant to the fixed architecture of the binding, values supported by experimental results. In this equation space (which is static in our rest frame) is differentiated twice whereas time already flows in the measured frame so is differentiated only once more. The reciprocal transference invariant [s^{2} = r^{2}  (ict)^{2}] (which equals zero at light speed) is not the same as the space time invariant, [s^{2} = r^{2}  (ct)^{2}] which is measured in the material frame alone, with now moving from past into future. It is important to realize that one of the velocities is opposite and inverse the other thereby generating the complex conjugate. This inverse velocity is measured in the light frame where time is a transit length and trajectory space is a number of collapsed quantum spatial lengths, symmetrical with the concept of quantum time (here associated with a parameter of intervals between the beats of an atomic clock). Thus we have light speed time as the ticking clock in static space and light speed space as the ticking clock in static time, so that static time at Big Bang is a photon transit length (different points of space being different points of time) and the number of quantum collapsed space points flowing through a set time point is the interval duration of space. The mutual approach speed is transit length divided by the equivalent number of beats (quantum lengths) in both frames. Using the beats of an atomic clock as a quantum parameter, the present now of beating time is thus seen to have a beating counterpart in static time which also applies before Big Bang, both counterparts together being dual aspects from an interval of duration and time is then redefined as an aspect of duration, measured in static space by the flow of time through a set space point (e.g. a charge point or a cesium atom in an atomic clock) and measured in static time by the flow of space through a set time point (e.g. a photon). References Special Relativity by A.P. French, Introductory Physics Series (1991 reprint), Massachusetts Institute of Technology The Cambridge Companion to Descartes, Chapter ten contributed by Daniel Garber, Cambridge University Press (1992)
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The full citation for this Article is: Turner, R. (2012). Time flow as Reciprocal Transference with Space. PHILICA.COM Article number 361. 
