Objects and measurements’ hidden nature

A few definite steps allow to fully recognise the nature of the Events and the action and function of the devices part of the industrial machinery and of the equipments to count and relate them (e.g., Triggers, microprocessors, PLCs, etc.). As an initial step, it is necessary to understand that the 4D space-time described by Minkowski and Einstein between 1905 and 1907, still presented as a basic concept to the future Electronics or Electrotechnics Engineers, is no more since long time witheld a theory representing the reality outcoming by the of the experiments.

** In**** 1915 Einstein extended Relativity Theory to include also some of the ideas underlined by the figure on side. T****o every point of a curved differentiable manifold **M,** can be attached a tangent space, a vector space containing all possible directions along which one can pass through the point. **If the parameter *t* identifying the spatial leaf (or, sheet) is such as to make the tangent vector unitary, then its physical meaning is that of the *proper Time**t*. **Reader may figures out the basic meaning of “differentiable manifold” recalling the 2D surface of the Earth or the waves formed in a liquid surface when perturbed by one point source. **

**After 1915 different 3D leaves of the foliation may have different or equal times and no one of the leaves is less real than another. A multiple-histories conception**

Time-identified Events

A key point regards Time. Time has been in the past considered to be the fundamental phenomena underlying Dynamics.

**”T****o every point of a curved differentiable manifold **M,** can be attached a tangent space, a vector space containing all possible directions along which one can pass through the point. T**he parameter *t* identifying the spatial leaf (or, sheet) is such as to make the tangent vector unitary. Its physical meaning is that of the *proper Time**t” ***(image credit csdn.net, 2014)**

Until 1907 all the 3D spatial environment was considered stratified by the universally valid time coordinate *t. *The relativistic point of view about Time and Events conceived in 1907 a 3D flat space labelled by mean of the Time parameter *t*. Time continued to allow to order sequentially all the physical Events, as an example, the measures of a Physical property like the spin or its collective counterpart, polarisation. Events identified with 3+1 coordinates. Still a *single-history* concept, where a bulk of flat 3D spatial hypersurfaces is crossed by one perpendicular time-like straight line and definite corrections have to be applied to times and distances to account for the relative speedths of the moving bodies. *Single-history* concept of 1908 by the laymen still today imagined the environment we are inhabiting.

** ****Reeb foliation. The visible “****leaves”, also named “sheets”, are 3D hypersurfaces. Each Observer, Detector or industrial machinery occupies a multitude of 3D leaves of the 4D foliation. Because of this reason, each Detector (e.g., a pixel in a CMOS-camera in a final inspection system) collects changes in the status of a multitude of detectors densely existing all around. Each of them sensitive only along an instant of Time (image Tambara Inst. of Mathematical Sciences, Univ. of Tokio, 2014)**

Ambiguity in the identification of the Events by their timing

In 1915, Einstein in its General Relativity revised deeply Minkowski's idea of 1907, applying new principles (general covariance and equivalence) over topological spaces. Since then, Time has no more the unambigously defined meaning of Event-identifier it had before. The topological spaces to whom we are referring are the Manifolds, resembling near each one point the known Euclidean space. The neighbourhood of each point of an N-dimensional manifold is homeomorphic to the Euclidean space of dimension N. The simplest 1D manifolds are the curves and the circles, and the 2D manifolds are named surfaces (e.g., plane, sphere).

Relativity conceives we, our devices and Machinery be living in a higher dimensional differentiable Manifold M. Readers may figure out what is meant as “differentiable Manifold” recalling the 2D surface of the Earth or the waves formed in a water surface by one point source, like the liquid manifolds below.

To understand what today is meant as a “measure”, including the containers’ detections of the tracking Triggers, we suggest to focus the multi-branched tree-like structures naturally arising in the figures below. In this example, a single point source perturbed the state initially flat of a liquid surface.

Several deriving outcomes are the effect of that disturbance:

- all of them equally real also when their measures are visibly different;
- after a perturbation, they are never visible completely identical outcomes;
- comparing different perturbations, they are never visible completely identical outcomes.

And, what about the Time indicated by clocks lying in different outcoming branches of the foliation ? After 1915 different leaves of the foliation M may have different or equal Times and no one of them is less real than another. Space dimensionality is ≥4, however superior to the three dimensions we are *biologically equipped* *to perceive* and mathematically conceive. Since decades the symbol M conventionally identifying a manifold, has been replaced by another named *S. S *derives by the Latin language prefix of Superspace and a still more actual denomination makes frequently use of a Greek language prefix *hyper*space. On the date when these notes have been compiled, a promising version of the hyperspace *S* is considered to have at least 5 dimensions in an epoch when some versions of the theories adopt 26 dimensions. With reference to the figure below, the hyperspace *S* is the manifold each of whose “points” A, B, C, … represents all of the infinite points in a 3-dimensional space:

- smooth lines numbered 19, 20, 21, 22 are wave crests of probability amplitude function ΨE (x, t), where E is the Energy, x a spatial coordinate and t the time parameter;
- dashed lines, same as before for an energy E + ΔE;
- S(G) and S’(G) are the Hamilton-Jacobi dynamical phases due to different waves. Their elliptic intersection points, magnified by the lens, regions of constructive interference.

Also, waves and manifolds are commonly associated and also at the macroscopic scale of our industrial Machinery and inspection devices.

** Imagine to have a lens powerful enough to magnify details <****10**^{-30 }cm. In this realm, it becomes possible to see the true nature of the Space. Hyperspace *S* (also named, superspace) is the manifold each of whose ** points** A, B, C, … represents the infinite amount of points existing in a 3D space. Smooth lines numbered 19, 20, 21, 22 are wave crests of probability amplitude function Ψ

_{E }

**(x,**

*t*

**), where E is the Energy, x is a spatial coordinate and**t

**is**

**the time parameter. Dashed lines, the same for an energy E +**Δ

**E.**

**S(G) and S’(G) are the Hamilton-Jacobi dynamical phases due to different waves, their elliptic intersection points being regions of constructive interference, what we normally name**The

*particles*.**submanifold H of**

*S*

**is the classical history experienced by the geometry of that 3D space, when space has been started off under some particular set of dynamical initial conditions**

**
**** Constructive interference showing the far reaching implications of the Principle of Superposition. T****wo gaussian wave pulses with a minimal amplitude difference, travelling ****in opposite directions**** on a nondispersive string. Visibly, they pass through each other without being disturbed. The net displacement is the sum of the two individual displacements**

A full understanding of this last decisive concept is visually aided by the figure on right side. Here, two gaussian wave pulses with a minimal amplitude difference, are travelling on a nondispersive string in opposite directions. Visibly, *they pass through each other and superimpose without any reciprocal disturbance*. The net displacement is the sum of the two individual displacements. Now, remember that a measurement instrument, whatever its technology, features a defined sensitivity, the stimulus' minimum amount, whose existence it can detect.

As an example, set the sensitivity be equal to what in the graphics on side has the value 1, an we’ll have the net result of:

**what**dot-like objects shall be observed (measured), each one of them associated to an Information (named*Signal*):**where**the superposition reaches amplitudes >1;**when**the gating system of the measurement instrument (Trigger, detector or a complete electronic inspector) lies in one of those time intervals (the*inspection window*) allowing further processing.

The submanifold H of S is *the classical history experienced by the geometry of that 3-dimensional space positive definite*, when space has been started off under some particular set of dynamical initial conditions. An entire 3D space, can be imagined as something half-way between a true mathematical point and what a *point* represents in the hyperspace *S*.

In particular, a temporary configuration of a:

*particle, is an Event*, a single point in the space-time;*space, is a 3-dimensional geometry*, a single point in the hyperspace*S.*

“An oscillating drop of water undergoes fission. The topology changes. A point marks the place of separation of the two masses of liquid. That point lacks the full neighborhood of points that characterizes a normal point. Such a critical point is ruled out from any proper manifold by the very definition of the term manifold in mathematics. Before the division, the surface of the drop constituted a manifold. After the division, it is again a manifold, consisting of two disparate pieces. At the instant of division it is not a manifold. But little attention does the drop pay to this distinction. It divides, despite all definitions. No more reason does one see in the definition of manifold* against *space changing its topology”

*John Archibald Wheeler, 1967*

**
**** John Archibald Wheeler at Princeton, 1971. The one with the bald spot in the front row is the relativist Tullio Regge (image credit R. Matthews)**

Signalling, in the detectors and equipments used in the Food and Meverage Machinery is frequently electromagnetic. The most modern design address is toward the transition to fiber optic signalling between all equipments. Another widespread classic idea needing to be updated to the experimental reality known in the Third Millennium, regards the signalling. The public idea assumes that signalling is happening in a common 3D space: transmitter and receiver should be exchanging informations carried by energy moving through the 3D space the laymen think to be inhabiting.

But, an arbitrary metric space A is defined to be *positive definite* if each of its finite subsets is positive definite with their induced metrics. 3-dimensional spaces have positive definite metric,** **what implies that **physical effects cannot propagate from one point of the 3D geometry to another**.

Why ? Because a physical quantity local to a point, and another local to another point, have no reciprocal coupling: they commute. The meaning of the sentence above in bold characters has far reaching consequences.

** ****The space-time manifold** M **as seen by the roditor perspective, looks flat and simple. The opposite than the topologies suggested, after comparison of theory and experiments. Then, the obvious question: “Why do we see a different (flat) reality ?” An answer is that we are not biologically equipped, in terms of amount of sensors and neurons, to perceive the fine details corresponding to extremely small time intervals. And, also if we’d be, then we’d not have enough memory where to record such an amount of informations**

It implies that also the appearances of material objects, a macroscopic case of the measurements (and, triggerings) of the Electronic Inspectors and in the industrial Machinery, are exclusively happening between different 3-geometries where we, our electronic inspection devices and Machinery are existing.

The first clear idea of this by Minkowski, dated 1908, was valid only for the flat, ideal, non existing Euclidean spaces. In 1967, these concepts were carried further by J. A. Wheeler, then the greatest living Relativist. He was capable to establish a firm bridge between the two most successful physical theories, General Relativity and Quantum Mechanics.

** The ****YE-1 Compact Muon Solenoid, part of the Large Hadron Collider (LHC), is a complex assemble of measurement instruments. The entire measurement process backed by a supercomputer, equipped with an impressive memory to record the huge flow of data following each collision event (image credit CERN, at Geneva, Switzerland, 2006)**

Topology-Spinors connection

In other sections and until now, we spoke about the spacetime, looking at its topological properties. There is an additional property to consider: the spin. There is a criteria to identify a topologic variety as a candidate to be the master plan of the physical space where they happen binary classifications based on measurements. The same effects we observe on macroscopic objects or that we can logically infer, have to be autonomously rendered by that topology. Imagine a cube. Attached, like in the figure below, to four of its corners four elasting strings.

** ****Imagine a cube and four elasting strings attached to its corners. Select any axis running through the center of the cube and rotate the figure about that axis through 360º. The cube shall return to the original configuration, but not the strings. Strings shall be entangled and no way to untangle them. The 360º rotation alters the orientation entanglement relation between the cube and its surroundings (abridged by image credit J. A. Wheeler et al., 1973)**

** When two surfaces are joint by different wormholes, full justice is made for the use of the mathematical term multiply connected space. The example is showing what they can be: 1) two multiply connected leaves. 2) a single multiply connected leaf joint in an area not visible in the image (image credit S. Hossenfelder, 2014)**

Now, select any axis running through the center of the cube and rotate the figure about that axis through 360º. You’ll see the cube returning to the original configuration, but not the strings. Strings shall be entangled and no way to untangle them. The 360º rotation alters the orientation entanglement relation between the cube and its surroundings. Two successive rotations by 360º restore the original orientation of the cube and the strings can now be untangled. The spinor is a particular mathematical operator accounting for the effects of these rotations with respect to the origin of a triad of coordinate axis. Until now we spoke only of the rotation of a cube and its surroundings. Now, we’ll try to figure out what shall happen when the cube is slowly rotated through 360º when passing along the entire space of other geometric surroundings.

We’ll discover that under the same identical rotation of 360º different 3-dimensional closed manifolds can be fully classified by total four properties:

- topology;
- differential structure;
- metric;
**spin structure.**

The figure below, next section, represents different kinds of 3-dimensional points.

All of them are closed 3-dimensional geometries but six of them, labelled as:

D_{+} D_{-} E_{++} E_{-+} E_{+-} E_{--}

present the handles which let them be identified as *wormholes.*

In a multiply connected space they have to be expected behaviours looking strange as seen from our many-3-geometries-at-once point of view. Imagine* *two identically coloured pink cubes. Also, oriented the same way with respect to a single triad. Let one of them enter the wormhole by one of its throats. Let the other cube move along the flat surface out of the handle, from the same throat where the other get in, til the other throat. You’ll discover they'll get rejoin themselves differently oriented with respect to the triad used as a reference when they get in !

This kind of geometric structures are an unavoidable feature of the space. The Readers may immediately consider the risk to introduce Closed Timelike Curves (CTCs) in the structure of the space. These risks really exist applying the General Relativity theory without the *conditioning* of the modern version of the Principle of Superposition, of quantomechanical origin, object of deeper analysis in other sections. As a matter of fact, CTCs really are constantly created, but on timescales extremely small (~10^{-}^{43} s), giving effects completely uneligible in our macroscopic measurements.

Triggers and Time

Simplest instance of electronic inspection measurement devices:

a way to differentiate leaves otherwise similar

*“Triggers are a way to differentiate leaves otherwise undistinguishable”*

The synthetic and technological meaning of what preceded is that General Relativity, a theory made of worldpoints named Events, constitutes *a device to calculate and constructing a leaf of history that slices through the higher dimensional space *S whose dimensionality is ≥4. What above has relation with the purpose of the Triggers adopted in the industrial automated Quality Control (electronic inspection) and in the Machinery. Knowingly, the purpose is to *acquire Information *about the phase, state, dynamic or kinematic conditions of an object.

That a triad:

- Clock,
- Encoder,
- Trigger,

is the necessary and sufficient precondition to let a microprocessor have information about the presence of objects and their kinematic, is a basic notion. But what is the rationale for that necessity to “*acquire Information” ?* The reason is that the Triggers, are *a way to differentiate leaves otherwise undistinguishable. * There is always at least one Trigger introducing objects into the Shifting-Registers. Shifting-Registers *clocked* (**Time**-related) and counting the Encoder pulses.

** 4D multiply connected manifold. The foliated character of space is here distinctly visible, jointly with those topologic peculiarities whose crest values in the multitude of constructive interfences, we name Events or Measurements. Each one of the differently coloured volumes visible is 4D. Each one black dot is a 3D volume: e**ach one of the ** points** A, B, C,… contains the infinite amount of points existing in a 3D space. The smooth lines numbered 19, 20, 21, 22 are wave crests of probability amplitude function ΨE

**(x, t), where E is the Energy, x a spatial coordinate and t the time parameter. Dashed lines, the same for an energy E +**Δ

**E.**

**S(G) and S’(G) are the Hamilton-Jacobi dynamical phases due to different waves, their elliptic intersection points being regions of constructive interference, what we name**

*particles*.**In the year 2000, it has been discovered (Deutsch, 2000) that the information flow at the quantum level follows the basic rules of the flow of information between different 3-geometries in a multiply connected 4D manifold like the one here depicted (abridged by image Wheeler**

*et al.,***1973)**

*“...measurements (and, triggerings) of the Electronic Inspectors, are exclusively happening between different 3-geometries where we, our devices and Machinery, exist”*

The figure above shows portion of the multiply connected manifold seen immediately before. limited to the leaves A, B, C, D+ and D_ in a representation privileging Time evolution. Here, *Ψ**E*** **(x,** ***t*) is a probability amplitude function, E is the Energy and x a spatial coordinate. What it is showing is a different way to visualise coexistence and separate evolution of several different 3-dimensional spaces. Looks too complex ?

Not that much, when thinking that Nature** **adopts similar designs also at our macroscopic scales. Below, an example of botanical branchings. The cuts reveal the inner foliated structure: a geometric dynamical reality referred to a foliated 3D space which, having existence extended along the Time-dimension, is a 4D space foliated with 3D spaces.

“...our Detectors, occupy a multitude of 3-dimensional leaves along a single constructive interference crest”

But, in 1967 it was first suggested that the space-time of 1915 does not exist at all. On the opposite, it is just one of the ways we perceive the fundamental Quantum Field. The idea received contributions by many, some of them nobelists. Between them Paul Dirac, Higgs, Bergmann, Pirani, Arnowitt, Deser, Bryce DeWitt, Charles Misner and John Archibald Wheeler.

What remains of Time

It is known that the nature of Time and its very existence are since thousands of years an object of innumerable philosophical discussions. More important, in 2013 the concept of Time had been experimentally proved *derived,* rather than fundamental. Time reduced to just an apparent effect of that particular kind of relation named *Entanglement* of a multitude of individual measurements happenings between different 3D spaces, foliated to form a 4D. We, and our Detectors, occupy a multitude of these 3D leaves along a single constructive interference crest. And that’s why we feel the effect of Time named *Dynamics.*

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