Introduction to a fundamental question

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The purpose of any photodetector is the conversion of light (photons) into electric currents (electrons).    Photodetectors are among the most common optoelectronic devices; they automatically record pictures in the Electronic Inspectors’ cameras, the presence of labels in the Label Inspectors or the fallen bottles lying in a Conveyor belt.  Photodetectors are fabricated from various semiconductor materials, since the band gap needs to be smaller than the energy of the photons detected.   Photon absorption generates electron–hole pairs which are subsequently separated by the applied electrical field.   Depending on the desired use, photodetectors are designed in many different ways.   The common language still today adopted in the textbooks of Electrotechniques & Electronics makes wide use of terms like particles or test particles, when referring to electrons.   Practical examples are the electrons absorbed by the atoms of the doped junctions in a Detector (i.e., a CCD- or CMOS- vision camera, the Receiver in a Trigger light barrier, etc.), or photons’ emission by the semiconductor in a LED.   Also the language commonly used when referring to the measurements made by of the collection of silicon Detectors in the Compact Muon Solenoid (CMS).   CMS is part of the CERN’s Large Hadron Collider at Geneva, Switzerland, depicted in the figure above.


















 All detectors, sensors or Observers, however small occupy a 3-dimensional volume. A basic fact frequently over sighted, with far reaching implications (image credit J. Anders, 2013)



In the technological and industrial applications, like those of the electronic inspection devices, an individual atom part of the Detector’s detects:

  • an incident electron, whose energy is transferred to the atom; 
  • the photon emitted in association to a change of orbital by an electron; 
  • the photon, absorbed by an atom.  

Relevant examples, being all CMOS- or CCD-camera’ sensors, and phototransistors’ doped atoms in the photoelectric sensors.  Detectors or sensors, when doing this, notoriously extend the function and capabilities of the human Observer.  

 The past history of the point P at the origin of the bicone from which emerged the signal, is an element of the history of a multitude of leaves of the foliation. This originates a fundamental question:  “Does each one Observer or Detector respond to every Event on his Past light cone ?”   



Each one Observer or Detector does not respond to every Event on his Past light cone also because the Observer, Detector or Sensor, occupies a multitude of 3-dimensional leaves of the foliation.  “Leaves” also named “sheets”, are hypersurfaces whose dimension is three.  Then, each Detector collects changes in the status of a multitude of detectors densely existing all around.  Each of them sensitive only along an instant of Time. The image represents the Reeb foliation (image credit Tambara Institute of Mathematical Sciences, University of Tokio, 2014)

In others of these pages devoted to the Physics of Triggering as a special elementary case of Measurement, they appear several spacetime bicones.  Appearing jointly with the rules considered  true over one century ago. Refer to the bicone at right side, representing the Past and Future. Each one of those points itself an Event. 

It is then reasonable to ask: 

does each one Observer or Detector respond to every Event on his Past light cone ?   A question which may be reformulated as:  does the Past light cone supply the appropriate geometry on which to specify physical conditions ? …e.g., temperature, voltages, forces…? 

The answer is negative, because:

  1. to have knowledge about the geometry on a Past light cone does not grant predictive power regarding the Future of that geometry.  Into the domain of the Future, influences flow from afar without ever once impinging upon the light cone. 
  2. the Observer, Detector or Sensor cannot be a detector of Events because is not a mathematical point.  Interactions, a synonimous of Measurements, happen at the smallest scales, interesting objects like quarks, gravitons or individual components in the superposition: waves.   It is their constructive interference that, to name just two a them, we name a photon or a quark. 















    Two Future cones originating by different Events, on different spatial hypersurfaces of constant time and moving along their own worldlines, illustrate the meaning of the term 'correlation’.  Present Events originating by Events in other times and other places. The Events correlated to both original Events lie in the intersection tetravolume, where are felt the effects of two different causes (two Events) in their Past.  Also if not here visible, there are other two (Past) cones, themselves having an intersection volume.  The most common kind of correlation between different events (figure abridged by Hans-Jurgen Borchers, 1996)






  Reeb foliation. The visible “leaves”, also named “sheets”, are hypersurfaces whose dimension is 3.  Observers or Detectors do not respond to every Event on their Past light cone. Also because each Observer, Detector or Sensor, occupies a multitude of 3-dimensional leaves of the foliation.  Then, each Detector 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 credit Tambara Institute of Mathematical Sciences, University of Tokio, 2014)


Meaning that the Observer, Detector or Sensor, occupies a multitude of leaves (or, sheets, or hypersurfaces).   It collects changes in the status of a multitude of detectors densely existing all around.  Each of them sensitive only along an instant of Time.    Collectively, they define a spacelike 3-D hypersurface, a rudimentary simultaneity.  A hint to the Time variable we all agree to be feeling. What can be inferred by the precedent point 2. is that in its moment of sensitivity, during its own individual measurement, each elementary detector (or, sensor) responds to the appropriate stimulus to:

  • local field strength, in Electrodynamics, as in its multiple Industrial applications, like in the Electronic Inspectors;
  • particle proximity, in particle Physics as in its Chemical and Biological applications;
  • local geometry, in General Relativity or its Geodesic and gravimetric applications.














  Two Events P and Q  and the cones including all the other Events which happened in P and  respective Pasts.  The boundary depicted in white colour, part of the union of the boundaries of the Events P and Q , is that one of the Events lying on a common Time t  hypersurface.  Each white coloured dot in that ellipsoidic shape is common to P and .  At a first sight, Minkowski Space allows a deep insight in the meaning of correlated Events.   In the reality, each one Observer, detector or sensor does not respond to every Event on his Past light cone.  The Past light cone does not fully supply the appropriate geometry on which to specify physical conditions for, e.g. temperature, voltages or forces.  Then, knowledge about the geometry on a Past light cone, does not grant predictive power regarding the Future of that geometry.  Into the domain of the Future, influences flow from afar without ever once impinging upon the light cone. 


What Time indicates is the location of a chosen 3-dimensional space in the infinitely wider 4-dimensional space.  In synthesis, dynamically complete initial values can only be specified in a 3-dimensional spacelike geometry, showing that Dynamics is a concept derived by Topology plus an initial condition, without any reference at all to Time.

Recent experiments dated October 2013 gave the final confirmation for this.

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quantumlimitedllowdoseimagi





  X-rays imaging of screw.  Each one illuminated pixel in the image is not corresponding, as it’d be expected, to an Event of X-ray absorption by particles in a single spatial leaf.   A Detector cannot be a detector of Events.  Rather,  it collects changes happened in the status of a multitude of detectors dotted densely about.  Each of them sensitive only along an instant of Time.  Collectively, they define a spacelike 3-D hypersurface floating in the infinitely wider 4-D space.  A rudimentary simultaneity originating our idea of Time



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