(click to enlarge)  Silicon Detectors in the Compact Muon Solenoid (CMS), part of the CERN’s Large Hadron Collider at Geneva, Switzerland

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A Fundamental Question

What Detectors detect?  Their purpose is known: 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.  Photodetectors are designed in many different ways, following the desired use.  Examples are the electrons absorbed by the atoms of the doped junctions in a Detector (for example, a CCD- or CMOS-Vision camera, the Receiver in a Trigger light barrier, etc.), or photons’ emission by the semiconductors in a Light Emitting Diode (LED). 


  







 A basic interaction where a photon of light impinges one of the electrons of an atom of Silicium in a common Photodetector, transferring part of its momentum 

 

In the technological and industrial applications, like those of the electronic inspection devices, an individual atom part of the Detector, 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.


















 (click to enlarge) All Detectors, Sensors or Observers occupy a 3D volume. A fact frequently over sighted, with far reaching implications (  J. Anders/2013)











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.  


Detectors Detect Wavefronts

The majority of the Detectors adopted by worldwide Industry are sensible to undulations in the electromagnetic fields.  Precisely, they detect electromagnetic wave-fronts.  Wave-fronts correspond to processes starting and terminating very rapidly.  A rarely seen example in the figure below, depicting a light-in-flight multiple recording of light focused by a lens. One single picosecond (0.3 mm) spherical pulse, from a mode-locked LASER, illuminated a white screen set at an oblique angle.  


 Light-in-flight ultrafast holographic imaging of 5 wave-fronts propagating toward a lens.  A hologram is recorded when object light and reference light simultaneously illuminate the hologram plate. The light-slices on side have been obtained using reference pulses just 1 picosecond long, equivalent to 0.3 mm. Clearly visible the expected focusing effect of the lens enacted over each wave-front after the interaction (  abridged by M.W. Evans, et al./2001)




Screen placed so that its normal passed trough the hologram plate. A portion of the pulse, appropriate delayed, has been used as a reference beam. A cylindrical lens fixed to the screen and, finally, by mean of multiple exposures of the reconstructed image, it has been recorded the focusing effect of the lens. The figure is relevant in that it displays the light wavefront before it impinges an object, until later when results scattered after interacting with the object’s atoms.  


 The Information conveyed by all electromagnetic and electric Signals lies in their wave-front. Information encoded as a change in a physical property. I.e., energy, frequency, amplitude, polarization angle, etc.


Wavefronts are what, after interaction and energy exchange with the atoms in a Detector, we name Signals. What better detailed in the couple of figures below.  The wave-fronts carry the Information encoded as a change  of, i.e., energy or polarisation.  


 The Information conveyed by all electromagnetic Signals is conveyed by the null-surface of each light-cone. Null-surface named wavefront in the Electronics technologies.  It is 4D-volume appearing us a 2D spherical spreading wavefront.  A Signal is detected when the external envelopes of several null-cones interact with several Detector’s atoms, until an energy exchange superior to the Detector's sensitivity threshold



Information Encoded as a Change

The nature of the Information itself, strictly lying in the asymmetry underlying all changes: 










  • Symbolic.  I.e., “0” rather than “1”, “x” rather than “y”, 
  • Physical.   I.e., an increase on energy from 1 J  to 10 J, a grey level digitised in the scale 0-65535 from changing from the black 65535 to the white 0, 
  • Logic.   I.e., “x = y”  rather than “x ≠ y”, “x ≺ y” (symbol “≺“ read as “precedes”)  rather than “x ≻ y” (symbol “≺“ read as “succeeds”),
  • etc.

An example in the figure below. Here depicted a group of electromagnetic waves originally with a single mode of vibration k, later interacting with an 2-state atom. After the interaction, the mode of vibration results reduced. A change in the energy content equivalent to a Signal detected by the Detector of which the atom is part.


 The Information conveyed by all electromagnetic Signals lies in their wavefront. Information encoded as a change in a physical property.  As an example, in the figure a group of  electromagnetic waves with a single mode of vibration k interact with a 2-state atom initially in the state Einitial.  The interaction let the atom transition its energetic level Einitial → Efinal.  After the interaction, the mode of vibration results reduced.  A change in the energy content equivalent to a Signal detected by the Detector of which the atom is part (  abridged by M.W. Evans, et al./2001)



Detectors Are Not Sensible to All Past Events

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 above, representing the Past and Future.  Each of those points itself an Event.  It is reasonable to ask: does each one Observer or Detector respond to every Event on his Past light cone ?    



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





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.  What happens in and around the causal Past light cone is visible in the figure below where:
    • a 2+1-dimensional space-time, where the third spatial dimension is not shown;
    • 0, 12 are three 3D spatial hyper-surfaces, crossed by the world-lines of a Detector and of a Signal;
    • violet colour the time-like world-line of a Detector or Observer;
    • yellow colour the world-line of a Signal: 
      • impinging at: 
        • T (t0, 0) the causal Past light-cone of the Detector at (t22), 
        • R  the causal Past light-cone of the Detector at (t11);
      • oufeeding the cone, thus terminating at: 
        •  its causal interactions with the Detector at (t11);
        • N  its causal interactions with the Detector at (t22).  After this 4D point, the Signal disappears at all by the comoving celestial sphere centred in the Detector's centre-of-mass.
  1. Observer or Detector cannot be a “detector of Events” because they are not a mathematical point.  Interactions happen at the smallest scales, interesting objects like quarks, gravitons or individual components in the superposition: waves.  On the opposite, a single pixel in a CMOS camera accounts for 1 million of atoms.  Each atom itself composed by tens of quarks and other particles.  Meaning that nor a single atom can really be considered a “detector of Events”.  Also a single particle or, better, its modern view as a tensioned tubular string, can be considered a “detector of Events”, however small has non-nil dimensions.  

It is their constructive interference that we name photons, neutrinos, gravitons or quarks.  Meaning that each Source, Observer, Detector or Sensor, occupies a multitude of leaves or, sheets, or hypersurfaces like those in the figure here at right side.  


 Detectors and Objects are correlated in the Hilbert space.  The coupling strength K between Detector and Obiect is defined as the inverse of the Detector’s response time.  A decisive parameter acting selecting determinate subspaces of the Hilbert space.  Then, eigenspaces belonging to distinct eigenvalues. What rephrased means subspaces that the Detector is able to distinguish.  The true meaning of the Signal-to-Noise (S/N) ratio.  At low coupling parameter K, like those tagged 2-5 in the figure, the object results on the opposite indistinguishable by noise.  In the figure we are not showing what corresponds to the minimal coupling (K1).  Random optical noise undistinguishable by the computer display’s own flicker and shot noises










 Step-by-step sequence showing the interaction of a Signal impinging and later disappearing out of the causal Past light-cone of a Detector. Implicitly showing how the Future evolution of a system is influenced by its environment










Reeb foliation. The visible “leaves” or “sheets”, are 3D hypersurfaces.  Observers or Detectors do not respond to every Event on their Past light cone.  Also because each Observer or Detector, 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 (  Tambara Inst. of Mathematical Sciences/Univ. of Tokio/2014)


As an example, the surface named Source in the figure below is a time-like hypersurface of space-time.  It represents either the surface of an extended light source evolving in Time, or an arbitrary 2D surface evolving in Time, chosen with some particular physical or mathematical attribute.  In this framework, the null-surfaces are the 3D hypersurfaces whose normal spatial vector has wherever zero length. Observer, Detector or Sensor collect changes in the status of a multitude of elementary detectors densely existing all around.  Each of them sensitive only along just an instant of Time. Collectively, they define in a spacelike 3D hypersurface, a rudimentary simultaneity.  A hint to the Time we feel.  What can be inferred by the precedent point 2. above, is that in its moment of sensitivity, during its own individual measurement, each elementary detector 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.



 All electromagnetic Signals refer to the Information transferred from a leaf to another in a foliated Manifold. The Information is contained in the null-surface spreading by the source. Null surfaces are the 3D hyper surfaces whose normal spatial vector has wherever zero length (  F. De Felice, C.J.S. Clarke/1990)







What Time indicates is the location of a chosen 3D space in the infinitely wider 4D space.  In synthesis, dynamically complete initial values can only be specified in a 3D 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.  


 Two Future light 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 4-volume. Here are felt the superposed effects of two causes, namely the Events P and Q, lying 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 









 Two Past light cones causally related to the Events and Q . They including all the Events happened in P's and Q's  respective Pasts. The boundary depicted in white colour, part of the union of the boundaries of the Events and Qis that one of the Events lying on a common Time t  hypersurface.  Each white coloured dot in that ellipsoidic shape is common to 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.  Thus, 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.  An Observer, Detector or a sensor cannot be a detector of Events. Rather, he or 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 3D hypersurface floating in the infinitely wider 4D space.  A rudimentary simultaneity originating our idea of Time (  abridged by Y. Choquet-Bruhat, in C. DeWitt, J.A. Wheeler, eds./1967)




Measurements in the Apparent Global Present







We’ll deepen in the following a subject whose effects are felt by whoever and by all Detectors and measurement devices.  Namely, the sensation of Present. As we saw elsewhere in this website, according to the theory of Relativity the local spacetime structure is minkowskian and depicted in the graphic below at left side. Imagine to have a Detector at the Event P: 

  • (left-side)  space-time Future and Past are defined relative to every Event P, and independent of any choice of reference frame;  
  • (right-side)  in conventional units (large numerical value of the speed of light) the light cone opens widely, so its exterior seems to degenerate into a space-like hypersurface of ‘absolute’ simultaneity.   

 The light-cones graphic at right side is the one at left side, after dividing the amounts ct in its ordinate axe by the speed of light c.  Both future and past light-cones look us compressed by a factor 299792458.  What we observe as an apparently global present is in fact the backward light cone with respect to the subjective here-and-now at the point P (  abridged by D. Zeh/2007)





What we observe as a global present, is in the reality the backward light cone.  Backward light-cone as seen by the point of view here-and-now at the point P.   In our macroscopic neighborhood, they are relevant only the speeds lower than that of light.  And is this what lets the apparent simultaneity look coincident with the forward light cone.  Future light-cone which is the space-time border to the open future that our present actions may affect.


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 or photons.  Practical examples are the electrons absorbed by the atoms of the doped junctions in a transistor part of a Detector, the photons' absorbed by a phototransistor or photons’ emission by the semiconductor in a LED diode.  

In all these subjects, the Detector (or, sensor) 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.  


Detectors or sensors, when doing this, notoriously extend the function and capabilities of the human Observer.  In the start of this pages devoted to the Physics of Triggering as a special elementary case of measurement, they appear several spacetime bicones, jointly with the accompanying rules considered truth 106 years ago.   

Today, with reference to the couple of figures on right side and below representing Past and Future cones pink and light blue coloured, and correlations between Events, we can ask ourselves: 

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:

to have knowledge about the geometry on a Past light cone does not grant the 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. 
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 named wave whose constructive interference is the photon, to name only some. 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.  An initial 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:

particle proximity, in particle Physics as in its Chemical and Biological applications;
local field strength, in Electrodynamics;
local geometry, in General Relativity or its Geodesic and gravimetric applications.


What really 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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