Same Causes Carry Out Same Effects

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Whoever practical experience points to the fact that certain conditions generate phenomena, while other conditions do not possess this property.  Likewise, it is incorrect to assert that the principle of causality invariably requires acceptance of the fact that every phenomenon has a unique cause.  For instance, a change in the volume of a bottle may be due  simultaneously to a variety of thermal and mechanical actions.  These various factors can act on a body in one direction, reinforcing one  another, or in different directions, diminishing the resultant effect.  Also, they can cancel out entirely  producing no resultant effect whatsoever.  This classic point of view was openly advocated by the French physicist Jean Bernoulli, when writing: “Nor would the same fruits be constant to the same trees, but would be  changed; and all trees might bear all kinds of fruit.”  It is important to understand that Bernouilli is writing what appeared true, what get out of repeated experiments, using instrumentation available over two hundred sixty years ago.  Indeed, if identical pieces of metal, when heated, behaved differently, expanding, contracting, melting and so forth without rhyme or reason, it would be impossible to predict the behaviour of metal under altered temperatures or make use of it in any way.  If the same set of conditions operated in different ways on identical organisms, stimulating vital processes or inhibiting them or even killing them outright, no living thing could exist, for it would be encountering unforeseeable and mortally dangerous events at every hand.  



 “The same cause operating on the same object generates, under different conditions, different effects”.  Henri Poincare’, in the year 1905 considered “The Living Brain of the Rational Sciences”, arrived closer than whoever else after Albert Einstein, to formulate first the Special Relativity Theory.  Between many other contributions, he created Topology and Chaos Theory













Practical human activities and the purposeful actions of human beings using the  instruments of production are possible only insofar as identical conditions give rise to  identical effects.  All of modern natural science, at any rate that engaged with  macroentities, essentially rests on the view that under the same circumstances, identical causes give rise to identical effects.  In the realm of classical mechanics, identical forces acting on bodies of the same mass generate identical accelerations; in the theory of elasticity, the same external actions affecting the same objects give rise to identical deformations; in the field of classical electrodynamics, identical current sources and charges placed in identical media generate electro-magnetic fields of the same intensity, etc.   What above may be resumed in the observation of another great French physicist and mathematician, Henri Poincare’ (see figure above), over one century ago considered “The Living Brain of the Rational Sciences”.  He famously claimed that: “if two organisms are identical or simply similar, this similarity could not have occurred by accident, and we can assert that they lived under the same conditions”.


 Since thousands of years physicists, mathematicians and philosophers interrogate themselves about the “unreasonable success” of Mathematics in our everyday life. Success directly felt by all the industrial applications

Motion, Change Create Different Conditions 










Of course, the idea of an absolute identity of conditions is an abstraction.  In nature we  do not find two identical leaves from a single tree.  Also, there are no two objects in  nature which would be in absolutely identical conditions.  What is more, one and the  same object cannot be twice in identical conditions, for the conditions of every object are the actions of other  objects, which, like the given one, are in a state of motion and change.  If we take into account the absence in the actual world of even two absolutely identical phenomena, then the necessary character of causal relations should be understood as an expression of the fact that the fewer the differences between the causes and conditions,  the fewer will be the differences between the effects produced by them.  In the limiting cases where the causes and conditions are identical, the effects will also be identical.  From the necessary nature of the relationship of the cause and its  effect there follows the conclusion that if definitely identical causes give rise to  different effects, then they are operating under different circumstances.  If causes operating under the same circumstances generate different effects, then the acting causes are different.


Homogeneity of Space and Time, Isotropy of  

Space are Associated to the Causal Relations 














The necessary character of causal relations is closely associated with the homogeneity  of time and space and the isotropy of space.  If for instance one and the same action  of a steam hammer on an ingot is the same, irrespective of whether the time is today or tomorrow, it then follows that time is homogeneous relative to causal relations.  True, during the time lapse both the hammer and the ingot may have changed, but this change is not the result of the action of time on things, it is inherent in the nature of the interacting entities.  A given set of conditions gives rise to one and the same effect, irrespective of the time at which the set of conditions operates.  The important thing is that the set of conditions and the time intervals during which they are realised be the same.  The same thing goes for space as well.  One and the same set of conditions generates  the same effects, irrespective of the region of space in which they are realised.   To take an example, one and  the same quantity of gasoline in a calorimetric bomb will release, upon being burnt, the same quantity of heat wherever the burning takes place (whether on the equator, at the north pole, or elsewhere on the earth), so long as the other combustion conditions are the same.  Carrying the conditions from one region of space to another does not alter the corresponding effect.  The behaviour of a body in specific conditions does not change either if we rotate it through some angle and thus alter all the conditions upon which the  behaviour of the body depends.  That causal relations are independent of translation in space and time and of rotation through a fixed angle might be expressed on the basis of the concept of symmetry.


Symmetry Causes Homogeneity and Isotropy





The German mathematician and physicist Herman Weyl is known for important insights in the meaning of a concept today nodal: symmetry.  Following him, we will say that an  object is symmetrical if it remains the same as before after being subjected to some kind of operation. Then we could say that the causal relations of natural phenomena, or at  least the causal relations of physical  phenomena, are symmetrical with respect to a  transfer in space and time and relative to a rotation through a fixed angle.


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Quantum Causal Theory How many points lie between two points? Twenty-five centuries ago the Greek philosopher Zeno first observed the kinematical paradox deriving by the idea that a line joining two points may be infinitely divided. …

Root Cause in Modern Physics

Causal Connection of the EventsIn the following we'll introduce the relevance of the history of the Events. The long time-ordered chaining of Events in the Past considered causes for a present Event. …

Root Cause in general relativity. The definitions of “Events”, whatever kind of Event, triggerings, measurements and “observations” included, and of the derived concept of causal relation between Events are part of the investigational fields of Theoretical Physics, Quantum Physics and Relativity. Why ? Because the majority of the evidences hint to a common origin. One characterised by extremely high values for energy density (then, high temperature) and geometrical curvature for the greater Environment where all, measurement instruments and Machinery included, operates. With reference to the figure below, four wordlines a, b, c, d intersecting today a 3D hypersurface, for example the worldline a at the point Q, are a System. It is frequently over looked the fact that all the worldlines were joint in a single dot, back in the Event O, origin of Time at t = 0. The nearly spherical surface in the past, crossed by the worldline a at P, represents a phase of the historical evolution when space-time was more homogeneous, not locally curved as it is today. This classic point of view, mainly derived by the ideas of Einstein, Minkowski, Lemaitre and Gamow, one time backed by Hubble and Eddington’s discoveries, started to hold as a paradigm. And it still holds today, at least in part. To reduce all this to mere theory, in opposition to facts, is no more possible. So many they are today its direct applications in our life and Machinery. As an example, all smartphones’ GPS location devices integrate routines with formulas of General Relativity to be so precise as they are, evidencing the correctness of the Theory. Higher Order Infinities How many 3D surfaces (or leaves, or sheets) contains the 4D solid above? The answer is the sum of: ∞3 points; in a coordinate system making diagonal the metric: 3 diagonal components of the metric specifiable per space point; then, ∞3 choices of the metric per space point. Therefore, a total amount of possible 3D leaves equal to: Amount later heavily reduced by the added dynamical condition of constructive interference, but however an impressively huge amount. These numbers are not shown as a sterile exercise of infinitesimal calculus, rather to enforce that since at least one century Nature answers to the continued questions by the Humanity, inviting us to replace infinities with Numbers so big to be easily confused with infinities. Classic version pre-2000 What is a Trigger ? Theory of Information point of view: "device to label the status of physical or logical entities” We’ll start to list, as seen by the point of view until 2000 considered standard, what is and what is not possible in terms of Events' Causal Connection. No interaction, gravitational, electromagnetic or nuclear, is possible with particles lying in the space out of the bicones: all what lies in that space (the “Elsewhere”) is causally disconnected by the object placed at the Triggered Event. In this classic approximation, only what lies in the Past light cone is causally connected with what lies in the Event position. The Future light cone traces the paths of light rays emitted in every possible direction from the Event at the origin. The Past light cone indicates the paths of light rays arriving at the Event's location at the Present moment. In this classic view, the Event has a purely geometric meaning: a dot of space-time. It is not necessarily the place where also happens an interaction. The rules about Events considered valid by Special Relativity, between 1905 and 1915, were: light beams emitted from the Event location travel exclusively along the Future light cone. (On the opposite, as we’ll see later with more details, in the modern Quantum Physics view, trajectories do not exist and particles are emitted in both directions, Future and Past); arriving at the Event's location at the Present, all fall within the Past light cone; launched from the Event's location, all travel on trajectories bounded by the Future light cone; they cannot exist two Events superposed in the same worldpoint: all Events are unique identifiers; Past and Future light cones of other Events, at different spatial locations, have light cones which are offset from those of the Event we have arbitrarily designated as being at the origin; the areas where the Past and Future light cones of two Events overlap, are in their common Past and Future respectively, but each Event will have regions of spacetime from which they can receive and send Information that are not shared with the others. After 1915, with the advent of the General Relativity, the point of view changed sensibly. Every worldpoint is still the origin of the bicone of the active Future and the passive Past but: the two zones are no more separated by an intervening region ef Events causally disconnected; it is possible for the cone of the active Future to overlap with that of the passive Past; it is possible to experience Events now that will in part be an effect of our future Events or decisions (Trigger and Measurement Events included). Adding to General Relativity the Principle of General Covariance, Einstein made a precise statement about the fact that global evolution does not exist. From his point of view, the time t is just a label we assign to one of the coordinate axes. The figure presented in the precedent section was published in 1973, before the discovery of the Inflationary mechanism by Starobinski, Linde and Guth. The figure here above, on the opposite, includes also this phase and is the model considered standard from 1982 til ~1993. Here, the qualitative evolution of the Hubble horizon is showed into the couple of dashed lines and of the scale factor with the external solid curve. The time coordinate is on the vertical axis, while the horizontal axes are space coordinates spanning a two-dimensional spatial section of the cosmological manifold. The inflationary phase extends from ti to tf, the standard cosmological phase from tf to the present time tc. The shaded areas represent causally connected regions at different epochs. At the beginning of the standard evolution the size of the currently observed Universe was larger than the corresponding Hubble radius. All of its parts emerged from a spatial region which was causally connected at the beginning of inflation, implying that the causal connection is maintained also after the inflation. That initial causal connection is what still today let a motor in the Blowformer Machine run following the same Physical Laws as the motor in the Palletiser, 150 m afar. The figure above also shows that there is a wide all-around sector which was causally connected but that receded so fast to have since long time moved out of our horizon. Then, disconnected also with respect to actual events. Focus on the Degrees of Freedom In the year 2000 Tom Banks and Willy Fischler discovered that the mass density parameter Ω is determined as the inverse of the number N of degrees of freedom, whose essence is visible in the figures below. The curvature parameter Ω0 encodes the system density, a relation between mass + energy and volume. But, the volume strictly depends on the number of degrees of freedom. And that’s why the amount of are since then considered an input parameter at the most fundamental level of physics. curvature determines the sum of the inner angles of a triangle, which in the three cases here depicted shall be: Ω0 > 1, Inner total angle > 360˚ Ω0 < 1, Inner total angle < 360˚ Ω0 = 1, Inner total angle = 360˚ Matter plus energy density parameter Ω0 is translated in a spatial curvature. Curvature depending by the number of degrees of freedom of the system. From this discovery of the year 2000 it has been possible to derive a new definition of Causal Connection between Events, close to everyday measurements, referred to our macroscopic scale. Causal connection exists only between points in a small subspace of the bicone. This, in turn, implies that the Environment, much smaller than expected, cannot be ignored Curvature determines the sum of the inner angles of a triangle, which in the three cases here depicted shall be: Ω0 > 1, Inner total angle > 360˚ Ω0 < 1, Inner total angle < 360˚ Ω0 = 1, Inner total angle = 360˚ Matter plus energy density parameter Ω0 is translated in a spatial curvature. Curvature depending by the number of degrees of freedom of the system. From this discovery of the year 2000 it has been possible to derive a new definition of Causal Connection between Events, close to everyday measurements, referred to our macro scopic scale. Causal connection exists only between points in a small subspace of the bicone. This, in turn, implies that the Environment, much smaller than expected, cannot be ignored Shortly later, Raphael Bousso, Oliver DeWolfe and Robert C. Myers have been capable to derive a new definition, today standard, of causal connection between Events. A perspective built over the new concept of Alexandrov interval. Alexandrov's intervals are commonly named Causal Diamonds.

The definitions of “Events”, whatever kind of Event, triggerings, measurements and “observations” included, and of the derived concept of causal relation between Events are part of the investigational fields of Theoretical Physics, Quantum Physics and Relativity. …

Same Causes Carry Out Same EffectsWhoever practical experience points to the fact that certain conditions generate phenomena, while other conditions do not possess this property. Likewise, it is incorrect to assert that the principle of causality …

  What are the “fundamental ingredients” of Cause and Effect? One of the classic philosophical answers lists:energy (and, its aggregate stable form, the matter)space,time. It is impossible to find a general definition for Energy. …


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When thinking to its applications in the industrial Machinery and equipments, whoever thinks to know what is a Trigger. Their most known examples all Container Presence electromagnetic detectors (i.e., photoelectric, inductive, by mean of ultrasounds, Gamma-rays) which let the Machinery operate. …

A Fundamental QuestionWhat 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. …

Information Retrieval approach to F&B Electromagnetic Measurements

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The subject of Classification is studied by Statistics and Applied Probability Theory. It is concerned with the investigation of sets of objects in order to establish if they can be summarized in terms of a small number of classes of similar objects. …

Electronic Inspectors non-classic components

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Introduction The language of Optoelectronics adopts its own special terminology, born along the developement of this branch of technology. In the following we are synthesizing in few lines the definition of the fundamental terms. Terms constantly repeated in the web pages of this site with reference to photodetectors in all their kinds. Signal-to-Noise Ratio The Signal-to-Noise ratio (S/N) is expressed in terms of the noise in a particular bandwidth. It may be alternatively expressed in: decibels, ratio of a number to the standard deviation of the number in a particular count duration. Equivalent Noise Input The Equivalent Noise Input (ENI) is defined as that value of input flux that produces an rms signal current that is just equal to the root mean square (RMS) value of the noise current in a specified bandwidth (usually 1 Hz). Other parameters such as frequency, the type of light modulation, and temperature should also be specified. Equivalent Noise Input characteristics are useful in determining the threshold of detection in equivalents of the input flux in watts or lumens. Noise Current There are various sources of noise or current fluctuation which interfere with the precise measurement of the signal current. Dark current has a random fluctuation as does signal current. When the individual pulse can be observed, these fluctuations are manifest in the random arrival of the dark or signal pulses. Sometimes, the noise in the associated components, such as thermal (or Johnson) noise in the coupling resistor or amplifier noise, is dominant. Noise Equivalent Power Noise equivalent power (NEP) is essentially the flux in watts incident on the detector which gives a Signal-to-Noise ratio of unity. The frequency bandwidth and the frequency at which the radiation is chopped must be specified as well as the spectral content of the radiation. The two most common spectral specifications are for total radiation from a black body whose temperature is 500 K or monochromatic radiation at the peak of the detector response. Detectivity Detectivity is the reciprocal of the Noise Equivalent Power and expressed in 1/watt. Has to be considered as a figure of merit providing the same information as the Noise Equivalent Power but describes the characteristics such that the lower the radiation level to which the photodetector can respond, the higher the detectivity. Specific Detectivity Because the Noise Equivalent Power for many types of IR photodetectors is proportional to the square root of the sensitive area (A) and to the square root of the bandwidth (B) of the measuring system, a specific detectivity (D*) has been defined which permits a comparison of sensors of different areas measured in different bandwidths. Incident Flux The response of a photodetector is evaluated in terms of the flux incident on the sensitive area of the detector. The flux may be specified as the: number of quanta per second at some wavelength, radiant flux in a narrow wavelength band, radiant flux over a wide band of wavelengths, luminous flux, luminous density, per unit area, in the plane of the device aperture, in a surface. Responsivity and Signal Current The term responsivity (R) is used to describe the sensitivity of the photosensor and is the ratio of the output current or voltage to the input flux in watt or lumen.

IntroductionThe language of Optoelectronics adopts its own special terminology, born along the developement of this branch of technology. In the following we are synthesizing in few lines the definition of the fundamental terms. …

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Optoelectronics is a complex subject, but this section has content aimed at people with differing levels of knowledge. Watch a video, read a tutorial or white paper, download one of the scientific papers that have been published about the most modern aspects of what the Food, Beverage and Pharma Control technologies shall be in the near future. …

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