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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