Many physical and chemical effects state this: doing X brings about results R:
X ⇒ R
Often doing X means excerting some action A on an object O:
→AO ⇒ R
Also often the results are emergence, disappearance, or change/transformation of something s:
→ AO ⇒ s ⇝ S (1)
where s ⇝ S means transformation of s into S.
For example, applying voltage V to the opposite sides of a piezoelectric crystal C results in its squeezing or expansion (i.e. size change either from S to s or from s to S):
→ VC ⇒ s ⇝ S
If s is nothing (∅) then we have emergence of something as a result of action A:
→AO ⇒ ∅ ⇝ S
For example, the direct piezoelectric effect is described by this formula. Indeed, it states that applying mechanical stress σ to a piezoelectric crystal C results in emergence of an electrical potential V across the sides of the crystal. Hence, in the above notation it looks as follows:
→σC ⇒ ∅ ⇝ V
If, conversely, S is nothing them we have disappearance of something as a result of action A:
→AO ⇒ s ⇝ ∅
Sometimes an action has not one but several consequences:
→AO ⇒ s1 ⇝ S1; ....; sk ⇝ Sk (2)
For example, when hydrogen gas is passed over black oxide of iron (Fe2O4) the oxide is reduced to the state of metallic iron and a mixture of vapour of water and excess of the free hydrogen gas is discharged from the end of the tube :
H2(g)------------------->passes overFe2O4 ⇒ Fe2O4 ⇝ Fe; ∅ ⇝ H2O(g) (3)
If results are actions transformation then instead of s ⇝ S notation it is better use the following one:
→AO1 ⇒ O2→B (4)
where O→B means O excerting action B.
For example, the third law of Newton is described by this formula:
O1→AO2 ⇒ O2→-AO1
To me anti-effect means that we either get the opposite result by doing the same thing, or get the same result by doing the opposite thing. Thus, anti-effects of the first kind have the formula
→AO ⇒ S ⇝ s (5)
meaning that the same action A as in the formula of direct effects (1) produces the opposite result.
Anti-effects of the second kind are described by the formula
→-AO ⇒ s ⇝ S (6)
meaning that the opposite action -A produces the same result as in the direct effect.
Anti-effects should not be confused with reverse effects, where cause and effect are inversed. For example, electro-mechanical effect is not an anti-effect to piezoelectrical effect, but rather its reverse. The formula for reverse effects of effects described by formula (1) is this:
s ⇝ S ⇒ O→A (7)
Anti-effects for reverse effects are described by the formulas
S ⇝ s ⇒ O→A (8)
s ⇝ S ⇒ O→-A (9)
where S ⇝ s means the reverse change from S back to s.
Some opaque materials become transparent when illuminated by a laser and vise versa. In the above notation these effects looks as follows:
→A(opaque O) ⇒ (opaque O) ⇝ (transparent O)
→A(transparent O) ⇒ (transparent O) ⇝ (opaque O)
It is obvious that these effects are dual as they are obtained from each other by transposing (transparent O) and (opaque O). The general formula of such mutually dual effects is this:
→AO ⇒ O ⇝ anti-O (10)
And here is an effect dual to (3):
H2O(g)------------------->passes over Fe ⇒ Fe ⇝ Fe2O4 ; ∅ ⇝ H2(g)
It is dual because Fe and Fe2O4 are transposed here as compared to (3), and H2(g) and H2O(g) are also transposed.
The effect is that if vapour of water be passed over metallic iron, the metal is again converted into black oxide and a mixture of hydrogen gas and undecomposed vapour of water issues from the end of the tube .
There are effects where a pair of entities are transposed only in certain places rather than in the entire formula. I call them sub-dual effects.
The example of sub-dual effects is the third law of Newton and Mössbauer effect:
O1→AO2 ⇒ O2→-A
O1→AO2 ⇒ O2→-A anti-O1
In Mössbauer effect emmision of a photon O2 by atomic nuclei O1 bound in a solid does not result in recoil of the nuclei but rather of the surrounding solid anti-O1. In the formula of Mössbauer effect O1 is transposed with anti-O1 (as compared to the preceeding formula of the third law of Newton) only after symbol ⇒.
Super-dual effects are effects that result in obtaining a union of opposites rather than obtaining opposite/dual results separately. Opposites do not get substituted by each other as in dual effects, but rather get united:
→XO ⇒ R
→Y O ⇒ R + anti-R
For example, deceleration of an electron produces the continuous spectrum of electromagnetic radiation. But if it is done in the presence of a high voltage ( > 10kV) then in addition to the continuous spectrum a discrete spectrum appears. It was discovered by Charles Glover Barkla in 1906 and was called a characteristic spectrum .
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