Unreal Nature

February 24, 2013

Correlative Coinvention

Filed under: Uncategorized — unrealnature @ 7:31 am

… in this case, the definition of the ability to measure something is not arbitrary, it creates the very object it measures.

… capture always implies the possibility of “reciprocal capture,” the correlative coinvention of two mutually referring identities. What physicist will the second law give birth to?

This is from Cosmopolitics I by Isabelle Stengers (2003):

… In an article from 1849, Thomson compared Carnot to Joule: Joule claimed that nothing is lost in nature, that energy is never destroyed, and yet Carnot’s ideal output implied that, when heat flows directly from a warm body to a cold body, the mechanical effect it might have produced is lost. In such cases, what else is produced in place of that lost effect? Thomson concluded that there could be no theory of heat until the question was answered.

[ ... ]

… I have discussed the state function defined by Clausius at some length for two reasons. [ ... ] Carnot’s work, completed by Clausius, is entirely focused on the manipulation, control, and production of measurement, although, at the same time, it also demonstrated the invention, the free and entirely counterintuitive production of meaning implied by the creation of certain types of measurements. We can, of course, measure anything, unilaterally decide to use the same type of measurement for the activity of laborers and the motion of the Galilean ball. But we then have no way of establishing a relationship between the measurement and “what” is being measured. In the case of the ball and other mechanical objects, this relationship appears, on the contrary, fully determined: the mechanical object is defined as measurable, defined by the equivalence used for the measurement. In the case of energy transformations, however, measurability is in no way a “given,” it must be created, fabricated from whole cloth; in this case, the definition of the ability to measure something is not arbitrary, it creates the very object it measures.

Correlatively, the measurement defined by Clausius entails requirements and obligations. And this is precisely the difference between Clausius and Thomson. For both men, not all energy transformations are equal, and the “second law of thermodynamics” makes nonequivalence explicit. Thomson, however, sought to apply this nonequivalence to processes themselves, as was the case in mechanics. As with conservation, the degradation of energy was supposed to characterize processes “in themselves.” Nonequivalence was supposed to be “objective” in the sense that it didn’t obligate the physicist to anything in particular, being “dictated” by phenomena. Clausius, for his part, reinvented the Lagrangian tradition transmitted to Carnot by clarifying the requirements and obligations of rational measurement, justified by a state function and, therefore, the power of the = sign. If all energy transformations are not equal, it is because only reversible transformations satisfy the requirements needed to define the appropriate state function. Rational measurement requires the reversible ideal. And — and this is the new factor differentiating mechanics from thermodynamics — it obligated the physicist to be conscious that he was a manipulator, an active participant in the definition of equivalence. The “change of state” measured by Clausius has nothing to do with the spontaneous transformations produced in nature. On the contrary, it implies that all spontaneous “natural” evolutions have been eliminated. Whereas the ideal is defined by the absurdity of a machine whose operation would produce a gratuitous increase of temperature differences, thereby confirming a world in which temperature differences are spontaneously equalized, this leveling off , like any spontaneous change, cannot be described. The description takes as its only objects transformations driven by outside manipulation, pseudo-changes wherein the system is in fact constrained by the  manipulator to transition from one equilibrium state to another that is infinitely near.

If, as Kant claimed, the Copernican revolution marks the point where scientists now ask questions, and subjects phenomena to their categories, there is, in the case of thermodynamics, no profound mystery about such submissions: the Copernican judge needs hands, he has to fabricate, here pilot, the subjected “object.” The reversible transformation is a human artifact and its artificial character has nothing to do with purification (smoothing the inclined plane, polishing the billiard balls, traveling to the Moon, where there is no air) and everything to do with creation.

The second reason has to do with the confrontation for which the “Carnot cycle” will be the arena, and entropy the prize.

… even though entropy may be a generalized state function, conserved through any cycle, ideal or not, its definition does not confer any power on the physicist once the cycle is no longer ideal. More precisely, the only power the physicist can claim is the power to define the sign of uncompensated heat, dQ’ > 0, and this power reflects what everyone knows: that uncompensated heat corresponds to a loss. The reverse case, where compensated heat is negative, would correspond to the “absurdity” of perpetual motion of the second kind, the free increase of temperature differences. But the loss can only be established or evaluated with respect to the ideal cycle, and is not connected to any description, realistic or fictional, of the processes responsible for its production. Therefore, the fact that irreversible energy transformations always result in an increase in entropy is simply another way of saying that they are always defined as a loss with respect to the reversible ideal.

Entropy, then, is a rather strange state function. It appears to subject every transformation to the “rational” logic of state functions, but doesn’t correspond to any definition, or any systematic relationship among measurable variables, this relationship being limited only to those cases where the transformation is reversible.

… the question of the ability to give a positive meaning to the increase in entropy corresponds to the introduction of a new actor, which will now occupy center stage: thermodynamic equilibrium.

… The definition of the state of equilibrium differs profoundly depending on whether we are speaking of mechanics or thermodynamics. The mechanical state of equilibrium is defined by a minimum of potential energy [think of a pendulum], but every dynamic state can also be characterized by a determinate value of that potential energy and no dynamic state is privileged. On the other hand, we cannot generally characterize a given thermodynamic situation by a corresponding value of its thermodynamic potential. Only the extreme case of potential, characterizing the equilibrium state, is defined. Therefore, only the equilibrium state corresponds to a state in the proper sense of the term, namely, one that is characterized, by means of the corresponding potential, in terms of the variables (pressure, temperature, etc.) that define the system. The increase in entropy during an irreversible change toward equilibrium (and more generally the change in thermodynamic potential between nonequilibrium initial state and the final state of equilibrium) can no more be measured than Clausius’s entropy. Only the sign of the change is defined.

… The irreversible increase of entropy no longer represents the fact that natural processes can’t be made dynamically equivalent without manipulation, it is now see as if it were “positively” describing the contrast between those natural processes and dynamic changes.

How are we to understand an “irreversible” change? How should we interpret the increase in entropy? Such questions are, as I hope I have shown, relative to an authentic history rather than the logical development of a problem that would have “resulted” from the first unification of natural processes under the umbrella of the conservation of energy. More specifically, such questions point out what can be called a “capture operation.” As we saw earlier, Engels hoped that the conservation of energy would introduce a crisis into physics, which refused to consider the operation of measurement on which it depended, and would force it to confront the qualitative difference among various forms of “motion.” My comments here have shown if not why, at least how this question as such failed to become a historical subject for physics.

… capture always implies the possibility of “reciprocal capture,” the correlative coinvention of two mutually referring identities. What physicist will the second law give birth to? How will she be able to determine what she requires of the “irreversible processes” to which her practice is now addressed, the kind of processes that force her to confront a dilemma: either she subjects them to thermodynamic measurement, thereby eliminating the irreversibility that singularizes them, or she treats them as irreversible, but can then describe them only from the point of view of the equilibrium state to which they lead under certain conditions. [ ... ] Which of these now divergent values will she advance: realism or a construction that celebrates the singularity of cases wherein description and reason coincide?

My most recent previous post from Stengers’s book is here.

-Julie

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