Wednesday, June 22, 2011

Macrostates and their Microstates: What Do These Represent

The experiential world we live in is structured around the micro- and macrostates. They are so tightly entwined and entangled within each other’s spatial-temporal worlds that we may find it difficult to articulate each of these states individually. Moreover, when observations are made at the micro-level, the states (quantum states) will collapse.  In addition, we tend to use the language of the macrostate to depict conditions/events at the level of the microstate because we lack the epistemic resources for navigating at this level.  Nevertheless, it is important to differentiate between these two states since that can help in understanding how and why certain theories of physics behave the way they do and why certain theories may require further fine-tuning when studied from the specificities of these two states due to issues of contradiction and conflict between the physical laws.

In proposing definitions to macro- and microstates, I argue for greater finesse by dividing the definitions into two parts; the first part represents the most general definition that is true for all cases involving macro- and microstates. For the second part, I will consider the scale in which micro- and macrostates operate in terms of interactions and range.

First, the microstates are the fundamental building blocks of nature, with the macrostates consisting of all these microstates. We can use the ball as an example. The microstates of the ball would be the molecular and chemical properties that make up the ball, while the macrostate is the ball that we can hold and touch. In addition, macrostates are the result of the overall performance of interactions between sets or pairs of particles (hence the averages) rather than of the unique properties of individual particles, even as the inverse is true for microstates (where the particularity of each individual state is taken into account). In other words, the properties and actions of a single particle are important to a microstate but less so to a macrostate.

To go forward with the example, let us now put the ball into action by heating it up.   As the ball is heated, we begin to notice a transformation in the temperature of the ball. Temperature fluctuation is a phenomenon manifested at a macro-level due to micro-level intervention that wrought changes to the macrostate. As the ball is heated, the ball’s molecules begin to vibrate (and, depending on how much heat, the molecules may also begin to move around). The physical movement of the ball’s molecules can cause deformation to the ball’s shape. In addition, depending on the properties of the ball’s molecules, the chemical interactions may also bring about changes such as to the ball’s color and texture. Hence, the examples above illustrate observable macro-level phenomena caused by alterations to physical states at the micro-level of which we have no direct access or apprehension. Of course, there are also quantum-level phenomena caused by micro-level interactions but they are less pertinent to us unless we are manipulating nano-devices, or if we are worried about long-term exposure of electromagnetic or radioactive waves to our biological systems (the possible correlation between cancer and exposure).

As the ball example illustrates, the macrostate operates within an easily observable scale (whether directly through our own senses or via the mediation of instruments that enable us to observe that object), while the microstate is usually within a space that is abstract and requires a certain amount of interpretation before it can be accessed and understood by a human observer. In the ball example, I can connect the macrostate with the everyday movement of objects in our everyday world with how we perceive and measure them.  The ball can also change its chemical composition, which means that there are changes to the microstates. Even if I cannot observe these changes directly, I can infer them from the transformations of the macrostate.  In more extreme examples such as chain reactions leading to the production and decay of sub-atomic particles whenever collisions happen between protons and protons or electrons and electrons in the accelerator ring of a supercollider, intensive processing and validation is required with the aid of sophisticated computerized systems before we can even begin to make sense of what the events mean.

Now let us turn to examples illustrating how macrostates and microstates operate across different ontologies and epistemologies. Ontology here refers to the field(s) of interactions and causalities where physical entities share a common spatial-temporal locality, situatedness and rules of actions. Two cases-in-point would be classical mechanics and quantum mechanics, each representing a different ontology. Classical mechanics consist of kinematical, dynamical and static interactions taking place mainly macroscopically in a measurably deterministic manner, whereas in quantum mechanics, one has to deal with indeterminacy when a measurement is made. Then, we look at epistemology as it connects with the ontological. Epistemology is knowledge construction and structures: it combines theories and laws to explain systems of beliefs, causes-and-effects, and justifications.  In the case of classical mechanics, its epistemic approach is quite dependent on its ontological condition. For example, in classical physics, we use Newton’s theory of gravitation to explain the interaction between celestial objects. Even though there has been a Newtonian approximation to the theory of special relativity and quantum mechanics, the dimension for the length of the waves produced is important for ensuring that the classical approximation continues to hold. 

On the other hand, in the case of quantum mechanics, one is faced with a multiplicity of interpretations such as the more orthodox Copenhagen interpretation that posits classical/quantum duality in its explication of experiment/theory, Bohm’s theory of non-locality, Schrödinger’s theory of wavefunctions and potential, and Born’s statistical matrix. While the ontology of belief does not change, there are different epistemic attempts at explaining the ontology of quantum mechanics.

Macrostates and microstates operate in a continuum of space and time. The macrostates and microstates may possibly exist within or outside the human phenomenal experience and space-time. Notwithstanding the nested relationship between microstates and macrostates, one can generalize by saying that many of the events and interactions taking place at the level of the macrostate represent those of near-direct observability (even if the medium of observations are through various microscopes and telescopes), while many of the events within the microstates are usually not observable without sophisticated mediation (think of computational mediation for collecting data from high-energy particle collisions) or through observable macro-effects stemming from the impact of the microstate on the macrostate (such as the example of the ball).

We may think that we can neatly divide the micro- and macrostates into different epistemological realms based on size, but in fact, here can be no arbitrary determination of size for the macrostate and the microstate. The macro and micro here refer not so much to size (a cell or a water molecule can be considered as much a macro-system as galaxies and planetary systems) but to the sort of interactions they present.  For interactions at the level of the microstate, they can bring about irreversible changes to the intrinsic properties of the body/particle involved. 

However, macro-level interactions, such as kinetic energy exchanges in the ball example, do not usually change the characteristics of the object, which means, for example, that the ball will return to its original condition once it stops bouncing.  Bouncing the ball will not cause its molecules to begin vibrating at a rate greater than its original state.  However, modifications at the level of the microstate can impact the macrostate. If we begin heating up the ball, we will see that the ball begins to change its shape and perhaps even its color (depending on the material used in the construction of the ball).

More importantly, we may never be able to return the ball to its original state. When heat is applied to the ball, it transfers external energy to the molecules of the ball, prompting the molecules to vibrate more rapidly and probably even to begin moving. At the same time, the energy causes reactions to take place within the chemical bonds of the molecules. While all these things are taking place at the level of the microstate, all that is happening can be observed macroscopically (energetic movements of the molecules lead to increase in temperature of the ball, the temperature being a macroscopic phenomenon). If we are able to peer into the space of interactions for the ball’s molecules, we may be able to observe the quantum effects of the molecules, especially their sub-particles such as electrons that decay and leap between different energy levels. As it is, as macro-observers, we are mainly concerned with what we can do at the macro-level.

What if there are inconsistencies in the behavior of the macrostate from that of its microstates? Thermodynamics has grappled with reconciling these seeming inconsistencies. Before the advent of quantum mechanics, macrostates were fundamental to analyzing the group conditions of gas molecules in the state of equilibrium. When we observe gas particles macroscopically, we are concerned with the measurement of averages. One of such measurement is temperature, which I have referred to above as a macro-phenomenon. As we begin to examine temperature from a microsopic angle, we see the particles’ movement within the space of their container. These particles move in random directions towards different corners of their container. Entropy measures the order and disorder within an enclosed system, and in this case, the enclosed system is a container of gas particles. Entropy can either increase (becoming increasingly disordered due to greater movements within the system) or remain constant. The Second Law of Thermodynamics, which accounts for entropy macroscopically, and from which Maxwell’s theory is derived, states that the gas particles will become more disordered over time, and that this change is irreversible.  However, according to Boltzmann’s equations, gas particles are able to flow back in time and are thus reversible. How can we resolve the conflict between Boltzmann’s calculations and the Second Law of Thermodynamics?

What is going on here is that the Boltzmann equation accounts for the microscopic and therefore the individual movements of each gas particle, while Maxwell’s theory is interested only in the initial and end state of the equilibrium. When the Second Law of Thermodynamics was formulated, the broad language of the macrostate was incorporated. The individuality of the particles was not taken into account.  The gas molecules were viewed as statistical averages and it was assumed that the velocities and movements of these molecules would always be uniform. Statistics operating at the macro-level fail to take into account the less-than-uniform movements of the particles.  The inability to deal with the ‘in-between’ state brought on the ‘molecular chaos’ explanation, which meant that certain microscopic ‘ordered’ configurations of the gas particles must be excluded without attempts at understanding the rationale of their behavior. The apparent ‘contradiction’ derived from the limitations of a framework that focuses mainly on the macrostate while ignoring individual variability in the microstates.  The seeming contradiction evaporates once we incorporate the language of the microstate as a part of the analysis of the equilibrium. This was done later through the integration of what is referred to as the H-theorem into the theory of equilibrium.

 I have earlier made reference to how macro- and microstates are nested within each other. A macrostate has a system of multiple microstates that can possibly also become the macrostates of other microstates. A single particle has a distribution of probabilities and wavefunctions to represent a multiplicity of micro-events it is able to produce.  This leads to cases where the contradictions between macro understanding and micro phenomena cannot be so easily reconciled.  An example of this is the double slit experiment; when an electron, which usually acts as a particle, produces an interference diffraction pattern characteristic of waves when it passes through the two-slit (and also even when it passes through only a single-slit, though the pattern will be different) barrier. Another simple example is the atomic model. An atom is a macrostate of sub-atomic microstates such as protons, probably also of neutrons and electrons. However, each of these sub-atomic particles also consists of more sub-particles, which can be demonstrated if we exert an external stimulation that can break the proton, neutron and electron into their sub-constituents. These sub- and sub-sub-atomic particles demonstrate behaviors quite unlike that found in the macroscopic world, such as non-locality (referring to how the actions of particles in different locations are able to effect each other through possibly ‘hidden variables’), which is also often referred to as quantum entanglement (in classical quantum physics, this is explained as the momentum or spin of one particle apparently dictating the momentum or spin of anther particle separated from it, though this case has been complicated in more modern interpretations that query how distant particles are able to communicate), and other quantum weirdness.

Given these radical differences, what do we do with cases where modeling requires us to deal with both classical and quantum ontologies simultaneously? We know that the macrostate is usually situated in classical mechanics and the microstate in quantum mechanics. However, there is an overlap between the classical and quantum areas. An example is a polymer. The bonds between molecules and atoms in a polymer can be easily explained using classical mechanical questions if we look at the macrostate of deformation and elasticity (or brittleness) of the polymer, or even of the kinds of bond that is being formed (i.e. covalent or ionic). However, if we want to begin understanding energy levels in terms of decays and quantum jumps as bonds are made or broken, we have to turn to quantum mechanics. In our model, we will need to find a way seamlessly, as much as possible, to demonstrate how these ontologies connect without needing to compromise on what is to be the dominant ontology (such as privileging one ontology over another just to provide an explication). 

What are the barriers to arriving at such seamless explanations?  As we have observed, the language of the macrostate has often been used to generate our comprehension of the microstates.  This is illustrated by the wave-particle duality paradox. It is important to note that no macroscopic objects can have both these properties at the same time. Yet, we do not have sufficient access to a language that can provide an explanation and resolve what seems to be an internal contradiction. After all, it is possible that when we possess the right epistemic language to address this paradox that the contradiction will evaporate because what we consider to be a paradox arises from partial knowledge and from the incompleteness of an epistemic framework that does not provide sufficient explanation to the ontology we are examining. This is a question that the scientists have to deal with in representing micro- and macrostates across different ontologies but also across different scales requiring different parameters and settings that may be difficult to realize without going into immense complexity. Another barrier is the problem of when and where the ‘agential cut’ can be made, ala-Barad; you do not want to be cutting away a ‘microstate’ because it is too minute, or cutting off a ‘macrostate’ that seems too distant and unimaginable. In the case of data selection in the Large Hadron Collider (LHC), how can you ensure that the selection of data (through ‘cuts’ made to select the raw data one wants to validate) does not cut us out from discovering micro- and macrostate of a new physics? This is a question that will probably have no definitive answer. Nevertheless, this does not mean that we cannot try to build tools and apparatuses that can help us better deal with the actual difficulties faced.

Viewed from another perspective, the “barriers” may be opportunities to realize what Donna Haraway calls the privilege of partial perspective.  Macro- and microstates neither hold nor represent universal perspectives within their situatedness because their perspectives and actions are limited by the ontologies from which they sprang. Haraway discusses feminist objectivity as being location-dependent, a form of situated knowledge. The notion of situated knowledge applies as much to macro- and microstates as to feminist science because these two seemingly disparate positions (one on feminist science and the other on the properties of physical states) operate on the premise that what is real is determined by the observers of these two positions. The hermeneutics of the real is represented by the observer’s perspective but the perspective must be partial because human observers can only be privy to that which is within their timeline and scale of perception/observability. Moreover, even for interactions taking place outside our immediate sense-perception or between different time scales, whatever the apparatuses used to detect and record their actions and behavior will never be able to capture every detail of the event.

Therefore, there is no real way, for now, to reconcile the differences between ontological scales. To segue into the cultural and the social, if our perspectives are partial, our conception of reality and ethics in these contexts can only be partial. In addition, the language that we use to talk about our reality is shaped by our macroscopic reality (the reality with which we have direct interest and contact). We lack the language to discuss a reality we cannot perceive except to provide comparative instances from a reality based on what we can more easily articulate. This means the reality of the microstate, which takes place outside our sense-perception, is apprehended through the language of the macrostate and possibly an ontology that may be alien to the microstate, hence bringing about seeming paradoxes and inconsistencies. What we need is an ontology that exists outside material solipsism. We may want to begin thinking about the possibility of creating an environment by which we can create a thought-experiment that does not hinge on the limitations of our verbal capacity or materiality to describe a process alien to our every-day experience. What we need to do is to create equivalences to the experience of peering into the box where Schrödinger’s cat resides or tracking exactly where that sub-atomic particle lands when it goes through one of the slits so that we can unveil the indeterminacy that accompanies the discussion of microstates.

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