Absolutes vs. relatives

Though my advisor has stressed this for the entirety of my grad school career, I today finally appreciated the significance of relative measurements over absolute ones.

An absolute measurement is one in which a value is extracted from a data set that is physically important in a particular model. A relative measurement, on the other hand, is one that extracts the effect of varying a parameter amongst two or more data sets.

Model specific parameters are obtained from absolute measurements. Curve fitting is usually performed to find the values of parameters. Alternatively, relative measurements establish relationships between two variables. For example, the reading on a scale will increase proportionally with the mass added on top of it. From this observation, one can infer that weight is linear with mass. A constant, namely the acceleration of a particle due to gravity at the earth's surface, is needed to obtain the absolute value of the weight from a single measurement.

The practical problem with absolute measurements is that they require certain standards to have any significance. At the start of graduate school, I would often puzzle over why a parameter from a curve fitting routine would so often differ from theory. I would often vary different parameters in my calculation and struggle in vain to determine which independent quantity I had measured "wrongly." However, I failed to realize that each measurement was against some standard. A time is measured relative to an internal clock in a circuit; a length is measured relative to a ruler; mass is measured relative to a scale which was calibrated relative to some mass standard.

From the above it seems that the nature of measurement itself is a relative process, and as such a measurement can not be "wrong." If standards differ between two measurements, the measured variable will differ as well. And no one can say which measurement produced the "correct" value. Both conclusions are correct so long as they are logically consistent with how they are derived from the measurement.

I am aware of the definitions of the second and other fundamental quantities, but the definitions are simply agreed to based upon the precision of the measurement that produced the standard. They are arbitrary.

If I have to assert anything from this, it is that I value relative measurements above absolute measurements in scientific papers. Relative measurements reveal physical truths where as absolute ones tell us how well data fit into some theory.

I hope to write more on this in the future once my thoughts have more fully materialized.

A physical standard for time

I've now completed Chapter 2 of Cook's "The Observational Foundations of Physics," my current lunchtime reading. In this chapter, Cook describes a thought experiment in which a beam of caesium atoms is polarized by a strong magnetic field, then enters a region where a strong RF field is applied. Following the RF region, the beam passes through another magnetic field such that atoms whose magnetic dipole moments are not flipped by the RF field are deflected into a beam block. Those atoms that do undergo an electronic transition that is accompanied by a flip of the magnetic dipole moment reach a detector that reports the intensity of the beam. A feedback mechanism adjusts the frequency of the RF field so that the beam intensity at the detector is maximized; in this way, a quantum standard of time is established through the frequency of the RF field that maximizes the atomic beam intensity (you may note the similarity to the Stern-Gerlach appartus).

Cook then proceeds to argue for his thesis, namely that the experiments and observations that are available to us dictate the form of our physical theories. He starts first with the theory. The time-evolution of the caesium atoms is described by the Schroedinger equation. This equation contains a first order time derivative which is a consequence of the wavefunction containing all information about the system at any one point in time. If only one initial condition is required to establish the wavefunction, then it must be first order in time (this is in contrast to the wave equation which is second order in time and whose solution requires an initial condition on the wavefunction and its derivative).

Cook next mathematically defines the operations of the experiment described above, postulating that the two magnetic states of the atoms are described by stationary states of a wavefunction. Using only mathematical arguments derived from the nature of the experiment, he obtains the form of the equations governing the time evolution of the system; the wavefunction is affected by a first order time derivative. This suggests that how we perform experiments determines the form of our theories. The time standard need not be quantum in nature as he repeats the argument for a classical, mechanical oscillator. Again he stresses that once the time standard is set, it is meaningless to ask whether or not its period remains invariant with time, since the standard defines time itself. It is recognized that differences between the same apparatus for establishing the standard exist when the apparatus are spatially separated due to the geometry of spacetime.

These are some of the thoughts I had while reading this chapter:

1. Many times physical theories are developed first and then experiments follow that verify their predictions. Does this fact weaken Cook's argument that experiments shape our theories? If the purpose of theory is to predict experimental outcomes, then why argue for the reverse? Which came first, the chicken or the egg?
2. Cook was careful to explain that his arguments are based on a physical world that is independent of a subjective observer. Still, I wonder how the human perception of time can be reconciled with these arguments. As stated earlier, it makes no sense to ask whether or not the time standard is invariant within the context of observation and theory. But a human can perceive large changes in the period of a slow mechanical oscillator. What is it that acts as an internal time standard for a subjective observer and can it be related to the physical standard?
3. Cook only obtains the form of the equations of motion for the systems he describes. On the other hand, the theories give meaning to his unspecified parameters, such as energy and the unit of electronic charge. What determines how these mental concepts are developed? Energy is a relatively easy concept to understand. Was this why the fathers of thermodynamics used it as a core concept in physics as opposed to some other mental construct?

Creativity in academia

I recently read this very interesting article that is a followup to the author's original book "Hackers," a look into the subculture of the computer geeks who laid the foundation for today's computer-based society. Two of the common qualities of these influential tech giants is their obsessive drive for quality and their playful creativity. Indeed, many modern companies, such as Google, go to great lengths to foster creativity in their employees by giving them freedom and resources to work on side projects and time to think about new products. The idea, I think, is to keep employees' minds fresh and slightly unfocused so that inspiration strikes more often to the company's benefit.

A similar and equally interesting article came out recently on Talking Philosophy's blog in which the author, Benjamin S. Nelson, discusses the creative process itself in relation to a man, John Kanzius, who invented a radio frequency generator to both attack cancer cells and split water molecules (awesome!). Philosophers, starting with Poincare, have broken the creative process into four successive steps: preparation, incubation, illumination, and verification. I will take these steps to be self-evident in their meaning, but I only wish to note that I believe that creative environments strive to improve the preparation and incubation steps so that illumination happens more often and with better results.

This being said, I wonder now why such environments are not fostered in academia. Graduate students are frequently overburdened with many menial tasks such as grading papers and acting as teaching assistants, attending class, writing portions of grant reports, attending frequent group meetings, and staying up-to-date on the relevant literature. Add to this exercise, chores, and hope for a meaningful social life and one can quickly see that this lifestyle does not support creative solutions to research problems. In no way are these other tasks without benefits, but if the resources of the mind are constantly employed for a menagerie of many simple duties, then what room is there to allow ideas to incubate in their minds?


I think academia could really benefit from adopting some of the creative strategies that many companies now use to better the quality of their products. What do you think?

Note: In college there was a video that was often shown in our engineering business classes from some evening tabloid (Dateline or something similar) which followed a company's process for developing a new and improved shopping cart. I can't remember the name of the show or the company, but it is highly relevant here. Does anyone know what I'm talking about?

 Update: Found part of the video: http://www.youtube.com/watch?v=M66ZU2PCIcM. The company's name is IDEO and focus on innovative designs. Their take on the creative process is very characteristic of the stance that some new companies are taking.

Let's be clear about what I mean

In Section 1.5 of "The Observational Foundations of Physics," Cook poses this question:

Why is it that mathematics appears as almost essential to physics, is it because the world is made that way, a notion that goes back to the Pythagoreans, or is it because we choose to study those aspects of the world that can be put into mathematical form... or do we bend the world to make it conform to our mathematics?

I'm not so sure that these questions can be answered by investigating the relationship between mathematics and observations as Cook proposes. Rather, the questions seem best dealt with in terms of language and meaning. What does Cook really mean when he asks whether or not the world was "made" to be mathematical? What are the "aspects" of the world that we study; are they objects or ideas? In what way do we "bend" the world?

I think Cook (and myself) may be constrained by the language in which the questions are posed. If that is the case, then it seems reasonable to assert that language plays a significant role in the formation of scientific hypotheses and consequently in science itself.

Notes from "The Observational Foundations of Physics"

Section 1.3, Measurements and Standards, is a continuation of the setup for the arguments for Cook's thesis on how measurement affects the logical structure of physics. First, Cook states that the equations of physics are simply relationships between physical states or quantities. These relationships are congruent to the relationships between observations. I am a bit unclear as to what congruent means here, but aside from that the setup so far seems fairly obvious.

He continues onto a more lengthy discussion of the role that standards play in measurement. Every measurement consists of comparing some quantity to a standard quantity. When measuring the length of an object, for example, one simply compares the object's length to the length of a ruler (the standard). Our system of standards plays a significant role in shaping the nature of physical theories.

What was very surprising is that, traditionally, standards for all physical measurements can be derived from four independent standards: length, mass, time, and current. These standards have since been replaced by other physical constants and quantities, but the number of independent standards has remained the same. For example, length is measured as a ratio between the speed of light in free space to a unit of time, which is derived from a standard of frequency from a certain atomic process.

The standard of voltage comes from the standard of frequency and the Josephson effect with help from another fundamental constant, the ratio of Planck's constant to the unit of electronic charge. Mass currently (as of the book's publishing) escapes a relation to the standard of frequency, but it's conceivable that it could be related to energy, voltage, and current through the quantum Hall effect.

The shift from mechanical standards to electronic and quantum standards has greatly increased the precision with which we can measure physical quantities. It has also changed the nature of our physical theories, Cook claims.

Lunchtime reading: The Observational Foundations of Physics

I have started reading "The Observational Foundations of Physics" by Sir Allan Cook during my lunch breaks. The book's purpose, as Cook states in the first sentence of Section 1.1, "is to attempt to unravel some ways in which the practice of physics determines the form and content of physics and physical theory." In other words, Cook wishes to understand how the practices found in physics affect physical theories and the practices themselves. It is as if there existed a feedback loop such that performing experiments changed not simply the theory used to describe a phenomenon but the nature of theory itself.

Further in Section 1.1, he poses these questions that are central to his analysis:

1. "Why should physics be so effective, and what does that tell us about the world of physics and our ways of gaining knowledge of it?"
2. "Is there a real world that exists independently of whether I or anyone else is looking at it, or are all the ideas I have about a world external to me just the construction of my mind?"

He defers a thorough answer to the second question until the end of the book, but does offer that he believes that most physicists, while working at the bench or on a computer, act as if an external world existed independent of their attention.

Section 1.2 deals with observations and sets many of the premises of his arguments. Observation and experiment are decided to be equivalent. Observations also consist of two aspects: objective and subjective. Of the subjective aspect, only the communal nature of observation is of consequence to his arguments. Science is a social construct and scientists hold great influence over each other such that the act of observation is never truly independent of people other than the experimenter.

Cook goes to some length to explain that physics is empirical, "with observation primary and theory secondary," but he concedes that rarely can observation be performed without some theory underlying the act of observing. He gives the example of reading a voltage from a digital multimeter. The direct observation is of figures on a LCD readout, a consequence of numerous electronic circuits that respond to potential differences between two probes and relates to the potential energy difference of electrons between two points in a circuit. Of course, electrons are theoretical constructs. The theories underlying an observation can in some ways assure an experimenter that the results are telling us something of the real world and not subject to some extraneous errors or misinterpretations. For simplicity, an observation is defined as the operations that lead to a measurement and result in  "raw data." The data is considered "raw" regardless of the complexity of the measurement.

Finally, theories are models of observations, not a model of the real world itself. "I take a theory to be a mathematical realisation of an abstract system that has properties corresponding to those of a set of observations... It is in that sense that I take a theory to be a model of the world of observations, with the implication that there is a more fundamental correspondence than just giving the right answers..." Theory is an abstraction of the real world, not vice versa.

Consistency vs. Accuracy

Here's an interesting footnote from Chap. 3 of Goodman's Introduction to Fourier Optics:

"The fact that one theory is consistent and the other is not does not necessarily mean that the former is more accurate than the latter."

The footnote is in reference to the Kirchhoff diffraction integral which was derived under two inconsistent assumptions for the boundary conditions on the field. Despite these inconsistencies, the theory gives a very good prediction for the diffracted field far from a large aperture.

Kirchhoff's theory is also a good demonstration of the fact that mathematical consistency and exactness does not mean that a theory makes good predictions or can be used to calculate physical quantities. Experimentation must validate a theory's ability to do so.