Wednesday, October 20, 2010

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?

Wednesday, October 13, 2010

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: 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.

Friday, October 8, 2010

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.

Wednesday, October 6, 2010

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.