God's Constants

When Max Planck was a young, precocious student circa 1875 his professor advised against a career in physics. Albert Michelson captured the widely held view that: “The more important fundamental laws and facts of physical science have all been discovered, and these are now so firmly established that the possibility of their ever being supplanted in consequence of new discoveries is remote.”

Michelson was referring of course to the physics of Newton, Maxwell and the ether that was supposed to pervade all space (and provide a mechanism for the measurement of absolute velocity). Fortunately for science, Michelson’s experiment (with Morley) helped Einstein banish the ether, and Planck followed his heart to help found the quantum universe.

Planck’s contributions centered around his discovery of the discreteness of energy, its so-called quantum nature, that he used to explain the thermal spectrum of radiating bodies. From Planck’s theory arose a fundamental constant “h” that determined the smallest amount by which energy could change and came to be called Planck’s constant. Over time h was seen to play a fundamental role in all of quantum physics. For instance, the Pauli “Uncertainty Principle” stated that the inherent uncertainties of measured quantities (eg energy and time) are determined by Planck’s constant.

Planck was a deeply religious man and greatly admired by younger physicists including Einstein and Bohr. His conception of nature placed great emphasis on its rationality that, he believed, demonstrated a creative intelligence. He thought that the fundamental constants of nature possessed specially designed values and sought to understand their underlying meaning.

Planck sought to combine the set of fundamental constants of nature to create universal measures of mass, length, time and temperature. He used the universal gravitational constant G, the constant speed of light c, Boltzmann’s constant k that relates kinetic energy to temperature and his own quantum constant h. By combining these four constants in various ratios, powers and square roots he defined the fundamental units of mass (M), length (L), time (t) and temperature (T). Due to the limitations of Blogger, I will not express these constants in terms of (G, c, k, h) but rather just give their numerical values. The interested reader is encouraged to look at the book The Constants of Nature by John Barrow. Another Blogger deficiency forces me to express exponents like this: 10(-3) means 0.001 and 10(+43) = 1 followed by 43 zeros. Thus Planck derived the following universal values:

M ~ 5 x 10(-5) gram = .00005 gram, about the mass of a small grain of sand

L ~ 10(-33) centimeter very small, even compared to an atomic nucleus 10(-13)

t ~ 10(-43) second, a REALLY SHORT time, and

T ~ 10(+32) degrees Kelvin, REALLY HOT

Because these are derived only from universal constants (G, c, k, h) they will have the same values wherever or whenever they are measured. They are universal constants.

But do they mean anything? Why are L and t so very small and T so very large? And a more fundamental question was the presence of G and h in each of the definitions. Gravity as described precisely by Einstein’s General Theory of Relativity applies to cases where the masses are large such as bowling balls, solar systems or galaxies. By contrast, quantum mechanics applies to the tiny domains of nuclei, atoms and molecules. The way to decide whether quantum properties are important is to calculate the quantum wavelength of the system from the ratio of h to the momentum of the system:

wavelength = h/mv, where m is the mass of the system and v it’s speed.

For the bowling ball rolling down the lane, the mass is so large and h so small that the wavelength is infinitesimal compared to the size of the bowling ball. Thus quantum effects are negligible.

This wide berth between the domains of gravity and quantum effects is fortunate since we still have no theory that combines both effects. (Einstein was searching for such a unified theory until he died and some particle physicists have proposed a way of constructing such a “theory of everything.”)

We do know, however, when and where such a quantum theory of gravity is necessary. Immediately after the Big Bang, the micro-universe was so hot that it was expanding at the speed of light and creating mass from energy at a furious rate. If we look at the universe when it contained the Planck mass (M), we find that the quantum wavelength of the universe then equals the Planck length (L), the age of the universe is the Planck time (t) and the temperature equals the Planck temperature (T).

Planck’s fundamental constants have a profound meaning, defining the universe when quantum effects and gravity were both so important that a unified theory is required to understand what was happening. Remarkable!