Divine Numbers By William Lama, Ph.D
University of Houston Constants of Nature (uh.edu)
Pythagoras, the Greek philosopher born around 580BC, made important contributions in mathematics, astronomy and the theory of music. He believed that everything could be explained by numbers, and he tried explain the universe through numerology. Pythagoras had some funny ideas, thinking that numbers were male or female, ugly or beautiful, or had a special meaning. Pythagoras (maths.org)
In these “postmodern” times people have become fascinated with “angel numbers.” It is believed that “angel numbers are messages from the spiritual universe that offer insight, wisdom and directionality.” A Guide to Angel Numbers and What They Mean
As a physicist I have always had an interest in and appreciation of numbers.
Max Planck’s Constant
When Max Planck was a student his professor Albert Michelson advised against a career in physics. Michelson captured the widely held view circa 1875: “The most 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.”
Fortunately for science, Planck followed his passion. Planck’s primary contribution was his discovery of the discreteness of energy, its so-called quantum nature. From Planck’s analysis of the visible spectral glow of hot objects he derived a fundamental constant “h” that determines the smallest amount by which energy could change, and came to be called Planck’s constant. When you hear about a “quantum jump” you should think small, since “h” is infinitesimal:
h = 0.00000000000000000000000000000000067 meters squared- kg/sec
Over time h was seen to play a fundamental role in all of quantum physics. For instance, Einstein showed that the “photelectric effect” could be explained if the energy E of a light wave was related to its frequency f by the same Planck constant h:
E = hf
Later Heisenberg showed that there are inherent uncertainties of measured quantities (say energy ΔE and time Δt) given by his “Uncertainty Principle”
ΔE Δt > h/4π
Quantum theory applies to the microscopic domain of nuclei, atoms and molecules. One decides whether the quantum properties of a system are important by calculating the quantum wavelength of the system,
wavelength = h/mv,
where m is the mass of the system and v its speed. My Westie Charlie weighs 22 pounds (m = 10 Kg) and his top speed is about 15 mph (v = 7 m/sec). Since h is so very small Charlie’s quantum wavelength is tiny compared to his size.
Charlie is a classical dog.
How to Teach Quantum Physics to Your Dog: Orzel, Chad: Amazon.com: Books
On the other hand, an electron moving at the speed of light has a quantum wavelength a billion times as large as the electron’s size. The electron is surely a quantum particle, that sometimes acts like a wave.
Planck Scale
Max Planck’s conception of nature emphasized a supreme rationality, demonstrating a “creative intelligence.” Planck believed that the fundamental constants of nature possessed specially “designed” values and hoped to understand the meaning of those special values.
Planck set out to combine a set of fundamental constants of nature to create universal measures of mass, length and time. He used the universal gravitational constant G, the constant speed of light c, and his quantum constant h. By combining these constants in various ratios and powers he defined fundamental units of mass (M), length (L), and time (T).
M = 0.00005 gm (about the mass of a small grain of sand)
L = 10^(-35) meter (0.00000000000000000000000000000000001)
T = 10^(-43) second (0.42zeros then 1)
Because these are derived from universal constants (G, c, h) they will have the same values wherever or whenever they are measured. They are universal constants.
Theoretical Physics - What is Planck Scale?
But do they mean anything?
The Big Bang theory says that at the instant T the mini-micro universe of radius L was expanding at the rate L/T = c, the speed of light. The quantum wavelength h/Mc was equal to the Planck length (L), and the mass was the Planck Mass M = h/Lc.
The Planck scale values have a profound meaning, defining the universe when quantum uncertainty was entangled with gravity, and the long sought “Grand Unified Theory” is required to understand what was happening. Remarkable!
It’s fitting that the Planck Satellite is busy measuring the cool afterglow of the Big Bang some 13.8 billion years later.
Planck Satellite: European Space Agency/NASA/JPL-Caltech
Just Six Numbers
Astronomer Martin Rees describes the six “dimensionless” constants, whose values are fundamental to physical theory, life and the structure of the universe.
Let’s look at one of these magical numbers. Nuclear fusion provides the Sun’s energy. In the conversion of hydrogen into helium the fusing of two protons and two neutrons creates one helium nucleus.
2p + 2n >>> He
The helium nucleus mass is 99.3% as much as the two protons and two neutrons; the remaining 0.7% is released as heat. This number, ε = 0.007, determines how long stars can live and whether they can support life on planets like ours.
Fine Tuning the Universe
ε is exceedingly “fine-tuned.” If ε were 0.006 rather than 0.007, the nuclear “glue” would be weaker, so that a proton could not be bonded to a neutron and the path to helium formation would be closed. We would have a really simple universe composed of hydrogen alone. On the other hand, if ε = 0.008, then two protons would have been able to bind together in the early universe. No hydrogen would remain to provide the fuel in stars.
Any universe with complex chemistry requires 0.006 < ε < 0.008.
Astronomer Fred Hoyle showed that a shift of ε by only 4% would severely deplete the amount of carbon that could be made. Hoyle argued, therefore, that our existence would have been jeopardized unless 0.00672 < ε < 0.00728. Fine tuning indeed.
Dr. William Lama has a PhD in physics from the University of Rochester. Taught physics in college and worked at Xerox as a principle scientist and engineering manager. Upon retiring, joined the PVIC docents; served on the board of the RPV Council of Home Owners Associations; served as a PV Library trustee for eight years; served on the PV school district Measure M oversight committee; was president of the Malaga Cove Homeowner's Association. Writes about science, technology and politics, mostly for his friends.
email: wlama2605@gmail.com
