# Physics 102-002 The Basic Facts and Ideas of the Sciences

Spring 2005 Mondays and Wednesdays from 16:00 to 17:15 in room 103 of Regener Hall.
My e-mail address is cahill@unm.edu. My office is room 176, and my phone number is 277-5318.
My office hours are by appointment. But in fact whenever you see me, I am available for questions about this course.

This course will introduce students of physics to the more important facts, methods, and ideas of astronomy, cosmology, physics, chemistry, biology, molecular biology, and biophysics. It will consist mainly of lectures and demonstrations. Students are required to read three superb paperback books:

The First Three Minutes by Steven Weinberg (Amazon),
Six Easy Pieces by Richard Feynman (Amazon), and
The New World of Mr Tompkins by George Gamow, Russell Stannard, and Michael Edwards (Amazon).

No prior knowledge of mathematics or of any science will be assumed.

A syllabus is available as the pdf file, syllabus.

### Basic facts about the known universe:

There are hundreds of billions of stars in a typical galaxy, like our galaxy, the Milky Way. The largest galaxies contain more than a trillion stars. Small galaxies, called "dwarf galaxies," contain as few as a million stars. There are hundreds of billions of galaxies in the known universe. So if there are 1011 galaxies and an ordinary galaxy has 1011 stars, then there must be something like 1022 stars in the known universe. Our sun is an average star.

### The Sun

An average star, like our sun, burns hydrogen forming helium. This burning is a fusion process and it takes place in the central third of the star at a temperature of about 15 million degrees Kelvin (0 K or absolute zero is -273 Celsius, so the two temperature scales are effectively the same at high temperatures). Since one degree Kelvin is one degree Celsius is 9/5 = 1.8 degrees Fahrenheit, the center of the sun is about 27 million degrees F.

### Why the Sun Shines

The net reaction that liberates energy in an average star is that four protons and four electrons (that is, four hydrogen atoms) turns into two protons and two neutrons and two electrons and two neutrinos, in such a way that the two protons and the two neutrons are tightly bound together into a helium nucleus (also called an alpha particle). If the two protons and the two neutrons did not form a nucleus of helium, this reaction would soak up rather than liberate energy. Instead, the mass of a helium atom is 6.644 × 10-27kilograms, while the mass of four hydrogen atoms is 6.908 × 10-27kilograms. The difference is 0.0468 × 10-27kilograms or 4.68 × 10-29kilograms. Since the speed of light c = 3 × 108 meters per second, Einstein's formula, E = mc2, gives for the energy released the value 4.68 × 10-29kg × (3 × 108 m/s)2 = 42.12 × 10-13Joules or 4.212 × 10-12J in mks units. Now one Joule = 6.2415 × 1018 electron Volts, so the burning of four H atoms releases 4.212 × 10-12 × 6.2415 × 1018 eV = 26.3 × 106 eV or 26.3 MeV. That's a lot of energy from only four atoms. In fact, the burning of the hydrogen atoms in 100 drops of water would produce enough energy to light a 40 Watt bulb for a century.

In 1938, Hans Bethe explained the detailed nuclear reactions that occur in a star like our Sun when hydrogen is burned to helium, work for which he won the Nobel prize in 1967. He died on March 6th of 2005 at the age of 98. During WWII, Bethe first worked on radar at MIT and then on the atomic bomb; he lead the theoretical group at Los Alamos. After the war, he argued that hydrogen bombs should not be built. He lost that argument. With Linus Pauling, Bethe argued that nuclear weapons should not be tested in the atmosphere. They won that argument when the Limited Test Ban Treaty was passed in 1963 during the Kennedy administration. Bethe has long argued that the number of nuclear weapons possessed by Russia, China, and other states should be fewer than a few hundred per state. Current nuclear arsenals are in the thousands. Bethe has been a firm supporter of the use of nuclear power for the generation of electricity.

### The Early Universe and the Big Bang

Some 14 billion (14,000,000,000 = 1.4 × 1010) years ago, the universe was much hotter than the center of the sun, which is about 15 million degrees K. The universe has been expanding and cooling since this Big Bang.

### Inflation

In the first instants after the Big Bang, space is believed to have expanded rapidly in one or more very brief intervals. This superluminal expansion is called inflation. Unlike evolution, inflation is a theory. But its consequences seems to be true.

Inflation would have made space flat. (Imagine rapidly blowing an enormous amount of air into an unbreakable, infinitely expandable balloon. The surface of the balloon would expand and become flat.) This consequence of inflation seems to be verified by recent experiments.

If the whole known universe inflated from a very tiny sphere that was in thermal equilibrium, then the whole known universe now should be homogeneous on very large scales and should look the same in all directions, should be isotropic. These consequences of inflation also seem to be verified by recent experiments.

### The First Three Minutes

After inflation, the universe cooled and continued to expand. It was a very hot plasma of all kinds of particles and antiparticles in thermal equilibrium. After about three minutes, most of the particles and antiparticles that could annihilate into photons had done so, leaving a small residue of protons, neutrons, and electrons and lots of photons and neutrinos and particles that cannot annihilate into photons. The protons, neutrons, and electrons later became gas, stars, dust, and galaxies. The particles that could not annihilate into photons do not interact with light; they constitute an unknown form of matter called "dark matter," which cannot be photographed because it does not interact with light. There were about 2 billion photons and a similar number of neutrinos for each proton and each neutron. But the charge of the universe is believed to be relatively small, so there were almost exactly as many protons as electrons. This hot ionized plasma of protons and electrons interacting with high-energy photons was a very radioactive environment. No structures made of protons, neutrons, and electrons was able to survive until about 230 seconds after the Big Bang, when the temperature dropped below 109 K.

Deuterium is an isotope of hydrogen consisting of one proton loosely bound to one neutron. When the temperature had dropped below 109 K, deuterium could survive long enough to absorb a neutron and another proton becoming a tightly bound nucleus with two protons and two neutrons -- a nucleus of helium. Almost all the neutrons and deuterium were quickly cooked into helium nuclei.

So after about 240 seconds, the universe was a hot plasma consisting mostly of ionized hydrogen (3/4) and helium (1/4), electrons, photons, neutrinos (and anti-neutrinos), and mysterious particles of dark matter.

### Dark Matter and Dark Energy

Paradoxically, most of the matter of the universe, both then and now, is in unknown forms called "dark matter," because they do not interact with light. And most of the energy of the universe is in an unknown form called "dark energy." Recent experiments indicate that the matter we know about is only 4% of the energy density of the universe. Dark matter is about 29%, and dark energy is about 67%.

### Transparency

After about four-hundred thousand years, the temperature of the universe had dropped to around 6,000 K. At this temperature, only about one photon in 2 billion had enough energy (13.6 eV) to ionize a hydrogen atom. Since there are about 2 billion photons per proton, hydrogen atoms and helium atoms are stable at temperatures lower than about 6000 K. So 400,000 years after the big bang, the electrons fell into stable orbits about the protons, forming hydrogen atoms, and about the alpha-particles, forming helium atoms. Since low-energy photons interact much less with neutral atoms than with free electrons and ions, the universe suddenly became transparent to light at about 400,000 years after the big bang.

Most of the photons of the universe have not been scattered since the onset of transparency. But with the expansion of the universe, the wave-lengths of these photons have been stretched from hundreds of nanometers to a few millimeters. These photons have been red-shifted from visible-light photons to microwave photons, which are 4,000 times less energetic. This radiation is the same as that inside a closed box whose walls are at a temperature of 2.725 K. It appears as radio noise on sensitive antennas, and was first identified in 1963.

Astronomers call transparency "recombination" as though there had been atoms earlier, before the Big Bang. (Recombination is a moronic term which the astronomers should have dropped.)

### The Red Shift

The universe continues to expand. Its present rate of expansion is about 72 kilometers per second (km/s) per megaparsec (Mpc). A megaparsec is about 3.1 million light years. (It is a moronic unit which the astronomers should have dropped a century ago.) So two stars separated by 3.1 million light years are moving away from each other by about 72 kilometers per second, but a megaparsec is too short a distance for the expansion of the universe to dominate random local velocities. So it would be better to say that two galaxies separated by 3.1 billion light years are moving apart at the rate of 72,000 kilometers per second. The Hubble parameter H0 is now about 72 km/s/Mpc. H0 was decreasing over the first 10 billion years, but it has been increasing over the past 4 billion years due to the dark energy. It is not a constant, and so "Hubble constant" is another moronic term which the astronomers should have dropped.

### Hubble Photos

Astronomers have used the Hubble Space Telescope to make images of many distant You may view images made by the Hubble Space Telescope by going to this archive.

Observations suggest that the energy density of the universe is very nearly critical, that is, just enough to keep the universe from collapsing. Atoms and the other kinds of matter and energy we know about account for only 4% of this critical energy density. Some 29% is due to "dark matter." Nobody knows what dark matter is. Very recently, however, some English astronomers seem to have discovered the first dark-matter galaxy, which they reported in the article article. The main component of the critical energy density is "dark energy." Nobody knows what this is either.

### The Mid-Term Exam

The scores on the mid-term exam ran from 40% to 90%. To find your score, multiply the number of questions you got right by 5. The grades on the mid-term are 90% = A+, 85% = A, 80% = A-, 75% = B+, 70% = B, 65% = B-, 60% = C+, 55% = C, 45% = C-, and 40% = C-.