Chapter 14: The Universe According to Quantum Theory. Our treatment of quantum theory continues in this chapter. In chapter 13 we confronted the mystery of wave-particle duality. But quantum theory's mysteries go well beyond this! Yet, while it is so mysterious, it works incredibly well! And furthermore, no experiment has ever conflicted with it. Most physicists hope that someday something will contradict it and a whole new theory will need to be constructed. (New theories have been constructed but all have been discarded.) We will look at three of the mysteries: Uncertainty, Quantum Jumps, and Nonlocality. The last is probably the most mysterious!

Sect. 14.1: Brief respite from QM: Spectra. Solids give continuous spectra (like rainbow) -- spectroscope. But excited (heat, collisions with projectiles like electrons) dilute gases give line spectra -- fingerprints of the elements. Early clue that atom was composite. Enabled constitution of stars! In 1913 Bohr constructed the planetary model of atom. Correctly predicted hydrogen spectrum. Introduced discrete energy levels for atoms, and quantum jumps. But Bohr theory failed with more complex atomic spectra. Schroedinger theory of psi-wave works fine for all atoms, and molecules as well..

Sect. 14.3: In 1927 Heisenberg published his uncertainty principle (indeterminacy is a better word). It is a mathematically rigorous deduction from Schroedinger's Equation. We cant derive it here, or even state it in full rigor, but qualitatively, it says that an accurate measurement of a particles position prohibits an accurate measurement of its speed, and vice versa.

Whenever make a measurement there is some inaccuracy. Suppose measure the position of a particle and get x (1-dimension). But ruler not perfect -- finite spaces between marks. In QM there is in addition that particle is described statistically. So must make several measurements and get average x. The uncertainty in x is a measure of the limits of knowledge of the position. Denote delta-x. Similarly if measure speed s there will be an uncertainty delta-s. Classically these could be made as small as possible, but not in QM: Heisenberg's uncertainty principle says delta-x times delta-s is approximately h/m. So the more precisely we know position x, the less precisely know speed s. Realm of possibilities. Bigger masses have smaller realms, i.e. can measure both more accurately. NOTE: death-knell for idea of mechanical clockwork universe, for to predict future need know precisely those two quantities for all particles. Idea of orbit or trajectory not possible! Example of Heisenberg's microscope.

Ex: electron in atom: delta-x is about 10^-8 m. Get delta-s about 7.2 x 10^4 m/s or about c/4000. But when try to confine to nucleus get much too high (need relativistic QM). Note typical speed likely to be about same size as delta-s. Neutrons are OK..

Why is delta-x times delta- s about h/m? Particle localized in position needs psi-wave packet. Construct by superimposing many different psi-waves with different speeds. More tight packet in position requires bigger spread in speeds. (Theorem of Fourier analysis).

Sect. 14.4&5: Quantum jumps are the instantaneous change in the psi-wave. We saw them in connection with spectra: the psi-wave of an electron in an excited level jumps to that of a lower level when a photon is emitted. It also happens in connection with the double slit: when the psi-wave arrives at the screen, it jumps to the psi-wave of a particle at the point of detection; also when one tries to determine which slit a particle goes through, the psi-wave jumps from that of a wave interference to that of a non-interference particle pattern. Schroedinger in particular hated this aspect of QM (quote, page 363).

The statistical nature of QM led Einstein to feel that QM, while spectacularly successful, must be incomplete. He carried on a debate primarily with Born and Bohr for decades! In 1935 Einstein, Podolsky and Rosen published the famous EPR paper. In it they gave a thought experiment which attempted to show that QM was incomplete. They showed that by looking a two-particle correlations, they could in principle measure both the position and speed of one particle, without disturbing it, by examining the other particle. Thus both the position and speed of a particle had real existence but could not be described by QM! But the experiment could not actually be done so the discussion remained philosophical. Einstein believed that there must be hidden variables (HVs) -- properties of electrons or photons as yet unknown that determine where they will go in a double-slit expt. QM makes only statistical predictions because it doesn't include these HVs. In the 1950s David Bohm devised a simpler experiment than EPR and it was hoped it could be done. If successful, it could decide whether HVs existed. In 1964, John Stewart Bell published a theorem (Bell's Interconnected Principle) based on Bohm's ideas on a clear way to test a wide variety of HV theories. Bell made only two basic assumptions (both of which EPR would have insisted upon): 1. objective reality, i.e. there exists a world outside of us whose properties are independent of our observations, and 2. locality, i.e. it is possible to do an experiment here, which will not be influenced by what happens far away (presumably no communication faster than lightspeed). Experiments have now been done and, despite possible far-fetched loopholes, seem to indicate that QM without HVs is correct, and that either one or both of the assumptions must be wrong and so must be abandoned. This requires a rethinking of all of science!

Look again at the double-slit. This is example of quantum jump at screen. Or, if try to detect which slit particle comes through, we saw interference disappears and psi-wave jumps to noninterference form. This can happen over large distance. Text looks at putting a detector far from slit. Another version, for photons, uses half-silvered mirror (beam-splitter). Can make delayed choice experiment. Can wait until just before interference is to take place, or not!

The net effect of experiments is that QM is supported, and local HV theories with objective reality are not. So we must be prepared to give up one or both of objective reality and locality. Most prefer to give up locality (Bell: the solution Einstein would have liked least) because of collapse of wave packet. Another suggestion has been made that we cannot use the usual rules of logic (due to Aristotle). In any event, something radical must be done to the way we look at the world.

The EPR and subsequent class of experiments are done with two-particle correlations. The particles are entangled -- that is, they are described by a single psi-wave; they behave as a biparticle. A measurement performed on one will affect the properties of the other, even if they are light-years apart! This is nonlocality at its maximum.

Expt. of Zou, Wang and Mandel (1991) uses photon down-converter to avoid criticism that somehow detector affects the photon by using a different photon in the detector, which can be far from path of the first photon. (Fig. 14.21). Explain

The Rarity-Tapster experiment is a good example of entanglement. It is a direct test of Bells theorem.(Fig. 14.23).

Elitzur-Vaidman experiment. This shows how QM can allow test of counterfactuals. Imagine collection of bombs, some good some dud. One to find one good one. Classically only way to test explodes the good bomb so don't find one.

Schroedinger's Cat. Recall: objects defined by psi-wave packets which evolve smoothly via Schroedinger Eq. But when make measurement, psi-wave packet jumps instantly to new form reflecting new info. This collapse of wave packet was detested by Schroedinger. Before collapse the psi-wave contains info about all possible outcomes of measurement -- the psi-wave is a superposition of all the possibilities. In 1935 Schroedinger gave the cat example, intending to show absurdity of this idea by extending it from microworld to a macroscopic object (cat). What constitutes an observation?

Observation creates reality (observer created universe: Wheeler). Einstein: Is the moon really there if nobody looks? What if a mouse looks? This leads some (Penrose, for example) to connect QM with consciousness. To some it is a key question, many others ignore.

Chapter 15: The Nucleus and Radioactivity

Nuclear physics began before the nucleus was discovered. In 1896, Becquerel discovered radioactivity. The nucleus itself waited another decade and a half to be discovered (Rutherford's analysis of the experiment by Geiger and Marsden).

Sect. 15.1: Rutherford showed that the mass of an atom is almost entirely confined to a tiny nucleus ranging from 1 to 10 fm (1 femtometer or 1 fermi = 10^-15 meters), which also contains the positive charge. Since the whole atom is about 10-8 m in size, the atom is mostly empty space! In turn, by 1932 it was known that the nucleus is composed of protons and neutrons (collectively called nucleons) which have similar masses and sizes (about 1 fm) , with positive and zero charges respectively. Since positive charges repel each other, according to electrostatics, and gravity is much too weak, some new force is needed to bind nucleons together. This is called the strong (nuclear) force. Unlike gravity and electricity it is a short range force -- it falls to zero rapidly at distances of only a few femtometers, so it is not felt outside the nucleus. This is one of four fundamental forces recognized by physics today. (If cosmic repulsion is verified, it may be considered a fifth.) The fourth fundamental force is called the weak (nuclear) force, and is responsible for radioactivity. It too has short range -- even shorter than the strong force, and is weaker than electric forces but still much stronger than gravity). [Section ends with questions that raise the anthropic principle, or religion?]

Sect. 15.2: Energy scale in nucleus about 1 million times greater than atomic. Reasons: (1) strong force about 100 times stronger than electromagnetic; (2) uncertainty principle -- confine nucleons to region 104 smaller than atom, so despite mass of nucleon 2000 times electrons, uncertainty and hence approx. speed much greater. Hence nuclear reactions much more energetic than atomic (chemistry). Atomic number (Z) (defines element), mass number = nucleon number (A) (defines which isotope). Neutron number N = A-Z.

Sect. 15.3: Becquerel was an expert on phosphorescent materials. Hearing of x-rays (1895) he wondered if his rocks emitted x-rays. Found uranium ore exposed film even without exposure to sun. Began collaboration with Pierre & Marie Curie married year before. Nobel: 1903. They recognized it was a property of certain chemical elements -- uranium, thorium, and discovered polonium and radium based on their radiation. They discovered radioactive materials emit charged particles, ionizing air: alpha (Rutherford & Royds 1909: helium nuclei: 2 protons, 2 neutrons) which could be stopped by tissue paper, and beta, more penetrating, which Becquerel showed were electrons moving about 0.5c. (Beta decay is due to weak force. Neutrons themselves beta decay. Neutrinos also emitted.) In 1900 gamma rays discovered by Villard: shortest wavelength electromagnetic radiation.

Sect. 15.4: Law of radioactive decay discovered by Rutherford & Soddy (1899 - at McGill). Nobel (chem) 1908. They recognized there was a gradual decrease in radioactivity. The number of decays/sec is proportional to the number of parent atoms present. This is what expect if the process is completely random!, Typical of QM (although not known then) can only give probability that any given nucleus will decay in a given time interval (no matter how long already lived). The result is an exponential decay. Human lifetimes not like this! Express as half-life. Parent & daughter nuclei. Alphas form inside nucleus and tunnel out!! (QM theory, 1928). Soddys rules: A==> A - 4, Z==> Z - 2. Betas (created at the moment of decay): A==>A, Z==> Z+1.

Sect. 15.5: Radioactivity provides a clock by which many things can be dated. The most famous is carbon-14, which can be used to date items that were once alive, like wooden artifacts, or clothing, provided they are not more than a few tens of thousands of years old. C-14 has a half-life about 6000 years (5730 more precisely). It beta decays into N-14. C-14 is rare in atmospheric carbon (about 1:10^12). It comes from cosmic ray bombardment of nitrogen. Assumes amt. of C-14 is relatively constant over a few millennia. Cross-check with tree-ring and other radioisotope data. Other, longer-lived radioisotopes can be used to date rocks, etc. to get geological chronology, which in turn can be used to date fossils, etc. Carl Sagan's calendar or Art Hobson's clock.

Creationism: One of the areas where some find a conflict between science and religious beliefs is in the apparent difference between the first chapter of the Biblical book of Genesis and the scientific picture established by dovetailing observations of astronomy, physics, geology, archeology and biology. There is a spectrum of creationist beliefs. The most extreme are those who take the Bible literally, saying Earth was created in 4004 BC, in 6 days, of 24 hours each, with all living things in their present forms. They reject all of the vast scientific evidence against their view. More moderate creationists allow for the 6 days being not literal 24-hrs but could be hundreds of millions of years long. The US Supreme Court has ruled that creationism is thinly-veiled religion and may not be taught in public schools. Now creationists are instead trying to undermine the teaching of evolution. This battle is being waged only in the US, and mainly in southern and rural states. Of course, you may believe what you want, but to be an educated citizen, you have to understand what science says (just as you must understand what Marxist economic theory says, even if you do not believe it).

Biological effects of nuclear radiation: This radiation is sufficiently energetic that it can ionize molecules. This can in turn cause damage in cells because they are pretty delicately balanced. Cells can die, or be mutated, especially if it is the DNA in the nucleus of the cell that is damaged. This in turn can lead to radiation sickness (if the bone marrow is affected) or cancer, like leukemia. Can also be used to treat tumors or diagnose (radioactive tracers).

Alphas and betas differ from photons (gammas and x-rays) in that particles lose energy at the end of their range while photons are absorbed exponentially en route. Their effects differ. A unit called rem (Roentgen Equivalent Man or Mammal) attempts to balance these differences. It is being replaced by the sievert (Sv) which is 100 times greater. The biological effects depend on whether the exposure is all at once or spread out over time. A major unknown is the effect of long-term low exposures. Is there a threshold? After all, body can often rid itself of damaged cells. Safest to assume no -- assumed linear relation. Background normal exposure is about 300 mrem per year in US.

Sect. 15.7: One of most difficult problems is weighing risks vs. benefits of a technology. When congress debated the rural electrification act (1935) they worried about people electrocuting themselves. Likewise automobiles kill people, so should we ban? How about DDT? Chernobyl reactor #4 accident in Ukraine, 1986 is used as an example involving radiation hazards. Cs-137 and I-131 in fallout. Worst US accident was Three-Mile Island in 1979 (We will discuss in Chapt. 17).

Chapter 16: Fusion and Fission

These are two major nuclear processes used for converting NuclE to other forms of energy. Do not confuse these two words!!

Sect. 16.1: We begin with fusion -- the process that makes the Sun and stars shine. We consider the process of forming deuterium, H-2 -- an isotope of hydrogen. First imagine pulling H-2 apart. We must overcome strong attraction, i.e. do work. Thus the energy of the separated n + p is greater than the H-2. Now, we must bring together n + p. Since there is no electric force, they feel nothing until they nearly touch. Then the strong force attraction pulls them together, and they form H-2, and release energy. This was a key process after the Big Bang. The energy comes out as gamma rays or thermal energy: NuclE = RadiantE + ThermalE. In general, fusion of light nuclei releases energy. Next consider trying to add another proton to form He-3. Now there is Coulomb repulsion to overcome. The proton and the H-2 will repel each other until they get close enough for the strong force to act. One way is to give the two particles high velocity so that KinE can overcome the electrical barrier (tunneling is important here), i.e. use high temperature -- millions of degrees needed. There is still a net gain of energy: ThermE(in) + NuclE = RadE +ThermE(out). The term ThermE(out) is generally much greater than ThermE(in). In the sun the process is similar but more complicated. The net result is 4 protons combine to form He, with a net release of energy. This is possible because the temperature is 15 million K in the suns center. Terrestrial fusion is discussed in Sect. 16.7 (weapons) and Chapter 17 (future energy source).

Sect. 16.2: Lets examine the build-up of heavier nuclei, like beryllium (Be) with Z = 4 by fusing two He-4's. (This is really NG because Be-8 is unstable and quickly becomes two He-4's.) Because the two heliums have double the charge of hydrogen, the electrical repulsion is four times as strong as in the previous building of He-3. So we need higher temperatures. Thus ThermE(in) is greater. But Therm(out) turns out to be less. Nevertheless it can be self-sustaining so long as the thermal output exceeds the input. The energy production decreases until finally we reach a limit where we get less out than we put in. This is at iron-56. The nuclear energy curve (of the nuclear energy per particle vs. A, Fig. 16.4) shows this. After iron the Therm(out) is less than ThermE(in) because nuclear energy is increasing, and it can't self-sustain. But it suggests going the other way -- fission to go from heavy to light.

Sect. 16.3: Here we discuss nucleosynthesis: How the various nuclei in the universe were created. After the Big Bang it was too hot for nucleons to stick together. If some should they were soon smashed apart again by collisions. But at age about 3 minutes nuclei began to form. Deuterium and helium-3, and 4 and lithium-7 were formed before, by about 4 minutes, the rapid expansion reduced the temperature and density to a point where fusion stopped. These five nuclei (plus protons -- the neutrons soon beta-decayed away) made up the primordial gas from which the first generation of stars eventually formed. It is in the centers of these stars where fusion could resume, forming the elements up to iron. Elements heavier than iron are made rapidly by fusion during supernova explosions and spewed into space. We are composed of this material. Evidence for this scenario: The big bang is evidenced by the Hubble expansion of the universe, and by the 3-degree cosmic background radiation. The initial primordial gas composition is verified by spectra of very old first-generation stars. Ripples in the background radiation show the beginnings of condensations of the primordial gas -- the very beginnings of galaxy formation at about 100,000 years (Fig. 16.5).

Sect. 16.4: This and next three sections are primarily historical narrative. They cannot be summarized very easily. All I can say is READ!

Discovery of fission: Fission was actually seen by Fermi in 1934, but for 4 years his and similar results by the Joliot-Curies in France and by others were misinterpreted. Fist -discovery of neutron: 1932: James Chadwick, a student of Rutherford, who had suggested the existence of combined electron-proton he named the neutron as way to overcome impossibility of nuclear electrons. Chadwick bombarded beryllium (and boron) with alphas from polonium, and detected a penetrating neutral radiation: He-4 + Be-9 => C-12 + n. (Nobel, 1935). In 1934 Joliot-Curies study other nuclei under alpha bombardment and find new man-made radioactive isotopes (Nobel, chem, 1935). Inspired, Italian theorist Enrico Fermi (a student of Born) decides to take a break from theory and try experiment. He wants to try neutron bullets in place of alphas. Key discovery: neutrons slowed bypassing through paraffin are more effective. When he gets new unknown radioactive species resulting from n + U, he assumes he has created first transuranium element Z=93 (Nobel, 1938). Ida Noddack disputes 93 - suggests fission instead - but ignored. Many groups start using neutron bullets and get similar results, but cannot identify the results of n+U and n+Th.

In Germany, Hahn, Meitner and Strassman do likewise. Meitner escapes Germany to Stockholm in 1938. Her nephew, Frisch had left in 1933 for London but is spending year in Copenhagen. In 1938 he visits her in Sweden. They discuss latest results of Hahn and Strassman, the confirmation of barium and lanthanum after n+U. In light of Bohr's liquid drop model of nucleus, they hit on an idea: nuclei are split approximately in half, not always the same way! Frisch coins word: fission (Hahn: Nobel, chem, 1944; Meitner should have shared, but she could not work in Sweden and she didn't share in the key experiment).

Sect 16.5&6: Once fission was recognized, the idea of a chain reaction was developed by Fermi and by Szilard. In fissioning, nuclei divide into two parts, but usually extra neutrons also come out. If these are slowed down they can cause further fissions. Can come out directly (prompt neutrons) or by being spit out by fission products which are too neutron rich (delayed neutrons). Szilard and Wigner saw the potential for a bomb, and approached Einstein to write a letter to Pres. Roosevelt. This led to the atomic bomb: Manhattan Project. Fermi, who escaped to US right after picking up his Nobel, demonstrated first controlled nuclear chain reaction in Chicago, 1942. This is forerunner of nuclear power reactor. Natural uranium is mostly U-238 which does not fission. 0.7% is U-235 which does. This can be separated (enriched) by gaseous diffusion (Oak Ridge) and was basis of Hiroshima bomb. When U-238 absorbs a slow neutron it becomes U-239 which quickly beta decays to neptunium: Np-239 which then quickly beta decays to plutonium: Pu-239. This is an alpha emitter, with a half-life of 24,000 years, and it fissions. Chemically separated from the uranium, it became the basis for Nagasaki bomb. In either case a critical mass is necessary.

Sect. 16.7: Fusion can also be used for a bomb (Teller); the high temperatures needed can be created by a fission bomb which triggers the thermonuclear fusion. This is most easily achieved by using deuterium and tritium (H-3, a radioactive isotope of hydrogen -- half-life 12 years): H-2 + H-3 => He-4 + n. Leads to H-bomb.