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Frequently Asked Questions About Quantum Mechanics and the Transactional Interpretation

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Frequently Asked Questions About Quantum Mechanics and the Transactional Interpretation Appendix A Frequently Asked Questions About Quantum Mechanics and the Transactional Interpretation A.1 Basic Questions and Answers At physics meetings at which talks are given, it is conventional to leave some time at the end of the presentation for questions about ideas that need clarification or that might not have been adequately covered during the formal presentation. Werner Heisenberg remarked [1] that no one who gave a talk at Niels Bohr’s Institute in Copenhagen ever finished the presentation, because Bohr always asked too many questions. So, in the spirit of Bohr’s inquisitiveness, here are some questions that may have been raised by material in this book, along with short answers. We will start with a few basic questions. Q: What is quantum mechanics? A: Quantum mechanics is the standard physics theory that deals with the smallest scale of physical objects in the universe, objects (atoms, nuclei, photons, quarks) so small that the lumpiness or quantization of otherwise apparently continuous physical variables becomes important. Q: What is the meaning of the angular frequency ω and wave number k of waves? A: Light waves have a characteristic frequency f indicating how many times per second the electric field of the light wave oscillates. The angular frequency ω is just the same characteristic expressed in radians of phase per second instead of oscillations per second, so ω = 2π f . Light waves also have a characteristic wavelength λ as they move through space, which is the spatial distance between one electric-field maximum and the next. The wave number k is a way of looking at the reciprocal of that characteristic, so that k = 2π/λ. The speed of light c is related to these quantities as c = f λ = ω/k. When we deal with particle-waves, for example using the de Broglie wavelength, we also characterize them in terms of ω and k. Q: What is quantization? © Springer International Publishing Switzerland 2016 169 J.G. Cramer, The Quantum Handshake, DOI 10.1007/978-3-319-24642-0 170 Appendix A: Frequently Asked Questions About Quantum Mechanics … A: It’s the idea that there are minimum size chunks for certain quantities like energy and angular momentum. The minimum energy chunk for light of frequency f is E = hf = ω, where h is Planck’s constant and is h divided by 2π. We call the particle of light carrying this minimum-size energy chunk ω a photon. Q: How big is Planck’s constant? A: Planck’s constant is very small. It represents the minimum unit of action (energy × time) in quantum physics, and it has the value h = 6.62606957×10−34 J · s = 4.135667516×10−15 eV ·s. Further, = h/2π = 1.054571726×10−34 J ·s = 6.58211928 × 10−16 eV · s. As an example of the use of h, red visible light has a wavelength of about λγ = 500 nanometers (nm). A photon of red light carries an energy of Eγ = hc/λγ = 2.48eV.AneV is an electron-volt, the energy required to move one charged electron through a potential of 1V. An electron-volt is a very small quantity of energy, roughly the amount of energy that an atomic electron gains or loses by jumping from one atomic orbit to another. Q: What if Planck’s constant was zero? A: Setting to zero is a way of taking the classical limit of quantum mechanics: the uncertainty principle goes away, and in that limit quantum mechanics becomes more or less equivalent to Newtonian mechanics. However, Planck’s treatment of black body radiation suggests that a universe in which Planck’s constant was zero would be very different than ours, because hot objects would rapidly radiate away all their energy as high-frequency electromagnetic radiation (the ultraviolet catastrophe), matter would be extremely cold, and the universe would be dominated by light. Q: What is angular momentum, why is it quantized, and why is it conserved? A: Angular momentum is the rotational momentum of a rotating or spinning object. It is the product of the angular rotation rate ω and the rotational inertia I of the object. In quantum mechanics, if one requires the state of an object that is slowly turned through 360◦ to return to exactly the same state as before, this has the rather unexpected consequence of requiring that angular momentum must be quantized in units of . Thus, it is 360◦ rotational symmetry that causes angular momentum to be quantized. Therefore, one would think that no object in our universe could have a non-zero angular momentum of less than one unit. As it turns out, this is wrong, because fermions (see below) have an intrinsic spin of half an unit and therefore do not have 360◦ symmetry. Angular momentum conservation is the rotational manifestation of Newton’s 3rd Law, which in it’s rotational form states that in the absence of external torques, the angular momentum of a system is an unchanging time-independent constant. Q: What is the difference between orbital angular momentum and spin angular momentum? A: In an atom, two distinct kinds of angular momentum are present: the angular momentum created by the electrons orbiting the nucleus and the intrinsic spin angu- lar momentum of the electrons themselves. The orbital angular momentum always Appendix A: Frequently Asked Questions About Quantum Mechanics … 171 comes in units of , while the electron spins are each /2. The total angular momen- tum is the vector sum of these components, and it can be quite complicated because of the variety of ways in which the component angular momentum vectors can couple. The parity (see below) of the system wave function depends on the orbital angular momentum, with odd values (1, 3, 5, …) giving odd parity and even values (0, 2, 4, …) giving even parity. Q: What is parity? A: A parity transformation means that the three spatial coordinates (x, y, and z) of a quantum system are reversed in sign and direction. If the quantum wave function remains the same under such a transformation, the system is said to have positive parity. Example: cos(x) = cos(−x). If the quantum wave function changes sign under such a transformation, the system is said to have negative parity. Example: sin(x) =−sin(−x). Each energy state of an atom or nucleus has a definite parity, either positive or negative. In a “quantum jump” atomic transition, if the parity changes the properties of the emitted photon will be different than if the parity remains the same. Parity is related to mirror-image symmetry. Q: Why is photon linear polarization, important in EPR experiments, constrained by angular momentum conservation? A: Photons are boson particles (see below) that have an intrinsic spin angular momentum of one unit. If this spin vector points in the direction of motion of the photon, the photon is in a state of left circular polarization; if the spin vector points against the direction of motion, it is in a state of right circular polarization. Because the photon travels at the speed of light, special relativity does not allow its spin to point in any other directions. States of linear polarization can be formed by a superposition of the right and left circular polarization states, as discussed in Sect. 6.6 and quantified by Eqs.6.4 and 6.5. Since angular momentum conservation constrains the spins of the photons of a system, it also constrains the states of linear polarization, and EPR experiments make use of this. Q: What is a fermion? A: Fundamental particles called fermions, including electrons, muons, neutrinos, and quarks, have an intrinsic angular momentum or “spin” of 1/2 , i.e. half an unit. Composite fermions, which are made up of three quarks, include neutrons, protons, and heavier baryons. Fermions obey Fermi-Dirac statistics and the Pauli exclusion principle, the requirement that only one fermion can occupy any particular quantum state. This leads to the electron-shell structure in atoms, to the neutron and proton shell structures in nuclei, and to valence behavior and chemical bonding in chemistry. In quantum wave mechanics, fermions are described using the Dirac wave equation. The half-integer spin of fermions means that one must rotate such particles through two full revolutions or 720◦ before they return to their original state. These peculiar 172 Appendix A: Frequently Asked Questions About Quantum Mechanics … fermion particles also come with antimatter twins (e.g., positrons for electrons and anti-quarks for quarks) of opposite parity (opposite mirror-symmetry).1 Q: What is a boson? A: Fundamental particles called bosons, including photons, gluons, the Z 0 and W ± weak-interaction particles, and the Higgs particle, the mediating particles for the fundamental forces, all have an intrinsic spin that is either zero or an integer multiple of . Composite bosons include alpha-particles, many atoms and nuclei, and π- and K -mesons. Bosons obey Bose–Einstein statistics and can form a “condensate” in which a large number of bosons all have identical wave functions and occupy the same quantum state. Lasers are an example of the operation of Bose–Einstein statistics for photons. In quantum mechanics, bosons are described by the electromagnetic wave equation for light and the Klein–Gordon equation for massive particles. Q: Is light made of particles or of waves? A: Light exhibits the behavior of both a particle and a wave. The Transactional Interpretation shows us that light moves from place to place as waves, but at locations where it is emitted or absorbed it obeys the boundary conditions of a particle carrying energy ω, momentum k, and angular momentum .
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