Discuss about the fundamental concept from the history of ancient natural philosophy.You may refer to your lecture notes and the course readings for this exam, but you may NOT refer to any sources not used in the course–e.g., Wikipedia, etc. Choose two examples of a fundamental concept from the history of ancient natural philosophy (i.e., Pre-Socratics, Plato, or Aristotle) that are still relevant to [1] relativity theory & [2] quantum mechanics, and discuss this relevance. (In other words, relate one ancient concept to relativity theory, and the other to quantum mechanics.) Additional instructions: In this course, we have explored many historical examples from which to choose. Some of these are: atomism; rationalism (i.e., for Plato and the Pythagoreans, the belief in the ‘physical reality’ of mathematical and geometrical objects); the idea of universal laws; the dualism of particles and forces; the dualism of permanence (e.g., matter) and change (e.g., waves). There are many other examples. Your discussion should include both how your chosen concepts remain relevant to quantum mechanics and relativity theory and how they differ from their original form in ancient natural philosophy. https://www.csus.edu/indiv/e/eppersonm/hist107/documents/Aristotle,%20Heisenberg,%20and%20Quantum%20Mechanics%20-%20Science%20News%20Article.pdf I have the lecture notes…The Decline of the Mechanical View Electricity as 2 ‘fluids’—positive and negative The desire to connect electricity to gravity—similar equations? Newton and Coulomb Newton and gravity: F = G m1m2 ——- r2 Coulomb and static electricity: F = K q1q2 ———- r2 Looks similar! Why? Is this a clue? Other analogous relations: Electric potential analogous to temperature / Electric charge analogous to heat See p.79 for more analogies Magnetism as 2 ‘fluids’ — similar to electricity as 2 fluids 2 Major Difficulties in treating electricity and magnetism as mechanical ‘fluids.’ Difficulty 1: electricity produces magnetism Galvani’s discovery—seemingly unlimited charge producible Oersted’s discovery: current produces magnetic field perpendicular to current flow Rowland’s discovery: velocity of current creates greater magnetic force (against Coulomb’s law which says force depends only on distance between charges.) Difficulty 2: the velocity of light If light is a ‘substance’ it is either a particle (Newton) or a mechanical wave (Huygens) If light is a substance it is weightless If light is a wave, it must travel through a medium that is undetectable (the ‘ether’ rehabilitated from Aristotle) Who was right? The double slit experiment of Young in 1801. Light is a wave! But… Ether and the Mechanical View—where is the ether? What is the evidence that it exists if we cannot measure it? (comparison to dark matter today?) Week 12 Lecture Outline Field as REPRESENTATION of physical reality. Gravity as example: lines of force Force does not ‘travel through space and time’ (e.g., no ‘time’ variable in Newton’s equation for gravity) Rowland’s experiment The electromagnet (solenoid): Impossible to model without the use of fields. New observation: fields are not mere representations; they have properties that directly produce physical effects. Change of electric field produces a magnetic field (Oersted’s experiment) Change of a magnetic field produces an electric field (Faraday) The REALITY of the field; it is more than mere representation The mathematical structure of a field determines changes in the physical structures associated with the fields. Maxwell’s equations: Describe the structure of electromagnetic fields. NO MATERIAL ACTORS in Maxwell’s theory; only mathematical structures that PRODUCES material/physical effects. Field effects propagate locally, via small steps; whereas for Newton, gravity is a global effect. Therefore, time is relevant in field theory whereas it is not in Newton’s theory of gravity. The Field and Ether Light propagates as an electromagnetic wave; but mechanical waves (from the previous paradigm) propagate through a physical medium. In the field theory, what is the medium? Or is there one at all? Field effects propagate in small steps, locally. Local references frames and coordinate systems Galilean (classical) relativity Ether and Motion If there is an ether, it should move ‘locally’ and reflect classical relativity. E.g., the speed of light should change depending on local motion of the local ether of the local moving reference frame. HOWEVER—the velocity of light is always the same in all local reference frames / coordinate systems! (Michelson-Morley experiment). The velocity of light does not depend on the motion of the emitting light source. Light waves propagate differently than sound waves, which do travel through a mechanical medium (air), reflecting classical relativity. Another clue: In two coordinate systems moving uniformly relative to one another, all the laws of physics work identically. This means: Classical relativity, by which you would normally ‘translate’ (transform) values from one moving coordinate system to another, DOES NOT WORK the way it does in classical mechanics. We need a new theory. Clocks and Rods in a world where the speed of light is constant in all coordinate systems: The units of time and length must change if the speed of light cannot. Quantum vs. Continuum Zeno revisited: the paradoxes of dividing a physical continuum – infinite within the finite The elementary quantum of matter and electricity: The atom and the electron The negative electron (and the electric field) flows through the wire (from – to +)—the opposite of what was believed in the classical view (+ to -) The elementary quantum of electromagnetism (light): the photon and the photoelectric effect The continuous waves of electromagnetism cannot be divided infinitely; the implication is infinite energy The ‘ultraviolet catastrophe’ Quantization of light solves the problem. Photons of specific energies react with electrons of specific energies. Light spectra – the proof that light IS quantum. But the problem remains—how to reconcile the wave nature of light with its quantum/photon nature. Bohr’s model of the atom The idea of ‘matter waves’ as a way of solving the problem of wave-particle duality DeBroglie’s idea—matter as a ‘standing wave’ phenomenon. Lecture Outline – Tuesday 5/11 Probability Waves Double slit experiment again How to statistical laws work in QM? Different than classical mechanics. Classical: Knowledge of individual cases à group statistics QM: No individual statistical laws/cases: Probabilities are instant à group statistics What is a probability wave exactly? It is a mathematical structure that represents probable physical states Thursday 5/13 Review: Probabilities are instantly calculable but only verifiable retrodictively after MANY iterations à group statistics Heuristic example: Is a 50/50 fair coin toss probability meaningful after only one toss? In classical statistics, yes, because there are classical deterministic laws governing the individual coin. In QM, no, because there is fundamental indeterminacy in individual measurements—no classical determinism at the level of individual measurements! Article: “Quantum Mysteries dissolve if possibilities are realities” Aristotle revisited: Potential states à Actual states BUT, via QM, it’s Potential states à Probable states à Actual states Probable states satisfy Aristotle’s Principle of Non-Contradiction and Excluded Middle; potential states do not. Probability waves revisited Changes in actual states reset potential states and this is reflected in revised probability valuations. How does QM deal with spacetime and relativity theory? Do actualizations of potential states (i.e., measurements) necessarily occur IN spacetime? Or is spacetime formed as a result of QM actualizations of potential states? Physics and Reality Physical vs. conceptual objects revisited Mechanical paradigm à Field paradigm Absolute time and space à Relativistic spacetime “Without the belief that it is possible to grasp the reality with our theoretical constructions, without the belief in the inner harmony of our world, there could be no science. This belief is and always will remain the fundamental motive for all scientific creation.” Einstein * Infeld, p.296 Week 10 Lecture Outline Rise of the mechanical view (paradigm) from the Aristotelian paradigm Puzzle solving The nature of motion Speed vs. acceleration – what’s the difference? Force not revealed by speed, but by acceleration (change in velocity) Comparison to the Aristotelian paradigm Emphasis on quantitative over qualitative measures Gravity as an example Acceleration is related to DISTANCE and MASS only Boyle’s clockwork metaphor revisited The mechanism of a watch is analogous to the mechanism of the universe in general. More on Gravity – An anomaly and a clue to understanding it: Difference between and relation of inertial vs. gravitational mass. The nature of heat Is heat a substance—i.e., an internal feature of a thing (per the Aristotelian / medieval paradigm)? If so, it is weightless! (anomaly!) Experiments / observations that show it is not. Rumford Joule Generalizing the concept of energy Motion (kinetic energy) can be converted to heat and also to potential energy, and vice versa. All forms of energy can be converted to all other forms. Philosophical background Return to Democritus (and Empedocles! Attraction (love) and Repulsion (strife) Fundamental reductionism Kinetic theory of matter: everything is particles in motion Brownian motion Experiments / observations that show it is not. Rumford Joule Generalizing the concept of energy Motion (kinetic energy) can be converted to heat and also to potential energy, and vice versa. All forms of energy can be converted to all other forms. Please do not use any outside sources. Let me know if you have any questions.