Philosophies
Pythagorianism
The philosophical school that extolled the importance of mathematics and pure form -- even giving them ontological significance.
"First Principles" Greek Thinkers
The trail from Thales of trying to identify the underlying fabric of the World is long, indeed, to the present day. They are the first Theories of Natural Science (not Physics yet, I don't think!). These "First Principles" pioneers include the few that I talked about, but also Zeno, Melissus, Empedocles, Anaxagoras, Anaximander, and Anaximenes. You can read about some of them in HW and SW.
Greek philosophy of change
The part of Heraclitus' philosophy that reality is a realm of change. In counter to this: Parmenides who argued for Permanence as the only reality—maybe the first to question the senses as reliable inputs. He also argued for the permanence of the universe, stating that "nothing can be created from nothing."
Philosophy of Permanance
Parmenides' ideas were to argue rationally to the conclusion that Permanence is the only reality. He was one of the first to argue that the senses were untrustworthy. Zeno was his associate who proposed various descriptions of motion and its apparent impossibility.
Plato's Theory of the Forms
Plato's notion of the Forms as the only reality, not of space and time, resonates with some approaches today toward mathematics.
The Aristotelian Causes
The lasting thing about Aristotle's philosophy for science is his insistence on the primacy of the four causes.
(Loco)motion for Aristotle
The kinds of motion that Aristotle required is both the idea that stayed around for so long, and the thing that eventually broke his back...scientifically.
This includes his cosmology.
Classical Logic
The logic as invented by Aristotle serves as a model of how argument should be stated for many centuries. This includes primarily Deduction (and the Syllogism) and secondarily (for him), Induction.
Scholasticism
At first, an optimistic incorporation of the ideas and works of Aristotle into the intellectual climate of Latin Europe. However, it becomes a static, authoritarian set of rules...against which high-Renaissance and early Enlightenment thinkers will eventually rebel.
Rationalism
The modern idea that knowledge comes from reason.
empiricism
The modern idea that knowledge comes from observation and experiment.
positivism
An extreme version of empiricism that says that all knowledge comes from "positive" data of the senses. Anything not conforming was often classified as "meaningless" to the ardent proponents of the late 19th century. Ernst Mach was an important positivist in physics.
logical empiricism
The branch of philosophy of science in the mid-20th century that attempted to analytically take the precise language of symbolic logic and the specification that meaningful science consists in correlating logical ideas with specifically observable consequences. The prescriptions were so restrictive and sterile that the project began to experience an unravelling in the form of paradoxes and their inability to deal with the "theory ladenness" of the act of observation (coming).
"Kuhnian" paradigms
The first of the systematic "historicist" philosophies of science emphasizing history over logicism. Kuhn's effort of the early 1960's involved the concept of "paradigms" as bodies of belief and practice taking place between "revolutions" for a given period of time and within a given scientific society or group.
"Lakatosian" research programs
Another of the historicist philosophies of science that emphasized history in a periodic analysis of scientific efforts. Not as radical as Kuhn's philosophy, it was not fleshed out very significantly due to the premature death of Imre Lakatos during the height of his development of the concepts.
neoPlatonism
In particular, in Renaissance Florence, the philosophy that extolled the virtues of Platonic thought as it pertained especially to the search for Beauty. Influenced the Florentine artistic community who adopted this search as a part of their mission. The Florentine Academy was started by the deMedici family, especially nourished by Lorenzo ("the Magnificent").
Historicists' Methodological Ideas
Kuhn and Lakatos both modeled science as an episodic ("revolutionary" for Kuhn) activity which carefully picks and chooses what notions are protected (the "hard core" in Lakatos' Research Programs) and which ideas are to be tested. This was new. Both respected the theory-ladenness of observation. But, while Lakatos maintained that science progresses, Kuhn did not.
Theory-ladenness
The realization that all observation is "laden" with prior ideas and experience and not the neutral activity required by the Logical Empiricists. In science, this is most usually associated with Indiana philosopher Norwood Hansen.
"Mechanical Philosophy"
The Mechanical Philosophy was the notion that the universe is run by strictly mechanical causes. There was an older, but still competing renaissance notion that there were "vital.
The philosophical school that extolled the importance of mathematics and pure form -- even giving them ontological significance.
"First Principles" Greek Thinkers
The trail from Thales of trying to identify the underlying fabric of the World is long, indeed, to the present day. They are the first Theories of Natural Science (not Physics yet, I don't think!). These "First Principles" pioneers include the few that I talked about, but also Zeno, Melissus, Empedocles, Anaxagoras, Anaximander, and Anaximenes. You can read about some of them in HW and SW.
Greek philosophy of change
The part of Heraclitus' philosophy that reality is a realm of change. In counter to this: Parmenides who argued for Permanence as the only reality—maybe the first to question the senses as reliable inputs. He also argued for the permanence of the universe, stating that "nothing can be created from nothing."
Philosophy of Permanance
Parmenides' ideas were to argue rationally to the conclusion that Permanence is the only reality. He was one of the first to argue that the senses were untrustworthy. Zeno was his associate who proposed various descriptions of motion and its apparent impossibility.
Plato's Theory of the Forms
Plato's notion of the Forms as the only reality, not of space and time, resonates with some approaches today toward mathematics.
The Aristotelian Causes
The lasting thing about Aristotle's philosophy for science is his insistence on the primacy of the four causes.
(Loco)motion for Aristotle
The kinds of motion that Aristotle required is both the idea that stayed around for so long, and the thing that eventually broke his back...scientifically.
This includes his cosmology.
Classical Logic
The logic as invented by Aristotle serves as a model of how argument should be stated for many centuries. This includes primarily Deduction (and the Syllogism) and secondarily (for him), Induction.
Scholasticism
At first, an optimistic incorporation of the ideas and works of Aristotle into the intellectual climate of Latin Europe. However, it becomes a static, authoritarian set of rules...against which high-Renaissance and early Enlightenment thinkers will eventually rebel.
Rationalism
The modern idea that knowledge comes from reason.
empiricism
The modern idea that knowledge comes from observation and experiment.
positivism
An extreme version of empiricism that says that all knowledge comes from "positive" data of the senses. Anything not conforming was often classified as "meaningless" to the ardent proponents of the late 19th century. Ernst Mach was an important positivist in physics.
logical empiricism
The branch of philosophy of science in the mid-20th century that attempted to analytically take the precise language of symbolic logic and the specification that meaningful science consists in correlating logical ideas with specifically observable consequences. The prescriptions were so restrictive and sterile that the project began to experience an unravelling in the form of paradoxes and their inability to deal with the "theory ladenness" of the act of observation (coming).
"Kuhnian" paradigms
The first of the systematic "historicist" philosophies of science emphasizing history over logicism. Kuhn's effort of the early 1960's involved the concept of "paradigms" as bodies of belief and practice taking place between "revolutions" for a given period of time and within a given scientific society or group.
"Lakatosian" research programs
Another of the historicist philosophies of science that emphasized history in a periodic analysis of scientific efforts. Not as radical as Kuhn's philosophy, it was not fleshed out very significantly due to the premature death of Imre Lakatos during the height of his development of the concepts.
neoPlatonism
In particular, in Renaissance Florence, the philosophy that extolled the virtues of Platonic thought as it pertained especially to the search for Beauty. Influenced the Florentine artistic community who adopted this search as a part of their mission. The Florentine Academy was started by the deMedici family, especially nourished by Lorenzo ("the Magnificent").
Historicists' Methodological Ideas
Kuhn and Lakatos both modeled science as an episodic ("revolutionary" for Kuhn) activity which carefully picks and chooses what notions are protected (the "hard core" in Lakatos' Research Programs) and which ideas are to be tested. This was new. Both respected the theory-ladenness of observation. But, while Lakatos maintained that science progresses, Kuhn did not.
Theory-ladenness
The realization that all observation is "laden" with prior ideas and experience and not the neutral activity required by the Logical Empiricists. In science, this is most usually associated with Indiana philosopher Norwood Hansen.
"Mechanical Philosophy"
The Mechanical Philosophy was the notion that the universe is run by strictly mechanical causes. There was an older, but still competing renaissance notion that there were "vital.
Physics Theories
Merton Mean Speed Theorem
This was the idea that uniformly accelerated motion led to the same distance traversed as constant-speed motion at the average speed of the accelerated motion. Important in Galileo's work. Proven by Oresme.
heliocentric model
The Copernican model of the solar system was an amalgam of modern and scholastic ideas. The simplicity of the idea, along with various natural explanations of observed features of the planets and their orientation was to its credit. It was not an overwhelming success, but quietly gained adherents within some of the astronomy community.
Huygens' theory of conservation of quantity of motion
Huygens, originally a Cartesian, held also in the conservation of something like momentum. However, he correctly interpreted the "quantity of motion" as having a direction as well as a magnitude. These were strictly geometrical ideas and anticipated by 30 years Newton's enunciation of vectors.
Descartes' theory of constancy of quantity of matter
Descartes was one of the first to hold the notion that something like momentum is conserved in motion. His was a strictly philosophical position, deriving from the idea that extension and motion were clear and distinct ideas and that God had started the original motion in the universe and that it would in no way be diminished in totality.
Newton's invention of the Binomial Theorem
The invention of the binomial theorem as an infinite series represenations of arbitrary functions was the underpinning of Newton's invention of calculus.
Calculus
The invention of calculus by Newton and Leibnitz as a universal prescription for what was being hinted at by many other mathematicians stands as maybe the single most important achievement in physics in millennia. With this tool, the ability to model forces and motion becomes possible and is quickly successful around Europe.
Newton's Principia
The three laws of motion, plus his gravitational theory and his few definitions of mass and momentum generally characterize Newton's mechanics.
Newton's Laws
The "Laws" of Newton included 2 which were closely paralleled by work of Descartes, Huygens, and Galileo. The Third Law was uniquely Newton's.
Newton's Law of Gravitation
Newton's Gravitational "Law" usually occupies as grand a status as the famous "Three Laws" and describes the force of attraction between any two masses.
Conservation of Momentum
The conservation of momentum is a direct result of the Third and Second Laws of Newton and holds for all collisions.
Conservation of Mechanical Energy
The beginnings of bigger ideas (conservation of total energy, and subsequently the conservation of mass-energy), the conservation of kinetic and then kinetic plus potential energies was a while in coming. Huygens and Leibnitz both had the ideas that something involving v^2 was conserved in some collisions, but a satisfactory understanding was nearly a century away from Newton's first understanding of momentum.
Hooke's Law
The force of an elastic object is proportional to the distance through which it is stretched or compressed. The potential energy is proportional to that distance-squared.
Collisions
There are three kinds of collisions:
1. elastic collisions - mechanical energy and momentum are conserved and no energy is lost due to heat, sound, etc.
2. inelastic collisions - only momentum is conserved...a more realistic real-life situation, where always some friction or sound or something removes energy, and eventually converts it to usually heat.
3. completely inelastic collisions - momentum is conserved, but kinetic energy maximally not conserved. These are collisions in which the bodies stick together after the collision.
angular momentum
A quantity having to do with rotations or twists - the momentum times a lever arm. The direction of angular momentum is perpendicular to the plane of the momentum and lever arm...and points in the direction of your right thumb, if your fingers follow the direction of the lever arm vector and then the momentum vector. Looking from above on the rotating stool demonstration, if I were turning counterclockwise, the angular momentum would point up. It is conserved.
gravitational potential energy
By choosing the zero of gravitational potential energy to be at infinity from any massive object, then the potential energy of another massive object can be written as a single relationship..it is inversely proportional to the distance between the two objects. Remember, potential energy is always a relative quantity, depending on differences, not an absolute zero point.
Newton's Absolute Space
Newton believed that Space was an absolute quantity. He knew that velocities were always measured with respect to other objects, and were relative things (like Galileo). But, he reasoned that accelerations are absolute quantities when measured against the absolute coordinate system of Space. While a mathematical construct, Newton believed it was real. He also believed that there was an Absolute Time.
Newton's theory of light
...that light was made up of particles.
Hugen's theory of light
...that light is made up of waves in the ether. (Plus, Hooke.)
Conservation of Energy
A 19th Century concept that combined the mechanical energy conservation ideas with the relationship between heat and energy most convincingly proposed by Joule into a general statement that All Energy is Conserved.
kinetic theory of gasses
First described by Daniel Bernoulli, the kinetic theory of gasses seeks to explain the bulk properties of gasses (volume, pressure, temperature, etc) in terms of the collisions of unseen atoms.
transverse light
The idea that light is made of transverse waves, rather than longitudinal waves like sound, was first put forth by Fresnel in order to explain polarized light.
luminiferous ether
The need for some substance for light to "wave" in was apparent to everyone in the 18th and 19th centuries. The "luminiferous ether" was the substance thought support light propagation. For a while, other ethers were presumed active to support the phenomena of gravitation, electricity, and magnetism. The properties of the luminiferous ether were particularly troubling, since light, as a transverse wave, would have implied shear forces in the ether plus, because the speed of light was known to be very high, would have required the ether to be stiffer than steel in order to support those shear forces.
Coulomb's Law
Originating with Coulomb (but also with the silent Cavendish), the force between two electric charges is proportional to the magnitude of the charges and inversely proportional to the distance between them squared - tantillizingly similar to Newton's Gravitational Law.
Maxwell's Distribution of speeds
James Clerk Maxwell first described the average distributions of speeds in a gas at a given temperature. Called eventually the Maxwell-Boltzmann Distribution.
Maxwell's equations
The collection of mathematical formulae that completely describe the behavior of electric and magnetic fields do to configurations of charges and currents. The solutions to Maxwell's Equations result in wave-like results that lead to electromagnetic waves, a coupling of the electric and magnetic fields.
Electric and Magnetic fields
The mathematical entity given mathematical form by Maxwell to describe Faraday's Lines of Force. Now understood to be the physical manifestation of the effects of charges and currents.
displacement current
Just as changing magnetic fields produce electric fields, Maxwell proposed that changing electric fields produce magnetic fields. The model in which this was discussed in class was a changing electric field due to the charging of a capacitor, where between the plates one can imagine a "displacement current" associated with the increasing E field and circular B fields in that same region. This additional time-dependent term (the "change" of the E field) leads to solutions for E and B in Maxwell's equations that are wave-like. This was the unique feature of Maxwell's theory that led to the prediction of electromagnetic waves found by Hertz.
electromagnetic waves
From a symmetry argument, Maxwell predicted a strict relationship between an electric field and a magnetic field in sourceless (i.e., no charges and no currents) region of space: they would be related by a constant, which he found had the value of the speed of light. The transverse electromagnetic waves propagate at the speed of light with E and B coupled together in phase.
Lorentz Force
This is an addition to the Maxwell theory due to Lorentz, which is a relation that describes the force on a charged particle due to its experiencing an Electric Field and/or a Magnetic Field (if the charged particle is moving relative to the magnetic field).
Poynting Vector
Basically, for our purposes, it is the direction that an electromagnetic wave propagates...perpendicular to both the direction of E and the direction of B and the direction of the momentum that an electromagnetic wave can deliver as Radiation Pressure. That momentum is p = U/c, where U is the energy of the wave and is proportional to E2.
blackbody radiation
Many materials can reach a state in which they absorb all radiation that falls on them, and emit radiation of all frequencies. The intensity of this emission has a characteristic shape as a function of frequency which is independent of the material. It is the reason that color of heated materials have traditionally been accurate measures of the temperature. This radiation is called Blackbody Radiation and its universal nature led to many attempts to explain it in terms of Maxwell's theory and conventional thermodynamics. All attempts failed until Planck in 1901.
Planck's quantum of action
Planck's notion that the radiation emitted by a blackbody is quantized into "bundles" of energy which are discrete. His was not a theory of light, he thought, but a statement about the oscillators presumed to be the emitters of radiation from the walls of the heated object.
Special Relativity
Einstein's Special Theory of Relativity was originally an attempt to account for strange consequences in electromagnetic phenomena when viewed from different, co-moving rest frames. It has since taken on a set of consequences which are often portrayed as only mechanics.
There are two postulates that make up relativity theory:
1. There is no experiment (mechanical or electromagnetic) that can determine whether one is moving in an intertial frame which is moving or at rest relative to some other frame.
2. The speed of light is the same, c, in all intertial frames of reference. This means, if true, that there is no way to measure the presence of an ether...and so the ether is not a scientifically meaningful concept (that's Mach's influence on Einstein...which we have all inherited.)
(remember: an inertial frame is one which moves at a constant velocity...which could be zero...as measured with respect to any other inertial frame.)
These have a number of consequences:
1. Simultaneity between events in co-moving reference frames is no longer a measurable, and hence, meaningful concept.
2. Time Dilation. A clock on a frame S' moving with respect to an observer in frame S appears to move slower to S than it does to S'. So, on earth....the "clock" of the decaying muon appears to be slower, and hence the muon lives to reach the surface.
3. Length Contraction. The length of an object in frame S' moving with respect to an observer in frame S appears to be shorter to S than it does to S'. So, in the rest frame of the cosmic ray muon, the atmosphere (which appears to it to be approaching it) looks to be shorter to it, and hence the muon lives to reach the surface.
4. Relativity of inertia. The mass of an object in frame S' moving with respect to an observer in frame S appears to get larger with velocity than it does to S'. To S', the object's mass is its "rest mass," and is a constant. This relative inertia is called "relativistic mass."
5. Mass-energy. Mass and energy are one and the same quantity and can manifest itself either way. They are related by the famous E = mc 2 relation, where m here refers to the relativistic mass. In the rest frame of the mass, the energy is E = m0c 2 where m0 is the rest mass.
6. Relativity of electric and magnetic fields. The presence of an electric field in a frame S' moving with respect to an observer in frame S will appear to the latter to be a combined electric and magnetic field, and visa versa.
7. Lorentz Transformations. The transformations of space and time coordinates between two co-moving frames mix the space and time coordinates in a particular way which actually determine the above conditions deductively. They also are the transformations which account for the solution to the conundrums of electromagnetism that we talked about in lecture.
Spacetime
The nature of relativity is that space and time are no longer separable into two different things and that proper use of them as coordinates in physical models requires that they be treated together...Spacetime is the term used to describe the totality of the combined quantities of space and time. The idea was first enunciated by Hermann Minkowski, who noticed that Special Relativity required a non-Euclidean geometry, the first time this had been done in a physically relevant context.
A Euclidean mathematical space in which "lengths" can be of arbitrary dimensions, but the quantity which would be invariant under transformations in a Euclidean space would preserve the "length" which is always expressible in terms of the coordinates as:
L2= a2+ b2+ c2+ d2+...
In "regular" three dimensional space of human experience, a, b and c would be the regular x, y, and z coordinates and that's all there would be. In Minkowski space, the "length" is the Interval, which in 4 spacetime dimensions is:
s2= (ct)2- x2-y2-z2
It is the difference in sign among some of the terms that makes this "length" non-Euclidean.
Rutherford Model of nucleus
The Rutherford model of the atom was the grade-school picture of a positive core surrounded by orbiting negative electrons.
Balmer Spectrum
Johann Balmer, an instructor in a girls school in Switzerland, in 1885 found that the emission spectra of Hydrogen had a strange regularity when analyzed in a prism. The regularity was 4 precisely determined lines corresponding to blue, purple, and red - he saw 4 lines. Nobody understood the reasons for this, but Balmer, quite by construction, was able to find a mathematical formula that would reproduce the wavelengths in terms of differences of integer quantities. It was this work that Bohr came to in 1913.
Bohr's atomic model
Niels Bohr's model of the atom was based on the Rutherford model, but involved the creation of a mathematical description relying on electrons orbiting the nucleus according to specific, quantized orbital radii. Transitions of electrons from one radial position to another would result in the emission of a single photon of an energy that corresponds to the energy difference precisely. His assumption that the orbital angular momentum could be quantized into specific amounts depending on Planck's Constant was the first use of Planck's ideas in a context which was different from Planck's original idea.
Photon
Einstein's idea for the explanation of the photoelectric effect was to presume that light consisted of particle-like characteristics as well as wavelike characteristics. This allowed him to assign a specific energy and momentum to photons, and in turn allowed for them to scatter from electrons as if they were billiard balls - same kinematics - with recoil and momentum conservation.
worldlines and Feynman diagrams
A worldline is nothing more than the plot of the trajectory of any object as it "moves" through spacetime. Here, the idea of combining space and time suggests that a particle is "moving" in spacetime, even though it might be sitting still in space. Description of collision processes as worldline trajectories has a visual representation referred to as Feynman Diagrams (although in relativistic quantum field theory, there is a sophisticated meaning to each of the lines in a Feynman Diagram).
deBroglie model of electrons
deBroglie's idea of 1923 was that the electron in an atom is not a particle orbiting the nucleus, but could be imagined to be a wave which finds itself in an standing-wave configuration at the Bohr radii. This was the first suggestion that, just like light, entities such as electrons also have combined particle-wave properties. This would require that electrons behave like waves and exhibit wave-like phenomena such as diffraction...which was observed fairly soon after deBroglie's proposition.
electron volts
An energy unit chosen for convenience in atomic and sub-atomic measures because of the tiny nature of masses of those entities. It is the amount of energy obtained by a particle of electric charge e which is accelerated through a voltage of 1 V. In these units, many calculations are easier, but also the need to keep track of 20-30 orders of magnitude of gram-sized units is eliminated. The proton, which in everyday units, has a mass of 1.67x-24 grams is 938.3 x10 6 eV/c 2, or 938.3Mev/c 2. (Notice that the units of mass are represented using Einstein's famous E=mc 2 formula. Often, the speed of light is ignored in the representation of masses, with the units adjusted at the end of a calculation. Then, the mass of the proton would be said to be equal to 938.3 MeV.)
Heisenberg Uncertainty Principle
The Heisenberg Uncertainty Principle is often misunderstood. It states that no measurement can be performed that can measure with arbitrary precision both the position and the momentum (velocity) of any object. Mathematically, the product of precision of these two quantities must be greater than Planck's constant, which is a very tiny number, and so for "everyday" objects, this limitation is not apparent. A debate has raged for decades as to how to interpret this odd result. The most celebrated interpretation notes that the inability to make such a measurement - in principle - leads to the unacceptability of making a claim about reality beyond the imprecision implied by the Uncertainty Principle. Said another way, it is necessary, then, to claim that objects which carry simultaneously both infinitely precise locations and infinitely precise speeds do not exist.
Quantum Mechanics
Generally, Quantum Mechanics had two different direct antecedents, the so-called "matrix mechanics" of Heisenberg and the wave function mechanics of Schrodinger. Heisenberg's approach, while formally identical with Schrodingers, has no real visualization or model to go along with it. Schrodinger's theory, while it has an interpretation that allows for an image of, say, an electron cloud, is burdened with interpretation of the Wavefunction as the representative of a quantum entity which is an imaginary mathematical object - not in any sense, "the electron" or "the proton." Max Born's interpretation of the wavefunction times its complex conjugate (which is a mathematically real quantity) as a probability density made it possible again to begin to form an image of what a quantum representation might be like. In this sense, the notion, say, of an electron orbiting the nucleus as like a little planet is gone. In its place, is a distributed probability of where an electron might be. In a Hydrogen atom, for example, the probability of finding an electron is highest in one of the quantum "shells" described by Bohr, but it also has (lower) probability of being at other locations. In this sense, the problem of a charged electron "little ball" accelerating and yet not radiating is eliminated in favor of not really being able to say where the electron really is.
quantum spin
Along with qualities such as mass and charge, many elementary particles possess another defining characteristic that behaves as if the particle had a little magnetic characteristic that behaved as if the particle were electrically charged and spinning on an axis. This "spin" angular momentum can take on only particular values, for the electron, proton, and neutron, for example, only values of ±1/2 h.
Schrodinger's Cat
A "parable" attributed to Schrodinger to illustrate the problems of interpretation in quantum mechanics and the inability to specify a quantum state without a measurement.
Pauli Exclusion Principle
The theory of Pauli, which was quite ad hoc (but subsequently required by Dirac's relativistic quantum mechanical model that predicted anti-particles) that no two electrons (or protons, or neutrons...anything with spin 1/2) can exist in the same quantum state. A quantum state is defined by its energy, angular momentum (if in an atom), and spin. So, this is the origin of the shell model of the atom as electrons "added" must arrange themselves to not violate the Pauli Exclusion Principle.
Doppler Shift
The change of frequency with relative motion in sound is called the Doppler Shift: a source going away shifts its frequency lower (wavelength longer) and a source coming toward, shifts the frequency higher (wavelength shorter). Light behaves the same way in principle, but with a different, special relativistic, formulation. The important thing is that objects receding have their emitted light shifted towards the red, while those coming toward us, to the blue.
There is also a shifting of wavelengths of light due to mass, a general relativistic Doppler effect. Light emitted from very massive objects will have their wavelengths shifted toward the red as well.
Expansion of the Universe
Hubble used two observations to reach his important conclusion, that all galaxies were moving away from us. Observation and measurement of galaxies containing Cepheid Variables gives a way of determining the distance to those galaxies. Further, the observation of red shifting of the spectra, allowed Hubble to determine the speed of galaxies. It was these tools that Hubble used to discover that the speed of all observed galaxies appeared to be linearly increasing with their distance from us. The constant of proportionality is called the Hubble Constant, H0. The inverse of the Hubble Constant is then the total time since the speed was zero, and the distance was zero...namely, the age of the universe. It is currently determined to be about 1.4-1.5 x 1010 years, or approximately 14 billion years.
Black Holes
Predicted from General Relativity...if an object can somehow shrink to a radius which is smaller than that radius at which the escape velocity is that of the speed of light, nothing can escape. This radius, called the Schwartzchild Radius, is a small size, and for most objects, is deep inside of the object. Hence, it is not possible to "get inside" of it from the outside. However, for stars which have collapsed due to their own gravitational attraction, the actual size of the star can become smaller than the Schwartzchild Radius. Any light that crosses over that radius from the outside will be trapped, and indeed any matter will be trapped as well. Hence, the object will not shine, it will be Black.
It is the observation of radiation given off by charged matter that is being accelerated into a black hole, that is the hint of the existence of such an object. Now, it is believed that stars can form black holes, but also that entire collections of stars can form a black hole and that such regions are likely to exist in the center of every galaxy.
Geometry of Spacetime
General Relativity is a theory of spacetime in the presence of mass and energy. As such, it is possible to contemplate (and now measure) the kind of geometry that our universe exhibits. This is best categorized by how parallel lines would behave (in this four-dimensional fabric of spacetime):
Parallel lines maintain their distance between them: this would be a flat geometry.
Parallel lines would meet: this would be a closed geometry, similar to that of the "spherical" earth.
Parallel lines would diverge: this would be an open geometry.
The balloon measurements of the CMB fluctuations can be related to the geometry in which this radiation is imbedded and these measurements suggest that it is flat.
Big Bang
The idea from Hubble's measurements, and confirmed many times by determination of the CMB, that the universe has expanded from a hot, dense origin to that which we see still expanding today. It is important to note that the expansion is ALL of the universe, including space and time itself, and that there is not a "vessel" of space into which the big bang explosion is propagating.
General Relativity
General Relativity is the theory of Einstein which includes the physics of non-inertial rest frames. Since, from his Principle of Equivalence, there is an identity between non-inertial frames and inertal frames in a gravitational field, this is a theory of gravity and spacetime in the presence of masses. It is "general" because it includes within it the special case of no-masses, and inertially moving frames...namely, the Special Theory of Relativity is imbedded as a special case.
Principle of Equivalence
The idea of Einstein that there is no difference between the situations experienced in a frame of reference which is undergoing constant acceleration and a frame of reference which is at rest relative to a source of gravitational field. Anything that can be shown to happen in one, must happen in the other.
Light Bending
From the Principle of Equivalence, a light beam which passes through a frame of reference which is accelerating would appear to an observer in that frame to be bending. Hence, the same phenomenon should occur in a frame which is stationary relative to a mass...a gravitational field. This has been observed many times, notably originally by Eddington in 1917 as light passed by the sun and was seen to have bent as a result and in comparison from that same star's location when the sun was not in the way. In modern experience, the multiple images of background objects formed when they pass by, and are "focussed" by an intermediate, massive object is dramatic evidence of light-bending. This phenemenon is called Gravitational Lensing.
Kepler's Laws
Kepler's three laws of planetary motion represent the first attempt to quantitatively apply mathematical ideas quantitatively to the motions of the planets. A total break with scholastic notions since an understanding of the heavens was not supposed to be possible. His laws are:
1. That the planets follow elliptical trajectories with the sun at a focus.
2. That the planets trace out equal areas relative to the sun in equal times anywhere on their orbit.
3. That the cube of the mean radius of each orbit divided by the square of the period is the same constant for each planet.
free-fall as constantly accelerated motion
The idea that free fall is an example of constant acceleration was due to Galileo. He defined constant accleration and then measured it. It is important to note that all bodies, regardless of the qualities that would have distinguished them in an Aristotelian framework, fall at the same rates...absent air resistance.
Galilean Relativity
The notion that in a moving reference frame, if it is moving at a constant speed, there is no experiment that one can perform in that frame to detect that motion. In Einstein's theory, even the phrase "in a moving frame" is not proper, as it implies that there is such a thing as a fixed at-rest frame.
projectile motion
The idea that, in absence of air resistance, a projectile is possessed of two independent velocities (horizontal and vertical are the most commonly chosen directions). The horizontal velocity is unchanged and the vertical velocity changes (gets smaller going up and larger going down) in the same way as an object thrown straight up would have in the gravitational influence of the earth. The resultant motion traces out the shape of a parabola. This is due to Galileo.
This was the idea that uniformly accelerated motion led to the same distance traversed as constant-speed motion at the average speed of the accelerated motion. Important in Galileo's work. Proven by Oresme.
heliocentric model
The Copernican model of the solar system was an amalgam of modern and scholastic ideas. The simplicity of the idea, along with various natural explanations of observed features of the planets and their orientation was to its credit. It was not an overwhelming success, but quietly gained adherents within some of the astronomy community.
Huygens' theory of conservation of quantity of motion
Huygens, originally a Cartesian, held also in the conservation of something like momentum. However, he correctly interpreted the "quantity of motion" as having a direction as well as a magnitude. These were strictly geometrical ideas and anticipated by 30 years Newton's enunciation of vectors.
Descartes' theory of constancy of quantity of matter
Descartes was one of the first to hold the notion that something like momentum is conserved in motion. His was a strictly philosophical position, deriving from the idea that extension and motion were clear and distinct ideas and that God had started the original motion in the universe and that it would in no way be diminished in totality.
Newton's invention of the Binomial Theorem
The invention of the binomial theorem as an infinite series represenations of arbitrary functions was the underpinning of Newton's invention of calculus.
Calculus
The invention of calculus by Newton and Leibnitz as a universal prescription for what was being hinted at by many other mathematicians stands as maybe the single most important achievement in physics in millennia. With this tool, the ability to model forces and motion becomes possible and is quickly successful around Europe.
Newton's Principia
The three laws of motion, plus his gravitational theory and his few definitions of mass and momentum generally characterize Newton's mechanics.
Newton's Laws
The "Laws" of Newton included 2 which were closely paralleled by work of Descartes, Huygens, and Galileo. The Third Law was uniquely Newton's.
Newton's Law of Gravitation
Newton's Gravitational "Law" usually occupies as grand a status as the famous "Three Laws" and describes the force of attraction between any two masses.
Conservation of Momentum
The conservation of momentum is a direct result of the Third and Second Laws of Newton and holds for all collisions.
Conservation of Mechanical Energy
The beginnings of bigger ideas (conservation of total energy, and subsequently the conservation of mass-energy), the conservation of kinetic and then kinetic plus potential energies was a while in coming. Huygens and Leibnitz both had the ideas that something involving v^2 was conserved in some collisions, but a satisfactory understanding was nearly a century away from Newton's first understanding of momentum.
Hooke's Law
The force of an elastic object is proportional to the distance through which it is stretched or compressed. The potential energy is proportional to that distance-squared.
Collisions
There are three kinds of collisions:
1. elastic collisions - mechanical energy and momentum are conserved and no energy is lost due to heat, sound, etc.
2. inelastic collisions - only momentum is conserved...a more realistic real-life situation, where always some friction or sound or something removes energy, and eventually converts it to usually heat.
3. completely inelastic collisions - momentum is conserved, but kinetic energy maximally not conserved. These are collisions in which the bodies stick together after the collision.
angular momentum
A quantity having to do with rotations or twists - the momentum times a lever arm. The direction of angular momentum is perpendicular to the plane of the momentum and lever arm...and points in the direction of your right thumb, if your fingers follow the direction of the lever arm vector and then the momentum vector. Looking from above on the rotating stool demonstration, if I were turning counterclockwise, the angular momentum would point up. It is conserved.
gravitational potential energy
By choosing the zero of gravitational potential energy to be at infinity from any massive object, then the potential energy of another massive object can be written as a single relationship..it is inversely proportional to the distance between the two objects. Remember, potential energy is always a relative quantity, depending on differences, not an absolute zero point.
Newton's Absolute Space
Newton believed that Space was an absolute quantity. He knew that velocities were always measured with respect to other objects, and were relative things (like Galileo). But, he reasoned that accelerations are absolute quantities when measured against the absolute coordinate system of Space. While a mathematical construct, Newton believed it was real. He also believed that there was an Absolute Time.
Newton's theory of light
...that light was made up of particles.
Hugen's theory of light
...that light is made up of waves in the ether. (Plus, Hooke.)
Conservation of Energy
A 19th Century concept that combined the mechanical energy conservation ideas with the relationship between heat and energy most convincingly proposed by Joule into a general statement that All Energy is Conserved.
kinetic theory of gasses
First described by Daniel Bernoulli, the kinetic theory of gasses seeks to explain the bulk properties of gasses (volume, pressure, temperature, etc) in terms of the collisions of unseen atoms.
transverse light
The idea that light is made of transverse waves, rather than longitudinal waves like sound, was first put forth by Fresnel in order to explain polarized light.
luminiferous ether
The need for some substance for light to "wave" in was apparent to everyone in the 18th and 19th centuries. The "luminiferous ether" was the substance thought support light propagation. For a while, other ethers were presumed active to support the phenomena of gravitation, electricity, and magnetism. The properties of the luminiferous ether were particularly troubling, since light, as a transverse wave, would have implied shear forces in the ether plus, because the speed of light was known to be very high, would have required the ether to be stiffer than steel in order to support those shear forces.
Coulomb's Law
Originating with Coulomb (but also with the silent Cavendish), the force between two electric charges is proportional to the magnitude of the charges and inversely proportional to the distance between them squared - tantillizingly similar to Newton's Gravitational Law.
Maxwell's Distribution of speeds
James Clerk Maxwell first described the average distributions of speeds in a gas at a given temperature. Called eventually the Maxwell-Boltzmann Distribution.
Maxwell's equations
The collection of mathematical formulae that completely describe the behavior of electric and magnetic fields do to configurations of charges and currents. The solutions to Maxwell's Equations result in wave-like results that lead to electromagnetic waves, a coupling of the electric and magnetic fields.
Electric and Magnetic fields
The mathematical entity given mathematical form by Maxwell to describe Faraday's Lines of Force. Now understood to be the physical manifestation of the effects of charges and currents.
displacement current
Just as changing magnetic fields produce electric fields, Maxwell proposed that changing electric fields produce magnetic fields. The model in which this was discussed in class was a changing electric field due to the charging of a capacitor, where between the plates one can imagine a "displacement current" associated with the increasing E field and circular B fields in that same region. This additional time-dependent term (the "change" of the E field) leads to solutions for E and B in Maxwell's equations that are wave-like. This was the unique feature of Maxwell's theory that led to the prediction of electromagnetic waves found by Hertz.
electromagnetic waves
From a symmetry argument, Maxwell predicted a strict relationship between an electric field and a magnetic field in sourceless (i.e., no charges and no currents) region of space: they would be related by a constant, which he found had the value of the speed of light. The transverse electromagnetic waves propagate at the speed of light with E and B coupled together in phase.
Lorentz Force
This is an addition to the Maxwell theory due to Lorentz, which is a relation that describes the force on a charged particle due to its experiencing an Electric Field and/or a Magnetic Field (if the charged particle is moving relative to the magnetic field).
Poynting Vector
Basically, for our purposes, it is the direction that an electromagnetic wave propagates...perpendicular to both the direction of E and the direction of B and the direction of the momentum that an electromagnetic wave can deliver as Radiation Pressure. That momentum is p = U/c, where U is the energy of the wave and is proportional to E2.
blackbody radiation
Many materials can reach a state in which they absorb all radiation that falls on them, and emit radiation of all frequencies. The intensity of this emission has a characteristic shape as a function of frequency which is independent of the material. It is the reason that color of heated materials have traditionally been accurate measures of the temperature. This radiation is called Blackbody Radiation and its universal nature led to many attempts to explain it in terms of Maxwell's theory and conventional thermodynamics. All attempts failed until Planck in 1901.
Planck's quantum of action
Planck's notion that the radiation emitted by a blackbody is quantized into "bundles" of energy which are discrete. His was not a theory of light, he thought, but a statement about the oscillators presumed to be the emitters of radiation from the walls of the heated object.
Special Relativity
Einstein's Special Theory of Relativity was originally an attempt to account for strange consequences in electromagnetic phenomena when viewed from different, co-moving rest frames. It has since taken on a set of consequences which are often portrayed as only mechanics.
There are two postulates that make up relativity theory:
1. There is no experiment (mechanical or electromagnetic) that can determine whether one is moving in an intertial frame which is moving or at rest relative to some other frame.
2. The speed of light is the same, c, in all intertial frames of reference. This means, if true, that there is no way to measure the presence of an ether...and so the ether is not a scientifically meaningful concept (that's Mach's influence on Einstein...which we have all inherited.)
(remember: an inertial frame is one which moves at a constant velocity...which could be zero...as measured with respect to any other inertial frame.)
These have a number of consequences:
1. Simultaneity between events in co-moving reference frames is no longer a measurable, and hence, meaningful concept.
2. Time Dilation. A clock on a frame S' moving with respect to an observer in frame S appears to move slower to S than it does to S'. So, on earth....the "clock" of the decaying muon appears to be slower, and hence the muon lives to reach the surface.
3. Length Contraction. The length of an object in frame S' moving with respect to an observer in frame S appears to be shorter to S than it does to S'. So, in the rest frame of the cosmic ray muon, the atmosphere (which appears to it to be approaching it) looks to be shorter to it, and hence the muon lives to reach the surface.
4. Relativity of inertia. The mass of an object in frame S' moving with respect to an observer in frame S appears to get larger with velocity than it does to S'. To S', the object's mass is its "rest mass," and is a constant. This relative inertia is called "relativistic mass."
5. Mass-energy. Mass and energy are one and the same quantity and can manifest itself either way. They are related by the famous E = mc 2 relation, where m here refers to the relativistic mass. In the rest frame of the mass, the energy is E = m0c 2 where m0 is the rest mass.
6. Relativity of electric and magnetic fields. The presence of an electric field in a frame S' moving with respect to an observer in frame S will appear to the latter to be a combined electric and magnetic field, and visa versa.
7. Lorentz Transformations. The transformations of space and time coordinates between two co-moving frames mix the space and time coordinates in a particular way which actually determine the above conditions deductively. They also are the transformations which account for the solution to the conundrums of electromagnetism that we talked about in lecture.
Spacetime
The nature of relativity is that space and time are no longer separable into two different things and that proper use of them as coordinates in physical models requires that they be treated together...Spacetime is the term used to describe the totality of the combined quantities of space and time. The idea was first enunciated by Hermann Minkowski, who noticed that Special Relativity required a non-Euclidean geometry, the first time this had been done in a physically relevant context.
A Euclidean mathematical space in which "lengths" can be of arbitrary dimensions, but the quantity which would be invariant under transformations in a Euclidean space would preserve the "length" which is always expressible in terms of the coordinates as:
L2= a2+ b2+ c2+ d2+...
In "regular" three dimensional space of human experience, a, b and c would be the regular x, y, and z coordinates and that's all there would be. In Minkowski space, the "length" is the Interval, which in 4 spacetime dimensions is:
s2= (ct)2- x2-y2-z2
It is the difference in sign among some of the terms that makes this "length" non-Euclidean.
Rutherford Model of nucleus
The Rutherford model of the atom was the grade-school picture of a positive core surrounded by orbiting negative electrons.
Balmer Spectrum
Johann Balmer, an instructor in a girls school in Switzerland, in 1885 found that the emission spectra of Hydrogen had a strange regularity when analyzed in a prism. The regularity was 4 precisely determined lines corresponding to blue, purple, and red - he saw 4 lines. Nobody understood the reasons for this, but Balmer, quite by construction, was able to find a mathematical formula that would reproduce the wavelengths in terms of differences of integer quantities. It was this work that Bohr came to in 1913.
Bohr's atomic model
Niels Bohr's model of the atom was based on the Rutherford model, but involved the creation of a mathematical description relying on electrons orbiting the nucleus according to specific, quantized orbital radii. Transitions of electrons from one radial position to another would result in the emission of a single photon of an energy that corresponds to the energy difference precisely. His assumption that the orbital angular momentum could be quantized into specific amounts depending on Planck's Constant was the first use of Planck's ideas in a context which was different from Planck's original idea.
Photon
Einstein's idea for the explanation of the photoelectric effect was to presume that light consisted of particle-like characteristics as well as wavelike characteristics. This allowed him to assign a specific energy and momentum to photons, and in turn allowed for them to scatter from electrons as if they were billiard balls - same kinematics - with recoil and momentum conservation.
worldlines and Feynman diagrams
A worldline is nothing more than the plot of the trajectory of any object as it "moves" through spacetime. Here, the idea of combining space and time suggests that a particle is "moving" in spacetime, even though it might be sitting still in space. Description of collision processes as worldline trajectories has a visual representation referred to as Feynman Diagrams (although in relativistic quantum field theory, there is a sophisticated meaning to each of the lines in a Feynman Diagram).
deBroglie model of electrons
deBroglie's idea of 1923 was that the electron in an atom is not a particle orbiting the nucleus, but could be imagined to be a wave which finds itself in an standing-wave configuration at the Bohr radii. This was the first suggestion that, just like light, entities such as electrons also have combined particle-wave properties. This would require that electrons behave like waves and exhibit wave-like phenomena such as diffraction...which was observed fairly soon after deBroglie's proposition.
electron volts
An energy unit chosen for convenience in atomic and sub-atomic measures because of the tiny nature of masses of those entities. It is the amount of energy obtained by a particle of electric charge e which is accelerated through a voltage of 1 V. In these units, many calculations are easier, but also the need to keep track of 20-30 orders of magnitude of gram-sized units is eliminated. The proton, which in everyday units, has a mass of 1.67x-24 grams is 938.3 x10 6 eV/c 2, or 938.3Mev/c 2. (Notice that the units of mass are represented using Einstein's famous E=mc 2 formula. Often, the speed of light is ignored in the representation of masses, with the units adjusted at the end of a calculation. Then, the mass of the proton would be said to be equal to 938.3 MeV.)
Heisenberg Uncertainty Principle
The Heisenberg Uncertainty Principle is often misunderstood. It states that no measurement can be performed that can measure with arbitrary precision both the position and the momentum (velocity) of any object. Mathematically, the product of precision of these two quantities must be greater than Planck's constant, which is a very tiny number, and so for "everyday" objects, this limitation is not apparent. A debate has raged for decades as to how to interpret this odd result. The most celebrated interpretation notes that the inability to make such a measurement - in principle - leads to the unacceptability of making a claim about reality beyond the imprecision implied by the Uncertainty Principle. Said another way, it is necessary, then, to claim that objects which carry simultaneously both infinitely precise locations and infinitely precise speeds do not exist.
Quantum Mechanics
Generally, Quantum Mechanics had two different direct antecedents, the so-called "matrix mechanics" of Heisenberg and the wave function mechanics of Schrodinger. Heisenberg's approach, while formally identical with Schrodingers, has no real visualization or model to go along with it. Schrodinger's theory, while it has an interpretation that allows for an image of, say, an electron cloud, is burdened with interpretation of the Wavefunction as the representative of a quantum entity which is an imaginary mathematical object - not in any sense, "the electron" or "the proton." Max Born's interpretation of the wavefunction times its complex conjugate (which is a mathematically real quantity) as a probability density made it possible again to begin to form an image of what a quantum representation might be like. In this sense, the notion, say, of an electron orbiting the nucleus as like a little planet is gone. In its place, is a distributed probability of where an electron might be. In a Hydrogen atom, for example, the probability of finding an electron is highest in one of the quantum "shells" described by Bohr, but it also has (lower) probability of being at other locations. In this sense, the problem of a charged electron "little ball" accelerating and yet not radiating is eliminated in favor of not really being able to say where the electron really is.
quantum spin
Along with qualities such as mass and charge, many elementary particles possess another defining characteristic that behaves as if the particle had a little magnetic characteristic that behaved as if the particle were electrically charged and spinning on an axis. This "spin" angular momentum can take on only particular values, for the electron, proton, and neutron, for example, only values of ±1/2 h.
Schrodinger's Cat
A "parable" attributed to Schrodinger to illustrate the problems of interpretation in quantum mechanics and the inability to specify a quantum state without a measurement.
Pauli Exclusion Principle
The theory of Pauli, which was quite ad hoc (but subsequently required by Dirac's relativistic quantum mechanical model that predicted anti-particles) that no two electrons (or protons, or neutrons...anything with spin 1/2) can exist in the same quantum state. A quantum state is defined by its energy, angular momentum (if in an atom), and spin. So, this is the origin of the shell model of the atom as electrons "added" must arrange themselves to not violate the Pauli Exclusion Principle.
Doppler Shift
The change of frequency with relative motion in sound is called the Doppler Shift: a source going away shifts its frequency lower (wavelength longer) and a source coming toward, shifts the frequency higher (wavelength shorter). Light behaves the same way in principle, but with a different, special relativistic, formulation. The important thing is that objects receding have their emitted light shifted towards the red, while those coming toward us, to the blue.
There is also a shifting of wavelengths of light due to mass, a general relativistic Doppler effect. Light emitted from very massive objects will have their wavelengths shifted toward the red as well.
Expansion of the Universe
Hubble used two observations to reach his important conclusion, that all galaxies were moving away from us. Observation and measurement of galaxies containing Cepheid Variables gives a way of determining the distance to those galaxies. Further, the observation of red shifting of the spectra, allowed Hubble to determine the speed of galaxies. It was these tools that Hubble used to discover that the speed of all observed galaxies appeared to be linearly increasing with their distance from us. The constant of proportionality is called the Hubble Constant, H0. The inverse of the Hubble Constant is then the total time since the speed was zero, and the distance was zero...namely, the age of the universe. It is currently determined to be about 1.4-1.5 x 1010 years, or approximately 14 billion years.
Black Holes
Predicted from General Relativity...if an object can somehow shrink to a radius which is smaller than that radius at which the escape velocity is that of the speed of light, nothing can escape. This radius, called the Schwartzchild Radius, is a small size, and for most objects, is deep inside of the object. Hence, it is not possible to "get inside" of it from the outside. However, for stars which have collapsed due to their own gravitational attraction, the actual size of the star can become smaller than the Schwartzchild Radius. Any light that crosses over that radius from the outside will be trapped, and indeed any matter will be trapped as well. Hence, the object will not shine, it will be Black.
It is the observation of radiation given off by charged matter that is being accelerated into a black hole, that is the hint of the existence of such an object. Now, it is believed that stars can form black holes, but also that entire collections of stars can form a black hole and that such regions are likely to exist in the center of every galaxy.
Geometry of Spacetime
General Relativity is a theory of spacetime in the presence of mass and energy. As such, it is possible to contemplate (and now measure) the kind of geometry that our universe exhibits. This is best categorized by how parallel lines would behave (in this four-dimensional fabric of spacetime):
Parallel lines maintain their distance between them: this would be a flat geometry.
Parallel lines would meet: this would be a closed geometry, similar to that of the "spherical" earth.
Parallel lines would diverge: this would be an open geometry.
The balloon measurements of the CMB fluctuations can be related to the geometry in which this radiation is imbedded and these measurements suggest that it is flat.
Big Bang
The idea from Hubble's measurements, and confirmed many times by determination of the CMB, that the universe has expanded from a hot, dense origin to that which we see still expanding today. It is important to note that the expansion is ALL of the universe, including space and time itself, and that there is not a "vessel" of space into which the big bang explosion is propagating.
General Relativity
General Relativity is the theory of Einstein which includes the physics of non-inertial rest frames. Since, from his Principle of Equivalence, there is an identity between non-inertial frames and inertal frames in a gravitational field, this is a theory of gravity and spacetime in the presence of masses. It is "general" because it includes within it the special case of no-masses, and inertially moving frames...namely, the Special Theory of Relativity is imbedded as a special case.
Principle of Equivalence
The idea of Einstein that there is no difference between the situations experienced in a frame of reference which is undergoing constant acceleration and a frame of reference which is at rest relative to a source of gravitational field. Anything that can be shown to happen in one, must happen in the other.
Light Bending
From the Principle of Equivalence, a light beam which passes through a frame of reference which is accelerating would appear to an observer in that frame to be bending. Hence, the same phenomenon should occur in a frame which is stationary relative to a mass...a gravitational field. This has been observed many times, notably originally by Eddington in 1917 as light passed by the sun and was seen to have bent as a result and in comparison from that same star's location when the sun was not in the way. In modern experience, the multiple images of background objects formed when they pass by, and are "focussed" by an intermediate, massive object is dramatic evidence of light-bending. This phenemenon is called Gravitational Lensing.
Kepler's Laws
Kepler's three laws of planetary motion represent the first attempt to quantitatively apply mathematical ideas quantitatively to the motions of the planets. A total break with scholastic notions since an understanding of the heavens was not supposed to be possible. His laws are:
1. That the planets follow elliptical trajectories with the sun at a focus.
2. That the planets trace out equal areas relative to the sun in equal times anywhere on their orbit.
3. That the cube of the mean radius of each orbit divided by the square of the period is the same constant for each planet.
free-fall as constantly accelerated motion
The idea that free fall is an example of constant acceleration was due to Galileo. He defined constant accleration and then measured it. It is important to note that all bodies, regardless of the qualities that would have distinguished them in an Aristotelian framework, fall at the same rates...absent air resistance.
Galilean Relativity
The notion that in a moving reference frame, if it is moving at a constant speed, there is no experiment that one can perform in that frame to detect that motion. In Einstein's theory, even the phrase "in a moving frame" is not proper, as it implies that there is such a thing as a fixed at-rest frame.
projectile motion
The idea that, in absence of air resistance, a projectile is possessed of two independent velocities (horizontal and vertical are the most commonly chosen directions). The horizontal velocity is unchanged and the vertical velocity changes (gets smaller going up and larger going down) in the same way as an object thrown straight up would have in the gravitational influence of the earth. The resultant motion traces out the shape of a parabola. This is due to Galileo.
Physics Experiments
Greek Astronomical Problems
The problems of venus, mars, mercury dominated astronomy. The Pythagorean original model is important, as all followed from it. The later attempts to save the appearances come primarily from Plato's students and are geometrical in origin.
early kinematics
The paradoxes of Aristotle's explanations for "violent motion" were apparent very early in the middle ages, but were studied most intensively at the universities of Oxford and Paris in the 14th century.
new sky events
The sudden emergence of supernovae in 1572 and 1604, along with the big comet of 1577 led to serious trouble for the naive Aristotelian model of the cosmos.
Galilean Kinematics
The work on accelerated motion is important, and demonstrated Galileo's ability to create experiments that extrapolate to circumstances that he could not measure. His abstractions to the underlying physics, "inside" of what he actually perceived, was brand new. His demonstration that the distance traveled in constantly accelerated motion was proportional to the square of the time was important. Also, his insistence on the very un-Aristotean idea that the acceleration of falling bodies was independent of the substance and the weight of the body was an important demonstration.
The idea that projectile motion was the superposition of two, independent motions, was a brand new way of thinking. That it was related to his (The Galilean) Principle of Relativity tied the whole thing together.
Finally, his interpretation of the motion of the pendulum as action under the same influence as falling bodies and the independence of the period of its oscillation from the mass (or substance) of the bob and the height of the oscillation was new.
Galilean Astronomy
His observation of the phases of Venus, the surface of the moon, the satellites of Jupiter, the multitude of never before seen stars, sunspots, and many other phenomena were, some of them, brand new. But, because of his careful analysis and publication, his observations and analyses stood out as important and influential.
Newton's mechanics experiments, 1
Newton made a number of mechanical measurements, most important so far is his determination of g and its comparison with the prediction from the moon's parameters.
Newton's mechanics experiments, 2
Newton made careful measurements of frictionless collisions using carefully characterized pendula which were 10' long. He made these measurements in a variety of media and even concluded the v^2 resistance of bodies due to fluids, like air.
Joules' Determination of Heat as energy
The stirring of water by a carefully controlled paddle system which was driven by falling weights allowed him to related the amount of heat added to the water to the amount of potential energy lost->kinetic energy gained by the paddles.
Roemer's determination of the speed of light
By measuring the differences in the eclipsing of Io behind Jupiter at different points during the earth's year, Roemer determined a finite speed of light as 130,000mi/s in 1675. This lent credence to Newton's idea of light as particles.
experimentum crucis
Newton's "crucial experiment" was to determine that white light was not "pure" but was composite, consisting of lights of other colors that could be separated and "reassembled" with prisms.
Aberration of Starlight
Proof that the earth orbits the sun, by showing that the apparent direction of a star is not the same at different times of the years. This was explained by James Bradley in 1729 as relating to the different speeds of the earth, relative to the speed of light. (This is the umbrella phenomenon.)
Young's Double Slit Experiment
In 1801 Thomas Young gave a lecture and demonstration to the British Royal Society that showed that diffraction was an interference phenomenon, which is a property of only waves. This was thought to be the definitive demonstration that Newton's particulate theory of light was not correct. Supporting evidence was the demonstration that light slows down in passing from one medium to a more dense medium. (Newton's theory required it to speed up.)
Voltaic Pile
In 1800, Alessandro Volta produced the first battery, making it possible to perform electrical experiments without requiring either biological specimens, or lightning.
Oersted's experiment
The observation that a force induced by a wire carrying current, actually causes a compass needle to line up perpendicularly to the wire: an aysmmetry that was astounding to everyone.
Faraday's Law
The observation by Faraday that a potential difference (voltage) appears across wires that intercept a changing magnetic field line configuration. Steady fields do nothing, the change is required.
Ampere's Law
The mathematical description (one of Maxwell's Equations) of a magnetic field as concentric disturbances around a wire carrying current.
Brownian Motion
The observation that pollen (and then all similarly-sized materials) behaved as if animated when suspended in water and observed through a microscope. The jerky movement was predicted to be due to the statistical bombardment of the water molecules and quantified by Einstein in 1905.
Michelson Morley Experiments
Starting in 1880 and for the next decade, Albert Michelson and Edward Morley attempted to measure the speed of the luminiferous ether as the earth moved through it. (It was "known" that the earth did not drag the ether along with it in its orbit because of the observation of stellar aberration.) The results of the Michelson Morley Experiments were uniformly confusing: they showed no effect of the ether motion.
Discovery of Electron
The discovery of the electron by J.J. Thompson in cathode rays was done by carefully passing the cathode ray beam through E and B fields and using the Lorentz Force to balance them. This configuration leads to the determination of e/m for a presumed particulate constituency of the beam.
Discovery of X-Rays
...by Roentgen in 1895, by noticing the fluorescence of a treated paper when exposed at a distance to something emerging from the end of a cathode ray tube.
Discovery of Radioactivity
Done by Becquerel in 1896 by inadvertently exposing uranium ore to photographic paper in the absence of any sunlight exposure.
Isolation of Radium
Experiments done by the Curies in 1897-8 isolated the most highly radioactive material known, Radium (and Polonium, separately) by chemically extracting it from pitchblend.
Alpha and beta particles
In 1898 Rutherford carefully analyzed the products of radioactive decay and found two species (eventually expanded to three by Villard in 1900). They were:
1. alpha radiation: which were easily stopped by a minimum amount of material. He found them to be positively charged and have the e/m characteristic of Helium ions.
2. beta radiation: which were much more penetrating through materials. These were responsible for what Becquerel saw, and it was he who found them to be negatively charged.
Rutherford Scattering
Rutherford, Geiger, and Marsden's experiment consisted of scattering of alpha particles through a thin, gold foil. The deflected alphas were then counted as they hit scintillating sheets, resulting in visible light bursts. The distribution of the scintillations for many, many scatterings was recorded and to their surprise, alphas were occasionally scattered backwards, inconsistent with the currently fashionable models of atomic systems. Subsequently, Rutherford concluded that the atom consists of a hard, heavy positive core and orbiting negative electrons. He did the calculations for a positive alpha particle impinging on the presumed positive nucleus and calculated how the electrostatic force of repulsion between the two of them would deflect alphas depending on their initial incidence angles.
Moseley's atomic X-Ray diffraction experiments
Harry Moseley built a sensitive apparatus that consisted of a long cathode ray tube (as a precise source of electron beams), a sample "train" (as a source of many chemical samples as targets for the electron beam), and an X-ray spectrometer (as a device to measure the wavelengths of X-rays that are emitted by the targets after they decay from atomic states excited by the electron collisions. He relied on Bohr's atomic theory that specified the energies of atomic transitions, which depended on the Atomic Number of the atomic species. He found that each element in the periodic table differed by one unit in Z and that many holes existed among the known chemical elements. These were subsequently found and agreed with his predictions.
Compton Scattering
The high-energy version of the photoelectric effect is when high energy light (in the form of X-rays or gamma rays) scatters from electrons. The scattering of photons by electrons was predicted by Einstein to behave just like billiard-ball collisions: the photon hits an electron and the two of them scatter according to the conservation of energy and momentum. However, the photon exhibits a momentum change by the frequency of the outgoing X-rays being different from the incoming X-ray. This outgoing frequency was measured by Compton and it agreed with (his) calculations of what Einstein's photon model would require.
Nuclear decay probability
Rutherford and Frederick Soddy (a chemist) painstakingly established the universal lifetime relation for all unstable nuclei that depends on a single number, specific for each species called the "lifetime." They were able to isolate the decays of many nuclear types and follow the chain of one element into another as alpha emission takes away 2 units of atomic number (taking element Z into element with Z-2) and beta emission adds 1 unit of atomic number (taking element Z into element Z+1).
Cepheid Variable Stars
Stars which have pulsating brightness (sometimes only over a few days), are called Cepheid Variable Stars. The period of this shift is very regular and can be correlated with the magnitude of the star, which in turn can be turned into a measurement of distance.
Tycho's catalog
The enormous amount of systematically cataloged data of more than 700 stars and planets over 20 years was the single most important experimental event of two millennia. It made Kepler's work possible as the precision required to map orbits accurately enough to show the slight deviation from circles could only come with decades of nightly recorded observations. Nobody had ever thought to do this and it implies new recognition of the importance of quantitative measurement of natural phenomena. It also suggests that the idea of an in-principle unknowable nature of the heavens was crumbling...at least in northern Europe during its time of philosophical and social upheaval.
Light-bending: Solar Eclipse Experiment
In 1919 Eddington announced that his expedition to Africa to observe the star background during a full eclipse of the sun confirmed Einstein's predictions that the sun would bend light.
The problems of venus, mars, mercury dominated astronomy. The Pythagorean original model is important, as all followed from it. The later attempts to save the appearances come primarily from Plato's students and are geometrical in origin.
early kinematics
The paradoxes of Aristotle's explanations for "violent motion" were apparent very early in the middle ages, but were studied most intensively at the universities of Oxford and Paris in the 14th century.
new sky events
The sudden emergence of supernovae in 1572 and 1604, along with the big comet of 1577 led to serious trouble for the naive Aristotelian model of the cosmos.
Galilean Kinematics
The work on accelerated motion is important, and demonstrated Galileo's ability to create experiments that extrapolate to circumstances that he could not measure. His abstractions to the underlying physics, "inside" of what he actually perceived, was brand new. His demonstration that the distance traveled in constantly accelerated motion was proportional to the square of the time was important. Also, his insistence on the very un-Aristotean idea that the acceleration of falling bodies was independent of the substance and the weight of the body was an important demonstration.
The idea that projectile motion was the superposition of two, independent motions, was a brand new way of thinking. That it was related to his (The Galilean) Principle of Relativity tied the whole thing together.
Finally, his interpretation of the motion of the pendulum as action under the same influence as falling bodies and the independence of the period of its oscillation from the mass (or substance) of the bob and the height of the oscillation was new.
Galilean Astronomy
His observation of the phases of Venus, the surface of the moon, the satellites of Jupiter, the multitude of never before seen stars, sunspots, and many other phenomena were, some of them, brand new. But, because of his careful analysis and publication, his observations and analyses stood out as important and influential.
Newton's mechanics experiments, 1
Newton made a number of mechanical measurements, most important so far is his determination of g and its comparison with the prediction from the moon's parameters.
Newton's mechanics experiments, 2
Newton made careful measurements of frictionless collisions using carefully characterized pendula which were 10' long. He made these measurements in a variety of media and even concluded the v^2 resistance of bodies due to fluids, like air.
Joules' Determination of Heat as energy
The stirring of water by a carefully controlled paddle system which was driven by falling weights allowed him to related the amount of heat added to the water to the amount of potential energy lost->kinetic energy gained by the paddles.
Roemer's determination of the speed of light
By measuring the differences in the eclipsing of Io behind Jupiter at different points during the earth's year, Roemer determined a finite speed of light as 130,000mi/s in 1675. This lent credence to Newton's idea of light as particles.
experimentum crucis
Newton's "crucial experiment" was to determine that white light was not "pure" but was composite, consisting of lights of other colors that could be separated and "reassembled" with prisms.
Aberration of Starlight
Proof that the earth orbits the sun, by showing that the apparent direction of a star is not the same at different times of the years. This was explained by James Bradley in 1729 as relating to the different speeds of the earth, relative to the speed of light. (This is the umbrella phenomenon.)
Young's Double Slit Experiment
In 1801 Thomas Young gave a lecture and demonstration to the British Royal Society that showed that diffraction was an interference phenomenon, which is a property of only waves. This was thought to be the definitive demonstration that Newton's particulate theory of light was not correct. Supporting evidence was the demonstration that light slows down in passing from one medium to a more dense medium. (Newton's theory required it to speed up.)
Voltaic Pile
In 1800, Alessandro Volta produced the first battery, making it possible to perform electrical experiments without requiring either biological specimens, or lightning.
Oersted's experiment
The observation that a force induced by a wire carrying current, actually causes a compass needle to line up perpendicularly to the wire: an aysmmetry that was astounding to everyone.
Faraday's Law
The observation by Faraday that a potential difference (voltage) appears across wires that intercept a changing magnetic field line configuration. Steady fields do nothing, the change is required.
Ampere's Law
The mathematical description (one of Maxwell's Equations) of a magnetic field as concentric disturbances around a wire carrying current.
Brownian Motion
The observation that pollen (and then all similarly-sized materials) behaved as if animated when suspended in water and observed through a microscope. The jerky movement was predicted to be due to the statistical bombardment of the water molecules and quantified by Einstein in 1905.
Michelson Morley Experiments
Starting in 1880 and for the next decade, Albert Michelson and Edward Morley attempted to measure the speed of the luminiferous ether as the earth moved through it. (It was "known" that the earth did not drag the ether along with it in its orbit because of the observation of stellar aberration.) The results of the Michelson Morley Experiments were uniformly confusing: they showed no effect of the ether motion.
Discovery of Electron
The discovery of the electron by J.J. Thompson in cathode rays was done by carefully passing the cathode ray beam through E and B fields and using the Lorentz Force to balance them. This configuration leads to the determination of e/m for a presumed particulate constituency of the beam.
Discovery of X-Rays
...by Roentgen in 1895, by noticing the fluorescence of a treated paper when exposed at a distance to something emerging from the end of a cathode ray tube.
Discovery of Radioactivity
Done by Becquerel in 1896 by inadvertently exposing uranium ore to photographic paper in the absence of any sunlight exposure.
Isolation of Radium
Experiments done by the Curies in 1897-8 isolated the most highly radioactive material known, Radium (and Polonium, separately) by chemically extracting it from pitchblend.
Alpha and beta particles
In 1898 Rutherford carefully analyzed the products of radioactive decay and found two species (eventually expanded to three by Villard in 1900). They were:
1. alpha radiation: which were easily stopped by a minimum amount of material. He found them to be positively charged and have the e/m characteristic of Helium ions.
2. beta radiation: which were much more penetrating through materials. These were responsible for what Becquerel saw, and it was he who found them to be negatively charged.
Rutherford Scattering
Rutherford, Geiger, and Marsden's experiment consisted of scattering of alpha particles through a thin, gold foil. The deflected alphas were then counted as they hit scintillating sheets, resulting in visible light bursts. The distribution of the scintillations for many, many scatterings was recorded and to their surprise, alphas were occasionally scattered backwards, inconsistent with the currently fashionable models of atomic systems. Subsequently, Rutherford concluded that the atom consists of a hard, heavy positive core and orbiting negative electrons. He did the calculations for a positive alpha particle impinging on the presumed positive nucleus and calculated how the electrostatic force of repulsion between the two of them would deflect alphas depending on their initial incidence angles.
Moseley's atomic X-Ray diffraction experiments
Harry Moseley built a sensitive apparatus that consisted of a long cathode ray tube (as a precise source of electron beams), a sample "train" (as a source of many chemical samples as targets for the electron beam), and an X-ray spectrometer (as a device to measure the wavelengths of X-rays that are emitted by the targets after they decay from atomic states excited by the electron collisions. He relied on Bohr's atomic theory that specified the energies of atomic transitions, which depended on the Atomic Number of the atomic species. He found that each element in the periodic table differed by one unit in Z and that many holes existed among the known chemical elements. These were subsequently found and agreed with his predictions.
Compton Scattering
The high-energy version of the photoelectric effect is when high energy light (in the form of X-rays or gamma rays) scatters from electrons. The scattering of photons by electrons was predicted by Einstein to behave just like billiard-ball collisions: the photon hits an electron and the two of them scatter according to the conservation of energy and momentum. However, the photon exhibits a momentum change by the frequency of the outgoing X-rays being different from the incoming X-ray. This outgoing frequency was measured by Compton and it agreed with (his) calculations of what Einstein's photon model would require.
Nuclear decay probability
Rutherford and Frederick Soddy (a chemist) painstakingly established the universal lifetime relation for all unstable nuclei that depends on a single number, specific for each species called the "lifetime." They were able to isolate the decays of many nuclear types and follow the chain of one element into another as alpha emission takes away 2 units of atomic number (taking element Z into element with Z-2) and beta emission adds 1 unit of atomic number (taking element Z into element Z+1).
Cepheid Variable Stars
Stars which have pulsating brightness (sometimes only over a few days), are called Cepheid Variable Stars. The period of this shift is very regular and can be correlated with the magnitude of the star, which in turn can be turned into a measurement of distance.
Tycho's catalog
The enormous amount of systematically cataloged data of more than 700 stars and planets over 20 years was the single most important experimental event of two millennia. It made Kepler's work possible as the precision required to map orbits accurately enough to show the slight deviation from circles could only come with decades of nightly recorded observations. Nobody had ever thought to do this and it implies new recognition of the importance of quantitative measurement of natural phenomena. It also suggests that the idea of an in-principle unknowable nature of the heavens was crumbling...at least in northern Europe during its time of philosophical and social upheaval.
Light-bending: Solar Eclipse Experiment
In 1919 Eddington announced that his expedition to Africa to observe the star background during a full eclipse of the sun confirmed Einstein's predictions that the sun would bend light.