in the early 1900s • The kinetic theory of gas Why statistical? Boltzmann’s theory • The statistical papers ...Paper I ...Paper II ...Papaer III • Brief mention to Paper IV and Paper V Tuesday, January 6, 15
(Swiss Federal Institute of Technology Zurich) Albert Einstein studied at ETH Zurich till 1900 In the intermediate exam he scored the highest. His proﬁciency diminished afterwords, and his relationship with his advisor Weber deteriorated. Tuesday, January 6, 15
(Swiss Federal Institute of Technology Zurich) Albert Einstein studied at ETH Zurich till 1900 In the intermediate exam he scored the highest. His proﬁciency diminished afterwords, and his relationship with his advisor Weber deteriorated. He had written his ﬁrst paper in 1900 and sent it to Boltzmann and Ostwald... no response. Tuesday, January 6, 15
(Swiss Federal Institute of Technology Zurich) Albert Einstein studied at ETH Zurich till 1900 In the intermediate exam he scored the highest. His proﬁciency diminished afterwords, and his relationship with his advisor Weber deteriorated. He had written his ﬁrst paper in 1900 and sent it to Boltzmann and Ostwald... no response. No jobs either. Tuesday, January 6, 15
(Swiss Federal Institute of Technology Zurich) Albert Einstein studied at ETH Zurich till 1900 In the intermediate exam he scored the highest. His proﬁciency diminished afterwords, and his relationship with his advisor Weber deteriorated. He had written his ﬁrst paper in 1900 and sent it to Boltzmann and Ostwald... no response. No jobs either. He submitted a dissertation in 1901, which he withdrew. By 1903 he had given up on the doctorate: “The whole comedy has become tiresome for me” (letter to his friend Michele Besso) Tuesday, January 6, 15
(Swiss Federal Institute of Technology Zurich) Albert Einstein studied at ETH Zurich till 1900 In the intermediate exam he scored the highest. His proﬁciency diminished afterwords, and his relationship with his advisor Weber deteriorated. He had written his ﬁrst paper in 1900 and sent it to Boltzmann and Ostwald... no response. No jobs either. He submitted a dissertation in 1901, which he withdrew. By 1903 he had given up on the doctorate: “The whole comedy has become tiresome for me” (letter to his friend Michele Besso) Still he published 5 papers in 1901-1904 Tuesday, January 6, 15
a temporary job at the Swiss patent ofﬁce In 1903 his position becomes permanent In 1903 Einstein marries (for the ﬁrst time) In 1904 his ﬁrst son Hans Albert was born. Tuesday, January 6, 15
a temporary job at the Swiss patent ofﬁce In 1903 his position becomes permanent In 1903 Einstein marries (for the ﬁrst time) In 1904 his ﬁrst son Hans Albert was born. what does a patent examiner do?? Tuesday, January 6, 15
a temporary job at the Swiss patent ofﬁce In 1903 his position becomes permanent In 1903 Einstein marries (for the ﬁrst time) In 1904 his ﬁrst son Hans Albert was born. what does a patent examiner do?? he evaluated patent applications for electromagnetic devices Tuesday, January 6, 15
a temporary job at the Swiss patent ofﬁce In 1903 his position becomes permanent In 1903 Einstein marries (for the ﬁrst time) In 1904 his ﬁrst son Hans Albert was born. what does a patent examiner do?? he evaluated patent applications for electromagnetic devices and in the case of Einstein that leaves a lot os spare time to study and for research... Tuesday, January 6, 15
21 “reviews” In 1905 Einstein publishes 5 papers “Physics was divided into separate fields, each of which was capable of devouring a short lifetime of work without having satisfied the hunger for deeper knowledge. [...] In this field, however, I soon learned to scent out that which might lead to fundamentals, and to turn aside from everything else, from the multitude of things that cluttered up the mind and divert it from the essential.” Autobiographical notes, 1947 Tuesday, January 6, 15
21 “reviews” In 1905 Einstein publishes 5 papers “Physics was divided into separate fields, each of which was capable of devouring a short lifetime of work without having satisfied the hunger for deeper knowledge. [...] In this field, however, I soon learned to scent out that which might lead to fundamentals, and to turn aside from everything else, from the multitude of things that cluttered up the mind and divert it from the essential.” Autobiographical notes, 1947 Tuesday, January 6, 15
21 “reviews” In 1905 Einstein publishes 5 papers “Physics was divided into separate fields, each of which was capable of devouring a short lifetime of work without having satisfied the hunger for deeper knowledge. [...] In this field, however, I soon learned to scent out that which might lead to fundamentals, and to turn aside from everything else, from the multitude of things that cluttered up the mind and divert it from the essential.” Autobiographical notes, 1947 Tuesday, January 6, 15
1800 by Dalton elements react in ﬁxed ratios! the debate over the existence of the atom some hydrogen + some oxygen = water if I double the hydrogen I MUST double the oxygen to obtain water! Tuesday, January 6, 15
1800 by Dalton elements react in ﬁxed ratios! the debate over the existence of the atom Mendeleev, 1869: periodic table ATOMIC WEIGHT Tuesday, January 6, 15
1800 by Dalton elements react in ﬁxed ratios! the debate over the existence of the atom Mendeleev, 1869: periodic table ATOMIC WEIGHT Tuesday, January 6, 15
for chemistry, 1909 Ostwald: I can derive thermodynamic laws without atoms. Atoms are useful to describe chemical interactions but they are only a mathematical tool Boltzmann: atoms are real and their properties, particularly their constant motion, govern the behavior of gasses Boltzmann, 1844-1906 VS the debate over the existence of the atom Tuesday, January 6, 15
forces at a distance on each other Maxwell, 1861: particles generate a ﬁeld, which interacts with other particle’s ﬁelds F -F Lorentz-Maxwell’s electormagnetic theory Tuesday, January 6, 15
forces at a distance on each other Maxwell, 1861: particles generate a ﬁeld, which interacts with other particle’s ﬁelds F -F Lorentz-Maxwell’s electormagnetic theory Tuesday, January 6, 15
the atomic debate •Maxwell, Lorentz, ﬁelds and electromagnetic waves •epistemology: what is a scientiﬁc theory? The physics debate, early 1900s Tuesday, January 6, 15
the 1900s! a theory has to be falsifiable POSITIVISM: A theory has to be provable “No amount of experimentation can ever prove me right; a single experiment can prove me wrong.” Tuesday, January 6, 15
(Boltzmann, Plank), best if hot... and maybe controversial •ﬁnd an observed phenomenon which can only be explained within that theory, or that predicts quantities consistently with that theory, but from simple concepts, as simple and as uncontroversial as possible structure: The epistemological debate of the 1900s! Tuesday, January 6, 15
(Boltzmann, Plank), best if hot... and maybe controversial •ﬁnd an observed phenomenon which can only be explained within that theory, or that predicts quantities consistently with that theory, but from simple concepts, as simple and as uncontroversial as possible •prediction: propose an experiment to observe this behavior structure: The epistemological debate of the 1900s! Tuesday, January 6, 15
molecules • Brownian motion • photoelectric effect • electrodynamics of moving bodies • equivalence of mass and energy In 1905 Einstein publishes 5 papers Tuesday, January 6, 15
molecules • Brownian motion • photoelectric effect • electrodynamics of moving bodies • equivalence of mass and energy In 1905 Einstein publishes 5 papers Tuesday, January 6, 15
molecules • Brownian motion • photoelectric effect • electrodynamics of moving bodies • equivalence of mass and energy “statistical” In 1905 Einstein publishes 5 papers Tuesday, January 6, 15
molecules • Brownian motion • photoelectric effect • electrodynamics of moving bodies • equivalence of mass and energy “statistical” In 1905 Einstein publishes 5 papers Tuesday, January 6, 15
molecules • Brownian motion • photoelectric effect • electrodynamics of moving bodies • equivalence of mass and energy “statistical” special relativity In 1905 Einstein publishes 5 papers Tuesday, January 6, 15
equivalence of mass and energy PARADIGM SHIFT! forever changed our perception of the world, with profound implications for cosmology and our understanding of the Universe, for philosophy... and GPS technology 1905: einstein’s miraculous year special relativity Tuesday, January 6, 15
molecules • Brownian motion • photoelectric effect “statistical” full acceptance of molecular and atomic theories foundation for quantum theory Tuesday, January 6, 15
consider a glass of water. say 8oz. how many molecules of water do you think we are talking about? 8oz ~ 224 g of water a mole is by deﬁnition 6.02 x 1023 molecules (try to remember this: it will be useful later!) Tuesday, January 6, 15
consider a glass of water. say 8oz. how many molecules of water do you think we are talking about? 8oz ~ 224 g of water a mole is by deﬁnition 6.02 x 1023 molecules (try to remember this: it will be useful later!) a mole of water weights 18 g Tuesday, January 6, 15
consider a glass of water. say 8oz. how many molecules of water do you think we are talking about? 8oz ~ 224 g of water a mole is by deﬁnition 6.02 x 1023 molecules (try to remember this: it will be useful later!) 224 / 18 x 6.02 x 1023 = 7.5 x 1024 molecules in glass of water a mole of water weights 18 g Tuesday, January 6, 15
consider a glass of water. say 8oz. how many molecules of water do you think we are talking about? 8oz ~ 224 g of water a mole is by deﬁnition 6.02 x 1023 molecules (try to remember this: it will be useful later!) 224 / 18 x 6.02 x 1023 = 7.5 x 1024 molecules in glass of water a mole of water weights 18 g a septillion molecule, a trillion trillion molecules, as many molecules as... Tuesday, January 6, 15
septillion look like? there are 7 million billion ants in the world. there are a billion times as many molecules in a glass of water Tuesday, January 6, 15
septillion look like? how many stars in our galaxy? there are 7 million billion ants in the world. there are a billion times as many molecules in a glass of water Tuesday, January 6, 15
septillion look like? how many stars in our galaxy? 1011 stars in our galaxy, there are 100 galaxies of galaxies of molecules in a glass of water there are 7 million billion ants in the world. there are a billion times as many molecules in a glass of water Tuesday, January 6, 15
septillion look like? how many stars in our galaxy? 1011 stars in our galaxy, there are 100 galaxies of galaxies of molecules in a glass of water there are 7 million billion ants in the world. there are a billion times as many molecules in a glass of water the US national debt is currently ~ $15,363,624,256,030.68 this is only 1.5x1013 Tuesday, January 6, 15
consider a glass of water. say 8oz. how many molecules of water do you think we are talking about? 8oz ~ 224 g of water a mole is by deﬁnition 6.02 x 1023 molecules (try to remember this: it will be useful later!) 224 / 18 x 6.02 x 1023 = 7.5 x 1024 molecules in glass of water a mole of water weights 18 g a septillion molecule, a trillion trillion molecules, as many molecules as... Tuesday, January 6, 15
consider a glass of water. say 8oz. how many molecules of water do you think we are talking about? 8oz ~ 224 g of water a mole is by deﬁnition 6.02 x 1023 molecules (try to remember this: it will be useful later!) 224 / 18 x 6.02 x 1023 = 7.5 x 1024 molecules in glass of water a mole of water weights 18 g a septillion molecule, a trillion trillion molecules, as many molecules as... Tuesday, January 6, 15
consider a glass of water. say 8oz. how many molecules of water do you think we are talking about? 8oz ~ 224 g of water a mole is by deﬁnition 6.02 x 1023 molecules (try to remember this: it will be useful later!) 224 / 18 x 6.02 x 1023 = 7.5 x 1024 molecules in glass of water a mole of water weights 18 g a septillion molecule, a trillion trillion molecules, as many molecules as... Avogadro’s number: N Tuesday, January 6, 15
describe the world in terms of forces, but what if we are not dealing with a solid body, but a gas or liquid?? Why statistical papers? Tuesday, January 6, 15
describe the world in terms of forces, but what if we are not dealing with a solid body, but a gas or liquid?? Why statistical papers? Tuesday, January 6, 15
1831-1879 The kinetic theory of gases : a gas is a collection of small particles (atoms or molecules), in constant, random motion. Boltzmann molecular kinetic theory The statistical motion of molecules govern the thermodynamic properties of gasses and liquids Tuesday, January 6, 15
1831-1879 The kinetic theory of gases : a gas is a collection of small particles (atoms or molecules), in constant, random motion. Boltzmann molecular kinetic theory The statistical motion of molecules govern the thermodynamic properties of gasses and liquids Tuesday, January 6, 15
1831-1879 The kinetic theory of gases : a gas is a collection of small particles (atoms or molecules), in constant, random motion. Boltzmann molecular kinetic theory The statistical motion of molecules govern the thermodynamic properties of gasses and liquids instead of considering each particle, let’s consider their average behavior (probability of being somewhere) Tuesday, January 6, 15
1831-1879 The kinetic theory of gases : a gas is a collection of small particles (atoms or molecules), in constant, random motion. Boltzmann molecular kinetic theory The statistical motion of molecules govern the thermodynamic properties of gasses and liquids instead of considering each particle, let’s consider their average behavior (probability of being somewhere) Tuesday, January 6, 15
1831-1879 The kinetic theory of gases : a gas is a collection of small particles (atoms or molecules), in constant, random motion. Boltzmann molecular kinetic theory The statistical motion of molecules govern the thermodynamic properties of gasses and liquids P, T, ρ, V instead of considering each particle, let’s consider their average behavior (probability of being somewhere) Tuesday, January 6, 15
1831-1879 The kinetic theory of gases : a gas is a collection of small particles (atoms or molecules), in constant, random motion. Boltzmann molecular kinetic theory microscopic properties macroscopic predictions The statistical motion of molecules govern the thermodynamic properties of gasses and liquids P, T, ρ, V instead of considering each particle, let’s consider their average behavior (probability of being somewhere) Tuesday, January 6, 15
the probability of a state with energy E is proportional to an exponential factor p(E) ~ e(-E/kT) Boltzmann molecular kinetic theory Tuesday, January 6, 15
the probability of a state with energy E is proportional to an exponential factor p(E) ~ e(-E/kT) Boltzmann molecular kinetic theory Tuesday, January 6, 15
the probability of a state with energy E is proportional to an exponential factor p(E) ~ e(-E/kT) Boltzmann molecular kinetic theory Tuesday, January 6, 15
the probability of a state with energy E is proportional to an exponential factor p(E) ~ e(-E/kT) E=mgh Boltzmann molecular kinetic theory Tuesday, January 6, 15
the probability of a state with energy E is proportional to an exponential factor p(E) ~ e(-E/kT) E=mgh p is larger where E is smaller Boltzmann molecular kinetic theory Tuesday, January 6, 15
the probability of a state with energy E is proportional to an exponential factor p(E) ~ e(-E/kT) E=mgh p is larger where E is smaller (from this you could derive the ideal gas law PV=nkT) Boltzmann molecular kinetic theory Tuesday, January 6, 15
prize for chemestry, 1909 Mach, 1836-1916 recall that not everyone believes atoms are real! What is all that statistics jibber-jabber?! I only trust Newtonian mechanics! Tuesday, January 6, 15
New Determination of Molecular Dimensions" Buchdruckerei K. J. Wyss, Bern, 1905. (30 April 1905) Also: Annalen der Physik, 19(1906), pp. 289-305. Tuesday, January 6, 15
letter to a close friend: So what are you up to, you frozen whale, you smoked, dried, canned piece of soul... I promise you four papers... Tuesday, January 6, 15
letter to a close friend: So what are you up to, you frozen whale, you smoked, dried, canned piece of soul... I promise you four papers... 1) ... a determination of the true sizes of atoms from the diffusion and viscosity of dilute solutions of neutral substances. Tuesday, January 6, 15
letter to a close friend: So what are you up to, you frozen whale, you smoked, dried, canned piece of soul... I promise you four papers... 1) ... a determination of the true sizes of atoms from the diffusion and viscosity of dilute solutions of neutral substances. Tuesday, January 6, 15
Avogadro’s number • a mole of carmon is 12 grams of carbon (12C) • a mole is N = 6.02 x 1023 molecules ... according to the kinetic theory of gas Tuesday, January 6, 15
with a simple concept: water ﬂows... how easily it ﬂows depends on its viscosity let’s call it ν let’s put a sugar molecule in the water: essentially a sphere. the viscosity of the ﬂuid changes because the molecules of sugar are obstructing the ﬂow: Tuesday, January 6, 15
> ν start with a simple concept: water ﬂows... how easily it ﬂows depends on its viscosity let’s call it ν let’s put a sugar molecule in the water: essentially a sphere. the viscosity of the ﬂuid changes because the molecules of sugar are obstructing the ﬂow: Tuesday, January 6, 15
> ν call Vs the fraction of total volume occupied by sugar start with a simple concept: water ﬂows... how easily it ﬂows depends on its viscosity let’s call it ν let’s put a sugar molecule in the water: essentially a sphere. the viscosity of the ﬂuid changes because the molecules of sugar are obstructing the ﬂow: Tuesday, January 6, 15
> ν call Vs the fraction of total volume occupied by sugar ν’ = ν • (1+ Vs) (from geometry and Newtonian laws!) start with a simple concept: water ﬂows... how easily it ﬂows depends on its viscosity let’s call it ν let’s put a sugar molecule in the water: essentially a sphere. the viscosity of the ﬂuid changes because the molecules of sugar are obstructing the ﬂow: Tuesday, January 6, 15
> ν call Vs the fraction of total volume occupied by sugar ν’ = ν • (1+ Vs) (from geometry and Newtonian laws!) for a mole (=180 g) of sugar (= N molecules of sugar): start with a simple concept: water ﬂows... how easily it ﬂows depends on its viscosity let’s call it ν let’s put a sugar molecule in the water: essentially a sphere. the viscosity of the ﬂuid changes because the molecules of sugar are obstructing the ﬂow: Tuesday, January 6, 15
> ν call Vs the fraction of total volume occupied by sugar ν’ = ν • (1+ Vs) (from geometry and Newtonian laws!) for a mole (=180 g) of sugar (= N molecules of sugar): start with a simple concept: water ﬂows... how easily it ﬂows depends on its viscosity let’s call it ν let’s put a sugar molecule in the water: essentially a sphere. the viscosity of the ﬂuid changes because the molecules of sugar are obstructing the ﬂow: Vs = ρ/m • (4π/3) • Rs 3 • N Tuesday, January 6, 15
> ν call Vs the fraction of total volume occupied by sugar ν’ = ν • (1+ Vs) (from geometry and Newtonian laws!) for a mole (=180 g) of sugar (= N molecules of sugar): start with a simple concept: water ﬂows... how easily it ﬂows depends on its viscosity let’s call it ν let’s put a sugar molecule in the water: essentially a sphere. the viscosity of the ﬂuid changes because the molecules of sugar are obstructing the ﬂow: Vs = ρ/m • (4π/3) • Rs 3 • N Tuesday, January 6, 15
> ν call Vs the fraction of total volume occupied by sugar ν’ = ν • (1+ Vs) (from geometry and Newtonian laws!) for a mole (=180 g) of sugar (= N molecules of sugar): start with a simple concept: water ﬂows... how easily it ﬂows depends on its viscosity let’s call it ν let’s put a sugar molecule in the water: essentially a sphere. the viscosity of the ﬂuid changes because the molecules of sugar are obstructing the ﬂow: Vs = ρ/m • (4π/3) • N = 1 / Rs 3 x (measurable quantities) Rs 3 • N Tuesday, January 6, 15
> ν call Vs the fraction of total volume occupied by sugar ν’ = ν • (1+ Vs) (from geometry and Newtonian laws!) for a mole (=180 g) of sugar (= N molecules of sugar): start with a simple concept: water ﬂows... ... 1 equation and 2 unknowns ... WE CANNOT SOLVE THIS :( how easily it ﬂows depends on its viscosity let’s call it ν let’s put a sugar molecule in the water: essentially a sphere. the viscosity of the ﬂuid changes because the molecules of sugar are obstructing the ﬂow: Vs = ρ/m • (4π/3) • N = 1 / Rs 3 x (measurable quantities) Rs 3 • N Tuesday, January 6, 15
> ν call Vs the fraction of total volume occupied by sugar ν’ = ν • (1+ Vs) (from geometry and Newtonian laws!) for a mole (=180 g) of sugar (= N molecules of sugar): start with a simple concept: water ﬂows... ... 1 equation and 2 unknowns ... WE CANNOT SOLVE THIS :( how easily it ﬂows depends on its viscosity let’s call it ν let’s put a sugar molecule in the water: essentially a sphere. the viscosity of the ﬂuid changes because the molecules of sugar are obstructing the ﬂow: 5/2 Vs = ρ/m • (4π/3) • N = 1 / Rs 3 x (measurable quantities) Rs 3 • N Tuesday, January 6, 15
small particles suspended in liquids at rest required by the molecular-kinetic theory of heat." Annalen der Physik, 17(1905), pp. 549-560.(May 1905; received 11 May 1905) Tuesday, January 6, 15
close friend: So what are you up to, you frozen whale, you smoked, dried, canned piece of soul... I promise you four papers... 1) ... a determination of the true sizes of atoms from the diffusion and viscosity of dilute solutions of neutral substances. 2) ... proves that, on the assumption of the molecular [kinetic] theory of heat, bodies of the order of magnitude of 1/1000 mm, suspended in liquids, must already perform an observable random movement that is produced by thermal motion; in fact, physiologists have observed motions of suspended small, inanimate, bodies, which they call "Brownian molecular motion." Tuesday, January 6, 15
close friend: So what are you up to, you frozen whale, you smoked, dried, canned piece of soul... I promise you four papers... 1) ... a determination of the true sizes of atoms from the diffusion and viscosity of dilute solutions of neutral substances. 2) ... proves that, on the assumption of the molecular [kinetic] theory of heat, bodies of the order of magnitude of 1/1000 mm, suspended in liquids, must already perform an observable random movement that is produced by thermal motion; in fact, physiologists have observed motions of suspended small, inanimate, bodies, which they call "Brownian molecular motion." Tuesday, January 6, 15
I can describe the observed Brownian motion from the basic assumptions of molecular kinetic theory + Newtonian mechanics, that is evidence that the molecular kinetic theory may be right. Tuesday, January 6, 15
I can describe the observed Brownian motion from the basic assumptions of molecular kinetic theory + Newtonian mechanics, that is evidence that the molecular kinetic theory may be right. This, and the measurement of molecules paper, put to rest the debate over the existence of atoms! Tuesday, January 6, 15
entire cup of tea is sweet diffusion is the motion of molecules under the thermal energy start with a simple concept: sugar diffuses in water... Tuesday, January 6, 15
entire cup of tea is sweet diffusion is the motion of molecules under the thermal energy this thermal motion generates the osmotic pressure start with a simple concept: sugar diffuses in water... Tuesday, January 6, 15
entire cup of tea is sweet diffusion is the motion of molecules under the thermal energy this thermal motion generates the osmotic pressure start with a simple concept: sugar diffuses in water... Tuesday, January 6, 15
entire cup of tea is sweet diffusion is the motion of molecules under the thermal energy this thermal motion generates the osmotic pressure start with a simple concept: sugar diffuses in water... Tuesday, January 6, 15
entire cup of tea is sweet diffusion is the motion of molecules under the thermal energy this thermal motion generates the osmotic pressure start with a simple concept: sugar diffuses in water... Tuesday, January 6, 15
entire cup of tea is sweet diffusion is the motion of molecules under the thermal energy this thermal motion generates the osmotic pressure credit: David Walker start with a simple concept: sugar diffuses in water... Tuesday, January 6, 15
entire cup of tea is sweet diffusion is the motion of molecules under the thermal energy this thermal motion generates the osmotic pressure credit: David Walker Discovered by Brown in 1827 watching pollen in solution..... start with a simple concept: sugar diffuses in water... Tuesday, January 6, 15
entire cup of tea is sweet diffusion is the motion of molecules under the thermal energy this thermal motion generates the osmotic pressure credit: David Walker Discovered by Brown in 1827 watching pollen in solution..... its alive!! start with a simple concept: sugar diffuses in water... Tuesday, January 6, 15
entire cup of tea is sweet diffusion is the motion of molecules under the thermal energy this thermal motion generates the osmotic pressure credit: David Walker Discovered by Brown in 1827 watching pollen in solution..... its alive!! start with a simple concept: sugar diffuses in water... Tuesday, January 6, 15
entire cup of tea is sweet diffusion is the motion of molecules under the thermal energy this thermal motion generates the osmotic pressure credit: David Walker Discovered by Brown in 1827 watching pollen in solution..... its alive!! It is the constant motion of the molecules of water that hit the particles of pollen which causes them to move. start with a simple concept: sugar diffuses in water... Tuesday, January 6, 15
entire cup of tea is sweet diffusion is the motion of molecules under the thermal energy this thermal motion generates the osmotic pressure credit: David Walker Discovered by Brown in 1827 watching pollen in solution..... its alive!! It is the constant motion of the molecules of water that hit the particles of pollen which causes them to move. It cannot be explained without kinetic energy of the atoms! start with a simple concept: sugar diffuses in water... Tuesday, January 6, 15
entire cup of tea is sweet diffusion is the motion of molecules under the thermal energy this thermal motion generates the osmotic pressure measure the diffusion velocity, which depends on the radius of the pollen Rp, (or of the sugar molecule Rs in his dissertation) (Kirchhoff, Lecture 26) all these are mechanical forces and measurable quantities D= cT/(6 πk) • 1/(N Rp) credit: David Walker start with a simple concept: sugar diffuses in water... Tuesday, January 6, 15
entire cup of tea is sweet diffusion is the motion of molecules under the thermal energy this thermal motion generates the osmotic pressure measure the diffusion velocity, which depends on the radius of the pollen Rp, (or of the sugar molecule Rs in his dissertation) (Kirchhoff, Lecture 26) all these are mechanical forces and measurable quantities D= cT/(6 πk) • 1/(N Rp) credit: David Walker start with a simple concept: sugar diffuses in water... Tuesday, January 6, 15
entire cup of tea is sweet diffusion is the motion of molecules under the thermal energy this thermal motion generates the osmotic pressure measure the diffusion velocity, which depends on the radius of the pollen Rp, (or of the sugar molecule Rs in his dissertation) (Kirchhoff, Lecture 26) all these are mechanical forces and measurable quantities D= cT/(6 πk) • 1/(N Rp) credit: David Walker start with a simple concept: sugar diffuses in water... Tuesday, January 6, 15
entire cup of tea is sweet diffusion is the motion of molecules under the thermal energy this thermal motion generates the osmotic pressure measure the diffusion velocity, which depends on the radius of the pollen Rp, (or of the sugar molecule Rs in his dissertation) (Kirchhoff, Lecture 26) all these are mechanical forces and measurable quantities D= cT/(6 πk) • 1/(N Rp) credit: David Walker start with a simple concept: sugar diffuses in water... Tuesday, January 6, 15
entire cup of tea is sweet diffusion is the motion of molecules under the thermal energy this thermal motion generates the osmotic pressure measure the diffusion velocity, which depends on the radius of the pollen Rp, (or of the sugar molecule Rs in his dissertation) (Kirchhoff, Lecture 26) all these are mechanical forces and measurable quantities D= cT/(6 πk) • 1/(N Rp) N = 1 / Rp x (measurable quantities) credit: David Walker start with a simple concept: sugar diffuses in water... Tuesday, January 6, 15
entire cup of tea is sweet diffusion is the motion of molecules under the thermal energy this thermal motion generates the osmotic pressure measure the diffusion velocity, which depends on the radius of the pollen Rp, (or of the sugar molecule Rs in his dissertation) (Kirchhoff, Lecture 26) all these are mechanical forces and measurable quantities D= cT/(6 πk) • 1/(N Rp) N = 1 / Rp x (measurable quantities) N: molecules in 1 mole of substance: 6.02x1023 (he actually got 2.1x1023 ... but close enough!) credit: David Walker start with a simple concept: sugar diffuses in water... Tuesday, January 6, 15
entire cup of tea is sweet diffusion is the motion of molecules under the thermal energy this thermal motion generates the osmotic pressure measure the diffusion velocity, which depends on the radius of the pollen Rp, (or of the sugar molecule Rs in his dissertation) (Kirchhoff, Lecture 26) all these are mechanical forces and measurable quantities D= cT/(6 πk) • 1/(N Rp) N = 1 / Rp x (measurable quantities) N: molecules in 1 mole of substance: 6.02x1023 (he actually got 2.1x1023 ... but close enough!) credit: David Walker Einstein can PREDICT the diffusion time from the size of a molecule assuming N start with a simple concept: sugar diffuses in water... Tuesday, January 6, 15
entire cup of tea is sweet diffusion is the motion of molecules under the thermal energy this thermal motion generates the osmotic pressure measure the diffusion velocity, which depends on the radius of the pollen Rp, (or of the sugar molecule Rs in his dissertation) (Kirchhoff, Lecture 26) all these are mechanical forces and measurable quantities D= cT/(6 πk) • 1/(N Rp) N = 1 / Rp x (measurable quantities) N: molecules in 1 mole of substance: 6.02x1023 (he actually got 2.1x1023 ... but close enough!) credit: David Walker Einstein can PREDICT the diffusion time from the size of a molecule assuming N Einstein can PREDICT N from the size and observed motion of a particle start with a simple concept: sugar diffuses in water... Tuesday, January 6, 15
to Einstein’s dissertation N = 1 / Rs 3 x (measurable quantities) N = 1 / Rs x (measurable quantities) Now Einstein can PREDICT N and the size of a molecule in a liquid suspension ... 2 equation and 2 unknowns ... WE CAN SOLVE THIS!! :) Tuesday, January 6, 15
The kinetic theory of gas will acquire large acceptance (from Ostwald too!) around 1909, when the experiments that Einstein suggested became feasible. Tuesday, January 6, 15
a wave as such it has a frequency (wavelength) that describes it. it propagates into the ether arbitrarily small amounts of it are allowed... • newton: light made of corpuscles Tuesday, January 6, 15
a wave as such it has a frequency (wavelength) that describes it. it propagates into the ether arbitrarily small amounts of it are allowed... • newton: light made of corpuscles Tuesday, January 6, 15
for physics, 1909 Under certain circumstances (high frequency radiation), light behaves as if it was made of particles (or minimal amounts of energy -- quanta, which is to say like particles)... • plank: could light be a particle after all? • maxwell: light is a wave • newton: light made of corpuscles Tuesday, January 6, 15
for physics, 1909 Under certain circumstances (high frequency radiation), light behaves as if it was made of particles (or minimal amounts of energy -- quanta, which is to say like particles)... but that surely is a mathematical abstraction! (does it remind you of anything???) • plank: could light be a particle after all? • maxwell: light is a wave • newton: light made of corpuscles Tuesday, January 6, 15
(1921) in the 1905 letter to that one close friend: .. I will soon receive the free reprints. The paper deals with radiation and the energetic properties of light and is very revolutionary, as you will see . . Tuesday, January 6, 15
some details of the interaction between matter and light cannot be described by light as a wave, but can be predicted assuming light is a particle then like is likely to be made of particles. Tuesday, January 6, 15
some details of the interaction between matter and light cannot be described by light as a wave, but can be predicted assuming light is a particle then like is likely to be made of particles. It is the ﬁrst clear assertion of the existence of photons. Fundamental paradigm shift which lead to quantum mechanics. Tuesday, January 6, 15
Einstein’s study of photoelectric effect We now know: matter is made of molecules and atoms If light is wave, I can always send MORE light and increase the energy imparted to the electron. Tuesday, January 6, 15
Einstein’s study of photoelectric effect We now know: matter is made of molecules and atoms If light is wave, I can always send MORE light and increase the energy imparted to the electron. Tuesday, January 6, 15
Einstein’s study of photoelectric effect We now know: matter is made of molecules and atoms If light is wave, I can always send MORE light and increase the energy imparted to the electron. Tuesday, January 6, 15
Einstein’s study of photoelectric effect We now know: matter is made of molecules and atoms If light is wave, I can always send MORE light and increase the energy imparted to the electron. Tuesday, January 6, 15
Einstein’s study of photoelectric effect We now know: matter is made of molecules and atoms If light is wave, I can always send MORE light and increase the energy imparted to the electron. Tuesday, January 6, 15
made of atoms Einstein’s study of photoelectric effect We now know: matter is made of molecules and atoms If light is wave, I can always send MORE light and increase the energy imparted to the electron. But if low frequency light CANNOT extract electrons, light must be a particle. Tuesday, January 6, 15
snapshot of enormous amounts of particles at the same energy E= hν Einstein’s study of photoelectric effect What about the diffraction, which proves that light is a wave? the dual wave-particle nature of light Tuesday, January 6, 15
paper is only a rough draft at this point, and is an electrodynamics of moving bodies, which employs a modification of the theory of space and time. Tuesday, January 6, 15
paper is only a rough draft at this point, and is an electrodynamics of moving bodies, which employs a modification of the theory of space and time. Everything is relative: length can change, time can last longer, simultaneous events are not necessarily simultaneous... the only thing that does not change is the speed of light. Tuesday, January 6, 15
of the paper on electrodynamics has also occurred to me. The principle of relativity, in conjunction with Maxwell's equations, requires that mass be a direct measure of the energy contained in a body; light carries mass with it. [...] The argument is amusing and seductive; but for all I know, the Lord might be laughing over it and leading me around by the nose. Tuesday, January 6, 15
a body is a measure of its energy content. ...One more consequence of the paper on electrodynamics has also occurred to me. The principle of relativity, in conjunction with Maxwell's equations, requires that mass be a direct measure of the energy contained in a body; light carries mass with it. [...] The argument is amusing and seductive; but for all I know, the Lord might be laughing over it and leading me around by the nose. Tuesday, January 6, 15
a body is a measure of its energy content. ...One more consequence of the paper on electrodynamics has also occurred to me. The principle of relativity, in conjunction with Maxwell's equations, requires that mass be a direct measure of the energy contained in a body; light carries mass with it. [...] The argument is amusing and seductive; but for all I know, the Lord might be laughing over it and leading me around by the nose. E=mc2 Tuesday, January 6, 15
John Stachel (Princeton, 2005) •"Einstein 1905: The Standard of Greatness" by John S. Rigden (Harvard, 2005) •Einstein for Everyone , John D. Norton, Einstein for Everyone (Nullarbor Press, 2007) •http://www.pitt.edu/~jdnorton/Goodies/ Einstein_stat_1905/index.html Tuesday, January 6, 15
arrow of time): p is larger where E is smaller but p is NEVER zero! in an isolated system entropy always grows, or: the system will ultimately ﬁnd itself in the state of maximum microscopic disorder, and maximum macroscopic order (thermal equilibrium) TEASER Why didn’t Ostwald like Boltzmann statistical approach to thermodynamics Tuesday, January 6, 15
arrow of time): p is larger where E is smaller but p is NEVER zero! in Boltzmann’s theory there is a tiny probability that that is not so in an isolated system entropy always grows, or: the system will ultimately ﬁnd itself in the state of maximum microscopic disorder, and maximum macroscopic order (thermal equilibrium) TEASER Why didn’t Ostwald like Boltzmann statistical approach to thermodynamics Tuesday, January 6, 15