unravelling

• the 19th Century

• problems everywhere you look

• quick survey...then details.

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“

Albert Michelson from his book, Light Waves and

Their Uses, 1903

The more important fundamental laws and facts of physical science have all been discovered and these are now so firmly established that the possibility of their ever being supplanted in consequence of new discoveries is exceedingly remote...Many other instances [of 'apparent exceptions'] might be cited, but these will suffice to justify the statement that our future discoveries must be looked for in the sixth place of decimals.

very famous quote which he lived to regret

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right.

• This famous bluster comes at the beginning of decades of advances which are mind-boggling

But: the decade of 1888-1898 was the warm-up to rapidly changing circumstances

Up until now the rate of surprises has been relatively civilizedWhile everything starts to fall apart–come together–fall apart…repeatedly

flies in the face of of Michelson’s extraordinarily rash statement

• We’ll barrel through 11 separate catastrophes encountered or worked on in just in this one decade

then, I’ll come back to some of the details

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1. specific heats

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specific heats: satisfying and yet sometimes disturbing...

•Two problems, gases and solids.•Remember, for a monotonic gas, Equipartion says:

cV/R = 3/2: for Helium: 1.52; Argon: 1.51 at room temperature...✔

Butfor H2: 2.44; N2: 2.45; O2: 2.5... ✔; but...Cl2: 3.02; HOH: 3.3; SO2: 3.79...?if diatomic and “dumbbells,” you expect CV/R = 5/2

•Maxwell worried about this: “...what I have now put before you I consider the greatest difficulty yet encountered by the molecular theory.” a talk from 1875 - there appeared to be missing vibrations, cV was sometimes too big...

that’s not all...later, a strange temperature dependence was found“...it is a very mysterious phenomenon, and it seems as though as the temperature falls, certain kinds of motions ‘freeze out’,” James Jean, 1910.

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heat capacity of H2•no classical explanation for the temperature variation

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but, that’s not all•Specific heats of solids had been confused for nearly a century

again, two problems:1. to account for the fact that many solids appear to approach the same value*2. the temperature dependence at low T

•

kcal/kmol•K

*expect from Equipartition:

cv /n = 3/2 R = 3/2 (1.986) = 6 kcal/mol•K called the Law of Dulong and Petit from 1817!

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2. atomic spectra

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since 1880’s•There are two ways that matter emits electromagnetic radiation thermal radiation (coming) discrete line-emission

•Kirchhoff and Bunsen first looked at hot materials with a prism saw regularities, which seemed to characterize individual elements

sodium

helium

hydrogen

mercury

argon

mercury

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hydrogen was simple•it appeared to quantifiable done by a schoolteacher, Johann Balmer in 1885...for 5 lines

he found:

c95, c

1612

, c2521

, c3632

, c95⇒ λ = 3645.6

n2

n2 − 4A

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so, is there a general formula?•In 1890 Johannes Rydberg and independently, Schuster found a complicated formula for many series

with the Balmer relation being the simplest example:

1λ

= Relement

[1

(m− a)2− 1

(n− b)2

]R, a, and b depend on the elementm is an integer that depends on the line seriesn is an integer that is variable

1λ

= RH

[122− 1

k2

]R is the Rydberg Constant for Hydrogen, R = 1.096776 x 10-7 m-1

k is an integer always larger than 2

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3. photoelectricity

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photofinish•A curiosity in Hertz’s discovery of EM waves he covered the receiver gap with a cardboard box he was surprised to discover that then the spark was weakened

by experimenting, he found that it was the line-of-sight presence of ultraviolet light from the sending-gap that somehow facilitated the strength of the receiverhe did little else to study this, beyond reporting his observation

•Herz’s students and others experimented immediately they found that upon illumination by ultraviolet light from a Mg

lamp:a neutral plate of polished metal (zinc usually) became positively charged

a negatively charged plate would lose its charge, while a positively charged plate would not

•An actual current of “photoelectricity” could be produced13

later•1899: J.J. Thomson suggested that the photoelectric current was electrons•1900: Philipp Leonard measured their the ratio of charge/mass (”e/m ratio”) and confirmed JJ’s suggestion- “photoelectrons” visible light could eject photoelectrons from some materials: Na, the

alkalis

•Maxwell’s EM theory could not explain odd features:a) change light intensity: the strength of the photocurrent did not changeb) change the light frequency: the strength of the photocurrent did changebut, below a minimum frequency, there was no emission of photoelectrons

c) switch light on and off quickly: photocurrent started/stopped immediately

Waves would suggest: “a) would change,” “b) would not change,” and “c) would not necessarily change”.

•Photoelectricity was not consistent with the deposition of the continuous energy of EM waves

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4. the ether

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remember: ether it is, or it isn’t•Remember the “umbrella” experiment? demonstrated that the earth orbits the sun however, also says something important about the ether

suppose you were walking in the rain with our tube, but you dragged the air with you while you walked?then you would catch raindrops by holding the tube vertical, rather than at an angleapparent

direction of the star

so,

which was measurable in the 18th century and was.

This “proved” that the earth does NOT drag the luminiferous ether with it in it’s orbit.

€

tanα = cΔtvEΔt

= cvE

≅3×108m / s

2.98×104m /s= 1.5707

⇒α = 89.994° = 20'' arc from zenith

By the 1880’s or so, the question was: What is the speed of the ether wind blowing by the earth? Experimental techniques developed to precisely determine c were available to make a very good measurement…

d = vE Δt

α

h = c Δtα

apparentdirection ofthe star

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mirror, S1

mirror, S2

beamsplitter, P

l2

l1

presume the velocityrelative to the ether is v

Michelson Morley experiment•here’s how they did it:measure the fringes in light interfering from the two paths...then rotate the instrument 90 degrees - and do it again.

The differences between the two configurations is related to the time difference

Surprise #2

v is velocity of earth relative to Ether...

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mirror, S1

mirror, S2

beamsplitter, P

l2

l1

Michelson and Morley did everything they could do to eliminate experimental uncertainty from their measurement.

even to the point of putting the device on a huge concrete slab floating in a bathtub of mecury...slowly rotating it to eliminate bias.

Their result: Δ = zero, zip, nada, nothing, 0

P

ctS2vtether direction

l2

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zero???•Houston, we have a problem: the stellar aberration experiment definitively indicates that

the earth does not drag the ether with it - known for a century

the MM experiment convincingly suggests that the earth does not move through the ether...it must drag it along 1888 (same year as Hertz)

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5. electron theory

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our first Laureate•Dutch physicist held in huge esteemweaned on Maxwell’s theory, he fixed it where it didn’t work,

extended itFirst and foremost: Maxwell’s theory was a theory of Bulk matterthere is nothing atomic or particulate about Maxwell’s Equations

Lorentz set out to establish a microscopic theory of electromagnetismaccounted for reflection and refraction of light and electrolysis

Hendrik Antoon Lorentz

1853-1928

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electrons•Lorentz developed a theory of electrons, in advance of their discovery: in Maxwell’s theory, there are actually 2 electric fields and 2

magnetic fields: one each for materials (D and H) and for vacuum (E and B)

•Lorentz guessed that: Electromagnetic radiation has, then, two particulate sources:

1. free charged particles accelerating (in free-space) and 2. bound charged particles–electrons–vibrating (in matter)

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“Zeeman Effect”•He imagined that matter consisted of negative electrons and positive ions reasoning that bound, (accelerating) vibrating electrons would set

up E fields and B fields, so that conversely an external B field could therefore affect their

motionand thereby affect the spectra of those gasses

•discovered experimentally as the splitting of Sodium emission lines by his student Peter Zeeman

•Called the Zeeman Effect

it led to their sharing of the Nobel Prize in 1902

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back to Lorentz•Two important and related issues converge on Lorentzelectron theory and ether

•Electron theory was in the air even before Lorentz: “If we accept atoms for the chemical elements we cannot avoid concluding that

also both positive and negative electricity is subdivided into certain elementary quanta which behave like atoms of electricity” Helmholtz, 1881.

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what is mass?•“Self-energy” of the electron Lorentz tried to show mathematically that the electron is

nothing more than a little ball of electromagnetic energycapable of deformation with velocity (like the MM experiment)andwith a mass as nothing more than an expression of the Newtonian inertia associated with the momentum content of the electron’s own electromagnetic field

The mass of an electron turns out to be: m = e2/(re c2). For re = 0, this is infinite.

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6. the electron

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“J. J. Thomson

on his confusion, 1897

Could anything at first sight seem more impractical than a body which is so small that its mass is an insignificant fraction of the mass of an atom of hydrogen

What are these particles? Are they atoms, or molecules, or matter in a still finer state of subdivision?

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•Some of you’ve read about the electron discovery...1897, J.J. Thomson investigates the “cathode rays” that emanate from a hot electrode in a “Crookes Tube”, bending them with magnets and electric fields

kinda clever +

-

in the mean time, as if queued, the electron shows up!

+

-E B

He had to work hard to get rid of all of the air in the tube...that foiled others

By tuning the E and B fields, then, he could make the beam be undeflected...

so: magnetic force = electric force

qBvy = qE

and, by measuring the deflection without the magnetic field, he could get rid of the velocity term in terms of dimensions of the tube

q/m = (E/B2) y/L2

This was not new!…Kaufmann in Berlin had made such measurements, but the Berlin/German intellectual climate couldn’t support speculative assertions - nobody believed JJ’s conclusion:

But, JJ was convinced he had discovered a particle of negative electricity (already named “electron”)

e/m = 1.76 x 1011 C/kg ...um, this is large.

The e/m for hydrogen was known to be 1000 times smaller! Either the charges are different or the electron has a tiny, tiny mass…which was soon determined to be the case. Our first elementary particle.

Crooke’s Tube: an old laboratory device, made better and better with vacuum pump technology

x x x

x x x

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then, it gets really strange.

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7. x-rays

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“Wilhelm Roentgen

on his discovery…

When you saw the screen shining ,'What did you think?', asked a reporter. 'I did not think, I investigated.' was the reply from Roentgen. 'What is it?', the reporter pressed. 'I don't know,' was the reply.

“In a few days I was disgusted with the whole thing. I could not recognize my own work in the reports any more. for exactly four full weeks I have been unable to make a single experiment! Other people could work, but not I. You have no idea how upset things were here.

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meanwhile, others played with the mysterious tubes

•Wilhelm Roentgen was an unspectacular, but respected physics professor at WurzburgIn 1895, at the age of 50,in darkness in his lab, he covered his tube with black cardboard

• by accident he had a sheet of paper on the wall treated with barium platinum-cyanide - a screen…and it was fluorescing–it was due to the tube.

• he knew that they could not be the cathode rays…they would be stopped• he played with position…he found that materials were transparent to the rays

(which he subsequently dubbed “X-Rays”)

when he put his hand in the beam…Wilhelm Conrad

Roentgen

1845-1923

he saw his bones. - He told his wife, Bertha.

Think about what must have been going on in his mind: As days went on, he realized that he was the sole human to possess

knowledge unlike anything ever seen – ever.He wrote later that he worried that if people found out what he was doing they would say, “Roentgen has really gone crazy.”

Anna Bertha Roentgen

1839-1919

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word’s out•He spilled the beans:

•January 1, 1896 he circulated a picture of the bones of his hand and a description of his experiments Within weeks, it was reprinted in Science, Nature, the French

Academie des Sciences and other journals Within a week of the Paris announcement, confirmation

occurred in 4 labs Within 5 weeks, X-Rays were used to set the broken arm of a

boy in Dartmouth Within a year, a thousand papers were published

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shy•He gave only one talk on the subject: an in-house seminar at his university incredibly, he published only twice more on the subject He moved to Munich in 1901 as a promotion

•And received the first Nobel PrizeBut, too shy to attend the ceremony, he forwarded his speech by mail

•He suffered terribly during WWI dying in poverty during the post-war inflation at the age of 73 in

1923

•Roentgen never allowed himself to profit from his discovery

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then, it gets really strange.

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8. radioactivity

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monopoly at the Musee d’Histoire Naturelle

•He was the 3rd in line to hold a position at the Paris Museum of Natural History (his son followed him) he received his PhD at the ripe age of 35, was in effect tenured and immediately

abandoned research for the genteel life of a professor at the Ecole Polytechniquehis little research had centered around the phosphorescence that various minerals had when exposed to light - work done with his father

•He was in the audience the day that Roentgen’s work was announced in 1896 sounded familiar to him, so he went back and placed a uranium rock with photographic

paper in the sun so that it could “charge” then developed the paper, saw a blackened image and

promptly reported to the Academie that phosphorescence causes X-Rays (wrong) Further work was hampered by bad weather

…so he wrapped the whole thing up and put it in a drawer for laterand that could have been it

Antoine-Henri Becquerel

1852-1908

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why did he develop it?

•a week later he dragged it out…and developed the film anyway

why? who knows

•what he found was the darkest blotches on the paper that he had ever seen•without the sun, the rock was emitting very energetic energy…spontaneously

•and spent the rest of his life studying them• He found that these mysterious rays would actually make air electrically conducting!

•Somehow, energy was being created…from nothing.•So, he dubbed them “Becquerel Rays”• He wasn’t the only one…

•Silvanus Thompson had observed the same thing (cloudy London)•he was preparing his publication, when he received Becquerel’s paper•he had also missed discovering EM waves, just being beaten by Hertz

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then, it gets really strange.

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9. extreme radioactivity

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believe it or not

•there aren’t many true-love stories in physics …honest!

Marie Skodowska Curie

1867-1934Pierre Curie

1859-1906

Marie Skodowska was a brilliant student in Poland and found the Sorbonne in Paris to be one of the few institutions in Europe which would accept a woman student in physics

there she met Pierre Curie, already an accomplished physicist (who, with his brother discovered piezoelectricity and the demagnetization of iron with heat, as well as the enunciation of what Marie later called the Conservation of Symmetry)they married in 1895 and together pursued her thesis work, a quantitative study of the ionization of Becquerel rays

in 1897 she invented a way of making a current of ionization created by the radioactivity (she coined that name)…and measuring that current using piezoelectricity

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the first ionization counter

•Mme Curie did just this. using the piezoelectric balance devices that Pierre and Jacques invented, she figured

out how to make very precise measurements of the strength of radioactive samples.

The ionization detector relies on the properties of a gas to ionize when a charged particle goes through it

that is, electrons are ejected by the passage, by essentially the Lorentz force, and sometimes they, in turn, cause additional electrons to be ejected…So, a charged particle gets ‘hairy’ - lots of free charge is created.

So, the air can begin to conduct, that is, a measurable current can flow.

-

+

E piezoelectric crystal

electrometer

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pitching in•They found a surprising thing: pitchblend…an ore which contains concentrations of UO2 was more radioactive than

uranium by itself“This fact is a very remarkable and leads one to believe that these minerals contain an element which is much more active than uranium.”

by using her new measuring tool, she and Pierre began the systematic study of the relative radioactivity of whatever they could chemically isolate in the pitchblend

this required the chemical reduction of literally tons of orebackbreaking work

By July of 1898 they announced isolation of a new product

an element 400 times more active than uranium

she called it Polonium (for her native country)

they also found radium, so radioactive that it was warm

In 1903, they were awarded the Nobel Prize in physics (jointly with Becquerel)

which led to Pierre’s being appointed to the Sorbonne and Marie…to a girls school

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Nobel in the family

•Not only was Madam Curie one of the first Laureates she was the first to win 2 Nobel Prizes and the first parent to have a child likewise win a Nobel Prize

their daughter Irene Joliot Curie grew up in her mother’s labMarie’s scientific notebooks are punctuated with observations of Irene’s progress walking, etc.

• Both women applied for and were consistently rebuffed for membership in the French Academy of Sciences Mme Curie led an international life after her second prize

with highs and lows given her reluctantly public existence• She singlehandedly instrumented, organized, and drove herself X-ray

trucks to the Allied front during WWI She was finally rewarded with French support for herself and her

long-wished for labhowever, her radiation sickness was too serious to allow her to make personal use of the facilities (she, Pierre, and Becquerel all suffered radiation illnesses)

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photoalbum

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10. nuclear radiations

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a force of nature•a transplanted New Zealander young student of JJ Thomson’s in, to Cambridge in 1897

already with an engineering background and a penchant for building things quickly, with few resourceshe was aggressive, loud, and driving, commanded respect and affection from everyone who worked with him - interested only in discovery“There is always someone, somewhere, without ideas of his own, who will measure that accurately.”

first work with JJ found that X-rays and Becquerel rays ionized gases to the same degree

actually concentrated on radioactivity, making quantitative measurementsa friendly competition with the Curies for many yearsstarted a program of detector development which lasted for years

Ernest Rutherford

1871-1937

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“Rutherford

1903

I have to keep going, as there are always people on my track. The best sprinters in this road are Becquerel and the Curies.

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his ionization chamber

• By putting a radioactive source between the plates of a capacitor, he too could measure the amount of ionization

Like the Curies’ work, but he measured the actual current.

• in 1898 he placed sandwiches of aluminum over the source and found that there were actually two kinds of radiation:

Radiation which was stopped easily by a little material - he called alpha, α

After a significant effort, they were found by him to be bendable in a magnetic field - positively charged, have an e/m which was unique, and likely to be doubly-ionized He atoms

Radiation which could penetrate more material - he called beta, β

This is what Becquerel saw, as paper blocked α’s and it was he who determined them to have negative charge and an e/m value the same as JJ’s electrons. They are electrons!

…a third, penetrating, radiation was found by Villard in 1900, dubbed gamma, γ

Rutherford started with JJ in 1897 studying gas ionization by X-rays

then began to then use ionization to study the production of Becquerel rays

Sketches from Rutherford’s logbook...

all very confusing…and exciting

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then, it gets really strange.

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11. blackbody radiation

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a black eye•There were other EM issuesin particular, there was a lack of understanding of thermal radiationa “blackbody” is an object which has reached an equilibrium in temperaturethe first consideration of this sort of radiation was by Kirchhoff who named it…

imagine an oven, heated from the outside…

radiation which is continuous (not discrete) rattles around inside continuously absorbed and re-emitted from the interior walls - at all wavelengths

Suppose a small hole is made…any EM waves that are incident on the hole will be absorbed, not to be re-emitted - that’s why he called it a blackbody

However, radiation is emitted…and the intensity of the wavelengths was found experimentally to depend only on the temperature, not the material, nor the way it was heated

makers of china and fine knives and swords knew this - Wedgewood had a calibrated “thermometer” based on color

This, then, was a universal phenomenon - there must be a significant physical explanation…but nobody could find one

many common radiators are pretty good blackbodies...your body, for example.

The Sun, why is it yellow? Because its surface is about 6000K:

infrared…micron wavelengthslow frequencies

ultraviolet…100’s angstrom wavelengthshigh frequencies

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all attempts failedThere were a number of attempts at an explanation:

a relatively ad hoc suggestion by Wein, which had a shape which could be fit to data with unphysical parameters that had to come from the data...reasonable, except at long wavelengths

experiments were very precise by 1900...

Raleigh and Jeans - the most physically motivated model:

…oscillators in the wall of a black body absorb and emit E&M radiation

Each oscillator has its own characteristic frequency, which when they are close together appear continuously distributed

U = 8πkT / λ4 ...was their prediction.

nobody could see anything wrong with the reasoning

the only problem was that it didn’t fit at all - notice that at small wavelengths this formula blows up: the Ultraviolet Catastrophe was what this disaster was called - after all, there’s no limit to the frequencies at which these oscillators may vibrate.

€

u(T ,λ) = (c1 λα )e−c2λT

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