# Entropy, information and Ludwig Boltzmann, 10th Ludwig Boltzmann Forum 20 February 2018

## Gerhard Fasol CEO, Eurotechnology Japan KK, Board Director, GMO Cloud KK. former faculty Cambridge University and past Fellow, Trinity College Cambridge

### Ludwig Boltzmann 20 February 1844 – 5 September 1906

We use Ludwig Boltzmann’s results every day. Here are some examples:

• The definition of the units of temperature, Kelvin, Celsius, are directly linked to Boltzmann’s constant
• The Stefan-Boltzmann radiation law tells us that the total energy emitted by a black body per unit surface area is proportional to the 4th power of the temperature, and allows us to measure temperatures at a distance. For example, the temperature of the surface of the sun can be measured using the Stefan-Boltzmann radiation law
• Boltzmann’s formula S = k log W links the macroscopic Entropy with the probability (W = Wahrscheinlichkeit) of a macrostate
• Boltzmann’s transport equations are used for many purposes, to simulate carrier transport in semiconductor devices, and to design airplanes, turbine blades and cars
• Ludwig Boltzmann’s philosophy of nature contributes to our understanding of nature and our world

Ludwig Boltzmann was proposed several times for the Nobel Prize: 1903, 1905 and three times in 1906, the year he took his life in Duino, Italy.

Ludwig Boltzmann achieved his Matura, Austria’s high-school examination required to enter University education at the age of 19 in 1863.

In 1865, at the age of 21, he published his first research paper entitled “Über die Bewegung der Elektrizität in krummen Flächen” (electricity in curved surfaces). It was the dawn of our electrical age, Maxwell created his Maxwell’s equations in 1861-1862, and on 15 February 1883, 20 years later, Tokyo Dentsu KK received the license to start its electricity business in Tokyo.

Among Ludwig Boltzmann’s teachers were Josef Loschmidt and Jozef Stefan.

Josef Loschmidt proposed structures for 300 chemical compounds including benzene, he determined the number of gas molecules in a given volume and the Loschmidt constant is named after him.

Jozef Stefan created the Stefan-Boltzmann Law with Ludwig Boltzmann, and used it to determine the temperature of the surface of the sun.

Ludwig Boltzmann traveled extensively, was in correspondence and discussions and scientific exchange with most major scientists of the time. He also moved professionally:

• University of Vienna
• 1867-1869 Privat-Dozent
• 1869-1873 Full Professor of Mathematical Physics in Graz
• 1873-1876 Full Professor of Mathematics in Vienna
• 1876-1890 Full Professor at University of Graz, Head of the Institute of Physics
• 1887-1888 Rektor (President) of the University of Graz
• 1890-1894 Professor University of München
• 1894-1900 Professor University of Vienna
• 1900-1902 Professor of Theoretical Physics University of Leipzig
• 1902- Professor University of Vienna

Ludwig Boltzmann supported and worked with women:

One of Ludwig Boltzmann’s students was Lise Meitner (November 1878 – 27 October 1968). Lise Meitner was part of Otto Han’s team that discovered nuclear fission, Otto Hahn was awarded the Nobel Prize. Lise Meitner was the second woman to earn a PhD degree in Physics at the University of Vienna. The Element 109, Meitnerium is named about Lise Meitner.

The first President of Osaka University (1931-1934), Nagaoka Kantaro (1865 – 1950) was Ludwig Boltzmann’s student in München around 1892-1893.

## The unit of temperature, Celsius or Kelvin, is directly linked to Boltzmann’s constant k

One Kelvin is defined such that the temperature of the triple point of water is exactly 273.16 Kelvin.
For this definition to be reproducible, the water needs to be defined: its defined as VSNOW = Vienna Standard Mean Ocean Water.
While this definition may have been best at the time it was set, clearly its not sufficient for today.

When the SI system of physical units will be redefined next year, the definition of the unit of temperature, Kelvin will be:

Kelvin is defined such, that the numerical value of the Boltzmann constant k is equal to exactly 1.380650 x 10^-23 JK^-1.

Thus the unit of temperature Kelvin is directly linked to Boltzmann’s constant.

For more details, see: Boltzmann constant and the new SI system of units

## What is Entropy?

Entropy measures information, entropy is the measure of information.

Macro-states, determined for example by the macroscopic quantities pressure (p), Volume (V), or Temperature (T), or number of particles (N), contain a very large number of micro-states.

Boltzmann’s Entropy S = k logarithm of the phase volume(= the probability) of a macro-state in terms of the possible micro-states.

## Different faces of Entropy

Entropy has many faces

• thermodynamic entropy, is a macroscopic state parameter of a system in equilibrium, like temperature, pressure, volume. However, can we measure entropy directly?
• microscopic, statistical entropy
• Boltzmann Entropy: S = k log W
• Gibbs entropy
• information theory
• Shannon’s entropy

## Shannon’s entropy

Shannon: “I thought of calling it “information”. But the word was overly used, so I decided to call it “uncertainty”. When I discussed it with John von Neumann, he had a better idea:

1. in the first place your uncertainty has been used in statistical mechanics (ie by Boltzmann) under that name, so it already has a name
2. in the second place, and more importantly, no one knows what entropy really is, so in a debate you will always have the advantage

## What can we learn from Ludwig Boltzmann?

• Empower young people, recognize and support talent early
• LB published first scientific work at age 21
• Full Professor at 25
• Head of Department at 32
• President of University at 43
• Talent is not linear – talent is exponential
• Move around the world. Connect. Interact.
• Empower women (LB promoted many women)
• Don’t accept authority for authority’s sake
• Science/physics issues need to be treated with the methods of physics/science
• No dogmas
• Support entrepreneurs (LB supported airplane developers before airplanes existed)

# Nanotechnology and critical raw materials, 10th Ludwig Boltzmann Forum 20 February 2018

## Wolfgang Kautek, Professor for Physical Chemistry at University of Vienna, Member of Scientific Board of Austrian Research Associations, President of the Erwin Schrödinger Society for Nanosciences (ESG), Chairman of the Research Group "Physical Chemistry" of the Austrian Chemical Society (GÖCh)

Modern nanotechnology is rapidly advancing in areas such as digital technologies (e.g. flat panel displays), lighting technologies (e.g. White LED’s), electric mobility (high performance permanent magnets for electrical motors), catalysts (e.g. for car exhaust treatment), and medical diagnostics and therapy. These technologies cause an exponential increase of the demand of Critical Raw Materials (“CRMs”, Fig. 1, Table 1).

This is in contrast to a world-wide extremely diverse production concentration and mining activities (Fig. 2) leading to supply risks which are influenced by market concentrations, producer governance indicators, substitutability, and recycling rates.

Therefore, concepts of recourse decoupling, between economic activity and resource use, have to be targeted. Examples of the author’s current research in graphene nanosheets as transparent conductors (Fig. 3) and the laser generation of colloidal nanoparticles for tumor diagnostics (Fig. 4) are discussed in awareness of critical raw material and conflict resources.

# Ceremony on the day of the 170th anniversary of Ludwig Boltzmann’s birthday

## Commemorating Ludwig Boltzmann’s death on September 5, 1906

On the 170th Anniversary day of Ludwig Boltzmann’s birth, on February 20, 2014, a ceremony was held at the “Ples” Building (Duino no. 76), the building in which Boltzmann passed away on September 5, 1906, to unveil a commemorative plate.

## Unveiling the plate to commemorate Ludwig Boltzmann

The text inscribed on the commemorative plate reads:

In questa casa si spense il grande Fisico Ludwig Eduard Boltzmann
V tej stavbi je preminil veliki Fizik Ludwig Eduard Boltzmann
In diesem Haus verschied der große Physiker Ludwig Eduard Boltzmann
In this building the great Physicist Ludwig Eduard Boltzmann passed away

S = k log W

Vienna – Dunaj 20/2/1844
Duino – Devin 5/9/1906

## Ludwig Boltzmann celebration program

• Unveiling ceremony of the commemorative plate
• Greeting by the Deputy Mayor of Duino Aurisina, Dr. Massimo Veronese
• Greeting by the United World College (UWC) Adriatic Rettore, Dr. Michael Price
• Vadim Lacroix: Sergej Rachmaninov – Preludio in do diesis min. op. 3. n. 2
• Speech by Ms Ilse Maria Fasol Boltzmann
• Candy Tong: Claude Debussy – Syrinx per flauto solo
• Speech by Professor Ginacarlo Ghirardi, Professor Emeritus at the Universita degli Studi di Trieste
• Scientific introduction by Professor Francesco Mussardo, Professor of Theoretical Physics at SISSA, Trieste
• Seif Labib & Vadim Lacroix: Franz Schubert – Fantasia in fa minor op. 103 D940, Allegro molto moderato e Largo

# Tokyo Institute of Technology President Yoshinao Mishima: Educational reforms at Tokyo Institute of Technology

(President of Tokyo Institute of Technology. Materials scientist specialized on nano-materials and high-performance materials)

Keynote presented at the 6th Ludwig Boltzmann Symposium on February 20, 2014 at the Embassy of Austria in Tokyo.

## Tokyo Institute of Technology – short history

• 1881: founded as The Tokyo Technical School
• 1929: elevated to a degree-conferring university as Tokyo Kogyo Daigaku (Tokyo Institute of Technology)
• 2004: reorganized as an independent administrative institution “National University Corporation Tokyo Institute of Technology”

## Tokyo Institute of Technology – Statistics as of May 1, 2013

• Undergraduate students: 4,790 (of which 180 are foreign students)
• Graduate students: 3,611 Masters students + 1,512 Doctorate students = 5,123 (of which 943 (18.4%) are foreign students)
• Research students: 90

## Tokyo Institute of Technology – The mission is to develop a new and vibrant society

• produce graduates with a broad understanding of science and technology with both the ability and the determination to take on leading roles in society
• create and support innovative science and technology that will lead to sustainable social development

## Tokyo Institute of Technology – Detailed mission statements cover three areas

• education: produce masters graduates who will thrive globally, and doctorate graduates who will come world’s top researchers are leaders
• contributions to society and international activities
• research: produce globally recognized results. Reform the research and support systems, in particular multi-step support for young researchers.

## Tokyo Institute of Technology aims to become a world class university with greater diversity in faculty and students by 2030

### Major educational reform plan (2013-…)

1. Reborn masters and doctoral courses
2. Reorganize departments, curriculum, courses
3. Change from year-based study to credit based study
4. Increase teaching in English, and numbers of foreign students
5. Align with world top class universities for student transfers and credit transfers
6. Enhance professional practice education for industry

A key challenge is that students primarily focus on earning credits to graduate, and lack a sense of mission to develop professional skills or to cooperate in our diverse global society. We need to change this type of behavior to create scientific leaders for the global arena.

We want to create a more flexible curriculum, that can be completed in a shorter time, so that students have more time for personal professional development and international exchange activities and communication skills.

## Tokyo Institute of Technology: The Board of Directors decided on three pillars for education reform on September 6, 2013

1. Build education system to become one of the world’s top universities
2. Innovate learning
3. Promote ambitious internationalization

We will move to a new and more flexible curriculum system, where undergraduate schools and graduate schools are blended.

## Tokyo Institute of Technology: new initiatives

We are introducing a number of initiatives including active learning, a faculty mentor system where every faculty member mentors 5-10 students, increased numbers of lectures in English, invited top global researchers, provide facilities for foreign researchers, and broaden academic cooperation agreements and mutual accreditation of credits and degrees.

# JVC Kenwood Chairman Haruo Kawahara: Revitalization of Japanese Industry

## (Representative Director and Chairman of the Board of JVC KENWOOD Corporation)

Keynote presented at the 6th Ludwig Boltzmann Symposium on February 20, 2014 at the Embassy of Austria in Tokyo.

JVC KENWOOD Corporation was incorporated on October 1, 2008, and has 20,033 employees as of October 1, 2013.

## KENWOOD overview

Total sales for fiscal year ending March 2013 was YEN 306.6 Billion (approx. US\$ 3 Billion).

JVC KENWOOD today has four business divisions:

• Car Electronics (CE): 33% of total sales
• car audio systems
• CD/DVD drive mechanisms
• optical pick-ups
• Professional Systems (PS): 30%
• security cameras
• professional video cameras
• Optical & Audio (O&A): 22%
• action camera
• home audio systems
• all-in one tower design audio systems
• camcorder with wifi
• 4K projektor
• Entertainment Software (SE): 13%
• Victor Entertainment Group
• Teichiku Entertainment

## Issues of the electrical industry of Japan:

• 1970s: overwhelmed with vertical integration and self-sufficiency
• 1980s: appreciation of the yen (1985 Plaza Accord)
• 1990s: collapse of the Bubble (1991), relocation of production to Asia, three excesses:
• debt
• facility
• employment
• 2000s: lost 20 years

## Going forward, Japan has the option of growth under new business models, or continue to stagnate with matured industries

While there is dramatic global market expansion in many business areas in the global electrical industry, e.g. for Lithium Ion Batteries, DVDs, Car navigation units, DRAM, Japan’s market shares are falling in most sectors. For example, Japanese market shares for LCD, DVD players, Lithium Ion batteries, or car navigation units have fallen from almost 100% global market share 5-10 years ago to 10%-20% today.

Restructuring mature industry can generate more economic benefit than innovating a new industry:

• large established market, although low growth
• reduced number of players in the market following consolidation

## Revitalization of JVCKENWOOD

• the current main business as the core – not new business
• speed, like “fresh food”
• eliminate hidden waste and loss costs
• eliminate vested rights

Kenwood in 2002 was in a disastrous condition:

• net income: YEN -27 Billion (= US\$ -270 million)
• debt: YEN 110 Billion (= US\$ 1.1 billion)
• accumulated losses: YEN 45 Billion (= US\$ 450 million)
• net worth: YEN -17 Billion (= US\$ -170 million)

Restructuring by March 2003:

1. Financial restructuring: Dept/equity swap. Moved from YEN 17 billion negative net worth to positive within 6 months
3. Cost restructuring: 30% cost reduction. Closed 3 factories. Voluntary retirement.
4. Management restructuring: management consolidation. Eliminate huge wastes and losses in subsidiaries.

Restructuring in FY2003 achieved a V-shape recovery. Net income margin was improved from -8% in FY3/2002 to 2%-4% in recent years.

In mature markets, growth is achieved through M&A, reducing the number of players in the market. As the top player in the market, profitable growth improved:

Main four players in the car electronics after-market before Kenwood-JVC merger:

1. Pioneer
2. Kenwood
3. Sony
4. JVC

after the JVCKENWOOD merger, and restructure to minimize losses from the TV business:

1. JVCKENWOOD

JVC and KENWOOD formed a capital and business alliance in July 2007, followed by management integration in October 2008, and a full merger in October 2011. The business portfolio was restructured, and in particular big losses in the TV business were reduced. Fixed costs were reduced by 40% by selling off assets, reduction of production and sales sites, and 25% voluntary retirement.

This structural reform was completed in the FY3/2001, and led to another V-shaped recovery, and to profitable growth under the new medium term business plan.

The JVC-KENWOOD merger led to big jumps in market share in many markets, and thus to very much improved profitability.

## Why did Japan’s mass production type electronics fail?

Answer: Japanese management failed to deal with globalization and digitalization.

Other factors that contributed to Japan’s failure are vertical integration, technology leakage from exporting production facilities, insufficient added value compared to the high Japanese labor costs, and lack of money for investment, because Japanese companies largely relied on bank loans instead of equity.

## Japan’s heavy electrical industry on the other hand is competitive – why?

1. Creative know-how in the heavy electrical industry is in human brains, therefore more difficult to leak to competitors under Japan’s employment circumstances.
2. huge capital investment is needed, and almost fully depreciated in Japan. Therefore the depreciation costs exceeds HR costs.

## How can Japan become competitive again?

Japan needs to accelerate growth strategies in those areas, where Japan has competitive advantage, and where Japanese industries can differentiate themselves. Examples are industrial areas which depend on a long-term improvements and advanced technologies, and techniques of craftsmen, and in next generation technologies.

## JVC KENWOOD takes action to innovate

• JVCKENWOOD invested in a venture capital fund: the WiL Fund I, LP to reinforce alliances with potential ventures in Japan and overseas
• JVCKENWOOD invested in ZMP Inc. to promote car telematics and car auto-control

# Kiyoshi Kurokawa: Quo vadis Japan? – uncertain times

## Groupthink can kill. Kiyoshi Kurokawa, Chairman of Japan’s Parliamentary Commission into the Fukushima Nuclear Disaster

(Academic Fellow of GRIPS and former Chairman of Fukushima Nuclear Accident Independent Investigation Commission by National Diet of Japan)

Keynote presented at the 6th Ludwig Boltzmann Symposium on February 20, 2014 at the Embassy of Austria in Tokyo.

Professor Kurokawa set the stage by describing the uncertain times, risks and unpredictabilities in which we live – while at the same time internet connects us all, all while the world’s population increased from about 1 billion people in 1750 to about 9 billion people today.

## Major global risks in terms of impact and likelihood are (General Annual Conference 2013 of the World Economic Forum):

• severe income disparity
• chronic fiscal imbalances
• rising greenhouse gas emissions
• cyber attacks
• water supply crisis
• management of population aging
• corruption

## Top trends for 2014, ranked by global significance (World Economic Forum, Outlook on global agenda 2014):

• rising social tensions in Middle East and North Africa
• widening income disparity
• persistent structural unemployment
• intensifying cyber threats
• diminishing confidence in economic policies
• lack of values in leadership
• the expanding middle class in Asia

## Many recent “Black Swan events” bring home that:

• accident happens
• machine breaks
• to err is human

## Fukushima Nuclear Accident Investigation Commission NAIIC of the Japanese Parliament:

Professor Kiyoshi Kurokawa chaired the Fukushima Nuclear Accident Independent Investigation Commission (NAIIC) by the National Diet of Japan, which was active from December 8, 2011 to July 5, 2012. While Parliamentary commissions to investigate accidents, problems and disasters are quite frequent in most Western democracies, this was the first time ever in the history of Constitutional Democratic Japan, that a Parliamentary investigation commission was constituted.

Examples of Parliamentary commissions in other western democracies are:

• Three Mile Island, USA 1979
• Space Shuttle Challenger, USA 1986
• 9.11 Terrorist Attack, USA 2001 and many many many more in USA
• Oslo’s shooting incident, Norway 2011
• Mad Cow Disease, UK 1997-, and several Parliamentary commissions every year in UK

## Fukushima Nuclear Accident Investigation Commission of the Japanese Parliament NAIIC key results: Fukushima nuclear disaster was caused by “regulatory capture”

The key result of the Parliamentary Commission is, that the Fukushima nuclear disaster was caused by “regulatory capture”, a phenomenon for which there are many examples all over the world and which is not specific to Japan. Regulatory capture was studied by Goerge J Stigler, who was awarded the Nobel Prize in 1982 for “for his seminal studies of industrial structures, functioning of markets and causes and effects of public regulation”.

Since the full report of the Independent Parliamentary Commission NAIIC is long and complex to read, few people are likely to read the full reports and watch the videos of all sessions.

Therefore short summary videos the key results of the Independent Parliamentary Commission NAIIC were prepared both in Japanese and in English.

## “Groupthink can kill”

We need leaders to be accountable, and we need to understand that “Groupthink” can lead to disasters.

We need the obligation to dissent instead of compliance.

The Nuclear Accident Independent Investigation Commission (NAIIC) was like a hole body CT scan of the Governance of Japan.

Richard Feynman when charing the Space Shuttle Accident investigation wrote in 1986: “for a successful technology, reality must take precedence over public relations, for nature cannot be fooled.

For his work chairing the Nuclear Accident Independent Investigation Commission (NAIIC) Professor Kurokawa was selected as one of “100 Top Global Thinkers 2012” by Foreign Policy “for daring to tell a complacent country that groupthink can kill”.

Professor Kurokawa was awarded the AAAS Scientific Freedom and Responsibility Award “for his courage in challenging some of the most ingrained conventions of Japanese governance and society.

## Ludwig Boltzmann – Energy, Entropy Leadership by Gerhard Fasol (6th Ludwig Boltzmann Symposium)

(Gerhard Fasol, CEO of Eurotechnology Japan KK. Served as Associate Professor of Tokyo University, Lecturer at Cambridge University, and Manger of Hitachi Cambridge R&D Lab.)

Keynote presented at the 6th Ludwig Boltzmann Symposium on February 20, 2014 at the Embassy of Austria in Tokyo.

## Ludwig Boltzmann, the scientist

Ludwig Boltzmann’s greatest contribution to science is that he linked the macroscopic definition of Entropy which came from optimizing steam engines at the source of the first industrial revolution to the microscopic motion of atoms or molecules in gases, this achievement is summarized by the equation S = k log W, linking entropy S with the probability W. k is the Boltzmann constant, one of the most important constants in nature, linked directly to temperature in the SI system of physical units. This monumental work is maybe Boltzmann’s most important creation but by far not the only one. He discovered many laws, and created many mathematical tools, for example Boltzmann’s Equations, which are used today as tools for numerical simulations of gas flow for the construction of jet engines, airplanes, automobiles, in semiconductor physics, information technology and many other areas. Although independently discovered, Shannon’s theory of noise in communication networks, and Shannon’s entropy in IT is also directly related to Boltzmann’s entropy work.

Ludwig Boltzmann was not only a monumental scientist, but also an exceptional leader, teacher, educator and promoter of exceptional talent, and he promoted many women.

One of the women Ludwig Boltzmann promoted was Henriette von Aigentler, who was refused permission to unofficially audit lectures at Graz University. Ludwig Boltzmann advised and helped her to appeal this decision, in 1874, Henriette von Aigentler passed her exams as a high-school teacher, and on July 17, 1876, Ludwig Boltzmann married Henriette von Aigentler, my great-grand mother.

Another woman Ludwig Boltzmann promoted was his student Lise Meitner (Nov 1878 – Oct 27, 1968), who later was part of the team that discovered nuclear fission, work for which Otto Hahn was awarded the Nobel Prize. Lise Meitner was also the second woman to earn a Doctorate degree in Physics from the University of Vienna. Element 109, Meitnerium, is named after Lise Meitner.

## Nagaoka Hantaro, First President of the University of Osaka – Ludwig Boltzmann’s pupil

The first President of Osaka University (1931-1934), Nagaoka Hantaro (1865 – 1950) was Ludwig Boltzmann’s pupil around 1892 – 1893 at Muenchen University.

## Ludwig Boltzmann, a leader of science

Ludwig Boltzmann was connected in intense discussions with all major scientists of his time, he travelled extensively including three trips to the USA in 1899, 1904 and 1905, about which he wrote the article “Die Reise eines deutschen Professors ins El Dorado”, published in the book “Populäre Schriften”.

Ludwig Boltzmann published his first scientific publication at the age of 21 years in 1865. He was appointed Full Professor of Mathematical Physics at the University of Graz in 1869 at the age of 25 years, later in 1887-1888 he was Rektor (President) of the University of Graz at the age of 43 years.

He spent periods of his professional work in Vienna, at Graz University (1869-1873 and 1876-1890), at Muenchen University (1890-1894). When working at Muenchen University, he discovered that neither he nor his family would not receive any pension from his employment at Muenchen University after an eventual retirement or in case he dies before retirement, and therefore decided to return to Vienna University in 1894, where he and his family were assured of an appropriate pension. During 1900-1902 he spent two years working in Leipzig, where he cooperated with the Nobel Prize winner Friedrich Wilhelm Ostwald.

Ludwig Boltzmann did not shy away from forceful arguments to argue for his thoughts and conclusions, even if his conclusions were opposite to the views of established colleagues, or when he felt that philosophers intruded into the field of physics, i.e. used methods of philosophy to attempt solving questions which needed to be solved with physics measurements, e.g. to determine whether our space is curved or not. Later in his life he was therefore also appointed to a parallel Chair in Philosophy of Science, and Ludwig Boltzmann’s work in Philosophy of Science is also very fundamentally important.

I discovered the unpublished manuscripts of Boltzmann’s lectures on the Philosophy of Science, stimulated and encouraged by myself, and with painstaking work my mother transcribed these and other unpublished manuscripts, and prepared them for publication, to make these works finally accessible to the world, many years after Ludwig Boltzmann’s death.

Ludwig Boltzmann was a down to earth man. He rejected the offer of Nobility by His Majesty, The Emperor of Austria, i.e. the privilege to be named Ludwig von Boltzmann (or a higher title) instead of commoner Ludwig Boltzmann. Ludwig Boltzmann said: “if our common name was good enough for my parents and ancestors, it will be good enough for my children and grand children…”

## Summary: understanding Ludwig Boltzmann.

Boltzmann’s thoughts and ideas are a big part of our understanding of the world and the universe.

His mathematical tools are used every day by today’s engineers, bankers, IT people, physicists, chemists… and even may contribute to solve the world’s energy problems.

Ludwig Boltzmann stood up for his ideas and conclusions and did not give in to authority. He rejected authority for authority’s sake, and strongly pushed his convictions forward.

## What can we learn from Ludwig Boltzmann?

• empower young people, recognize and support talent early.
• exceptional talent is not linear but exponential.
• move around the world. Connect. Interact.
• empower women.
• don’t accept authority for authority’s sake.
• science/physics/nature need to be treated with the methods of physics/science.
• no dogmas.
• support entrepreneurs, Ludwig Boltzmann did.

# Boltzmann constant k, “What is temperature?” and the new definition of the SI system of physical units

(by Gerhard Fasol, CEO of Eurotechnology Japan KK. Served as Associate Professor of Tokyo University, Lecturer at Cambridge University, and Manger of Hitachi Cambridge R&D Lab.)

Keynote presented at the 6th Ludwig Boltzmann Symposium on February 20, 2014 at the Embassy of Austria in Tokyo.

(in preparing this talk, I am very grateful for several email discussions and telephone conversations, and for unpublished presentations and documents, to Dr Michael de Podesta MBE CPhys MInstP, Principal Research Scientist at the National Physical Laboratory NPL in Teddington, UK, who has greatly assisted me in understanding the current status of work on reforming the SI system of units, and also his very important work on high-precision measurements of Boltzmann’s constant. Dr Michael de Podesta’s measurements of Boltzmann’s constant are arguable among the most precise, of not the most precise measurements of Boltzmann’s constant today, and therefore a very important contribution to our system of physical units).

## Boltzmann constant k, the definition of the unit of temperature and energy

Temperature is one of the physics quantities we use most, and understanding all aspects of temperature is at the core of Ludwig Boltzmann’s work. People measured temperature long before anyone knew what temperature really is: temperature is a measurement of the average kinetic energy of the atoms of a substance. When we touch a body to “feel” its temperature, what we are really doing is to measure the “buzz”, the thermal vibrations of the atoms making up that body.

For an ideal gas, the kinetic energy per molecule is equal to 3/2 k.T, where k is Boltzmann’s constant. Therefore Boltzmann’s constant directly links energy and Temperature.

However, when we measure “Temperature” in real life, we are not really measuring the true thermodynamic temperature, what we are really measuring is T90, a temperature scale ITS-90 defined in 1990, which is anchored by the definition of temperature units in the System International, the SI system of defining a set of fundamental physical units. Our base units are of fundamental importance for example to transfer semiconductor production processes around the world. For example, when a semiconductor production process requires a temperature of 769.3 Kelvin or mass of 1.0000 Kilogram, then accurate definition and methods of measurement are necessary to achieve precisely the same temperature or mass in different laboratories or factories around the world.

## The SI system of physical units

The SI system consists of seven units, which at the moment are defined as follows:

• second: The second is the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom.
• metre: The meter is the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second.
• kilogram: The kilogram is the unit of mass; it is equal to the mass of the international prototype of the kilogram.
• Ampere: The ampere is that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed 1 meter apart in vacuum, would produce between these conductors a force equal to 2 x 10-7 newton per meter of length.
• Kelvin: The kelvin, unit of thermodynamic temperature, is the fraction 1/273.16 of the thermodynamic temperature of the triple point of water.
• mole:
1. The mole is the amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon 12
2. When the mole is used, the elementary entities must be specified and may be atoms, molecules, ions, electrons, other particles, or specified groups of such particles.
• candela: The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540 x 1012 hertz and that has a radiant intensity in that direction of 1/683 watt per steradian.

The definitions of base units has long history, and are evolving over time. Today several of the definitions are particularly problematic, among the most problematic are temperature and mass.

## SI base units are closely linked to fundamental constants:

• second:
• metre: linked to c = speed of light in vacuum
• kilogram: linked to h = Planck constant.
• Ampere: linked to e = elementary charge (charge of an electron)
• Kelvin: linked to k = Boltzmann constnt
• candela:

## Switch to a new framework for the SI base units:

Each fundamental constant Q is a product of a number {Q} and a base unit [Q]:

Q = {Q} x [Q],

for example Boltzmann’s constant is:
k = 1.380650 x 10-23 JK-1.

Thus we have two ways to define the SI system of SI base units:

1. we can fix the units [Q], and then measure the numerical values {Q} of fundamental constants in terms of these units (method valid today to define the SI system)
2. we can fix the numbers {Q} of fundamental constants, and then define the units [Q] thus that the fundamental constants have the numerical values {Q} (future method of defining the SI system)

Over the next few years the SI system of units will be switched from the today’s method (1.) where units are fixed and numerical values of fundamental constants are “variable”, i.e. determined experimentally, to the new method (2.) where the numerical values of the set of fundamental constants is fixed, and the units are defined such, that their definition results in the fixed numerical values of the set of fundamental constants. This switch to a new definition of the SI system requires international agreements, and decisions by international organizations, and this process is expected to be completed by 2018.

Today’s method (1.) above is problematic: The SI unit of temperature, Kelvin is defined as the fraction 1/273.16 of the thermodynamic temperature at the triple point of water. The problem is that the triple point depends on many factors including pressure, and the precise composition of water, in terms of isotopes and impurities. In the current definition the water to be used is determined as “VSNOW” = Vienna Standard Mean Ocean Water. Of course this is highly problematic, and the new method (2.) will not depend on VSNOW any longer.

In the new system (2.) the Kelvin will be defined as:

Kelvin is defined such, that the numerical value of the Boltzmann constant k is equal to exactly 1.380650 x 10-23 JK-1.

## Measurement of the Boltzmann constant k:

In order to link the soon to be fixed numerical value of Boltzmann’s constant to currently valid definitions of the Kelvin, and in particular to determine the precision and errors, it is necessary to measure the value of Boltzmann’s current in terms of today’s units as accurately as possible, and also to understand and estimate all errors in the measurement. Several measurements of Boltzmann’s constants are being performed in laboratories around the world, particularly at several European and US laboratories. Arguably today’s best measurement has been performed by Dr Michael de Podesta MBE CPhys MInstP, Principal Research Scientist at the National Physical Laboratory NPL in Teddington, UK, who has kindly discussed his measurements and today’s status of the work on the system of SI units and its redefinition with me, and has greatly assisted in the preparation of this article. Dr Podesta’s measurements of Boltzmann’s constant have been published in:
Michael de Podesta et al. “A low-uncertainty measurement of the Boltzmann constant”, Metrologia 50 (2013) 354-376.

Dr Podesta’s measurements are extremely sophisticated, needed many years of work, and cooperations with several other laboratories. Dr. Podesta and collaborators constructed a highly precise resonant cavity filled with Argon gas. Dr. Podesta measured both the microwave resonance modes of the cavity to determine the precise radius and geometry, and determined the speed of sound in the Argon gas from acoustic resonance modes. Dr Podesta performed exceptionally accurate measurements of the speed of sound in this cavity, which can be said to be the most accurate thermometer globally today. The speed of sound can be directly related to 3/2 k.T, the mean molecular kinetic energy of the Argon molecules. In these measurements, Dr. Podesta very carefully considered many different types of influences on his measurements, such as surface gas layers, shape of microwave and acoustic sources and sensors etc. He achieved a relative standard uncertainty of 0.71. 10-6, which means that his measurements of Boltzmann’s constant are estimated to be accurate to within better than on millionth. Dr. Podesta’s measurements directly influences the precision with which we measure temperature in the new system of units.

Over the last 10 years there is intense effort in Europe and the USA to build rebuild the SI unit system. In particular NIST (USA), NPL (UK), several French institutions and Italian institutions, as well as the German PTB (Physikalische Technische Bundesanstalt) are undertaking this effort. To my knowledge there is only very small or no contribution from Japan to this effort, which was surprising for me.

## What is today’s best value for the Boltzmann constant k:

Today’s accepted best value of Boltzmann’s constant is the “2010 Codata value”:

k = 1.380 6488 . 10-23 JK-1, and the standard uncertainty is:
su = 0.000 0013 . 10-23 JK-1