Eye to Eye With Einstein Lecture III: Brownian Motion and the Existence of Atoms Professor Henry Gre

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Eye to Eye With Einstein Lecture IIIBrownian
Motion and the Existence of AtomsProfessor
Henry GreensideDuke University
Albert Einstein 1879-1955
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Three Talks About Einsteins 1905
DiscoveriesImplications For Our 21st World

• Today Relativity and Emc2.
• October 9 What is light? Einsteins concept of
  the photon and a glimpse of the quantum world.
• October 23 What is matter made of? Einsteins
  idea to use Brownian motion to establish the
  existence and properties of atoms.

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Further Information
http//www.phy.duke.edu/hsg/einstein/ hsg_at_phy.du
ke.edu
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The Importance of Atoms

• If , in some cataclysm, all of scientific
  knowledge were to be destroyed, and only one
  sentence passed on to the next generation of
  creatures, what statement would contain the most
  information in the fewest words? I believe it is
  the atomic hypothesis (or the atomic fact, or
  whatever you wish to call it) that
• all things are made of atoms---little
  particles that move
• around in perpetual motion, attracting
  each other when
• they are a little distance apart, but
  repelling upon being
• squeezed into one another.
• Richard Feynman Lectures in Physics, Vol. I,
  1963.

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The Elements Song by Tom Leher
There's Antimony, Arsenic, Aluminium, Selenium
and Hydrogen and Oxygen and Nitrogen and
Rhenium Nickel, Neodynium, Neptunium,
Germanium and Iron, Americium, Ruthenium,
Uranium Europium, Zirconium, Lutetium,
Vanadium and Lathanium and Osmium and Astatine
and Radium Gold and Protactinium and Indium
and Gallium and Iodine and Thorium and Thulium
and Thallium
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Why Some 1905 Prominent Scientists Didnt Believe
in Atoms
versus
If atoms were little balls, they would move
according to Newtons laws of motion a(1/m)F and
so, in principle, their motion could be predicted
precisely for all time. In particular, Newtons
equations of motion are symmetric under time
reversal so all phenomena should be similar going
forward in time as backward in time, e.g., a
planetary orbit. But experiments involving heat
and diffusion suggested that there were
irreversible phenomena, e.g., the spreading of
heat in a bar of metal or the spreading of a
droplet of ink in a glass of water. Difficult to
reconcile this irreversible behavior with the
deterministic reversible behavior of individual
atoms. Further, atoms seemed to be forever
unobservable so inappropriate for establishing
foundation of science.
Ernst Mach (1838-1916)
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Atoms Must Be Impossibly Small
Benjamin Franklin
In these experiments, one circumstance struck me
with particular surprise. This was the sudden,
wide, and forcible spreading of a drop of oil on
the face of the water, which I do not know that
anybody has hitherto considered. If a drop of oil
is put on a highly polished marble table, or on a
looking-glass that lies horizontally, the drop
remains in its place, spreading very little. When
put on water it spreads instantly many feet
round, becoming so thin as to produce the
prismatic colours for a considerable space, and
beyond them so much thinner as to be invisible
except in its effect of smoothing the waves at a
much greater distance. It seems as if a mutual
repulsion between its particles took place as
soon as it touched the water, and a repulsion so
strong as to ace on other bodies swimming on the
surface, as straw, leaves, chips, etc., forcing
them to receded every way from the drop as from a
centre, leaving a large clear space. The quantity
of this force and the distance to which it will
operate I have not yet ascertained but I think
it is a curious inquiry and I wish to understand
whence it arises. Note A teaspoon of oil (few
cc) spreads out to cover about a half an acre
(2000 square meters).
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Brownian Motion, Discovered 1827
Botanist Robert Brown, (1773-1858)
A challenge for the audience how would you
establish that this endless motion is not due to
the activity of living organisms? 2 micron
particles in water (left) and in concentrated DNA
solution (right), 4 s of data http//www.deas.harv
ard.edu/projects/weitzlab/research/brownian.html
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Existence of Atoms Less Interesting ThanIdea of
Brownian Motion
Within eight years after Einsteins 1905 paper
about atoms, William Henry Bragg and his son
William Lawrence showed that one could study
atomic structure of crystals by X-ray
diffraction, thus giving direct confirmation and
quantitative information about existence and
properties of atoms, leading to Physics Nobel
Prize in 1915.
Rosalind Franklins X-ray picture of DNA
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Scanning Tunneling Microscope of 1986
1986 Physics Nobel Prize Heinrich Rohrer and Gerd
Binnig
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Manipulating Individual Atoms is Now Routine
Xenon on nickel (110)
Kanji characters for atom
Carbon Monoxide Man
Scanning Tunneling Spectroscope Images from the
Almaden IBM Lab http//www.almaden.ibm.com/vis/stm
/gallery.html
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An Artist in Action Making An Atomic Corral
http//www.almaden.ibm.com/vis/stm/corral.html
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Enormous Storage Capacity at Atomic Level
In principle, about 1016 bits of information
could be stored on surface of 1 cm cube of
material. Library of Congress contains more than
29 million books and printed materials, 2.7
million recordings, 12 million photographs, 4.8
million maps, and 58 million manuscripts. Total
of about 10 terabytes 1014 bits so could store
100 such libraries on surface of a 1 cm cube!
versus
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The Mechanism of Brownian Motion
Concept of a random walk
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Einsteins Insight of 1905A Way to Measure
Boltzmanns Constant k
Einsteins specific prediction in pure water at
temperature 17o C (290 K or 63o F), a particle of
diameter 0.001 mm (1 micron) will move an average
horizontal distance equal to 0.006 mm in one
minute.
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Applications and Implications of Brownian Motion

• Biology
• Finance
• Fractals as a new and important way of describing
  geometric structures.

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Most Important Single Insight in Biology

• It is not the theory of evolution, which explains
  speciation, and how new forms arise by random
  changes that enhance survival.
• It is that all biological organisms are made of
  atoms and so the many remarkable properties of
  organisms (metabolism, reproduction, catalysis,
  photosynthesis) can eventually be deduced from an
  understanding of the properties of atoms.

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Protein Folding
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Brownian Motion Explains Diffusion
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Random Walk (Diffusion) of Gamma Rays
Light from the nuclear core takes about one
million years to get to the surface, then about 8
minutes to travel to Earth.
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Implications of Brownian Motion for Living
Creatures

• Diffusion limits to size of creatures
• Diffusion minimum speed of swimming bacteria.
• How muscles work and how cells transport goods.

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Ratchet and Pawl A Perpetual Motion Machine?
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Brownian Motion and Kinesin
Ronald Vale http//valelab.ucsf.edu/microassays/re
s-sngl-mol-flr.html
See animations of kinesin walkers on the web page
http//mc11.mcri.ac.uk/wrongtrousers.html Rob
Cross lab
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Financial Time Series as a Brownian Motion
Which plot is the price of IBM stock from 1956
to 1996? Which plot is the x-coordinate of
Brownian motion?
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Self-Similarity of Brownian Motion
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Examples of Fractal Systems
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Examples of Fractal Systems
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Conclusion I Einsteins Impact

• Special relativity revolutionized our concepts of
  time (not absolute), space, speed (c the same for
  everyone), mass, and energy (the latter two are
  related). Used daily by engineers and scientists
  of many disciplines.
• Photon hypothesis was a key step toward our
  modern quantum theory of light, atoms, molecules,
  matter. This theory in turn underlies nearly all
  aspects of modern technology, computation,
  communication, manufacturing.
• Brownian motion was brilliant insight, but atoms
  are so well studied now that main legacy is how
  to think about perpetual molecular collisions,
  especially for living organisms.

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Conclusion II Importance of Physics in Modern
Life

• Physicists are a lot like farmers most people
  never meet one but your day-to-day life is
  greatly influenced by their achievements. (True
  for scientists, not just laymen.)
• Physicists more than any other kind of scientist
  remain closest to the natural philosophy of the
  world the big questions children wonder about
  regarding how and why.
• Physicists have a strong aesthetic sense of
  beauty the concise elegant fundamental equations
  are great achievements, provide strong motivation
  that further unifying insights will be obtained.
• Finally, physicists, like most modern scientists,
  are some of the few modern day explorers left. A
  sense of adventure and of the unknown is a big
  part of what drives us to do our research.

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What Else Was Einstein Famous For?

• Universal agreement that his greatest achievement
  was his general theory of relativity dated 1916,
  a theory of gravity.
• He made many other important contributions but
  not in the same class of revolutionary impact as
  his 1905 papers and his theory of gravity
  Bose-Einstein condensation, insight that led to
  lasers, a penetrating critique of quantum
  mechanics.

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Einsteins Opening Words of His May 1905 Paper
In this paper it will be shown that, according
to the molecular-kinetic theory of heat, bodies
of a microscopically visible size suspended in
liquids must, as a result of thermal molecular
motions, perform motions of such magnitudes that
they can be easily observed with a microscope. It
is possible that the motions to be discussed here
are identical with so-called Brownian molecular
motion however, the data available to me on the
latter are so imprecise that I could not form a
judgment on the question. (John Stachel, ed.,
Einstein's Miraculous Year Five papers that
changed the face of physics, Princeton University
Press, 1998, 85 Einstein's original papers are
included in the Collected Papers of Albert
Einstein, vol. 2)
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Second Paragraph of the May 1905 Paper

• If it is really possible to observe the motion
  to be discussed here, along with the laws it is
  expected to obey, then classical thermodynamics
  can no longer be viewed as strictly valid even
  for microscopically distinguishable spaces, and
  an exact determination of the real sizes of atoms
  becomes possible. Conversely, if the predictions
  of this motion were to be proved wrong, this
  would provide a weighty argument against the
  molecular-kinetic conception of heat.
• Continuity versus discontinuity for light in the
  March photon paper, here atoms versus
  thermodynamics.

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Einsteins Motivation Find A Way to Measure
Boltzmanns Constant k
If for some gas we measure its pressure P, its
volume V, its absolute temperature T and if we
know the value of Boltzmanns constant k, then we
can deduce the number of particles N in the
volume. By freezing the gas to get a solid, we
can then deduce the size of a molecule, since we
know how many molecules are needed to fill up the
volume. From k, we can also deduce average
speeds of molecules in the gas.
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The Schrodinger Equation