# Warped Passages

## Unravelling the mysteries of the universe's hidden dimensions

### Lisa Randall

#### Key

; ADD model; Anarchic principle; Conceptual leap; Effective theory; Elecronvolt; General Relativity; Grand Unified Theory; ; Hierarchy problem; Higgs; Hořava-Witten Theory; Internal symmetry; Kaluza-Klein; M-theory; Multiverses; Planck length; Photoelectric effect; Photon; Perturbation theory; Quantum Chromo Dynamics; Rolled-up dimensions; Standard Model; String Theory; Superstring Theory; Theory of Everything; Virtual Particles; Wavefunction;
##### Why?
• This book contains various interesting episodes behind the development of modern physics, not only explaining the essence of particle physics and extra dimensions.
• It is diffcult for 2D Flantlander to imagine 3D cube. Similarly we, 3D animal, have no concrete terms to understand extra dimensions, other than mentioning vague expressions such as; extra, additional, invisible, unseen, bulk, mass, rolled-up, curled-up, hidden, small, compact, subtlety, counterintuitive, mysterious, ...

#### 0. Preface:

• The tone (of books about science) often seemed condescending to readers, overly worshipful of scientists, or boring. I felt the authors mystified the results or glorified the men who found them, rather than describing science itself and the process by which scientists made their connections.
• I've bulleted the points that I'll refer to later on when I present more recent ideas about extra dimensions.
• The recent work on extra dimensions relies on both more traditional and more modern theoretical physics concepts to motivate the questions it answers and its methods.
• I've described some newer, or speculative notions that have been studied for the last thirty years - namely supersymmetry and string theory.
• Supersymmetry is an extension of known particle physics; String theory is different, which is based on theoretical questions and ideas.
• I'm an agnostic on this subject. But string theory has been a rich resource for new ideas.
• Extra dimensions can be infinite in size yet remain unseen, or that we can be living in a three spatial dimensional sinkhole in a higher dimensional universe.
• An example of quasirystalline pattern (> Right figure):
• Elegant way of this pattern; 3D shadow of a higher dimensional crystalline pattern. What looked like a completely inexplicable pattern in 3D reflects an ordered structure in the higher dimensional world.
• Physicists today speculate that theories of extra dimensions also will illuminate connections in particle physics and cosmology.
• String theory, which postulates that the most basic units in nature are not particles but fundamental, oscillating strings; which requires more dimensions of space.
• Role of branes, membrane-like objects within string theory, which are as essential to the theory as strings themselves.
• 3D pocket of space:
• Not only are we not in the center of the universe, as Copernicus shocked the world 500 years ago, but we just might be living in an isolated neighborhood with three spatial dimension that is a part of a higher-dimensional cosmos.

#### 0. 序文:

• 今までの科学書は権威的で退屈
• ここでは最新の超次元についての核心にずばり迫る。
• 超次元については、物理学の伝統を最新の理論に依存している。
• ここではより新しい概念を提起する。
• 超対象は既存の素粒子論の延長にあるが、弦理論は理論に基づいている。
• それについては不可知論の立場ではあるが、弦理論は魅力的なアイデアを提供してくれる。
• 超次元の大きさは目に見えない無限大かも知れないし、我々は高次元宇宙の中の三次元の穴の中に住んでいるのかも知れない。
• Penrose tiling:

#### >Top 1. Entryway Passage:

• Three from Two:
• We can use 2D information to construct 3D. We often use to reduce higher dimensional objects to lower dimensions - slicing, projection, holography, and sometimes just ignoring the dimension.
• A single eye constructs a 2D projection of 3D reality. You need two eyes to reproduce 3D.
• A hypercube:
• consists of 8 cubes attached in 4D space. (>a few projections)
• Practical projection (Medicine, etc.):
• X-ray; records 2D project.
• CAT (Computer assisted tomography) scan combine multiple X-ray imaged to reconstruct 3D representation.
• MRI (Magnetic resonance imaging) scan, on the other hand, reconstructs 3D object from slices.
• Holograph: records relations between light in different places.
• Stereo; let you hear where instruments were being played in relation to each other.
• Ink on a paper is 3D, but we lose nothing by thinking of it as 2D.
• Wire; looks 1D, but is has 2D cross section and therefore 3D in all.
• Conceptual leap:
Nothing wrong with ignoring extra dimension: selecting relevant information and suppressing details is the sort of pragmatic fudging; we can focus on the issue of interest.
• Newton's law: didn't need the details of general relativity.
• Studying a cell; don't need to know about quarks inside the proton.
• >Top Effective theory:
• There is nothing wrong with ignoring an extra dimension that's too small to be seen.
• Selecting relevant information and suppressing details; so that you can focus on the issue of interest, and not obscure it with inessential details. (conceptual leap)
• Concentrate on the particles and forces that have "effects" at the distance in question.
• >Top we formulate observations in terms of the things that are actually relevant to the scales we might detect. (Conceptual leap)
• This practie is not scientific fraud, but a way of disregarding the clutter of superfluous information.
• If something is beyond the resolution of the scales, you don't need its detailed structure; it is an effective way to obtain accurate answers efficiently.

#### 1. 入り口の通路:

• 3Dの表現方法:
• スライス、投影、ホログラフ、追加次元の無視
• 単眼は2D像。3Dにするには両眼が必要
• インク、ワイアも本来は3D
• 超立方体; 超方形 chāo fāngxíng
• 概念上のジャンプ:
• ニュートン力学
• 細胞
• 有効理論:
• 必要な情報に注目するのは非科学的ではない。

#### >Top 2. Restricted Passage: Rolled-up Extra Dimensions

• Rolled-up dimensions in physics:
• String theory, the most promising candidate for a theory combining quantum mechanics and gravity.
• Einstein's theory:
• Early 20C, Einstein's theory of relativity opened the door of extra dimensions of space; it works equally well for three or four or ten dimensions. Why, then, do there seem to be only three?
• In 1919, Polish mathematician Teodor Kaluza recognized this possibility and boldly proposed a fourth spatial dimension, a new unseen dimension of space.
• Kaluza's goal with this extra dimension was to unify the forces of gravity and electromagnetism.
• Kaluza wrote his paper in 1919. Einstein wavered about the merits of the idea, delayed the publication of Kaluza's paper for two years, but eventually acknowledged its originality. Yet Einstein still wanted to know what this dimension was. Where was it and why was it different? How far did it extend?
• Oscar Kleing proposed that the extra dimension would be curled up in the form of circle, just $10^{-35}$ m
• >Top Planck length; $1.616 × 10^{-35}$ m
• Daily life of objects:
• Paint of a wall; paint's depth
• Clothesline's thickness
• A hose over a football field
• >Top Rolled-up dimensions:
• Focus on any point along the infinite dimension. Notice that at each and every point there sits the entire compact space, namely circle. The hose consists of all these circles glued together.
• There are two infinite dimensions rather than one, plus a single additional dimension curled up into a circle.
• When tow out of four dimensions are curled into a donut, you have a donut at every point in space.
• Compact spaces: Kalabi-Yau manifolds
• Planck-length extra dimensions would have no visible trace of their existence.
• Dimensions have to be small to be invisible?
• Could an extra dimension possibly extend for ever without our seeing it?
• Even the radical possibility of an infinite extra dimension cannot be excluded if it is sufficiently different from the three familiar infinite dimensions.
• >Top 4D Kaluza-Klein universe with a single tiny, rolled-up dimension would appear to us to have one dimension fewer than the four it actually has.
• In an effective theory all that matters are the things that you can actually perceive.
• Gravitational force:
• Radial lines extending outwards from the planet's center:
• the density of these lines determines the strength of gravitational attraction that the planet

#### 2. 限定的な通路: 巻き上げられた余剰次元

 Order of magnitude Range Unit Example Planck length $10^{-35}$ ℓp Quantum foam Sub atomic $10^{-15}$ atto-m electron, quark Atomic-cellular $10^{-12}$ femto-m proton, neutron $10^{-9}$ pm H atom $10^{-6}$ nm DNA helix, virus Human scale $10^{-3}$ μm bacteria $10^{0}$ mm mosquito $10^3$ m human $10^6$ km Mt. Everest Astro-nomical $10^9$ Mm Earth $10^{12}$ Gm Sun $10^{15}$ Tm solar system $10^{18}$ Pm ly $10^{21}$ Exa-m galactic arm $10^{24}$ Zetta-m Milky Way
• 巻き上げられた次元
• Gravitational force:

#### >Top 3. Exclusive Passage: Branes, Braneworlds, and the Bulk

• Slices or brane:
• 3D world could be a 3D slice of a higher dimensional world.
• The word "membrane" motivated the choice of the word "brane" because membranes, like branes, are layers that either surround or run through a substance.
• Some branes are slices inside the space, but others are slices that bound space, like slices of bread in a sandwich.
• Membrane has 2D, but branes can have any number of dimensions.
• A pipe with a square cross-section:
• An infinitely long pipe of this type would have four infinitely long straight walls; two of which are bounded on either side by walls and one that extends infinitely.
• Reflective boundary condition: if things bounce back from a brane, energy is not lost; nothing goes beyond the branes.
• When things get to a boundary brane, they bounce back, just as billiard balls. (reflective boundary condition) Nothing goes beyond the branes.
• Such branes would have lower dimension than the full space.
• Trapped on branes:
• inside a black hole
• drops of water on a 2D shower curtain
• bacteria trapped between microscope slides
• Sam Loyd's fifteen game
• Brane-bound objects never venture into the extra dimensions that extend off the brane.
• Braneworlds:
• Gravity would extend into the extra dimensions, but stars, planets, people, and everything else that we sense could be confined to a 3D brane. A brane might be our habitat.
• Our senses are attuned to the chemistry, light, and sound surrounding us. Because fundamental forces and particles are likely to be different, the creatures of other branes, should they exist, are unlikely to bear much resemblance to the life of our brane.
• >Top The universe can contain multiple branes that interact only via gravity or don't interact at all. Such set-ups are sometimes called multiverses.
• Brane-bound particles would never have direct contact with particles bound on another brane.
• Dark matter and dark energy; we surmise from their gravitational effects but whose identity is a mystery.

#### 3. 排他的な通路: ブレイン、ブレイン世界、バルク:

• スライスまたはブレイン:
• ブレインとは空間の中のスライス、または空間を区切るスライス
• 膜は2Dだが、ブレインは何次元にもなり得る。
• Lower-demensional surface:
• ブレインに囚われて
• ブラックホール内
• 2Dのシャワーカーテンについた水滴
• 薄片に挟まれた細菌
• ブレインに囚われた物体は敢えて超次元方向へ動こうとしない。
• ブレイン世界:
• 重量は超過次元まで作用するが、我々が感知する物体は3Dブレインに閉じていう。
• 多元的宇宙
• ダークマター、ダークエネルギー

#### >Top 4. Approaches to Theoretical Physics:

• Ultimate goal; to find a simple, elegant, unifying theory capable of explaining all observations.
• Top-down approach:
• Theorists start with the theory to be correct and try to derive its consequences so that they can connect it to the much more disordered world we observe.
• Platonic approach; tries to gain insights from more fundamental truth.
• Young Einstein; rooted his work in experiments and physical reality; so-called thought experiments were grounded in physical situations.
• Karl Schwartzschild first derived black holes as a mathematical consequence of general relativity.
• Bottom-up approach:
• Model builders try to deduce an underlying theory by making connections among observed elementary particles and their interactions. They search for clues in physical phenomena.
• Aristotelian approach; rooted in empirical observations.
• Old Einstein; changed his approach after learning the value of mathematics when developed general relativity.
• >Top String Theory:
• basic premise is that strings, not particles, are the most fundamental objects of nature. The particles we observe are mere consequences of strings; arise from the different vibrational modes of an oscillating string.
• is defined at an energy scale that is about ten million billion times larger than those we an experimentally explore with our current instrument.
• its invisible extra dimensions have to be different from the 3D that we see.
• string theory's gravity operates in six or seven additional dimensions of space.
• Why aren't they all the same? Discovering how and why nature hides string theory's extra dimensions would be a stunning achievement.
• We are all searching for the language of the universe:
• Theorists focus on the inner logic of the grammar; might aspire to grasp the subtleties of Italian literature, but run the risk of starving to death before learning how to ask for dinner!
• Model builders focus on the nouns and phrases that are most useful.; model builders would know how to ask for lodging and acquire the vocabulary that would be essential to finding they way around.
• Now; we can certainly ask where the extra dimensions are, and why we haven't seen them.; whether these unseen dimensions could have any import in our world.
• The Heart of Matter:
• Physical objects around us appear to be continuous and uniform, but in reality they are not.
• Particle physics; smaller distance reveal truly novel phenomena.; new worlds operate via more fundamental physical laws.
• Nucleons; protons and neutrons.
• Proton: made of 2 up quarks and 1 down quark
• Neutron: made of 1 up quark and 2 down quarks
• bound together through the strong force.
• Electron: cannot be divided into smaller particles and contains no substructure within.
• >Top Standard Model:
• Stephen Weinberg coined the term Standard Model.; fundamental building blocks of matter.
• up quark, down quark, and electron lie at the core of matter.
• we now know that there exist additional, heavier quarks and heavier electron-like particles that are nowhere to be found in ordinary material.
• muon, with precisely the same charge as the electron, ha a mass that is 200 times greater than electron's.
• tau, which also has the same charge, has a mass that is 10 times greater still.
• heavier elementary particles r not constituents of matter; were a part of the early universe immediately after the Big Bang.
• No one know why the heavy Standard Model particles exist; why their masses are so different from those of the constituents of more familiar matter.
• Could there be others yet detected?
• Why is gravity so much weaker than the other known forces.
• We're confident that more fundamental structure awaits discovery and that the search for more fundamental principles will be rewarded.
• Braneworld ideas:
• have provided new insights into general relativity, particle physics, and string theory.
• we don't yet know which of these ideas correctly describe nature.; but we'll ultimately discover that branes are a part of he cosmos, and we are confined to them.

#### 4. 理論物理学へのアプローチ:

• 究極のゴール
• トップダウンアプローチ
• 理論家
• プラトン的
• 若きアインシュタイン
• シュヴァルツシルト
• ボトムアップアプローチ
• モデル構築者
• アリストテレス的
• 古きアインシュタイン

• ひも理論

• 宇宙の原語
• 理論家: 文法の内部構造
• モデル構築者: 実用的な単語重視

• Standard Model of Physics (標準モデル): >下図

• Field os phtysics how they are connected:

 1st generation 2nd generation 3rd generation Force-carrying gauge bosons u-qk (2.3MeV) c-qk (1.3 GeV) t-qk (173 GeV) gluon (0) Higgs (126 GeV) d-qk (4.8 MeV) s-qk (95 MeV) b-qk (4.3 GeV) $\gamma$ (0) electron (0.5 MeV) muon $\mu$ (106 MeV) tau $\tau$ (1.8 GeV) Z-bozon (91 GeV) $\nu_e$ (<2.2 eV) $\nu_{\mu}$ (<0.2 MeV) $\nu_{\tau}$ (<16 MeV) W-boson (80 GeV)

#### >Top 5. Relativity; The Evolution of Einstein's Gravity:

• Beginning of 19C: Lord Kelvin said, "There is nothing new to be discovered in physics now. All that remains is more and more precise measurement."; which was famously incorrect.
• very soon, relativity and quantum mechanics revolutionized physics.
• Special Relativity:
• Einstein's first insight about reference frames and relativity came from thinking about electromagnetism.
• Einstein realized that if there were an aether, there would also be a preferred observational vantage,
• Einstein's critical insight was that ideas about time had to be reformulated; space and time could no longer be considered independently.
• The laws of special relativity that follow lead to all the surprising consequences, such as time dilation, the observer dependence of simultaneity, and Lorentz contraction of a moving object.
• Equivalence principle:
• the effects of acceleration cannot be distinguished from those of gravity.
• follows from the equivalence of inertial and gravitation mass, two quantities that in principle could have been different from each other.
• Ireland's Cliffs of Moher, "It's not the fall that kills you, but the crash when you stop."
• Tests of General Relativity:
• Gravitational redshift of light:
• The rising ball slows down as it moves against the force of gravity. But the ball's energy is not lost; it is converted into potential energy, releasing kinetic energy, or energy of motion.
• a photon loses momentum as it escapes from a gravitational field; the photon loses kinetic energy but gains potential energy as it fights its way out of the gravitational field.
• Bending of light:
• the famous relation $E=mc^2$ means that energy and mass are closely connected.
• the sun's gravity influence mass, and likewise affects the trajectory of light; first confirmed during the solar eclipse of 1919.
• It is one of the tools that was used to probe the distribution of mass in the universe and look for dark matter in the form of small, burn-out stars.
• Gravitational lensing;
• light emitted by a bright star will bend when it passes by the dark star. Light passing on the left will bend in the opposite direction that light passing on the right and light passing on the top will bend in the opposite direction than light passing on the bottom; this will create multiple images of a bright object behind a dark star.
• Graceful curves of the universe:
• Einstein no longer saw gravity as a force that acts directly on an object. Instead, he described it as a distortion of the geometry of spacetime that reflects the different accelerations required to cancel gravity in different places.
• the force of gravity is understood in terms of the curvature of spacetime, which in turn is determined by the matter and energy that are present.
• Curved space and curved spacetime:
• >Top Theory of General Relativity:
• Free fall along a geodesic:
• in curved spacetime, the geodesics of different observers will in general be different.
• A massive object distorts the surrounding space, creating a gravitational field.
• In reality, the full 4D spacetime are warped. Time is warped.
• $E=mc^2$ (Einstein's equations)
• General relativity has further advantage that it incorporales any type of energy - including that of the gravitational field itself - into the distribution of matter and energy.
• Distorting space: >Fig.
• the space surrounding the ball looks like 2D. But really, the full 4D spacetime are warped. Time is warped because it too is a dimension from the vantage point of special & general relativity.
• it' important to keep in mind is that the object distorting spacetime can have any number of dimensions.; a brane will play the role of the sphere in this picture.
• Einstein's equations changed the outlook for cosmologists. Now, if scientists new the matter and energy content of the universe, they could calculate its evolution.
• In an empty universe, space would be completely flat, with no ripples or undulations - no curvature at all.
• But when energy and matter fill the universe, they distort spacetime, producing interesting possibilities for the universe's structure and behavior over time.
• General relativity has lots of consequences:
• eliminated the annoying action-at-a-distance of Newtonian gravity, which asserted that an object's gravitational effects would be felt everywhere as soon as it appeared or moved.
• With general relativity, we know that before gravity can act, spacetime has to deform. This process does not happen instantaneously, IT takes time. Gravity waves travel at the sped of light. Gravitational effects can kick in at a given position only after the time it takes for a signal to travel there and distort spacetime.
• Black holes; the geometry of spacetime is extremely distorted;
• Karl Schwarzschild discovered that black holes were a consequence of Einstein's equations almost immediately after general relativity's development.
• It was not until 1960s that they could be real things in our universe.
• GPS system:
• to calculate position within a meter, we must measure tie to better than one part in $10^{13}$
• But even if we had perfect clocks, time dilation wold slow them down by a bout one part in $10^{10}$; this error would be 1000 times too big for our desired GPS system.

#### 5. 相対論: アインシュタインの重力の進化

• 重力赤方偏移

• 一般相対性理論:
• Distorting space:

#### >Top 6. Quantum Mechanics: Principled uncertainty, Principal uncertainties, and the uncertainty principle:

• Quantum mechanics, counterintuitive as it is, fundamentally altered the way scientists view the world.
• Much of modern science evolved from quantum mechanics; statistical mechanics, particle physics, chemistry, cosmology, molecular biology, evolutionary biology, and geology were all either invented or revised as a result of its development.
• Modern world; such as computers, DVD players, and digital cameras wouldn't be possible without the transistor and modern electronics relied on quantum phenomena.
• Physicists developed quantum theory to interpret experimental results that classical physics could not explain. And quantum theory, in turn, suggested further experiments with which to test hypotheses.
• Shock and awe:
• Scientists had to suspend their disbelief before they could accept the quantum mechanical premises.
• Even theoretical pioneers, such as Max Planck, Erwin Schrödinger, and Albert Einstein, never really converted to the quantum mechanical way of thinking.
• Einstein voiced, "God does not play dice with the universe."
• Radical nature of the scientific advances in early 20C reverberated in modern culture.
• Quantum mechanics is difficult to understand because its consequences are so counterintuitive and surprising. Its fundamental principles run counter to the premises underlying all previously known physics - and counter to our own experiences.
• Quantum effects generally become significant at distance of about an angstrom, the size of an atom.
• We see only huge aggregates of atoms, so many that classical physics overwhelms quantum effects.
• Werner Heisenberg explained, "We simply have to remember that our usual language does not work any more, that we are in the realm of physics where our words don't mean much."
• Old quantum theory:
• began in 1900; Max Planck suggested that light could be delivered only in quantized units.
• the fundamental unit is equal to a quantity, now known as Planck's constant, $h$, multiplied by the frequency, $f$.; the energy of light could be $if, 2hf, 3hf,$ and so on.
• Blackbody ultraviolet catastrophe:
• Classical calculations predicted that far greater energy would be emitted in high-frequency radiation.
• Measurements showed that different frequencies do not contribute democratically to blackbody radiation; the very high frequencies contribute less than the lower ones. Only the lower frequencies emit significant energy. This is why radiation objects are "red-hot" and not "blue-hot."
• Only frequencies below some specific upper limit could contribute to radiation from a blackbody.
• >Top Photoelectric effect:
• Below the threshold, no electrons are emitted from the metal regardless of the light intensity or the length of time of exposure.
• $E=\franc{ha}{\lambda}$
where, $E$: work function, $\lambda$: cut-off wavelength
• 1921: Einstein was awarded Nobel Prize in Physics.
• But he was reluctant to accept that these quanta were actually massless particles, which carried energy and momentum but had no mass.
• 1923: Compton scattering:
• a quantum of light hits an electron and is deflected.
• Measurement showed that the quanta of light behaved precisely as if the quanta were massless particles that quanta were indeed particles (now called photon)
• Quantization and the atom:
• Atom's true properties were not accepted until the beginning of 20C.
• 1897, J.J. Thomson identified electrons and proposed that the electron was an ingredient of the atom; plum pudding model, positively charged component spread the atom with negatively charged electrons (the pieces of fruit) embedded inside.
• 1910, Ernest Rutherford; discovered a hard, compact atomic nucleus much smaller than the atom; shooting alpha particles from Rn-222 at atoms.
• "It was quite the most incredible event that has ever happed in my life, as if you fired a 15 inch shell at a piece of tissue paper and it came back and hit you."
• the positive charge was not spread throughout the atom, but was confined to a much smaller inner core (nucleus)
• James Chadwick; the discover of the neutron.
• Niels Bohr; electrons acting as if they were waves, oscillated up and down sa they circulated about the nucleus.
• It can only have a wavelength that would permit the wave to go up and down a fixed number of times.
• He made his assumption simply to account for the stable electron orbits.
• Electron Quantization:
• an electron's orbit had to have a radius that fit a formula he proposed.
• he made his assumption simply to account for the stable electron orbits.
• they oscillated up and down once over a fixed distance;
• that distance is the wavelength; that would permit the wave to go up and down a fixed number of times.
• Bohr could explain why photons were emitted or absorbed only a the measured frequencies.
• >Top Max Born:
• proposed a surprising interpretation; that the wave was a function of position whose square gives the probability for finding a particle. (wavefunction)
• We cannot know the particle's exact location; only specify the probability of finding it somewhere.; probability wave
• Schrödinger:
• developed the wave equation that shows the evolution of the wave associated with a quantum mechanical particle.
• if you were to perform the double-slit experiment with electrons, you would see what Young saw for light: a wave lie pattern on the screen behind the slits
• The uncertainty principle and special relativity:
• The position-momentum uncertainty principle says the product of uncertainties in position and in momentum must exceed Planck's constant.
• According to special relativity, when momenta are high, so are energies.
• Combining these two facts tells us that the only way to explore short distances is with high energies.
• >Top Elecronvolt (eV):
• an electronvolt is the energy required to move an electron against a potential difference, such as could be provided by a very weak batter of 1 volt.
• Particle physics often use the units (MeV, GeV, TeV) to measure not just energy, but mass, momentum.
• The proton mass is 1 GeV.
• Weak scale energy; 250 GeV = $10^{-16}$ grams.
• Weak scale length is $10^{-16}$ cm; the maximum distance over which particles can influence each other through this force
• Planck scale energy: $(M_{Pl}): 10^{19}$ GeV
• Planck scale length: $10^{-33}$ cm; extremely small distance.
• The Planck scale energy determines the strength of gravity; it is the energy that particles would have to have for gravity to be a strong force.
• Bosons and Fermions:
• those particles could be fundamental particles such as the electron and quarks.
• whether an object is a boson or a fermion depends on a property called intrinsic spin.
• Photon is a boson and has a spin -1.
• Quantum spin can take the value 0, 1, 2 or any integer number units
• Fermions have half-integer values such as $\frac{1}{2}, \frac{3}{2}$
• Protons, neutrons, and electrons are all fermions with spin $-\frac{1}{2}$
• The Pauli exclusion principle states that two fermions of the same type will never be found in the same place; so matter can't just collapse.
• Bosons act in exactly the opposite fashion to fermions.; they can be found in the same place.
• they are like crocodiles - they prefer to pile up on top of one another.
• Two light beams can shine in exactly the same place. In fact, lasers are based on this fact.; produce their strong, coherent beams.
• 4e condensate (BEC):
• a state of matter of a dilute gas of bosons cooled to close to 0 K (-273.15ºC)
• 1938: superfluidity and superconductivity.

#### 6. 量子力学: 不確定問題

• Backbody spectrum:
x: frequency
• lower waverlength corresponds to lower frequncy, or lower energy, or lower temperature.)
y: relative intensity.
• Universe now: 2.7 degrees above aboslute zeor.

• Blackbody: emits most of its radiation at low frequnecies, and high frequencies be cut out.
• An analogy: ordering dessert
• Photoelectric effect (光電効果):

• Standard Model:

#### >Top ７. The Standard Model of Particle Physics: Matter's most basic known structure:

• Quarks; the building blocks of the proton:
• 1 $cm^3$ pea in a 2m × 1m × $\frac{1}{2}$m mattress takes up one-millionth; a quark occupies in a proton.
• the Standard Model and its key ideas will contribute to a deeper understanding of matter's fundamental structure and the way physicists think about the world today.
• 1819 Hans Oersted;
• deduced that there should be a single theory describing both electricity and magnetism; must be two sides of the same coin. (electromagnetism)
• 'Field' is any quantity that permeates space; the value of the field at any location tells us how intense the field is there.
• first half 19C, Michael Farady; introduced the concepts of electric an magnetic fields; ubiquity of electric fields; action at a distance.
• it would be extraordinary if something in one place could instantly affect another object some distance away. How would the effect be communicated?
• The electric and magnetic fields change no faster than the finite speed of light allows.
• Maxwell's electromagnetic theory gave Einstein the insight about the constant speed of light that instigated his monumental work.
• The quantum electromagnetic theory attributes the electromagnetic force to the exchange of photon
• >Top Photon:
• the first example of a gauge boson, elementary particle that is responsible for communicating a particular force.
• Two electrons enter the interaction region, exchange a photon, and then emerge with their resultant paths. (the Feynman diagram) >Fig.
• Richard Feynman; QED (Quantum ElectroDynamics): predicts how photon exchange produced the electromagnetic force.
• Quantum field theory: particles can be produced or destroyed anywhere and at any time.
• In 1960s: Sheldon Glashow, Steven Weinberg, Abdus Salam:
• independently developed the electroweak theory; the of the weak force.
• Weak gauge bosons produces the effects of the weak force, just as photon exchange communicates electromagnetism; W+, W, Z
• The weak force; distinguishes left from right, or violates parity symmetry; chirality
• When a neutron interacts with a weak gauge boson, a proton might emerge.
• a down quark contained in the neutron into an up quark contained in the proton.
• Violation of parity symmetry is not the only novel property of the weak force.
• over a very short distance ($10^{-16}$ cm); quite unlike gravity and electromagnetism.
• The photon coveys the electromagnetic force to large distances.
• the weak force can actually convert one particle type into another.
• A neutron interacts with a weak gauge bozon, a proton might emerge. <Fig>
• However, because neutron and proton have different masses and carry different charges, the neutron must decay into a proton plus other particles, so as to conserve charge, energy, and momentum.;
• Beta decay:
• it produces but also an electron and a neutrino (antineutrino) <Fig>
• neutrino has no electric charge and does not decay, it was invisible to detectors and no one knew it existed.
• without the neutrino, beta decay looked as if it wouldn't conserve energy.
• Enrico Fermi; named neutrino.
• >Top Quarks and the Strong Force:
• Quantum Chromo Dynamics (QCD); the last of the Standard Model force that we can explain with gauge boson exchange.
• 1950s-60s: many particles were discovered successively; collectively, these particles are called hadrons.
• Hadrons were all much more massive than the electron; comparable in mass to the proton (2,000 times the electron's mass)
• Light quarks and leptons found in matter; heavier quarks and leptons also exit.
• These heavy particles are unstable; they decay to lighter quarks and leptons.
• There are three generations, each of which contains successively heavier versions of each particle type.
• these particle varieties are known as flavors.
• Gell-Mann proposed three varieties of quark; up, down, and strange.
• the strong force was the last force to be understood.
• Proton=2 up quarks ($+\frac{2}{3}$)+1 down quark ($-\frac{1}{3}$)=+1 electric charge.
• Neutron= 1 up quark + 2 down quark = zero electric charge.
• Quarks never appear as free unaccompanied objects.
• The known fundamental particles:
• three of the four known forces: electromagnetism, the weak force, and the strong force.
• the Standard Model; identified by their charges and by handedness.
• these particles as either quarks or leptons (E.g.: electrons and neutrinos)
• all of the lighter stable quarks and leptons have heavier replicas.
• Muon, first seen in cosmic rays, was nothing other than a heavier version of electron (200 time heavier); is negatively charged.
• Muon is unstable and quickly converts into an electron and two neutrinos.
• Muon decay:
• muon turns into a muon neutrino and a virtual $W^-$ gauge boson, which then converts to an electron and ana electron antineutrino.
• The 2nd generation particles have charges identical to those oft heir first generation counterparts but are heavier.

#### 7. 素粒子物理学の標準モデル:

• Feynman Diagram

• Interaction with a $W^-$ gauge bozon

• Beta decay:

• Muon decay:

 >Top Quarks: experience strong force Leptons 1st generation (stable) Up-L 3 MeV Down-L 7 MeV Up-R 3 MeV Down-R 7 MeV $e$ neutrino-L 〜0 $e$-L 0.5 MeV $e$-R 0.5 MeV 2nd generation Charm-L 1.2 GeV Strange-L 120 MeV Charm-R 1.2 GeV Strange-R 120 MeV $\mu$ neutrino-L 〜0 $\mu$-L 106 MeV $\mu$-R 106 MeV 3rd gneration Top-L 174 GeV Bottom-L 4.3 GeV Top-R 174 GeV Bottom-R 4.3 GeV $\tau$ neutrino-L 〜0 $\tau$-L 1.8 GeV $\tau$-R 1.8 GeV Quarks-L: weak force Leptons-L: weak force
 Three generations of the Standard Model; Left- and Right- handed quarks and leptons are listed separately. Each column contain particles with the same charge (different flavors) The weak force can change elements of the first coulmn into elements of the second, and the fifth comun into the sixth. The quarks experience the strong force, whereas the leptons do not.