motion mountain - vol. 4 - quantum theory - the adventure of physics

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Christoph Schiller

M M

Te Adventure of Physics

Volume IV

Fall, Flow and Heat

Edition 9, available as ree pdwith lms at www.motionmountain.net
http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/http://www.motionmountain.net/


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Editio trigesima.

Proprietas scriptoris Chrestophori Schillersecundo anno Olympiadis trigesimae primae.

Omnia proprietatis iura reservantur et vindicantur.Imitatio prohibita sine auctoris permissione.Non licet pecuniam expetere pro aliqua, quaepartem horum verborum continet; liberpro omnibus semper gratuitus erat et manet.

Tirtieth edition.

Copyright by Christoph Schiller,from the third year of the th Olympiadto the second year of the st Olympiad.

Tis pdf file is licensed under the Creative Commons

Attribution-Noncommercial-No Derivative Works . GermanyLicence, whose full text can be found on the websitecreativecommons.org/licenses/by-nc-nd/./de,with the additional restriction that reproduction, distribution and use,in whole or in part, inanyproduct or service, be itcommercial or not, is not allowed without the written consent ofthe copyright owner. Te pdf file was and remains free for everybodyto read, store and print for personal use, and to distributeelectronically, but only in unmodified form and only at no charge.
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o Britta, Esther and Justus Aaron


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Die Menschen strken, die Sachen klren.


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PREFACE

Primum movere, deinde docere.*

Antiquity

This book series is or anybody who is curious about motion in nature. How dohings, people, animals, images and empty space move? Te answer leadso many adventures, and this volume presents those due to the discovery that

there is a smallest possible change value in nature. Tis smallest change value, thequantum o action, leads to what is called quantum physics. In the structure o modernphysics, shown inFigure , quantum physics covers our o eight points. Te presentvolume introduces the oundations o quantum theory, explains the structure o atomsand the appearance o probabilities, wave unctions and colours.

Te present introduction to quantum physics arose rom a threeold aim I have pur-sued since 99: to present the basics o quantum motion in a way that is simple, up todate and captivating.

In order to besimple, the text ocuses on concepts, while keeping mathematics to thenecessary minimum. Understanding the concepts o physics is given precedence over

using ormulae in calculations. Te whole text is within the reach o an undergraduate.In order to beup to date, the text is enriched by the many gems both theoretical and

empirical that are scattered throughout the scientic literature.In order to becaptivating, the text tries to startle the reader as much as possible. Read-

ing a book on general physics should be like going to a magic show. We watch, we areastonished, we do not believe our eyes, we think, and nally we understand the trick.When we look at nature, we ofen have the same experience. Indeed, every page presentsat least one surprise or provocation or the reader to think about. Numerous interestingchallenges are proposed.

Te motto o the text, die Menschen strken, die Sachen klren, a amous statementon pedagogy, translates as: o ortiy people, to clariy things. Clariying things andadhering only to the truth requires courage, as changing the habits o thought producesear, ofen hidden by anger. But by overcoming our ears we grow in strength. And weexperience intense and beautiul emotions. All great adventures in lie allow this, andexploring motion is one o them. Enjoy it.

Christoph Schiller

* First move, then teach. In modern languages, the mentioned type ofmoving(the heart) is called motiv-ating; both terms go back to the same Latin root.

MotionMountainTheAdventureofPhysics

copyright

ChristophSchillerJune1990January2018

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Galilean physics, heat and electricityThe world of everyday motion:human scale, slow and weak.

Adventures: sport, music, sailing, cooking, describing

beauty and understanding its origin (vol. I);

using electricity, light and computers,

understanding the brain and people (vol. III).

Special relativity

Adventures: light,

magnetism, length

contraction, time

dilation and

E0 = mc2

(vol. II).

Quantum theory

Adventures: biology,

birth, love, death,

chemistry, evolution,

enjoying colours, art,

paradoxes, medicine

and high-tech business(vol. IV and vol. V).

Quantum theory

with classical gravity

Adventures: bouncingneutrons, under-

standing tree

growth (vol. V).

Final, unified description of motionAdventures: describing precisely all motion, understanding

the origin of colours, space -time and particles, enjoying

extreme thinking, calculating masses and couplings,

catching a further, tiny glimpse of bliss (vol. VI).

h, e, k limit

tiny

motion

PHYSICS:

Describing motion with precision,

i.e., using the least action principle.

Quantum field theory

(the standard model)

Adventures: building

accelerators, under-

standing quarks, stars,

bombs and the basis oflife, matter & radiation

(vol. V).

General relativity

Adventures: thenight sky, measu-

ring curved and

wobbling space,

exploring black

holes and the

universe, space

and time(vol. II).

Classical gravity

Adventures:

climbing, skiing,

space travel,

the wonders of

astronomy and

geology (vol. I).

An arrow indicates an

increase in precision byadding a motion limit.

G limits

uniform

motion

climits

fast

motion

F I G U R E 1 A complete map of physics, the science of motion, as first proposed by Matvei Bronshtein

(b. 1907 Vinnytsia, d. 1938 Leningrad). The Bronshtein cube starts at the bottom with everyday motion,

and shows the connections to the fields of modern physics. Each connection increases the precision of

the description and is due to a limit to motion that is taken into account. The limits are given for

uniform motion by the gravitational constant G, for fast motion by the speed of lightc, and for tinymotion by the Planck constanth, the elementary chargee and the Boltzmann constantk.


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U

Marginal notes reer to bibliographic reerences, to other pages or to challenge solutions.

In the colour edition, marginal notes, pointers to ootnotes and links to websites aretypeset in green. Over time, links on the internet tend to disappear. Most links can berecovered viawww.archive.org, which keeps a copy o old internet pages. In the reepd edition o this book, available at www.motionmountain.net,all green pointers andlinks are clickable. Te pd edition also contains all lms; they can be watched directlyin Adobe Reader.

Solutions and hints orchallengesare given in the appendix. Challenges are classiedas easy (e), standard student level (s), difficult (d) and research level (r). Challenges orwhich no solution has yet been included in the book are marked (ny).

A

Learning allows us to discover what kind o person we can be. Learning widens know-ledge, improves intelligence and provides a sense o achievement. Tereore, learningrom a book, especially one about nature, should be efficient and enjoyable. Avoid badlearning methods like the plague! Do not use a marker or a pencil to highlight or un-derline text on paper. It is a waste o time, provides alse comort and makes the textunreadable. And do not learn rom a screen. In particular, never, ever, learn rom the in-ternet, rom videos, rom games or rom a smartphone. Most o the internet, almost allvideos and all games are poisons and drugs or the brain. Smartphones are dispensers odrugs that make people addicted and prevent learning. Nobody putting marks on paperor looking at a screen is learning efficiently or is enjoying doing so.

In my experience as a pupil and teacher, one learning method never ailed to trans-orm unsuccessul pupils into successul ones: i you read a text or study, summarizeevery section you read, in your own words and images, aloud. I you are unable to doso, read the section again. Repeat this until you can clearly summarize what you read inyour own words and images, aloud. And enjoythe telling aloud! You can do this aloneor with riends, in a room or while walking. I you do this with everything you read, youwill reduce your learning and reading time signicantly; you will enjoy learning romgood texts much more and hate bad texts much less. Masters o the method can use iteven while listening to a lecture, in a low voice, thus avoiding to ever take notes.

A

A teacher likes pupils and likes to lead them into exploring the eld he or she chose. Hisor her enthusiasm is the key to job satisaction. I you are a teacher, beore the start o alesson, picture, eel and tell yoursel how you enjoy the topic o the lesson; then picture,eel and tell yoursel how you will lead each o your pupils into enjoying that topic asmuch as you do. Do this exercise consciously, every day. You will minimize trouble inyour class and maximize your teaching success.

Tis book is not written with exams in mind; it is written to make teachers and stu-dentsunderstandandenjoyphysics, the science o motion.


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F

Te latest pd edition o this text is and will remain ree to download rom the internet.

I would be delighted to receive an email rom you at [email protected], especiallyon the ollowing issues:

What was unclear and should be improved?Challenge 1 s What story, topic, riddle, picture or lm did you miss?

Also help on the specic points listed on thewww.motionmountain.net/help.htmlwebpage is welcome. All eedback will be used to improve the next edition. You are welcometo send eedback by mail or by sending in a pd with added yellow notes, to provideillustrations or photographs, or to contribute to the errata wiki on the website. I youwould like to translate a chapter o the book in your language, please let me know.

On behal o all readers, thank you in advance or your input. For a particularly useul

contribution you will be mentioned i you want in the acknowledgements, receive areward, or both.

S

Your donation to the charitable, tax-exempt non-protorganisation thatproduces, trans-lates and publishes this book series is welcome. For details, see the web page www.motionmountain.net/donation.html. Te German tax office checks the proper use oyour donation. I you want, your name will be included in the sponsor list. Tank you inadvance or your help, on behal o all readers across the world.

Te paper edition o this book is available, either in colour or in black and white, romwww.amazon.comorwww.createspace.com. And now, enjoy the reading.


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C

M Te effects of the quantum of action on rest Te consequences of the quantumofactionforobjects Why quantum? Teeffect of thequantum of actionon motion Te surprises of the quantum of action ransformation, lifeand Democritus Randomness a consequence of the quantum of action Waves a consequence of the quantum of action Particles a consequence ofthe quantum of action Quantum information Curiosities and fun chal-lenges about the quantum of action Te dangers of buying a can of beans A summary: quantum physics, the law and indoctrination

L

How do faint lamps behave? Photons What is light? Te sizeof photons Are photons countable? Squeezed light Te positionsof photons Are photons necessary? Interference: how can a wave bemade up of particles? Interference of a single photon Reflection anddiffraction deduced from photon arrows Refraction and partial reflectionfrom photon arrows From photons to waves Can light move faster thanlight? Real and virtual photons Indeterminacy of electric fields Cantwo photons interfere? Curiosities and fun challenges about photons Asummary on light: particle and wave

M

Wine glasses, pencils and atoms no rest No infinite measurement preci-sion Cool gas Flows and the quantization of matter Fluid flowsand quantons Knocking tables and quantized conductivity Matter quan-

tons and their motion matter waves Mass and acceleration of quantons Why are atoms not flat? Why do shapes exist? Rotation, quantization ofangular momentum, and the lack of north poles Rotation of quantons Silver, Stern and Gerlach polarization of quantons Curiosities and fun

challenges about quantum matter First summary on the motion of quantumparticles

States and measurements the wave function Visualizing the wave function:rotating arrows and probability clouds Te state evolution the Schrdingerequation Self-interference of quantons Te speed of quantons Dis-persion of quantons unnelling and limits on memory damping of quan-tons Te quantum phase Can two electron beams interfere? Are there

coherentelectronbeams? Te leastactionprinciple in quantum physics Te motion of quantons with spin Relativistic wave equations Boundmotion, or composite vs. elementary quantons Curiosities and fun chal-lenges about quantum motion of matter A summary on motion of matterquantons

P ?

Distinguishing macroscopic objects Distinguishing atoms Why doesindistinguishabilityappear in nature? Can quantum particles be counted? What is permutation symmetry? Indistinguishability and wave function


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B

CAcknowledgements Film credits Image credits

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S
http://www.motionmountain.net/


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T Q C

In our quest to understand how things move,

we discover that there is a smallest change value in nature,

implying that motion is uzzy,

that boxes are never tight,

that matter is composed o elementary units,

and that light and interactions are streams o particles.

Te smallest change value explains why antimatter exists,

why particles are unlike gloves,

why copying machines do not exist,

why probabilities are reasonable,and how all colours in nature are ormed.


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MINIMUM ACTION QUANTUM

THEORY FOR POETS

Natura [in operationibus suis] non facitsaltus.**

th century

Climbing Motion Mountain up to this point, we completed three legs. Weame across Galileos mechanics (the description o motion or kids), thenontinued with Einsteins relativity (the description o motion or science-ction

enthusiasts), and nally explored Maxwells electrodynamics (the description o mo-tion or business people). Tese three classical descriptions o motion are impressive,beautiul and useul. However, they have a small problem: they are wrong. Te reason issimple: none o them describeslie.

Whenever we observe a ower or a buttery, such as those oFigure , we enjoy thebright colours, the motion, the wild smell, the sof and delicate shape or the ne detailso their symmetries. However, we know:

Classical physics cannot explain any characteristic length or time scale ob-

served in nature.

Now, owers and animals but also many non-living systems have characteristic sizes,size ranges and proportions; and they have characteristic rhythms. And indeed, classicalphysics cannot explain their origin, because

Te classical constants o nature the gravitational constant, the ideal gasconstant , the speed o light , the vacuum permittivity0and the vacuumpermeability0 do not allow dening length or time scales.

In act, the classical constants do not even allow us to measure speed or orce values, even

though these measurements are ractions o and4/; because in order to measureractions, we need to dene them rst; however, dening ractions also requires lengthor time scales, which classical physics does not allow.Without measurements, there are also no emotions! Indeed, our emotions are

triggered by our senses. And all the impressions and all the inormation that our sensesprovide us are among others measurements. Since classical physics does not providemeasurement scales, we know:

** Nature [in its workings] makes noRef. 1 jumps.


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F I G U R E 2 Examples of quantum machines ( Linda de Volder).

Classical physics does not allow understanding senses or emotions.

Te reason or all these limitations is the ollowing connection:

Classical physics alone cannot be used to build any measurement device.Every sense contains measurementdevices. And every measurement device, like any pat-tern or rhythm, needs an internal scale, or, more generally, an internal measurementunit.Because classical physics does not provide any scale, classical physics does not explainhow measurement devices work, not how senses work, and not how emotions appear.

o understand emotions and lie, we need to gobeyondclassical physics. ake any ex-ample o a pleasant situation,*such as a beautiul evening sky, a waterall, a happy child

or a caress. Classical physics is not able to explain any aspect o the situation:Challenge 2 s First, thecolours and their origin remain mysterious. Secondly, all shapes, sizes and proportionsremain mysterious. Tirdly, the timing and the duration o the involved processes can-not be understood. Fourthly, all the sensations and emotions produced by the situationremain mysterious. o understand and explain these aspects, we needquantum theory.

* Te photograph onpage shows a female glow worm, Lampyris noctiluca, as commonly found in theUnited Kingdom ( John yler,www.johntyler.co.uk/gwfacts.htm).


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In act, we will nd out that both lieandevery type o pleasureare examples o quantummotion. Emotions are quantum processes.

In the early days o physics, the impossibility to describe lie and pleasure was not

seen as a shortcoming, because neither senses nor material properties nor scales werethought to be related to motion. And pleasure was not considered a serious subject oinvestigation or a respectable researcher anyway. oday, the situation is different. In ouradventure we have learnedVol. I, page 408 that our senses o time, hearing, touch, smell and sight areprimarilydetectors o motion. Without motion, there would be no senses. Furthermore,all detectors are made o matter. During the exploration on electromagnetism we beganto understand that all properties o matter are due to motions o charged constituents.Density, stiffness, colour and all other material properties result rom the electromag-netic behaviour o the Lego bricks o matter:Vol. III, page 227 namely, the molecules, the atoms and theelectrons. Tus, the properties o matter are also consequences o motion. Moreover,we saw that these tiny constituents arenotcorrectlyVol. III, page 243 described by classical electrodyna-

mics. We even ound that light itsel does not behave classically.Vol. III, page 147 Tereore the inabilityo classical physics to describe matter, light and the senses is indeed due to its intrinsiclimitations.

In act, every ailure o classical physics can be traced back to a single, undamentaldiscovery made in 899 byRef. 2 Max Planck:*

In nature, action values smaller than = 1.06 1034Js are not observed.All attempts to observe physical action values smaller than this ail.**In other words, innature as in a good cinema lm there is always some action. Te existence o a smal-lest action value the so-calledquantum principle is in complete contrast with clas-

sical physics. (Why?)Challenge 3 s Despite this contrast, the quantum principle has passed an enorm-ous number o experimental tests, many o which we will encounter in this part o ourmountain ascent. Above all, the quantum principle has never ailed even a single test.

* Max Planck (), professor of physics in Berlin, was a central figure in thermostatics and mod-ern physics. He discovered and named the Boltzmann constantand thequantum o action, oen calledPlancks constant. His introduction of the quantum hypothesis gave birth to quantum theory. He also madethe works of Einstein known in the physical community, and later organized a job for him in Berlin. Hereceived the Nobel Prize for physics in . He was an important figure in the German scientific estab-lishment; he also was one of the very few who had the courage to tell Adolf Hitler ace to acethat it wasa bad idea to fire Jewish professors. (He got an outburst of anger as answer.) Famously modest, with manytragedies in his personal life, he was esteemed by everybody who knew him.** In fact, this story is a slight simplification: the constant originally introduced by Planck was the (unre-

duced) constant = 2. Te factor2leading to the final quantum principle was added somewhat later,by other researchers.Tis somewhat unconventional, butdidactically useful, approach to quantum theory is due to Niels Bohr.Nowadays, it is hardly ever encountered in the literature, despite its simplicity.Ref. 3,Ref. 4

Niels Bohr (b. Copenhagen, d. Copenhagen) was one of the great figures of modern physics.A daring thinker and a polite man, he made Copenhagen University into the new centre of development ofquantum theory, overshadowing Gttingen. He developed the description of the atom in terms of quantumtheory, for which he received the Nobel Prize in Physics. He had to flee Denmark in aer theGerman invasion, because of his Jewish background, but returned there aer the war, continuing to attractthe best physicists across the world.


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F I G U R E 3 Max Planck (18581947) F I G U R E 4 Niels Bohr

(18851962)

Te undamental constant, which is pronounced aitch-bar, is called the quantum oaction, or alternativelyPlancks constant. Planck discovered the quantum principle whenstudying the properties o incandescent light,Vol. III, page 147 i.e., o light emanating rom hot bodies. Butthe quantum principle also applies to motion o matter, and even, as we will see later, tomotion o empty space, such as gravitational waves.

Te quantum principle states that no experiment can measure an action smaller than. For a long time, Einstein tried to devise experiments to overcome this limit. But heailed in all his attempts: nature does not allow it, as Bohr showed again and again. Tesame occurred to many other researchers.

We recall that in physics as in the theatre action is a measure or thechangeoc-curring in a system.Vol. I, page 246 Te quantum principle can thus rephrased as

In nature, a change smaller than = 1.06 1034Js cannot be observed.Tereore, a smallest action implies that there is a smallest change value in nature. I wecompare two observations, there will always be change between them. Tus the quantumo action would perhaps be better named thequantum o change.

Can a minimum change really exist in nature? o accept the idea, we need to explorethree points, detailed inable . We need to show that a smaller change isnever observedin nature, show that smaller change valuescan neverbe observed, and nally, show thatall consequenceso this smallest change, however weird they may be, apply to nature. Inact, this exploration constitutes all o quantum physics. Tereore, these checks are all

we do in the remaining o this part o our adventure. But beore we explore some o theexperiments that conrm the existence o a smallest change, we directly present some oits more surprising consequences.

Since action is a measure o change, a minimum observable action means that two suc-cessive observations o the same system always differ by at least . In every system, thereis alwayssomethinghappening. As a consequence we nd:


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TA B L E 1 How to convince yourself and others that there is a smallest

action, or smallest changein nature. Compare this table with the twotables in volume II, that about maximum speed on page26, and that

about maximum force on page109.

S

Te smallest action valueisobserver-invariant.

Check all observations.

Local change or action values< are not observed.

Check all observations.

Local change or action values< cannot be produced.

Check all attempts.

Local change or action values< cannot even be imagined.

Solve all paradoxes.

Te smallest local change or actionvalueis a principle of nature. Deduce quantum theoryfrom it.Show that all consequences,however weird, areconfirmed by observation.

In naturethere is no rest.Everything moves, all the time, at least a little bit.Page 15 Natura acit saltus.*rue, these jumpsare tiny, as

is too small to be observable by any o our senses. Nevertheless, rest can

be observed only macroscopically, and only as a long-time or many-particle average. For

example, the quantum o action implies that in a mountain an archetypal system atrest all the atoms and electrons are continually buzzing around. In short,

Tere is motioninside matter.Since there is a minimum action or all observers, and since there is no rest, we de-

duce:

In naturethere is no perectly straight or perectly uniorm motion.Forget all you have learnt so ar: Inertial motion is an approximation! An object can

move in straight, uniorm motion only approximately, and only when observed over longdistances or long times. We will see later that the more massive the object is, the betterthe approximation is. (Can you conrm this?)Challenge 4 s So macroscopic observers can still talkabout space-time symmetries; and specialrelativity can thus be reconciled with quantumtheory.

Also ree all, or motion along a geodesic, exists only as a long-time average. Sogeneralrelativity, which is based on the existence o reely-alling observers, cannot be

* Nature makes jumps.


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correct when actions o the order o are involved. Indeed, the reconciliation o thequantum principle with general relativity and thus with curved space is a big chal-lenge. (Te solution is simple only or weak, everyday elds.) Te issues involved are so

mind-shattering that they orm a separate, nal, part o this adventure. We thus exploresituations without gravity rst.

Have you ever wondered why leaves are green? You probably know that they are greenbecause they absorb blue (short-wavelength) and red (long-wavelength) light, while al-lowing green (medium-wavelength) light to be reected. How can a system lter out thesmall and the large, and let the middle pass through? o do so, leaves must somehowmeasurethe requency. But we have seen that classical physics does not allow measure-ment o time (or length) intervals, as any measurement requires a measurement unit,and classical physics does not allow such units to be dened.Vol. I, page 435 On the other hand, it

takes only a ew lines to conrm that with the help o the quantum o action (andthe Boltzmann constant, both o which Planck discovered), undamental units orallmeasurable quantities can be dened, including time and thereore requency. (Can yound a combination o the speed o light , the gravitational constant and the quantumo actionthat gives a time?Challenge 5 s It will only take a ew minutes.)

In short,measurements are only possible at all because o the existence o the quantumo action.

All measurementsare quantum effects.When Planck saw that the quantum o action allowed dening all units in nature, he was

as happy as a child; he knew straight away that he had made a undamental discovery,even though (in 899) quantum theory did not yet exist. He even told his seven-year-oldson Erwin about it, while walking with him through the woods around Berlin.Ref. 5 Planckexplained to his son that he had made a discovery as important as universal gravity.Indeed, Planck knew that he had ound the key to understanding many o the effectsthat were then unexplained.

In nature,all times and all requencies are due to the quantum o action.All processes that take time are quantum processes. I you preer, waitingis a quantumeffect! In particular, without the quantum o action, oscillations and waves could not

exist:

Every colour is a quantum effect.But this is not all. Planck also realized that the quantum o action allows us to understandthesizeo all things.

Every size is a quantum effect.


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O

H

H

F I G U R E 5 An artists impression of a water molecule made of

two hydrogen (H) and one oxygen (O) atom.

Can you nd the combination o

,

and

that yields aChallenge 6 e length? With the quantum o

action, it was nally possible to determine the maximum size o mountains, o trees ando humans.Vol. I, page 335 Planck knew that the quantum o action conrmed what Galileo had alreadydeduced long beore him: that sizes are due to undamental, smallest scales in nature.

Max Planck also understood that the quantum o actionwas thelast missingcon-stant o nature. With , it becomes possible to dene anaturalunit oreveryobservableproperty in nature. ogether,, and allow to dene units that are independent oculture or civilization even extraterrestrials would understand them.*In short,al-lows understandingallobservables. Tereore, withit is possible to draw the diagramshown inFigure that encompassesallmotion in nature, and thus allo physics.

In our environment, the size o all objects is related and due to the size o atoms. Inturn, the size o atoms is a direct consequence o the quantum o action. Can you derivean approximation or the size o atoms, knowing that it is given by the motion o electrons

omasseand charge , constrained by the quantum o action?Challenge 8 s Tis connection, a simpleormula, was discovered in 9 by Arthur Erich Haas, 5 years beore quantum theorywas ormulated. Atom sizes are quantum effects.

At the time, Haas was widely ridiculed.**Nowadays, his ormula or the size o atoms isound in all textbooks, includingPage 185 this one. In determining the size o atoms, the quantumo action has another important consequence:

Gullivers travelsare impossible.

Tere are no tiny people and no giant ones. Classically, nothing speaks against the idea;but the quantum o action prevents it. Can you supply the detailed argument?Challenge 9 s

* In fact, it is also possible to define all measurement units in terms of the speed of light, the gravitationalconstantand the electron charge. Why is this notChallenge 7 s fully satisfactory?** Before the discovery of, the only simple length scale for the electron was the combination2/(40e2) 3 m; this is ten thousand times smaller than an atom. We stress that any length scalecontaining is a quantum effect, and not a classical length scale,because is the quantum of electric charge.


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F I G U R E 6 Max Born (18821970)

But i rest does not exist, how canshapesexist? Any shape o everyday lie, including

that o a ower, is the result o body parts remaining at restwith respect to each other.Now, all shapes result rom interactions between the constituents o matter, as shownmost clearly in the shapes o molecules. But how can a molecule, such as the water mo-lecule H2O, shown inFigure 5,have a shape? In act, a molecule does not have axedshape, but its shape uctuates, as would be expected rom the quantum o action. Des-pite the uctuations, every molecule does have an average shape, because different anglesand distances correspond to different energies. Again, these average length and angle val-ues only exist because the quantum o action yields undamental length scales in nature.Without the quantum o action, there would benoshapes in nature.

All shapes are quantum effects.

All shapes in everyday lie are due to molecular shapes, or to their generalizations.Temasso an object is also a consequence o the quantum o action, as we will see

later on. Since all material properties such as density, colour, stiffness or polarizability are dened as combinations o length, time and mass units, we nd:

All material properties arise rom the quantum o action.In short, the quantum o action determines the size, shape, colour, mass, and all otherproperties o objects, rom stones to whipped cream.

W ?

Quantum effects surround us on all sides. However, since the quantum o action is sosmall, its effects on motion appear mostly, but not exclusively, in microscopic systems.Te study o such systems was called quantum mechanicsby Max Born, one o the majorcontributors to the eld.*Later, the termquantum theorybecame more popular.

* Max Born (b. Breslau, d. Gttingen) first studied mathematics, then turned to physics. A pro-fessor at Gttingen University, he made the city one of the world centres of physics. He developed quantummechanics with his assistants Werner Heisenberg and Pascual Jordan, and then applied it to scattering,


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TA B L E 2 Some small systems in motion and the observed action values for their changes.

S A M

LightSmallest amount of light absorbed by a coloured surface 1 quantumSmallest impact when light reflects from mirror 2 quantumSmallest consciously visible amount of light c. 5 quantumSmallest amount of light absorbed in flower petal 1 quantumBlackening of photographic film c. 3 quantumPhotographic flash c. 1017 classical

Electricity

Electron ejected from atom or molecule c. 2 quantumElectron extracted from metal c. 2 quantumElectron motion inside microprocessor c.

6 quantum

Signal transport in nerves, from one molecule to the next c. 5 quantumCurrent flow in lightning bolt c. 1038 classicalMaterials

earing apart two neighbouring iron atoms c. 2 quantumBreaking a steel bar c. 1035 classicalBasic process in superconductivity 1 quantumBasic process in transistors 1 quantumBasic magnetization process 1 quantum

Chemistry

Atom collision in liquid at room temperature

motion mountain - vol. 4 - quantum theory - the adventure of physics

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