Table Of Contentt h e f r on t i e r s c o l l e c t i o n
t h e f r o n t i e r s c ol l e ct i o n
Series Editors:
A.C.Elitzur M.P.Silverman J.Tuszynski R.Vaas H.D.Zeh
Thebooksinthiscollectionaredevotedtochallengingandopenproblemsattheforefrontof
modernscience,includingrelatedphilosophicaldebates.Incontrasttotypicalresearchmono-
graphs,however,theystrivetopresenttheirtopicsinamanneraccessiblealsotoscientifically
literatenon-specialistswishing to gain insight intothe deeper implications and fascinating
questionsinvolved.Takenasawhole,theseriesreflectstheneedforafundamentalandin-
terdisciplinaryapproachtomodernscience.Furthermore,itisintendedtoencourageactive
scientistsinallareastoponderoverimportantandperhapscontroversialissuesbeyondtheir
ownspeciality.Extendingfromquantumphysicsandrelativitytoentropy,consciousnessand
complexsystems–theFrontiersCollectionwillinspirereaderstopushbackthefrontiersof
theirownknowledge.
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Mind,MatterandtheImplicateOrder
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QuantumMechanicsattheCrossroads
NewPerspectivesfromHistory,PhilosophyandPhysics
EditedbyJ.Evans,A.S.Thorndike
ParticleMetaphysics
ACriticalAccountofSubatomicReality
ByB.Falkenburg
ThePhysicalBasisoftheDirectionofTime
ByH.D.Zeh
Asymmetry:TheFoundationofInformation
ByS.J.Muller
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QuantumMechanicsandtheParticipatingObserver
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ByM.Schlosshauer
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Chaos,Emergence,Life
ByA.Scott
ForacompletelistoftitlesinTheFrontiersCollection,seebackofbook
Mark P. Silverman
QUANTUM
SUPERPOSITION
Counterintuitive Consequences
of Coherence, Entanglement,
and Interference
With97Figuresand13Tables
123
MarkP.Silverman
TrinityCollege
DepartmentofPhysics
Hartford,CT06106
USA
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Bar-IlanUniversity, UniversityofGießen,
UnitofInterdisciplinaryStudies, CenterforPhilosophyandFoundationsofScience
52900Ramat-Gan,Israel 35394Gießen,Germany
email:[email protected] email:[email protected]
MarkP.Silverman H.DieterZeh
DepartmentofPhysics,TrinityCollege, UniversityofHeidelberg,
Hartford,CT06106,USA InstituteofTheoreticalPhysics,
email:[email protected] Philosophenweg19,
69120Heidelberg,Germany
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UniversityofAlberta,
DepartmentofPhysics,Edmonton,AB,
T6G2J1,Canada
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ISBN 978-3-540-71883-3 e-ISBN 978-3-540-71884-0
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To Sue, Chris, and Jennifer
Preface
In the course of a long career as a physicist, I have investigated quantum
mechanics with electron interferometry and microscopy, radiofrequency and
microwave spectroscopy, coherent laser spectroscopy, nuclear magnetic and
electron paramagnetic resonance, atomic beams, radioactive nuclei, and of
course pencil, paper, and computers. Throughout this time I have had other
scientific interests as well, but none has held such permanent fascination for
me as trying to understand the structure and interactions of the quantum
world.Perhapsonereasonis thateverything atsomesufficiently deeplevelof
fundamentality is a quantum system.
Therangeoftopicsdiscussedinthisbookreflect,inpart,mydiversequan-
tum interests, but all involve, in one way or another, the unifying element
of quantum superposition. Although by its very etymology the word ‘quan-
tum’ (Latin for ‘how much’) intrinsically stresses the idea of discreteness in
nature, what is actually most distinctive about quantum mechanics, in my
opinion,is the unique characterand far-reachingconsequencesofthe concept
of superposition – a superpositionnot of forces orfluxes or any other directly
measurable, tangible physical quality, but of abstract amplitudes conveying
a measure of probability.
Quantumsuperpositionscanbeovertlyspatial,asinthefamiliarexample
ofsuperposedwavesissuingfromtwoslitsleadingtoaperiodicdistributionof
independentparticlesonadistantscreen;overtlytemporalasinthesuperposi-
tionofexcited-stateamplitudesresultinginensemblequantumpropertiesthat
oscillateintime,orsubtlyinternalasinthespin-basedsymmetryrestrictions
onmultiparticle wavefunctions fromwhichdifferentquantumstatisticsarise.
Quantum superposition can occur in systems ranging in size and complex-
ity from single elementary particles,to widely separatedatoms in ‘entangled’
states, to mesoscopic electronic circuits, to degenerate stars of unimaginable
densities and pressures. The number of interesting systems whose properties
areattributabletosuperpositionofquantumamplitudesisvirtuallylimitless.
A monograph,however,is not, but the technicalessaysincluded here provide
a sampling of the diversity of quantum interference phenomena arising from
conceptually different kinds of quantum superposition.
VIII Preface
It was originallymy intention to have completed this book in time for the
tenth anniversary of its predecessor, More Than One Mystery: Explorations
in Quantum Interference, which, I believe, was at the time (1995) the first
book to be published that wasdevotedspecifically to the subject ofquantum
interference. Alas, other research commitments and a heavy teaching sched-
ule thwarted my plan, but I believe the updated and considerably expanded
finalproducthasactuallybenefitedfromthedelay.Indeed,someofthequan-
tum effects and experiments I proposed well over ten years ago were realized
recently, some even as I was working on the corresponding chapters.
The title of the present book – which is not simply MTOM 2, or Son of
MTOM, or some such reflection on its progenitor – deserves an explanation.
Likemanya physicist,I foundthe vividimageryofRichardFeynman’scolor-
ful expressionscaptivating, althoughI did not alwaysagreewith the content.
Inparticular,hiscontention(inthefamousLectures),whichwassubsequently
repeatedoftenbyothers,thatthephenomenonoftwo-slitelectroninterference
contains ‘the only mystery’ of quantum mechanics, bothered me. As a scien-
tist developing novel quantum interference experiments involving correlated
pairs of particles in entangled states, or single particles propagating around
magnetic flux tubes in a space with ‘holes’, or the effects of potentials on the
fluctuations of particlesrestrictedby the spin–statistics relation,or otherun-
usualexamplesofquantumsuperpositionsconceptuallydistinctfromYoung’s
two-slitexperiment,IthoughtFeynman’sassertiontobemisleadinglynarrow.
It was,after all, an offhandremark to stimulate a class of strugglingCalTech
undergraduates. And so I wrote a book drawn from my own researches illus-
trating why – if one adopts Feynman’s idiom – there really is ‘more than one
mystery’ to quantum mechanics.
In the yearssince publication of MTOM, I have come to regretthat title,
foritappearedto suggest– particularlytosomeoneunfamiliarwithits origin
–apointofviewtheveryoppositetothatwhichIheldthenandholdnow.Ido
notregardquantummechanicsasa‘mystery’.Rather,itisahighlydeveloped
and well-understood physical theory, perhaps the most carefully scrutinized
and best understood of all physical theories. The glib assertions by many
scientists and science popularizers that ‘nobody understands quantum me-
chanics’ – another Feynman idiom – is balderdash. Competent physicists (as
opposed to poorly informed science writers or science philosophers), who use
quantum mechanics ona daily basis to elucidate successfully countless physi-
cal phenomena, clearly must understand the instrument with which they are
working. When they pretend otherwise, I am reminded of the exchange be-
tween analyst Jack Ryan and Director of Central Intelligence William Cabot
in the film adaptation of Tom Clancy’s thriller, The Sum of All Fears:
JR: ...I don’t think that adds up.
WC: It adds up. You just don’t like what it adds up to.
Preface IX
What quantum mechanics ‘adds up to’ is that it is an irreducibly statistical
theory,albeit unlike any necessitatedsimply by ‘incomplete knowledge’,with
nonlocal features inexplicable from the perspective of classical physics. But
somethingthatisstrangeisnotnecessarilyincomprehensible,althoughitmay
not be visualizable. Mathematicians, for example, may understand very well
the principles of a 10-dimensional geometry even if no 10-dimensional figure
can be drawn.
In this book I discuss quantum superposition – the “heart of the mat-
ter” to quote another Feynmanism – in its manifold variations. Technical
essays in MTOM have been expanded throughout with new material. I have
enlarged the chapter on the electron two-slit experiment to include discus-
sion of controversial issues like Schro¨dinger’s cat, Wheeler’s delayed-choice
thought experiment, and macroscopic manifestation of quantum interference
– issues that I have found to be sensationally distorted, especially in publica-
tions for the general reader. The original chapter on correlated particles now
constitutes two chapters with new sections on distinctions between quantum
ensembles, correlated emission from excited atoms, coherence properties of
thermal electrons, and more thorough considerationof the coherence proper-
ties of field-emitted electrons. Several sections were added to the chapter on
the physicsof chiralsystems.Appendices havebeen addedthatclarify points
raised in the text or provide supplementary technical discussions.
I have also added a chapter that addresses one of the most challenging
problems in physics: the collapse of a sufficiently massive relativistic degen-
erate star to a black hole, depicted in the scientific and popular literature as
an invisible gaping singularity in space-time where the laws of physics break
down. There is no doubt that black holes must be among the most exotic
denizens ofthe cosmos,but the wildflightsoffancythathavebecome partof
theirmythology(infinitedensities,‘wormholes’throughspace-timetodistant
parts of the universe, portals to other universes, etc.) must rival in absurdity
the worst of what I have seen written about Schro¨dinger’s cat or the many-
worlds interpretation of quantum mechanics. It may be prosaic to say, but
a star – even the most bizarre star – if it is a real physical object, and not
merely a solutionto some setofdifferentialequations,cannotbe aninfinitely
denseholeinspace-time.Wedonotyetknowallthelawsofphysics,norfully
understand the consequences of those laws we think we know, but we know
enough, I believe, to conceive of mechanisms that would prevent the forma-
tionofsuchacomic-bookcaricatureofastar.InthelastchapterImakesome
suggestionswherebyquantumsuperposition,operatinginsystems ofextreme
densities and pressures, could stabilize degenerate matter at a macroscopic
size comparable to that of a neutron star or quark star.1
1 The nature of dark matter in the universe is another outstanding problem of
astrophysics and cosmology for which quantum superposition may provide the
solution (by formation of a condensate of extremely low mass bosons). I have
X Preface
Ihopethereaderwillfindtheessaysinthisbookasedifyingandthought-
provoking to read, as the author found them to write.
Trinity College, Mark P. Silverman
January 2007
Books by Mark P. Silverman
• AndYetItMoves:StrangeSystemsandSubtleQuestionsinPhysics (Cam-
bridge University Press, 1993)
• MoreThanOneMystery:ExplorationsinQuantumInterference(Springer,
New York, 1995)
• Waves and Grains: Reflections on Light and Learning (PrincetonUniver-
sity Press, 1998)
• Probing the Atom: Interactions of Coupled States, Fast Beams, and Loose
Electrons (Princeton University Press, 2000)
• AUniverseofAtoms,anAtomintheUniverse (Springer,NewYork,2002)
discussedthissolutioninthebookAUniverseofAtoms,AnAtomintheUniverse
(Springer,New York,2002).
Contents
1 The Enigma of Quantum Interference...................... 1
1.1 The Most Beautiful Experiment ........................... 1
1.2 Two-Slit Interference of Single Electron Wave Packets........ 3
1.3 Confined Fields and Electron Interference .................. 11
1.4 ‘No-Slit’ Interference of Single Photons:
Superposition, Probability, and Understanding .............. 22
1.5 Macroscale Objects in Quantum Superpositions ............. 27
1.6 Quantum Mechanics and Relativity:
The ‘Wrong-Choice’ Experiment........................... 38
2 Correlations and Entanglements I:
Fluctuations of Light and Particles ........................ 45
2.1 Ghostly Correlations of Entangled States ................... 45
2.2 A Dance of Correlated Fluctuations.
The ‘Hanbury Brown Twiss’ .............................. 54
2.3 Measurable Distinctions Between Quantum Ensembles ....... 60
2.4 Correlated Emission from Coherently Excited Atoms......... 65
2.5 The Quantum Optical Perspective......................... 70
2.6 Coherence of Thermal Electrons........................... 77
2.7 Comparison of Thermal Electrons and Thermal Radiation .... 86
2.8 Brighter Than a Million Suns:
Electron Beams from Atom-Size Sources.................... 88
2.9 Correlations and Coincidences: Experimental Possibilities.....100
2A Consequences of Spectral Width on Photon Correlations .....106
2B Chemical Potential at T =0 K............................107
2C Probability Density of a Sum of Random Variables ..........108
2D Correlated Fluctuations of Electrons at Two Detectors .......109
3 Correlations and Entanglements II:
Interferometry of Correlated Particles .....................111
3.1 Interferometry of Correlated Particles ......................111
