Kvantemekanisk måling

	Kvantemekanik
Baggrund
	Bra-ket notation • Gammel kvanteteori • Hamilton-funktion • Interferens • Klassisk mekanik
Grundlæggende koncepter
	Atommodel • Bølgefunktion • CPT-teoremet • Bølgefunktionens kollaps • Ikke-lokalitet • Komplementaritet • Dekohærens • Kohærens • Måling • Sammenfiltring • Spin • Superposition • Tunnelering • Kvantespring • Kvanteteleportation • Kvantetilstand • Partikel-bølge-dualitet • Partikel i en boks • Paulis udelukkelsesprincip • Symmetri i kvantemekanik • Ubestemthed • Virtuel partikel
Eksperimenter
	Bells tests • Bose-Einstein-kondensat • Dobbeltspalte • Frank-Hertz • Kvante Hall-effekten • Mach-Zehnder • Stern–Gerlach
Formuleringer
	Born-Oppenheimer • Hartree-Fock • Heisenberg • Interaktion • Kurve-integraler • Matrix-mekanik • Relativistisk kvantemekanik • Schrödinger
Ligninger
	Dirac • Klein–Gordon • Pauli • Rydberg • Schrödinger
Fortolkninger
	• Københavnerfortolkningen • de Broglie–Bohm • Skjulte variabler • Mange-verdens • Schrödingers kat
Avancerede emner
	Dc-squid • Degenereret stof • Josephson-kontakt • Kvantecomputer • Kvanteelektrodynamik • Kvantefeltteori • Kvantekaos • Kvantekemi • Kvantekromodynamik • Kvanteoptik • Kvante-statistisk mekanik • Kvante-informationsteori • Kvanteø • Kvasipartikel • Rapid single flux quantum • Resonanstunneldiode • Resonanstunneltransistor • Single electron transistor • Spredningsteori • Tunneldiode • Tæthedsmatrix
Videnskabsmænd
	Bell • Bogoljubov • Bohm • Bohr • Born • Bose • de Broglie • Compton • Dirac • Debye • Ehrenfest • Einstein • Everett • Fock • Fermi • Feynman • Heisenberg • Hilbert • Jordan • Kramers • von Neumann • Pauli • Lamb • Laue • Planck • Raman • Rydberg • Schrödinger • Sommerfeld • Weyl • Wigner • Zeeman • Zeilinger
	v; d; r;

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Kvantemekanik forudsætter en omhyggelig definition af kvantemekanisk måling. Kvantemekanisk måling problemstillingen ligger til grund for kvantemekanikfortolkninger - og der er i dag (2015) ikke konsensus om kvantemekanisk måling.^[1]^[2]

Et af de områder, hvor kvantemekanikken har haft størst betydning uden for fysikerkredse, er kvantemekanisk målingsteori. Helt kort fortalt postulerer kvantemekanikken, at man ikke kan adskille personen, der foretager en måling, fra det, der bliver målt. Det betyder ofte, at man vil ændre en partikels tilstand, når man måler på den.

Kvantemekanisk måling er karakteriseret af, at der ved en måling sker der en kvantemekanisk sammenfiltring mellem partiklen og måleapparaturet, der efterlades "noget", et aftryk, i apparaturet. Der var og stadig er til diskussion om hvad der egentligt sker, når man måler kvantemekanisk.^[1] Bølgen kollapser tilsyneladende pludseligt og der sker en dekohærens forårsaget af måleapparaturet.^[1] Uheldigvis har visse sprogbrug fået nogle til at tro, at målinger bliver påvirket af, om de bliver observeret.

Superposition

Uddybende artikel: Kvantemekanisk superposition

Når man i kvantemekanikken giver afkald på de klassiske begreber, som position, fart og impuls, åbner man muligheden for at have partikler, der ikke er i en defineret tilstand (eller egentilstand) af f.eks. impuls. Man siger at en sådan partikel er i en superposition af impuls, hvor den populært sagt er i flere tilstande samtidig uden at have valgt hvilken én endnu. Partiklen bliver så at sige først nødt til at vælge i det øjeblik man måler på den, og den antager så straks en defineret tilstand. Når en partikel ikke er i en defineret tilstand, kan man som sagt ikke bruge det klassiske begreb længere, og man er nødt til at arbejde med forventningsværdier. Forventningsværdien er i bund og grund bare middelværdien af de tilstande, som partiklen kan være i.

Det er partiklers kvantemekaniske superpositionsegenskab, der giver anledning til mange af de fænomener, som kvantemekanikken er berømt for. F.eks. danner superposition grundlaget for kvantecomputeren og for paradokset om Schrödingers kat. Ofte er man også interesseret i at have en partikel i en superposition for at kunne foretage en anden måling præcist, fordi Heisenbergs usikkerhedsrelationer ikke tillader én at kende begge dele på én gang.

Stern-Gerlach-eksperimentet

Uddybende artikel: Stern-Gerlach-eksperimentet

Et af kvantemekanikkens mest bizarre resultater kan vises i en tænkt udgave af det forsøg, som Otto Stern og Walther Gerlach lavede i 1922. I det oprindelige eksperiment sendte man en stråle af sølvatomer igennem et inhomogent magnetfelt, hvilket får afbøjer atomerne forskelligt alt efter deres elektroners kvantemekanisk spin. Når strålen rammer en skærm vil man se to adskilte stråler, fordi elektronerne kan have to spin-tilstande. Dette var i modstrid med den klassiske teori, og eksperimentet dannede et fundamentalt bevis for partiklers spin.

For rigtig at forstå spins bizarre egenskaber kan man tænke sig tre Stern-Gerlach-apparater (S-G) sat efter hinanden. For hvert apparat deler strålen sig i to, og kun den ene fortsætter videre til næste apparat. Det første S-G virker langs z-aksen og deler strålen i to, z+ og z-, hvilket betyder, at de hhv. har spin op og spin ned. Den ene stråle (z+) fortsætter nu ind i det næste S-G, der virker langs x-aksen. Strålen deles igen i to, men denne gang er det efter spin i x-aksens retning: x+ og x- (vi kan kalde det hhv. spin "højre" og spin "venstre"). Til sidst fortsætter kun x+ ind i det sidste S-G, der igen virker langs z-aksen. Overraskende nok kommer der igen to stråler ud af det sidste S-G, der igen er opdelt efter spin op og spin ned.

Klassisk set ville man forvente at der kun kom én stråle med spin op ud til sidst, for alle partikler med spin ned blev frasorteret allerede i første trin. Kvantemekanikkens resultat kan kun tolkes sådan, at man ændrer på partiklens tilstand, når man foretager en måling. Matematisk set betyder det, at man sætter partiklen i en superposition (se ovenfor) af spin op og spin ned, når man foretager målingen i x-aksens retning.

Schrödingers kat

Uddybende artikel: Schrödingers kat

Et af de mest kendte paradokser inden for den moderne fysik handler om Schrödingers kat. Det er et tankeeksperiment, som Erwin Schrödinger fremsatte i 1935. Man forestiller sig, at man har en lukket kasse med en kat, et radioaktivt materiale, en Geigertæller og en beholder med giftgas. Geigertælleren er forbundet med giftgasbeholderen således, at hvis Geigertælleren giver udslag, så udsendes giftgassen. Inden for et givet tidsinterval er der altså en vis sandsynlighed for at der sker et henfald i det radioaktive materiale, så katten dræbes. Men hvorvidt katten er levende eller død, vil man ikke kunne afgøre før man åbner kassen, og dermed kan man betragte katten som værende i en superposition mellem levende og død.

Se også

Svag kvantemekanisk måling (en:weak measurement)

Kilder/referencer

^ ^a ^b ^c J D Cresser 2009, Quantum Physics Notes, Department of Physics Macquarie University: Chapter 13 Observables and Measurements in Quantum Mechanics Citat: "...One of the most difficult and controversial problems in quantum mechanics is the so-called measurement problem. Opinions on the significance of this problem vary widely. At one extreme the attitude is that there is in fact no problem at all, while at the other extreme the view is that the measurement problemis one of the great unsolved puzzles of quantum mechanics...Any quantum measurement then appears to require three components: the system, typically a microscopic system, whose properties are to be measured, the measuring apparatus itself, which interacts with the system under observation, and the environment surrounding the apparatus whose presence supplies the decoherence needed so that, ‘for all practical purposes (FAPP)’, the apparatus behaves like a classical system...This larger system could include, for instance, the measuring apparatus itself, so that instead of making a projective measurement on the system itself, one is made on the measuring apparatus. We will not be discussing these aspects of measurement theory here...", backup, Notekatalog
^ Elliott Tammaro∗ Department of Physics, Chestnut Hill College, Philadelphia, Pennsylvania, USA: Why Current Interpretations of Quantum Mechanics are Deficient, pdf Citat: "...Quantum mechanics under the Copenhagen interpretation is one of the most experimentally well verified formalisms. However, it is known that the interpretation makes explicit reference to external observation or “measurement.” One says that the Copenhagen interpretation suffers from the measurement problem...We argue, and where possible, demonstrate, that all common interpretations have unresolved deficiencies. Among these deficiencies are failures to resolve the measurement problem, fine-tuning problems, logical/mathematical inconsistencies, disagreement with experiment, and others. Short-comings as severe as these call into question the viability of any of the common interpretations. When appropriate, we indicate where future work may resolve some of these issues...At this point in time it appears that a stalemate has been reached with regard to the interpretation of quantum mechanics. Surprisingly, despite the roughly ninety years since its conception, there is currently no single widely accepted interpretation.
The variety of interpretations has acted to divide the physics community into camps. For example, one might be a “Bohmian” or an “Everettian” or in the “I shut up and calculate” camp. There is virtually no travel between camps, but there is much in the way of campaigning for new recruits...The decoherence program attempts to bypass the difficulties associated with the Copenhagen interpretation by claiming that while the evolution of a perfectly isolated system is governed by Process 2 alone, no quantum system is truly isolated during the measurement proces...Does decoherence actually solve the preferred basis problem? We will argue that decoherence does not solve preferred basis problem, and more generally, that unitary dynamics alone cannot do so [26]...An essential point is that the system of interest, the measuring apparatus, and the environment must necessarily form a closed system. Well known is that this demands that the evolution of the full system is unitary. Often overlooked, however, especially within the context of measurement problem resolutions, is the fact that closed systems must also conserve energy. Does the decoherence formalism satisfy this well established dictum? Let us demonstrate that it does not...XI. CONCLUDING REMARKS We challenge the viability of common interpretations of quantum mechanics. We have argued, and where possible, demonstrated, that each interpretation exhibits significant deficiency, in the form of fine-tuning problems/adhoc assumptions, internal inconsistencies, incompleteness, disagreement with experiment, among others..."

[Cresser-1] J D Cresser 2009, Quantum Physics Notes, Department of Physics Macquarie University: Chapter 13 Observables and Measurements in Quantum Mechanics Citat: "...One of the most difficult and controversial problems in quantum mechanics is the so-called measurement problem. Opinions on the significance of this problem vary widely. At one extreme the attitude is that there is in fact no problem at all, while at the other extreme the view is that the measurement problemis one of the great unsolved puzzles of quantum mechanics...Any quantum measurement then appears to require three components: the system, typically a microscopic system, whose properties are to be measured, the measuring apparatus itself, which interacts with the system under observation, and the environment surrounding the apparatus whose presence supplies the decoherence needed so that, ‘for all practical purposes (FAPP)’, the apparatus behaves like a classical system...This larger system could include, for instance, the measuring apparatus itself, so that instead of making a projective measurement on the system itself, one is made on the measuring apparatus. We will not be discussing these aspects of measurement theory here...", backup, Notekatalog

[2] Elliott Tammaro∗ Department of Physics, Chestnut Hill College, Philadelphia, Pennsylvania, USA: Why Current Interpretations of Quantum Mechanics are Deficient, pdf Citat: "...Quantum mechanics under the Copenhagen interpretation is one of the most experimentally well verified formalisms. However, it is known that the interpretation makes explicit reference to external observation or “measurement.” One says that the Copenhagen interpretation suffers from the measurement problem...We argue, and where possible, demonstrate, that all common interpretations have unresolved deficiencies. Among these deficiencies are failures to resolve the measurement problem, fine-tuning problems, logical/mathematical inconsistencies, disagreement with experiment, and others. Short-comings as severe as these call into question the viability of any of the common interpretations. When appropriate, we indicate where future work may resolve some of these issues...At this point in time it appears that a stalemate has been reached with regard to the interpretation of quantum mechanics. Surprisingly, despite the roughly ninety years since its conception, there is currently no single widely accepted interpretation.
The variety of interpretations has acted to divide the physics community into camps. For example, one might be a “Bohmian” or an “Everettian” or in the “I shut up and calculate” camp. There is virtually no travel between camps, but there is much in the way of campaigning for new recruits...The decoherence program attempts to bypass the difficulties associated with the Copenhagen interpretation by claiming that while the evolution of a perfectly isolated system is governed by Process 2 alone, no quantum system is truly isolated during the measurement proces...Does decoherence actually solve the preferred basis problem? We will argue that decoherence does not solve preferred basis problem, and more generally, that unitary dynamics alone cannot do so [26]...An essential point is that the system of interest, the measuring apparatus, and the environment must necessarily form a closed system. Well known is that this demands that the evolution of the full system is unitary. Often overlooked, however, especially within the context of measurement problem resolutions, is the fact that closed systems must also conserve energy. Does the decoherence formalism satisfy this well established dictum? Let us demonstrate that it does not...XI. CONCLUDING REMARKS We challenge the viability of common interpretations of quantum mechanics. We have argued, and where possible, demonstrated, that each interpretation exhibits significant deficiency, in the form of fine-tuning problems/adhoc assumptions, internal inconsistencies, incompleteness, disagreement with experiment, among others..."

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