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Topic: Wavefunction collapses

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	Wavefunction Collapse
		During a measurement, the wavefunction instantaneously changes into a state consistent with one of the possible measurement outcomes.
		Some think there is something special about the human mind that is able to collapse wavefunctions, and that the world is a blur of waves until a human observes it.
		The wavefunction of two entangled particles cannot be represented as two waves in a three dimensional space, but as a single wave in a six dimensional space.
	members.aol.com /jmtsgibbs/Collapse.htm (293 words)

	Measurement problem - Wikipedia, the free encyclopedia
		The problem is that the wavefunction in quantum mechanics evolves according to the Schrödinger equation into a linear superposition of different states, but the actual measurements always find the physical system in a definite state, typically a position eigenstate.
		In this specific interpretation, it was the presence of a conscious being that caused the wavefunction to collapse.
		The role of the wavefunction is to create a "quantum potential" that influences the motion of the "real" particle in such a way that the probability distribution for the particle remains consistent with the predictions of the orthodox quantum mechanics.
	en.wikipedia.org /wiki/Measurement_problem (937 words)

	Wavefunction collapse - Wikipedia, the free encyclopedia
		However, when the wavefunction collapses, which is the other process, from an observer's perspective the state seems to "jump" to one of the basis states and uniquely acquire the value of the property being measured that is associated with that particular basis state.
		Upon performing measurement of an observable A, the probability of collapsing to a particular eigenstate of A is directly proportional to the squared modulus of the (generally complex) amplitude associated with it.
		The cluster of phenomena described by the expression wavefunction collapse is a fundamental problem in the interpretation of quantum mechanics known as the measurement problem.
	en.wikipedia.org /wiki/Wavefunction_collapse (467 words)

	Wavefunction collapse
		However, when the wavefunction collapses the state instantaneously jumps to one of the basis states and acquires the value of the property being measured associated with that basis state.
		The probability of collapsing to a particular basis state is directly proportional to the square modulus of the (generally complex) amplitude associated with it.
		Why the wavefunction collapses is a fundamental question in the interpretation of quantum mechanics, and is addressed directly by both the Copenhagen interpretation (which asserts that it is collapsed by "measurement") and the Everett many-worlds interpretation (which claims that the collapse is merely a result of quantum decoherence).
	www.ebroadcast.com.au /lookup/encyclopedia/qu/Quantum_collapse.html (239 words)

	CONK! Encyclopedia: Quantum_mechanics (Site not responding. Last check: 2007-10-08)
		During a measurement, the change of the wavefunction into another one is not deterministic, but rather unpredictable, i.e., random.
		The basic idea is that when a quantum system interacts with a measuring apparatus, their respective wavefunctions become entangled, so that the original quantum system ceases to exist as an independent entity.
		During a measurement, the probability that a system collapses from a given initial state to a particular eigenstate is given by the square of the absolute value of the probability amplitudes between the initial and final states.
	www.conk.com /search/encyclopedia.cgi?q=Quantum_mechanics (3985 words)

	Chapter 6
		The wavefunction is no longer interpreted as a probability, but is the source of a quantum force (also a hidden variable) which acts on the particles in addition to all of the classical forces like the electromagnetic and gravitational forces.
		This wavefunction is not arbitrary--given the initial state wavefunction and the characteristics of the Stern-Gerlach apparatus, the Schrödinger equation dictates this form.
		Reduction, or collapse, of the wavefunction requires going from a pure state consisting of a superposition to a final state consisting of only one term because the reduced wavefunction must describe the detector being in either one state or the other, but not both.
	www.faculty.virginia.edu /consciousness/new_page_9.htm (4205 words)

	Wavefunction collapse
		In quantum mechanics, the collapse of the wavefunction is a name given historically to one of two processes by which quantum systems apparently evolve.
		However, when the wavefunction collapses, from an observer's perspective the state seems to "jump" to one of the basis states and uniquely acquire the value of the property being measured that is associated with that particular basis state.
		The question is swept under the rug by the Copenhagen interpretation (which simply postulates that it is indeed collapsed by the act of "measurement," which unfortunately isn't well-defined) and the Everett many-worlds interpretation (which asserts that the apparent collapse is merely a subjective illusion resulting from quantum decoherence).
	www.sciencedaily.com /encyclopedia/wavefunction_collapse (373 words)

	Learn more about Quantum mechanics in the online encyclopedia. (Site not responding. Last check: 2007-10-08)
		During a measurement, the eigenstate to which the wavefunction collapses is probabilistic, not deterministic.
		One of the consequences of wavefunction collapse is that certain pairs of observables, such as position and momentum, can never be simultaneously ascertained to arbitrary precision.
		During a measurement, the probability that a system collapses to each eigenstate is given by the absolute square of the inner product between the eigenstate vector and the state vector just before the measurement.
	www.onlineencyclopedia.org /q/qu/quantum_mechanics_1.html (2428 words)

	Kids.net.au - Encyclopedia Quantum mechanics - (Site not responding. Last check: 2007-10-08)
		For example, an electron in an unexcited atom is pictured classically as a particle circling the atomic nucleus, whereas in quantum mechanics it is described by a static probability cloud surrounding the nucleus.
		When a measurement is performed on an observable of the system, the wavefunction turns into one of a set of wavefunctions called eigenstates of the observable.
		During the process of wavefunction collapse, the wavefunction does not obey the Schrödinger equation.
	www.kids.net.au /encyclopedia-wiki/qu/Quantum_mechanics (1520 words)

	Chapter 6
		The wavefunction is no longer interpreted as a probability, but is the source of a quantum force (also a hidden variable) which acts on the particles in addition to all of the classical forces like the electromagnetic and gravitational forces.
		This wavefunction is not arbitrary--given the initial state wavefunction and the characteristics of the Stern-Gerlach apparatus, the Schrödinger equation dictates this form.
		Reduction, or collapse, of the wavefunction requires going from a pure state consisting of a superposition to a final state consisting of only one term because the reduced wavefunction must describe the detector being in either one state or the other, but not both.
	faculty.virginia.edu /consciousness/new_page_9.htm (3984 words)

	Quantum mechanics - Wikipedia, the free encyclopedia (Site not responding. Last check: 2007-10-08)
		During a measurement, the change of the wavefunction into another one is not deterministic, but rather unpredictable, i.e.
		The probabilistic nature of quantum mechanics thus stems from the act of measurement: the object interacts with an apparatus, and their respective wavefunctions become entangled.
		There are some interpretations of quantum mechanics that do away with the concept of "wavefunction collapse" by altering the concept of what constitutes a "measurement" in quantum mechanics.
	www.bucyrus.us /project/wikipedia/index.php/Quantum_mechanics (4168 words)

	2. Some Basic Ideas about Quantum Mechanics
		This is known as the collapse of the wavefunction and the probability of the wavefunction collapsing into a particular eigenfunction depends on how much that eigenfunction contributed to the original superposition.
		When the measurement is made the wavefunction collapses into one of these eigenfunctions, with a probability determined by the composition of the original superposition.
		However, one of the most important characteristics of a wavefunction is that the square of its magnitude is a measure of the probability of finding a particle described by the wavefunction at a given point in space.
	newton.ex.ac.uk /research/qsystems/people/jenkins/mbody/mbody2.html (2015 words)

	The double slit experiment and the collapse of the wavefunction
		At any time, the square magnitude of the wavefunction plotted in the figure would be proportional to the probability of detecting the particle at that point, if the whole plane was covered with electron detectors which would be activated at that instant in time.
		The wavefunction itself develops in time according to the time dependent Schroedinger equation under the influence of the potentials, which in this case consists of a barrier region with two slits.
		The shooting up of the wavefunction when it hits the barrier at the center is due to the sharpness of the potential.
	www.fen.bilkent.edu.tr /~yalabik/applets/collapse.html (655 words)

	[No title]
		During a measurement, the change of the wavefunction into another one is not deterministic, but rather unpredictable, i.e., random.
		The basic idea is that when a quantum system interacts with a measuring apparatus, their respective wavefunctions become entangled, so that the original quantum system ceases to exist as an independent entity.
		During a measurement, the probability that a system collapses from a given initial state to a particular eigenstate is given by the square of the absolute value of the probability amplitudes between the initial and final states.
	mysteriousenergy.com /qt.htm (2292 words)

	[No title]
		If one has a wavefunction extending the length of the universe, then from the universe's point of view it doesn't make a whole lot of diffence whether it is a mind or an apparatus that provokes a universe-wide collapse, nor does it matter much whether it is slow or fast.
		So something is needed to collapse the wavefunction (slow or fast) and this something is just a piece of the classical world that QM was meant to explain.
		So the wavefunction is a very unclassical entity in what is otherwise a desperate (understandably so) attempt to hang on to classical imagery.
	www.panix.com /~dave/quantum/posts/post12 (965 words)

	Relic Forums - View Single Post - Schroeningers Cat and other Paradoxes
		This quantum wavefunction evolves deterministically - if you know the quantum wavefunction of a system, and the quantum wavefunction of everything else in the Universe, you could calculate the quantum wavefunction of the system at any point in the past or future.
		Thus an observation "collapses" the wavefunction, such that either x is 1 and y is 0 or x is 0 and y is 1.
		From the camera's perspective, the cat's wavefunction "collapsed", but from someone else's perspective, the camera itself entered a hybrid state.
	forums.relicnews.com /showpost.php?p=254113&postcount=7 (1456 words)

	sciforums.com - Wave/Particle Duality
		When it's measured, the wavefunction collapses and the wave transforms to a particle.
		In the many-worlds interpretation there's no collapse of the wavefunction, but the wavefunction splits in many different little wavefunctions, each of them represent a result of a quantum succes.
		In Bohm's interpretation remember, there is no collapse of the wave function, as the system (both particles) are in a single conected state.
	www.sciforums.com /showthread.php?t=24383 (1681 words)

	Chapter 7
		Consciousness manifests the immanent from the transcendent by collapsing the wavefunction.
		The transcendental realm is hypothesized to contain the wavefunction, yet the wavefunction as normally conceived is a function of time and space, which are absent in the transcendental realm and in fact do not appear "until" wavefunction collapse.
		Thus, the concepts of wavefunctions and wavefunction collapse in the transcendental realm are meaningless.
	faculty.virginia.edu /consciousness/new_page_11.htm (5138 words)

	Measurement problem - Encyclopedia Glossary Meaning Explanation Measurement problem (Site not responding. Last check: 2007-10-08)
		The best known example is the "paradox" of the Schrödinger's cat: a cat is apparently evolving into a linear superposition of basis vectors that can be characterized as an "alive cat" and states that can be described as a "dead cat".
		One could either imagine that the wavefunction collapses, or one could think of the wavefunction as an auxilliary mathematical tool with no direct physical interpretation whose only role is to calculate the probabilities.
		One of the many problems of the Bohm interpretation is that it does not explain what happens with the wavefunction once the particle is observed.
	www.encyclopedia-glossary.com /en/Measurement-problem.html (692 words)

	Another way to get rid of collapse
		The error is in attributing a wavefunction to a quantum entity.
		The wavefunction is indeed necessary, and the calculation of probabilities of outcomes would be impossible without it.
		What we say is that this is not a wavefunction, but a parameterized family of wavefunctions belonging to a parameterized family of experiments.
	www.lns.cornell.edu /spr/2002-12/msg0046789.html (595 words)

	Quantum mechanics Details, Meaning Quantum mechanics Article and Explanation Guide
		One of the earliest and easiest to understand is the "wave mechanics" formulation invented by Erwin Schrödinger, in which the instantaneous state of a system is described by a "wavefunction" that encodes the probability distribution of all measurable properties, or "observables".
		For example, an electron in an unexcited atom is pictured classically as a particle moving in a circular trajectory around the atomic nucleus, whereas in quantum mechanics it is described by a static, spherically symmetric probability cloud surrounding the nucleus (Fig.
		During a measurement, the change of the wavefunction into another one is probabilistic, not deterministic.
	www.e-paranoids.com /q/qu/quantum_mechanics_1.html (3305 words)

	[No title] (Site not responding. Last check: 2007-10-08)
		But as soon as someone tries to measure a >> property of that entity, the wavefunction collapses (jumps) to another >> wavefunction, an eigenfunction of the equation.
		Von Neumann is willing to consider both the wavefunctions of the quantum entities and the measurement apparatus and the resulting joint wavefunction.
		The advantages of attaching the wavefunction to the experiment is that it gets rid of collapse in a much more natural way than hidden variables, MWI, and so forth.
	www.panix.com /~dave/quantum/posts/post3 (519 words)

	IIDB - does the universe define it's self?
		The collapse of the wavefunction is a predictable result of quantum systems.
		A bit of elaboration: according to some theories the wavefunction collapses as soon as a quantum event engenders a quasi-classical one: as soon as the decay of a radioactive atom makes a microscopic track in a crystal of mica the event is no longer subject to any degree of quantum uncertainty.
		Even if a conscious observer does not find and observe the track in the mica crystal for millions of years, the collapse of the wavefunction is a done deal.
	www.iidb.org /vbb/showthread.php?t=37100 (1563 words)

	Quantum
		The wavefunction around which the entire theory is based is an unobservable entity.
		In this case then either different observers see different wavefunctions for the same object, or quantum mechanics demands that there is an absolute 'arrow of time' showing in which order the events are taking place.
		We have to interpret the wavefunction in order to simulate what happens when an event occurs, that is, when we measure it.
	interconnected.org /matt/archive/quantum/quantum.html (877 words)

	Read about Wavefunction collapse at WorldVillage Encyclopedia. Research Wavefunction collapse and learn about ... (Site not responding. Last check: 2007-10-08)
		interpretations of quantum mechanics, wavefunction collapse is one of two processes by which
		The contribution of each basis state to the overall wavefunction is called the
		The cluster of phenomena described by the expression wavefunction collapse is a fundamental problem in the interpretation of quantum mechanics known as the
	encyclopedia.worldvillage.com /s/b/Wavefunction_collapse (410 words)

	Blogger: Email Post to a Friend
		There are, however, certain wavefunctions that are associated with a definite value of a particular observable.
		Its wavefunction is a wave, of arbitrary shape, extending over all of space, and its position and momentum are observables.
		For example, the free particle in our previous example will usually have a wavefunction that is a wave packet centered around some mean position x0, neither an eigenstate of position nor of momentum.
	www.blogger.com /email-post.g?blogID=10039116&postID=110534533247416014 (705 words)

	syllabus-examinable
		Knowledge of the wavefunction for a particle whose momentum is known.
		For the barrier, understanding of why the 6 unknown coefficients that appear when trying to solve the TISE can be reduced to 4 (when we assume that the wavefunction represents a particle incident from the left of the barrier).
		Knowledge that a wavefunction ``collapses'' to an eigenstate of the relevant operator when a measurement is made.
	www.magres.nottingham.ac.uk /teaching/qm/f32aq4/syllabus-examinable (1281 words)

	Science Forums and Debate - Entangled particles for communication (Site not responding. Last check: 2007-10-08)
		Measurement collapses the wave function - it's no longer in a superposition of two states.
		I was under the impression that, when presented with a beam splitter, a single photon has a 50/50 chance of passing through or reflecting.
		If mirrors are set up to reconverge the paths, the wavefunction actually interfere with itself, producing a typical wave interference pattern on a photographic plate (after successive photons are subjected to the same setup).
	www.scienceforums.net /forums/printthread.php?t=9273 (2346 words)

	Four Reasons
		A probability ‘wavefunction’ (not a physical wave) is said to emanate from the source, and the photon can be anywhere allowed by that wavefunction.
		At this moment, the wavefunction ‘collapses’ from a cloud around the candle to a single point.
		De Broglie suggested that, in addition to the normal wavefunction of the Copenhagen Interpretation, there is a second wave that determines a precise position for the particle at any particular time.
	www.higgo.com /quantum/fourreasons.htm (6606 words)

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