Quantum Measurement - Revision history

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 * Probability: The probability of obtaining a particular eigenvalue is given by the squared modulus of the inner product of the system's state vector with the corresponding eigenvector.
 * State After Measurement: After the measurement, the system is left in the eigenstate corresponding to the measured eigenvalue. This is known as the collapse of the wave-function.
-The understanding of [[Quantum Measurement]] has not changed significantly since David Bohm said this in 1951:<ref>David Bohm, Quantum Theory'' Prentice Hall (1951) ISBN 978-0486659695</ref><blockquote>The quantum theory as developed thus far provides in principle, a way to calculate the probable results of any measurement that one wishes to carry out. To calculate the average value of any observable A, we simply write ''&#256; = &int; &psi;*A&psi; dx,'' where ''&psi;'' is the wave function of the system under investigation. If the quantum theory is to be able to provide a complete description of everything that can happen in the world, however, it should also be able to describe the process of observation itself in terms of the wave functions of the observing apparatus and those of the system under observation. Furthermore, in principle, it ought to be able to describe the human investigator as he looks at the observing apparatus and learns what the results of the experiment are, this time in terms of the wave functions of the various atoms that make up the investigator, as well as those of the observing apparatus and the system under observation. In other words, the quantum theory could not be regarded as a complete logical system unless it contained within it a prescription in principle for how all of these problems were to be dealt with.</blockquote>
+While progress certainly has been made, the understanding of [[Quantum Measurement]] has not changed significantly since David Bohm said this in 1951:<ref>David Bohm, Quantum Theory'' Prentice Hall (1951) Chapter 22 ISBN 978-0486659695</ref><blockquote>The quantum theory as developed thus far provides in principle, a way to calculate the probable results of any measurement that one wishes to carry out. To calculate the average value of any observable A, we simply write ''&#256; = &int; &psi;*A&psi; dx,'' where ''&psi;'' is the wave function of the system under investigation. If the quantum theory is to be able to provide a complete description of everything that can happen in the world, however, it should also be able to describe the process of observation itself in terms of the wave functions of the observing apparatus and those of the system under observation. Furthermore, in principle, it ought to be able to describe the human investigator as he looks at the observing apparatus and learns what the results of the experiment are, this time in terms of the wave functions of the various atoms that make up the investigator, as well as those of the observing apparatus and the system under observation. In other words, the quantum theory could not be regarded as a complete logical system unless it contained within it a prescription in principle for how all of these problems were to be dealt with.</blockquote>
 ==Issues==

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 * Probability: The probability of obtaining a particular eigenvalue is given by the squared modulus of the inner product of the system's state vector with the corresponding eigenvector.
 * State After Measurement: After the measurement, the system is left in the eigenstate corresponding to the measured eigenvalue. This is known as the collapse of the wave-function.
-The understanding of [[Quantum Measurement]] has not changed significantly since David Bohm said this in 1951:<ref>David Bohm, Quantum Theory'' Prentice Hall (1951) ISBN 978-0486659695</ref><blockquote>The quantum theory as developed thus far provides in principle, a way to calculate the probable results of any measurement that one wishes to carry out. To calculate the average value of any observable A, we simply write ''&#256; = &int; &psi;*A&psi; dx,'' where &psi; is the wave function of the system under investigation. If the quantum theory is to be able to provide a complete description of everything that can happen in the world, however, it should also be able to describe the process of observation itself in terms of the wave functions of the observing apparatus and those of the system under observation. Furthermore, in principle, it ought to be able to describe the human investigator as he looks at the observing apparatus and learns what the results of the experiment are, this time in terms of the wave functions of the various atoms that make up the investigator, as well as those of the observing apparatus and the system under observation. In other words, the quantum theory could not be regarded as a complete logical system unless it contained within it a prescription in principle for how all of these problems were to be dealt with.</blockquote>
+The understanding of [[Quantum Measurement]] has not changed significantly since David Bohm said this in 1951:<ref>David Bohm, Quantum Theory'' Prentice Hall (1951) ISBN 978-0486659695</ref><blockquote>The quantum theory as developed thus far provides in principle, a way to calculate the probable results of any measurement that one wishes to carry out. To calculate the average value of any observable A, we simply write ''&#256; = &int; &psi;*A&psi; dx,'' where ''&psi;'' is the wave function of the system under investigation. If the quantum theory is to be able to provide a complete description of everything that can happen in the world, however, it should also be able to describe the process of observation itself in terms of the wave functions of the observing apparatus and those of the system under observation. Furthermore, in principle, it ought to be able to describe the human investigator as he looks at the observing apparatus and learns what the results of the experiment are, this time in terms of the wave functions of the various atoms that make up the investigator, as well as those of the observing apparatus and the system under observation. In other words, the quantum theory could not be regarded as a complete logical system unless it contained within it a prescription in principle for how all of these problems were to be dealt with.</blockquote>
 ==Issues==

@@ Line 6: / Line 6: @@
 * Probability: The probability of obtaining a particular eigenvalue is given by the squared modulus of the inner product of the system's state vector with the corresponding eigenvector.
 * State After Measurement: After the measurement, the system is left in the eigenstate corresponding to the measured eigenvalue. This is known as the collapse of the wave-function.
-The understanding of [[Quantum Measurement]] has not changed significantly since David Bohm said this in 1951:<ref>David Bohm, Quantum Theory'' Prentice Hall (1951) ISBN 978-0486659695</ref><blockquote>The quantum theory as developed thus far provides in principle, a way to calculate the probable results of any measurement that one wishes to carry out. To calculate the average value of any observable A, we simply write &#256; = &int; &psi;*A&psi; dx, where &psi; is the wave function of the system under investigation. If the quantum theory is to be able to provide a complete description of everything that can happen in the world, however, it should also be able to describe the process of observation itself in terms of the wave functions of the observing apparatus and those of the system under observation. Furthermore, in principle, it ought to be able to describe the human investigator as he looks at the observing apparatus and learns what the results of the experiment are, this time in terms of the wave functions of the various atoms that make up the investigator, as well as those of the observing apparatus and the system under observation. In other words, the quantum theory could not be regarded as a complete logical system unless it contained within it a prescription in principle for how all of these problems were to be dealt with.</blockquote>
+The understanding of [[Quantum Measurement]] has not changed significantly since David Bohm said this in 1951:<ref>David Bohm, Quantum Theory'' Prentice Hall (1951) ISBN 978-0486659695</ref><blockquote>The quantum theory as developed thus far provides in principle, a way to calculate the probable results of any measurement that one wishes to carry out. To calculate the average value of any observable A, we simply write ''&#256; = &int; &psi;*A&psi; dx,'' where &psi; is the wave function of the system under investigation. If the quantum theory is to be able to provide a complete description of everything that can happen in the world, however, it should also be able to describe the process of observation itself in terms of the wave functions of the observing apparatus and those of the system under observation. Furthermore, in principle, it ought to be able to describe the human investigator as he looks at the observing apparatus and learns what the results of the experiment are, this time in terms of the wave functions of the various atoms that make up the investigator, as well as those of the observing apparatus and the system under observation. In other words, the quantum theory could not be regarded as a complete logical system unless it contained within it a prescription in principle for how all of these problems were to be dealt with.</blockquote>
 ==Issues==

@@ Line 6: / Line 6: @@
 * Probability: The probability of obtaining a particular eigenvalue is given by the squared modulus of the inner product of the system's state vector with the corresponding eigenvector.
 * State After Measurement: After the measurement, the system is left in the eigenstate corresponding to the measured eigenvalue. This is known as the collapse of the wave-function.
-The understanding of [[Quantum Measurement]] has not changed significantly since David Bohm said this in 1951:<ref>David Bohm, Quantum Theory'' Prentice Hall (1951) ISBN 978-0486659695</ref><blockquote>The quantum theory as developed thus far provides in principle, a way to calculate the probable results of any measurement that one wishes to carry out. To calculate the average value of any observable A, we simply write &#256; = &int; &psi;*A&psi; dx, where &psi is the wave function of the system under investigation. If the quantum theory is to be able to provide a complete description of everything that can happen in the world, however, it should also be able to describe the process of observation itself in terms of the wave functions of the observing apparatus and those of the system under observation. Furthermore, in principle, it ought to be able to describe the human investigator as he looks at the observing apparatus and learns what the results of the experiment are, this time in terms of the wave functions of the various atoms that make up the investigator, as well as those of the observing apparatus and the system under observation. In other words, the quantum theory could not be regarded as a complete logical system unless it contained within it a prescription in principle for how all of these problems were to be dealt with.</blockquote>
+The understanding of [[Quantum Measurement]] has not changed significantly since David Bohm said this in 1951:<ref>David Bohm, Quantum Theory'' Prentice Hall (1951) ISBN 978-0486659695</ref><blockquote>The quantum theory as developed thus far provides in principle, a way to calculate the probable results of any measurement that one wishes to carry out. To calculate the average value of any observable A, we simply write &#256; = &int; &psi;*A&psi; dx, where &psi; is the wave function of the system under investigation. If the quantum theory is to be able to provide a complete description of everything that can happen in the world, however, it should also be able to describe the process of observation itself in terms of the wave functions of the observing apparatus and those of the system under observation. Furthermore, in principle, it ought to be able to describe the human investigator as he looks at the observing apparatus and learns what the results of the experiment are, this time in terms of the wave functions of the various atoms that make up the investigator, as well as those of the observing apparatus and the system under observation. In other words, the quantum theory could not be regarded as a complete logical system unless it contained within it a prescription in principle for how all of these problems were to be dealt with.</blockquote>
 ==Issues==

@@ Line 6: / Line 6: @@
 * Probability: The probability of obtaining a particular eigenvalue is given by the squared modulus of the inner product of the system's state vector with the corresponding eigenvector.
 * State After Measurement: After the measurement, the system is left in the eigenstate corresponding to the measured eigenvalue. This is known as the collapse of the wave-function.
-The understanding of [[Quantum Measurement]] has not changed significantly since David Bohm said this in 1951:<ref>David Bohm, Quantum Theory'' Prentice Hall (1951) ISBN 978-0486659695</ref><blockquote>The quantum theory as developed thus far pro-in principle, a way to calculate the probable results of any measurement that one wishes to carry out. To calculate the average value of any observable A, we simply write &#256; = &int; &psi;*A&psi; dx, where y is the wave function of the system under investigation. If the quantum theory is to be able to provide a complete description of everything that can happen in the world, however, it should also be able to describe the process of observation itself in terms of the wave functions of the observing apparatus and those of the system under observation. Furthermore, in principle, it ought to be able to describe the human investigator as he looks at the observing apparatus and learns what the results of the experiment are, this time in terms of the wave functions of the various atoms that make up the investigator, as well as those of the observing apparatus and the system under observation. In other words, the quantum theory could not be regarded as a complete logical system unless it contained within it a prescription in principle for how all of these problems were to be dealt with.</blockquote>
+The understanding of [[Quantum Measurement]] has not changed significantly since David Bohm said this in 1951:<ref>David Bohm, Quantum Theory'' Prentice Hall (1951) ISBN 978-0486659695</ref><blockquote>The quantum theory as developed thus far provides in principle, a way to calculate the probable results of any measurement that one wishes to carry out. To calculate the average value of any observable A, we simply write &#256; = &int; &psi;*A&psi; dx, where &psi is the wave function of the system under investigation. If the quantum theory is to be able to provide a complete description of everything that can happen in the world, however, it should also be able to describe the process of observation itself in terms of the wave functions of the observing apparatus and those of the system under observation. Furthermore, in principle, it ought to be able to describe the human investigator as he looks at the observing apparatus and learns what the results of the experiment are, this time in terms of the wave functions of the various atoms that make up the investigator, as well as those of the observing apparatus and the system under observation. In other words, the quantum theory could not be regarded as a complete logical system unless it contained within it a prescription in principle for how all of these problems were to be dealt with.</blockquote>
 ==Issues==

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 * Eigenstates and Eigenvalues: When a measurement is performed, the system collapses to one of the eigenstates of the observable, and the measurement result is the corresponding eigenvalue.
 * Probability: The probability of obtaining a particular eigenvalue is given by the squared modulus of the inner product of the system's state vector with the corresponding eigenvector.
-* State After Measurement: After the measurement, the system is left in the eigenstate corresponding to the measured eigenvalue. This is known as the collapse of the wavefunction.
+* State After Measurement: After the measurement, the system is left in the eigenstate corresponding to the measured eigenvalue. This is known as the collapse of the wave-function.
 ==Issues==
 ===First kind of quantum measurement===