Additions:
In a theory of emergent spacetime, Bell’s theorem is not an issue. Spacetime is determined by the configuration of matter. The detail configuration of matter at the level of individual electrons and photons is not known, and cannot be determined. Configuration is non-local, and escapes the constraint of Bell’s theorem. We can only express ""P(AB|a, b, λ)"" when the backward light cone contains both Alice’s and Bob’s measurements. Since their measurements have common cause, and the unknowns are contained in non-local configuration, we cannot factorise probabilities and we do not have to sacrifice either locality or causality as fundamental principles.
Deletions:
In a theory of emergent spacetime, Bell’s theorem is not an issue. Spacetime is determined by the configuration of matter. The detail configuration of matter at the level of individual electrons and photons is not known, and cannot be determined. Configuration is non-local, and escapes the constraint of Bell’s theorem. We can only express ""P(AB|a, b, λ)"" when the backward light cone contains both Alice’s and Bob’s measurements. Since their measurements have common cause, and the unknowns are contained in non-local configuration, we cannot factorise probabilities. We thus do not have to sacrifice either locality or causality as fundamental principles.
Additions:
In a theory of emergent spacetime, Bell’s theorem is not an issue. Spacetime is determined by the configuration of matter. The detail configuration of matter at the level of individual electrons and photons is not known, and cannot be determined. Configuration is non-local, and escapes the constraint of Bell’s theorem. We can only express ""P(AB|a, b, λ)"" when the backward light cone contains both Alice’s and Bob’s measurements. Since their measurements have common cause, and the unknowns are contained in non-local configuration, we cannot factorise probabilities. We thus do not have to sacrifice either locality or causality as fundamental principles.
In spite of this result, no information travels from the results of one measurement to the other. At the time when Bob measures the spin of the second particle, there is no way he can say that his result is affected by Alice’s measurement of the first, because he does not yet know Alice’s result. Alice and Bob’s results must be brought together before a correlation can be found establishing that Bell’s inequality is violated. The question, however, remains. If nothing travels faster than light, how can the correlation come about?
Deletions:
In spite of this result, no information travels from the results of one measurement to the other. At the time when Bob measures the spin of the second particle, there is no way he can say that his result is affected by Alice’s measurement of the first, because he does not yet know Alice’s result. Alice and Bob’s results must be brought together before a correlation can be found establishing that Bell’s ine quality is violated. The question, however, remains. If nothing travels faster than light, how can the correlation come about?
Additions:
>>""“In a theory in which parameters are added to quantum mechanics to determine the results of individual measurements, without changing the statistical predictions, there must be a mechanism whereby the setting of one measuring device can influence the reading of another instrument, however remote. Moreover, the signal involved must propagate instantaneously.” — John Stewart Bell (1964) On the Einstein Podolsky Rosen Paradox."" >> It is often suggested that the implication of Bell’s theorem is that, if quantum mechanics is correct, we must sacrifice at least one of locality, causality, and realism. Since physics makes no sense without realism, it seems we must have a problem with either locality, causality, or both. However, Bell’s inequality does not directly refer to quantum systems, but rather to classical systems in which the unknowns can be described by hidden parameters. Strictly it does not say that quantum mechanics is non-local, but rather that a theory which reproduces the results of quantum mechanics and in which the unknowns can be described by classical local hidden variables would have to allow either instantaneous propagation or retrocausality.
Deletions:
>>""“In a theory in which parameters are added to quantum mechanics to determine the results of individual measurements, without changing the statistical predictions, there must be a mechanism whereby the setting of one measuring device can influence the reading of another instrument, however remote. Moreover, the signal involved must propagate instantaneously.” — John Stewart Bell (1964) On the Einstein Podolsky Rosen Paradox."" >> It is often suggested that the implication of Bell’s theorem is that, if quantum mechanics is correct, we must sacrifice at least one of locality, causality, and realism. Since physics makes no sense without realism, it seems we must have a problem with either locality, causality, or both. However, Bell’s inequality does not directly refer to quantum systems, but rather to classical systems in which the unknowns can be described by hidden parameters. It does not say that quantum mechanics is non-local, but says that a classical theory which reproduced the results of quantum mechanics would have to be non-local.
Additions:
However, if we understand probability theory in a modern Bayesian context, then this expresses a state of knowledge about the results of the two measurements. In fact there can be no //simultaneous// knowledge of two events with spacelike separation, and the factorisation of probabilities is strictly meaningless at the time of the measurements. Later it becomes possible to bring the measurement results together and the factorisation of probabilities is violated according to the laws of quantum mechanics, but since the events have common cause (they are not independent) and since this requires the prior emergence of spacetime from non-local processes it is not necessary to postulate any superluminal effect.
Deletions:
owever, if we understand probability theory in a modern Bayesian context, then this expresses a state of knowledge about the results of the two measurements. In fact there can be no simultaneous knowledge of two events with spacelike separation, and the factorisation of probabilities is strictly meaningless at the time of the measurements. Later it becomes possible to bring the measurement results together and the factorisation of probabilities is violated according to the laws of quantum mechanics, but since the events have common cause (they are not independent) and since this requires the prior emergence of spacetime from non-local processes it is not necessary to postulate any superluminal effect.
Additions:
The central issue in Bell’s theorem lies in the factorisation of independent probabilities in classical probability theory. Specifically, it is assumed that if two variables, ""A(a, λ) = ±1"" and ""B(b, λ) = ±1"" to be measured independently with an assumed spacelike separation, where ""a"" and ""b"" are unit vectors in directions chosen by Alice and Bob, and ""λ"" is a hidden variable (or any number of hidden variables), then the joint probability can be factorised:
owever, if we understand probability theory in a modern Bayesian context, then this expresses a state of knowledge about the results of the two measurements. In fact there can be no simultaneous knowledge of two events with spacelike separation, and the factorisation of probabilities is strictly meaningless at the time of the measurements. Later it becomes possible to bring the measurement results together and the factorisation of probabilities is violated according to the laws of quantum mechanics, but since the events have common cause (they are not independent) and since this requires the prior emergence of spacetime from non-local processes it is not necessary to postulate any superluminal effect.
Deletions:
The central issue in Bell’s theorem lies in the factorisation of independent probabilities in classical probability theory. Specifically, it is assumed that if two variables, ""A(a, λ) = ±1"" and ""B(b, λ) = ±1"" to be measured independently with an assumed spacelike separation, where ""a"" and ""b"" are unit vectors in directions chosen by Alice and Bob, and ""&lamda;"" is a hidden variable, then the joint probability can be factorised:
However, if we understand probability theory in a modern Bayesian context, then this expresses a state of knowledge about the results of the two measurements. In fact there can be no simultaneous knowledge of two events with spacelike separation, and the factorisation of probabilities is strictly meaningless at the time of the measurements. Later it becomes possible to bring the measurement results together and the factorisation of probabilities is violated according to the laws of quantum mechanics, but since the events have common cause (they are not independent) and since this requires the prior emergence of spacetime from non-local processes it is not necessary to postulate any superluminal effect.
Additions:
""P(AB|a, b, λ) = P(A|a, λ)P(B|b, λ)"".
Deletions:
""P(AB|a, b, λ) = P(A|a, λ)P(B|b, λ)""
.
Additions:
The central issue in Bell’s theorem lies in the factorisation of independent probabilities in classical probability theory. Specifically, it is assumed that if two variables, ""A(a, λ) = ±1"" and ""B(b, λ) = ±1"" to be measured independently with an assumed spacelike separation, where ""a"" and ""b"" are unit vectors in directions chosen by Alice and Bob, and ""&lamda;"" is a hidden variable, then the joint probability can be factorised:
Deletions:
The central issue in Bell’s theorem lies in the factorisation of independent probabilities in classical probability theory. Specifically, it is assumed that if two variables, ""A(a, λ = ±1"" and "B(b, λ = ±1"" to be measured independently with an assumed spacelike separation, where ""a"" and ""b"" are unit vectors in directions chosen by Alice and Bob, and ""&lamda;"" is a hidden variable, then the joint probability can be factorised:
Additions:
The central issue in Bell’s theorem lies in the factorisation of independent probabilities in classical probability theory. Specifically, it is assumed that if two variables, ""A(a, λ = ±1"" and "B(b, λ = ±1"" to be measured independently with an assumed spacelike separation, where ""a"" and ""b"" are unit vectors in directions chosen by Alice and Bob, and ""&lamda;"" is a hidden variable, then the joint probability can be factorised:
""P(AB|a, b, λ) = P(A|a, λ)P(B|b, λ)""
.
However, if we understand probability theory in a modern Bayesian context, then this expresses a state of knowledge about the results of the two measurements. In fact there can be no simultaneous knowledge of two events with spacelike separation, and the factorisation of probabilities is strictly meaningless at the time of the measurements. Later it becomes possible to bring the measurement results together and the factorisation of probabilities is violated according to the laws of quantum mechanics, but since the events have common cause (they are not independent) and since this requires the prior emergence of spacetime from non-local processes it is not necessary to postulate any superluminal effect.
Additions:
>>""“In a theory in which parameters are added to quantum mechanics to determine the results of individual measurements, without changing the statistical predictions, there must be a mechanism whereby the setting of one measuring device can influence the reading of another instrument, however remote. Moreover, the signal involved must propagate instantaneously.” — John Stewart Bell (1964) On the Einstein Podolsky Rosen Paradox."" >> It is often suggested that the implication of Bell’s theorem is that, if quantum mechanics is correct, we must sacrifice at least one of locality, causality, and realism. Since physics makes no sense without realism, it seems we must have a problem with either locality, causality, or both. However, Bell’s inequality does not directly refer to quantum systems, but rather to classical systems in which the unknowns can be described by hidden parameters. It does not say that quantum mechanics is non-local, but says that a classical theory which reproduced the results of quantum mechanics would have to be non-local.
Deletions:
>>""“In a theory in which parameters are added to quantum mechanics to determine the results of individual measurements, without changing the statistical predictions, there must be a mechanism whereby the setting of one measuring device can influence the reading of another instrument, however remote. Moreover, the signal involved must propagate instantaneously” — John Stewart Bell (1964) On the Einstein Podolsky Rosen Paradox"" >> It is often suggested that the implication of Bell’s theorem is that, if quantum mechanics is correct, we must sacrifice at least one of locality, causality, and realism. Since physics makes no sense without realism, it seems we must have a problem with either locality, causality, or both. However, Bell’s inequality does not directly refer to quantum systems, but rather to classical systems in which the unknowns can be described by hidden parameters. It does not say that quantum mechanics is non-local, but says that a classical theory which reproduced the results of qm would have to be non-local.
Additions:
>>""“In a theory in which parameters are added to quantum mechanics to determine the results of individual measurements, without changing the statistical predictions, there must be a mechanism whereby the setting of one measuring device can influence the reading of another instrument, however remote. Moreover, the signal involved must propagate instantaneously” — John Stewart Bell (1964) On the Einstein Podolsky Rosen Paradox"" >> It is often suggested that the implication of Bell’s theorem is that, if quantum mechanics is correct, we must sacrifice at least one of locality, causality, and realism. Since physics makes no sense without realism, it seems we must have a problem with either locality, causality, or both. However, Bell’s inequality does not directly refer to quantum systems, but rather to classical systems in which the unknowns can be described by hidden parameters. It does not say that quantum mechanics is non-local, but says that a classical theory which reproduced the results of qm would have to be non-local.
Deletions:
>>""“In a theory in which parameters are added to quantum mechanics to determine the results of individual measurements, without changing the statistical predictions, there must be a mechanism whereby the setting of one measuring device can influence the reading of another instrument, however remote. Moreover, the signal involved must propagate instantaneously” — John Stewart Bell (1964) On the Einstein Podolsky Rosen Paradox >> It is often suggested that the implication of Bell’s theorem is that, if quantum mechanics is correct, we must sacrifice at least one of locality, causality, and realism. Since physics makes no sense without realism, it seems we must have a problem with either locality, causality, or both. However, Bell’s inequality does not directly refer to quantum systems, but rather to classical systems in which the unknowns can be described by hidden parameters. It does not say that quantum mechanics is non-local, but says that a classical theory which reproduced the results of qm would have to be non-local.
Additions:
>>""“In a theory in which parameters are added to quantum mechanics to determine the results of individual measurements, without changing the statistical predictions, there must be a mechanism whereby the setting of one measuring device can influence the reading of another instrument, however remote. Moreover, the signal involved must propagate instantaneously” — John Stewart Bell (1964) On the Einstein Podolsky Rosen Paradox >> It is often suggested that the implication of Bell’s theorem is that, if quantum mechanics is correct, we must sacrifice at least one of locality, causality, and realism. Since physics makes no sense without realism, it seems we must have a problem with either locality, causality, or both. However, Bell’s inequality does not directly refer to quantum systems, but rather to classical systems in which the unknowns can be described by hidden parameters. It does not say that quantum mechanics is non-local, but says that a classical theory which reproduced the results of qm would have to be non-local.
Deletions:
>>""“In a theory in which parameters are added to quantum mechanics to determine the results of individual measurements, without changing the statistical predictions, there must be a mechanism whereby the setting of one measuring device can influence the reading of another instrument, however remote. Moreover, the signal involved must propagate instantaneously” — John Stewart Bell (1964) On the Einstein Podolsky Rosen Paradox>> It is often suggested that the implication of Bell’s theorem is that, if quantum mechanics is correct, we must sacrifice at least one of locality, causality, and realism. Since physics makes no sense without realism, it seems we must have a problem with either locality, causality, or both. However, Bell’s inequality does not directly refer to quantum systems, but rather to classical systems in which the unknowns can be described by hidden parameters. It does not say that quantum mechanics is non-local, but says that a classical theory which reproduced the results of qm would have to be non-local.
Additions:
""
""[[http://en.wikipedia.org/wiki/John_Stewart_Bell John Bell]] adapted the EPR experiment to a form which is easier to test experimentally and demonstrated [[http://en.wikipedia.org/wiki/Bell%27s_Theorem Bell’s inequality]], by which the experimental predictions of quantum theory can be tested against theories of local hidden variables. He proposed using a process which emits two particles with equal and opposite [[http://en.wikipedia.org/wiki/Spin_(physics) spin]]. Initially spin is not aligned, but it can be measured in any axis. When spin is measured, it aligns with the axis chosen for the measurement. This implies that the other particle must be aligned on the same axis, with opposite spin. It appears that the fact of a spin measurement on one particle not only affects the result of measurement spin of the other, but actually determines the axis on which the spin of the second particle is aligned. Bell’s inequality shows that quantum theory and local hidden variables theories predict different correlations between the results of measurements on different axes, and enables us to experimentally determine which is correct.
>>""“In a theory in which parameters are added to quantum mechanics to determine the results of individual measurements, without changing the statistical predictions, there must be a mechanism whereby the setting of one measuring device can influence the reading of another instrument, however remote. Moreover, the signal involved must propagate instantaneously” — John Stewart Bell (1964) On the Einstein Podolsky Rosen Paradox>> It is often suggested that the implication of Bell’s theorem is that, if quantum mechanics is correct, we must sacrifice at least one of locality, causality, and realism. Since physics makes no sense without realism, it seems we must have a problem with either locality, causality, or both. However, Bell’s inequality does not directly refer to quantum systems, but rather to classical systems in which the unknowns can be described by hidden parameters. It does not say that quantum mechanics is non-local, but says that a classical theory which reproduced the results of qm would have to be non-local.
In practice, quantum mechanics is overwhelming supported by experiment. However, we do not have to sacrifice either locality or causality, but we do have to be careful about how we state them. We have to dismiss naive statements based on an assumption of background spacetime.
Deletions:
""""[[http://en.wikipedia.org/wiki/John_Stewart_Bell John Bell]] adapted the EPR experiment to a form which is easier to test experimentally and demonstrated [[http://en.wikipedia.org/wiki/Bell%27s_Theorem Bell’s inequality]], by which the experimental predictions of quantum theory can be tested against theories of local hidden variables. He proposed using a process which emits two particles with equal and opposite [[http://en.wikipedia.org/wiki/Spin_(physics) spin]]. Initially spin is not aligned, but it can be measured in any axis. When spin is measured, it aligns with the axis chosen for the measurement. This implies that the other particle must be aligned on the same axis, with opposite spin. It appears that the fact of a spin measurement on one particle not only affects the result of measurement spin of the other, but actually determines the axis on which the spin of the second particle is aligned. Bell’s inequality shows that quantum theory and local hidden variables theories predict different correlations between the results of measurements on different axes, and enables us to experimentally determine which is correct. As stated by Bell, the implication is that, if quantum mechanics is correct, we must sacrifice at least one locality, causality, and realism.
In practice, quantum mechanics is overwhelming supported by experiment. Physics makes no sense if we sacrifice realism. It seems we must have a problem with either locality, causality, or both. In relational quantum gravity we do not have to sacrifice either locality or causality, but we do have to be careful about how we state them. We have to dismiss naive statements based on an assumption of background spacetime. Bell's theorem does not lead us to reject locality or causality, but rather to reject the notion of a fundamental spacetime.
Additions:
Deletions:
Additions:
Deletions:
>>""“No reasonable defnition of reality could be expected to permit this” — Einstein, Podolsky & Rosen.""----
Additions:
>>""“No reasonable defnition of reality could be expected to permit this” — Einstein, Podolsky & Rosen.""----
Deletions:
>>""“No reasonable defnition of reality could be expected to permit this” — Albert Einstein, Podolsky & Rosen.""----
Additions:
>>""“No reasonable defnition of reality could be expected to permit this” — Albert Einstein, Podolsky & Rosen.""----
Deletions:
>>""“No reasonable defnition of reality could be expected to permit this” — Albert Einstein, Podolsky Rosen.""----
Additions:
""| Schrödinger put a cat in a box with a capsule of cyanide, triggered to break with a 50% chance by a quantum mechanical process killing the cat (oh, he didn’t actually do it, but he thought about it). A physicist looking at the box does not know whether the quantum process has broken the capsule or not, so he describes it with a quantum state, that is to say a wave function in which the process has part broken the cyanide capsule, and part not. If the wave function collapses when the observation takes place, then, prior to openning the box, he should describe the cat with a quantum state as well, in which the cat is part alive and desperately trying to get out of the box before the cyanide gets him, and part dead and lying in a heap on the floor. Mouse-over the image to open the box and observe the cat. |
""
Deletions:
""| Schrödinger put a cat in a box with a capsule of cyanide, triggered to break with a 50% chance by a quantum mechanical process killing the cat (oh, he didn’t actually do it, but he thought about it). A physicist looking at the box does not know whether the quantum process has broken the capsule or not, so he describes it with a quantum state, that is to say a wave function in which the process has part broken the cyanide capsule, and part not. If the wave function collapses when the observation takes place, then, prior to openning the box, he should describe the cat with a quantum state as well, in which the cat is part alive and desperately trying to get out of the box before the cyanide gets him, and part dead and lying in a heap on the floor. Mouse-over the image to open the box and observe the cat. |
""
Additions:
""| Schrödinger put a cat in a box with a capsule of cyanide, triggered to break with a 50% chance by a quantum mechanical process killing the cat (oh, he didn’t actually do it, but he thought about it). A physicist looking at the box does not know whether the quantum process has broken the capsule or not, so he describes it with a quantum state, that is to say a wave function in which the process has part broken the cyanide capsule, and part not. If the wave function collapses when the observation takes place, then, prior to openning the box, he should describe the cat with a quantum state as well, in which the cat is part alive and desperately trying to get out of the box before the cyanide gets him, and part dead and lying in a heap on the floor. Mouse-over the image to open the box and observe the cat. |
""
>>""“No reasonable defnition of reality could be expected to permit this” — Albert Einstein, Podolsky Rosen.""----
""“That one body may act upon another at a distance through a vacuum without the mediation of anything else, by and through which their action and force may be conveyed from one to the other, is to me so great an absurdity, that I believe no man, who has in philosophical matters a competent faculty of thinking, can ever fall into it” — Isaac Newton."">>We observe interference fringes which can be calculated from waves, but there is no direct observation of the wave function or of the infinite speed implicit in collapse. In order to highlight the very deep conflict between relativity and quantum mechanics, Einstein, Rosen and Podolsky imagined that a quantum mechanical process generates two particles flying in opposite directions with equal momenta. The momenta of the particles is not known, so the rules of quantum mechanics dictate that it is governed by a wave function. The two particles become separated. Alice measures the momentum of one particle, and Bob will measure the momentum of the second particle, at a distance remote from Alice. According to conservation of momentum, at the precise time at which Alice does her measurement, the outcome of Bob’s measurement is determined. So, the quantum state of a particle can be instantaneously changed by the remote action of an observer, in apparent conflict with relativity which prevents the instantanteous transmission of an effect.
Deletions:
""| Schrödinger put a cat in a box with a capsule of cyanide, triggered to break with a 50% chance by a quantum mechanical process killing the cat (oh, he didn’t actually do it, but he thought about it). A physicist looking at the box does not know whether the quantum process has broken the capsule or not, so he describes it with a quantum state, that is to say a wave function in which the process has part broken the cyanide capsule, and part not. If the wave function collapses when the observation takes place, then, prior to openning the box, he should describe the cat with a quantum state as well, in which the cat is part alive and desperately trying to get out of the box before the cyanide gets him, and part dead and lying in a heap on the floor. Mouse-over the image to open the box and observe the cat. |
""
>>""“No reasonable defnition of reality could be expected to permit this” — Albert Einstein», Podolsky Rosen.""----
""“That one body may act upon another at a distance through a vacuum without the mediation of anything else, by and through which their action and force may be conveyed from one to the other, is to me so great an absurdity, that I believe no man, who has in philosophical matters a competent faculty of thinking, can ever fall into it” — Isaac Newton»."">>We observe interference fringes which can be calculated from waves, but there is no direct observation of the wave function or of the infinite speed implicit in collapse. In order to highlight the very deep conflict between relativity and quantum mechanics, Einstein, Rosen and Podolsky imagined that a quantum mechanical process generates two particles flying in opposite directions with equal momenta. The momenta of the particles is not known, so the rules of quantum mechanics dictate that it is governed by a wave function. The two particles become separated. Alice measures the momentum of one particle, and Bob will measure the momentum of the second particle, at a distance remote from Alice. According to conservation of momentum, at the precise time at which Alice does her measurement, the outcome of Bob’s measurement is determined. So, the quantum state of a particle can be instantaneously changed by the remote action of an observer, in apparent conflict with relativity which prevents the instantanteous transmission of an effect.
Additions:
""| Schrödinger put a cat in a box with a capsule of cyanide, triggered to break with a 50% chance by a quantum mechanical process killing the cat (oh, he didn’t actually do it, but he thought about it). A physicist looking at the box does not know whether the quantum process has broken the capsule or not, so he describes it with a quantum state, that is to say a wave function in which the process has part broken the cyanide capsule, and part not. If the wave function collapses when the observation takes place, then, prior to openning the box, he should describe the cat with a quantum state as well, in which the cat is part alive and desperately trying to get out of the box before the cyanide gets him, and part dead and lying in a heap on the floor. Mouse-over the image to open the box and observe the cat. |
""
Deletions:
""| Schrödinger put a cat in a box with a capsule of cyanide, triggered to break with a 50% chance by a quantum mechanical process killing the cat (oh, he didn’t actually do it, but he thought about it). A physicist looking at the box does not know whether the quantum process has broken the capsule or not, so he describes it with a quantum state, that is to say a wave function in which the process has part broken the cyanide capsule, and part not. If the wave function collapses when the observation takes place, then, prior to openning the box, he should describe the cat with a quantum state as well, in which the cat is part alive and desperately trying to get out of the box before the cyanide gets him, and part dead and lying in a heap on the floor. Mouse-over the image to open the box and observe the cat. |
""
