User:TheLastWordSword/Interpretations of quantum mechanics#Tabular comparison

Tabular comparison

The most common interpretations are summarized in the table below. The values shown in the cells of the table are not without controversy, for the precise meanings of some of the concepts involved are unclear and, in fact, are themselves at the center of the controversy surrounding the given interpretation.

No experimental evidence exists that distinguishes among these interpretations. To that extent, the physical theory stands, and is consistent with itself and with reality; difficulties arise only when one attempts to "interpret" the theory. Nevertheless, designing experiments which would test the various interpretations is the subject of active research.

Most of these interpretations have variants. For example, it is difficult to get a precise definition of the Copenhagen interpretation as it was developed and argued about by many people.

class=wikitable

style="text-align:center; background:lightgrey;"

!Interpretation

!Author(s)

!Deterministic?

!Wavefunction
real?

!Unique
history?

!Hidden
variables?

!Collapsing
wavefunctions?

!Observer
role?

!Local?

!Counterfactual
definiteness?

!Universal
wavefunction
exists?

align=center

| style="background:lightgrey;"|Ensemble interpretation

| style="background:lightgrey;"|Max Born, 1926

| style="background:lightyellow;"|Agnostic

|bgcolor=pink|No

| style="background:lightgreen;"|Yes

| style="background:lightyellow;"|Agnostic

|bgcolor=pink|No

|bgcolor=lightyellow|Agnostic

|bgcolor=pink|No

align=center

| style="background:lightgrey;"| Hydrodynamic Interpretation

| style="background:lightgrey;"|Erwin Madelung, 1926

| style="background:lightgreen;"|Yes

|bgcolor=lightgreen|Yes

| style="background:lightgreen;"|Yes

|bgcolor=lightgreen|Yes

| style="background:pink;"|No

| style="background:lightgreen;"|Yes

|bgcolor=lightgreen|Yes

align=center

| style="background:lightgrey;"|Copenhagen interpretation

| style="background:lightgrey;"|Niels Bohr, Werner Heisenberg, 1927

|bgcolor=pink|No

|bgcolor=pink|No{{ref|note1|1}}

| style="background:lightgreen;"|Yes

|bgcolor=pink|No

| style="background:lightgreen;"|Yes{{ref|note1|2}}

| style="background:lightgreen;"|Causal

|bgcolor=lightyellow|Agnostic

|bgcolor=pink|No

align=center

| style="background:lightgrey;"|de Broglie–Bohm theory

| style="background:lightgrey;"|Louis de Broglie, 1927, David Bohm, 1952

| style="background:lightgreen;"|Yes

| style="background:lightgreen;"|Yes{{ref|note3|3}}

| style="background:lightgreen;"|Yes{{ref|note4|4}}

| style="background:lightgreen;"|Yes

|bgcolor=pink|No

|bgcolor=pink|No{{ref|note17|17}}

| style="background:lightgreen;"|Yes

align=center

| style="background:lightgrey;"|von Neumann interpretation

| style="background:lightgrey;"|John von Neumann, 1932, John Archibald Wheeler, Eugene Wigner

|bgcolor=pink|No

| style="background:lightgreen;"|Yes

|bgcolor=pink|No

| style="background:lightgreen;"|Yes

| style="background:lightgreen;"|Causal

|bgcolor=pink|No

| style="background:lightgreen;"|Yes

align=center

| style="background:lightgrey;"|Quantum logic

| style="background:lightgrey;"|Garrett Birkhoff, 1936

| style="background:lightyellow;"|Agnostic

| style="background:lightgreen;"|Yes{{ref|note5|5}}

|bgcolor=pink|No

| style="background:lightyellow;"|Interpretational{{ref|note6|6}}

| style="background:lightyellow;"|Agnostic

|bgcolor=pink|No

align=center

| style="background:lightgrey;"|Time-symmetric theories

| style="background:lightgrey;"|Olivier Costa de Beauregard, 1947, Satosi Watanabe, 1955

| style="background:lightgreen;"|Yes

|bgcolor=pink|No

| style="background:lightgreen;"|Yes

|bgcolor=pink|No

| style="background:lightgreen;"|Yes

align=center

| style="background:lightgrey;"|Many-worlds interpretation

| style="background:lightgrey;"|Hugh Everett, 1957

| style="background:lightgreen;"|Yes

|bgcolor=pink|No

| style="background:lightgreen;"|Yes

|bgcolor=pink|No

| style="background:lightgreen;"|Yes

align=center

| style="background:lightgrey;"|Popper's interpretationMarie-Christine Combourieu: Karl R. Popper, 1992: About the EPR controversy. Foundations of Physics 22:10, 1303-1323

| style="background:lightgrey;"|Karl Popper, 1957Karl Popper: The Propensity Interpretation of the Calculus of Probability and of the Quantum Theory. Observation and Interpretation. Buttersworth Scientific Publications, Korner & Price (eds.) 1957. pp 65–70.

| style="background:pink;"|No

| style="background:lightgreen;"|Yes

|bgcolor=lightgreen|Yes

|bgcolor=pink|No

| style="background:lightgreen;"|(Yes){{ref|note13|13}}

| style="background:lightgreen;"|Yes

|bgcolor=pink|No

align=center

| style="background:lightgrey;"|Stochastic mechanics

| style="background:lightgrey;"|Edward Nelson, 1966

|bgcolor=pink|No

| style="background:lightgreen;"|Yes

|bgcolor=lightgreen|Yes{{ref|note16|16}}

|bgcolor=pink|No

|bgcolor=lightgreen|Only for position {{ref|note16|16}}

|bgcolor=pink|No

align=center

| style="background:lightgrey;"|Many-minds interpretation

| style="background:lightgrey;"|H. Dieter Zeh, 1970

| style="background:lightgreen;"|Yes

|bgcolor=pink|No

| style="background:lightyellow;"|Interpretational{{ref|note7|7}}

| style="background:lightgreen;"|Yes

|bgcolor=pink|No

| style="background:lightgreen;"|Yes

align=center

| style="background:lightgrey;"|Consistent histories

| style="background:lightgrey;"|Robert B. Griffiths, 1984

| style="background:lightyellow;"|Agnostic{{ref|note8|8}}

|bgcolor=pink|No

| style="background:lightyellow;"|Interpretational{{ref|note6|6}}

| style="background:lightgreen;"|Yes

|bgcolor=pink|No

align=center

| style="background:lightgrey;"|Objective collapse theories

| style="background:lightgrey;"|Ghirardi–Rimini–Weber, 1986,
Penrose interpretation, 1989

|bgcolor=pink|No

| style="background:lightgreen;"|Yes

|bgcolor=pink|No

| style="background:lightgreen;"|Yes

|bgcolor=pink|No

align=center

| style="background:lightgrey;"|Transactional interpretation

| style="background:lightgrey;"|John G. Cramer, 1986

|bgcolor=pink|No

| style="background:lightgreen;"|Yes

|bgcolor=pink|No

| style="background:lightgreen;"|Yes{{ref|note9|9}}

|bgcolor=pink|No

|bgcolor=pink|No{{ref|note14|14}}

|bgcolor=lightgreen|Yes

|bgcolor=pink|No

align=center

| style="background:lightgrey;"|Relational interpretation

| style="background:lightgrey;"|Carlo Rovelli, 1994

| style="background:lightyellow;"|Agnostic

|bgcolor=pink|No

| style="background:lightyellow;"|Agnostic{{ref|note10|10}}

|bgcolor=pink|No

| style="background:lightgreen;"|Yes{{ref|note11|11}}

| style="background:lightgreen;"|Intrinsic{{ref|note12|12}}

| style="background:lightgreen;"|Yes

| style="background:pink;"|No

|bgcolor=pink|No

{{note label|note1|1}} According to Bohr, the concept of a physical state independent of the conditions of its experimental observation does not have a well-defined meaning. According to Heisenberg the wavefunction represents a probability, but not an objective reality itself in space and time.
{{note label|note2|2}} According to the Copenhagen interpretation, the wavefunction collapses when a measurement is performed.
{{note label|note3|3}} Both particle AND guiding wavefunction are real.
{{note label|note4|4}} Unique particle history, but multiple wave histories.
{{note label|note5|5}} But quantum logic is more limited in applicability than Coherent Histories.
{{note label|note6|6}} Quantum mechanics is regarded as a way of predicting observations, or a theory of measurement.
{{note label|note7|7}} Observers separate the universal wavefunction into orthogonal sets of experiences.
{{note label|note8|8}} If wavefunction is real then this becomes the many-worlds interpretation. If wavefunction is less than real, but more than just information, then Zurek calls this the "existential interpretation".
{{note label|note9|9}} In the TI the collapse of the state vector is interpreted as the completion of the transaction between emitter and absorber.
{{note label|note10|10}} Comparing histories between systems in this interpretation has no well-defined meaning.
{{note label|note11|11}} Any physical interaction is treated as a collapse event relative to the systems involved, not just macroscopic or conscious observers.
{{note label|note12|12}} The state of the system is observer-dependent, i.e., the state is specific to the reference frame of the observer.
{{note label|note13|13}} Since Popper holds both CFD and locality to be true, it is under dispute whether his view is an interpretation (which is what he claimed) or a modification of Quantum Mechanics (which is what many Physicists claim), and, in case of the latter, if it has been empirically refuted or not by Bell test experiments.
{{note label|note14|14}} The transactional interpretation is explicitly non-local.
{{note label|note15|15}} The assumption of intrinsic periodicity is an element of non-locality consistent with relativity as the periodicity varies in a causal way.
{{note label|note16|16}} In the stochastic interpretation is not possible to define velocities for particles, i.e. the paths are not smooth. Moreover, to know the motion of the particles at any moment, you have to know what the Markov process is. However, once we know the exactly initial conditions and the Markov process, the theory is in fact a realistic interpretation of quantum mechanics; trajectories are continuous.
{{note label|note17|17}} The kind of locality violated by the theory is weaker than that assumed in deriving Bell inequalities. In particular, this kind non-locality is compatible with no signaling theorem and so with relativity.
{{note label|note18|18}} The interpretation is compatible with the view of a deterministic world as a whole, but does not exclude indeterminism.
{{note label|note19|19}} There are no hidden variables associated with the state of the quantum entity, but there are hidden variables associated with the measurement-interactions.

My own interpretive approach holds that each particle can be said to contain a string of information, and that this string of information is isomorphic to the particle's normalized relationship to all other particles with which it is interacting, and that these interactions occur in discrete rather than continuous intervals of time. Thus, block-style error correction codes reflect the robustness and endurance of particles in energetic relationships which do not exceed a critical threshold. (Robust baryonic particles such as protons react to powerful forces with energetic responses, rather than being torn asunder. The energy of particle colliders must exceed this threshold value to perform their functions.) The total information of a Feynman diagram is proportional to the total information of the particle, and "local" relationships would tend to predominate in both number of interactions and representation in the information.

First, current theory holds that the wave-function is not real, but reflects a Bayesian uncertainty as to the position of the particle. This Bayesian uncertainty would increase in "free" particles, and decrease in larger particles, or particles locally bound in a larger framework (say, an atom or molecule). Thus, it is easier to be certain as to the location of a molecule as compared to a single atom, and similarly with a comparison of an atom to a subatomic particle, in agreement with experimental evidence. P;D

So let's make that the first item.

Second, real physical phenomena can range from (local and seemingly deterministic) to (non-local and seemingly non-deterministic)

Tabular comparison

Most of these interpretations have variants. For example, it is difficult to get a precise definition of the Copenhagen interpretation as it was developed and argued about by many people.

class= "wikitable sortable"

style="text-align:center; background:lightgrey;"

!Interpretation

!Author(s)

!Deterministic?

!Wavefunction
real?

!Unique
history?

!Hidden
variables?

!Collapsing
wavefunctions?

!Observer
role?

!Local?

!Counterfactual
definiteness?

!Universal
wavefunction
exists?

align=center

| style="background:lightgrey;"|Ensemble interpretation

| style="background:lightgrey;"|Max Born, 1926

| style="background:lightyellow;"|Agnostic

|bgcolor=pink|No

| style="background:lightgreen;"|Yes

| style="background:lightyellow;"|Agnostic

|bgcolor=pink|No

|bgcolor=lightyellow|Agnostic

|bgcolor=pink|No

align=center

| style="background:lightgrey;"| Hydrodynamic Interpretation

| style="background:lightgrey;"|Erwin Madelung, 1926

| style="background:lightgreen;"|Yes

|bgcolor=lightgreen|Yes

| style="background:lightgreen;"|Yes

|bgcolor=lightgreen|Yes

| style="background:pink;"|No

| style="background:lightgreen;"|Yes

|bgcolor=lightgreen|Yes

align=center

| style="background:lightgrey;"|Copenhagen interpretation

| style="background:lightgrey;"|Niels Bohr, Werner Heisenberg, 1927

|bgcolor=pink|No

|bgcolor=pink|No{{ref|note1|1}}

| style="background:lightgreen;"|Yes

|bgcolor=pink|No

| style="background:lightgreen;"|Yes{{ref|note1|2}}

| style="background:lightgreen;"|Causal

|bgcolor=lightyellow|Agnostic

|bgcolor=pink|No

align=center

| style="background:lightgrey;"|de Broglie–Bohm theory

| style="background:lightgrey;"|Louis de Broglie, 1927, David Bohm, 1952

| style="background:lightgreen;"|Yes

| style="background:lightgreen;"|Yes{{ref|note3|3}}

| style="background:lightgreen;"|Yes{{ref|note4|4}}

| style="background:lightgreen;"|Yes

|bgcolor=pink|No

|bgcolor=pink|No{{ref|note17|17}}

| style="background:lightgreen;"|Yes

align=center

| style="background:lightgrey;"|von Neumann interpretation

| style="background:lightgrey;"|John von Neumann, 1932, John Archibald Wheeler, Eugene Wigner

|bgcolor=pink|No

| style="background:lightgreen;"|Yes

|bgcolor=pink|No

| style="background:lightgreen;"|Yes

| style="background:lightgreen;"|Causal

|bgcolor=pink|No

| style="background:lightgreen;"|Yes

align=center

| style="background:lightgrey;"|Quantum logic

| style="background:lightgrey;"|Garrett Birkhoff, 1936

| style="background:lightyellow;"|Agnostic

| style="background:lightgreen;"|Yes{{ref|note5|5}}

|bgcolor=pink|No

| style="background:lightyellow;"|Interpretational{{ref|note6|6}}

| style="background:lightyellow;"|Agnostic

|bgcolor=pink|No

align=center

| style="background:lightgrey;"|Time-symmetric theories

| style="background:lightgrey;"|Olivier Costa de Beauregard, 1947, Satosi Watanabe, 1955

| style="background:lightgreen;"|Yes

|bgcolor=pink|No

| style="background:lightgreen;"|Yes

|bgcolor=pink|No

| style="background:lightgreen;"|Yes

align=center

| style="background:lightgrey;"|Many-worlds interpretation

| style="background:lightgrey;"|Hugh Everett, 1957

| style="background:lightgreen;"|Yes

|bgcolor=pink|No

| style="background:lightgreen;"|Yes

|bgcolor=pink|No

| style="background:lightgreen;"|Yes

align=center

| style="background:lightgrey;"|Popper's interpretationMarie-Christine Combourieu: Karl R. Popper, 1992: About the EPR controversy. Foundations of Physics 22:10, 1303-1323

| style="background:pink;"|No

| style="background:lightgreen;"|Yes

|bgcolor=lightgreen|Yes

|bgcolor=pink|No

| style="background:lightgreen;"|(Yes){{ref|note13|13}}

| style="background:lightgreen;"|Yes

|bgcolor=pink|No

align=center

| style="background:lightgrey;"|Stochastic mechanics

| style="background:lightgrey;"|Edward Nelson, 1966

|bgcolor=pink|No

| style="background:lightgreen;"|Yes

|bgcolor=lightgreen|Yes{{ref|note16|16}}

|bgcolor=pink|No

|bgcolor=lightgreen|Only for position {{ref|note16|16}}

|bgcolor=pink|No

align=center

| style="background:lightgrey;"|Many-minds interpretation

| style="background:lightgrey;"|H. Dieter Zeh, 1970

| style="background:lightgreen;"|Yes

|bgcolor=pink|No

| style="background:lightyellow;"|Interpretational{{ref|note7|7}}

| style="background:lightgreen;"|Yes

|bgcolor=pink|No

| style="background:lightgreen;"|Yes

align=center

| style="background:lightgrey;"|Consistent histories

| style="background:lightgrey;"|Robert B. Griffiths, 1984

| style="background:lightyellow;"|Agnostic{{ref|note8|8}}

|bgcolor=pink|No

| style="background:lightyellow;"|Interpretational{{ref|note6|6}}

| style="background:lightgreen;"|Yes

|bgcolor=pink|No

align=center

| style="background:lightgrey;"|Objective collapse theories

| style="background:lightgrey;"|Ghirardi–Rimini–Weber, 1986,
Penrose interpretation, 1989

|bgcolor=pink|No

| style="background:lightgreen;"|Yes

|bgcolor=pink|No

| style="background:lightgreen;"|Yes

|bgcolor=pink|No

align=center

| style="background:lightgrey;"|Transactional interpretation

| style="background:lightgrey;"|John G. Cramer, 1986

|bgcolor=pink|No

| style="background:lightgreen;"|Yes

|bgcolor=pink|No

| style="background:lightgreen;"|Yes{{ref|note9|9}}

|bgcolor=pink|No

|bgcolor=pink|No{{ref|note14|14}}

|bgcolor=lightgreen|Yes

|bgcolor=pink|No

align=center

| style="background:lightgrey;"|Relational interpretation

| style="background:lightgrey;"|Carlo Rovelli, 1994

| style="background:lightyellow;"|Agnostic

|bgcolor=pink|No

| style="background:lightyellow;"|Agnostic{{ref|note10|10}}

|bgcolor=pink|No

| style="background:lightgreen;"|Yes{{ref|note11|11}}

| style="background:lightgreen;"|Intrinsic{{ref|note12|12}}

| style="background:lightgreen;"|Yes

| style="background:pink;"|No

|bgcolor=pink|No

{{note label|note1|1}} According to Bohr, the concept of a physical state independent of the conditions of its experimental observation does not have a well-defined meaning. According to Heisenberg the wavefunction represents a probability, but not an objective reality itself in space and time.
{{note label|note2|2}} According to the Copenhagen interpretation, the wavefunction collapses when a measurement is performed.
{{note label|note3|3}} Both particle AND guiding wavefunction are real.
{{note label|note4|4}} Unique particle history, but multiple wave histories.
{{note label|note5|5}} But quantum logic is more limited in applicability than Coherent Histories.
{{note label|note6|6}} Quantum mechanics is regarded as a way of predicting observations, or a theory of measurement.
{{note label|note7|7}} Observers separate the universal wavefunction into orthogonal sets of experiences.
{{note label|note8|8}} If wavefunction is real then this becomes the many-worlds interpretation. If wavefunction is less than real, but more than just information, then Zurek calls this the "existential interpretation".
{{note label|note9|9}} In the TI the collapse of the state vector is interpreted as the completion of the transaction between emitter and absorber.
{{note label|note10|10}} Comparing histories between systems in this interpretation has no well-defined meaning.
{{note label|note11|11}} Any physical interaction is treated as a collapse event relative to the systems involved, not just macroscopic or conscious observers.
{{note label|note12|12}} The state of the system is observer-dependent, i.e., the state is specific to the reference frame of the observer.
{{note label|note13|13}} Since Popper holds both CFD and locality to be true, it is under dispute whether his view is an interpretation (which is what he claimed) or a modification of Quantum Mechanics (which is what many Physicists claim), and, in case of the latter, if it has been empirically refuted or not by Bell test experiments.
{{note label|note14|14}} The transactional interpretation is explicitly non-local.
{{note label|note15|15}} The assumption of intrinsic periodicity is an element of non-locality consistent with relativity as the periodicity varies in a causal way.
{{note label|note16|16}} In the stochastic interpretation is not possible to define velocities for particles, i.e. the paths are not smooth. Moreover, to know the motion of the particles at any moment, you have to know what the Markov process is. However, once we know the exactly initial conditions and the Markov process, the theory is in fact a realistic interpretation of quantum mechanics; trajectories are continuous.
{{note label|note17|17}} The kind of locality violated by the theory is weaker than that assumed in deriving Bell inequalities. In particular, this kind non-locality is compatible with no signaling theorem and so with relativity.
{{note label|note18|18}} The interpretation is compatible with the view of a deterministic world as a whole, but does not exclude indeterminism.
{{note label|note19|19}} There are no hidden variables associated with the state of the quantum entity, but there are hidden variables associated with the measurement-interactions.