An intricate quantum statistical effect and the foundation of quantum mechanics

Fritz W. Bopp

REVIEW 4 major objections 5 minor 47 references

An intricate quantum statistical effect and the foundation of quantum mechanics

T0 review · 4 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read A quantum statistical effect says all measurements can be postponed to the universe's final state.

desk verdict An honest but unsupported two-boundary determinism sketch; the load-bearing dominance step is not rigorous and the Born-rule derivation is asserted rather than derived. read the letter →

arxiv 1909.01391 v2 pith:7D5Q7DNY submitted 2019-09-03 quant-ph gr-qchep-ph

Fritz W. Bopp This is my paper · ORCID

classification quant-phgr-qchep-ph PACS 03.65.Ta

keywords two-timeboundaryquantummechanicsfinal-statedensitymatrixpostponedmeasurementsmacroscopiccausalityBose-EinsteincorrelationsbigbangcrunchBornruleemergencefreewillin

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper argues that quantum randomness is not fundamental: in a universe with a fixed initial and final density matrix, every measurement can be postponed to the end of the universe, where the final state selects exactly one macroscopic path. The motivating evidence is a statistical Bose-Einstein enhancement of identical pions that appears to force backward causation on real emission probabilities, which the author treats as a failure of collapse-based interpretations. If enough witnesses of each macroscopic decision survive to the final time, every projection can be folded into an effective final density matrix, making the whole evolution deterministic and non-causal. Because a fully fixed final state would rule out willful agents, the paper adds a big-bang/big-crunch version in which the expanding and contracting phases share a matching border state, allowing external agents to act while preserving the deterministic core.

What carries the argument

The load-bearing object is the effective final density matrix \( \tilde{\tilde{\rho}}_{f,f^*} \), built by absorbing every postponed measurement into the fixed final boundary, together with the trace formula \( \mathrm{prob}_{M} = \mathrm{Tr}(\rho_{i^*,i} U(\tau_f-\tau_i) \tilde{\tilde{\rho}}_{f,f^*} U^*(\tau_{f^*}-\tau_{i^*}))/\mathrm{Tr}(\rho_{i^*,i} U(\tau_f-\tau_i) \rho_{f,f^*} U^*(\tau_{f^*}-\tau_{i^*})) \). The paper's dominant-state approximation reduces that matrix to a single rank-one term, so one macroscopic path corresponds to the whole universe, and the positional asymmetry \( (\tau_{\mathrm{now}}-\tau_{\mathrm{big\,bang}}) \ll (\tau_{\mathrm{final}}-\tau_{\mathrm{now}}) \) turns the non-causal boundary selection into an apparently causal decision tree. In the bidirectional extension, the matching border state \( |\mathrm{border}\rangle \) plays an analogous role, making the expanding and contracting halves of a big-bang/big-crunch universe macroscopically identical.

What would settle it

Perform the paper's 'crazy' gedanken experiment with identical bosons: measure the early-time two-particle correlation \( C(Q_{\mathrm{inv}}) \), then insert a late absorber that removes one crossing of the pair. The two-boundary model predicts the early-time correlation changes retroactively when the late absorber acts, whereas ordinary quantum dynamics with an early measurement fixes the correlation at the earlier time; observing the ordinary unchanged correlation would falsify the postponed-measurement mechanism.

Watch

Extended reading notes

Core claim

On the paper's own terms, quantum dynamics without projective jumps is an exact theory of the whole universe, while macroscopic dynamics is an approximate description that holds only in the present epoch. The central claim is that a harmless-looking statistical enhancement—identical bosons emitted with twice the probability when their momenta coincide—becomes, once the measurement boundary is moved later, a physical case of backward causation: a late absorption can retroactively remove the earlier interference enhancement. That motivates moving all projections to the final boundary. With a finite universe lifetime, every measurement can be postponed to the end of the universe and encoded in an effective final density matrix, and because that matrix is dominated by a single component, one unique macroscopic history wins. The macroscopic arrow of time then comes from the asymmetry that the past is short while the future is long, and the Born rule comes from relative path weights rather than from an added axiom.

Load-bearing premise

The whole argument depends on the assumption that every macroscopic decision leaves enough witnesses that survive to the end of the universe, allowing the final state to select or reject that branch; that end time itself is assumed by fiat, and if either condition fails the deterministic final-state picture cannot determine a unique macroscopic path.

Editorial extensions

If this is right

Wave-function collapse never happens: each projection is only a bookkeeping change in the effective final density matrix.
The Born rule becomes a consequence rather than a postulate, with measured probabilities given by the relative sizes of final-state path weights.
Macroscopic causality is an emergent approximation valid only in the present epoch; in closed boxes or other witness-free settings, coexisting macroscopic states remain, which the paper says demystifies paradoxes like Schroedinger's cat.
A fixed final state rules out willful agents, so the paper introduces the bidirectional big-bang/big-crunch universe specifically to let agents manipulate both the wavefunction and its CPT-conjugate partner.
In the early universe, before witnesses survive, no unique macroscopic description may exist; even a single Hubble parameter in the Friedmann equations could be questionable, and the transition into a macroscopic phase favors a homogeneous state without requiring inflation.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If final-boundary selection is taken seriously, it predicts a sharp operational criterion for classicality: a macroscopic branch is real only if it leaves records that last to the final boundary, so perfectly isolated large systems should retain quantum coexistence.
The same mechanism imposes a quantitative cosmological constraint the paper does not emphasize: the universe's total lifetime must be many orders of magnitude larger than its current age, so observational evidence of an imminent big crunch would undercut the explanation of causality.
The retrocausal pion gedanken could in principle be probed statistically in heavy-ion data by comparing event classes defined by late-stage conditions; a shift in the early-time two-particle correlation would be a final-state-selection signal absent from single-boundary treatments.
Replacing inflation with boundary-selected homogeneity is a distinctive cosmological prediction: fluctuation statistics would come from the matching of expanding and contracting phases rather than from inflationary quantum fluctuations, which could be discriminated by non-Gaussianity measurements.

Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Colleague,

The paper is a speculative but genuinely self-aware attempt to replace collapse with a two-boundary, deterministic quantum cosmology. The author knows his own weak points: he flags the dominant-state expansion as not rigorous and the willful-agents problem as a real cost of the fixed-final-state picture. That honesty makes the paper worth reading, but not as an established result.

What is new here is mostly packaging. The core two-density-matrix picture and the matching-state idea come from his earlier papers [14-16], and this version adds cosmological consequences (early-universe homogeneity without inflation, absence of macroscopic description before freeze-out). That is a natural extension of the same framework, not a new mechanism.

There is real merit in the way he connects the witness argument to the HBT/Bose-Einstein enhancement examples. The idea that measurements can be postponed to a final boundary is coherent within the two-state-vector formalism, and the comparison to Everett and ABL is useful. But the load-bearing step is the claim that the final density matrix has a single dominant component (Eqs. 5-6). The author explicitly says this is not rigorous, and the stress-test hits the right nerve: if there are exponentially many branches with similar weights, the largest individual term is not enough. Nothing in the paper rules out such degeneracy, and no operational rule is given for the "huge" exponents. Since this dominance is what produces the unique macroscopic path, the determinism claim does not follow.

The Born-rule discussion in Eqs. (16)-(18) is similarly heuristic. Even if one accepts the dominance assumption, the transition from "one of two exponents is larger" to a product of expanding and contracting amplitudes equal to ||^2 is asserted rather than derived. The square amplitude is entering by construction in the effective final state, not emerging from the dynamics. So the paper does not provide the derivation it advertises in the abstract.

For whom is this? Someone working on retrocausal or two-boundary interpretations of quantum mechanics will find it a clear statement of one vision, and a useful source of objections. It will not convince a mainstream reader, and it offers no empirical handle. Still, the author is thinking carefully and engaging seriously with prior work, so I would not desk-reject it in a foundations journal. But I would send it to a referee who knows the two-state-vector literature and ask specifically whether the dominance/degeneracy step can be saved. My own verdict would be: not established, but a legitimate speculative contribution.

Recommendation: engage with it seriously if you work in foundations; otherwise skim the abstract and move on.

Referee Report

4 major / 5 minor

Summary. The paper proposes that a quantum statistical effect, exemplified by Bose-Einstein enhancement in heavy-ion collisions, motivates a two-boundary formulation of quantum mechanics in which all measurements are postponed to a finite final time τ_final. An effective final density matrix then selects a unique macroscopic path, making the universe deterministic and non-causal. The paper extends this to a bi-directional big bang / big crunch scenario with a common 'border' state, intended to allow free will, and claims to derive Born's rule from the product of expanding and contracting components. The central assertion is that quantum randomness is not fundamental but is a consequence of the relative sizes of path weights in the final state.

Significance. If the derivation were sound, the paper would offer a deterministic foundation for quantum mechanics and a derivation of the Born rule, which would be a major result in the foundations of physics. The paper engages seriously with the two-state-vector formalism and the idea of witness-based postponement of measurement, and the Bose-Einstein correlation example is empirically grounded. However, the load-bearing steps are either explicitly labeled non-rigorous or are introduced as postulates, and the claimed Born-rule derivation is circular. The paper provides no machine-checked proofs or reproducible computations; its value is therefore mainly as a speculative proposal rather than as a proven result.

major comments (4)

[Section 2, Eqs. (5)-(6)] The dominant-state approximation, which the paper itself labels 'not rigorous' in the paragraph preceding Eq. (5), is the step that converts the effective final density matrix into a unique macroscopic path. The approximation ignores the possibility of many comparable coefficients: for N independent binary decisions with equal amplitudes, the effective final density matrix has 2^N equal eigenvalues, and Eq. (6) fails. Without a bound on the eigenvalue gap or an argument excluding such degeneracy, the uniqueness claim does not follow. This is load-bearing for the entire deterministic picture.
[Section 5, Eq. (18)] The claimed derivation of Born's rule is circular. The probability is defined as a product of an expanding and a contracting component, and the equality to the squared amplitude |<e⊗|e↑>|^2 is asserted without an independent derivation of those components from the preceding path-counting argument. Since the squared amplitude is the Born-rule expression, the rule enters by construction rather than being derived. To be a genuine derivation, the paper would need to show explicitly that the product of the two components equals the squared amplitude as a consequence of the path weights.
[Section 3 and Section 5, Eqs. (16)-(17)] The path weights 2^{-huge} are introduced without a combinatorial or dynamical derivation. No rule is given for computing 'huge' from the Hamiltonian or the boundary states, and the claim that probability(huge>huge′) = 1/2 assumes a measure over future paths that is never specified. If many paths contribute with comparable weights, a pairwise comparison of the two largest exponents does not define a probability. This step is needed for Eq. (18) and is therefore load-bearing.
[Section 2, 'effective basic rules' bullet list] The assertion that 'for each and every macroscopic decision there are enough witnesses' is an essential postulate, but no quantitative criterion is provided, such as the required number of witnesses, decoherence timescales, or survival probability up to τ_final. If even one macroscopic decision lacks surviving witnesses, the final-state measurement cannot select or deselect that branch, and the deterministic picture breaks. The finite lifetime τ_final is introduced as a regularization to avoid limits, but the universality of witness survival is a substantive assumption that is not proved.

minor comments (5)

[Section 1, introduction] The paper states that the argument 'will contain no ad hoc assumptions,' but later introduces τ_final, the big bang / big crunch matching state, and the surjection hypothesis as postulates; this apparent contradiction should be reconciled.
[Throughout] The notation ~ρ and ~~ρ is confusing; please use distinct symbols consistently and define them at first use.
[Figures 4, 5, and 13] The figure captions are too terse to convey the described gedanken experiments; consider expanding them so the figures are self-contained.
[References] Reference [45] cites a Wikipedia article for the 'textbook level' claim of Bose-Einstein correlations; a primary textbook or review article would be more appropriate.
[Throughout] The phrase 'path way' should be 'pathway' throughout the manuscript.

Circularity Check

2 steps flagged · score 6.0 of 10

Eq. (18)'s Born-rule "consequence" is the Born rule restated, and the effective final state is built from the very decisions it is said to determine.

self definitional [Section 5, Eq. (18)]
"which has the consequence: prob. [e↑ ] = (expanding component)·(contracting component) = |<e⊗|e↑>|2 prob. [e↓ ] = (expanding component)·(contracting component) = |<e⊗|e↓>|2 (18) It means the ,,Born rule” holds [40]."

The right-hand side is the standard modulus-squared amplitude. The "expanding component" and "contracting component" are introduced only as the two factors whose product is taken to be the probability; no rule is given for deriving those factors from the branch weights 2^{-huge} in Eq. (16). In the two-boundary formalism this product is precisely the numerator of the ABL formula already adopted in Eq. (8), so calling the result a consequence of the physical process is a relabeling: the Born rule was put in when the probability was written as a product of two amplitudes.
self definitional [Section 2, after Eq. (4)]
"Each of zillion branching of the macroscopic path way corresponds to a measurement decision which can be again and again be accounted for in this way by a change of the eﬀective ﬁnal density matrix ﬁnally yielding ~~ρf,f∗."

The effective final density matrix ~~ρ_f,f* is defined by successively inserting the postponed measurement projectors M′ into ρ_f,f*. The paper then reads off that this final state selects/deselects the macroscopic branches. Since the state was built out of those very branch decisions, the "determination" of the unique path is true by construction and carries no independent predictive content beyond the initial assumption that witnesses encode every decision.

full rationale

The first half of the paper, relying on the observed Bose-Einstein/HBT enhancement to motivate postponed measurements, is not circular: the enhancement is an external experimental fact and the witness-to-τ_final mechanism is a stated postulate. The dominant-state approximation in Eqs. (5)-(6) is explicitly "not rigorous" and is a genuine correctness risk (degenerate final spectra would break it), but it is an unsupported assumption rather than a definitional circle. Similarly, the self-citations [14,15,16] are used mainly to label a "correspondence transition rule" and prior versions of the idea, not to furnish the unique content. The circularity is concentrated in two places: the effective final state is assembled from the measurement outcomes it is said to determine, and Eq. (18) rewrites the two-boundary probability formula as a "derivation" of Born's rule. These steps make the central deterministic/Born-rule claims partially true by construction, so the paper is not fundamentally circular, but the claimed derivations are not free of input-equivalent assumptions.

Assumptions & free parameters 3 free parameters · 7 assumptions · 3 invented entities

The central claim is carried almost entirely by postulates and approximations rather than derivation: a finite universe lifetime, universal witness survival, a dominant final-state component, a symmetric big bang/big crunch with a matching border state, and a surjection hypothesis giving every agent a time-reversed copy. The quantitative core reduces to standard trace manipulations plus an asserted counting rule for decision paths. These are what the reader must accept for the conclusion to follow.

free parameters (3)

τ_final (finite lifetime of universe) = not specified; must be much larger than present age
Assumed finite so measurements can be postponed to the end of the universe (Section 1). Finiteness, not magnitude, is load-bearing.
τ/2 (matching time between expanding and contracting phases) = half the total big bang/big crunch period
Chosen for simplicity in Section 5 to define the maximum-expansion time; no physical derivation is given.
quantum-to-macroscopic transition position = not specified, claimed irrelevant
The argument requires a boundary between quantum dynamics and macroscopic dynamics; the author argues that its exact location is irrelevant as long as witnesses reach τ_final, but the existence of such a boundary is assumed.

assumptions (7)

ad hoc to paper The universe has a finite lifetime τ_final.
Introduced in Section 1: 'To avoid the definition of limits I assume a finite life time of the universe τ_final.'
domain assumption For every macroscopic decision, enough witnesses survive to τ_final to select or deselect the corresponding path.
Section 2, 'resulting effective basic rules': 'For each and every macroscopic decision there are enough witnesses so that measurements at τ_final can select / deselect it.'
ad hoc to paper The effective final density matrix expansion has a single dominant term.
Section 2: the author calls the dominant state approximation 'not rigorous as it requires the existence of a reasonably convergent expansion of the density matrix.'
ad hoc to paper The universe undergoes a big bang / big crunch cycle with expanding and contracting phases each lasting τ/2.
Section 5: chosen to avoid arbitrary assumptions about matching, while the author concedes it 'is not absolutely essential.'
ad hoc to paper Surjection hypothesis: macroscopic dynamics extends over [0, τ/2] and macroscopic objects live in both the expanding and the contracting phase.
Section 5: introduced as 'an obvious interpretation' to allow free will; no independent justification.
domain assumption Our present position is very early in the total lifetime: (τ_now - τ_big bang) << (τ_final - τ_now).
Section 3: 'The source of the observed macroscopic causal time direction is the asymmetry of our position.'
ad hoc to paper Macroscopic measurements average out quantum phase effects, the 'correspondence transition rule'.
Section 3: invoked to prevent direct macroscopic backward causation; not given a quantitative form.

invented entities (3)

Matching common final (border) state
purpose: Replaces the two fixed final states of the quantum world and its conjugate so that external manipulations automatically update the future, allowing free will (Section 4, Eq. (15)).
No observable signature is specified; it is a postulated object of the formalism.
Conjugate contracting world with CPT-reversed copies of macroscopic objects
purpose: Gives each agent a counterpart in the contracting half so manipulations on both sides can alter the shared final state (Section 5, surjection hypothesis).
Serves as a bookkeeping device; no testable consequence is derived.
Dominant border state at maximum expansion
purpose: Provides the single component linking expanding and contracting phases, making the two worlds macroscopically identical (Section 5, Eq. (12)).
Its dominance is assumed through the non-rigorous dominant state approximation.

how reviews work

0 comments

Cite this review

Pith. "Pith review of An intricate quantum statistical effect and the foundation of quantum mechanics." pith.science (2026). https://pith.science/paper/7D5Q7DNY

@misc{pith2026190901391,
  author       = {Pith},
  title        = {Pith review of: An intricate quantum statistical effect and the foundation of quantum mechanics},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/7D5Q7DNY}},
  note         = {Machine review of arXiv:1909.01391}
}

read the original abstract

An intricate quantum statistical effect guides us to a deterministic, non-causal quantum universe with given fixed initial and final state density matrix. A concept is developed on how and where something like macroscopic physics can emerge. The concept does not allow to incorporate philosophically indispensable free will decisions. If the quantum world and its conjugate evolve independently one can replace both fixed final states by a matching common one. This allows for external manipulations done in the quantum world and its conjugate which do not otherwise alter the basic structure. In a big bang / big crunch universe the expanding part can be attributed to the quantum world and the contracting part to the conjugate one. The obtained bi-linear picture has a number of beautiful and exciting consequences.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

47 extracted references · 44 canonical work pages

[1]

Abreu, S., et al.: Proceedings, Workshop on Heavy Ion Collisions at the LHC: Last Call for Predictions. J. Phys. G35, 054001 (2008). DOI 10.1088/0954-3899/35/5/054001

work page doi:10.1088/0954-3899/35/5/054001 2008
[2]

Physical Review 134(6B), B1410 (1964)

Aharonov, Y., Bergmann, P.G., Lebowitz, J.L.: Time symmetry in the quantum process of measurement. Physical Review 134(6B), B1410 (1964)

work page 1964
[3]

Aharonov, Y., Cohen, E., Elitzur, A.C.: Can a future choice aﬀect a past measurement’s outcome? Annals of Physics 355, 258–268 (2015)

work page 2015
[4]

Entropy 19(3) (2017)

Aharonov, Y., Cohen, E., Landsberger, T.: The two-time interpretation and macroscopic time-reversibility. Entropy 19(3) (2017)

work page 2017
[5]

digitalcommons.chapman.edu (2010)

Aharonov, Y., Popescu, S., Tollaksen, J.: A time-symmetric formulation of quantum mechanics. digitalcommons.chapman.edu (2010)

work page 2010
[6]

Journal of Physics A: Mathematical and General 24(10), 2315 (1991)

Aharonov, Y., Vaidman, L.: Complete description of a quantum system at a given time. Journal of Physics A: Mathematical and General 24(10), 2315 (1991)

work page 1991
[7]

Physics Letters B 169(4), 364–368 (1986)

Andersson, B., Hofmann, W.: Bose-Einstein correlations and color strings. Physics Letters B 169(4), 364–368 (1986)

work page 1986
[8]

Physics 1(3), 195–200 (1964)

Bell, J.S.: On the Einstein-Podolsky-Rosen paradox. Physics 1(3), 195–200 (1964)

work page 1964

Show all 47 references

[9]

Prentice-Hall, Erglewood Cliﬀs (1951)

Bohm, D.: Quantum Theory. Prentice-Hall, Erglewood Cliﬀs (1951)

1951
[10]

Bohm, D.: A suggested interpretation of the quantum theory in terms of” hidden” variables. i. Physical review 85(2), 166 (1952)

1952
[11]

Bohr, N.: Can quantum-mechanical description of physical reality be considered com- plete? Physical review 48(8), 696 (1935)

1935
[12]

Annalen der Physik 472(7-8), 407–414 (1966)

Bopp, F.: Elementarvorgaenge der Quantenmechanik in stochastischer Sicht. Annalen der Physik 472(7-8), 407–414 (1966)

1966
[13]

Theoretisch-Physikalischen Kolloquium der Universit¨ at Ulm (15.November 2001)

Bopp, F.W.: Strings and Hanbury-Brown-Twiss correlations in hadron physics. Theoretisch-Physikalischen Kolloquium der Universit¨ at Ulm (15.November 2001)

2001
[14]

Bopp, F.W.: Time Symmetric Quantum Mechanics and Causal Classical Physics. Found. Phys. 47(4), 490–504 (2017). DOI 10.1007/s10701-017-0074-7

2017 doi
[15]

In: Proceedings of the 4th International Electronic Conference on Entropy and Its Ap- plications, Basel, Switzerland, 2017

Bopp, F.W.: Causal Classical Physics in Time Symmetric Quantum Mechanics. In: Proceedings of the 4th International Electronic Conference on Entropy and Its Ap- plications, Basel, Switzerland, 2017. DOI: (2018). DOI 10.3390/ecea-4-05010. URL http://inspirehep.net/record/1653462...

2018
[16]

Bopp, F.W.: A bi-directional big bang/crunch universe within a two-state-vector quan- tum mechanics? Foundations of Physics 49(1), 53–62 (2019)

2019
[17]

arXiv preprint arXiv:1902.03951 (2019)

Chowdhury, D., Martin, J., Ringeval, C., Vennin, V.: Inﬂation after planck: Judgment day. arXiv preprint arXiv:1902.03951 (2019)

2019 arXiv
[18]

Foundations of Physics 47(3), 327–354 (2017)

Davidson, M.: On the M¨ ossbauer eﬀect and the rigid recoil question. Foundations of Physics 47(3), 327–354 (2017). DOI 10.1007/s10701-017-0064-9. URL https://doi. org/10.1007/s10701-017-0064-9

2017 doi
[19]

Davidson, M.: Bohmian Trajectories for KerrNewman Particles in Complex Space-Time. Found. Phys. 48(11), 1590–1616 (2018). DOI 10.1007/s10701-018-0217-5

2018 doi
[20]

De Broglie, L.: La m´ ecanique ondulatoire et la structure atomique de la mati` ere et du rayonnement. J. Phys. Radium 8(5), 225–241 (1927)

1927
[21]

Nature Astronomy pp

Di Valentino, E., Melchiorri, A., Silk, J.: Planck evidence for a closed universe and a possible crisis for cosmology. Nature Astronomy pp. 1–8 (2019)

2019
[22]

Springer (2009)

D¨ urr, D., Teufel, S.: Bohmian mechanics. Springer (2009)

2009
[23]

Einstein, A., Podolsky, B., Rosen, N.: Can quantum-mechanical description of physical reality be considered complete? Physical review 47(10), 777 (1935)

1935
[24]

The European Physical Journal C 78(11), 983 (2018)

Ferreres-Sol´ e, S., Sj¨ ostrand, T.: The space–time structure of hadronization in the Lund model. The European Physical Journal C 78(11), 983 (2018)

2018
[25]

Reviews of Modern Physics 20(2), 367 (1948)

Feynman, R.P.: Space-time approach to non-relativistic quantum mechanics. Reviews of Modern Physics 20(2), 367 (1948)

1948
[26]

Glauber, R.: Oral communication after a conference talk about Bose-Einstein- correlations
[27]

Physical Review D 23(2), 347 (1981)

Guth, A.H.: Inﬂationary universe: A possible solution to the horizon and ﬂatness prob- lems. Physical Review D 23(2), 347 (1981)

1981
[28]

Hanbury Brown, R., Twiss, R.Q.: Interferometry of the intensity ﬂuctuations in light. I. Basic theory: the correlation between photons in coherent beams of radiation. In: Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, pp. 300–324...

1957
[29]

Physics Letters,(Section) B 239 (1990)

Hern´ andez, J., Stone, J., Porter, F., Morrison, R., Montanet, L., Gieselmann, K., Aguilar-Benitez, M., Conforto, G., Caso, C., Roos, M., et al.: Review of particle prop- erties. Physics Letters,(Section) B 239 (1990)

1990
[30]

Springer (2016)

’t Hooft, G.: The Cellular Automaton Interpretation of Quantum Mechanics. Springer (2016)

2016
[31]

arXiv preprint arXiv:1912.06462 (2019)

Hossenfelder, S., Palmer, T.: Rethinking superdeterminism. arXiv preprint arXiv:1912.06462 (2019)

2019 arXiv
[32]

Springer Science & Business Media (2013)

Joos, E., Zeh, H.D., Kiefer, C., Giulini, D.J., Kupsch, J., Stamatescu, I.O.: Decoherence and the appearance of a classical world in quantum theory. Springer Science & Business Media (2013)

2013
[33]

Physical review letters 114(10), 101302 (2015)

Kaloper, N., Padilla, A.: Sequestration of vacuum energy and the end of the universe. Physical review letters 114(10), 101302 (2015)

2015
[34]

Physikalisches Kolloquium der Univer- sit¨ at Siegen (19 Juni 2008)

Kiefer, C.: Zeitpfeil und Quantumgravitation. Physikalisches Kolloquium der Univer- sit¨ at Siegen (19 Juni 2008)

2008
[35]

World Scientiﬁc (2005)

Kittel, W., De Wolf, E.A.: Soft multihadron dynamics. World Scientiﬁc (2005)

2005
[36]

Leifer, M.S., Pusey, M.F.: Is a time symmetric interpretation of quantum theory possible without retrocausality? Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 473(2202), 20160607 (2017)

2017
[37]

Mermin, N.D.: What is quantum mechanics trying to tell us? American Journal of Physics 66(9), 753–767 (1998)

1998
[38]

Sakurai, J.J., Napolitano, J., et al.: Modern quantum mechanics, vol. 185. Pearson Harlow (2014)

2014
[39]

Zeitschrift f¨ ur Physik131(4), 629–662 (1952)

S¨ ussmann, G.: Die spontane lichtemission in der unit¨ aren quantenelektrodynamik. Zeitschrift f¨ ur Physik131(4), 629–662 (1952)

1952
[40]

Vaidman, L.: Derivations of the born rule (2019)

2019
[41]

Entropy 21(5) (2019)

Vaidman, L.: Quantum nonlocality. Entropy 21(5) (2019). DOI 10.3390/e21050447. URL https://www.mdpi.com/1099-4300/21/5/447

2019 doi
[42]

arXiv preprint arXiv:1512.00740 (2015)

Wharton, K.B.: Towards a realistic parsing of the feynman path integral. arXiv preprint arXiv:1512.00740 (2015)

2015 arXiv
[43]

arXiv preprint arXiv:1906.04313 (2019) 20 F

Wharton, K.B., Argaman, N.: Bell’s theorem and spacetime-based reformulations of quantum mechanics. arXiv preprint arXiv:1906.04313 (2019) 20 F. W. Bopp

2019 arXiv
[44]

Princeton University Press (2014)

Wheeler, J.A., Zurek, W.H.: Quantum theory and measurement. Princeton University Press (2014)

2014
[45]

Wikipedia: Bose-Einstein-correlations
[46]

Springer Science & Business Media (2001)

Zeh, H.D.: The physical basis of the direction of time. Springer Science & Business Media (2001)

2001
[47]

Re- views of Modern Physics 75(3), 715 (2003)

Zurek, W.H.: Decoherence, einselection, and the quantum origins of the classical. Re- views of Modern Physics 75(3), 715 (2003)

2003

Pith tools

Reviewed August 14, 2026 · model on record in the stance chip above.

[1] [1]

Abreu, S., et al.: Proceedings, Workshop on Heavy Ion Collisions at the LHC: Last Call for Predictions. J. Phys. G35, 054001 (2008). DOI 10.1088/0954-3899/35/5/054001

work page doi:10.1088/0954-3899/35/5/054001 2008

[2] [2]

Physical Review 134(6B), B1410 (1964)

Aharonov, Y., Bergmann, P.G., Lebowitz, J.L.: Time symmetry in the quantum process of measurement. Physical Review 134(6B), B1410 (1964)

work page 1964

[3] [3]

Aharonov, Y., Cohen, E., Elitzur, A.C.: Can a future choice aﬀect a past measurement’s outcome? Annals of Physics 355, 258–268 (2015)

work page 2015

[4] [4]

Entropy 19(3) (2017)

Aharonov, Y., Cohen, E., Landsberger, T.: The two-time interpretation and macroscopic time-reversibility. Entropy 19(3) (2017)

work page 2017

[5] [5]

digitalcommons.chapman.edu (2010)

Aharonov, Y., Popescu, S., Tollaksen, J.: A time-symmetric formulation of quantum mechanics. digitalcommons.chapman.edu (2010)

work page 2010

[6] [6]

Journal of Physics A: Mathematical and General 24(10), 2315 (1991)

Aharonov, Y., Vaidman, L.: Complete description of a quantum system at a given time. Journal of Physics A: Mathematical and General 24(10), 2315 (1991)

work page 1991

[7] [7]

Physics Letters B 169(4), 364–368 (1986)

Andersson, B., Hofmann, W.: Bose-Einstein correlations and color strings. Physics Letters B 169(4), 364–368 (1986)

work page 1986

[8] [8]

Physics 1(3), 195–200 (1964)

Bell, J.S.: On the Einstein-Podolsky-Rosen paradox. Physics 1(3), 195–200 (1964)

work page 1964