Quantum mechanics provides the physical basis of teleological evolutions

Giuseppe Castagnoli

arxiv: 2601.07849 · v11 · submitted 2026-01-08 · ⚛️ physics.gen-ph

Quantum mechanics provides the physical basis of teleological evolutions

Giuseppe Castagnoli This is my paper

Pith reviewed 2026-05-16 16:07 UTC · model grok-4.3

classification ⚛️ physics.gen-ph

keywords quantum algorithmscomputational speedupteleological evolutionfuture attractoranthropic principlequantum cosmologyliving systems

0 comments

The pith

Quantum speedup in algorithms arises because their evolutions are pulled by a future goal that acts as an attractor.

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

The paper claims that quantum algorithms run faster than classical ones because they evolve toward a solution that functions as a future attractor influencing the present state. This teleological structure, where the end result shapes the path, accounts for the observed computational advantage. Under a quantum cosmological assumption combined with the fine-tuned universe version of the anthropic principle, the same physical mechanism is said to underpin the goal-directed character of living systems.

Core claim

The quantum computational speedup of quantum algorithms is due to their teleological character, their being evolutions toward a goal (the solution of the problem) with an attractor in the very goal they will produce in the future (the solution of the problem again). Under the quantum cosmological assumption and for the Fine-tuned Universe version of the Anthropic Principle, the physical basis of the teleological character of quantum algorithms applies as well to the evolutions of the living for which the teleological notion was originally conceived.

What carries the argument

The teleological attractor placed in the future goal of the evolution, which pulls the quantum state toward the solution.

If this is right

Quantum algorithms achieve speedup precisely because the solution they will output already influences their intermediate states.
The same attractor mechanism provides a physical basis for goal-directed processes once the anthropic and cosmological premises are accepted.
Living systems inherit a teleological character from the underlying quantum evolution under those premises.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

If the attractor mechanism holds, classical simulations of quantum algorithms might need to incorporate explicit future constraints to match observed speeds.
The view suggests searching for measurable correlations between present biological states and future outcomes that exceed classical expectations.
It opens the possibility of designing hybrid quantum-biological models where teleology is treated as a calculable dynamical feature.

Load-bearing premise

The quantum cosmological assumption together with the fine-tuned universe version of the anthropic principle lets the teleological basis of quantum algorithms apply to living evolutions.

What would settle it

A demonstration of quantum speedup in an algorithm constructed without any future-goal attractor would contradict the central claim.

read the original abstract

We show that the quantum computational speedup of quantum algorithms is due to their teleological character, their being evolutions toward a goal (the solution of the problem) with an attractor in the very goal they will produce in the future (the solution of the problem again). We also show that, under the quantum cosmological assumption and for the Fine-tuned Universe version of the Anthropic Principle, the physical basis of the teleological character of quantum algorithms applies as well to the evolutions of the living for which the teleological notion was originally conceived.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper claims quantum speedup comes from a future solution acting as an attractor in the evolution, then extends the idea to biology via cosmology, but supplies no derivation or dynamics to make the mechanism work.

read the letter

The central claim is that quantum algorithms run faster because they evolve toward a goal that already exists as a future attractor, and that this teleological feature carries over to living systems under quantum cosmology plus a fine-tuned anthropic principle. That is the one thing a colleague needs to know up front: the argument is an interpretive overlay rather than a new calculation or model. What the paper does is take the observed speedup in algorithms like Grover or Shor and redescribe it in explicitly teleological language, then argue that the same physical basis applies to biological evolution once the right cosmological assumptions are granted. The writing is clear on that point and the author is consistent in following the logic from computation to biology. The soft spots are straightforward. The attractor is defined as the solution itself, so the explanation loops back on the thing it is trying to explain rather than deriving the speedup from an independent dynamical rule. Standard quantum mechanics already accounts for interference and oracle queries through forward unitary evolution; nothing in the paper shows how adding a future boundary condition changes the complexity bounds or reproduces the known scaling. The biological extension rests entirely on the quantum cosmological assumption and the fine-tuned-universe version of the anthropic principle, neither of which is derived or tested here. No equations, no new predictions, and no comparison against existing retrocausal or two-time formalisms appear. This is the sort of piece that might interest readers who follow foundational reinterpretations of quantum mechanics and their possible reach into biology. It does not contain the formal grounding or reproducible content that would normally justify sending it to referees. I would not bring it to a reading group and would not cite it. A serious editor should desk-reject rather than put it through peer review.

Referee Report

2 major / 1 minor

Summary. The manuscript claims that the computational speedup of quantum algorithms arises from their teleological character, defined as evolutions directed toward a future goal (the problem solution) that functions as an attractor; it further asserts that the same quantum-mechanical basis, under a quantum-cosmological assumption and the fine-tuned-universe anthropic principle, accounts for teleological evolution in living systems.

Significance. If a concrete dynamical model were supplied, the work would offer a unified physical account of apparent purpose in both quantum computation and biology. In its present form the argument supplies no new equations, no alternative boundary-value problem, and no quantitative mapping from the attractor premise to known complexity scalings, so the significance remains that of an interpretive re-description rather than a predictive mechanism.

major comments (2)

[Abstract] Abstract and opening paragraphs: the assertion that speedup 'is due to' the future goal acting as attractor is not supported by any derivation; the standard Schrödinger evolution and circuit construction remain strictly forward in time with no retrocausal term or two-time boundary condition introduced to let the solution influence the present dynamics.
[Biological evolutions] Section on biological extension: the claim that the teleological basis 'applies as well to the evolutions of the living' rests on an unelaborated quantum-cosmological assumption and anthropic principle without a specific mapping, scaling relation, or falsifiable prediction that would distinguish the proposal from conventional evolutionary dynamics.

minor comments (1)

[Main text] Notation for the 'attractor in the goal' is introduced without a formal definition or Hamiltonian term; an explicit equation would clarify whether the construction is equivalent to standard unitary evolution or introduces new physics.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful and constructive report. We respond point by point to the major comments, clarifying the interpretive character of the arguments while indicating where the manuscript will be revised for greater precision.

read point-by-point responses

Referee: [Abstract] Abstract and opening paragraphs: the assertion that speedup 'is due to' the future goal acting as attractor is not supported by any derivation; the standard Schrödinger evolution and circuit construction remain strictly forward in time with no retrocausal term or two-time boundary condition introduced to let the solution influence the present dynamics.

Authors: We agree that the manuscript introduces no new dynamical equations, retrocausal terms, or two-time boundary conditions. The claim is that the known computational speedup can be interpreted as arising from the teleological structure in which the problem solution functions as an attractor in the state space; the standard forward Schrödinger evolution is used, with the encoding of the problem and the choice of initial state and Hamiltonian directing the dynamics toward that future solution. We will revise the abstract and opening paragraphs to state explicitly that this is an interpretive re-description of existing quantum dynamics rather than a derivation of new equations. revision: partial
Referee: [Biological evolutions] Section on biological extension: the claim that the teleological basis 'applies as well to the evolutions of the living' rests on an unelaborated quantum-cosmological assumption and anthropic principle without a specific mapping, scaling relation, or falsifiable prediction that would distinguish the proposal from conventional evolutionary dynamics.

Authors: The extension to living systems is presented under the explicit quantum-cosmological assumption and the fine-tuned-universe anthropic principle stated in the manuscript. No quantitative mapping, scaling relation, or new falsifiable prediction is supplied because the section seeks only to indicate that the same quantum-mechanical basis invoked for algorithms can, under those assumptions, be viewed as applying to biological teleology. We will revise the relevant section to emphasize the conceptual and non-predictive nature of this extension and to note that it does not replace or contradict standard evolutionary dynamics. revision: partial

Circularity Check

1 steps flagged

Speedup attributed to teleological character defined as evolution toward the solution itself

specific steps

self definitional [Abstract]
"We show that the quantum computational speedup of quantum algorithms is due to their teleological character, their being evolutions toward a goal (the solution of the problem) with an attractor in the very goal they will produce in the future (the solution of the problem again)."

The teleological character is defined as having the solution as its own future attractor; claiming that speedup 'is due to' this character therefore equates the speedup with the definitional premise that the evolution reaches the solution, without deriving the complexity advantage from unitary dynamics or interference.

full rationale

The paper's central claim equates quantum speedup with the 'teleological character' of algorithms, but this character is introduced by definition as an evolution whose attractor is the future solution (the problem's answer). No independent dynamical mechanism—such as a modified Schrödinger equation, retrocausal term, or two-time boundary condition—is derived to produce Grover or Shor scaling from first principles. The argument therefore reduces the observed fact that the algorithm reaches the solution to a restatement of that fact under new terminology, without external derivation or falsifiable prediction beyond the input definition. The cosmological and anthropic extensions inherit the same definitional structure.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 1 invented entities

The central claim rests on reinterpreting quantum evolution as teleological without new equations or data; it introduces the future attractor as an explanatory entity and invokes the quantum cosmological assumption plus a specific Anthropic Principle version.

axioms (2)

domain assumption Quantum cosmological assumption that the universe follows quantum rules from the beginning
Invoked to extend the algorithmic teleology to biological evolution
domain assumption Fine-tuned Universe version of the Anthropic Principle
Required to make the teleological basis apply to living systems

invented entities (1)

Future attractor in the goal of the evolution no independent evidence
purpose: To explain quantum speedup and teleological character of algorithms and living systems
Postulated as the mechanism that pulls the evolution toward the solution; no independent falsifiable handle is given

pith-pipeline@v0.9.0 · 5371 in / 1420 out tokens · 31141 ms · 2026-05-16T16:07:26.225521+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Foundation/RealityFromDistinction.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

quantum speedup ... due to their teleological character, their being evolutions toward a goal ... with an attractor in the very goal they will produce in the future
IndisputableMonolith/Foundation/DimensionForcing.lean eight_tick_period_forces_D3 unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

time-symmetrization ... causal loops ... retrocausality along unitary quantum evolutions
IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

Fine-tuned Universe version of the Anthropic Principle

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

25 extracted references · 25 canonical work pages · 3 internal anchors

[1]

Castagnoli and D

G. Castagnoli and D. R. Finkelstein, Theory of the quantum speedup,Proc. Roy. Soc. Lond. A457, 1799–1807 (2001)

work page 2001
[2]

Castagnoli, The quantum correlation between the selection of the problem and that of the solution sheds light on the mechanism of the quantum speed up,Phys

G. Castagnoli, The quantum correlation between the selection of the problem and that of the solution sheds light on the mechanism of the quantum speed up,Phys. Rev. A82, 052334 (2010)

work page 2010
[3]

Castagnoli, Completing the Physical Representation of Quantum Algorithms Provides a Quantitative Explanation of Their Computational Speedup,Found

G. Castagnoli, Completing the Physical Representation of Quantum Algorithms Provides a Quantitative Explanation of Their Computational Speedup,Found. Phys.48, 333–354 (2018)

work page 2018
[4]

Castagnoli, E

G. Castagnoli, E. Cohen, A. K. Ekert, and A. C. Elitzur, A Relational Time-Symmetric Framework for Analyzing the Quantum Computational Speedup,Found. Phys.49, 1200–1230 (2019)

work page 2019
[5]

Castagnoli, Unobservable causal loops as a way to explain both the quantum computational speedup and quantum nonlocality,Phys

G. Castagnoli, Unobservable causal loops as a way to explain both the quantum computational speedup and quantum nonlocality,Phys. Rev. A104, 032203 (2021)

work page 2021
[6]

Castagnoli, The physical basis of teleological evolutions, arXiv:2310.18927v13 [physics.gen- ph] (2025)

G. Castagnoli, The physical basis of teleological evolutions, arXiv:2310.18927v13 [physics.gen- ph] (2025)

work page arXiv 2025
[7]

Einstein, B

A. Einstein, B. Podolsky, and N. Rosen, Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?,Phys. Rev.47, 777 (1935). 18

work page 1935
[8]

Aharonov, P

Y. Aharonov, P. G. Bergman, and J. L. Lebowitz, Time Symmetry in the Quantum Process of Measurement,Phys. Rev.134, B1410 (1964)

work page 1964
[9]

The Two-State Vector Formalism of Qauntum Mechanics: an Updated Review

Y. Aharonov and L. Vaidman, The Two-State Vector Formalism: an Updated Review, arXiv: quant-ph/0105101 (2007)

work page internal anchor Pith review Pith/arXiv arXiv 2007
[10]

Aharonov, E

Y. Aharonov, E. Cohen, and A. C. Elitzur, Can a future choice affect a past measurement outcome?,Ann. Phys.355, 258–268 (2015)

work page 2015
[11]

Bojowald,Quantum Cosmology: A Fundamental Description of the Universe, Lecture Notes in Physics, Vol

M. Bojowald,Quantum Cosmology: A Fundamental Description of the Universe, Lecture Notes in Physics, Vol. 835 (Springer, 2011)

work page 2011
[12]

J. D. Barrow and F. J. Tipler,The Anthropic Cosmological Principle(Oxford University Press, 1988)

work page 1988
[13]

L. K. Grover, A fast quantum mechanical algorithm for database search,Proc. 28th Annual ACM Symposium on the Theory of Computing(ACM Press, New York, 1996), pp. 212–219

work page 1996
[14]

G. L. Long, Grover algorithm with zero theoretical failure rate,Phys. Rev. A64, 022307 (2001)

work page 2001
[15]

A Quantum Random Walk Search Algorithm

N. Shenvi, J. Kempe, and K. B. Whaley, A Quantum Random Walk Search Algorithm, arXiv:quant-ph/0210064 (2002)

work page internal anchor Pith review Pith/arXiv arXiv 2002
[16]

J. A. Wheeler and R. P. Feynman, Classical Electrodynamics in Terms of Direct Interparticle Action,Rev. Mod. Phys.21, 425–439 (1949)

work page 1949
[17]

J. S. Bell, On the Einstein Podolsky Rosen Paradox,Physics Physique Fizika1, 195–200 (1964)

work page 1964
[18]

A. K. Ekert, Quantum cryptography based on Bell’s theorem,Phys. Rev. Lett.67, 661 (1991)

work page 1991
[19]

Laland, T

K. Laland, T. Uller, M. Feldman et al, Does evolutionary theory need a rethink?,Nature514, 161–164 (2014)

work page 2014
[22]

Allen and J

C. Allen and J. P. Neal, Teleological notions in biology,Stanford Encyclopedia of Philosophy, https://philpapers.org/rec/ALLTNI-5 (2020)

work page 2020
[23]

K. R. Dronamraju,Haldane and Modern Biology(Johns Hopkins University Press, Baltimore, 1968)

work page 1968
[24]

Nagel,Mind and Cosmos: Why the Materialist, Neo-Darwinian Conception of Nature Is Almost Certainly False(Oxford University Press, New York, 2012)

T. Nagel,Mind and Cosmos: Why the Materialist, Neo-Darwinian Conception of Nature Is Almost Certainly False(Oxford University Press, New York, 2012)

work page 2012
[25]

Peled, A

B. Peled, A. Teeni, E. Cohen, and A. Carmi, Study of entanglement via a multi-agent dynam- ical quantum game,PLoS ONE18(1), e0280798 (2023)

work page 2023
[26]

Rovelli, Relational Quantum Mechanics,Int

C. Rovelli, Relational Quantum Mechanics,Int. J. Theor. Phys.35, 637–658 (1996)

work page 1996
[27]

C. A. Fuchs, On Participatory Realism, arXiv:1601.04360 [quant-ph] (2016). 19 Acknowledgements Thanks are due to Eliahu Cohen, Artur Ekert, Avshalom Elitzur and David Finkelstein for useful comments, Daniel Sheehan for organizing the San Diego AAAS Pacific Division conferences on retrocausality, a far-looking forum for the discussion of frontier, also uno...

work page internal anchor Pith review Pith/arXiv arXiv 2016

[1] [1]

Castagnoli and D

G. Castagnoli and D. R. Finkelstein, Theory of the quantum speedup,Proc. Roy. Soc. Lond. A457, 1799–1807 (2001)

work page 2001

[2] [2]

Castagnoli, The quantum correlation between the selection of the problem and that of the solution sheds light on the mechanism of the quantum speed up,Phys

G. Castagnoli, The quantum correlation between the selection of the problem and that of the solution sheds light on the mechanism of the quantum speed up,Phys. Rev. A82, 052334 (2010)

work page 2010

[3] [3]

Castagnoli, Completing the Physical Representation of Quantum Algorithms Provides a Quantitative Explanation of Their Computational Speedup,Found

G. Castagnoli, Completing the Physical Representation of Quantum Algorithms Provides a Quantitative Explanation of Their Computational Speedup,Found. Phys.48, 333–354 (2018)

work page 2018

[4] [4]

Castagnoli, E

G. Castagnoli, E. Cohen, A. K. Ekert, and A. C. Elitzur, A Relational Time-Symmetric Framework for Analyzing the Quantum Computational Speedup,Found. Phys.49, 1200–1230 (2019)

work page 2019

[5] [5]

Castagnoli, Unobservable causal loops as a way to explain both the quantum computational speedup and quantum nonlocality,Phys

G. Castagnoli, Unobservable causal loops as a way to explain both the quantum computational speedup and quantum nonlocality,Phys. Rev. A104, 032203 (2021)

work page 2021

[6] [6]

Castagnoli, The physical basis of teleological evolutions, arXiv:2310.18927v13 [physics.gen- ph] (2025)

G. Castagnoli, The physical basis of teleological evolutions, arXiv:2310.18927v13 [physics.gen- ph] (2025)

work page arXiv 2025

[7] [7]

Einstein, B

A. Einstein, B. Podolsky, and N. Rosen, Can Quantum-Mechanical Description of Physical Reality Be Considered Complete?,Phys. Rev.47, 777 (1935). 18

work page 1935

[8] [8]

Aharonov, P

Y. Aharonov, P. G. Bergman, and J. L. Lebowitz, Time Symmetry in the Quantum Process of Measurement,Phys. Rev.134, B1410 (1964)

work page 1964

[9] [9]

The Two-State Vector Formalism of Qauntum Mechanics: an Updated Review

Y. Aharonov and L. Vaidman, The Two-State Vector Formalism: an Updated Review, arXiv: quant-ph/0105101 (2007)

work page internal anchor Pith review Pith/arXiv arXiv 2007

[10] [10]

Aharonov, E

Y. Aharonov, E. Cohen, and A. C. Elitzur, Can a future choice affect a past measurement outcome?,Ann. Phys.355, 258–268 (2015)

work page 2015

[11] [11]

Bojowald,Quantum Cosmology: A Fundamental Description of the Universe, Lecture Notes in Physics, Vol

M. Bojowald,Quantum Cosmology: A Fundamental Description of the Universe, Lecture Notes in Physics, Vol. 835 (Springer, 2011)

work page 2011

[12] [12]

J. D. Barrow and F. J. Tipler,The Anthropic Cosmological Principle(Oxford University Press, 1988)

work page 1988

[13] [13]

L. K. Grover, A fast quantum mechanical algorithm for database search,Proc. 28th Annual ACM Symposium on the Theory of Computing(ACM Press, New York, 1996), pp. 212–219

work page 1996

[14] [14]

G. L. Long, Grover algorithm with zero theoretical failure rate,Phys. Rev. A64, 022307 (2001)

work page 2001

[15] [15]

A Quantum Random Walk Search Algorithm

N. Shenvi, J. Kempe, and K. B. Whaley, A Quantum Random Walk Search Algorithm, arXiv:quant-ph/0210064 (2002)

work page internal anchor Pith review Pith/arXiv arXiv 2002

[16] [16]

J. A. Wheeler and R. P. Feynman, Classical Electrodynamics in Terms of Direct Interparticle Action,Rev. Mod. Phys.21, 425–439 (1949)

work page 1949

[17] [17]

J. S. Bell, On the Einstein Podolsky Rosen Paradox,Physics Physique Fizika1, 195–200 (1964)

work page 1964

[18] [18]

A. K. Ekert, Quantum cryptography based on Bell’s theorem,Phys. Rev. Lett.67, 661 (1991)

work page 1991

[19] [19]

Laland, T

K. Laland, T. Uller, M. Feldman et al, Does evolutionary theory need a rethink?,Nature514, 161–164 (2014)

work page 2014

[20] [22]

Allen and J

C. Allen and J. P. Neal, Teleological notions in biology,Stanford Encyclopedia of Philosophy, https://philpapers.org/rec/ALLTNI-5 (2020)

work page 2020

[21] [23]

K. R. Dronamraju,Haldane and Modern Biology(Johns Hopkins University Press, Baltimore, 1968)

work page 1968

[22] [24]

Nagel,Mind and Cosmos: Why the Materialist, Neo-Darwinian Conception of Nature Is Almost Certainly False(Oxford University Press, New York, 2012)

T. Nagel,Mind and Cosmos: Why the Materialist, Neo-Darwinian Conception of Nature Is Almost Certainly False(Oxford University Press, New York, 2012)

work page 2012

[23] [25]

Peled, A

B. Peled, A. Teeni, E. Cohen, and A. Carmi, Study of entanglement via a multi-agent dynam- ical quantum game,PLoS ONE18(1), e0280798 (2023)

work page 2023

[24] [26]

Rovelli, Relational Quantum Mechanics,Int

C. Rovelli, Relational Quantum Mechanics,Int. J. Theor. Phys.35, 637–658 (1996)

work page 1996

[25] [27]

C. A. Fuchs, On Participatory Realism, arXiv:1601.04360 [quant-ph] (2016). 19 Acknowledgements Thanks are due to Eliahu Cohen, Artur Ekert, Avshalom Elitzur and David Finkelstein for useful comments, Daniel Sheehan for organizing the San Diego AAAS Pacific Division conferences on retrocausality, a far-looking forum for the discussion of frontier, also uno...

work page internal anchor Pith review Pith/arXiv arXiv 2016