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The Einstein-Podolsky-Rosen argument in spacetime and in what sense quantum mechanics is fundamentally incomplete

Petkov, Vesselin

Published Dec 14, 2025• 0 citations
OpenAlex

Abstract

Two problems with the Einstein-Podolsky-Rosen argument originate from the difficult-to-explain continual dismissal of Minkowski’s demonstration that the concept of spacetime represents a real four-dimensional world and is not just a mathematical space. The uncritical employment of the traditional three-dimensional language to the description of this argument leads (e.g., in its Bohm's version) to those problems: (1) due to the collapse of the common wavefunction of the constituents 1 and 2 of a disintegrated system, caused by the measurement of 1's spin (event $E_{1}$), and due the conservation of the total spin, 2's spin is \textit{instantaneously} determined (event $E_{2}$), which in three-dimensional language inescapably means that $E_{2}$ is \textit{caused} by $E_{1}$ (using merely a different word -- `correlation' -- does not explain anything in three-dimensional language); (2) events $E_{1}$ and $E_{2}$ are simultaneous \textit{only} for an observer $A$, who was at rest with respect to the disintegrated system, and therefore the total spin is not conserved for arbitrarily large periods of time for all observers in relative motion with respect to $A$ and there exists a class of observers $B$ for whom event $E_{2}$ occurs \textit{before} $E_{1}$, which demonstrates the inadequacy of the fundamental implicit assumption that the physical world is three-dimensional. When the reality of spacetime is explicitly recognized, (1) the paradoxes of the non-conservation of the total spin and that $E_{2}$ happens before $E_{1}$ for observers $B$ do not arise (because there is no `before' and `after' in spacetime) and the statement that there is a correlation between $E_{1}$ and $E_{2}$ makes a perfect sense, and (2) a spacetime model of the quantum object can then be considered (by also taking into account the non-fully-realized experimental fact that the quantum object \textit{actually} exists everywhere where its wavefunction is different from zero) in order to address the fundamental incompleteness of quantum mechanics -- that it deals not with the quantum object itself, but only with its states. The paper ends with a discussion of a prediction by the proposed spacetime model of the electron that can be tested experimentally probably by the quadratic Stark effect.

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From a phenomenological and experimental viewpoint, quantum mechanics is remarkably successful in explaining effects and processes in the microscopic world. Recently, however, a growing body of literature has revisited the theory's own formal foundations, specifically addressing issues of self-consistency and completeness. As a major historical example of these foundational challenges, the Einstein-Podolsky-Rosen (EPR) argument famously claimed that the theory is incomplete. While many valid criticisms and refutations of the EPR logic exist, they generally rely on a combination of technical results and conceptual objections to EPR's interpretive assumptions, thus transcending the plain quantum framework itself. Motivated by these trends of examining the theory's structural limits, here we revisit the EPR argument. Focusing on elements essential to the EPR reasoning, we first analyze general quantum correlations for EPR states: (i) the fact that their observables are always associated with non-commuting operators, and (ii) the nature of the correlated information obtained through measurement. From these two points alone, and relying strictly on the core rules of quantum mechanics, we demonstrate how to overturn the alleged EPR incompleteness without invoking any extraneous propositions. Consequently, we show that the standard formalism alone suffices to resolve such type of skepticism regarding the theory's physical reach. This offers, at least in a paradigmatic instance, a powerful indication of a structurally well-founded, self-consistent quantum theory.

quant-pharXiv:2608.10006•Aug 11, 2026•0 citations

Completeness Revisited: A Temporal Resolution of the Einstein–Podolsky–Rosen Argument

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The Einstein–Podolsky–Rosen (EPR) argument was originally posed as a challenge to the completeness of quantum mechanics, rather than its empirical adequacy. While subsequent developments—most notably Bell’s theorem and experimental tests of nonlocal correlations— have constrained classes of hidden-variable theories, they have not resolved the underlying on- tological question raised by EPR: whether the quantum state exhausts physical reality. In this paper, we revisit the EPR criterion of completeness from the perspective of a temporally grounded physical framework, the Temporal Inertia Framework (TIF). We argue that the orig- inal EPR dilemma rests on an implicit assumption that physical reality must be specified on spacelike hypersurfaces, an assumption shared by both EPR and Bohr. By relaxing this assump- tion and allowing physical correlations to arise from shared temporal structure rather than local spatial variables or superluminal influence, one may satisfy the EPR realism criterion without violating relativistic causality or Bell-type constraints. Quantum mechanics is thus interpreted as operationally complete but ontologically incomplete, with quantum indeterminacy emerging from dynamical interactions with a proposed underlying temporal structure.

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Based on a thought experiment the Einstein-Podolsky-Rosen paper’s authors concluded that in quantum mechanics the mathematical objects called wave functions fail to describe the physical reality and consequently quantum theory is incomplete. They left open the question of whether or not a complete description of the physical reality exists, but expressed their belief that such a complete theory is possible. In this paper I show that indeed a theory that gives a complete description of the physical reality exists.

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Does Energy Discreteness Follow Directly From the Maxwell-Boltzmann Probability?

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In Newtonian mechanics there exists a continuous x i.e. for a conservative force: .5mv(x)v(x) + V(x) = E with x taking any value. This is associated with the idea of dx→0. As a result one may choose an x and x+dx with dx→0 and v(x) and v(x+dx) become arbitrarily close in value. It is almost as if their identities merge. In (1) entropy and average energy are calculated using the Maxwell-Boltzmann MB factor exp(-e/T) and a continuous energy. The results E= NT (k=1) and S = -ln(T/To) with To being an integration constant show that one must have T>To because T→0 does not lead to S→0. Thus there is a problem if one uses continuous energy. In other words continuous energy is rejected.. (1) then considers an equally spaced energy i.e. e=bn, n=0,1,2,3 … and calculates energy and entropy again. In this case S→0 as T→0. Thus (1) concludes that it is entropy which leads to the discretization of energy In this note we try to argue that discretization of energy is already implied by the MB factor. The MB factor exp(-energy/T) where T is a math parameter called temperature represents a probability. In other words, different energies have different probabilities i.e. one must distinguish between them. Having two energy values merge is a problem now because one has a second parameter T which may also go to zero i.e. e2-e1→0 and T→0 leads to trouble because exp(-e2/T) does not tend to zero as it should if e1=0. We argue that the underlying reason for e1 and e2 being discretely different is that one cannot use the probability/T formalism i.e. MB factor unless interactions occur. We argue that such two body interactions cannot ultimately transfer or remove a de→0 and keep e1 and e2 distinct. In other words the interaction/collision is ultimately linked to a finite energy transfer even though T→0. As a result energy should be discretized in an equilibrium scenario. This argument does not make use of entropy explicitly although implicitly having exp(-e2/T)-->0 as T→0 (say for a 2 level system) means that the particle is in state e1 which may be associated with an entropy of 0 if one ignores internal features of this state. We also note that the continuous energy result E=NT, and not just the entropy, leads to trouble because as T becomes extremely tiny E which is an average of say e1 and e2 with e1=0 as an example approaches T in magnitude. The smaller T becomes the smaller e2 becomes which e2 and e1 no longer have separate identities, but in such a case one does not have an equilibrium scenario either. In other words exp(-e/T) implies interactions between distinguishable states with respect to energy.

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•May 3, 2026•0 citations
Two problems with the Einstein-Podolsky-Rosen argument originate from the difficult-to-explain continual dismissal of Minkowski’s demonstration that the concept of spacetime represents a real four-dimensional world and is not just a mathematical space. The uncritical employment of the traditional three-dimensional language to the description of this argument leads (e.g., in its Bohm's version) to those problems: (1) due to the collapse of the common wavefunction of the constituents 1 and 2 of a disintegrated system, caused by the measurement of 1's spin (event E1E_{1}E1​), and due the conservation of the total spin, 2's spin is \textit{instantaneously} determined (event E2E_{2}E2​), which in three-dimensional language inescapably means that E2E_{2}E2​ is \textit{caused} by E1E_{1}E1​ (using merely a different word -- correlation' -- does not explain anything in three-dimensional language); (2) events $E_{1}$ and $E_{2}$ are simultaneous \textit{only} for an observer $A$, who was at rest with respect to the disintegrated system, and therefore the total spin is not conserved for arbitrarily large periods of time for all observers in relative motion with respect to $A$ and there exists a class of observers $B$ for whom event $E_{2}$ occurs \textit{before} $E_{1}$, which demonstrates the inadequacy of the fundamental implicit assumption that the physical world is three-dimensional. When the reality of spacetime is explicitly recognized, (1) the paradoxes of the non-conservation of the total spin and that $E_{2}$ happens before $E_{1}$ for observers $B$ do not arise (because there is no before' and `after' in spacetime) and the statement that there is a correlation between E1E_{1}E1​ and E2E_{2}E2​ makes a perfect sense, and (2) a spacetime model of the quantum object can then be considered (by also taking into account the non-fully-realized experimental fact that the quantum object \textit{actually} exists everywhere where its wavefunction is different from zero) in order to address the fundamental incompleteness of quantum mechanics -- that it deals not with the quantum object itself, but only with its states. The paper ends with a discussion of a prediction by the proposed spacetime model of the electron that can be tested experimentally probably by the quadratic Stark effect.
From a phenomenological and experimental viewpoint, quantum mechanics is remarkably successful in explaining effects and processes in the microscopic world. Recently, however, a growing body of literature has revisited the theory's own formal foundations, specifically addressing issues of self-consistency and completeness. As a major historical example of these foundational challenges, the Einstein-Podolsky-Rosen (EPR) argument famously claimed that the theory is incomplete. While many valid criticisms and refutations of the EPR logic exist, they generally rely on a combination of technical results and conceptual objections to EPR's interpretive assumptions, thus transcending the plain quantum framework itself. Motivated by these trends of examining the theory's structural limits, here we revisit the EPR argument. Focusing on elements essential to the EPR reasoning, we first analyze general quantum correlations for EPR states: (i) the fact that their observables are always associated with non-commuting operators, and (ii) the nature of the correlated information obtained through measurement. From these two points alone, and relying strictly on the core rules of quantum mechanics, we demonstrate how to overturn the alleged EPR incompleteness without invoking any extraneous propositions. Consequently, we show that the standard formalism alone suffices to resolve such type of skepticism regarding the theory's physical reach. This offers, at least in a paradigmatic instance, a powerful indication of a structurally well-founded, self-consistent quantum theory.
The Einstein–Podolsky–Rosen (EPR) argument was originally posed as a challenge to the completeness of quantum mechanics, rather than its empirical adequacy. While subsequent developments—most notably Bell’s theorem and experimental tests of nonlocal correlations— have constrained classes of hidden-variable theories, they have not resolved the underlying on- tological question raised by EPR: whether the quantum state exhausts physical reality. In this paper, we revisit the EPR criterion of completeness from the perspective of a temporally grounded physical framework, the Temporal Inertia Framework (TIF). We argue that the orig- inal EPR dilemma rests on an implicit assumption that physical reality must be specified on spacelike hypersurfaces, an assumption shared by both EPR and Bohr. By relaxing this assump- tion and allowing physical correlations to arise from shared temporal structure rather than local spatial variables or superluminal influence, one may satisfy the EPR realism criterion without violating relativistic causality or Bell-type constraints. Quantum mechanics is thus interpreted as operationally complete but ontologically incomplete, with quantum indeterminacy emerging from dynamical interactions with a proposed underlying temporal structure.
Based on a thought experiment the Einstein-Podolsky-Rosen paper’s authors concluded that in quantum mechanics the mathematical objects called wave functions fail to describe the physical reality and consequently quantum theory is incomplete. They left open the question of whether or not a complete description of the physical reality exists, but expressed their belief that such a complete theory is possible. In this paper I show that indeed a theory that gives a complete description of the physical reality exists.
In Newtonian mechanics there exists a continuous x i.e. for a conservative force: .5mv(x)v(x) + V(x) = E with x taking any value. This is associated with the idea of dx→0. As a result one may choose an x and x+dx with dx→0 and v(x) and v(x+dx) become arbitrarily close in value. It is almost as if their identities merge. In (1) entropy and average energy are calculated using the Maxwell-Boltzmann MB factor exp(-e/T) and a continuous energy. The results E= NT (k=1) and S = -ln(T/To) with To being an integration constant show that one must have T>To because T→0 does not lead to S→0. Thus there is a problem if one uses continuous energy. In other words continuous energy is rejected.. (1) then considers an equally spaced energy i.e. e=bn, n=0,1,2,3 … and calculates energy and entropy again. In this case S→0 as T→0. Thus (1) concludes that it is entropy which leads to the discretization of energy In this note we try to argue that discretization of energy is already implied by the MB factor. The MB factor exp(-energy/T) where T is a math parameter called temperature represents a probability. In other words, different energies have different probabilities i.e. one must distinguish between them. Having two energy values merge is a problem now because one has a second parameter T which may also go to zero i.e. e2-e1→0 and T→0 leads to trouble because exp(-e2/T) does not tend to zero as it should if e1=0. We argue that the underlying reason for e1 and e2 being discretely different is that one cannot use the probability/T formalism i.e. MB factor unless interactions occur. We argue that such two body interactions cannot ultimately transfer or remove a de→0 and keep e1 and e2 distinct. In other words the interaction/collision is ultimately linked to a finite energy transfer even though T→0. As a result energy should be discretized in an equilibrium scenario. This argument does not make use of entropy explicitly although implicitly having exp(-e2/T)-->0 as T→0 (say for a 2 level system) means that the particle is in state e1 which may be associated with an entropy of 0 if one ignores internal features of this state. We also note that the continuous energy result E=NT, and not just the entropy, leads to trouble because as T becomes extremely tiny E which is an average of say e1 and e2 with e1=0 as an example approaches T in magnitude. The smaller T becomes the smaller e2 becomes which e2 and e1 no longer have separate identities, but in such a case one does not have an equilibrium scenario either. In other words exp(-e/T) implies interactions between distinguishable states with respect to energy.
Twentieth-century physics was shaped by two profound revolutions. The first, Einstein's relativity, banished absolute space and time from the foundations of physics. Motion, Einstein showed, possesses no absolute meaning—only relative motion between observers merits physical description. The second, quantum mechanics, dismantled the classical notion of determinacy. A physical quantity, before measurement, is not merely unknown but genuinely indefinite, suspended in a superposition of possibilities. These two revolutions, for all their splendor, have never spoken a common language. General relativity describes a world of continuous, deterministic geometry; quantum mechanics, a world of discrete, probabilistic events. Their unification—a theory of quantum gravity—remains the central unsolved problem of theoretical physics. We diagnose this impasse not as a technical failure, but as a conceptual incompleteness. The two revolutions, in their original domains, stopped short of questioning a premise both inherited from classical thought: that physical reality, determinacy, and facts themselves are absolute—that they exist independently of the framework through which they are described. Einstein relativized motion but left the existence of spacetime geometry absolute. Quantum mechanics relativized the values of observables but left the fact of an outcome unexplained, consigning it to the mysterious "measurement process." Neither theory asked: in what sense is a fact—that a quantity has a definite value, that an event has occurred, that a physical reality is thus and not otherwise—itself relative to a descriptive framework? This is the question the present work undertakes to answer. In doing so, it completes the program of relativity—not by appending new terms to old equations, but by extending the principle of relativity to its ultimate domain: being itself.