A new understanding of Einstein-Rosen bridges

TL;DR

The paper argues that standard QFTCS, built on a fixed arrow of time, encounters unitarity and information-clarity problems near horizons. It proposes a direct-sum quantum theory (DQFT) in which quantum states live in geometric superselection sectors associated with parity-conjugate regions of spacetime, connected by discrete symmetries and governed by inverted harmonic oscillator dynamics near horizons. This framework yields horizon-local unitary evolution, reinterprets ER=EPR as horizon-level entanglement across SSS rather than geometric wormholes, and extends to inflation where direct-sum inflation (DSI) predicts parity asymmetries in the CMB with observational support from Planck data. The work also unifies BH, Rindler, de Sitter, and inflationary physics under a common IHO-centric horizon structure, offering a testable path toward gravity–quantum unification and observer complementarity without invoking Planck-scale modifications. Overall, DQFT provides a mathematically explicit, observationally testable route to reconcile QFT with curved spacetime and gravity through horizon-induced two-time structures and geometric superselection rules.

Abstract

The formulation of quantum field theory in Minkowski spacetime, which emerges from the unification of special relativity and quantum mechanics, is based on treating time as a parameter, assuming a fixed arrow of time, and requiring that field operators commute for spacelike distances. This procedure is questioned here in the context of quantum field theory in curved spacetime (QFTCS). In 1935, Einstein and Rosen (ER), in their seminal paper (Einstein and Rosen 1935 Phys. Rev. 48 73-77), proposed that "a particle in the physical Universe has to be described by mathematical bridges connecting two sheets of spacetime" which involved two arrows of time. Recently proposed direct-sum quantum theory reconciles this ER's vision by introducing geometric superselection sectors associated with the regions of spacetime related by discrete transformations. We further establish that the quantum effects at gravitational horizons involve the physics of quantum inverted harmonic oscillators that have phase space horizons. This new understanding of the ER bridges is not related to classical wormholes, it addresses the original ER puzzle and promises a unitary description of QFTCS, along with observer complementarity. Furthermore, we present compelling evidence for our new understanding of ER bridges in the form of large-scale parity asymmetric features in the cosmic microwave background, which is statistically 650 times stronger than the standard scale-invariant power spectrum from the typical understanding of inflationary quantum fluctuations when compared with the posterior probabilities associated with the model given the data. We finally discuss the implications of this new understanding in combining gravity and quantum mechanics.

Figures (10)

• Figure 1: Phase space of inverted harmonic oscillator representing doubly degenerate positive and negative energy solutions in \ref{['BKsol1']} and \ref{['sol2BK']}. The negative energy trajectories are given by $Q>0,\, P<0$ and $Q<0,\, P>0$ whereas the positive energy trajectories are $Q>0,\,P>0$ and $Q<0,\,P<0$. These double degenerate trajectories are related by \ref{['discreteTPQ']} whereas the positive and negative energy regions are related by \ref{['BKPE']}.
• Figure 2: The figure represents the Left, Right ($z^2\gtrsim t^2$) and Future, Past ($t^2\gtrsim z^2$) regions of Rindler spacetime. The curved lines in the Left and Right regions are constant acceleration $ae^{-a\xi}$ curves with arrows of time $t_R: \infty \to -\infty$ (Left) and $t_R: -\infty \to \infty$ (Right). Future and Past Rindler with arrows indicate changing $z: \pm\infty \to \mp\infty$, $t_R: \mp\infty \to \pm\infty$. The Fuzzy colored lines indicate the Rindler Horizons for Left (Yellow), Right (Green), Future (Cyan), and Past (Pink).
• Figure 3: The picture depicts the new understanding of quantum harmonic oscillator in a direct-sum Hilbert space. Time is a parameter in quantum theory. In contrast, the spatial position is an operator. A quantum state here is described by a direct-sum of two components in parity conjugate points in physical space.
• Figure 4: The DQFT representation of Minkowski spacetime in terms of compactified coordinates $T_p = \arctan\left( t_p+r \right) + \arctan\left( t_p-r \right)$, $T_p\in \left( -\pi+R\to \pi+R \right)$ and $R = \arctan\left( t_p+r \right) -\arctan\left( t_p-r \right)$, $R\in \left( 0,\,\pi \right)$ where $r$ is being the radial coordinate. The left and right triangles are $\mathcal{P}\mathcal{T}$ conjugates of each other. A quantum field operator in DQFT is a direct-sum of two components corresponding to parity-conjugate regions of physical space, with positive energy states defined with opposite arrows of time.
• Figure 5: The picture represents the spacetime conformal diagram of quantum SBH according to DQFT. It contains four regions $I,\, II,\, III,\, IV$, which define geometric SSS to describe quantum fields in Schwarzschild spacetime (applying the near-horizon approximation $r\approx 2GM$). In this picture, the regions $I$ ($III$) and $II$ ($IV$) are related by discrete transformation $\left( U,\,V \right)\to \left( -U,\,-V \right)$. The curved black lines with arrows represent integral curves of killing vector $\partial_t$\ref{['boostUV']} in each region, or in other words, these are the curves of $T^2-X^2 = {\rm constant<0}$ (Region I and II) and $T^2-X^2= {\rm constant}>0$ (Region III and IV). It is trivial to see an analogy between the spacetime of Schwarzschild BH and the phase space of IHO \ref{['phihoeq']}. The red horizontal lines are identified with $r=0$. The quantum field components in the exterior are $\hat{\Phi}_{I}$ and $\hat{\Phi}_{II}$ at parity conjugate regions with opposite arrows of time $t: -\infty \to \infty$ and $t: \infty \to -\infty$ respectively. Whereas in the interior quantum field (component) $\hat{\Phi}_{int}$ evolve according to \ref{['intfield']}.