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首页微观虫洞与纠缠几何:ER=EPR理论的新诠释
在本文中,我们探讨了微观虫洞与纠缠几何之间的联系,特别是在爱因斯坦-罗森(ER)桥和爱因斯坦-波多尔斯基-罗森(EPR)对之间的新视角。最近的研究者提出了一个理论,认为 ER 桥可以被看作是两个黑洞处于最大纠缠状态的体现,这种观点被称为 ER = EPR 关系。这一设想主要是在二次帕拉蒂尼理论的框架下进行讨论的,这是一种替代一般相对论的引力理论,它基于量子力学的修正,特别是通过引入额外的度量张量项。 在二次帕拉蒂尼理论中,一个关键的发现是所有带电解都具有虫洞结构,这与传统空间时间观念不同,暗示着可能存在一种微观的、泡沫状的几何结构。这种结构是由量子真空的波动驱动的,其中包含了粒子-反粒子对的自发创造和湮灭过程。这些粒子对在量子纠缠中形成,尽管它们是通过虫洞相互连接的,但这种连接是非纠缠的。然而,由于这些粒子是从真空中生成的,它们必须以单态存在,这就意味着它们天然地相互纠缠。 这一理论不仅加深了我们对黑洞行为的理解,也挑战了经典物理学对于虫洞的理解。ER = EPR 关系的支持表明,量子纠缠可能不仅仅是量子信息传输的一种机制,也可能与宇宙基本结构的深层次联系有关。此外,这个研究对于探索量子引力、量子宇宙学以及可能的虫洞旅行或信息传输途径提供了新的思考方向。 总结来说,这篇发表于《欧洲物理杂志C》的文章,通过对二次帕拉蒂尼理论的分析,揭示了微观虫洞如何作为量子纠缠几何的一种体现,从而将黑洞物理与量子力学的奇妙特性相结合,为我们理解宇宙的量子性质和微观结构提供了新的见解。
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Eur. Phys. J. C (2014) 74:2924
DOI 10.1140/epjc/s10052-014-2924-1
Regular Article - Theoretical Physics
Microscopic wormholes and the geometry of entanglement
Francisco S. N. Lobo
1,a
, Gonzalo J. Olmo
2,b
, D. Rubiera-Garcia
3,c
1
Centro de Astronomia e Astrofísica da Universidade de Lisboa, Campo Grande, Ed. C8, 1749-016 Lisbon, Portugal
2
Departamento de Física Teórica and IFIC, Centro Mixto Universidad de Valencia-CSIC, Universidad de Valencia, Burjassot, 46100 Valencia, Spain
3
Departamento de Física, Universidade Federal da Paraíba, João Pessoa, Paraíba 58051-900, Brazil
Received: 14 March 2014 / Accepted: 26 May 2014 / Published online: 7 June 2014
© The Author(s) 2014. This article is published with open access at Springerlink.com
Abstract It has recently been suggested that Einstein–
Rosen (ER) bridges can be interpreted as maximally entan-
gled states of two black holes that form a complex Einstein–
Podolsky–Rosen (EPR) pair. This relationship has been
dubbed as the ER = EPR correlation. In this work, we con-
sider the latter conjecture in the context of quadratic Palatini
theory. An important result, which stems from the under-
lying assumptions as regards the geometry on which the
theory is constructed, is the fact that all the charged solu-
tions of the quadratic Palatini theory possess a wormhole
structure. Our results show that spacetime may have a foam-
like microstructure with wormholes generated by fluctua-
tions of the quantum vacuum. This involves the spontaneous
creation/annihilation of entangled particle–antiparticle pairs,
existing in a maximally entangled state connected by a non-
traversable wormhole. Since the particles are produced from
the vacuum and therefore exist in a singlet state, they are
necessarily entangled with one another. This gives further
support to the ER = EPR claim.
1 Introduction
In the context of the firewall debate [1,2] (see [3]for
earlier work), it has recently been argued that Einstein–
Podolsky–Rosen (EPR) correlations [4] and Einstein–Rosen
(ER) bridges [5] are actually related [6]. For instance, the
ER bridge between two black holes is created by EPR-
like correlations between the microstates of the two black
holes [6]. This conjecture has been schematically dubbed the
ER = EPR correlation. More specifically, the ER bridge is a
special kind of EPR correlation, where the entanglement has
a geometric manifestation. Despite the fact that the two black
holes exist in separate and non-interacting spacetimes, their
a
e-mail: flobo@cii.fc.ul.pt
b
e-mail: gonzalo.olmo@csic.es
c
e-mail: drubiera@fisica.ufpb.br
geometry is connected by an ER bridge, and the entanglement
is represented by identifying the bifurcate horizons [6]. Note
that the ER bridge construction is due to the fact that specific
coordinate systems naturally cover the two asymptotically
flat regions of maximally extended spacetimes [5], and the
key ingredient of the bridge construction is the existence of
an event horizon. Thus, although the geometry is connected
through the bridge/tunnel, the two exterior geometries are
not in causal contact and information cannot be transmitted
across the bridge [7]. This is an essential point to be consis-
tent with the fact that entanglement does not imply non-local
signal propagation in order to conserve causality.
Recently, the ER = EPR claim received further support
through specific models. Indeed, it was shown that the holo-
graphic dual of two colored quasiparticles can be constructed
in maximally supersymmetric Yang–Mills theory entangled
in a color singlet EPR pair [8,9]. In the holographic dual the
entanglement is encoded in a geometry of a non-traversable
wormhole on the worldsheet of the flux tube connecting the
pair. In this context, it was also pointed out that the proposed
bulk dual of an entangled quark–anti-quark pair described
above [8] corresponds to the Lorentzian continuation of the
tunneling instanton describing a Schwinger pair creation in
the dual field theory [10]. This observation supports and fur-
ther explains the claim in [8] that the bulk dual of an EPR
pair is a string with a wormhole on its world sheet. It was
also suggested that this constitutes an AdS/CFT realization
of the creation of a Wheeler wormhole [11].
Wheeler used the source-free Maxwell equations, coupled
to Einstein gravity, with the seasoning of nontrivial topology,
to build models for classical electrical charges and all other
particle-like entities in classical physics [11]. This analy-
sis culminated in the “geon” concept, coined by Wheeler
to denote a “gravitational–electromagnetic entity”. Building
on this pioneering work, Misner and Wheeler [12], in 1957,
presented a tour de force wherein Riemannian geometry of
manifolds of nontrivial topology was investigated with an
123
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