# How Can Teleportation involve Time Travels?

**Albert Einstein**'s **Theory** of **General Relativity** permits the **existence** of __ Closed-Timelike Curve__s (

__s) [__

**CTC**__1__], which are paths within Space - Time that, if traversed, would enable a

**traveler**to interact with their own

__self, whether that traveler be__

**Past****human**or

**elemental particle**.

**Kurt Gödel**was among the

**first**to highlight the

**possibility**of CTCs, and subsequent research has proposed various

**Space - Time configurations**accommodating these

**curves**.

However, such scenarios of __ Time Travel__ inevitably introduce

**paradoxes**, such as the infamous

__[__

**Grandfather Paradox**__2__], wherein the time traveler inadvertently alters the past in a way that prevents their

**own existence**. This concept troubled even Einstein, who was close friends with Gödel. The

**reconciliation**of CTCs with quantum mechanics poses a formidable challenge, tackled through various approaches, including

**Path-Integral Techniques**[

__3__].

## The Removed “Memories” Approach...

Any theory aiming to **unify** quantum mechanics and gravity must address the **complexities** inherent in closed timelike curves, which introduce **nonlinearities** that challenge the **Linearity** [__4__] of conventional quantum mechanics. **Deutsch** proposed a **resolution** in his influential work, suggesting a **Self-Consistency Condition** (__Equation 1__) concerning the **states** within CTCs. This condition demands equivalence between measurements at the CTC's entrance and exit. However, this **formulation** necessitates the assumption of __ Factorization__, implying

**invalidation**of

**Future**[

__5__] "

**memories**". However, Deutsch's theory has faced

**criticism**for

**apparent inconsistencies**.

**Equation 1**. Deutsch Self-Consistency Condition form

where [math]\small{\rho_{CTC}}[/math] is the **density matrix** (further information in ** here**, Section 1) of the system state, [math]\small{A}[/math] inside the CTC; [math]\small{Tr_{A}}[/math] is the

__of [math]\small{A}[/math]; [math]\small{U}[/math] is the__

**Trace**__; [math]\small{\rho_{A}}[/math] is the__

**Unitary Matrix****density matrix**of [math]\small{A}[/math] and [math]\small{U^{\dagger}}[/math] is the

**transpose unitary matrix**.

## A New View: Overcoming the CTCs

In contrast, while acknowledging the **strangeness** of time travel **quantum mechanics**, **P-CTC**s, based on the __ Novikov Principle__, appear to offer a

**less problematic framework**. The concept of

**Probabilistic Closed Timelike Curve**s (

**P-CTC**s) [

__6__] was initially conceived to tackle the

**enigma**posed by the

**integration**of quantum mechanics into the framework of General Relativity, particularly concerning closed-timelike curves. However, its implications extend

**beyond**this

**specific domain**, offering insights into the

**potentiality**of time travel in

**alternative scenarios**.

**Equation 2**. P-CTC External System Time Evolution Equation

**N** [math]\small{[\rho]}[/math]
is the **Time Evolution** of **External System**; [math]\small{\rho}[/math] is the **density matrix** of external system; [math]\small{Tr_{E}}[/math] is the **trace** of the **Hilbert space** (further information in ** here**, Section 2), [math]\small{E}[/math] over the system into the CTC; [math]\small{C_{A}}[/math] is the

**partial trace**of [math]\small{A}[/math]; [math]\small{U_{AE}}[/math] is the

**unitary matrix**coupling the

**internal**and

**external systems**; [math]\small{{C_{A}}^{\dagger}}[/math] is the

**transpose partial trace**of [math]\small{A}[/math].

Fundamentally, any quantum theory that permits non-linear processes like the __ Projection__ onto specific states, such as the

**Entangled States**(further information in

**, references) associated with P-CTCs, inherently allows for the prospect of time travel, even in the**

__here__**absence**of Space - Time configurations supporting closed-timelike curves. The P-CTS mechanism translates mathematically to the

**time evolution**of the

**external system**being , with the

**absence**of evolution enforced if

**certain conditions**(

__Equation 2__) are met. The

**paradigm**of

**non-general relativistic P-CTCs**can be instantiated through the

**generation**and

**projection**onto entangled pairs of particle-antiparticle. This method mirrors renowned

__'s__

**Wheeler**__[__

**Thought Experiment**__7__] of a telephone call through time.

**Figure 1**. A typical Macroscopic Example of Quantum Tunneling: a Ball (Subatomic Particle) which overcomes a Wall (Potential Energy Barrier)

Although the process of projection is inherently nonlinear, defying **deterministic implementation** within conventional quantum mechanics, it can be executed in a **probabilistic manner**. Consequently, **experimental validation** of P-CTCs is achievable through __ Quantum Teleportation__ experiments, where outcomes corresponding to the desired entangled-state output are selectively post-processed. Should it transpire that the linearity of quantum mechanics is merely an

**approximation**, and projection onto specific states indeed manifests, such occurrences could potentially be witnessed at the singularities (further information in

**) of black holes.**

__here__In such a scenario, even in the absence of general relativistic closed-timelike curves, the realization of time travel might still be **feasible**. The theoretical framework of P-CTCs elucidates that quantum time travel can be conceived as a **form** of **retrograde** __ Quantum Tunneling__ (

__Figure 1__), permitting

**temporal traversal devoid**of a classical trajectory from future to past. P-CTCs rely on

__(__

**Destructive Interference**__Figure 2__) to prevent self-contradictory events, emphasizing a different self-consistency condition from

**Deutsch's approach**.

## Two Different Perspectives

Illustrating the link between **P-CTC**s and **teleportation** provides **further insights**, showcasing their **behavior** through __ Qubit__s. This demonstration underscores the

**compatibility**of P-CTCs with

__s and the extension to infinite-dimensional scenarios. Presently,__

**Higher-Dimensional System****no definitive conclusion**favors either approach (Deutsch or P-CTCs), given their respective foundations and consistency with

**different theoretical frameworks**. The

**aspiration**in elaborating on the theory of P-CTCs is that it may furnish valuable insights for formulating a

**Quantum Theory**of

**Gravity**. By shedding light on one of the most

**enigmatic ramifications**of general relativity—the prospect of time travel—this theory may contribute significantly to our understanding of Gravity at the quantum level.

**Figure 2**. A classic Experiment of Waves Interference: Ripples in the Water

- arXiv. "Can we travel to the past? Irreversible physics along closed timelike curves
"
__https://arxiv.org/pdf/1912.04702.pdf__ - ResearchGate. "Grandfather paradox from a new perspective"
__https://www.researchgate.net/publication/361446083_Grandfather_paradox_from_a_new_perspective#fullTextFileContent__ - Galileo.phys. "Path Integrals in Quantum Mechanics"
__https://galileo.phys.virginia.edu/classes/751.mf1i.fall02/PathIntegrals.htm__ - ScienceDirect. "Consistency and linearity in quantum theory"
__https://pdf.sciencedirectassets.com/271541/1-s2.0-S0375960100X01843/1-s2.0-S0375960198002898/main.pdf?X__ - LinkedIn. "Time Travel is Real: Unraveling the Wonders of Traveling to the Future"
__https://www.linkedin.com/pulse/time-travel-real-unraveling-wonders-traveling-future-manjunath-m-r/__ - American Physical Society. "Closed Timelike Curves via Postselection: Theory and Experimental Test of Consistency"
__https://journals.aps.org/prl/pdf/10.1103/PhysRevLett.106.040403__ - Horizon IIT. "The Delayed Choice Quantum Eraser – does the future affect the past?"
__https://horizoniitm.github.io/dcqe/__