We see that LNIFs that correspond to Newton’s first order non-tidal “gravity pseudo-force” (Levi-Civita connection) require two arrows of time in opposite directions in accord with
Accommodating
Retrocausality with Free Will
Yakir Aharonov 1;2, Eliahu Cohen 1;3 & Tomer Shushi 4
1 School of Physics and Astronomy, Tel Aviv University, Tel Aviv, Israel. E-mail:
2 Schmid College of Science, Chapman University, Orange, California, USA. E-mail:
3 H. H. Wills Physics Laboratory, University of Bristol, Bristol, UK. E-mail:
4 University of Haifa, Haifa, Israel. E-mail:
Editors: Kunihisa Morita, Danko Georgiev & Kelvin McQueen
Article history: Submitted on September 22, 2015; Accepted on December 17, 2015; Published on January 11, 2016.
"Retrocausal models of quantum mechanics add
further weight to the conflict between causality
and the possible existence of free will. We analyze
a simple closed causal loop ensuing from the interaction
between two systems with opposing thermodynamic
time arrows, such that each system can forecast
future events for the other. The loop is avoided
by the fact that the choice to abort an event thus
forecasted leads to the destruction of the forecaster’s
past. Physical law therefore enables prophecy of future
events only as long as this prophecy is not revealed
to a free agent who can otherwise render it
false. This resolution is demonstrated on an earlier
finding derived from the two-state vector formalism,
where a weak measurement’s outcome anticipates a
future choice, yet this anticipation becomes apparent
only after the choice has been actually made. To
quantify this assertion, weak information is described
in terms of Fisher information. We conclude that an
already existing future does not exclude free will nor
invoke causal paradoxes. On the quantum level, particles
can be thought of as weakly interacting according
to their past and future states, but causality remains
intact as long as the future is masked by quantum
indeterminism.”
The future is unmasked in post-quantum theory in which the action-reaction feedback-control loop between quantum information and classical be-ables destroys locally random quantum noise i.e. retrocausal signaling via entanglement.
arXiv:1408.2836 [pdf, ps, other]
Quantum interview
Antony Valentini
Comments: 21 pages, "Elegance and Enigma: The Quantum Interviews", ed. M. Schlosshauer (Springer, 2011)
Subjects: Quantum Physics (quant-ph); General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th)
It is argued that immense physical resources - for nonlocal communication, espionage, and exponentially-fast computation - are hidden from us by quantum noise, and that this noise is not fundamental but merely a property of an equilibrium state in which the universe happens to be at the present time. It is suggested that 'non-quantum' or nonequilibrium matter might exist today in the form of relic particles from the early universe. We describe how such matter could be detected and put to practical use. Nonequilibrium matter could be used to send instantaneous signals, to violate the uncertainty principle, to distinguish non-orthogonal quantum states without disturbing them, to eavesdrop on quantum key distribution, and to outpace quantum computation (solving NP-complete problems in polynomial time).
arXiv:quant-ph/0203049 [pdf, ps, other]
Subquantum Information and Computation
Antony Valentini
Comments: 10 pages, Latex, no figures. To appear in 'Proceedings of the Second Winter Institute on Foundations of Quantum Theory and Quantum Optics: Quantum Information Processing', ed. R. Ghosh (Indian Academy of Science, Bangalore, 2002). Second version: shortened at editor's request; extra material on outpacing quantum computation (solving NP-complete problems in polynomial time)
arXiv:1508.01940v2 [gr-qc] 7 Jan 2016
Quantum Field Theory in Accelerated Frames
Arundhati Dasgupta,∗ 4401 University Drive, University of Lethbridge, Lethbridge T1K 3M4.
∗ E-mail:
"In this paper we re-investigate the Bogoliubov transformations which relate the Minkowski inertial vacuum to the vacuum of an accelerated observer. We implement the transformation using a non-unitary operator used in formulations of irreversible systems by Prigogine. We derive a Lyapunov function which signifies an irreversible time flow. We extend the formalism to the black hole space-time which has similar near-horizon geometry of an accelerated observer, and in addition show that thermalization is due to presence of black hole and white hole regions. Finally we discuss an attempt to generalize quantum field theory for accelerated frames using this new connection to Prigogine transformations.
I. INTRODUCTION
In 2015 the world celebrates 100 years of General Relativity (GR). Einstein discovered GR while trying to generalize the theory of special relativity to non-inertial and accelerating frames. In this new theory physics was invariant under ‘general coordinate transformations’ including transformations to frames of accelerated observers. Simultaneously as GR quantum mechanics (QM) was being developed as a theory of the atomic and molecular regime. Initially the theory of QM was formulated using ‘Galilean’ invariant Schro ̈dinger equation. The QM for inertial or constant velocity frames, which respected the laws of Einstein’s special theory of relativity was formulated much later. Quantum field theory (QFT) was developed initially by Dirac [1] and then in the 1950’s and 1960’s by various physicists who generalized quantum mechanics for relativistically invariant systems [2]. The obvious question which follows is what is QFT in accelerated frames, and how does one reconcile this with gravity as GR? Can this lead to the formulation of a quantum GR? This has been a notoriously difficult task [3], however, our perspective is that the clues for a quantum GR theory are hidden in QFT for accelerated observers. In this paper we investigate QFT for accelerated observers using a formulation in complex physics due to Prigogine [4], and try to obtain some insights from the formulation for a quantum theory of GR.
We begin by re-investigating an accelerated observer in Minkowski space-time, where the physics is well understood. An accelerated observer’s frame of reference is described using the Rindler coordinates [5, 6]. In this frame, the Minkowski causal diamond appears as causally disconnected into two Rindler universes with time flowing in the forward direction in one universe and reverse direction in the other. An accelerating observer restricted to one Rindler universe sees the Minkowski vacuum as a state with particles distributed in a thermal spectrum with a temperature proportional to his/her proper acceleration. This can be observed by obtaining the creation and annihilation operators of the Rindler QFT’s as linear transforms of the Minkowski operators [8, 9]. The transformation known as the Bogoliubov transformation can also be implemented on the vacuum states. We formalize these transformations, and obtain them as non-unitary operators which act on the density matrices of the Minkowski space-time. The density matrices of two Rindler Hilbert spaces (one with time flowing forward and the other with time flowing backward) are obtained using this and the individual operators of the Rindler Hilbert space are also obtained using non-Unitary transformations. We find that these ‘formalized’ transformations have been previously studied in physics of irreversible systems due to Prigogine [4].
I. Prigogine [4] had reformulated complex physics, where systems are characterized by thermalization and irreversible time evolution using new ‘star-Hermitian’ operators. These were non- unitary operators, and ‘star-Hermitian’ is an operation which in addition to Hermitian conjugation involves time reversal. Curiously these operators were defined by implementing a linear transform from density matrices of normal ‘unitary’ Hilbert space to density matrices of an irreversible system. In the transformed Hilbert space the time evolution is not unitary and ‘entropy’ production occurs due to presence of an anti-Hermitian term in the star Hermitian evolution operator. The presence of entropy and irreversibility in the transformed Hilbert space is identified by building a Lyapunov function which decreases in any physical process. We show that each of the Rindler vacuum density matrix is a very similar ‘non-unitary’ operator transform of the Minkowski vacuum density matrix: the operators are non-unitary. The time evolution equation in the ‘Rindler’ Hilbert-space is non-unitary and we construct a Lyapunov function for the Rindler observer and show that this has irreversible behavior, signifying the existence of ‘entropy’. However, what is interesting is that unlike the systems discussed in [4], the transformation connects Hilbert spaces of two different coordinate systems, with two different times. Thus, if we flow the Lyapunov function in Minkowski time, there is no entropy creation. If instead we flow the Lyapunov function using the Rindler Hamiltonian, there is monotonic flow.
We also clarify some of the criticisms of Prigogine’s formalism by providing a very concrete and transparent system for its implementation. In particular, for the Rindler system, we show that the initial unitary Hilbert space is mapped to two different Hilbert spaces by two versions of the Prigogine transformation. One Hilbert space has the time as reverse of the time of the other Hilbert space. Irreversibility arises in one Hilbert space due to the ignorance of one of the Hilbert spaces, and choosing one of the Prigogine transformation over the other, representing unidirectional time flow.
We then generalize the above formalism to the case of the black hole space-time. The near horizon region of the black hole has the same metric as that of the Rindler observer. The bifurcate horizon disconnects two asymptotics (I and II as in Figure 2), which play the same role as two Rindler universes. The Kruskal vacuum of the [9] of the space-time plays the role of the Minkowski vacuum and a transformation of this to the individual I and II Rindler vacuums is derived as a Prigogine transformation. The black hole space-time is different from the Minkowski space-time, as it has black hole and white hole regions, where matter can propagate in one direction only, into the black hole and out of the black hole. This gives the entropy of the black hole a real existence ‘independent of observer’ as opposed to Minkowski-Rindler example, but induced due to boundary conditions.
Having formulated two different examples of QFT as observed by accelerating observers, we finally formulate a general theory of transforms of quantum density matrices of QFT from inertial to non-inertial frames, and discuss the implications of this.
For other discussions/derivations on Rindler space-time thermodynamics see [10, 11] and for discussions on accelerated frames see [12, 13] and references therein. In the next discussion we describe the formulation due to Prigogine for physics of complex systems and the star-Hermitian operators. We introduce the generic quantum field theory vacuum and discuss the transformation to the Rindler vacuum in the second section. In the third section we formalize these transformations as Prigogine transformations. In this section we also construct the Lyapunov function and the time evolution which shows irreversible behavior in the Rindler frame. The fourth section deals with accelerating observer near a black hole horizon. The fifth section generalizes QFT for accelerating frames using the connection to the Prigogine transformation. The sixth section is a conclusion.
3
A. The Complex Physics
Nature is inherently complex, and systems evolve irreversibly. In physics we idealize and iso- late systems and formulate reversible, unitary laws describing the dynamics. In reality synergistic behavior of systems comprised of many fundamental entities is prevalent in natural phenomena. A typical system is the ‘ideal gas’ consisting of molecules whose individual dynamics is reversible and unitary but collectively they are ‘thermalized’ and possess entropy. It is generally agreed that ‘entropy’ arises due to loss of information of the system, and irreversibility results due to ‘random interactions’ amongst the constituents which introduces a degree of unpredictability in the system. The origin of ‘entropy’ and unidirectional time evolution was initiated from Boltz- mann’s H-theorem [14]. Since then variations of the H-theorem have tried to re-interpret the origin of entropy. One such attempt is due to Prigogine whose ideas tried to bring to the physics of complex systems the concept of microscopic entropy. In a very fundamental formulation of irre- versible systems, he introduced operators which transformed density matrices of a typical Hilbert space into density matrices of a Hilbert space whose time evolution had irreversible behavior. In the transformed Hilbert space the time evolution equation was non-unitary [4]. There is a very subtle difference between the usual ‘thermalization process’ where the irreversibility emerges in the macroscopic averaging process, and the irreversibility of the Prigogine formulation, here irre- versibility is introduced using a non-unitary transform from a unitary Hilbert space in the quantum regime, and thus microscopic in origin.
...
VI. CONCLUSIONS
Thus we showed that the Bogoliubov transformation which maps Minkowski vacuum to the vacuum of a Rindler observer is a Prigogine transformation. The existence of a Lyapunov function shows that the Rindler observer perceives irreversibility. The Rindler observer sees one half of a direct product space, one in which time flows forward and the other in which time flows backward. The Prigogine transformation chooses one of the spaces with one time flow, and thus physics for a Rindler observer is irreversible. The transformation which takes the Minkowski density matrix to the other Rindler Hilbert space’s density matrix, in this example happens to be identical. However, it can be labeled as star-Unitary operator 2. Thus there are two Prigogine transformations, one which maps to Hilbert space in which time is flowing forward, and the other to the Hilbert space in which time flows backward. In the Rindler example there is no loss of information, entire information is contained in the direct product of two Hilbert spaces (HI ⊗HII). Mapping to one HI or HII gives rise to irreversible physics.
The tracing mechanism, which traces over one of the HI or HII basis states when the Minkowski state is written in the direct product Hilbert space basis is a different from the Prigogine map discussed here.The star-Unitary operators ‘break’ the time reversal symmetry of the direct product space HI ⊗HII, by projecting the Minkowski density matrices defined in the direct product space, to one of the Rindler Hilbert spaces. Thus this transformation, is ‘microscopic’ as implemented on the density matrices, and does not involve a tracing mechanism. The end result is though the same, the remaining density matrix/quantum state is written in one of the Hilbert spaces, HI or HII. This is a concrete example of the implementation of the Prigogine formulation, and clarifies the role of the star-Unitary operator in a evidently time reversal symmetric system. There is a breaking of symmetry due to the use of the star-Unitary operators. However, there are two star- Unitary operators for each time direction (in this example the ‘time directions’ are represented by HI and HII Hilbert spaces). This is in agreement with a discussion on the Prigogine formalism [22].
The same formalism can be used for Bifurcate Killing horizons where the near horizon observer is accelerating with respect to the background metric. However for the black hole, additional boundary conditions due to presence of white whole and black hole regions cause thermalisation not present in the Minkowski- Rindler example.
Our eventual aim is to develop a generic QFT for accelerated observers, including that which is valid in arbitrary curved space-times. To define quantum field theory in space-times without Killing vectors, one needs to use the formalism of Algebraic Quantum Field Theory and Hadamard condition [20], and this is
27
work in progress [21]. One also has to address the problems of interaction of the QFT and renormalization in accelerating frames as in [12].
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