Quantum fluctuations near a space–time singularity

1989 ◽  
Vol 67 (10) ◽  
pp. 935-938
Author(s):  
K. D. Krori ◽  
P. Borgohain ◽  
Dipali Das Kar
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Bianchi Type ◽  
Quantum Fluctuations ◽  
Space Time ◽  
Operator Technique ◽  
Time Singularity ◽  
Quantum Uncertainty ◽  
Initial Epoch ◽  
The Universe

The well-known operator technique in quantum mechanics is used to study quantum fluctuations near the space–time singularity using Kantowski–Sachs and Bianchi type VIo metrics. In both cases the wave function of the universe is found to diverge near the space–time singularity, indicating the divergence of the quantum uncertainty near the initial epoch.

On the Vanishing of the Cosmological Vacuum Energy

1997 ◽  
Vol 12 (16) ◽  
pp. 1127-1130 ◽  
Author(s):  
M. D. Pollock
Keyword(s):  
Wave Function ◽  
Schrödinger Equation ◽  
Ground State ◽  
Schrodinger Equation ◽  
Vacuum Energy ◽  
Ground State Solution ◽  
Space Time ◽  
State Solution ◽  
Superstring Theory ◽  
The Universe

By demanding the existence of a globally invariant ground-state solution of the Wheeler–De Witt equation (Schrödinger equation) for the wave function of the Universe Ψ, obtained from the heterotic superstring theory, in the four-dimensional Friedmann space-time, we prove that the cosmological vacuum energy has to be zero.

The Future of Fundamental Physics

Daedalus ◽  
2012 ◽  
Vol 141 (3) ◽  
pp. 53-66
Author(s):  
Nima Arkani-Hamed
Keyword(s):  
Twentieth Century ◽  
Quantum Mechanics ◽  
Short Distance ◽  
Quantum Fluctuations ◽  
Building Blocks ◽  
Space Time ◽  
First Century ◽  
Fundamental Physics ◽  
Theoretical Structure ◽  
Radical Ideas

Fundamental physics began the twentieth century with the twin revolutions of relativity and quantum mechanics, and much of the second half of the century was devoted to the construction of a theoretical structure unifying these radical ideas. But this foundation has also led us to a number of paradoxes in our understanding of nature. Attempts to make sense of quantum mechanics and gravity at the smallest distance scales lead inexorably to the conclusion that space-time is an approximate notion that must emerge from more primitive building blocks. Furthermore, violent short-distance quantum fluctuations in the vacuum seem to make the existence of a macroscopic world wildly implausible, and yet we live comfortably in a huge universe. What, if anything, tames these fluctuations? Why is there a macroscopic universe? These are two of the central theoretical challenges of fundamental physics in the twenty-first century. In this essay, I describe the circle of ideas surrounding these questions, as well as some of the theoretical and experimental fronts on which they are being attacked.

A NOTE ON THE ANALOGY BETWEEN KOLMOGOROV TURBULENCE AND QUANTUM GRAVITY

2010 ◽  
Vol 21 (11) ◽  
pp. 1329-1340 ◽  
Author(s):  
SAURO SUCCI
Keyword(s):  
Quantum Gravity ◽  
Quantum Fluctuations ◽  
Space Time ◽  
Scaling Properties ◽  
Fluid Turbulence ◽  
New Class ◽  
Kolmogorov Turbulence ◽  
Time Quantum ◽  
Dynamic Growth ◽  
The Universe

Based on a formal analogy between space-time quantum fluctuations and classical Kolmogorov fluid turbulence, we suggest that the dynamic growth of the Universe from Planckian to macroscopic scales should be characterized by the presence of a fluctuating volume-flux (FVF) invariant. The existence of such an invariant could be tested in numerical simulations of quantum gravity, and may also stimulate the development of a new class of hierarchical models of quantum foam, similar to those currently employed in modern phenomenological research on fluid turbulence. The use of such models shows that the simple analogy with Kolmogorov turbulence is not compatible with a fine-scale fractal structure of quantum space-time. Hence, should such theories prove correct, they would imply that the scaling properties of quantum fluctuations of space-time are subtler than those described by the simple Kolmogorov analogy.

scholarly journals Chaotic inflation in spatially homogeneous Bianchi type V space–time

2017 ◽  
Vol 95 (12) ◽  
pp. 1267-1270
Author(s):  
Raj Bali ◽  
P. Kumari
Keyword(s):  
Bianchi Type ◽  
Space Time ◽  
Late Time ◽  
De Sitter ◽  
Spatially Homogeneous ◽  
Inflationary Parameters ◽  
Type V ◽  
The Universe ◽  
Anisotropic Phase ◽  
Bianchi Type V

Chaotic inflationary scenario in spatially homogeneous Bianchi type V space–time following Linde (Phys. Lett. B, 129, 177 (1983). doi: 10.1016/0370-2693(83)90837-7 ) and the condition [Formula: see text] based on theory of super cooling during the cosmological phase transition proposed by Kirzhnits and Linde (Ann. Phys. 101, 195 (1976). doi: 10.1016/0003-4916(76)90279-7 ), is discussed. It has been found that the model represents anisotropic phase of the Universe in general but at late time, it isotropizes. The deceleration parameter q = −1 indicates that the model leads to de Sitter space–time. It is found that inflationary parameters, namely, slow roll parameters, and anisotropic parameters are in excellent agreement with the Planck Collaboration’s 2013 results (Astron. Astrophys. 571, A22 (2014). doi: 10.1051/0004-6361/201321569 ).

scholarly journals Nonlinear Spinor Field in Non-Diagonal Bianchi Type Space-Time

2018 ◽  
Vol 173 ◽  
pp. 02018
Author(s):  
Bijan Saha
Keyword(s):  
Spinor Field ◽  
Bianchi Type ◽  
Space Time ◽  
Coupling Constant ◽  
Nonlinear Spinor ◽  
Bianchi Models ◽  
Rotationally Symmetric ◽  
Big Crunch ◽  
The Universe

Within the scope of the non-diagonal Bianchi cosmological models we have studied the role of the spinor field in the evolution of the Universe. In the non-diagonal Bianchi models the spinor field distribution along the main axis is anisotropic and does not vanish in the absence of the spinor field nonlinearity. Hence within these models perfect fluid, dark energy etc. cannot be simulated by the spinor field nonlinearity. The equation for volume scale V in the case of non-diagonal Bianchi models contains a term with first derivative of V explicitly and does not allow exact solution by quadratures. Like the diagonal models the non-diagonal Bianchi space-time becomes locally rotationally symmetric even in the presence of a spinor field. It was found that depending on the sign of the coupling constant the model allows either an open Universe that rapidly grows up or a close Universe that ends in a Big Crunch singularity.

scholarly journals THE POINT PROCESSES OF THE GRW THEORY OF WAVE FUNCTION COLLAPSE

2009 ◽  
Vol 21 (02) ◽  
pp. 155-227 ◽  
Author(s):  
RODERICH TUMULKA
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Quantum Theory ◽  
Existence And Uniqueness ◽  
Joint Distribution ◽  
Physical Theory ◽  
Point Processes ◽  
Space Time ◽  
Wave Function Collapse ◽  
Relativistic Version

The Ghirardi–Rimini–Weber (GRW) theory is a physical theory that, when combined with a suitable ontology, provides an explanation of quantum mechanics. The so-called collapse of the wave function is problematic in conventional quantum theory but not in the GRW theory, in which it is governed by a stochastic law. A possible ontology is the flash ontology, according to which matter consists of random points in space-time, called flashes. The joint distribution of these points, a point process in space-time, is the topic of this work. The mathematical results concern mainly the existence and uniqueness of this distribution for several variants of the theory. Particular attention is paid to the relativistic version of the GRW theory that was developed in 2004.

INTERPRETATION AND PREDICTABILITY OF QUANTUM MECHANICS AND QUANTUM COSMOLOGY

1988 ◽  
Vol 03 (07) ◽  
pp. 645-651 ◽  
Author(s):  
SUMIO WADA
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Quantum Theory ◽  
Physical Meaning ◽  
Quantum Cosmology ◽  
Degrees Of Freedom ◽  
Interpretation Of Quantum Mechanics ◽  
Probabilistic Interpretation ◽  
The Universe ◽  
Classical Picture

A non-probabilistic interpretation of quantum mechanics asserts that we get a prediction only when a wave function has a peak. Taking this interpretation seriously, we discuss how to find a peak in the wave function of the universe, by using some minisuperspace models with homogeneous degrees of freedom and also a model with cosmological perturbations. Then we show how to recover our classical picture of the universe from the quantum theory, and comment on the physical meaning of the backreaction equation.

scholarly journals Possible Unification of Quantum Mechanics and General Relativity Theory Based on the Three-Dimensional Quantized Spaces

2018 ◽  
Author(s):  
Jae-Kwang Hwang
Keyword(s):  
General Relativity ◽  
Wave Function ◽  
Quantum Mechanics ◽  
Dimensional Space ◽  
Three Dimensional ◽  
Energy Transition ◽  
Space Time ◽  
Relativity Theory ◽  
General Relativity Theory ◽  
Dimensional Space Time

Three-dimensional quantized space model is newly introduced. Quantum mechanics and relativity theory are explained in terms of the warped three-dimensional quantized spaces with the quantum time width (Dt=tq). The energy is newly defined as the 4-dimensional space-time volume of E = cDtDV in the present work. It is shown that the wave function of the quantum mechanics is closely related to the warped quantized space shape with the space time-volume. The quantum entanglement and quantum wave function collapse are explained additionally. The special relativity theory is separated into the energy transition associated with the space-time shape transition of the matter and the momentum transition associated with the space-time location transition. Then, the quantum mechanics and the general relativity theory are about the 4-dimensional space-time volume and the 4-dimensional space-time distance, respectively.

scholarly journals Modified Lorentz transformations and quantum mechanics

2021 ◽  
Author(s):  
Jae-Kwang Hwang
Keyword(s):  
Wave Function ◽  
Quantum Mechanics ◽  
Euclidean Space ◽  
Coordinate System ◽  
Space Time ◽  
Lorentz Transformations ◽  
Relative Time ◽  
Absolute Time ◽  
Time Shape ◽  
The Absolute

Abstract We live in the 4-D Euclidean space. The 4th dimension is assigned as the absolute time (ct) axis and energy axis (cPt = E0) based on 4-dimensional Euclidean space. This 4th dimension can be indirectly felt through the observable relative time (ctl) and observable total energy (cPtl = E). The space-time distance is d(x1x2x3x4) = ctl. The modified Lorentz transformations are introduced by the time-matching of the absolute times in the 4-D Euclidean space. The size of x’ (or Dx’) of the moving object is expanded to the size of x = gx’ (or Dx = gDx’). These modified Lorentz transformations are approximated to the Lorentz transformations as t à tl when v/c << 1 and to the Galilean transformations as v/c is close to zero. The relative time (tl) and energy (E) are defined as the 4-dimensional distance and 4-dimensional volume, respectively. The geometrical space-time shape has the (x1,x2,x3,ct) coordinate system with the metric signature of (+ + + +) but not the (x1,x2,x3,ctl) coordinate system with the metric signature of (+ - - -). Therefore, d(x1x2x3x4)2 = (ctl)2 = (ct)2 +x2 = x12 + x22 + x32 + x42 and V(x1x2x3x4) = E = mc2 = D(ct)Dx1Dx2Dx3 from (x1,x2,x3,x4) of the geometrical space-time shape. The warped shape can be described as the wave function of the quantum mechanics. The instant force action, twin paradox and possible space travel are explained by the absolute time and wave function collapse of the modified Lorentz transformations and quantum mechanics.

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