Holographic wave function and space-time

2019 ◽  
Author(s):  
Vitaly Kuyukov
Keyword(s):  
Wave Function ◽  
Space Time

Holographic wave function and space-time

The Superstring Propagator and the Signature of Space-Time

1997 ◽  
Vol 12 (14) ◽  
pp. 987-998 ◽  
Author(s):  
M. D. Pollock
Keyword(s):  
Wave Function ◽  
Apparent Horizon ◽  
Scalar Particle ◽  
Space Time ◽  
Functional Integral ◽  
Global Symmetry ◽  
Hamiltonian Constraint ◽  
Superstring Theory ◽  
Acceptable Solution ◽  
Higher Derivative

The Faddeev (Newton–Wigner) propagator K for the heterotic superstring theory is derived from the Wheeler–DeWitt equation for the wave function of the Universe Ψ, obtained in the four-dimensional (mini-superspace) Friedmann space-time ds2=dt2-a2(t)dx2, after reduction from the ten-action. The effect of higher-derivative terms ℛ2 is to break the local invariance under time reparametrization to a global symmetry t→λt, and consequently there are no ghost or gauge-fixing contributions, a functional integral over the (constant) Lagrange multiplier λ being sufficient to enforce the Hamiltonian constraint implicitly. After Wick rotation of the time, [Formula: see text], the only physically acceptable solution for K decreases exponentially on the Planck time-scale ~ t P , explaining from the quantum cosmological viewpoint why the signature of space-time is Lorentzian rather than Euclidean. This is analogous to the case of the (two-dimensional) free relativistic scalar particle, discussed recently by Redmount and Suen, who found that the propagator decreases exponentially outside the light-cone on the scale of the Compton wavelength of the particle (in accordance with the Heisenberg indeterminacy principle). These two seemingly different forms of acausality are thus physically excluded in the same way. The propagator for the Schwarzschild black hole of mass M is also obtained from the Schrödinger equation for the wave function on the apparent horizon, due to Tomimatsu, and the Hawking temperature T H =(8π M)-1 is derived from the Euclidean form of this equation.

scholarly journals Space-time from Collapse of the Wave-function

2019 ◽  
Vol 74 (2) ◽  
pp. 147-152 ◽  
Author(s):  
Tejinder P. Singh
Keyword(s):  
Hilbert Space ◽  
Wave Function ◽  
Quantum Theory ◽  
Minkowski Space ◽  
Time Scales ◽  
Quantum Interference ◽  
Quantum Dynamics ◽  
Space Time ◽  
Minkowski Space Time ◽  
Macroscopic Objects

AbstractWe propose that space-time results from collapse of the wave function of macroscopic objects, in quantum dynamics. We first argue that there ought to exist a formulation of quantum theory which does not refer to classical time. We then propose such a formulation by invoking an operator Minkowski space-time on the Hilbert space. We suggest relativistic spontaneous localisation as the mechanism for recovering classical space-time from the underlying theory. Quantum interference in time could be one possible signature for operator time, and in fact may have been already observed in the laboratory, on attosecond time scales. A possible prediction of our work seems to be that interference in time will not be seen for ‘time slit’ separations significantly larger than 100 attosecond, if the ideas of operator time and relativistic spontaneous localisation are correct.

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.

scholarly journals Introduction: space–time and the wave function

Synthese ◽  
2015 ◽  
Vol 192 (10) ◽  
pp. 3055-3070 ◽  
Author(s):  
Albert Solé ◽  
Carl Hoefer
Keyword(s):  
Wave Function ◽  
Space Time

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.

scholarly journals Klein-Gordon Equation and Wave Function in Robertson-Walker and Schwarzschild space-tim

2021 ◽  
Author(s):  
Sangwha Yi
Keyword(s):  
Wave Function ◽  
Wave Equations ◽  
Gordon Equation ◽  
Space Time ◽  
Wave Functions ◽  
Relativity Theory ◽  
General Relativity Theory ◽  
Gauge Fixing ◽  
Klein Gordon ◽  
Klein Gordon Equation

In the general relativity theory, we find Klein-Gordon wave functions in Robertson-Walker and Schwarzschild space-time. Specially, this article is that Klein-Gordon wave equations is treated by gauge fixing equations in Robertson-Walker space-time and Schwarzschild space-time.

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.

scholarly journals Phase profile of the wave function of canonical tensor model and emergence of large space–times

2021 ◽  
Author(s):  
Naoki Sasakura
Keyword(s):  
Wave Function ◽  
Saddle Point ◽  
Saddle Points ◽  
Space Time ◽  
Tensor Rank ◽  
Tensor Model ◽  
Large Space ◽  
Time Dynamics ◽  
Point Analysis ◽  
Phase Profile

In this paper, to understand space–time dynamics in the canonical tensor model of quantum gravity for the positive cosmological constant case, we analytically and numerically study the phase profile of its exact wave function in a coordinate representation, instead of the momentum representation analyzed so far. A saddle point analysis shows that Lie group symmetric space–times are strongly favored due to abundance of continuously existing saddle points, giving an emergent fluid picture. The phase profile suggests that spatial sizes grow in “time,” where sizes are measured by the tensor-geometry correspondence previously introduced using tensor rank decomposition. Monte Carlo simulations are also performed for a few small N cases by applying a re-weighting procedure to an oscillatory integral which expresses the wave function. The results agree well with the saddle point analysis, but the phase profile is subject to disturbances in a large space–time region, suggesting existence of light modes there and motivating future computations of primordial fluctuations from the perspective of canonical tensor model.

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