The Wheeler–DeWitt equation* It has some amazing properties [1]. It is timeless and it is describing a world of only space.
Timelessness and vanishing trajectories and spacetime
The full quantum state of gravity and matter depends on the three-dimensional metric only, but is invariant under three-dimensional coordinate transformations. It does not contain any external time parameter t [1]. The reason for this ‘timeless’ nature is obvious.
In general relativity, a four-dimensional spacetime is the analogue to a particle trajectory in mechanics. After quantization, the trajectory vanishes, and so does spacetime. What remains is space, and the configuration of space is the space of all three-geometries.
The timelessness of the Wheeler-DeWitt equation is not simply the same as that arising from a universal wave function [1]. The Wheeler-DeWitt equation comes from the attempt to canonically quantize gravity. Because of the gauge-redundancy of gravity, "time evolution" takes one state into the same state.
Singular ontology of space in Quantum loop gravity
An equation of this form also occurs in loop quantum gravity and Rovelli arrives in similar conclusions. Rovelli combines some relativist concepts of "relative present" and extented to justify this. But he does not go far enough to suggest what this timelessness means
Time and laws
Einstein’s theory of general relativity has introduced a dynamical spacetime into physics and has thus dramatically changed our attitude towards the formulation of fundamental laws. On the other hand, one expects that the consistent unification of general relativity with quantum theory will lead to a completely new type of understanding of time as well as the type of possible laws in physics, because time dependence is a main aspect as fundamental physical laws refer to dependences on space and time
Implications for our understanding of time
The Wheeler-DeWitt theory challenges our conventional understanding of time as a linear and absolute concept. It suggests that time may be an emergent property of the universe, rather than a fundamental aspect. This has implications for how we view the past, present, and future, and may lead to new theories and understandings of the nature of time.
* The Wheeler-DeWitt equation is a mathematical equation formulated by physicists John Wheeler and Bryce DeWitt in the 1960s. It is a key component of the Wheeler-DeWitt theory, which attempts to reconcile quantum mechanics and general relativity. The equation describes the wave function of the universe and is used to study the concept of timelessness in the universe.
The Wheeler-DeWitt theory is a theoretical framework and has not been proven through empirical evidence [2]. However, it has been extensively studied and has provided insights into the fundamental nature of the universe. The Wheeler-DeWitt equation is based on the idea that time is not a fundamental aspect of the universe, but rather emerges from the interactions between matter and energy. This means that the equation does not have a time variable, indicating that timelessness may be a fundamental aspect of the universe [2].
Currently, the Wheeler-DeWitt equation cannot be solved in its entirety. This is because it is a complex equation that involves both quantum mechanics and general relativity, which have not yet been fully reconciled. However, scientists have been able to make progress in understanding the equation through numerical simulations and approximations. (Reference:
1. On the Concept of Law in Physics
CLAUS KIEFE
2. https://www.physicsforums.com/threads/wheeler-dewitt-and-timelessness.779866
The Wheeler-DeWitt equation imposes the constraints on the wavefunction of spacetime geometries. That’s why it doesn’t have any time dependence. Constraints are imposed on states and hold for all times. There are many subtleties involved, since the space of spacetime geometries is not known.
There is no single equation exist to describe three-dimension of nature that it is changing constantly, while math is one-dimension and never change
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