It depends on what the final theory of quantum gravity will look like.The challenge of combining gravity with quantum mechanics can be understood as follows. The central feature of quantum mechanics is the principle of overlay – that the wave functions that describe two different particles or systems can overlap. Thus, two systems described by two different wave functions [math -Psi_1 (x,t)[/math and [math -psi_2 (x,t)[/math can instead be used as a single composite system with the wave function [math -Psi (x,t)=-Psi_1 (x,t)+” Psi_2 (x,t)[/math).Wave functions must be defined in a set. In quantum mechanics, the set is understood as the coordinates [math(x,t)[/math of space-time) in which our system is embedded.So we can always write down what the wave function of a particle that passes through two slots in the double-gap experiment at the same time must look like. Similarly, we can write down the superposition of two particles in relation to their impulses and not their locations by working in the [math(p,t)[/math instead of in the [math(x,t)[/math basis, wherein the impulses [mathp[/math through the usual Fourier transformation are related to the place [mathx[/math,
[math -displaystyle-psi (p,t) -sim -int-mathrm dx e-ipx-psi (x,t) -tag*
Whether we work in the base of the place or in the pulse base, there is an implicit assumption at work in this regulation – this is the assumption of a flat background geometry in which we give each point of space-time a set of coordinates [math(x, y, z, t)[/math.Now the General Theory of Relativity (ART) teaches us that physics should be independent of the respective coordinates used to describe a system. In addition, any theory that matches ART must be well defined on both curved and flat surfaces. It turns out that while we can perform quantum mechanical calculations to our heart’s content with wave functions defined in flat space, the case of wave functions that live in curved space becomes difficult. The complications associated with space-time curvature can be solved by using sufficiently sophisticated mathematical methods. The resulting framework is known as Quantum Field Theory on Curved Spacetime (QFT-CS). Using THE methods of QFT-CS, Stephen Hawking obtained his historical result that a black hole must emit heat radiation at a rate that is inversely proportional to its mass.
However, QFT-CS does not qualify as a theory of “quantum gravity”, as explained below.Quantum mechanics is about assigning different attributes to a system and then constructing states of the system according to the individual attributes. These states can then be superimposed, and the resulting system then manifests all non-intuitive phenomena associated with quantum behavior, such as interference and entanglement. As already mentioned, gravity in modern conception results from the non-trivial geometry of a region of space-time induced by a certain distribution of matter. Some of the geometric attributes that can be assigned to a specific area of space-time are length, area, volume, angle, and so on. A theory of quantum gravity should be able to tell us how we can write down the wave function, which is not defined on a particular area of space-time, but on a wave function of a certain area of space-time, which allows us to construct states that correspond to the overlays of different geometries. However, as mentioned earlier, traditional quantum mechanics only tells us how we can write the wave function on a particular geometry, but not the wave function of a given geometry. The traditional language of quantum mechanics is therefore insufficient to describe quantum states of geometry. For the same reasons, QFT-CS is not a theory of “quantum gravity”. There, curved space-time serves only as an arena on which quantum states can be defined, but there is no idea of states of geometry itself, but of the matter moving on this geometry.
Loop Quantum Gravity (LQG) is a candidate for the unification of both theories.From the beginning, the concept of smooth, continuous background geometry is abandoned in favor of discrete geometry consisting of elementary objects called “simplices” – a complicated term for elementary geometric objects such as Triangles and tetrahedrons. Just as Lego blocks can be glued together into complicated structures, a collection of triangles or tetrahedrons can also form a two-dimensional or two-dimensional structure. three-dimensional geometry. LQG allows us to calculate the quantized values of the geometric attributes associated with these simplicitys. It provides us with a framework for the study of the quantums of geometry – literally – and for the construction of overlays of different states of geometry. However, there are still many shortcomings in the LQG approach. Two main obstacles are (a) the lack of an understanding of how we can obtain (approximately) smooth, continuous space-time by sticking together our elementary simplicitys, and b) a lack of understanding of how matter – particles such as Electrons and neutrinos – should be described in the form of quantum geometry.