Why Quantum Defies Gravity…?
The Story of Unification
Newtonian mechanics defines the gravity as a force that attracts objects that depends on the product of the masses and the square of the distance between them. This concept has been dominant for three centuries. However, the question of what mediates between them and the concept of the space remained open for centuries.
In the 19th century, James Clerk Maxwell combined the theories of Faraday, Ampere and others through his famous framework known as electromagnetism. This unified the two apparently different forces — Electric Force and Magnetic Force — into Electromagnetic Force (EM Force). He also predicted the existence of the oscillation of electromagnetic fields that matched with the speed of light. This prediction led to identification of light with the waves of the EM field.
Albert Einstein, in 1905, by keeping the dielectric permittivity (ε0) and the magnetic permeability (μ0) constant, as per Maxwell’s EM theory, explained the motion of material bodies, in his paper titled “On The Electrodynamics Of Moving Bodies” which is otherwise known as Special Relativity Theory (SRT).
According to the SRT, the space and time are not only absolute entities but are also intertwined. Einstein published his special relativity theory in 1905, based on electromagnetism, when quantum theory was still in its infancy. His special relativity theory greatly influenced the notion of photons which helped identify the electromagnetism with quantum mechanics leading to the development of the Quantum Electro Dynamics (QED).
This was also the era of elementary particles. The discovery of elementary particles led to the identification of two other forces namely Weak and Strong Nuclear Forces. Till then, the Gravity and the Electromagnetic forces were the only known forces.
By 1915, Einstein defined the gravity as the manifestation of the spacetime curvature, in contrast to Newton, who considered it a property of matter. This is considered to be a remarkable achievement in physics.
In the first half of 20th century, Feynman, Gell-Mann, t’Hooft, Weinsberg and Abdus Salam, among many others, unified the weak force with electromagnetic force under the “electroweak” framework.
Only during the last quarter of the 20th century, the Standard Model , “somewhat”, unified, the strong, the weak and the electromagnetic forces with the description as excitation of quantum mechanical vacuum, leaving the gravity force at bay.
The Obstacle for the Unification…
The greatest obstacle of the unification hinges on how quantum mechanics and relativity theories treat space and time.
The quantum mechanics defines systems with wave function Ψ(x, t). Two different systems described by two different wave functions — Ψ1(x, t) and Ψ2(x, t) — can be treated as one single entity under superposition, as shown below.
Ψ(x, t) = Ψ1(x, t) + Ψ2(x, t)
If you notice the equation, the function is described on an arbitrary space co-ordinates at an arbitrary time. Meaning, the quantum system is embedded on the space and time or spacetime. In other words, the quantum systems works in the background of the FLAT co-ordinates and time which are assumed to be fixed or absolute.
Now, things get murkier when quantum mechanics is attempted to be unified with the relativity theory. In quantum mechanics, time is treated just as a parameter. Moreover, unstable (i.e. creations and annihilation of) particles and their types (particles or anti-particles) cannot be treated with the Schrodinger’s equation. However, Dirac solved it by using fields instead of wave functions leading to the birth of Quantum Field Theory. (More in my below blog)
Since gravity is more associated with the curved space, the attempts to define quantum systems on a curved surface led to more complications in the framework known as Quantum Field Theory on Curved Spacetime (QFT-CS). While QFT-CS gave Stephen Hawking the revolutionary result of emission of thermal radiation from black holes at a rate inversely proportional to its mass, it does not go well with the (quantum) gravity.
Why?
Quantum Mechanics is all about assigning attributes to a system. Based on these attributes, the states of the systems are obtained. Here we write the wave functions defined ON the given region of the spacetime.
However, as the General Relativity Theory describes, the gravity arises as the result of the curved spacetime or non-trivial geometry (surface area or volume of the spacetime).
Hence we need a quantum theory describing the wave function OF a given region of the spacetime. From there, one can derive the superposition of different geometries. Here, the quantum mechanics fails to describe quantum states of geometry for quantum gravity. In QFT-CS as well, the curved spacetime merely serves as a “platform” on which quantum states are defined and the matter moves about on that geometry. For the same reasons, the QFT-CS is also not a theory of “quantum gravity”.
Ref: https://doi.org/10.48550/arXiv.1402.2757
