For a quantum field theory to be well-defined, it must be asymptotically free or asymptotically safe. The theory must be characterized by a choice of finitely many parameters, which could, in principle, be set by experiment. For example, in quantum electrodynamics, these parameters are the charge and mass of the electron, as measured at a particular energy scale.
On the other hand, in quantizing gravity, there are infinitely many independent parameters needed to define the theory. The process of mathematically reducing the infinite number of parameters to a finite set of parameters is called renormalization. For a given choice of those parameters, one could make sense of the theory, but since we can never do infinitely many experiments to fix the values of every parameter, we do not have a meaningful physical theory:
- At low energies, the logic of the renormalization group tells us that, despite the unknown choices of these infinitely many parameters, quantum gravity will reduce to the usual Einstein theory of general relativity.
- On the other hand, if we could probe very high energies where quantum effects take over, then every one of the infinitely many unknown parameters would begin to matter, and we could make no predictions at all.
As explained below, there is a way around this problem by treating quantum gravity as an effective field theory. Since quantum mechanics couldn't reduce the number of parameters quantum gravity is termed as non-re-normalizable!There are a number of other approaches to quantum gravity. The approaches differ depending on which features of general relativity and quantum theory are accepted unchanged, and which features are modified. Examples include the following,
- Supergravity
- Path-integral based models of quantum cosmology
- Causal Dynamical Triangulation
- Regge calculus
- Causal sets
- Asymptotic safety
- Twistor models
- Noncommutative geometry.
- String-nets giving rise to gapless helicity ±2 excitations with no other gapless excitations
- Acoustic metric and other analog models of gravity
- MacDowell–Mansouri action
- An Exceptionally Simple Theory of Everything
- Group field theory
Anyway, I don't want to just simply close this chapter at this point. I would like to step back here and give it a second thought on gravity because after going through all these concepts, theories, hypothesis one thought keep rolling into my mind. Every time I read about general theory of relativity or quantum gravity or theories like String theory or M theory or whenever I see physicists trying to define Grand Unified Theory, so called, GUT, which will be capable of defining everything in this universe.
I ask myself 'What's wrong with science? Why should mathematics fail if we are on right track? Why is it so hard for physicists, who resolved the other three forces and united them into one single theory, to resolve gravity in terms of quantums? Why does it make physicist to dream about so many complications and come up with theories like Super-string theory, Membrane theory and loop quantum gravity theory, etc? Are they not starting physics all over again with their new complicated theories? After all these, what I could finally think of is that the basic understanding of the gravity itself may be wrong!
Conclusion:
According to me, Gravity can be a special force but it cannot be too special to demand such complications. If you consolidate the inventions of the other three fundamental forces, it goes as follows.
1. Strong force was found and that is happening because they internally share photons during their interactions. Hence it could be united with electromagnetic force.
2. Next, weak force was found and that is at higher temperature and high energy environment, it is nothing but another form of electromagnetic force because it was found that photons are shared during weak interactions.
Then what could be stopping gravity to be like Strong force or weak force? Since strong is the strongest of all the fundamental forces, we will ignore it for the analysis. Lets consider the weak force. We have seen that this force is no longer weak at high energy environments but it became weaker when the temperature and energy goes down. We all also know that objects would have not been formed if the weak force is not weaker.
Now, my point here is to consider gravity just like another weak force, probably, we can name it as the weakest force of all. This force could also be another form of electromagnetic force but it became weaker and weaker under low energy environments. We also know that on moon, there is no life is formed because the gravitational force of the moon is not enough to support it like how earth does it.
This approach demands one more possibility. We all know that gravitational force interacts with masses. Science has not found how the objects gain their masses. Hopefully, the Large Hydron Collider would find the Higgs boson and explain mass. However, lets consider that it is Higgs boson that caused the objects to gain the mass. If this is true, then according to me, gravitational force interacts with Higgs boson.
Lets consider the interaction is happening with Higgs bosons, then that tells us that gravitational force also involves carrier particles which are familiar to Higgs bosons. Quantum physics says that Higgs bosons are another sub-atomic carrier particle evolved from the electromagnetic force.
Just for record, earth also behaves as a gigantic magnet due to it's electromagnetic force radiating from it's burning core. Taking all these into consideration, I personally believe that gravity is another form of electromagnetic force, the only hard-stop is that we haven't resolved the mystery behind the Mass. If we do, then gravity will no longer be a mystery!
