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The gauge bosons of the standard model of particle physics are responsible for 3 of the 4 known forces in the universe. A force is conferred is through the exchange of virtual bosons. So for example in electromagnetism, an exchange of virtual photons results in an exchange of momentum which results in two like charges repelling each other.
Gravity is missing from this picture because in General relativity, gravity is not a force, but is a curvature of space-time. The problem is that stars and planets are made of molecules, atoms and radiation. And the forces that hold the atoms together are due to discrete units of virtual particles. It is the exchange or swapping of these virtual bosons that holds or breaks up atoms and molecules.
Quantum mechanics conflicts with general relativity, because QM treats every thing as being discrete, and GR treats everything as being continuous. We need a theory that combines the two because we live in one reality, not two different realities.
This is why most physicists believe General relativity is incomplete. Why can’t quantum mechanics be the one that is incomplete?
Of the 4 fundamental forces, 3 have very robust quantum mechanical theories. Only gravity lacks a quantum description. Quantum mechanics also has almost all of classical physics within in its limits. Classical physics like general relativity, does not have quantum effects. We have learned is that Quantum physics is the fundamental language of reality.
One way to quantize gravity is to quantize space-time itself. This is what loop quantum gravity or LQG does. It shows that the fabric of space-time is not continuous, but is made up of discrete quanta, like the pixels on a TV screen. This is different than string theory, because in string theory, space is the background or the canvas, on which strings vibrate.
This means that distance has a minimum quantity of 10^-35 m. Area has a minimum value of 10^-70 m^2, and volume has a minimum value of 10^-105 m^3 – below which it cannot go. Time also has a minimum quantity of 10^-43 seconds, or about Planck time.
Space time is made up for finite loops with nodes connecting them. The nodes is where the quanta volumes of space reside. It has a volume that is a multiple of 10^-99 cm^3. The loops in between the nodes represent 2 dimensional areas. Large quantities of loops and nodes are called “spin networks.” Space is defined by the geometry of this spin network. Time is defined by the movement of this spin network. The spin network and quantum movements of time, is called a spin foam. Time ticks like a digital clock with each tick being 10^-43 secs.
When mass and energy are added to this spin foam, the shape of the volumes of the spin network is distorted, distorting space and time. This distortion is what we perceive as gravity.
LQG makes a testable prediction that photons of higher energy travel slightly slower than low-energy photons. But this has not been observed.
A second way to quantize gravity is to theorize a completely new mathematical framework of reality based on a new understanding of fundamental particles. This is string theory. It replaces the fundamental particles with one dimensional fiber-like strings.
Different vibrations of strings behave just like the elementary particles of the standard model. But the biggest problems is that these strings would need to vibrate not just in the 3 dimensions, but in at least 6 more spatial dimensions in order to mathematically account for the various particles.
It does’t appear that additional large dimensions in our universe exist, so physicists think that these dimensions could be very small and hidden from our perceptions.
If you treat the universe as strings vibrating in 9 dimensions, a particular closed string vibration results in a graviton particle. So this would allow for the existence of a force-carrying particle for gravity just like the other 3 three forces.
The promise of string theory is that all the fundamental constants, and properties of particles could come out of it. But 9 spatial dimensions is a problem. Another problem is that it requires the existence of super symmetry, where each particle has a shadow partner particle with different masses. No such supersymmetric particles have been found at the LHC.