Let me share with you, how I have made the first great contribution to the quantum theory of gravity. It was a full 16 years before that young genius Einstein invented the theory of relativity and 26 years before those young upstarts Heisenberg , Schrodinger invented Modern Quantum Mechanics. As a matter of fact I, Max Planck did it without even realizing it.
That is my rendering of Planks Eureka Moment. Planks Eureka moment was not the discovery of planks constant h, but rather a simple reconfiguration of units of length, mass and time something that any 5th class child can do.However this has now become the foundation for quantum gravity. Once again i am getting ahead of the story. Seems like i have this non-linear tennet ingrained in me.
G=6.7 X 1011 square-meters per second kilogram
h= 6.626 X 10-34 kilogram-square meters per second
c= 2.99 X 108 meters per second
The above 3 are the so called fundamental constants of nature. Well, why the heck are they so strange ? some are unimaginably small and the others are stupendously huge. This is no way to express important quantities like fundamental constants. Lets change the units of mass, length and time so that these constants equal 1. That would be neat. So it works out if :
length= 10-33 cm
mass= 10-5 gm
time= 10-42 seconds
Now space appears smooth to us. By space i mean space ofcourse. However if we see with a powerful enough microscope, space will not appear to be smooth. According to Quantum everything that can fluctuate, does fluctuate. Space suffers from quantum jitters.
How powerful does the microscope should be in order to observe the fluctuating texture of space ? You guessed it. The microscope would have to discern features whose size is the Plank Length – 10-33 cm ! Thats the scale of the quantum texture of space.
And how long do the features last before fluctuating again ? You are on a roll – Plank Time : 10-42 seconds ! Many physicists think that there is a sense in which Plank Length is the smallest distance that can ever be resolved. Likewise, the Plank Length is the shortest interval of time.
Lets not leave out the Plank Mass. Two colliding protons, if they have enough energy; on collission would disappear and leave behind a black hole. And whats the mass equivalent to this amount of energy ? – Plank Mass 10-5 gm.
By the way, planck mass black hole would be about one Planck length in size and it would last for one Planck unit of time before exploding into photons and other debris.
The Planck or “Natural ” constants in a way serve to characterize nature itself. They divide the realm of continuous space and time from the distortion of the meaning of these concepts themselves. They are at the core of any Quantum Theory of gravity. I dont think the Human mind has yet reached a stage to comprehend the notion of non-linear time or jittery space. Hopefully, mathematics can.
PS: I have mixed up the spelling of ‘Planck’ everywhere in the article. Never Mind.