by Prasad Ganti
“The God Equation” is a recent book written by Michio Kaku, the popular Physicist and String theorist. This book comes on top of several other popular ones he wrote earlier. It emphasizes on the holy grail of Physics – unifying all the four fundamental forces of nature. From the weakest one, Gravity which spans over astronomical distances to the strong force which rules over the length of an atomic nucleus. The book presents the concepts in a very lucid style. And not many equations although the title has the word “equation” in it. Below is my summary.
Mathematical equations are used to define physical and conceptual parameters and the relationships between them. More than three hundred years back Isaac Newton came up with an equation describing the gravitational force as attraction between two bodies. The bodies could be apples or oranges or planets, or stars. Using this equation, the trajectory of the planets or spacecraft or falling apples or terrestrial ballistics could be calculated. It was a triumph of human thought in expressing a pragmatic concept so succinctly.
Then came James Clerk Maxwell about two hundred years ago, who showed that electricity and magnetism are related to each other. A changing electric field can generate magnetism and vice-versa. His set of equations described the electromagnetic radiation as a wave propagating through changing electric and magnetic fields. These waves encompass a wide range from radio, to microwaves, to infrared, to visible light, to ultra violet, to X rays, to Gamma rays etc. Each varying from the other in frequency and thus the wavelength. He calculated the speed of such a wave which is now recognized as the speed of light. Our eyes are only sensitive to the visible part of the electromagnetic spectrum. But all the types of radiation being described by the set of Maxwell’s equations is a triumph of the human mind in relating the abstract concepts to the practical reality.
About a hundred years back, Albert Einstein stretched Newton’s equations to incorporate some “out of the world” concepts like space time curvature. In the special theory of relativity, he set the speed of light as a cosmic speed limit for most practical purposes. And described what happens when objects travel at very high speeds and why they cannot exceed the speed of light. He postulated time as a dimension like the three dimensions of space.And that time can slow down if an object is travelling at very high speeds.
Einstein’s crowning achievement was the General theory of relativity which considers accelerated motion and gravity as equivalent to each other. Further in the presence of gravity, space curves, and time slows down. All these concepts were expressed using mathematical equations. In fact, for space curvature, Einstein had to use Bernard Riemann’s geometry. Riemann’s geometry is a stretch of Euclid’s geometry which stood for thousands of years and deals with flat spaces. Concepts like Black holes, Gravity waves came as a result of multiple solutions to Einstein’s equations.
Parallelly, during the twentieth century, a lot was happening at the atomic and subatomic levels. Atoms and its constituents like electrons, protons and neutrons were discovered. The forces binding these particles were being formulated into mathematical equations. These particles were also postulated to be waves. Erwin Schrodinger came up with an equation to describe the electrons as particles and waves. Paul Dirac improved upon this equation to add space and time together (known as Einstein’s relativistic effects). All these postulations were part of a broader field called Quantum mechanics.
QED (Quantum Electro Dynamics) resulted from the combination of Dirac’s theory of electrons with Maxwell’s theory of light. Thus were combined Quantum mechanics and electromagnetism. Only gravity remained outside the orbit of a unified theory of everything. Einstein himself spent decades but was not successful. In the last three decades or so, a new theory called string theory is being developed which can help with this unification. But the theory needs the existence of ten space dimensions and one time dimension as a foundation. But we see only three space dimensions in our life. Speculation is that the extra dimensions are curled into tiny spaces, much smaller than nuclear lengths, in the order of Planck’s length.
Experimentation at such small lengths or higher dimensions is nearly impossible. The kind of energies required are huge, much much beyond the reach of the current particle accelerators. Even the biggest one LHC (Large Hadron Collider) in Switzerland, which produced evidence for the Higgs Boson, incidentally known as the God particle. If the God’s particle can be found, if the miniscule perturbations of space resulting from Gravity waves can be discovered, can the God equation be that far behind? I am optimistic.