Piero Scaruffi

These are excerpts and elaborations from my book "The Nature of Consciousness"

The Classical World: Utopia Since we started with the assumption that our Physics is inadequate to explain at least one natural phenomenon, consciousness, and therefore cannot be "right" (or, at least, complete), it is worth taking a quick look at what Physics has to say about the universe that our consciousness inhabits. Our view of the world we live in has undergone a dramatic change over the course of this century. Quantum Theory and Relativity Theory have changed the very essence of Physics, painting in front of us a completely different picture of how things happen and why they happen.  Let’s first recapitulate the key concepts of classical Physics. Galileo laid them down in the 16th century. First of all, a body in free motion does not need any force to continue moving. Second, if a force is applied, then what will change is the acceleration, not the velocity (velocity will change as a consequence of acceleration changing). Third, all bodies fall with the same acceleration. A century later, Newton expressed these findings in the elegant form of differential calculus and immersed them in the elegant setting of Euclid's geometry. Three fundamental laws explain all of nature (at least, all that was known of nature at the time).  The first one states that the acceleration of a body due to a force is inversely proportional to the body’s “inertial” mass. The second one states that the gravitational attraction that a body is subject to is proportional to its “gravitational” mass. The third one indirectly states the conservation of energy: to every action there is always an equal reaction. They are mostly rehashing of Galileo’s ideas, but they state the exact mathematical relationships and assign numerical values to constants.  They lent themselves to formal calculations because they were based on calculus and on geometry, both formal systems that allowed for exact deduction. By applying Newton’s laws, one can derive the dynamic equation that mathematically describes the motion of a system: given the position and velocity at one time, the equations can determine the position and velocity at any later time. Newton’s world was a deterministic machine, whose state at any time was a direct consequence of its state at a previous time. Two conservation laws were particularly effective in constraining the motion of systems: the conservation of momentum (momentum being velocity times mass) and the conservation of energy. No physical event can alter the overall value of, say, the energy: energy can change form, but ultimately it will always be there in the same amount. In 1833 the Irish mathematician William Hamilton, building on the 1788 work of the Italian mathematician Luigi Lagrange (the trajectory of an object can be derived by finding the path which minimizes the “action”, such action being basically the difference between the kinetic energy and the potential energy), realized something that Newton had only implied: that velocity, as well as position, determines the state of a system. He also realized that the key quantity is the overall energy of the system.  By combining these intuitions, Hamilton redefined Newton’s dynamic equation with two equations that derived from just one quantity (the Hamiltonian function, a measure of the total energy of the system), that replaced acceleration (a second-order derivative) with the first-order derivative of velocity, and that were symmetrical (once velocity was replaced by momentum). The bottom line was that position and velocity played the same role and therefore the state of the system could be viewed as described by six coordinates, the three coordinates of position plus the three coordinates of momentum. At every point in time one could compute the set of six coordinates and the sequence of such sets would be the history of the system in the world. One could then visualize the evolution of the system in a six-dimensional space, the “phase” space. In the Nineteenth century two phenomena posed increasing problems for the Newtonian picture: gases and electromagnetism. Gases had been studied as collections of particles, but, a gas being made of many minuscule particles in very fast motion and in continuous interaction, this model soon revealed to be a gross approximation. The classical approach was quickly abandoned in favor of a stochastic approach, whereby what matters is the average behavior of a particle and all quantities that matter (from temperature to heat) are statistical quantities. In the meantime, growing evidence was accumulating that electric bodies radiated invisible waves of energy through space, thereby creating electromagnetic fields that could interact with each other, and that light itself was but a particular case of an electromagnetic field. In the 1860s the British physicist James Maxwell expressed the properties of electromagnetic fields in a set of equations. These equations resemble the Hamiltonian equations in that they deal with first-order derivatives of the electric and magnetic intensities. Given the distribution of electric and magnetic charges at a time, Maxwell’s equation can determine the distribution at any later time. The difference is that electric and magnetic intensities refer to waves, whereas position and momentum refer to particles. The number of coordinates needed to determine a wave is infinite, not six... As a by-product of his equations, Maxwell also discovered that light is an electromagnetic wave. Basically, Michael Faraday had shown that changes in magnetic fields produce electric fields; Maxwell realized that the opposite is also true: changes in electric fields cause magnetic fields. His equations describe this endless dance between electric and magnetic fields. By then, it was already clear that Science was faced with a dilemma, one which was bound to become the theme of the rest of the century: there are electromagnetic forces that hold together particles in objects and there are gravitational forces that hold together objects in the universe, and these two forces are both inverse square forces (the intensity of the force is inversely proportional to the square of the distance), but the two quantities they act upon (electric charge and mass) behave in a completely different way, thereby leading to two completely different descriptions of the universe. The inverse square law indirectly also implied that the “vacuum” has a role: the attraction decreases exponentially with distance; hence there is a relationship between a force and space. These two forces act at a distance, but somehow their "strength" depends on the distance, as if the "nothing" in between two bodies contributed to the measured strength at each side. Newton's laws of motion apply to inertial frames and those laws are the same for all inertial frames. However, Maxwell noticed that an electric phenomenon in one inertial frame was a magnetic phenomenon in another. An electric phenomenon in movement gives rise to a magnetic phenomenon, and viceversa, but the "movement" depends on who is observing: if you observe the electric phenomenon while it is moving in front of you, you perceive a magnetic phenomenon; if you "ride" on the electrical phenomenon (which is therefore at rest from your viewpoint), you perceive instead only an electrical phenomenon. Maxwell's equations showed that the electromagnetic phenomenon "oscillates" like a wave and all such waves travel at 300 thousand kms/hour (in the vacuum). Light is one particular electromagnetic wave, hence that speed is now known as "the speed of light". What we perceive as different colors of light correspond to different frequencies, not velocities. And some frequencies of electromagnetic waves we can't perceive at all. The interaction between distant bodies does not happen instantaneously as Newton thought but is mediated by a "field". Another catch hidden in all of these equations was that the beautiful and imposing architecture of Physics could not distinguish the past from the future, something that is obvious to all of us. All of Physics' equations were symmetrical in time. There is nothing in Newton's laws, in Hamilton's laws, in Maxwell's laws or even in Einstein's laws that can discriminate past from future. Physics was reversible in time, something that goes against our perception of the absolute and (alas) irrevocable flow of time.   Back to the beginning of the chapter "The New Physics" | Back to the index of all chapters