In Search of a Theory of Everything

by Demetris Nicolaides

  According to the standard model of quantum theory, the forces of attraction or repulsion between the particles of matter (the quarks and leptons) are caused by the constant exchange of particles of force—called force-carrying particles or messenger particles since they carry the message of the force. The exchange of force particles transfers energy between the particles of matter, causing a change in their own energy, speed, and direction of motion and making them attract or repel.

  The massless photons mediate the electromagnetic force; the massless gluons transfer the nuclear strong force (gluons, “glue,” bind the quarks to form protons and neutrons, for example); the massive W+, W–, and Z0 particles (of positive, negative, and zero electric charge, respectively), the nuclear weak force; and the massless gravitons are speculated to mediate gravity.6 As regards the gravitons, a complete theory that describes them has yet to be discovered, and, equally important, no experiment so far has confirmed their existence.

  The electric repulsive force between two electrons, for instance, is mediated by the continual exchange of photons that, traveling at the speed of light, are emitted and absorbed by the electrons. Namely, one electron rebounds by emitting a messenger photon, and the other electron rebounds by absorbing the photon. Repeated processes of this kind mean that the exchanged photons knock the interacting electrons further and further apart. It is this continual exchange of photons that manifests itself as the electric repulsive force between the two electrons. Similar processes can explain the other forces.

  Through the continual exchange of the particles of force, the particles of matter move nonstop and combine with one another to form atomic nuclei, atoms, molecules, and composite objects like bows and lyres. Thus, even an apparent static equilibrium of an object at the macroscopic level, down to the microscopic level, is really an eventful, complex, and endless process of particle exchange. Nature is constantly changing.

  Logos

  Newton’s third law of motion or the more detailed description of a force by the standard model may be viewed as part of Logos. In the third law, the underlying unity is the equality of the strength of the opposite forces. In the microscopic interpretation of force, unity is expressed by the conservation laws obeyed by the particles through their interactions (strife); that is, as the particles of matter collide with the particles of force, their net energy (or momentum, to name just two properties that are conserved) before collision equals their net energy (or momentum) after collision—again, the Heraclitean unity between competing opposites is expressible mathematically in physics; that is, energy before = energy after, or, momentum before = momentum after. Of course, the actual equations are more descriptive, detailed, and written with mathematical symbols.

  Also, matter and antimatter are opposites in strife. Their Logos are the various laws they obey, including gravity (of Newton or of Einstein, his general relativity), electromagnetism (of Maxwell or quantum theory’s), the standard model, string theory, loop quantum gravity, and so on. And the underlying unity consists of the various conservation laws with which each process involving matter and antimatter must comply. The resulting harmony in the strife of matter and antimatter is the general organization of the world (a notion to be revisited in the section “Organization”).

  In modern physics we are striving to understand various phenomena, first by isolating them and finding which laws they obey. But as in Heraclitean philosophy, according to which true understanding is achieved by identifying common characteristics that different things have, the real picture emerges only when we manage to connect our understanding of isolated and seemingly different phenomena and discover the bigger truth, the Logos they all obey. In modern physics one of the key scientific principles, which is part of Logos, is the Heisenberg uncertainty principle. It will help us understand the doctrine of Heraclitean change from within the context of quantum theory.

  The Uncertainty Principle

  The most consequential, mind-boggling law of quantum theory—its very heart and soul—is the Heisenberg uncertainty principle. This principle discusses how nature limits our ability to make exact measurements regardless of how smart or patient we are or the sophistication of our experimental apparatus. Namely, as a consequence of the very act of observation, the observer always disturbs the object being observed a certain minimum way, causing the result of a measurement to be uncertain. We can measure very accurately the position and velocity of a large-mass object, such as a car or a planet, without significantly disturbing it. We can watch it move and even predict its path of motion. But if instead we had a small-mass object, such as a microscopic particle—an electron, a proton, an atom, even a molecule—we could not measure exactly both its position and its velocity; nor could we observe it in a path of motion or predict its path. Quantum theory can describe only where (say) an electron is likely to be, not where it was, is, or will be. Before the uncertainty principle was discovered, absolute accuracy in a measurement, at least in theory, was considered axiomatic, but not anymore.

  Suppose we want to observe an electron, hoping to “see” where it is and determine how fast it is moving. To do so, we, the observer, must shine a light of a certain wavelength (“color”) upon it—bounce a photon off it. The light (the photon), which is scattered by the electron, will then enter our microscope, be focused, and be seen by our eye. It is the scattered photon that we actually see in an act of observation. Now to illustrate how the observation itself creates the uncertainty in a measurement, we discuss such an act in two steps. Step one discusses what happens to the electron when light is shined upon it—when the photon collides with it. Step two discusses how clearly the electron can be seen (focused) through the microscope. It is the combination of the effects from these two steps that produces the celebrated uncertainty principle.

  Step One: The Collision

  As a result of their collision, the bouncing photon transfers some of its energy (and momentum) to the electron and disturbs it (much like when one billiard ball disturbs the motion of another when they collide). But there is no law that can determine the amount of energy imparted on the electron by the photon. Thus, the photon pushes and disturbs and changes the velocity of the electron unpredictably. This means that the electron may have a range of possible recoil velocities; hence, its velocity cannot be known precisely: there is an uncertainty in its velocity. On the other hand, the disturbance introduced by a photon bounced off a car or a planet is undetectably small because, compared to an electron, the mass of a car or a planet is huge; just think how much more difficult it is for anyone to push and disturb a real car, which weighs a lot, compared to pushing a toy car, which does not weigh much. The velocity and location of a car or planet can be measured almost with absolute precision. This is in fact another reason that classical physics (Newton’s, Maxwell’s, Einstein’s), which does not include the uncertainty principle, works quite well for macroscopic objects.

  Now, concerning the electron, we can reduce the uncertainty in its velocity by using a photon of smaller energy so that its push to the electron is gentler. But a photon’s energy is inversely proportional to its wavelength: the smaller the energy, the longer the wavelength (the “redder” the color is), a relationship that brings me to step two. Unfortunately, while a photon with a longer wavelength has less energy, which reduces the uncertainty in the velocity of the electron, it simultaneously increases the uncertainty in the position of the electron—the image of the electron gets fuzzier. Why?

  Step Two: The Microscope

  Because the determination of the position of the electron depends on the wavelength. This dependence, which is known as the resolving power of a microscope, regulates how clearly something can be seen—how well the scattered light can be focused and thus how accurately the electron can be located. The longer the employed wavelength, the fuzzier the image of the electron will be, and the greater the uncertainty in its position. What we see through the microscope is really a fuzzy flash created from the photon scat
tered by the electron. The electron, which is a point-particle, is somewhere within this flash, but where exactly is indeterminable. Its position cannot be known precisely. The flash may be focused into a region no smaller than the wavelength of light (the law of the resolving power states). Hence, the uncertainty in the position of the electron may be equal to or greater than the wavelength of light, but never smaller than it! So at best, the minimum uncertainty is equal to the wavelength: we cannot magnify (zoom in at) a region which is smaller than the wavelength of light we use to see something. Since the position cannot be known precisely, the electron has a range of possible locations it can occupy, just as it has a range of possible recoil velocities to move with.

  Given that light of zero wavelength does not exist—that is, we cannot observe if the light source is turned off—the uncertainty in the position can never be zero: we cannot see with absolute precision where the electron is. Nonetheless, we can reduce the uncertainty in the position by using light of a smaller wavelength, though unfortunately this action simultaneously increases the uncertainty in the velocity—for as seen in step one, the smaller the wavelength, the greater both the light energy and the disturbance imparted on the electron (i.e., the greater the range of possible recoil velocities).

  Position-Velocity Uncertainty

  The wavelength of light used in an observation has conflicting effects; there is a trade-off in the determination of the position and velocity of a particle. The result is the position-velocity uncertainty principle: the more precise the position, the more uncertain the velocity, and vice versa.7 Heisenberg proved mathematically that the product of the two uncertainties can never be less than a certain minimum positive number—which is roughly equal to Planck’s constant, a fundamental constant of nature, divided by the mass of the particle.8 Consequently, absolutely precise knowledge of either property is unattainable because if one of the uncertainties were zero, their product would also be zero, a result that would be in clear violation of the principle. In classical physics, on the other hand, of which the uncertainty principle is not part, these uncertainties could each be zero—thus, a particle’s position and velocity could, at least in principle, be determined exactly—leading to what is known as classical determinism, which is the opposite of quantum indeterminism (that is, quantum probability), the consequence of the uncertainty principle.

  Classical Determinism Versus Quantum Probability

  In the macroscopic world of classical physics, by knowing the forces that act on an object as well as the object’s exact position and velocity at some initial time, we can determine its exact position and velocity (its trajectory) for all past and future time. So its motion is precisely determinable: a path can be plotted, even watched live, point by point continuously from an initial instant to any future one. Because of this capability, classical physics is said to be deterministic. We can plot the precise orbit of a space shuttle, for example, just by knowing the forces acting on it and the initial conditions (its position and velocity at some initial instant), and we can watch it fly through space and time as predicted by our equations. It is therefore easy to predict a solar eclipse—when the earth, the new moon, and the sun will align—but absolutely impossible to measure or predict where an electron in an atom was is or will be. Why?

  According to quantum theory, the subatomic world of particles is profoundly different than everyday experience; it cannot be described by classical physics. Inherent in the uncertainty principle, which limits the accuracy of a measurement, particle properties (such as position, velocity, momentum, and energy) cannot be assigned an exact value, neither initially nor at any time later. Thus, they must unavoidably be expressed only as probabilities, which then lead to quantum indeterminism. The wave functions, which are solutions to the so-called Schrödinger equation, can be used to calculate such quantum probabilities—for example, the probability of finding a particle at a certain location at a certain instant of time. A probability is a number that represents the tendency (the potentiality) of an event to take place, not its actual occurrence (the actuality). Hence, the best we can do is to theoretically predict only probable outcomes and experimentally measure the one outcome that actually occurs, although even then, our experimental knowledge is limited by the uncertainty principle. Consequently, a particle’s path of motion can neither be predicted (nor plotted), nor can it be observed; it is indeterminable: establishing a definite, traceable, point-by-point orbit is an impossibility. In fact, the very notion of an orbit is inadmissible in quantum theory. Whence tiny particles come and whither they go can never be known. The determinism of classical physics is therefore replaced by the probability of quantum theory. And the consequences of this fact are staggering (affecting even human free will; see chapter 14). The true nature of nature, for example, is different (“disconnected”) than the way it appears to be (continuous) through mere observation.

  Observations Are Disconnected Events

  During the act of observation, all we see through the microscope is a flash of light somewhere within which the particle exists. But where exactly it is within this flash at each instant, and what it does when we are observing it, whether at rest or in motion, are all indeterminable. Even worse, nature does not allow us to know what happens between consecutive observations. Consecutive observations have time and space gaps; flashes are seen one at a time and spatially separated. Hence, inherent in the uncertainty principle observations, any observations of both the microscopic and macroscopic world, are always disconnected events! Roughly speaking, it is as if we are observing nature by continuously blinking—our observations are dotted, intermittent, quantum!

  This is a profound result and in direct contradiction with apparent reality according to which the changes in the daily phenomena are observed to occur continuously. The act of watching an arrow in flight, for example (an interesting thought experiment to be revisited in chapter 9) is really a series of disconnected observations, which to our imperfect eyes appear to occur continuously only because the time and space gaps between subsequent observations are undetectably short. The arrow’s apparent continuity of motion is therefore an illusion. The shortness in these gaps is, incidentally, a consequence of the fact that in an observation, the disturbance introduced by a photon bounced off a macroscopic object such as car or an arrow is undetectably small because these objects have comparatively more mass (inertia) than the mass of microscopic objects such as electrons and protons. This is, recall, also the reason that macroscopic objects have (actually, appear to have) definite orbits while microscopic objects do not.

  So observing anything, anything at all, can happen only discontinuously. It is, roughly speaking, like cinematography (motion pictures), where a series of separate drawings, each, say, of a ball at a different position, is flashed before us rapidly (with short time gaps). Now, (1) if the position of the ball is changed gradually in each subsequent drawing, that is, the distances (the space gaps) between each new position of the ball and the previous one are sufficiently short, then, when the drawings are flashed before us, the ball is observed to move continuously (thus with a definite orbit). But this continuity in observation is really an illusion of the deceptive senses that cannot notice the short gaps. Case (1) corresponds more to how we observe macroscopic objects. On the other hand, (2) if the space gaps are sufficiently long, then, when the drawings are flashed before us, the ball is observed to move discontinuously. Case (2) will correspond more to how we observe microscopic particles, but only after the following two modifications: first, do not think of the ball to be the actual particle; rather, it roughly corresponds to the flash of light (the wavelength) somewhere within which the observed particle exists; and second, as we will argue in “Nature as a Process” later, even if we do observe a similar type particle (say, an electron) at consecutive observations, it is indeterminable if it is the same particle (electron), even when the time and space gaps between observations are short. These two modifications, which capture more ac
curately how we observe microscopic particles, make it impossible to plot a definite path of motion for any microscopic particle.

  Now, the reason that the phenomena are observed to occur discontinuously might be that the very phenomena themselves occur discontinuously (even when we are not observing); they may not just be observed to occur discontinuously. In any case, the discontinuity in observations has astounding consequences: in the section “Nature as a Process,” we will use it to question the very identity of a particle, and in chapter 9 we will use it to question the reality of motion itself. But to understand such consequences we must first change the topic.

  Change

  The Heraclitean doctrine that everything is constantly changing and nothing is ever the same has three implications. First, there is a change; second, the change is constant; and third, because nothing is ever the same, the constant change is unidirectional. (That’s why we learn calculus, the mathematics of change.) Modern physics agrees with all three: first, change occurs in two different ways: (1) through motion and (2) through the transformations of matter and energy; second, the uncertainty principle of quantum theory and the theory of general relativity affirm that change is constant,9 and in addition, as seen just earlier, quantum theory ascertains it is also discontinuous; and third, the second law of thermodynamics discusses how change is unidirectional—the universe becomes increasingly disordered.

  (1) Motion Causes Change

  Change caused by motion is discussed in the following three cases.

  A. The motion of the particles of matter causes their rearrangement in an object and consequently causes change in its various qualities (e.g., density and temperature). For example, atoms are more compressed in denser objects and jiggle faster in hotter objects.