When the concept of Zero is analyzed, it is frequently related to another equally deep and complicated concept – Nothing. If in science, Zero is closely associated with mathematics, then Nothing is primarily related to the material world. The question of whether Nothing can be found in the real physical world is often discussed in relation to the vacuum which, at some point in the history of the development of physics, is thought about as an empty space. Nevertheless, theories of modern physics have demonstrated that even in a vacuum, when all the matter is evacuated from a certain region of space, and this region is isolated from ordinary fields – gravitation field, electromagnetic fields etc – there still remain physical fields called vacuum zero fluctuations that can not be removed in principle. These vacuum fields are properties of space. In this chapter I will analyze another physics theory – namely, Quantum Physics – and will consider its less discussed relations to the concept of Nothing. One of the very first Greek philosophers, Thales (624–548 BCE) from Miletus, declared that Something can not appear from Nothing and it can not disappear, turning into Nothing. This idea, in some aspects, was further developed by Zeno from Elea (495–430 BCE) when he created his paradoxes of motion. These paradoxes can be understood as an analysis of the possibility of infinite division of time and space intervals. When we come to Quantum Physics, the very first appearance of the idea of the smallest possible portion of energy, quantum, was stimulated by the analysis of the spectrum of radiation of heated body – black-body radiation. German physicist Max Planck (1858–1947) demonstrated in 1899 that if we assume that there exists a smallest portion of radiation energy that can not be further divided into smaller parts, we arrive at the description of spectrum of the black-body radiation that perfectly matches the observable reality. In contrast, if we assume that radiation energy can be divided an infinite number of times and there does not exist the smallest possible portion, we arrive at the radiation spectrum which is in a sharp contradiction with observable reality. This contradiction is so strong that it has acquired a special term – the ultraviolet catastrophe. Certain parallels in Zeno’s reasoning and approach used in Quantum Physics can clearly be seen and will be discussed. In the conclusion, I will briefly touch on a similar situation in another field of physics when at the other extreme, departure from the idea of the possibility of the infinitely large quantities, this time velocities of motion, gave birth to another theory of modern physics – Einstein’s theory of special relativity.
When the concept of Zero is analyzed, it is frequently related to another equally deep and complicated concept – Nothing. If in science, Zero is closely associated with mathematics, then Nothing is primarily related to the material world. The question of whether Nothing can be found in the real physical world is often discussed in relation to the vacuum which, at some point in the history of the development of physics, is thought about as an empty space. Nevertheless, theories of modern physics have demonstrated that even in a vacuum, when all the matter is evacuated from a certain region of space, and this region is isolated from ordinary fields – gravitation field, electromagnetic fields etc – there still remain physical fields called vacuum zero fluctuations that can not be removed in principle. These vacuum fields are properties of space. In this chapter I will analyze another physics theory – namely, Quantum Physics – and will consider its less discussed relations to the concept of Nothing. One of the very first Greek philosophers, Thales (624–548 BCE) from Miletus, declared that Something can not appear from Nothing and it can not disappear, turning into Nothing. This idea, in some aspects, was further developed by Zeno from Elea (495–430 BCE) when he created his paradoxes of motion. These paradoxes can be understood as an analysis of the possibility of infinite division of time and space intervals. When we come to Quantum Physics, the very first appearance of the idea of the smallest possible portion of energy, quantum, was stimulated by the analysis of the spectrum of radiation of heated body – black-body radiation. German physicist Max Planck (1858–1947) demonstrated in 1899 that if we assume that there exists a smallest portion of radiation energy that can not be further divided into smaller parts, we arrive at the description of spectrum of the black-body radiation that perfectly matches the observable reality. In contrast, if we assume that radiation energy can be divided an infinite number of times and there does not exist the smallest possible portion, we arrive at the radiation spectrum which is in a sharp contradiction with observable reality. This contradiction is so strong that it has acquired a special term – the ultraviolet catastrophe. Certain parallels in Zeno’s reasoning and approach used in Quantum Physics can clearly be seen and will be discussed. In the conclusion, I will briefly touch on a similar situation in another field of physics when at the other extreme, departure from the idea of the possibility of the infinitely large quantities, this time velocities of motion, gave birth to another theory of modern physics – Einstein’s theory of special relativity.
The article discusses the new approaches to the four Zeno’s Paradoxes: “The Arrow”, “The Achilles”, “The Dichotomy” and “The Moving Rows”. Paradoxes are analyzed in relation to the current research in the field of elementary particle Physics and promising areas of the quantum theory of gravity development. Provided with the necessary philosophical interpretation Physics concepts are used to clarify Zeno’s Paradoxes and to search for answers to them. The involvement of modern approaches is shown to be ineffective in solving the paradoxes due to their scope losses when analyzed by the microworld Physics on ultra-small scales. The work’s main part is devoted to demonstrating this circumstance – the questions posed by paradoxes are deprived of the possibility of getting the answers (at least, in their classical interpretation). As a possible explanation stands the ground of mixing the properties of the macroworld and the microworld in the paradoxes statements (which is historically justified given the intuitive homogeneity of big and small, and the origin of non-classical Physics – quantum mechanics – only in the 20th century), meaning the transition from observation of the large physical objects to the infinitely small in terms of discreteness and continuity. However, the principles of space organization on ultra-small scales are beginning to be clarified in general terms only now, and, perhaps, these principles may turn out to be quite far from classical ideas on fundamental physical reality.
This chapter presents the basic physical ideas that underpin the quantum theory. Historians place the beginnings of the quantum theory at 1900. That year Max Planck published his famous formula for the distribution of energy as a function of frequency in black-body radiation. Curiously, although radiation theory gave birth to quantum mechanics, the interaction of matter and electromagnetic radiation is a rather advanced topic in quantum mechanics and it took almost fifty years for an acceptable formulation to be achieved. One reason for this is that photons are quanta of the electromagnetic field, and the quantum theory of fields requires a relativistic treatment to be entirely successful. The corpuscular nature of light was only half of the input that gave birth to quantum mechanics. The other half concerns matter. Given that the discreteness of photons manifests itself during the emission and absorption process, it is not surprising to find that quantum oddities afflict the behaviour of material particles too.
Quantum Mechanics and its Interpretations Peter E. Hodgson (bio) Quantum Mechanics is an elegant and indeed beautiful formalism, and enables the results of many physical measurements to be calculated with great accuracy. But from the earliest days there has been intense debate about the interpretation of quantum mechanics, and it shows no signs of being settled; if anything, it is becoming more intense over the years. It should therefore be evident that the most that can be done here is to try to show where the real difficul-ties lie, and how the failure to recognize that quantum mechanics is an essentially statistical theory has led to a series of confusing quantum paradoxes. It is just these paradoxes that have often been used to support theological speculations. The Discovery of the Quantum The quantum nature of the physical world was discovered by Max Planck in the early years of the twentieth century. He was studying thermodynamics and his attention was drawn to the frequency distribution of black-body radiation. This radiation is emitted from a small hole in a heated enclosure with rough walls, which ensures [End Page 62] that the radiation reaches statistical equilibrium before emission. The frequency distribution is found to be independent of the material lining the walls of the oven, so Planck realized that it must be a fundamental characteristic of all matter. This frequency distribution had been measured by several experimentalists, and Planck resolved to try to see how it can be derived theoretically. Already Rayleigh and Jeans had used classical radiation theory to derive an expression that fitted the data well at low frequencies but tended to infinity at high energies, which was of course unacceptable. The physicist Wien had derived a formula that fitted the data at high frequencies but failed at low frequencies. Planck used an ingenious argument based on entropy to interpolate between these two formulae and obtained a formula, now known as the Planck distribution, that fitted the data perfectly. His next task was to understand the physics behind his formula. He used the familiar technique of assuming that the energy is emitted in small finite amounts, and then let their size tend to zero, so as to represent a continuous distribution. To his great surprise, the intermediate formula with discrete amounts of energy, called quanta, gave the Planck distribution, but the final result, with infinitely small quanta, did not. All his instincts as a physicist rebelled against this conclusion. Surely energy must be emitted continuously. He tried hard to find a way to avoid this unwelcome conclusion, but without success. He had to admit that it is a feature of the world. Soon it was confirmed by Einstein’s interpretation of the photoelectric effect. This story shows clearly that physicists do not impose their ideas on the world, but recognize and accept what they find, whether or not it agrees with their original ideas. The world is made by God in ways that often we cannot imagine. [End Page 63] The Old Quantum Theory A few years later Rutherford discovered that the atom has a small central nucleus containing most of its mass surrounded by a number of electrons. Bohr used the idea of the quantum to build his model of the atom. He assumed that the electrons go around the nucleus in discrete orbits, and that radiation is emitted when an electron falls from one orbit to a lower one. With this model, he was able to calculate to high accuracy the frequencies of the radiation emitted from an excited hydrogen atom. This was a great achievement, but to get his result he had to assume that the electrons stayed in their orbits, whereas classical theory predicted that they would continuously lose energy and rapidly spiral into the nucleus. Quantum Mechanics and its Interpretations These problems were solved by the development of quantum mechanics in the 1920s by Heisenberg, Schrodinger, Dirac, and others. This enabled what is called the wave function to be calculated for any physical system, and from the wave function the probabilities of occurrence of measurable quantities can be found. It is a beautiful theory, and is the indispensable means of calculation for atomic, nuclear...
The idea of the photon has stirred the imaginations of physicists ever since 1905 when Einstein originally proposed the use of light quanta to explain the photoelectric effect. This concept is formalized in the quantum theory of radiation, which has had unfailing success in explaining the interaction of electromagnetic radiation with matter, seemingly limited only by the ability of physicists to perform the indicated calculations. Nevertheless, it has its conceptual problems—various infinities and frequent misinterpretations. Consequently an increasing number of workers are asking, “to what extent is the quantized field really necessary and useful?” In fact the experimental results of the photoelectric effect were explained by G. Wentzel in 1927 without the quantum theory of radiation. Similarly most electro-optic phenomena such as stimulated emission, reaction of the emitted field on the emitting atom, resonance fluorescence, and so on, do not require the quantization of the field for their explanation. As we will see, these processes can all be quantitatively explained and physically understood in terms of the semiclassical theory of the matter–field interaction in which the electric field is treated classically while the atoms obey the laws of quantum mechanics. The quantized field is fundamentally required for accurate descriptions of certain processes involving fluctuations in the electromagnetic field: for example, spontaneous emission, the Lamb shift, the anomalous magnetic moment of the electron, and certain aspects of blackbody radiation. (The Compton effect also fits here, but see later under references 8b and c.) Here we will outline how the photon concept originated and developed, where it is not required and is often misused, and finally where it plays an essential role in the understanding of physical phenomena. In our discussion we will attempt to give a logically consistent definition of the word “photon”—a statement far more necessary than one might think, for so many contradictory uses exist of this elusive beast. In particular consider the original coining of the word by G. N. Lewis: “[because it appears to spend] only a minute fraction of its existence as a carrier of radiant energy, while the rest of the time it remains an important structural element within the atom…, I therefore take the liberty of proposing for this hypothetical new atom which is not light but plays an essential part in every process of radiation, the name photon!” (our exclamation point). Clearly the present usage of the word is very different.
The theory of relativity is essentially the culmination of classical physics. Although revisions in our concepts of space and time are necessitated by both the special and general theories of relativity, the notion of causality, in which a cause precedes its effect, remains intact in the relativistic formulations of electrodynamics and mechanics and of gravitation. An upper limit is set on the speed of bodies, and of the propagation of energy, and physical quantities are often defined operationally, but once we adjust ourselves to these new rules, our representations of physical processes proceed pretty much as they did in classical physics. On the other hand, quantum theory seems to require a much more profound philosophical revision of our thought patterns. Even the viability of the usual meaning of a causal connection between one event and another is there called into question. SOME HISTORICAL BACKGROUND We begin with a brief and highly selective review of the experimental and theoretical problems that formed the conceptual backdrop to the emergence of quantum theory. We focus attention first on an important phenomenon – blackbody radiation – that was instrumental for the formulation of quantum mechanics. A blackbody is defined as a surface that absorbs all of the electromagnetic radiation that falls onto it. It is picturesquely so named since any light incident on such a body would be absorbed, making it appear black (at least at typical temperatures in our environment). A blackbody also emits radiation.
The word “quantum” means “how much”, “quantity”, “share”, “portion”, and so on. The language of quantum physics is peculiar although in essence it is not different from a conventional language. There are few people nowadays who do not accept the reality of atoms as they do, say, the motion of the Earth around the Sun. “The Universe is made up, in reality, of nothing but atoms and the void; all the rest exists only in the mind. After twenty centuries of oblivion the idea of atoms was resurrected by the French philosopher and sage Pierre Gassendi. The amplitude of a wave is its maximum height. The definitions of the wavelength and velocity are clear from the drawing. In the closing years of the last century, Max Planck, like many before him, was looking for a universal formula for the spectral function of an absolutely black body.