A fresh look at Planck's quantum, h, re-interprets action as the companion of power in a dynamic interplay of energies in a multi particle system of the micro world. An exchange of energy, δE, requires a characteristic duration, δτ, with δE and δτ tied together in a natural way. Action, the product δEδτ, must have a nonzero lower limit, h, as a classical necessity everywhere in physics. Zero h would constitute a singularity. The veritable quantum is action, not energy. Black body radiation formulas (Wien, Planck, and Rayleigh) all require this non zero h. Planck's thermodynamic approach was not consistently developed further. Einstein in his 1905 description of the photo effect chose the single "quantum of light" as statistically independent actor in radiation. The resulting discussions about the wave-particle dualism, the meaning of uncertainty, the collapse of wave packets when observed, self-interference, and related problems can be avoided by the consistent view of the ensemble interpretation. In agreement with action defined as δEδτ only co-operative phenomena produce the effects we observe. In particular, this concerns the photon, directly associated with h, as naturally interactive quantum. Careful experiments on low intensity interference suggest to take the photon out of the isolation, thus changing the general view of quantum physics with surprising consequences. Do photons transport energy or action? To understand where 20th century physics has gone a glance at the historical background is in order.
A fresh look at Planck's quantum, h, re-interprets action as the companion of power in a dynamic interplay of energies in a multi particle system of the micro world. An exchange of energy, δE, requires a characteristic duration, δτ, with δE and δτ tied together in a natural way. Action, the product δEδτ, must have a nonzero lower limit, h, as a classical necessity everywhere in physics. Zero h would constitute a singularity. The veritable quantum is action, not energy. Black body radiation formulas (Wien, Planck, and Rayleigh) all require this non zero h. Planck's thermodynamic approach was not consistently developed further. Einstein in his 1905 description of the photo effect chose the single "quantum of light" as statistically independent actor in radiation. The resulting discussions about the wave-particle dualism, the meaning of uncertainty, the collapse of wave packets when observed, self-interference, and related problems can be avoided by the consistent view of the ensemble interpretation. In agreement with action defined as δEδτ only co-operative phenomena produce the effects we observe. In particular, this concerns the photon, directly associated with h, as naturally interactive quantum. Careful experiments on low intensity interference suggest to take the photon out of the isolation, thus changing the general view of quantum physics with surprising consequences. Do photons transport energy or action? To understand where 20th century physics has gone a glance at the historical background is in order.
How can we construct a picture of the photon from the wealth of observation material available to us? The photon appears to have a split personality: it is neither a wave nor a particle but something else which, depending on the experimental situation, exhibits a wave- or a particle-like behavior. In other words, in the photon (as in material particles such as the electron) the particle–wave dualism becomes manifest. Whereas classically the wave and the particle pictures are separate, quantum mechanics accomplishes a formal synthesis through a unified mathematical treatment. Let us look first at the wave aspect familiar from classical electrodynamics, which seems to be the most natural description. It makes all the different interference phenomena understandable, such as the “interference of the photon with itself” on the one hand and the appearance of spatial and temporal intensity correlations in a thermal radiation field on the other (which are obviously brought about by superposition of elementary waves emitted independently from different atoms). It might come as a surprise (at least for those having quantum mechanical preconceptions) that the classical theory is valid down to arbitrarily small intensities: the visibility of the interference pattern does not deteriorate even for very small intensities – the zero point fluctuations of the electromagnetic field advocated by quantum mechanics do not have a disturbing effect – and is valid not only for conventional interference experiments but also for interference between independently generated light beams (in the form of laser light).
This paper argues that the quantization of energy and the relationship E = hf are not fundamental axioms of quantum mechanics but structural consequences of two postulates: that time is discrete at the Planck scale, and that each discrete temporal unit carries equal action. Planck's constant is identified as the action content of one Planck-time tick, and the Nyquist-Shannon sampling theorem is applied to derive the maximum physical frequency. The paper further argues that wave-particle duality dissolves under this framework — a photon is always a wave, and point-like detection events are what quantized energy transfer looks like at the receiving end, not evidence for particle ontology. The double-slit experiment, quantum eraser, and interaction-free measurements are re-examined and shown to require no paradoxical interpretation when particle language is abandoned. The paper is a conceptual contribution intended to motivate formal development. Prior work by Caldirola on the chronon is discussed and distinguished.
Chapter 4 deals with Quantum Mechanical (QM) phenomena. The first section describes the first attempts at quantization of energy, momentum, angular momentum, etc. We start with Plank's solution to the black-body problem, introducing the concept of photons: discrete packets of electromagnetic energy. We show how Plank's description of black-body radiation is perfectly fit by the cosmic microwave radiation, providing the strongest evidence for the Big-Bang at the origin of the Universe. We then describe Bohr's solution to the paradoxical stability of atoms, introducing quantization of angular momentum (or action) and correctly predicting the energy levels of the hydrogen atom. We show how Einstein used Plank's idea to explain the photo-electric effect (an effect exploited in CCD cameras and solar cells) and how he used Bohr's understanding of energy levels in atoms to provide an intuitive explanation of Plank's law. Einstein insight opened the way to the field of spectroscopy and the development of the laser. In the second section, following the lead of Dirac, we show that QM is equivalent to Linear Algebra in the space of complex functions (which describe the state of the system). We show that Schrödinger's equation is a natural consequence of that description, once the relation between energy and frequency established by Plank (for photons) and de Broglie (for particles) is taken into account. In the context of the chiral ammonia molecule we discuss the queerness of QM which describes physical systems as superposition of states (such as left and right chirality state of a molecule, dead and alive cat). We show that this queerness is nonetheless supported by experiments and is behind much of our technology: masers and lasers, atomic clocks, semiconductors (diodes, transistors, etc.). In the following section we introduce the representation of operators in QM (the equivalent of matrices in linear algebra): momentum, position, energy, etc. which correspond to measurements on the system. We show that the non-commutability of some operators (common with matrix operations) leads to Heisenberg uncertainty principle: the position and momentum of a particle cannot be determined with absolute precision. We discuss the solution of Schrödinger's equation for free particles demonstrating their equivalence with EM phenomena: particles undergo refraction and diffraction, exemplifying the particle/wave duality inherent to QM systems. We discuss QM tunneling and its use in the Scanning Tunneling Microscope. In the following section we study Dirac's equation: the successful attempt by Dirac to unify QM with Einstein's relativity, with the resulting prediction of anti-particles and spin. We then solve for the energy levels of electrons in the hydrogen atom (from Schrödinger's equation) and show that the existence of spin profoundly affects the behavior of electrons in an atom: they cannot share the same energy level, a rule known as Pauli's exclusion principle. Pauli's principle is central to the understanding of the chemical properties of atoms and fully explains Mendeleev's periodic table of the elements. In the next section we discuss along with two exactly soluble systems (diatomic rotational and vibrational levels), various approximations used to study systems (e.g. molecules) for which there are no analytical solutions. In particular, we introduce Pauling's variational approach, Hückel molecular orbital theory and time independent perturbation theory. We apply those approaches to determine the energy levels in alkenes, in multi-electron atoms and in systems under constant electric or magnetic field (such as in Magnetic Resonance Imaging). In the last section we discuss time dependent perturbation theory. We use it to establish the rules allowing for transitions between energy levels and revisit Einstein description of absorption/emission phenomena.
A fundamental tenet in the study of organization in inanimate and living matter is the quantization of energy. In inanimate systems where temperature is a critical organizing parameter, the quantum of action is an atomic-level phenomenon described in terms of Planck’s constant, first defined as the ratio of the photon energy to the frequency of its electromagnetic wave. In living systems, where the cycle time of metabolic processes is the organizing variable, the quantum of action is a cell-level phenomenon described in terms of an analog of Planck’s constant, namely the ratio of the metabolic energy to the frequency of the enzymatic or mitochondrial oscillators. This chapter elucidates the relation between these two measures of quantum action. We review the role of Planck’s constant in physics, first, as a fundamental parameter for explaining the empirical laws of black body radiation, and its more modern developments. We also describe the theoretical and empirical rationale for the cellular-level quanta. We exploit this analysis to elucidate how energy transformation in physical processes, where temperature is the organizing parameter, relates to energy transduction in biological processes, which are essentially isothermal. We then link the cell level to the organismal level of metabolism and obtain a scaling relationship for the biological Planck quantum of action as a function of the size of the biological system studied. Finally, we discuss these ideas in light of quantum-like processes in biological organisms and systems: identifying generalized quantum principles that apply not just at microscopic levels but also at macroscopic levels, relevant to biology, where we used to consider classical physics alone to be relevant. This chapter provides a direct analogy between quantization of energy in solids first demonstrated by Debye and biochemical energy production in cellular mitochondria. The Planck constant proved to be a fundamental constant of matter as it appeared both in the Schoedinger equation and the Heisenberg uncertainty principle. Recently, quantum biology has garnered major scientific interest, but so far it has only focused on physical quantum effects in biological systems, such as photosynthesis, not truly biological quantization. We point to metabolism, as an indispensable process that underlies all life forms’ existence, and show that its quantization can be better understood in terms of a corresponding quantum of action. We estimate its value, compare it to Planck’s quantum of action in physics and explain their different scales. We hypothesize that energy quantization of metabolism in biological systems is an important conceptual advance that can provide insights into both healthy and pathological physiology.
The principle of least action, which has so successfully been applied to diverse fields of physics looks back at three centuries of philosophical and mathematical discussions and controversies. They could not explain why nature is applying the principle and why scalar energy quantities succeed in describing dynamic motion. When the least action integral is subdivided into infinitesimal small sections each one has to maintain the ability to minimize. This however has the mathematical consequence that the Lagrange function at a given point of the trajectory, the dynamic, available energy generating motion, must itself have a fundamental property to minimize. Since a scalar quantity, a pure number, cannot do that, energy must fundamentally be dynamic and time oriented for a consistent understanding. It must have vectorial properties in aiming at a decrease of free energy per state (which would also allow derivation of the second law of thermodynamics). Present physics is ignoring that and applying variation calculus as a formal mathematical tool to impose a minimization of scalar assumed energy quantities for obtaining dynamic motion. When, however, the dynamic property of energy is taken seriously it is fundamental and has also to be applied to quantum processes. A consequence is that particle and wave are not equivalent, but the wave (distributed energy) follows from the first (concentrated energy). Information, provided from the beginning, an information self-image of matter, is additionally needed to recreate the particle from the wave, shaping a “dynamic” particle-wave duality. It is shown that this new concept of a “dynamic” quantum state rationally explains quantization, the double slit experiment and quantum correlation, which has not been possible before. Some more general considerations on the link between quantum processes, gravitation and cosmological phenomena are also advanced.
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...