This paper further explores intuitions we highlighted in previous papers already: 1. The concept of the matter-wave traveling through the vacuum, an atomic lattice or any medium can be equated to the concept of an electric or electromagnetic signal traveling through the same medium. 2. There is no need to model the matter-wave as a wave packet: a single wave – with a precise frequency and a precise wavelength – will do. 3. If we do want to model the matter-wave as a wave packet rather than a single wave with a precisely defined frequency and wavelength, then the uncertainty in such wave packet reflects our own limited knowledge about the momentum and/or the velocity of the particle that we think we are representing. The uncertainty is, therefore, not inherent to Nature, but to our limited knowledge about the initial conditions. 4. The fact that such wave packets usually dissipate very rapidly, reflects that even our limited knowledge about initial conditions tends to become equally rapidly irrelevant. Indeed, as Feynman puts it, “the tiniest irregularities” tend to get magnified very quickly at the micro-scale. In short, as Hendrik Antoon Lorentz noted a few months before his demise, there is no reason whatsoever “to elevate indeterminism to a philosophical principle.”
This paper further explores intuitions we highlighted in previous papers already: 1. The concept of the matter-wave traveling through the vacuum, an atomic lattice or any medium can be equated to the concept of an electric or electromagnetic signal traveling through the same medium. 2. There is no need to model the matter-wave as a wave packet: a single wave – with a precise frequency and a precise wavelength – will do. 3. If we do want to model the matter-wave as a wave packet rather than a single wave with a precisely defined frequency and wavelength, then the uncertainty in such wave packet reflects our own limited knowledge about the momentum and/or the velocity of the particle that we think we are representing. The uncertainty is, therefore, not inherent to Nature, but to our limited knowledge about the initial conditions. 4. The fact that such wave packets usually dissipate very rapidly, reflects that even our limited knowledge about initial conditions tends to become equally rapidly irrelevant. Indeed, as Feynman puts it, “the tiniest irregularities” tend to get magnified very quickly at the micro-scale. In short, as Hendrik Antoon Lorentz noted a few months before his demise, there is no reason whatsoever “to elevate indeterminism to a philosophical principle.”
It has already been noted (section 2.8) that high frequency electromagnetic radiation can exhibit particle-like behaviour. For example, in the sensitive type of detector known as a photomultiplier tube (described in Wehr and Richards, Physics of the Atom , 2nd edn, Addison-Wesley, section 10.5), a beam of low-intensity X-rays is detected as a sequence of isolated sharp pulses, such as would be produced by a stream of particles arriving at the detector. As was pointed out, it is not surprising that it is usually high-frequency radiation which travels in particle form; as shown in figure 2.39, a wave group of high-frequency radiation can be compressed into a very short time span. However, when we speak of a particle, we mean something more than an entity which arrives in a short time span. A particle has a definite size, or more exactly it has a well-defined energy and momentum. It was discovered around about 1900 that the same is true of an X-ray wave packet: all packets of a given frequency radiation carry the same energy and momentum. This revolutionary discovery means that we must treat the wave packets as particles on exactly the same footing as more familiar particles such as electrons. The electromagnetic particle is called a photon . There is a wealth of experimental evidence which may be used to define the properties of a photon. We shall be highly selective, however, and simply present two particularly clear-cut experiments, the photoelectric effect and Compton scattering, which enable one to define the energy and momentum of the photon in terms of the frequency and wave number of the corresponding wave. These experiments will be described in detail in section 4.1.
A satisfactory explanation of the confounding wave-particle duality of matter is presented in terms of the reality of the wave nature of a particle. In this view, a quantum particle is an objectively real wave packet consisting of irregular disturbances of underlying quantum fields. It travels holistically as a unit and thereby acts as a particle. Only the totality of the entire wave packet at any instance embodies all the conserved quantities, for example the energy-momentum, rest mass, and charge of the particle, and as such must be acquired all at once during detection. On this basis, many of the bizarre behaviors observed in the quantum domain, such as wave function collapse, the limitation of prediction to only a probability rather than an actuality, the apparent simultaneous existence of a particle in more than one place, and the inherent uncertainty can be reasonably comprehended. The necessity of acquiring the wave function in its entirety for detection, as evinced by the appearance of collapse of the wave function, supports the paradigm of reality of the wave function described here. Quanta 2016; 5: 93–100.
In the early decades of this century physics was revolutionised by the advent of quantum mechanics. Observed atomic spectra could only be explained if the seemingly unshakeable concept of a particle moving along a path (trajectory), sharply defined and uniquely determined by the initial position and momentum coordinates, was dropped in favour of a description of electrons as standing waves or wave packets, whose position and momentum carry inherent uncertainties. In the course of the quantum revolution, generations of physicists were taught that the concept of classical paths is wrong on the atomic scale.
Uncertainty may result from (1) an impossibility to measure what we want to measure, or an impossibility to observe the system, (2) the limited precision of our measurement, (3) the measurement fundamentally disturbing the system and, as such, causing the information to be unreliable, (4) an uncertainty that is inherent to Nature (Copenhagen interpretation). We agree with Lorentz’s and Einstein’s viewpoint: there is no need to elevate indeterminism to a philosophical principle. The more important question is: how does quantum physics model it? How does it deal with it? This paper wants to offer some thoughts on that, supporting Lorentz’s (and Einstein’s) position: we only have statistical indeterminism. Quantum physics should, therefore, not be seen as a radical departure from classical physics. Quantum-mechanical uncertainty is nothing but statistical indeterminism. This is, effectively, the fifth interpretation of uncertainty which should be added to the list above, and may well be the final one. The position is illustrated with a detailed discussion of the wavefunction(s) in the context of Schrodinger’s wave equation for the hydrogen atom. We also further explore the question in regard to the (possible) physical dimension of the real and imaginary part of the wavefunction. To paraphrase Feynman, we wonder what could be ‘sloshing back and forth’ between the real and imaginary part of the wavefunction? We think it is kinetic and potential energy. We, therefore, briefly present our two-dimensional oscillator model again, but using the metaphor of a multi-piston radial engine as a metaphor this time.
The quantum microscopic world view: I promised an explanation of quantum theory in two steps. In the first step Schrödinger’s wave is something that moves in familiar threedimensional space. You could almost believe, as Schrödinger himself did at first, that there is something real waving that corresponds to the fundamental stuff of matter (electrons, quarks, photons, . . . ), something like Maxwell’s dynamical field of electromagnetism that in the old theory carries what we perceive as light. But alas, the Schrödinger wave function is not even an ordinary number. Its symbol stands for a whole array of numbers, including an amplitude at each point whose square is the probability that a detector will click there, and components in a set of “internal dimensions” that are new features of Nature. Worse, the Schrödinger wave for two detectors moves in six spatial dimensions, three to locate each detector. Adding more detectors requires more dimensions. Whatever it is, the Schrödinger wave is not a “real” field like Maxwell’s.
The interaction between atomic Bose-Einstein condensate (BEC) and light field in an optical ring cavity gives rise to many interesting phenomena such as supersolid and movable self-trapped matter wave packets. Here we examined the collision of two self-trapped atomic matter wave packets in an optical ring cavity, and abundant colliding phenomena have been found in the system. Depending on the magnitude of colliding velocity, the collision dynamics exhibit very different features compared with the cavity-free case. When the initial colliding velocities of the two wave packets are small, they correlatedly oscillate around their initial equilibrium positions with a small amplitude. Increasing the collision velocity leads to severe scattering of the BEC atoms; after the collision, the two self-trapped wave packets usually break into small pieces. Interestingly, we found that such a medium velocity collision is of great phase sensitivity, which may make the system useful in precision matter wave interferometry. When the colliding velocity is further increased, in the bad cavity limit, the two wave packets collide phenomenally similar to two classical particles-they first approach each other, then separate with their shape virtually maintained. However, beyond the bad cavity limit, they experience severe spatial spreading.