Particles and photons appear to be total opposites; the former has rest mass which requires space to exist; the latter has kinetic energy which requires time to occur (oscillate). But they do share certain properties (e.g., quantization) that remain invariant when one is transformed (swapped) for the other. This gauge invariance is developed in some detail.The symmetry between particle and photon turns out to be one of inversion. It is the equalities of special relativity that support this inversion and the accompanying invariances: mass transformed to energy; space transformed to time. The great advantage of these symmetries (inversions) is that they provide guidance for an object little understood (the photon) based upon an object well understood (the particle). On this basis, progress can be made in the understanding of some long-standing issues: wave-particle duality, time’s arrow, the constant speed of light and nonlocality.
Particles and photons appear to be total opposites; the former has rest mass which requires space to exist; the latter has kinetic energy which requires time to occur (oscillate). But they do share certain properties (e.g., quantization) that remain invariant when one is transformed (swapped) for the other. This gauge invariance is developed in some detail.The symmetry between particle and photon turns out to be one of inversion. It is the equalities of special relativity that support this inversion and the accompanying invariances: mass transformed to energy; space transformed to time. The great advantage of these symmetries (inversions) is that they provide guidance for an object little understood (the photon) based upon an object well understood (the particle). On this basis, progress can be made in the understanding of some long-standing issues: wave-particle duality, time’s arrow, the constant speed of light and nonlocality.
The photon is typically regarded as a unitary object that is both particle-discrete and wave-continuous. This is a paradoxical position and we live with it by making dualism a fundamental feature of radiation. It is argued here that the photon is not unitary; rather it has two identities, one supporting discrete behavior and the other supporting continuous (wave) behavior. There is photon kinetic energy that is always discrete/localized on arrival; it never splits (on half-silvered mirrors) or diffracts (in pinholes or slits). Then there is the photon’s probability wavefront that is continuous and diffractable. Acknowledging that the photon has two identities explains the photon’s dual nature. And wave-particle duality is central to quantum mechanics. Understanding it leads to new insights into the photon’s constant velocity and its entanglement with another photon.
Momentum and velocity are two well-known physical observables in classical physics (and quantum physics as well because quantum particles have impulse and move through space in a certain amount of time based on an external clock and ruler). They are, however, measured in different ways. Velocity describes motion through x in some time t, while p is measured through impulses. Thus one does not need a clock to measure momentum. It may be measured in terms of the damage done to a foil, compression of a spring etc. Thus p=m1v1=m2v2 etc., i.e. a numerical number associated with momentum does not automatically yield the velocity unless one knows rest mass. In many situations rest mass is known (i.e. one deals with an electron etc) and so there seems to be a tendency to consider momentum and velocity to be almost the same thing when they are distinctly different. In fact, we argue that the notion of wavefunction W(x) and density P(x)=W*(x)W(x) are associated with momentum and velocity respectively. In fact, for a free particle these two measurables are linked with completely different spatial probabilities. Constant velocity impies P(x)=constant while exp(ipx) describes the two-dimensional x-probability associated with p which is based on a constant mo and v. In special relativity for a free particle (i.e. p constant, v constant), there are two well known Lorentz invariants: EE = pp + momo (c=1) and A = -Et + px. One may note that v does not appear explicitly even though one may write E and p in terms of v i.e. E = mo/sqrt(1-vv) and p=Ev. The first invariant describes E in terms of rest mass and p (measured through impulse). The second involves p,E and x,t with x and t appearing as independent even though ultimately x(t) and v=dx/dt=constant = x/t if x and t both start at 0. This independence is crucial because it means one may consider fluctuations which keep A constant separately. For example, if t→ t+ hbar/E and x→ x+hbar/p, then A remains constant. This leads to the idea of the quantum wavelength and a spatial probability independent of t, namely exp(ipx). One average, however, x=vt, but how does this appear in Lorentz invariants? There is no explicit v. We argue that the Lorentz invariant A = -Et + px must convert E from a function of p to one in v and that this occurs through a Legendre transformation. Thus the form of the invariant is itself a Legendre transformation with E being transformed into L, the Lagrangian. There is, however, a second important feature because p=dL/dv (partial) and given that p is constant, dp/dt=0 so d/dt dL/dv partial =0 which is in the form of an extremization. We argue that this is not an accident. dL/dv=p follows from E being constant, so, in other words, it follows from the px term. This same term leads to exp(ipx) which means that one does not have smooth x=vt motion within a wavelength. Thus, we argue that when one transforms to the second measurable v, the notion of this fluctuation behaviour must also be manifested. In other words, v=constant or dv/dt is not enough. The extremization behaviour of the Lagrangian, we argue, is thus not a mathematical convenience, but gives an indication that even though the extreme path x=vt is followed on average, other paths are sampled. We argue that this idea is incorporated into special relativity, in fact within a single Lorentz invariant A = -Et + px.
Radiation was a big challenge for the quantum pioneers since the photon was massless, probabilistic and appeared to be both wave and particle. Einstein's special relativity equated mass with energy and space with time. But the equality of mass with energy, then and now, is regarded as quantitative and the equality of space with time is anything but equal; space hosts material entities; time hosts nothing. Exploring these equality issues raises some questions as to how measurable entities-particles and photons-depend upon dimensions. The particle resides in a dimension, space, while also progressing (or persisting) in a dimension, time. The photon certainly progresses in one dimension, space; does it reside there as well? These questions lead to some new conclusions regarding the nature of the photon, its dualism and its nonlocal behavior.
Part I looks at duality for the photon; Part II does the same for the electron. The traditional division of kinetic energy between radiation (E = hf) and matter-in-motion (E = 1/2 mv2) is reexamined permitting new insights into duality. \n \nAn in-flight photon displays wave characteristics. Such a photon can interfere with itself and take all available space paths as a wave. In addition, photons pass through one another like waves whereas particles impact each other. It is only when the photon terminates on a material object and gives up its energy – and ceases to be a photon – that particle characteristics appear, namely: 1) the photon is finally space located; and 2) oscillation ceases. This suggests that the photon’s wave and particle nature do not overlap. Understanding photon termination as a release of mass stored, rather than particle impact, permits a better understanding of presumed wave-particle duality for the photon.
The Lorentz transformation of special relativity is based on velocity. Although this velocity may be differentiated by time, the notion of force is not needed to obtain the Lorentz matrix for a particle with rest mass. In particular, in special relativity one considers frames moving at constant velocities. In the case of a photon, the Lorentz transformation preserves the form of Maxwell’s electromagnetic equations. As a result, there does not seem to be a focus on force, rather the emphasis is on the two 4-vectors (p,E) and (x,t) for a particle with rest mass and photon. Nevertheless, a particle with momentum (and the capability to interact) imparts an impulse. In fact, one may think of energy changing due to an impulse (which includes force). Thus from an information point of view, one may ask: Does this force which creates a change in energy/momentum “disappear” as the particle/photon moves at constant speed only to “reappear” when it strikes a surface? If not, where is the information of this force stored? We argue it is associated with a change in energy and momentum of a free particle which in turn is linked to an internal ruler/clock i.e. the quantum frequency and wavelength from exp(-iEt+ipx) which preserves the force because a spatial probability distribution is created (for the wavelength). This force is linked with a direction i.e. the direction of p through the two dimensionality of exp(ipx). Thus, we argue that the force does not disappear, rather it is manifest in the internal clock and ruler which define spacetime for the free quantum particle, but in a probabilistic manner with the distribution being deterministic to ensure it maps to spatial invariance. One might at first find it surprising that force, usually associated with acceleration (i.e. deterministic motion) is now associated with probability cos(px) in space (, but deterministic probability, not random), but E,p and x,t are intertwined through the Lorentz invariant -Et+px for both a particle with rest mass and photon, so if E and p change, it is not necessarily surprising that t,x also change. Thus an impulse may change p and E, but then remains manifest in the system through the internal clock and ruler gradations in such a way that speed is still constant on average.
To describe Light, Newton used a Particle, which, on the one hand, is an element, invariant in space and time, but, on the other hand, whose properties depend on the Color of Light. This dependence of the property of this element is similar to the dependence of the kinetic energy of a material point on speed. But this abstract point does not have the Rest Mass invariant for all speeds. This initial contradiction was simply taken for the specificity of a given particle called a photon, which Einstein linked with the Planck's quantum of energy. Newton's corpuscular theory of light initially encountered difficulties in describing the interference and diffraction of light. But the description of coherent light will raise the question of the size-geometry of this elementary particle. Taking into account the geometry of a photon allows us to really, and not abstractly, show its invariant specificity, which ensures the stitching not only of individual photons into a coherent wave, but also stitching of the corpuscular and wave theory. In this case, the postulated Heisenberg Uncertainty Principle is translated into the mathematical property of the Fourier transform, which determines measurability. Moreover, Newton's Elementary Particle shows how to determine the real specificity of a material particle that has lost its Mass invariance due to its Einstein dependence on velocity and, taking into account the principle of Logarithmic Relativity, allows us to correctly systematize Elementary (Fundamental) Particles.