Vinaire's Blog

Reference: Disturbance Theory

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Wave function – Wikipedia

A wave function in quantum physics is a mathematical description of the quantum state of a system. The wave function is a complex-valued probability amplitude, and the probabilities for the possible results of measurements made on the system can be derived from it. The most common symbols for a wave function are the Greek letters ψ or Ψ (lower-case and capital psi, respectively).

A wave function describes the configuration of high frequency, compacted regions of the electromagnetic field. The probability amplitude measures the density of disturbance in that region. The disturbance is the back and forth oscillation of electric and magnetic energies.

The wave function is a function of the degrees of freedom corresponding to some maximal set of commuting observables. Once such a representation is chosen, the wave function can be derived from the quantum state.

This is basically a Hamiltonian look at the interplay of forces and energies.

For a given system, the choice of which commuting degrees of freedom to use is not unique, and correspondingly the domain of the wave function is also not unique. For instance it may be taken to be a function of all the position coordinates of the particles over position space, or the momenta of all the particles over momentum space; the two are related by a Fourier transform. Some particles, like electrons and photons, have nonzero spin, and the wave function for such particles includes spin as an intrinsic, discrete degree of freedom; other discrete variables can also be included, such as isospin. When a system has internal degrees of freedom, the wave function at each point in the continuous degrees of freedom (e.g., a point in space) assigns a complex number for each possible value of the discrete degrees of freedom (e.g., z-component of spin) — these values are often displayed in a column matrix (e.g., a 2 × 1 column vector for a non-relativistic electron with spin 1⁄2).

The high disturbance densities of the field appear as “particles”.  They are not discrete “particles” as they are continuous with the surrounding field. There is a gradient of frequencies between the dense region and surrounding field. Spin is the eddy-like rotation of disturbance at high frequency. Only certain values of spin are stable.

According to the superposition principle of quantum mechanics, wave functions can be added together and multiplied by complex numbers to form new wave functions and form a Hilbert space. The inner product between two wave functions is a measure of the overlap between the corresponding physical states, and is used in the foundational probabilistic interpretation of quantum mechanics, the Born rule, relating transition probabilities to inner products. The Schrödinger equation determines how wave functions evolve over time, and a wave function behaves qualitatively like other waves, such as water waves or waves on a string, because the Schrödinger equation is mathematically a type of wave equation. This explains the name “wave function,” and gives rise to wave–particle duality. However, the wave function in quantum mechanics describes a kind of physical phenomenon, still open to different interpretations, which fundamentally differs from that of classic mechanical waves.

The quantum “particles” are high frequency, compact disturbances that have curved upon themselves like eddies. Only certain configurations of such disturbances are stable.

In Born’s statistical interpretation in non-relativistic quantum mechanics, the squared modulus of the wave function, |ψ|², is a real number interpreted as the probability density of measuring a particle’s being detected at a given place – or having a given momentum – at a given time, and possibly having definite values for discrete degrees of freedom. The integral of this quantity, over all the system’s degrees of freedom, must be 1 in accordance with the probability interpretation. This general requirement that a wave function must satisfy is called the normalization condition. Since the wave function is complex valued, only its relative phase and relative magnitude can be measured—its value does not, in isolation, tell anything about the magnitudes or directions of measurable observables; one has to apply quantum operators, whose eigenvalues correspond to sets of possible results of measurements, to the wave function ψ and calculate the statistical distributions for measurable quantities.

There is no particle to be detected at any position. There are no probability densities. There are only disturbance densities and frequency gradients. They take care of relativistic considerations. Absolute values of these frequency gradients and disturbance densities in terms of inertia are measurable against the background of emptiness of zero inertia. This gives us a different interpretation of the quantum phenomena than the current one.

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Reference: Disturbance Theory

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Rest Mass – Wikipedia

The invariant mass, rest mass, intrinsic mass, proper mass, or in the case of bound systems simply mass, is that portion of the total mass of an object or system of objects that is independent of the overall motion of the system. More precisely, it is a characteristic of the system’s total energy and momentum that is the same in all frames of reference related by Lorentz transformations. If a center of momentum frame exists for the system, then the invariant mass of a system is equal to its total mass in that “rest frame”. In other reference frames, where the system’s momentum is nonzero, the total mass (a.k.a. relativistic mass) of the system is greater than the invariant mass, but the invariant mass remains unchanged.

Due to mass-energy equivalence, the rest energy of the system is simply the invariant mass times the speed of light squared. Similarly, the total energy of the system is its total (relativistic) mass times the speed of light squared.

The word “rest” means that mass is not being pushed through the surrounding field. The surrounding field is a continuation of mass. When the mass is pushed through the surrounding field there is the resistance of inertia and acceleration. When there is no manifestation of acceleration the mass is “at rest”. A mass moving at uniform velocity is “rest mass”. When a mass is accelerating, there is force and energy in addition to the mass. This may be looked upon as “equivalent additional mass”.

The Lorentz transformations look at field from the viewpoint of matter and gives it a “mass” that is equivalent to its energy.

Systems whose four-momentum is a null vector (for example a single photon or many photons moving in exactly the same direction) have zero invariant mass, and are referred to as massless. A physical object or particle moving faster than the speed of light would have space-like four-momenta (such as the hypothesized tachyon), and these do not appear to exist. Any time-like four-momentum possesses a reference frame where the momentum (3-dimensional) is zero, which is a center of momentum frame. In this case, invariant mass is positive and is referred to as the rest mass.

A field is defined as having cycles and not mass (tight cycles at the upper end of the electromagnetic scale). Therefore, a field is massless but not “cycle-less” or “inertia-less”.  To be able to move faster than light, a particle must have less inertia than a photon. The above description in terms of “four-momentum” is part of a mathematical theory.

If objects within a system are in relative motion, then the invariant mass of the whole system will differ from the sum of the objects’ rest masses. This is also equal to the total energy of the system divided by c². See mass–energy equivalence for a discussion of definitions of mass. Since the mass of systems must be measured with a weight or mass scale in a center of momentum frame in which the entire system has zero momentum, such a scale always measures the system’s invariant mass. For example, a scale would measure the kinetic energy of the molecules in a bottle of gas to be part of invariant mass of the bottle, and thus also its rest mass. The same is true for massless particles in such system, which add invariant mass and also rest mass to systems, according to their energy.

Here the definition of “invariant” or rest mass is based on a center of momentum frame. An absolute definition of “rest mass” is possible only from the reference point of zero inertia.

For an isolated massive system, the center of mass of the system moves in a straight line with a steady sub-luminal velocity (with a velocity depending on the reference frame used to view it). Thus, an observer can always be placed to move along with it. In this frame, which is the center of momentum frame, the total momentum is zero, and the system as a whole may be thought of as being “at rest” if it is a bound system (like a bottle of gas). In this frame, which exists under these assumptions, the invariant mass of the system is equal to the total system energy (in the zero-momentum frame) divided by c². This total energy in the center of momentum frame, is the minimum energy which the system may be observed to have, when seen by various observers from various inertial frames.

An isolated massive system moving at uniform velocity has zero acceleration same as a system at rest.  This is the center of momentum frame. The uniform velocity is not relevant because it is based on an arbitrary reference frame.

Note that for reasons above, such a rest frame does not exist for single photons, or rays of light moving in one direction. When two or more photons move in different directions, however, a center of mass frame (or “rest frame” if the system is bound) exists. Thus, the mass of a system of several photons moving in different directions is positive, which means that an invariant mass exists for this system even though it does not exist for each photon.

The “rest mass” basically boils down to a measure of INERTIA in the reference frame of Emptiness, which provides the reference point of zero inertia.

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