Comments on Thermodynamic temperature

Reference: Disturbance Theory

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Thermodynamic temperature

Thermodynamic temperature is the absolute measure of temperature and is one of the principal parameters of thermodynamics.

Thermodynamics is a branch of physics concerned with heat and temperature and their relation to energy and work. The absolute measure of temperature is one of the principal parameters of thermodynamics.

Thermodynamic temperature is defined by the third law of thermodynamics in which the theoretically lowest temperature is the null or zero point. At this point, absolute zero, the particle constituents of matter have minimal motion and can become no colder. In the quantum-mechanical description, matter at absolute zero is in its ground state, which is its state of lowest energy. Thermodynamic temperature is often also called absolute temperature, for two reasons: one, proposed by Kelvin, that it does not depend on the properties of a particular material; two that it refers to an absolute zero according to the properties of the ideal gas.

The concept of absolute zero provides a reference point of the ground state of matter, which is the state of lowest energy. It is the same for all matter.

The International System of Units specifies a particular scale for thermodynamic temperature. It uses the kelvin scale for measurement and selects the triple point of water at 273.16 K as the fundamental fixing point. Other scales have been in use historically. The Rankine scale, using the degree Fahrenheit as its unit interval, is still in use as part of the English Engineering Units in the United States in some engineering fields. ITS-90 gives a practical means of estimating the thermodynamic temperature to a very high degree of accuracy.

The thermodynamic temperature provides an absolute scale.

Roughly, the temperature of a body at rest is a measure of the mean of the energy of the translational, vibrational and rotational motions of matter’s particle constituents, such as molecules, atoms, and subatomic particles. The full variety of these kinetic motions, along with potential energies of particles, and also occasionally certain other types of particle energy in equilibrium with these, make up the total internal energy of a substance. Internal energy is loosely called the heat energy or thermal energy in conditions when no work is done upon the substance by its surroundings, or by the substance upon the surroundings. Internal energy may be stored in a number of ways within a substance, each way constituting a “degree of freedom”. At equilibrium, each degree of freedom will have on average the same energy: kBT/2 where kB is the Boltzmann constant, unless that degree of freedom is in the quantum regime. The internal degrees of freedom (rotation, vibration, etc.) may be in the quantum regime at room temperature, but the translational degrees of freedom will be in the classical regime except at extremely low temperatures (fractions of kelvins) and it may be said that, for most situations, the thermodynamic temperature is specified by the average translational kinetic energy of the particles.

TEMPERATURE = a measure of the mean of the energy of the kinetic motions (translational, vibrational and rotational) of matter’s particles. For most situations, the thermodynamic temperature is specified by the average translational kinetic energy of the particles. The Boltzmann constant (kB) is a physical constant relating the average kinetic energy of particles in a gas with the temperature of the gas.

INTERNAL ENERGY = the full variety of kinetic motions along with potential energies of particles, and also occasionally certain other types of particle energy in equilibrium with these.

DEGREES OF FREEDOM = the number of ways in which the internal energy may be stored within a substance. At equilibrium, each degree of freedom will have on average the same energy = kBT/2

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November 26, 2017 – 6:14 AM Categories: P-Postulates | Post a comment

Comments on Einstein Solid

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Heat capacity of an Einstein solid as a function of temperature. Experimental value of 3Nk is recovered at high temperatures.
Reference: Disturbance Theory

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Einstein Solid – Wikipedia

The Einstein solid is a model of a solid based on two assumptions:

  • Each atom in the lattice is an independent 3D quantum harmonic oscillator
  • All atoms oscillate with the same frequency (contrast with the Debye model)

While the assumption that a solid has independent oscillations is very accurate, these oscillations are sound waves or phonons, collective modes involving many atoms. In the Einstein model, however, each atom oscillates independently. Einstein was aware that getting the frequency of the actual oscillations would be difficult, but he nevertheless proposed this theory because it was a particularly clear demonstration that quantum mechanics could solve the specific heat problem in classical mechanics.

A 3D quantum harmonic oscillator would be made up of high frequency, compacted cycles of electromagnetic field that have slowed down considerably due to their high inertia. Their motion is no longer linear, but a combination of circular, rotational and linear, which shows up as oscillatory.

Einstein treated each atom as an independent 3D harmonic oscillator, whose energy could only increase in quantum intervals of ‘hω’. Einstein assumed the same frequency for all atoms for the sake of simplicity.

The original theory proposed by Einstein in 1907 has great historical relevance. The heat capacity of solids as predicted by the empirical Dulong-Petit law was required by classical mechanics, the specific heat of solids should be independent of temperature. But experiments at low temperatures showed that the heat capacity changes, going to zero at absolute zero. As the temperature goes up, the specific heat goes up until it approaches the Dulong and Petit prediction at high temperature.

The classical mechanics predicts the heat capacity of solids to be independent of temperature. It did not explain the observed dependence at lower temperatures. Einstein could show this dependence with his quantum model even if not very accurately.

By employing Planck’s quantization assumption, Einstein’s theory accounted for the observed experimental trend for the first time. Together with the photoelectric effect, this became one of the most important pieces of evidence for the need of quantization. Einstein used the levels of the quantum mechanical oscillator many years before the advent of modern quantum mechanics.

The continuous change in properties, which is a feature of classical mechanics, is seen in context of normal dimensions. When we view properties at atomic dimensions, as in the case of black body radiation, the quantum effects of frequency cycles become prominent.

In Einstein’s model, the specific heat approaches zero exponentially fast at low temperatures. This is because all the oscillations have one common frequency. The correct behavior is found by quantizing the normal modes of the solid in the same way that Einstein suggested. Then the frequencies of the waves are not all the same, and the specific heat goes to zero as a T3 power law, which matches experiment. This modification is called the Debye Model, which appeared in 1912.

Einstein demonstrated the quantum effects on specific heats of solids at low temperatures which classical mechanics could not explain. Einstein did make simplified assumptions as regard the frequency of atoms, which were modified later in Debye model.

When Walther Nernst learned of Einstein’s 1906 paper on specific heat, he was so excited that he traveled all the way from Berlin to Zürich to meet with him.

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November 22, 2017 – 8:47 AM Categories: Einstein | Post a comment

Comments on Wave Function

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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November 22, 2017 – 5:59 AM Categories: P-Postulates | Comments (1)

Comments on Matter (old)

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Reference: Disturbance Theory

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Matter – Wikipedia

In the classical physics observed in everyday life, matter is any substance that has mass and takes up space by having volume. This includes atoms and anything made up of these, but not other energy phenomena or waves such as light or sound. More generally, however, in (modern) physics, matter is not a fundamental concept because a universal definition of it is elusive; for example, the elementary constituents of atoms may be point particles, each having no volume individually.

Matter represents substance. Substance is something that can be felt and experienced. It is the essential aspect of any interaction. Without substance there can be no interaction, feeling and experience. Matter is one aspect of substance. The other aspect is field. An interface occurs between field and matter within an atom. In the atom we observe the field increasing in frequency toward the center, where it ends up as matter with mass.

Space is a manifestation of the extension property of field and matter. Without field and matter there is no space. The gaps between material objects are filled with gaseous matter and field. A vacuum is not entirely empty even when there are no atoms and molecules of gaseous material in it. There is still field in that vacuum for space to appear.

The idea that the fundamental constituents of atoms may be point particles is a mathematical conjecture. In reality, matter in atom reduces to field. The “volume” of matter reduces to cycles of field.

All the everyday objects that we can bump into, touch or squeeze are ultimately composed of atoms. This ordinary atomic matter is in turn made up of interacting subatomic particles—usually a nucleus of protons and neutrons, and a cloud of orbiting electrons. Typically, science considers these composite particles matter because they have both rest mass and volume. By contrast, massless particles, such as photons, are not considered matter, because they have neither rest mass nor volume. However, not all particles with rest mass have a classical volume, since fundamental particles such as quarks and leptons (sometimes equated with matter) are considered “point particles” with no effective size or volume. Nevertheless, quarks and leptons together make up “ordinary matter”, and their interactions contribute to the effective volume of the composite particles that make up ordinary matter.

Matter has shaped science’s viewpoint of reality. Even when field is discovered as a more basic substance, Science still uses matter as its reference point. This has led to considerable confusion in theoretical physics, which is now taken over by increasingly compartmentalized mathematical theories of Newton, Einstein and Quantum Mechanics.

Atom is not made up of point particles, but of field that is increasing in frequency toward the center of the atom. The “point particles” are high frequency regions of the field. The cycles of very high frequencies get compacted and appear as mass. Thus we have protons and neutron as regions of very high frequency and compactness at the core of the atom. The electrons are regions of relatively lower frequency and compactness that surround the nucleus of the atom.

Rest Mass is best understood as the inertia of a “particle”. Volume is best understood in terms of the cycles that make up the “particle”. Photons may be massless, but they are not inertia-less. They may not be matter but they are made up of cycles, which is the substance of field. Science, with its fixation on matter tries to evaluate field properties in terms of classical material properties of mass and volume. It refuses to go for a deeper understanding in terms of inertia and cycles. “Particles” such as quarks and leptons are mathematical conjectures that have not been encountered in reality.

Matter exists in states (or phases): the classical solid, liquid, and gas; as well as the more exotic plasma, Bose–Einstein condensates, fermionic condensates, and quark–gluon plasma.

These states of matter are essentially hybrids of field and matter.

For much of the history of the natural sciences people have contemplated the exact nature of matter. The idea that matter was built of discrete building blocks, the so-called particulate theory of matter, was first put forward by the Greek philosophers Leucippus (~490 BC) and Democritus (~470–380 BC).

Matter has been contemplated upon since the beginning of human consciousness.

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November 20, 2017 – 6:51 AM Categories: P-Postulates | Post a comment

Comments on Rest Mass

rest mass

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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November 19, 2017 – 7:18 PM Categories: P-Postulates | Comments (1)