Quantization Of Time And Energy

[steve_bank]

You just quoted a definition as mass per unit volume! Are you forgetting V, or claiming it too varies in multiples of atoms?

... If we ignore it's also determined by velocity and volume, yes. Why should we?

Direct application of Newton's Laws.


The result of random collisions of discrete atoms each with a finite energy creates a force per unit area the Pacal Newtons/m^2

So that is what statistical mechanics is all about, learn something new every day. If you want to refute Newton, be my guest.

You're not telling me anything new. Talking about refuting Newton, are you perchance denying that the amount of momentum transferred in an elastic collision depends on relative velocity? That relative velocity depends on the angle between two vectors?

More hand waving specious argument. The link demonstrates macro pressure is the sum of individual collisions with the wall. Pressure is quantized.

You can search the net for odds and ends to throw at me and you will undoubtedly find things I can not respond to, items I doubt you really comprehend and apply. Refute the link which I summarized, if you say pressure is continuous and infinitely divisible.

 

[bigfield]

Kinetic energy of the gas = 0.5 * ( summ of mass of atoms) * (average velocity)^2 Energy is quantized by individual atoms.

While the mass of an atom is discrete, this does not mean that the total energy of the atom is also discrete.

E = 1/2 mv^2
dv = [2/m]^1/2 * [1/2E^1/2] dE

A finire change in energy DE yields a finite change in velocity dv. dE is quantized unless you can cite an example of of an energy source that is not quantized.

You can't reasonably presuppose that kinetic energy changes is discrete amounts and then ask others to prove you wrong.

 

[Jokodo]

I know what you are saying, same issue as with electrons and current. You are back into the issue with reals and integers. Current is continuous because velocity is continuous.

n = number of particles.
m - atomic mass
total mass = n*m.

The total mass of a gas is m*n. Mass is quantized. Velocity is the average of all paericle velocities.

Two ways to change energy and pressure.

Three - you could also move the walls in or out, changing volume. But I get your drift.

At constant temperature add more atoms and equilibrium is reestablished. Velocity is constant so total energy increases in multiples of atoms.

Incorrect already. Steve, meet adiabatic heating. Adding more atoms does increase temperature.

To change gas energy at constant mass , energy has to be added to the tank. Heat the tank with coal and coal is composed of atoms with thermal energy per atom. You are thinking continuum mechanics. 1 atom of carbon = x joules of heat. 2 atoms of carbon = 2x joules of heat.

Yes. And those x joules or 2x joules will go towards accelerating a number of molecules each by a y * 2x joules, where y can take any real value between 0 and 1 and the different ys add up to 1. An individual molecule's acceleration is not quantized. The amount of energy that leaves the box to heat the surroundings is not quantized.

At least, you have provided no reason to think it is.

The step is not continuous and divisible. Heat is quantized.

Energy either organic or nuclear is per atom. Thenenergy in a waterfall driving a turbine can only chnges in multiples of molecules.

So you don't think height differential and velocity of the molecules have anything to do with it? Or are you assuming they're quantized too? Circular reasoning much?

E = 1/2 mv^2
dv = [2/m]^1/2 * [1/2E^1/2] dE

A finire change in energy DE yields a finite change in velocity dv. dE is quantized unless you can cite an example of of an energy source that is not quantized.

You do realise that there are no absolute velocities in a relativistic universe? What does quantized velocity even mean in this context?

The link shows pressure is quantized. Where is a continuous infinitely divisible energy source? No hand waving, an example. How can velocity change continuously when energy is quantized?

You provided several examples yourself.

Energy is quantized, therefore energy transfer to a particle is quantized. The dv is so small we treat velocity as a continuum.

In combustion heat is released by breaking discrete bonds and discrete changes of state in the atoms. Combustion is quantized. Heat of combustion is KJ/mole. Quantized.

heat transfer q = mcdt Heat transfer is quantized by mass. Heat conducts from atom to atom.

https://en.wikipedia.org/wiki/Combustion

Is efficiency also quantized? Does the energy released per molecule during combustion go to accelerate one and only one molecule?

 

[Jokodo]

You just quoted a definition as mass per unit volume! Are you forgetting V, or claiming it too varies in multiples of atoms?

... If we ignore it's also determined by velocity and volume, yes. Why should we?

Direct application of Newton's Laws.


The result of random collisions of discrete atoms each with a finite energy creates a force per unit area the Pacal Newtons/m^2

So that is what statistical mechanics is all about, learn something new every day. If you want to refute Newton, be my guest.

You're not telling me anything new. Talking about refuting Newton, are you perchance denying that the amount of momentum transferred in an elastic collision depends on relative velocity? That relative velocity depends on the angle between two vectors?

More hand waving specious argument. The link demonstrates macro pressure is the sum of individual collisions with the wall.

Not something I ever disputed.

Pressure is quantized.

Not something that follows from this unless the atoms/molecules have a fixed velocity, which is demonstrably not the case.

You can search the net for odds and ends to throw at me and you will undoubtedly find things I can not respond to, items I doubt you really comprehend and apply. Refute the link which I summarized, if you say pressure is continuous and infinitely divisible.

Your link doesn't claim otherwise, so I have no reason to try and refute it.

 

[steve_bank]

I am stunned, I am discombobulated. I do not now how I can go on...

Rather than derail the other thread I never said space is quantized. I do not know what space is. In science space is measured by meters which is not infinitly divisible. Matter is not infinitely divisible unless you debate atomic theory.

Energy is reduced to individual atoms and molecules and particles across known energy sources.

Show an infinitely divisible non quantized energy source. That is all it takes to make your case.

 

[steve_bank]

Kinetic energy of the gas = 0.5 * ( summ of mass of atoms) * (average velocity)^2 Energy is quantized by individual atoms.

While the mass of an atom is discrete, this does not mean that the total energy of the atom is also discrete.

E = 1/2 mv^2
dv = [2/m]^1/2 * [1/2E^1/2] dE

A finire change in energy DE yields a finite change in velocity dv. dE is quantized unless you can cite an example of of an energy source that is not quantized.

You can't reasonably presuppose that kinetic energy changes is discrete amounts and then ask others to prove you wrong.

If energy is quantized than enegy can not be trasferd to an object in multiples of a discret number. As a result velocity ican only change in discrete steps. It is not radical/ Current is treated as a Newtonian continuum but in reality nit can only change multiple electron increments. We treat mass as a continuous variable infinitely divisible yet it is quantized. Whay would Newtonian variables be any different.

What I ember from QM is that it is said as you go from quantum particles to Newtonian aggregates of particles the density of quantum sates becomes such that the quantization is not discernible and variables appear continuous. Pressure is an example.

When you throw a baseball you are not throwing a solid continuous object, you are transferring energy to each quantized atom and molecule each with finite mass..

As dE goes to zero is there a minimum amount of energy or can E get arbitrarily close to zero?

Continuous Newtonian variable failed to accurately model observed black body radiation. Planck came up with quantization as a solution that worked. In BB radiation I believe wavelength is not continuously variable.

 

[Jokodo]

I am stunned, I am discombobulated. I do not now how I can go on...

Rather than derail the other thread I never said space is quantized. I do not know what space is. In science space is measured by meters which is not infinitly divisible. Matter is not infinitely divisible unless you debate atomic theory.

Energy is reduced to individual atoms and molecules and particles across known energy sources.

Show an infinitely divisible non quantized energy source. That is all it takes to make your case.

The energy released e. g. in the chemical reaction between oxygen and hydrogen is quantized alright. No-one in this thread is disputing this.
This does not imply that the energy an individual molecule in the surrounding receives from this event in the form of acceleration is quantized. At least you have provided no reason to think it is, and indeed this would be incompatible with General Relativity, and more generally with Lorentz equivalence: Quantized acceleration implies quantized velocity implies absolute velocity implies a preferred reference frame.

 

[Jokodo]

While the mass of an atom is discrete, this does not mean that the total energy of the atom is also discrete.



You can't reasonably presuppose that kinetic energy changes is discrete amounts and then ask others to prove you wrong.

e
If energy is quantized than enegy can not be trasferd to an object in multiples of a discret number. As a result velocity ican only change in discrete steps. It is not radical/ Current is treated as a Newtonian continuum but in reality nit can only change multiple electron increments. We treat mass as a continuous variable infinitely divisible yet it is quantized. Whay would Newtonian variables be any different.

What I ember from QM is that it is said as you go from quantum particles to Newtonian aggregates of particles the density of quantum sates becomes such that the quantization is not discernible and variables appear continuous. Pressure is an example.

When you throw a baseball you are not throwing a solid continuous object, you are transferring energy to each quantized atom and molecule each with finite mass..

As dE goes to zero is there a minimum amount of energy or can E get arbitrarily close to zero?

Let's stick with kinetic energy since that is what you've been talking all along since you brought up pressure: In a nonelastic collision between two bodies, the body formed by the merger of the two heats up in proportion to the kinetic energy released on impact (mediated by friction during the deformation process and whatnot, but heating up is the end result). The amount of kinetic energy is proportional on the two bodies' initial relative velocities. For the sake of concreteness, let's assume two bullets who were previously sharing Earth's rest frame. Assume further, as you do, that their acceleration out of this frame due to combustion of the black powder can only take discrete values. It still holds that their relative velocity depends on their angle too. So unless angles are quantized, the energy released in such a collision has to be continuous, and indeed can go arbitrarily close to zero when the bullets are shot at an arbitrarily close angle.

And that's before we even talk about frame equivalence and relativity.

 

[bigfield]

If energy is quantized

You haven't shown that it is.

At most, you've pointed out that selected components of a system's energy are discontinuous if we assume that a variety of variables are constants, ignore subatomic structures and ignore relativity.

As dE goes to zero is there a minimum amount of energy

No, according to both quantum mechanics and relativity. The onus is on you to show otherwise, and perhaps collect a Nobel Prize.

 

[Juma]

I am stunned, I am discombobulated. I do not now how I can go on...

Rather than derail the other thread I never said space is quantized. I do not know what space is. In science space is measured by meters which is not infinitly divisible. Matter is not infinitely divisible unless you debate atomic theory.

Atomic theory? As in the antique greek theory?
According to modern science atoms consists of particles. The particles consists of quarks. We dont know wether these consists of yet smaller parts. But there is no natural law that prevents it.

 

[Jokodo]

I am stunned, I am discombobulated. I do not now how I can go on...

Rather than derail the other thread I never said space is quantized.

You said that pressure is quantized. Pressure measured in Pascals is J per cubic meter (among other equivalent formulations). Even if you are right that energy is quantized, and especially if you are, space needs to be quantized for pressure to be. If it isn't, you could always just increase the volume of the box by an arbitrary amount to reduce pressure by an arbitrary amount.

I do not know what space is. In science space is measured by meters which is not infinitly divisible.

Says who?

Matter is not infinitely divisible unless you debate atomic theory.

"matter" and "meter" are two very different concepts, even though their English labels may sound similar under a sloppy pronounciation.

I've already replied to the rest of your post.

 

[steve_bank]

SI pressure is Pascal's = Newtons/m^2. It is derived from statistical mechanics in the last link.

Relating space whatever that means to pressure has no meaning. Pressure is a resultant force from particles, be it gas in a tank or a mass on a table. In SI space is a dimension in meters.

A common pressure sensor is a thin diaphragm with a strain gauge to measure defection.

In a tank such a gauge experiences a force in Newton's that causes a deflection. The pressure is continuous in the sense that it never goes to zero. However the instantaneous pressure varies with time by the number of atoms hitting the diaphragm at any moment. The deflection of diaphragm can only change in proportion to multiples of atoms.

In a racket thrust comes from gas particles doing work against the rocket, equal and opposite reaction. When the rocket engine shuts down the change in velocity is quantized by multiples of gas particles. While engaged thrust never goes to zero and can be called continuous. However as in the tank the pressure in the engine varies instant by instant by the number of gas particles being created. Thrust is quantized, The final velocity is in proportion to the number of gas partcles.

 

[steve_bank]

I am stunned, I am discombobulated. I do not now how I can go on...

Rather than derail the other thread I never said space is quantized. I do not know what space is. In science space is measured by meters which is not infinitly divisible. Matter is not infinitely divisible unless you debate atomic theory.

Atomic theory? As in the antique greek theory?
According to modern science atoms consists of particles. The particles consists of quarks. We dont know wether these consists of yet smaller parts. But there is no natural law that prevents it.

Quantum theory applied to atoms. By Equipartition Of Energy the energy of an atom is distributed among the degrees of freedom of the atom . See the link on statistical mechanics.

 

[steve_bank]

[bigfield

You are hand waving. Planck based his theory of BB radiation on quantization. AE and Planck got their Nobels for quantization. AEs Photo Electric effect which provided part of the foundation for the start of QM.

It was not CM for continues mechanics, it was QM for quantized mechanics.

Read the links on statistical mechanics,

And most importantly cite an energy source that can be infinitely divisible, meaning continuous. For any energy source cite one that is not quantized by particles. Nuclear, wind, hydro, solar, nuclear, fossil. Show that a change energy, the capacity to do work, can be made arbitrarily small.

 

[steve_bank]

Photons and electrons are discern quantized emery carriers. The only way to reconcile observation with theory was quantization of energy.

AE quantization of light photons
Planck quantization of BB radiation
Millikan quantization of electricity the electron

As I have said, I am just a worker be engineer, who has applied physics. Everything I have posted on quantization is a consequence of the above three. It is any syandard basic physics and modern physics text. I am not pulling anything out of my ass.

The fact that I say velocity can only change in multiples of quantized energy is a simple consequence of established theory.

Again, at the macro Newtonian scale velocity and other variables like heat and temperature appear continuous because the quantization granularity is well blow threshold, it has no effect at the macro scale.



https://en.wikipedia.org/wiki/Photoelectric_effect

In 1905, Albert Einstein solved this apparent paradox by describing light as composed of discrete quanta, now called photons, rather than continuous waves. Based upon Max Planck's theory of black-body radiation, Einstein theorized that the energy in each quantum of light was equal to the frequency multiplied by a constant, later called Planck's constant. A photon above a threshold frequency has the required energy to eject a single electron, creating the observed effect. This discovery led to the quantum revolution in physics and earned Einstein the Nobel Prize in Physics in 1921.[49] By wave-particle duality the effect can be analyzed purely in terms of waves though not as conveniently.[50]

Albert Einstein's mathematical description of how the photoelectric effect was caused by absorption of quanta of light was in one of his 1905 papers, named "On a Heuristic Viewpoint Concerning the Production and Transformation of Light". This paper proposed the simple description of "light quanta", or photons, and showed how they explained such phenomena as the photoelectric effect. His simple explanation in terms of absorption of discrete quanta of light explained the features of the phenomenon and the characteristic frequency.

The idea of light quanta began with Max Planck's published law of black-body radiation ("On the Law of Distribution of Energy in the Normal Spectrum"[51]) by assuming that Hertzian oscillators could only exist at energies E proportional to the frequency f of the oscillator by E = hf, where h is Planck's constant. By assuming that light actually consisted of discrete energy packets, Einstein wrote an equation for the photoelectric effect that agreed with experimental results. It explained why the energy of photoelectrons was dependent only on the frequency of the incident light and not on its intensity: a low-intensity, the high-frequency source could supply a few high energy photons, whereas a high-intensity, the low-frequency source would supply no photons of sufficient individual energy to dislodge any electrons. This was an enormous theoretical leap, but the concept was strongly resisted at first because it contradicted the wave theory of light that followed naturally from James Clerk Maxwell's equations for electromagnetic behavior, and more generally, the assumption of infinite divisibility of energy in physical systems. Even after experiments showed that Einstein's equations for the photoelectric effect were accurate, resistance to the idea of photons continued since it appeared to contradict Maxwell's equations, which were well understood and verified.

https://en.wikipedia.org/wiki/Black-body_radiation

The problem was solved in 1901 by Max Planck in the formalism now known as Planck's law of black-body radiation.[25] By making changes to Wien's radiation law (not to be confused with Wien's displacement law) consistent with thermodynamics and electromagnetism, he found a mathematical expression fitting the experimental data satisfactorily. Planck had to assume that the energy of the oscillators in the cavity was quantized, i.e., it existed in integer multiples of some quantity. Einstein built on this idea and proposed the quantization of electromagnetic radiation itself in 1905 to explain the photoelectric effect. These theoretical advances eventually resulted in the superseding of classical electromagnetism by quantum electrodynamics. These quanta were called photons and the black-body cavity was thought of as containing a gas of photons. In addition, it led to the development of quantum probability distributions, called Fermi–Dirac statistics and Bose–Einstein statistics, each applicable to a different class of particles, fermions and bosons.

https://www.nobelprize.org/prizes/physics/1918/summary/

The Nobel Prize in Physics 1918 was awarded to Max Karl Ernst Ludwig Planck "in recognition of the services he rendered to the advancement of Physics by his discovery of energy quanta."

https://www.nobelprize.org/prizes/physics/1923/summary/

The Nobel Prize in Physics 1923 was awarded to Robert Andrews Millikan "for his work on the elementary charge of electricity and on the photoelectric effect."

 

[steve_bank]

Heat quantized, related to Plank's constant

It is well known that electrical and thermal conductivity go hand inn hand.

https://physics.aps.org/story/v2/st2

Just as light waves can be described as collections of photons, the vibrations of a crystal lattice can be analyzed in terms of phonons, which can travel through a material, transporting energy in the form of heat. Luis Rego and George Kirczenow, of Simon Fraser University in Burnaby, Canada, show that the conductance of a thin, cold, phonon-carrying wire is quantized in units of k2pi2
k2pi2T/3 h, where k is Boltzmann’s constant, T is temperature, and h is Plank’s constant. (The quantum of electrical conductance is e2/h, where e is the charge of the electron, and it occurs most famously in the quantum Hall effect.) The existence of the thermal quantum was deduced implicitly last year by Michael Roukes, of the California Institute of Technology, and his colleagues, but Rego and Kirczenow go on to analyze how an experiment could observe it.

The equations and numbers do not copy.

https://en.wikipedia.org/wiki/Thermal_conductance_quantum

The thermal conductance of any electrically insulating structure that exhibits ballistic phonon transport is a positive integer multiple of g 0The thermal conductance quantum was first measured in 2000.[1] These measurements employed suspended silicon nitride nanostructures that exhibited a constant thermal conductance of 16g 0 {\displaystyle g_{0}} g_{0} at temperatures below approximately 0.6 kelvin.

 

[Jokodo]

SI pressure is Pascal's = Newtons/m^2. It is derived from statistical mechanics in the last link.

Relating space whatever that means to pressure has no meaning.

You just defined pressure as Pascals = Newtons/m². Where m² is square metres. A measure of space.

Pressure is a resultant force from particles, be it gas in a tank or a mass on a table. In SI space is a dimension in meters.

... and it's an integral part of the definition of pressure, as you yourself told us one paragraph up!

A common pressure sensor is a thin diaphragm with a strain gauge to measure defection.

In a tank such a gauge experiences a force in Newton's that causes a deflection. The pressure is continuous in the sense that it never goes to zero. However the instantaneous pressure varies with time by the number of atoms hitting the diaphragm at any moment. The deflection of diaphragm can only change in proportion to multiples of atoms.

That might be true only if it instantly rebounded after being deflected by a collision, and possibly not even then. In which case the diaphragm would be useless for measuring pressure.

In a racket thrust comes from gas particles doing work against the rocket, equal and opposite reaction. When the rocket engine shuts down the change in velocity is quantized by multiples of gas particles. While engaged thrust never goes to zero and can be called continuous. However as in the tank the pressure in the engine varies instant by instant by the number of gas particles being created. Thrust is quantized, The final velocity is in proportion to the number of gas partcles.

What's true is that for each particle leaving the exhaust, the rocket's momentum gained is the opposite of the particle's momentum gained.

The rest only follows if no energy is lost to heat and radiation and the exhaust is moving away in a perfectly focused beam exactly 180° from the rocket's direction of movement, with no single particle, not even a photon, straying even a fraction of an archsecond. As soon as some particle strays a bit to the left, the equal and opposite reaction bit implies that the rocket is pushed to the right. As soon as a second particle strays to the right, by the same logic the rocket is pushed to the left. The result is friction and heating of the rocket's rear, and that energy is lost to acceleration.

Do you claim that angles are quantized? Because if not, the net acceleration of the rocket can't be either.

 

[Jokodo]

Photons and electrons are discern quantized emery carriers. The only way to reconcile observation with theory was quantization of energy.

AE quantization of light photons
Planck quantization of BB radiation
Millikan quantization of electricity the electron

As I have said, I am just a worker be engineer, who has applied physics. Everything I have posted on quantization is a consequence of the above three. It is any syandard basic physics and modern physics text. I am not pulling anything out of my ass.

Please describe how quantized acceleration works in a universe where all subluminal velocities are relative!

 

[Jokodo]

Nuclear, wind, hydro, solar, nuclear, fossil. Show that a change energy, the capacity to do work, can be made arbitrarily small.

Hydro and wind: If you think they're quantized, you're assuming your conclusion. The force of an air molecule or a water molecule against the turbine is determined by its mass and its velocity. If velocities can be arbitrarily small, so can that force. You want to show that it doesn't, you don't get to assume it does and than use the tautology to derive that indeed it does.

 

[bigfield]

And most importantly cite an energy source that can be infinitely divisible, meaning continuous. For any energy source cite one that is not quantized by particles. Nuclear, wind, hydro, solar, nuclear, fossil. Show that a change energy, the capacity to do work, can be made arbitrarily small.

Those generators all (except for solar photovoltaic) rely on turbines. Turbines work by transferring kinetic energy from the fluid flow to the rotor. The pressure at the pressure head is governed by the velocities of the fluid and the rotor. The velocity of the fluid is governed by the pressure in the nozzle, which is a function of the cross-section of the nozzle. We can make arbitrarily small changes to the size and shape of the nozzle or the rotor blades, which results in arbitrarily small changes to the kinetic energy imparted on the rotor.

In a tank such a gauge experiences a force in Newton's that causes a deflection. The pressure is continuous in the sense that it never goes to zero. However the instantaneous pressure varies with time by the number of atoms hitting the diaphragm at any moment. The deflection of diaphragm can only change in proportion to multiples of atoms.

Since we're treating atoms as classical objects, the force of each atom's impact on the diaphragm is a function of the atom's momentum. Each atom's velocity could have an arbitrary direction and an arbitrary magnitude. This means that each collision exerts an arbitrary amount of force on the diaphragm, and therefore an arbitrarily amount of pressure. We can be certain that the deflection of the diaphragm is not required to change in multiples of the number of atoms.

And as with the turbine, the volume of the tank or the diaphragm can be changed by arbitrarily-small amounts.