Quantization Of Time And Energy

[skepticalbip]

....snip....

Show that a change energy, the capacity to do work, can be made arbitrarily small.

What is the kinetic energy of a proton moving at a velocity of one centimeter per century? How about the kinetic energy of that proton moving at the velocity of one angstrom per eon? The problem isn't in how small an amount of energy can be but in our ability to measure it.

To make the kinetic energy of that proton be arbitrarily small only requires making its velocity arbitrarily slow.

 

[Jokodo]

....snip....

Show that a change energy, the capacity to do work, can be made arbitrarily small.

What is the kinetic energy of a proton moving at a velocity of one centimeter per century? How about the kinetic energy of that proton moving at the velocity of one angstrom per eon? The problem isn't in how small an amount of energy can be but in our ability to measure it.

... and what's the net change in the Sun's velocity from colliding with such a proton? What's the net difference in the kinetic energy of a proton ejected from the Sun's corona with or without that collision?

 

[Juma]

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."

As I stated earlier: energy of particles trapped in potential well are quantized. By the effect of particles having wavelenth.
Free particles does not have quantized energy.
Its that simple.

 

[steve_bank]

I left BB radiation, Photoelevytiv Effect, and quntization of charge to the last after it all played out. AE made his rep by using quantized energy to explain expaeriment, the photon.

Plasnck built on it to descibe BB radiastion.

bigfiled

I designed power concersion systems. You are looking at it from Newtonian mechanics.

Water falling onto a turbine from a macro view has a kinetic energy proportional to say kg/liter. At that sacle in calculations I treat kinetic energy as a continuous infinitely divisible variable.

Looking through it from QM the mass in falling water can only change in multiples of molecules. The kinetic energy in falling water changes in multiples of particles for constant velocity.

Same with wind.

The quantum efficiency of a photodetector is electrons/photons.

Without quantization you run up against problems with infinities.

What is the smallest possible amount of energy transfer? Is there a fuel source who's potential energy is infinitely divisible?

For falling water driving a turbine electrical generator I could develop an equation for electrons/water molecules but it would have no utility.

 

[steve_bank]

....snip....

Show that a change energy, the capacity to do work, can be made arbitrarily small.

What is the kinetic energy of a proton moving at a velocity of one centimeter per century? How about the kinetic energy of that proton moving at the velocity of one angstrom per eon? The problem isn't in how small an amount of energy can be but in our ability to measure it.

... and what's the net change in the Sun's velocity from colliding with such a proton? What's the net difference in the kinetic energy of a proton ejected from the Sun's corona with or without that collision?

I'll have to take that one step at a time....pun intended. Keep those icurve balls coming, an American metaphor.

My continuing question for you is given a fuels source of any kind what is the minimum possible energy transfer, is there no lower bound?

 

[bigfield]

I designed power concersion systems. You are looking at it from Newtonian mechanics.

I'm looking at it from Newtonian mechanics because that is what you are doing. You keep mentioning quantum mechanics but your argument doesn't actually reference quantum mechanics.

Water falling onto a turbine from a macro view has a kinetic energy proportional to say kg/liter. At that sacle in calculations I treat kinetic energy as a continuous infinitely divisible variable.

Looking through it from QM the mass in falling water can only change in multiples of molecules. The kinetic energy in falling water changes in multiples of particles for constant velocity.

We might get away with that assumption if we are dealing with, say, a droplet travelling in a vacuum.

Falling water is subject to acceleration by gravitational force; it's doing work. We can make infinitesimally-small changes to the amount of work done by the droplet by changing the height of its starting point and/or the height of its landing surface.

What is the smallest possible amount of energy transfer?

I already answered this question, with reference to your diaphragm example: The force of each molecule's impact is a function of its momentum. Since the molecule's momentum is a vector that could point in an arbitrary direction and an arbitrary magnitude, the magnitude of the force applied to the diaphragm's deflection could be infinitesimally small. Therefore, the energy transferred from molecule to diaphragm could be infinitesimally small.

Without quantization you run up against problems with infinities.

Only if you think that Achilles never catches up to the tortoise.

 

[steve_bank]

No. I am looking at Newtonian mechanics through QM.

Hang a bucket on a spring force gauge. Add a ball bearing and the indicator moves in an amount dz. add another ball bearing and the indicator moves 2dz. In this case force is quantized by the ball bearings.

A water or wind turbine is no different. Mass is quantized by atoms and molecules. Kinetic energy in the falling water, at constant velocity, can only change in multiples of H2O. If you want to argue that there is nothing more to say. Basic chemistry and arithmetic.

Falling water is not doing work while falling , work is being done by gravity adding kinetic energy to each molecule. Each molecule then does work on the turbine..

Your analysis of the gas molecule is bogus. Read through the last link I posted on gs analysis via statistical mechanics.

Force being a vector means it can have an infinitely small energy? Work that out mathematically.Did you read the links on Planck and BB radiation, and on the Photoelectric Effect?

Quantization of energy is now around 120 years old.

 

[steve_bank]

I'll reframe the question.

Add a finte amout of energy to an object and the result will be a finite step or change in velocity. Any disagreement?

The question then is how small an increment of energy can be transferred.

So, cite any energy or fuel source that can be infinitesimally divided. Without answering that all else is empty hand waving. If there is no lower bound how do you achieve it?

 

[bigfield]

No. I am looking at Newtonian mechanics through QM.

What concepts are you drawing on from quantum mechanics?

Hang a bucket on a spring force gauge. Add a ball bearing and the indicator moves in an amount dz. add another ball bearing and the indicator moves 2dz. In this case force is quantized by the ball bearings.

Only if gravity is constant. If you move the gauge higher or lower in the gravity well, the force per ball-bearing increases or decreases. You can make arbitrarily-small changes to the potential energy of the ball bearings by adjusting the height of the gauge.

A water or wind turbine is no different. Mass is quantized by atoms and molecules. Kinetic energy in the falling water, at constant velocity, can only change in multiples of H2O. If you want to argue that there is nothing more to say. Basic chemistry and arithmetic.

You can also change the kinetic energy of falling water by changing the height of its starting point and/or the height of it's finishing point.

Falling water is not doing work while falling , work is being done by gravity adding kinetic energy to each molecule. Each molecule then does work on the turbine.

I stand corrected on the terminology.

Force being a vector means it can have an infinitely small energy?

Forces don't have energy.

We know that forces can be arbitrarily small, because several fundamental forces are inversely proportional to the distance from point in space. For example: imagine two ball bearings in space, and then keep moving them apart from one another. The gravitational force between them approaches zero as the distance between them grows; there is no smallest gravitational force between them.

 

[bigfield]

I'll reframe the question.

Add a finte amout of energy to an object and the result will be a finite step or change in velocity. Any disagreement?

The question then is how small an increment of energy can be transferred.

So, cite any energy or fuel source that can be infinitesimally divided. Without answering that all else is empty hand waving. If there is no lower bound how do you achieve it?

The potential energy of a ball-bearing in a gravity well can be infinitesimally divided by rolling it down a flight of stairs with an infinite number of steps. There is no minimum quantum of work that can be done of the ball bearing.

 

[bigfield]

What is the smallest possible amount of energy transfer?

I already answered this question, with reference to your diaphragm example: The force of each molecule's impact is a function of its momentum. Since the molecule's momentum is a vector that could point in an arbitrary direction and an arbitrary magnitude, the magnitude of the force applied to the diaphragm's deflection could be infinitesimally small. Therefore, the energy transferred from molecule to diaphragm could be infinitesimally small.

This is probably easier to visualise with a different thought experiment. Instead of a gas molecule bouncing off of a diaphragm, imagine a cue ball and an 8 ball. If you shoot the cue ball directly at the 8 ball, you'll transfer all of the cue ball's kinetic energy to the 8 ball. If you angle the shot, you'll reduce the energy transferred to the 8-ball. As the angle of the shot increases, the work done on the 8 ball approaches zero.

 

[steve_bank]

What is the smallest possible amount of energy transfer?

I already answered this question, with reference to your diaphragm example: The force of each molecule's impact is a function of its momentum. Since the molecule's momentum is a vector that could point in an arbitrary direction and an arbitrary magnitude, the magnitude of the force applied to the diaphragm's deflection could be infinitesimally small. Therefore, the energy transferred from molecule to diaphragm could be infinitesimally small.

This is probably easier to visualise with a different thought experiment. Instead of a gas molecule bouncing off of a diaphragm, imagine a cue ball and an 8 ball. If you shoot the cue ball directly at the 8 ball, you'll transfer all of the cue ball's kinetic energy to the 8 ball. If you angle the shot, you'll reduce the energy transferred to the 8-ball. As the angle of the shot increases, the work done on the 8 ball approaches zero.

Still avoiding the question, what would the min limit be? No limit? Your muscles are fueld by ATP which is quantized by molecules. No matter which way you go there is quantization. The change in velocity and hence the energy transfer from your muscles via the stick is quantized.

You are trying to refute Einstein and Planck.

The question of Zeno's Paradox is not the same as quantized energy.

 

[steve_bank]

I'll reframe the question.

Add a finte amout of energy to an object and the result will be a finite step or change in velocity. Any disagreement?

The question then is how small an increment of energy can be transferred.

So, cite any energy or fuel source that can be infinitesimally divided. Without answering that all else is empty hand waving. If there is no lower bound how do you achieve it?

The potential energy of a ball-bearing in a gravity well can be infinitesimally divided by rolling it down a flight of stairs with an infinite number of steps. There is no minimum quantum of work that can be done of the ball bearing.

I get tingly when someone says gravity well...

What is the energy source for gravity?

Drop a ball and at any point F=MA where A = g. Mass is quantized, unless you wish to argue solid matter is not comprised of atoms with atomic weights. When the ball hits a board the energy transferred is quantized. Adding mass to the ball can only be done in discrete increments of atoms, therefore kinetic energy can only change in discrete steps.

Gravitons are theoretical and has issues, so I can not argue the energy transfer via gravity directly. I would say gravity can only operate with an energy balance with the energy in the ball, which is quantized by mass. The change in velocity pf the ball is quantized by quantized matter. g is an acceleration no different than the acceleration of a rocket in space. Inertial and gravitational acceleration are equivalent.

 

[Jokodo]

This is probably easier to visualise with a different thought experiment. Instead of a gas molecule bouncing off of a diaphragm, imagine a cue ball and an 8 ball. If you shoot the cue ball directly at the 8 ball, you'll transfer all of the cue ball's kinetic energy to the 8 ball. If you angle the shot, you'll reduce the energy transferred to the 8-ball. As the angle of the shot increases, the work done on the 8 ball approaches zero.

Still avoiding the question, what would the min limit be? No limit? Your muscles are fueld by ATP which is quantized by molecules. No matter which way you go there is quantization. The change in velocity and hence the energy transfer from your muscles via the stick is quantized.

Your question has been explicitly answered multiple times by multiple posters. Yes, the velocity transfer in a collision can be arbitrarily small as the angle can be arbitrarily small.

You are trying to refute Einstein and Planck.

Not in any way you seem able to articulate.

The question of Zeno's Paradox is not the same as quantized energy.

It is.

 

[bigfield]

This is probably easier to visualise with a different thought experiment. Instead of a gas molecule bouncing off of a diaphragm, imagine a cue ball and an 8 ball. If you shoot the cue ball directly at the 8 ball, you'll transfer all of the cue ball's kinetic energy to the 8 ball. If you angle the shot, you'll reduce the energy transferred to the 8-ball. As the angle of the shot increases, the work done on the 8 ball approaches zero.

Still avoiding the question, what would the min limit be? No limit?

Actually, I stated my answer plainly, but to be clear, there is no limit on the minimum amount of energy that can be transferred. I've given multiple examples to illustrate that, as well.

 

[steve_bank]

This is probably easier to visualise with a different thought experiment. Instead of a gas molecule bouncing off of a diaphragm, imagine a cue ball and an 8 ball. If you shoot the cue ball directly at the 8 ball, you'll transfer all of the cue ball's kinetic energy to the 8 ball. If you angle the shot, you'll reduce the energy transferred to the 8-ball. As the angle of the shot increases, the work done on the 8 ball approaches zero.

Still avoiding the question, what would the min limit be? No limit?

Actually, I stated my answer plainly, but to be clear, there is no limit on the minimum amount of energy that can be transferred. I've given multiple examples to illustrate that, as well.

Then end of debate. Thanks.

 

[bigfield]

Drop a ball and at any point F=MA where A = g. Mass is quantized, unless you wish to argue solid matter is not comprised of atoms with atomic weights. When the ball hits a board the energy transferred is quantized. Adding mass to the ball can only be done in discrete increments of atoms, therefore kinetic energy can only change in discrete steps.

Gravitons are theoretical and has issues, so I can not argue the energy transfer via gravity directly. I would say gravity can only operate with an energy balance with the energy in the ball, which is quantized by mass. The change in velocity pf the ball is quantized by quantized matter. g is an acceleration no different than the acceleration of a rocket in space. Inertial and gravitational acceleration are equivalent.

You claimed that energy is quantised because there is a minimum amount of energy that can be transferred between objects, and I've provided several examples showing otherwise.

All of your arguments so far requires that we add mass to a system and hold all other parameters constant. It's trivially obvious that adding particles to a system adds discrete quantities of energy, but it does not follow that energy in general exists in quanta.

 

[bigfield]

Actually, I stated my answer plainly, but to be clear, there is no limit on the minimum amount of energy that can be transferred. I've given multiple examples to illustrate that, as well.

Then end of debate. Thanks.

You're welcome. Thanks for the interesting discussion.

 

[Jokodo]

I left BB radiation, Photoelevytiv Effect, and quntization of charge to the last after it all played out. AE made his rep by using quantized energy to explain expaeriment, the photon.

Plasnck built on it to descibe BB radiastion.

bigfiled

I designed power concersion systems. You are looking at it from Newtonian mechanics.

Water falling onto a turbine from a macro view has a kinetic energy proportional to say kg/liter. At that sacle in calculations I treat kinetic energy as a continuous infinitely divisible variable.

Looking through it from QM the mass in falling water can only change in multiples of molecules.

That's not QM, that's just basic materials science, and it's only approximately true: More specifically, the rest mass is multiples of molecules, but total mass/relativistic mass depends on the reference frame in Special Relativity.

The kinetic energy in falling water changes in multiples of particles for constant velocity.

Same with wind.

You said it yourself: for constant velocity.

 

[steve_bank]

End of debate jokodo. Hopefully all parties come away with a new insight or food for thought.