[guest39538]

the ISU quantum equation.

I recognize the bottom line of your equation as the volume of a sphere, I am still considering the top line. 

The top line,
That part of the equation identifies the various volumes (pieces) that make up the two or more converging quantum spherical waves.
https://www.thenakedscientists.com/forum/gallery/43933_25_07_17_11_46_46.jpeg
[/color][/size]
There are the two Vertical Caps, and there are the two parent spheres, i.e., four pieces that make up the two spheres. Each element of the left side of the equation has a counterpart on the right side that gives the formula to calculate the volume of the piece.

Does it firstly say 1 third times pi ?

Yes.

H is radius?

so 1/3 * pi * r²  ?

Obviously the converged arena radius.

[Bogie_smiles (OP)]

No, H and h are the heights of the two spherical caps.


The radii of the two spheres are R and r.


You can go to Wolfram Math and call up sphere-sphere intersection/overlap.

[guest39538]

No, H and h are the heights of the two vertical caps.


The radii of the two spheres are R and r.

Thank you for explaining that , I am almost able to ''read'' it . 

So we have 1/3 times pi * Height squared *  (in brackets do first)?

In brackets 3 times radius - height ?

[Bogie_smiles (OP)]

http://mathworld.wolfram.com/Sphere-SphereIntersection.html



This link has all the details.
Note: I mistakenly called the two "caps", vertical caps, when in fact Wolfram calls them spherical caps.

[Bogie_smiles (OP)]

No, H and h are the heights of the two vertical caps.


The radii of the two spheres are R and r.

Thank you for explaining that , I am almost able to ''read'' it . 

So we have 1/3 times pi * Height squared *  (in brackets do first)?

In brackets 3 times radius - height ?

Yes, and then divide by the volume of the sphere R


Make measurements as the two spheres converge and overlap, put them into the equation, and do that for all of the pieces on the right side of the equation, until the sum of all the pieces equals 1.
 

[guest39538]

http://mathworld.wolfram.com/Sphere-SphereIntersection.html



This link has all the details.

Thank you for the link, I have friends here at the moment so will look that over proper later.  If it was a half and half convergence we could just do the volume of the sphere / 2 . 

Added - second thoughts that would not work .

[guest39538]

No, H and h are the heights of the two vertical caps.


The radii of the two spheres are R and r.

Thank you for explaining that , I am almost able to ''read'' it . 

So we have 1/3 times pi * Height squared *  (in brackets do first)?

In brackets 3 times radius - height ?

Yes, and then divide by the volume of the sphere R


Make measurement as the two spheres converge and overlap, put them into the equation, and do that for all of the pieces on the right side of the equation, until the sum of all the pieces equals 1.
 

I will ''get it' I think, not that difficult. 

added- So how/where do you get your numerical value inputs from ?

[Bogie_smiles (OP)]

No, H and h are the heights of the two spherical caps.


The radii of the two spheres are R and r.

Thank you for explaining that , I am almost able to ''read'' it . 

So we have 1/3 times pi * Height squared *  (in brackets do first)?

In brackets 3 times radius - height ?

Yes, and then divide by the volume of the sphere R


Make measurement as the two spheres converge and overlap, put them into the equation, and do that for all of the pieces on the right side of the equation, until the sum of all the pieces equals 1.
 

I will ''get it' I think, not that difficult. 

added- So how/where do you get your numerical value inputs from ?

Do you have a ruler? Draw them, showing a little more overlap each drawing, measure the lengths and put the measurements into the equation, and compare the results to 1. I used an Excel spreadsheet when I proved it out.

From Wolfram: In order for the overlap of two equal spheres to equal half the volume of each individual sphere, the spheres must be separated by a distance

d   =   (x^3-12x+8)_2   
(18)
   =   2sqrt(3)sin(2/9pi)-2cos(2/9pi)   
(19)
   =   0.694592710...

Note that you are looking to get the overlap of the two spheres to equal 1/2 of the sum of the volume of the two equal spheres that you start with. However, in reality, the volumes of the two spheres will not necessarily be equal to start with, so that complicates it.


The value of d = the distance between the two center points of the parent spheres. Keep in mind that as the volumes of the two spheres increase, the center points move further apart and the value of d changes. Using Excel, it is just an iterative process of trial and error to get the equation to equal 1, but a programmer could write a little code that would make it easy.

[guest39538]

The value of d = the distance between the two center points of the parent spheres. Keep in mind that as the volumes of the two spheres increase, the center points move further apart and the value of d changes. Using Excel, it is just an iterative process of trial and error to get the equation to equal 1, but a programmer could write a little code that would make it easy.

I will get a ruler and protractor to do a manual measure in the next few days,  I don't feel it is hard to put in input values once the equation is ''readable'' though.  Thanks for explaining it to me.

[Bogie_smiles (OP)]

The value of d = the distance between the two center points of the parent spheres. Keep in mind that as the volumes of the two spheres increase, the center points move further apart and the value of d changes. Using Excel, it is just an iterative process of trial and error to get the equation to equal 1, but a programmer could write a little code that would make it easy.

I will get a ruler and protractor to do a manual measure in the next few days,  I don't feel it is hard to put in input values once the equation is ''readable'' though.  Thanks for explaining it to me.

With equal spheres, each containing a quantum of energy, the length d will always be same percentage of the radius when the equation equals 1..

When the two spheres are of different volumes, keep in mind that they both are defined as quantum, i.e., having the same amount of energy. That means that the two spheres will have different internal density, and will be contributing different amounts of energy per volume to the lens shaped overlap space. It will grow on you, lol.

[guest39538]

The value of d = the distance between the two center points of the parent spheres. Keep in mind that as the volumes of the two spheres increase, the center points move further apart and the value of d changes. Using Excel, it is just an iterative process of trial and error to get the equation to equal 1, but a programmer could write a little code that would make it easy.

I will get a ruler and protractor to do a manual measure in the next few days,  I don't feel it is hard to put in input values once the equation is ''readable'' though.  Thanks for explaining it to me.

With equal spheres, each containing a quantum of energy, the length d will always be same percentage of the radius when the equation equals 1..

When the two spheres are of different volumes, keep in mind that they both are defined as quantum, i.e., having the same amount of energy. That means that the two spheres will have different internal density, and will be contributing different amounts of energy per volume to the lens shaped overlap space. It will grow on you, lol.

Well I don't normally do math, but I am running out of things to learn , so math was my final challenge to myself.


Added  - I think the final plan of my world domination was to learn math ,  unexpectedly giving  the audience shock , giving them all a heart attack when I show I can do math lol. 

Math equations are just ''words'' put as representatives, once the ''words'' are known and the 'sentence' structure is understood, it is simply putting in values instead of the ''words''. 

P.s Was in bed for ~9 pm and got up at 4.30 am,  two days in a row I have done that ,  putting my body back into a schedule mode ,  turning chaos into organised.   

[Bogie_smiles (OP)]

Reply #371


https://www.thenakedscientists.com/forum/gallery/43933_27_01_18_2_29_16.jpeg


This post includes some duplication of content recently posted in order to get it into the sequence leading up to the mechanics of quantum gravity in the ISU. This continues from reply #344 above (https://www.thenakedscientists.com/forum/index.php?topic=70348.msg547042#msg547042):

37) It is the ISU sphere-sphere overlap quantum equation, and as the description says, it works with the process of quantum action, at both the macro and micro levels. The diagram, showing the sphere-sphere intersection has two spheres and each sphere has a cap (called a spherical cap at Wolfram Math http://mathworld.wolfram.com/Sphere-SphereIntersection.html).
VcapR/VR is the volume of cap R divided by the volume of sphere R. That gives you the ratio of the volume of cap R to the volume sphere R (think of it as the percentage of sphere R that is included in cap R). Follow that same approach for each of the four parts of the left side of the equation, by using the corresponding part of the right side of the equation to do the calculation, and you must assign values to each element in the diagram to fill into the equation in order to do the calculation. You end up with four percentages. Add the four percentages together to get the sum, and compare that sum to 100%. When it reaches 100%, you have accumulated one quantum of energy in the overlap space, and that marks the point that the third wave has a quantum of energy emitted spherically from the overlap space.

Note: The calculations, using the equation, are to determine when, during the course of wave/wave overlap, a new third wave becomes quantum. There is a lot of significance given to the feature of the ISU model that I call the gravitational wave energy density profile of space, since all of the wave action going on in the density profile are subject to becoming quantum increments the make up wave-particles at the micro level, or as big crunches that become big bangs at the macro level:
1) The profile consists of nothing but gravitational waves traversing space.
2) Each gravitational wave originates as a spherical third wave emitted by the convergence of two or more “parent” waves.
3) The gravitational wave fronts carry energy across space.
4) Every point in space has a net energy density value caused by the local presence of gravitational wave fronts that are carrying energy past that point from all directions.
5) The net value of the energy density at each point is continually changing because there is a constant inflow of wave fronts to and through each point from the gravitational wave energy density profile.
6) Everything that occupies space is therefore composed of gravitational wave energy of some density value.
7) There are thresholds and limits related to energy density that govern the way those gravitational waves get organized to establish the presence of the things that we observe in space.
8 ) Every object in space has formed there after a big bang event initiates the formation of a new big bang arena, and will be negated into its constituent wave energy when it gets captured in a new local big crunch.
9) Entropy is defeated, meaning that the progress of how useful energy gets used up is continually advancing (entropy increases) until the cold dead matter of old, aging and maturing arenas gets renewed into low entropy when a big crunch reaches critical capacity and collapse/bangs, releasing a huge ball of hot dense wave energy.
10) The ISU model features the processes of big bang arena action at the macro level, and quantum action at the micro level, that together orchestrate the continual change from matter to energy and back to matter across the big bang arena landscape of the greater universe.

38) This image is a revision of the large scale action depicted in an earlier image. It represents a patch of the landscape of the greater universe that shows the macro objects and large scale structure that is composed of gravitational wave energy, wave-particle by wave-particle. It includes visible arena boundaries to help improve on the earlier version of the image:
https://www.thenakedscientists.com/forum/gallery/43933_03_07_18_1_33_57.jpeg


39) At the opposite end of the size scale in the ISU, are the tiniest meaningful wave convergences. I have called them hints of mass, or high energy spots at the convergence of gravitational waves, and when they occur within the space occupied by a wave-particle, they are the quanta that make up the total energy of the particle and account for the mass of the particle.
https://www.thenakedscientists.com/forum/gallery/43933_26_07_17_4_28_57.jpeg


40) In the following image, the high energy density spots are shown at the center of the wave particle, and the spherically outflowing gravitational wave energy is shown converging with the directionally inflowing gravitational wave energy arriving from the gravitational wave energy density profile of space:
https://www.thenakedscientists.com/forum/gallery/43933_26_07_17_4_41_02.jpeg



The cause of quantum gravity in the ISU to be continued …

[Bogie_smiles (OP)]

Reply #372

https://www.thenakedscientists.com/forum/gallery/43933_27_01_18_2_29_16.jpeg


41) The wave-particle has location and momentum in the gravitational wave energy density profile of space. The wave-particle core contains the mass, and each high density spot in the core is a fraction of its total mass. For talking purposes let’s examine, for example, the proton and the electron wave-particles at rest to establish a ball park estimate of the number of high density spots that they are composed of at any instant:
From what we know about the proton in collisions:
(https://www.thenakedscientists.com/forum/gallery/43933_22_07_17_12_57_30.jpeg)

… they display amazing detail at high energies. They are often described at rest though, for discussion purposes, and so the proton and the electron in this post are at rest.

42) From what I hypothesize about the process of quantum action, we can derive a ball park figure (Wagner=wild arse guess not easily refuted) of the number of quanta within the proton and electron at rest.

43) Given that ball park figure, we can then take the generally accepted energy value of the proton wave-particle at rest, divide by the ball park number of quanta in the proton, and derive the energy value of one quantum of energy within the standing wave pattern of the proton at rest:

a) The premise is that the wave-particles are composed of energy in quantum increments. The standing wave pattern of the wave-particle is filled with quanta in the form of gravitational wave convergences in various stages of reaching their peak completion, and which average out to equal one quantum of energy each for each quantum period.

b) A quantum period for a wave-particle is the length of time it takes for the process of quantum action to refresh each of the quanta in the standing wave pattern. To “refresh the internal quanta” means to produce replacement quantum wave convergences for each of the convergences that are disbursed as spherical third waves.

c) Each quanta is refreshed by the continual flow of gravitational third wave energy produced within the particle space, and from the directionally arriving energy of the gravitational wave energy density profile of space. Within the wave-particle, as the quanta reach their peak, they produce a third wave containing a quantum of energy which expands spherically to form new wave convergences within the standing wave pattern.

d) For a particle at rest, the wave energy emitted from the particle boundary is equally exchanged with the wave energy inflowing from the surrounding gravitational wave energy density profile of space.

e) Our resulting estimate the number of quanta contained in a proton at rest, and given the defined energy of a proton at rest in some standard unit of measure, we then can calculate the corresponding amount of energy of a quantum that equates to the quanta making up the contained energy of a proton at rest.

44) Using the ratio of the rest energy of an electron vs. a proton, which is 1/1836, to equate the number of quanta in the proton to the number of quanta in the electron, we have a basis for a calculation.

45) We are supposing that the number of quanta in an electron is equal to the number of quanta at the surface of the proton, based on some logic about the interactions between electrons and protons in an atom. For this exercise it serves as a mathematical relationship between the energy of the proton and the electron:

a) Area/Volume = (4 pi r^2)/(4/3 pi r^3) = 3/r = 1/1836

b) Therefore r=3*1836 = 5508, thus the radius of the proton is equal to 5508 quanta across that diameter within the standing wave pattern of the proton wave-particle

c) 4 pi r^2 = surface area of a sphere

d) 4/3 pi r^3 = volume of a sphere

e) pi = 3.14159265

46) The calculations yield:

a) Quanta in an electron = 381,239,356

b) Quanta in a proton = 699,955,457,517

47) Those figures serve is useable numbers for talking purposes in the ISU model, and demonstrate the detailed action going on in the micro realm.





The cause of quantum gravity in the ISU to be continued …

[guest39538]

a) Quanta in an electron = 381,239,356

b) Quanta in a proton = 699,955,457,517

To clarify , what do you mean exactly, when you say quanta ?

[Bogie_smiles (OP)]

a) Quanta in an electron = 381,239,356

b) Quanta in a proton = 699,955,457,517

To clarify , what do you mean exactly, when you say quanta ?

Note: Quanta, in the ISU, are whole units of quantum energy. You may recall me saying that wave-particles are composed of gravitational wave energy in quantum increments. The quanta are those quantum increments. As you can tell, the wild guess as to how many quanta make up the proton and electron at rest shows huge numbers ...
The wave-particle quantum, orchestrated by the process of quantum action, should not to be confused with the “quantum of action" known as Planck’s constant. The wave-particle quantum is orders of magnitude smaller, in terms of its energy, than Planck's constant. It is the energy at the peak of the parent wave convergences of gravitational wave energy within the wave-particle space; it marks the energy of the third wave that emerges from the convergence of two or more parent waves within the core of the wave-particle. A single proton is said to have about 700 billion of them, each having a momentary presence, and then producing a third wave that contains a quantum of energy, and that expands at the local speed of light until it intersects with other “parent” third waves to form new quanta within the particle space.

[guest39538]

are whole units of quantum energy.

Do you mean a volume of point energies? 

Sorry , I have heard before , Quanta refereed to as photons, so I am slightly confused  what you mean exactly.   Could you please elaborate furthermore ? 

[Bogie_smiles (OP)]

are whole units of quantum energy.

Do you mean a volume of point energies? 

Sorry , I have heard before , Quanta refereed to as photons, so I am slightly confused  what you mean exactly.   Could you please elaborate furthermore ? 

You’re right about the photon being described as a single quantum of light. Below are some links, and I have cut and pasted some content from them to reiterate the definitions and usages of quantum and quanta in modern science for the benefit of this discussion, as I explain why the quanta that I use for wave particles are so much smaller than Planck’s constant.

The definition of quantum (and quanta) below is consistent with the way I use the terms in regard to the wave particle (quantum increments), as well as in regard to the energy of a Big Crunch/Bang (arena particles), both wave-particle and big bangs are quantized in the ISU, as I’m sure you have picked up on.

Note that the wave-particle in the ISU is not your fundamental standard model particle; fundamental particles in the standard model of particle physics are said to have no internal composition, i.e., they are described as point particles that the mathematicians can easily deal with.

In the ISU, 1) because the wave-particle has to be consistent with wave particle duality for all particles of all energies, including photons of all frequencies, 2) because all of the ISU wave-particles are speculated to be both wave and particle at the same time in all of their actions, and 3) because the way that wave-particles all have individual presence, location, momentum, and freely interact with each other and with the gravitational wave energy density profile of space, quantum by quantum, it is necessary to expect wave-particles to have a great deal of internal composition. And in that regard, the ISU doesn’t disappoint: the core of the wave-particles can have the hundreds of millions and/or hundreds of billions of quanta, as hypothesized in reply #372 and elsewhere, to meet all of the above ISU requirements.

Photons are still quantum particles in the ISU, and each energy level of photon energy in the electromagnetic spectrum is understood to be a photon having a different energy value, and still referred to as a quantum of electromagnetic wave energy for talking purposes. As you can see, that means that the energy of a photon in the microwave range is called a quantum of light energy, and the energy of an X-Ray is called a quantum of light energy, but they are near the opposite ends of the electromagnetic spectrum in terms of the energy that they carry. As the links and definitions below confirm, they are quantized, and Planck’s constant is the minimum energy difference and common denominator between photons of differing energy levels and wavelengths.

In the ISU, photons are wave-particles with mass, just like protons and electrons and any wave-particle. They are unique in that they are emitted by electrons at the local speed of light. The core of a photon particle will contain a consistent number of quanta (high energy density spots) that corresponds with the energy level of that particular photon frequency/wavelength. In the ISU, it is that differing number of quanta in the core of each photon wave-particle that determines the different frequencies that the different photon wave-particles consists of; each frequency reflects itself by a slightly different rhythm to the pulsing of energy that is emitted from the photon wave-particle core.

You have brought up a valid distinction between the usage of quantum and quanta in regard to wave-particles in the ISU vs the Standard Model of Particle Physics, and I hope I have given you some basis to see why there is that difference.
————————————
https://www.merriam-webster.com/dictionary/quantum
plural quanta play \ˈkwän-tə\
1
a : quantity, amountb : portion, partc : gross quantity : bulk2
a : any of the very small increments or parcels into which many forms of energy are subdivided
b : any of the small subdivisions of a quantized physical magnitude (such as magnetic moment)
——————————————

https://en.wikipedia.org/wiki/Quantum
In physics, a quantum (plural: quanta) is the minimum amount of any physical entity (physical property) involved in an interaction. The fundamental notion that a physical property may be "quantized" is referred to as "the hypothesis of quantization".^[1] This means that the magnitude of the physical property can take on only discrete values consisting of integer multiples of one quantum.
For example, a photon is a single quantum of light (or of any other form of electromagnetic radiation), and can be referred to as a "light quantum", or as a light particle. Similarly, the energy of an electron bound within an atom is quantized and can exist only in certain discrete values. (Indeed, atoms and matter in general are stable because electrons can exist only at discrete energy levels within an atom.) Quantization is one of the foundations of the much broader physics of quantum mechanics. Quantization of energy and its influence on how energy and matter interact (quantum electrodynamics) is part of the fundamental framework for understanding and describing nature.
——————————————

https://en.wikipedia.org/wiki/Planck_constant
The Planck constant (denoted h, also called Planck's constant) is a physical constant that is the quantum of action, central in quantum mechanics.
First recognized in 1900 by Max Planck, it was conceived as the proportionality constant between the minimal increment of energy, E, of a hypothetical electrically charged oscillator in a cavity that contained black body radiation, and the frequency, f, of its associated electromagnetic wave. In 1905, the value E, the minimal energy increment of a hypothetical oscillator, was theoretically associated by Albert Einstein with a "quantum" or minimal element of the energy of the electromagnetic wave itself. The light quantum behaved in some respects as an electrically neutral particle, as opposed to an electromagnetic wave. It was eventually called a photon.
————————————-

https://en.wikipedia.org/wiki/Photon
The photon is a type of elementary particle, the quantum of the electromagnetic field including electromagnetic radiation such as light, and the force carrier for the electromagnetic force (even when static via virtual particles). The photon has zero rest mass and always moves at the speed of light within a vacuum.
Like all elementary particles, photons are currently best explained by quantum mechanics and exhibit wave–particle duality, exhibiting properties of both waves and particles. For example, a single photon may be refracted by a lens and exhibit wave interference with itself, and it can behave as a particle with definite and finite measurable position or momentum, though not both at the same time. The photon's wave and quantum qualities are two observable aspects of a single phenomenon - they cannot be described by any mechanical model;^[2] a representation of this dual property of light that assumes certain points on the wavefront to be the seat of the energy is not possible. The quanta in a light wave are not spatially localized.
The modern concept of the photon was developed gradually by Albert Einstein in the early 20th century to explain experimental observations that did not fit the classical wave model of light. The benefit of the photon model was that it accounted for the frequency dependence of light's energy, and explained the ability of matter and electromagnetic radiation to be in thermal equilibrium. The photon model accounted for anomalous observations, including the properties of black-body radiation, that others (notably Max Planck) had tried to explain using semiclassical models. In that model, light was described by Maxwell's equations, but material objects emitted and absorbed light in quantized amounts (i.e., they change energy only by certain particular discrete amounts). Although these semiclassical models contributed to the development of quantum mechanics, many further experiments^[3][4] beginning with the phenomenon of Compton scattering of single photons by electrons, validated Einstein's hypothesis that light itself is quantized.^[5][6] In 1926 the optical physicist Frithiof Wolfers and the chemist Gilbert N. Lewis coined the name "photon" for these particles.^[7] After Arthur H. Compton won the Nobel Prize in 1927 for his scattering studies,^[8] most scientists accepted that light quanta have an independent existence, and the term "photon" was accepted.

[guest39538]

You’re right about the photon being described as a single quantum of light.

Thank you for explaining that to me in detail.  I could read the math easy enough in the post prior. However, can a photon occupy the same spatial ''point''  as a different photon?  This in essence would allow for an infinite amount of photons , could  occupy a single spatial point ?

[Bogie_smiles (OP)]

You’re right about the photon being described as a single quantum of light.

Thank you for explaining that to me in detail.  I could read the math easy enough in the post prior. However, can a photon occupy the same spatial ''point''  as a different photon?  This in essence would allow for an infinite amount of photons , could  occupy a single spatial point ?

This answer is in regard to the ISU model, and differs in some respects from generally accepted science.

Yes, to part 1, photons are waves and particles at the same time, and their wave state can occupy the same space as the wave state of other photons; thus you get wave interference pattens in two slit experiments (for that matter, all wave particles can share the same space in their wave state). Note that in the ISU model, the outflowing "light" energy from a photon wave-particle is the spherically outflowing gravitational wave energy of the photon particle core.

The particle state of the photon has a dense core of wave intersections (quanta) where the number of quanta determine the local frequency of the wave emission. The core is continually emitting the spherical wave state, and that is why, in the ISU, they are both wave and particle at the same time. But the photon is traveling through the energy density profile of space in one direction, the direction of its motion when emitted by an electron, and therefore is getting all of its “replacement” energy out of the density profile of space from that one forward direction. This specific directional nature and speed of light velocity means that the particle state does not normally occupy the same space with other particle states.

[guest39538]

You’re right about the photon being described as a single quantum of light.

Thank you for explaining that to me in detail.  I could read the math easy enough in the post prior. However, can a photon occupy the same spatial ''point''  as a different photon?  This in essence would allow for an infinite amount of photons , could  occupy a single spatial point ?

This answer is in regard to the ISU model, and differs in some respects from generally accepted science.

Yes, to part 1, photons are waves and particles at the same time, and their wave state can occupy the same space as the wave state of other photons; thus you get wave interference pattens in two slit experiments (for that matter, all wave particles can share the same space in their wave state). Note that in the ISU model, the outflowing "light" energy from a photon wave-particle is the spherically outflowing gravitational wave energy of the photon particle core.

The particle state of the photon has a dense core of wave intersections (quanta) where the number of quanta determine the local frequency of the wave emission. The core is continually emitting the spherical wave state, and that is why, in the ISU, they are both wave and particle at the same time. But the photon is traveling through the energy density profile of space in one direction, the direction of it’s motion when emitted by an electron, and therefore is getting all of its “replacement” energy out of the density profile of space from that one forward direction. This specific directional nature and speed of light velocity means that the particle state does not normally occupy the same space with other particle states.

Ok, thank you for explaining, I have no further questions at this time.