There is an assumption in some current theories of the nature of the universe that ‘space’ and ‘matter’ are separate physical entities, whose interaction takes place virtually at a metaphysical level. As the saying - the theoretical equivalent of a law - goes, ‘matter tells space how to curve, and space tells matter how to move‘. But this apparent ‘physical law’ only describes an effect between bodies of matter, not in an entirely different arena in which ‘space’ appears to act on itself, and ‘matter’ on huge scales is merely a helpless participant.
When ‘explaining’ cosmological redshift, cosmologists are fond of pointing out that distant galaxies are not speeding ‘through’ space - it is space itself that is expanding, carrying galaxies with it. Distant galaxies are transported at speeds exceeding the speed of light - by 'space'. This assumption appears to be unquestioned, regarded as a truth that needs no explanation by 'physical law'.
Simply by pushing on itself, 'space' is capable of carrying huge loads of matter far away from where they once were. Yet 'space' is given no physical qualities to carry out this work. Its 'power’ is the power of geometry.
However, there is a condition on this power of space. It expands only where it is ‘empty’. Where ‘gravity’ operates - that geometric ‘force’ capable of telling matter how to move - space does not expand. But what is the distinction between intergalactic space and galactic space?
Recent observations appear to show that expanding space is expanding more quickly than it once did. This ‘acceleration’ seems to require a repulsive ‘force’. At this point, geometric spatial expansion takes on a much more active role in the evolution of the universe. Yet this ‘revelation’ ignores the fact that spatial expansion, the expansion of a spatial volume, already requires an acceleration of three powers of radial distance simply to expand at a constant rate. Adding a constant volume of space per time unit will not do it. An constantly increasing volume must be added. This already indicates a kind of ‘super force’ at work.
If spatial expansion is now to be regarded as a ‘force’, then it should always have been regarded as a ‘force’ rather than as a ‘physical geometric entity‘. And what is expanding? It is a spatial field. But ‘space’ is the overwhelming existent state of the universe. In other words, this ‘repulsive force’ of expanding space exists in the context of massive bodies such as stars, which are themselves ‘space’, and in the context of ‘particles’, which are themselves at their root spatial motions, as well as in ‘empty’ space. If the ‘repulsive force’ of space is puny, overwhelmed by gravity which is itself overwhelmed by nuclear and magnetic forces, it is nevertheless a primary force. The idea that ‘space’ ends with ‘mass’ may be fallacious. The idea that these two entities, ‘space’ and ‘mass’, are fundamentally different, or that ‘mass’ exists independently of ‘space’, may also be fallacious. It may be more true to say that ‘mass’ is a manifestation of the spatial field, an energetic field which then becomes the fundamental field of the universe. At that point the notion of independent yet related entities no longer applies; ‘mass’ and ‘space’ are simply forms of a single energy field. That this field is described only in geometric terms then requires either that mass be also described in geometric terms.
The essence of a force is the acceleration it produces. A volume of space which is expanded by the addition of a constant volume will expand at an ever decreasing rate. Such a force is unlikely to be responsible for universal evolution. A volume of space which is expanded at an ever-increasing rate, such as is the apparent acceleration ‘observed’ by the Chandra telescope, seems similarly unlikely.
The field which could produce such an acceleration would be unlikely to create the harmonic universe we see.
The Planckian description of time and space dimensions utilizes a constant speed, the speed of light, to arrive at ‘natural units’. It seems only ‘natural’ that a similar description of an expanding spatial volume would utilize a similar constant rate of expansion. And from this constant expansion rate, an evolutionary scenario emerges which can encompass the creation of mass within an energetic field. That is the purpose of this scenario.

This is a scenario for a universal system whose fundamental form is that of an expanding energy field by whose expansion all descendant systems are created. The essential feature of this scenario is that there is no differentiation between ‘space’ and ‘matter’. In this scenario ‘matter’ is a rotational form of ‘space’ (or ‘space‘ is a non-rotational form of ‘matter‘), so both ‘space’ and ’matter’ are ways of describing what is ultimately energy. ‘Matter’ does not simply curve spacetime; matter is curved spacetime - rotating energy - and this rotation sets it apart from ‘non-material‘ spatial energy flows. Rather than energy being the property, or quantity of the property, of changing the state of a system, energy at its root is the ability to create a system by expanding, and this ability underlies all evolving physical systems.
Space and time ‘dimensions’ are ways of measuring the flows of energy.

In this scenario ‘gravity’ can be described as the curvature of space or as an attractive ‘force’. Space can be described as an energetic field. The ‘beauty’ of this scenario is that out of a single path - outward - the universe creates an endlessly increasing number of possible and actual paths, some good and some not so good.
It eliminates the need for a highly unlikely inflation scenario and eventual heat death necessary if there is a finite amount of matter in the universe (and if ‘space‘ and ‘matter‘ are treated as separate physical entities), since the expansion of ‘space’ naturally creates ‘matter’ in a constant ratio.
It may produce a mathematical description which reconciles the conflict between classical and quantum theories without the need for a ‘graviton’ or a Higgs field.
The scenario assumes that the field expands at a constant rate (say c). This natural limit creates pressure in the form of curvature within the field, since all regions within the field cannot expand at c. On average, the field expands only at half its potential, or to put it another way, the field has the capacity to create twice the volume it actually creates.
This leads to an interesting (and admittedly elementary) result. Using nameless spatial and time units, say the field expands to a radius of one spatial unit in one time unit, creating a volume of 4.1905 cubic spatial units, and has the capacity to produce a volume of 8.38095 units. The radius of the larger volume is approximately 1.2595. Imposed on the smaller radius, this could be said to represent a ‘curvature ratio’ of 1.2595 to 1. As the field expands this ratio remains constant. If we take ‘spatial curvature’ as ‘gravitational curvature’, this implies that approximately 21 percent of the volume of the field is subject to gravitational curvature, while 79 percent is not, although I don’t think it is that cut and dried. If gravitational curvature represents mass energy, then it could be said that a maximum of 21 percent of the universe would be in the form of ‘mass energy’ and the rest in the form of ‘vacuum energy‘, regardless of the age of the universe - although how much of the ‘mass energy’ is actually in the form of ‘massive bodies’ and how much is in the form of spacetime curvature between them, I don’t know. The further question is how ‘mass’ is arrived at.
On the scale of one, taking the basic formula by which gravitational force is measured (inverse to the square of the distance from a ‘center‘) and adopting it as a formula for gravitational curvature, it seems reasonable that of the curvature produced by the additional radius of .2595 found above, by far the greatest part will take place within a radius .1 (or .01, or .001, or . . .) of a ‘center of curvature’, i.e. a ‘center of mass’ of a single ‘particle‘ of mass.
It seems a single rotational period is the simplest to model, although such a rotation (as I have modeled it on three axes) does not produce a 360 degree rotation. And how the curvature will be determined between bodies I do not know.

Here the question is whether currently available mathematical ’tools’ can be used to translate a rotating space, rotating on three axes, into a formula for ’mass’. It seems that concepts such as Planck length and Planck time, the gravitational constant, and angular momentum should allow for some kind of determination. The gravitational constant may be problematic, but if the spinning region does turn out to be a region of ’mass’, it seems a gravitational (or inertial) value should be attributable to it. The spinning region would at least have angular momentum. Not knowing the math involved, I wonder whether it is possible to arrive at a translation of rotation into mass which can be incorporated into consistent theories.
There are eight possible combinations of simultaneous three-axial rotation, and interestingly, two distinct kinds of motion arise on a hypothetical spherical surface from these combinations. (I am not suggesting that a sphere will arise, but it seems a spherical rotation on three axes is necessary to model rotation responding to force from all directions.) I am not in a position to model (any further than I already have) these two distinct kinds of motion, but it would be interesting if three-axial spin could be modeled using computer simulation. Then further combinations could also be modeled.

I believe that combinations of spin are possible which can absorb more energy than the field can produce, at which time bodies will exchange energy between them, or radiate energy out to the field as photons.
This radiation will take the form of a kind of ‘breathing’. (And on a large scale, rather than stars ‘collapsing’ under gravitational pressure, they are finding more efficient spin mechanisms.)
If the circumference of the spinning region is set to 1, indicating both a circumference equal to the radius of the original volume, and also that a point on the surface of a sphere corresponding to the extent of the spinning region returns to its original position in 1 time unit, then its radius is ~ .0159, and its volume ~ .0168 cubic units. Interestingly, the ratio between the original surface area of the expanding sphere and the surface area of the spinning region is ~ 39.25 to 1, which is very close to the ratio of gravitational curvature or force between their radii, ~ 39.5 to 1.
This indicates to me that this ‘particle’ has gravitational mass.

The motion of various points on the surface of the spinning region follows various curves, which indicates that there is a torque applied to the spinning region, and a constant acceleration in the form of constant change of direction or curvature.
If the energy of this ‘particle’ can be derived from the formula E = hf for a massless particle, then its E = ~ 4.136 x 10^-15 x ~5.391 x 10^44 = ~2.23 x 10^29 eV.s
(if the frequency is taken as the number of cycles per second). If one electron volt is equivalent to ~1.783 x 10^-36 kg, then the mass of this ‘particle’ would be ~ 3.97 x 10^-7 kg, compared with a Planck mass of ~ 2.176 x 10^-8 kg, the mass of an electron of ~ 9.109 x 10^-31 kg, and the mass of a proton of ~ 1.6726 x 10^-27 kg.

I can easily understand why no one responded to this thread of yours ngeo, it's quite a mouthful!

I'll address it piecemeal, with (hopefully) a summary at the end.As a summary of the current state of play, against which you will introduce your ideas, I think you've started badly.

First, the workhorse in cosmology is Einstein's theory of General Relativity. At its heart, GR is just a bunch of equations; the extent to which it's a good description ('explanation'?) of the universe depends upon how well predictions from this theory (i.e. manipulating the equations, plugging in numbers, etc) match good observational results.

Next, how one chooses to interpret the terms in the equations is at least somewhat a matter of personal choice/taste ... it may very well be that, in order to work with the equations effectively, you need to make up some mental categories; you may, for philosophical reasons, choose to associate the entities with 'reality'. However, none of this is required, from the theory. In fact, we already know that GR and QFT (quantum field theory) are mutually incompatible, so 'reality' can't be some mental image of both (and there's no certainty that theories which replace these will have similar terms at all).You're really going off the rails here ngeo - we have a theory (GR), we apply to the universe; we make lots and lots of observations; we compare what comes out of GR with what we see and we find good agreement - where's the 'unquestioned assumption'?If you like to look at it this way, OK. However, I'd say this picture creates a huge, unnecessary barrier to understanding the theory(-ies) - it introduces (intuitive) ideas from the world of classical physics that are not required in GR.Now you've lost me - what (in cosmology, or astrophysics, or GR) are you referring to here?I think you're referring to 'dark energy'. If so, then your summary is either strange or wrong - perhaps we could have a new thread, in the Q&A section, on this topic (so that you understand the theory better)?All this may, or may not, be a good foundation for a new (cosmological, physical?) theory. However, without something more (e.g. equations), it strongly resembles a 'word salad'.(to be continued)

(continued)Why?Why?Such as?In what sense can a 'path' be considered 'good' or 'not so good'?I can see how this would (could?) get rid of an 'eventual heat death', but not inflation - can you clarify please?I expect that you'll be saying more about this 'may' later, so I won't comment here, except to ask whether it might also produce a novel interpretation of the observational resolution of the EPR paradox.I'm confused about the dimensions here - 'c' has dimensions of LT^-1, volume (and presumably your 'field') of L³ - what is it that 'expands at c'?

I also think there's an inconsistency about this 'expansion' - do all volumes, no matter how big or small, expand at the same rate?Where did this number come from? Are you assuming a 3D flat field?I don't follow this at all; for example, why 2 (and not any other number >1)?Do you have a 'singularity' (infinite curvature) for a point particle? at any (every?) point in space??[/quote]The question then is, what form (or path) does this curvature, or mass, take? I believe that the curvature at a ‘center of mass’ will be a rotational flow of energy, maintained and required by the field. However, this rotation should not be on a single axis, but simultaneously on three axes in order for the rotation to account for energetic flow from all directions in space.[/quote]This seems to be an odd definition of 'rotation' - if we took a point on the surface of a sphere, what shape would be traced out by this rotation 'simultaneously on three axes'?I think you've put your finger on it ... without the math, it's hard to 'see' what sense to make of all these words.

I'm also wondering whether this idea gives rise to an isotropic universe, and whether you could avoid internal inconsistency (e.g. presumably, in your picture, 'curvature' should be invariant under translations and rotations of coordinate axes)?What are they?So what are photons, in this idea of yours? They are not 'space' and not 'matter' (or are they?)In what sense is a 'spin mechanism' 'efficient'?I don't see how you got these numbers - could you please show the working?You lost me - which comes first, the 'points following various curves' or the 'torque' (or, which gives rise to what)?Where did these numbers come from? Isn't it 10^30? what units are 'eV.s'?So?(to be continued)

Hi Nereid, I will try to respond to your comments in order.

Writing to the internet is like making an ongoing draft. My choice of words is always subject to change. Regarding ‘some current theories of the nature of the universe’, I am referring to statements to the effect that an ’explosion of space and matter’ characterizes the early universe. The idea of a ‘hotter’ and ‘denser’ early universe is also an idea I would characterize as a ‘current theory of the nature of the universe’. I believe there is also an assumption of finiteness of mass/energy which troubles me, and an assumption that ‘all’ this mass/energy exploded into existence over a certain time period. Whether or not these characterizations must be applied to GR or QFT as being the current ‘state of play’ in cosmology, I do not know. I have nothing against either one; what I could say about them would be only a hazy generalization. But I continually come up against statements that imply a separate existence for something called ‘space’ and something called ‘matter’ - and a messy relationship between something called ‘energy’ and something called ‘mass’. If you know of good observational results that put ‘space’, ‘energy’ and ‘mass’ in their proper place in a coherent explanation for universal evolution, let me know too.

I think the ‘unquestioned assumption’ I am referring to regarding spatial expansion is the assumption that ‘space’ can be both a measuring tool, used only to relay information about real events, and a physical entity which itself can expand. I have read too often that “space itself is expanding” to believe that whoever says this regards ‘space’ only as a measuring tool. The dual use of ’space’ as background metric and physical player leads to ’expanding confusion’. The physical expansion of space is an unquestioned assumption precisely because to probe into that physical system threatens the use of ‘space’ as a background metric. In other words, it is a place no one seems to want to look. I have no problem with expanding or curved space, nor with spatial (time and distance) measurements to describe events. But I have a problem if they are used interchangeably, and I believe they are.

I see that as you read my ‘word salad’ at ‘space‘ and ‘mass‘ (which seems to have an unfinished either/or in it) you begin to understand what I am getting at. (The unfinished ‘or’ would be - “or that space be described in terms of a force.”)

An accelerated expansion in the current ‘state of play’ appears to require an evolution where at different times different forces - the ‘force’ of inflation (expanding space par excellence), radiation pressure, and gravity - interact with each other, as ‘space‘ flies apart(?), in such a way that in one epoch one dominates and in our epoch another dominates. I don’t know enough science to call it questionable. I am only suggesting a scenario in which matter is constantly created in a constantly expanding universe, providing a self-made purpose: growth. Why would the universe not expand at an increasing rate? Because you would have a hard time figuring out any relationship between mass and energy, let alone the apples and oranges relationship that already exists when people say “the universe” is ‘4 percent normal matter, 23 percent dark matter, and 73 percent dark energy’. Scientists are okay with this? Let someone tell me how faultless logic leads to the kind of cosmological miscegenation above - and give me a physical entity that logically defines 100 percent of “the universe“ as it is ‘known’.

The growth of the universe from a single path - spatial expansion - to an endless number of paths can be traced from the creation of particles to atomic systems to molecules to cells to humans. All universal evolution can be pictured as being powered by the ability to expand. And there is no switch to turn off the power. Good paths are characterized by harmony: what fits. Paths that are not so good do not fit so well. Like poison, etc.

It may be this this scenario resembles inflation, but it is a never-ending and constant inflation, not an exponential inflation.

I hope someone with more mathematical ability than me will see fit to graft this idea onto a framework in which spatial expansion is constant and the relative motion of bodies takes place according to a space curvature geometry within this frame.

In this scenario, the radius of the expanding field increases constantly at c.

The idea is that a rotating volume, since it is constantly accelerated, does not expand at all. In other words gravitational ‘space’ does not expand.

The formula for the volume of a sphere is (I hope) 4/3 pi r^3. So a sphere of radius 1 will have a volume of 4/3 pi (which I hope is the number I gave - my calculator is faulty.)

I will leave it to you to figure out the eight combinations; I have drawn the motions laboriously on paper. There are two distinct patterns of spin, neither of which shows a complete rotation. If you are interested enough in this scenario to look at them, I will try to get hold of them but I believe there is only one copy of these drawings and I don’t have it. I don’t know whether it can be done on a PC. Once I approached a supercomputer facility about it but got the brush off; they were too busy doing ‘renderings’ for animated movies. There is a theorem, Euler’s rotation theorem, which apparently provides for any rotation being given as a composition of rotations about three axes representable by a 3 x 3 matrix operating on a vector (not my words). Maybe that would do it.

In this scenario it looks like what is created is neutrinos. I am not a scientist, I don’t know. I don’t know about flavors and colors. A photon may be a collection of neutrinos or a disturbance in the spatial ‘medium’. I don’t know that either. But I do know that those three-axial spins are interesting!

If a particle is a rotating energy storage device, it takes energy from the field. If two particles are close together, they may find their spins are compatible (they can spin harmonically together). There may develop a temporary deficit in the field energy, in which case the particle combination emits energy to the field, causing a temporary deficit in the particle combination, etc. ‘Breathing’ ensues.

Torque is the twisting energy of the field in maintaining the spin of the particles. The numbers come from the quantum formula for energy, E=hf, where in the Planck regime the f is 1.

To anyone who is interested in this thread, I believe that the three-axial spin I have been mentioning is not as efficient as a two-axial spin. I have edited the first post here accordingly. I believe the 'particle' produced may be a photon, in view both of the motion of the particle on two axes, and of the fact that photon 'energy' is measured as a succession of photons passing a point (i.e. frequency) which means that each single photon has a potential energy of h. Two-axial spin may also explain the behavior of photons passing through a filters or a beam splitter.

To address this part:

That's not correct. Space is expanding everywhere. It's only a very small percent per second at any point. This adds up to large amounts over large distances, but very small amounts over, say, the size of a bowling ball. All the other attractive forces between the molecules, atoms, particles in the ball counteract the repulsion caused by expanding space, so equilibrium is reached. Without the expansion of space, that bowling ball would have reached equilibrium at a very slightly smaller size.

Over astronomical distances, the main attractive force is gravity, so the expansion of space may overcome the attractive forces and equilibrium is not reached.

This has actually been discussed in a few other threads here, as well.

Aristocrates, I am not familiar with the mathematical intricacies of the scenario you are describing, but I wonder what kind of "equilibrium" would be reached in a universe in which a fundamental force did not exist. The paragraph you refer to was itself a reference to an incomplete statement that in order to be consistent, if space is treated geometrically, then matter should be treated geometrically; or else space should be treated as a force as gravity is treated as a force.

I have edited the original post to extend, correct and simplify it. I wonder whether anyone has any comment on the new draft.

I calculated the radius at which the electron is created by the expansion of the field at c, plus the frequency of the electron. I now see that this radius is very close to the Bohr radius. However I calculated it by a completely different method and without knowing the Bohr radius.

Please stop doing that.

Rules For Posting To This Board
I'd rather see the document transformed over time, via new articles in the thread. Otherwise, one is at risk of reading feedback articles that don't make sense because the original statement has changed, and quotations may appear to be misquotations. If you have made mistakes, let them live, don't hide them, and correct them further on.

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Exactly.

ngeo, if you have the original copy please repost that in the openning post of this thread and then post your latest revision as the latest post in the thread. Thanks.

Josh

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I have revised the original draft of this post to simplify, correct and extend it.
This is a scenario for a stable, expanding universal system which evolves in the sense of creating new systems out of existing systems (which is growth - so the universe can be said to be a system for growth).

In this system, ’space’ is an energetic field. The force of the field not only acts to continuously to expand the field but also acts everywhere at all times within the expanding field. Within this field, by the energy of the field, matter is created. This occurs because the fundamental energetic capacity of the field is to expand at a constant rate of c. The constant expansion rate creates potential in the field since all regions of the field cannot expand at c. Only at its outer limit does the field expand at its full potential. Within the field the average expansion rate is c/2. Thus the field has the potential to create twice its volume.

This potential creates pressure within the field. Rotation occurs in response to the pressure. In order to absorb energy from every direction within the field, this rotation must be at least (and at least initially) on the equivalent of two axes. The two axes of rotation in this scenario correspond to an electric and a magnetic axis. Since what is rotating is energetic space, there is a continuum from the rotating space to expanding space, and it may be that ’empty space’ can be said to be an electromagnetic field.

In the vicinity of spinning regions, the field does not expand; its energy is absorbed in rotation. In a simple creation model with one spinning region, after one Planck time there will be a spherical field within which is a smaller sphere representing a rotating region. At some radius between the outer sphere and the inner sphere, space can be said to be not expanding, while outside the inner sphere space is expanding, and within the inner sphere space may be contracting. In the context of universal spatial expansion, neutrality or contraction of space is equivalent to a gravitational field near the inner sphere. This field may be felt to the limit of the outer sphere, although at its very limit the field expands at c.

Thus in this scenario, mass is rotating energetic space (represented perhaps by moment of inertia). Rotation is continuously maintained by the energy of the field. In the vicinity of the body of matter, space does not expand and may be perceived as contracting. The full potential of the field is used to maintain the body of matter and to expand at c.

As the field expands it retains its potential, since space does not expand in the region of the massive body but expands at c at the limit; so its potential is always to create twice the volume of space that is actually created. In terms of radius, the radius of a volume twice that actually created is ~1.2595 to 1. This ratio is universally constant. It may be said that this ratio implies a curved radius, or curvature of spacetime, in the ratio of 79% relatively uncurved and ~21% completely curved.

The assumption of this scenario, that space is an energetic spatial field, creates differences from current theory. If current theory assumes that energy is intrinsic to or contained within a particle, this scenario differs by assuming that a particle is a creation of the field, and that its energy is intrinsic to the field rather than to the particle. Similarly, if current theory assumes that mass is intrinsic to a particle, this scenario differs by assuming that mass is an effect of the rotation of the particle by the field’s energy.

This scenario takes the formula E=hf as a possible way to indicate that rotational energy creates the equivalent of mass.. If a particle’s energy is found in its frequency, then in this scenario the frequency is the frequency of rotation. The Planck constant, h, is the energy of a single rotation in one second - that is, ~6.626 x 10^-34 Joules per second. The speed with which rotation occurs determines the energy of the particle. In the way this formula is currently used, the particle is a photon, but in this scenario it may be any particle.

A spherical field of one ‘Planck volume’ - that is, with a radius of ~10^-35 meters - does not appear to have the energy to create a particle (an ‘inner sphere’ with a circumference of ~10^-36 meters) rotating at a frequency of one turn per Planck time i.e., a rotational speed of c. Such a particle would have a frequency of 10^43 Hz, an energy of ~10^9 Joules, and a mass of ~10^-7 Kg. If the energy of the particle represents half the potential of the field, the field has a potential of ~10^10 Joules. Rotation being an acceleration, to accelerate such a particle at c, i.e. ~10^8 m/sec^2, would require a force of 1 Newton, using the formula F=ma. Such an acceleration seems possible given the energy of the field. However, if one such particle is created each Planck time, then two such particles ~10^-35 meters apart would have a gravitational attraction of ~10^45 Newtons, which is not possible. If such a particle were created, the second particle could not be created since that event would deplete the field.

However, a ‘Planck volume’ would have the energy to create a proton or an electron over time. A force is required to maintain rotational motion since rotation requires acceleration. If a particle is measured by rotational frequency, the frequency of a proton is ~10^23 Hz and the frequency of an electron is ~10^20 Hz. Using the formula E=hf, the energy of a proton is then ~10^-11 Joules per second and the energy of an electron is ~10^-14 Joules per second. Their masses are ~10^-27 Kg and ~10^-31 Kg respectively.

Using these figures, in one Planck time (~10^-43 seconds) a proton will make ~10^-20 of one turn and an electron will make ~10^-23 of one turn - that is, a proton rotates at ~10^-20 c, and an electron at ~10^-23 c. Force being required to maintain the rotation, taking the rotational speed as an acceleration, the acceleration of a proton is then ~10^-12 m/sec^2, and the acceleration of an electron is ~10^-15 m/sec^2. Multiplying mass by acceleration, the force required to rotate a proton is ~ (10^-27 x 10^-12 =) 10^-39 Newtons, and the force required to rotate an electron is ~10^-46 Newtons.

Assuming that a proton, being a higher frequency particle, is created first, then using the formula for gravitational attraction F = G (m1 x m2) / r2, the force of gravitational attraction between a proton and an electron at the radius at which the electron is created, ~10^-12 metres assuming a constant expansion of c, is approximately the force required to rotate a proton - to within one order of magnitude. However the exact rotational speed, and hence the acceleration, of the proton is not known since the exact circumference of the proton is not known. Its speed is derived from the rotation of a particle around a sphere with a circumference of one Planck length, but this is unlikely. Also two rotational axes mean a single full rotation is the equivalent of two rotations; and the distance traveled by a point on the surface of the sphere per time unit, given two axes of rotation, is not 1 but the root of 2 (Pythagoras’ theorem). However the closeness of the two forces is an indicator that gravitational force is related to the force required to create and maintain a particle in this scenario. In other words, gravitational attraction is a response to the force of rotation.


There may be several different ways to model the action of particles. Two mirror image particles may annihilate or they may co-ordinate their spins. If they remain in close contact with each other, and their rotation speed is reduced while at the same time they share some field energy, it may be that an additional rotating field around their point of contact is created. It may be that two such particles will flip so that one axis of rotation contains twice the current of each of the particles’ similar axis alone, while the perpendicular axis rotates around the current loop. The compact loop would be an electric circuit, while the perpendicular rotating axis would be a magnetic circuit. Two particles with identical rotation may create an elongated ‘electric’ loop with a magnetic circuit similar to more compact loop. While the magnetic circuit of the compact loop would be largely occupied in maintaining the particle, the elongated loop would require less magnetic strength, so its magnetic circuit would be free to cover a larger region of space. It may be seen that the compact loop represents a proton and the elongated loop an electron. This does not explain the existence of anti-particles.

Whatever the model, we see that in this scenario there is a potential for a governing or stabilizing mechanism to achieve balance among the particles the field creates, and an evolutionary scenario which does not require a highly unstable set of initial conditions. The ‘governor’ is the potential of the local field to create spatial rotation, which slows down or speeds up according to the local field energy. The highest frequency possible in this scenario is ~10^43 Hz, but as shown above this is not likely.

If the dimensions in this scenario are derived from Planck length and Planck time, then the original volume might be termed as a ‘Planck volume’ (but not a Planck mass). This would be ~10^-105 cubic meters. So in one cubic meter of space there would be ~10^105 Planck volumes. After one second (~1.85 x 10^43 Planck times) the volume of space would be ~10^28 cubic meters, or ~10^132 Planck volumes, of which (if the initial ratio is correct) ~21 percent, or ~10^131 Planck volumes is in the ‘form’ of massive objects. If the volume of space required for the creation of a proton and an electron has a radius of ~10^-12 meters, then it has a volume of ~10^-36 cubic meters, or ~10^70 Planck volumes. This means that in one second the field has the potential to create ~10^60 electrons and protons.

Is the OP truly the OP (as in, the words which you wrote, on 2 November, 2005)? Or is it an edited version?

To add to/extend what 01101001 said, an obvious case of revisionism will be seen by a not insignificant number of folk as a sure signal "don't waste your time here". It matters little what your intention may (or may not) have been; the perception you create is a very negative one.

Nereid, I am sorry not to have remembered or heeded the forum rule. The OP posted is not complete - I don't think that exists any more, certainly not on my computer and not in my memory. It is only the quotes you posted in your comments. I am not sure about the significance of 'revisionism' in this case. I don't seek any glory or money out of this, the benefit to me will be if the idea of space as an energetic field, which creates matter by its own action within its field, is explored further by someone with more ability than me.

I have to say with regard to wasting time, that anyone who follows the steps I followed will find that the radius at which the electron is created in this scenario is very close to the Bohr radius, and at that radius the gravitational force between the proton and the electron is very close to the force required to accelerate the proton. I believe that suggests a relation between gravitational force and rotation. Believe it or not, I found the Bohr radius after I had posted the revised draft.

I am not sure it is valid to use the formula F=ma in this system. In addition the mass which is accelerated in this system is already the product of an acceleration. In other words in this system mass is rotating space, and rotation is an acceleration. So I am not sure it is valid to assign an acceleration to a system which is already accelerated. However, since in this scenario mass is a result of rotation, rotation creates mass; particles which complete one rotation must then be massive particles, and since equivalents of mass can be calculated, I provisionally use the figures for proton and electron mass as they are currently known. I do not yet understand the concepts which underlie the designation of ‘kilograms’ as units of mass.

So a feature of this scenario is the small ‘secondary’ force which is required to maintain the acceleration of the particle. The closeness of this force to the gravitational force between the proton and the electron, suggesting that the force of gravity is a response to rotation, may result from the continual need to replenish the proton’s internal field. If energy is taken from the external field, this may be in response to a diminishing rotation rate. Since c is the limiting speed for any motion, there must be a time period within which the proton’s ‘rotational mass’ is replenished. If a proton loses a small amount of energy in each rotation, and this amount is replenished from the field each rotation, then this suggests a periodic addition of energy per rotation. The question then is, a proton being a product of acceleration, why does the acceleration diminish? Does it diminish in the presence of another body, or does it occur regardless of the presence of another body?

If a proton, of 1836 times the mass of an electron, rotates at a frequency of 2.26e23 Hz and requires a force of 6.02e-39 N to rotate it, this suggests an energy of 2.663e-62 Joules to produce one rotation with an energy of 6.626e-34 Joules.

If an electron rotates at a frequency of 1.234e20 Hz and requires a force of 1.81e-45 N to accelerate it, this suggests an energy of 1.466e-65 Joules to produce one rotation with an energy of 6.626e-34 Joules.

Thus it appears a proton requires ~1836 times the energy of an electron to complete one rotation. This seems natural since the proton is moving ~1836 times the speed of electron. A higher speed of rotation requires a corresponding quickdr addition of energy. Since speed is the result of distance change divided by time change, the addition of energy can be regarded as an increase in distance per time unit, or as a decrease in time per distance unit, or as a combination of the two. By the same token, this addition of energy must be in response to a loss of energy in the form either of a decrease in distance per time unit, or an increase in time per distance unit, or a combination of the two. This suggests a slightly variable rotational speed.

It may be that the particle radius expands and contracts periodically. So as it expands it ‘pressurizes’ the adjacent region, and as it contracts it ‘depressurizes’ the adjacent region. This effect must be felt, however faintly, throughout the field. As above, when particles come close together they diminish the field between them which causes their speed to decrease, so there is a limit to how close particles can come.

In looking at the rate of expansion of as sphere at various radial distances, it appears that the ‘mean’ rate of expansion, with half the volume of a sphere either faster or slower, is ~.79 of the distance from the center of the sphere. Put another way, if half the distance from the center to the outer edge represents an expansion of.5 c, then the outer volume, expanding at more than .5c, is ~.875 of the total volume, while the inner volume, expanding at less than .5 c, is ~.125 of the total volume.

An interesting feature of an expanding sphere is that after the first few Planck times, the addition of one Planck radius adds only ~.17 of a Planck radius to the two lateral sides that would make up a ‘cubic volume’ added to the surface of a sphere. That is, as the radius of the sphere expands by one Planck length, forming one Planck length ‘height’ of a cubic volume, the ‘width’ and ‘length’ of the cubic volume (representing the other two sides of the cube added from the previous radius) expand by only ~.17 of a Planck length (i.e. an expansion rate of .17c, suggesting an expansion pressure of .83c). This ratio becomes more and more constant as the sphere expands. It suggests that no matter how large the sphere becomes, it will maintain a constant pressure for rotation orthogonal to the direction of expansion.

It appears that rotation on the radial axis will be the stronger of the two rotations in this scenario. The problem for rotation on the second axis is to transmit energy at c through a field whose main motion is outward at c. In other words, the effect of a transmission rate of c through a field which is expanding at .9c is a rate of .1c. A slightly different problem exists where the field is expanding only at .1 c. Its expansion pressure will be .9 c. Can energy be transmitted against this pressure?

So a likely region within which rotation on two axes will begin lies at the midpoint of expansion, namely the radius around .5 c. While there is a constant pressure of ~.83c orthogonal to the direction of expansion, which should translate into a strong rotational motion regardless of which side of the .5c boundary it is on, a second, radially-oriented, rotation can only occur when, for example, a slightly less than .5c outward motion outward can become a slightly more than .5c inward motion by the action of a wave of energy traveling at c through the (less than) .5c expanding field (i.e. in the opposite direction). It becomes much more difficult to envision at slightly more than .5c outward motion producing a slightly less than .5c inward motion in opposition to a slightly more than .5c expanding field.

If this scenario is accurate, a proton with a rotational speed 1836 times that of an electron, created after ~8e19 Planck times, will be in the region of .5c expansion, slightly inside the midpoint, while an electron, created after ~1.5e23 Planck times, will be in the region slightly outside the midpoint.

It occurred to me in the particle creation scenario above that there are two interpretations of frequency of rotation: one, that the frequency is a small fraction of c around a Planck length circumference; and the other, that the frequency is a speed of c around a larger circumference. So for example a proton frequency of ~2.26381e23 Hz would be a rotational speed of c around a circumference of ~8.19415 Planck lengths. And an electron frequency of ~1.2339e20 would be a rotational speed of c around a circumference of ~1.50336e23 Planck lengths.

This give a radius for an electron of ~2.38267e23 Planck lengths, or ~3.8665e-13 meters, which takes the electron farther away from the Bohr radius than it is above. However, there are different radii involved in this scenario. One is the radius at which the particle is created; another is the radius of the particle itself; and a third is the distance between the two particles. There are different possible systems involved; for example, in one system the electron would be an orbital sheath, while in another the electron would have a circular orbit around which it rotated, or would form a circular orbit by its rotation. At this point I do not know which of these systems (if any) will work in this scenario (if the scenario works at all). So I don’t believe the Bohr radius is necessarily ruled out by this interpretation.

However, the interpretation of frequency in which both particles move at c brings up what is to me an even more startling feature than the Bohr radius feature. The product of the two frequencies above for the proton and electron, namely ~2.7933e43 Hz, is extremely close to the ‘Planck frequency’ which I said above would be the limiting frequency in this scenario, namely the inverse, ~1.855e43 Hz, of the Planck time. This would explain why, in this scenario, an electron does not fall into a proton: if their combined frequencies are any greater (their radii any smaller), they will deplete the field. This would also explain why an electron has the frequency it does. However, it does not explain why the proton has the frequency it does. Nor does this scenario yet include a neutron.

If an electron has an orbital radius of ~3.27455e24 Planck lengths (Bohr radius 5.29177e-11 m) then it has an orbital circumference of ~2.057e25 Planck lengths. If it both orbits and rotates at c with a rotational (not orbital) frequency of ~1.2357e20 Hz, then it completes one rotation (not orbit) every ~1.5e23 Planck times. Orbiting at c, it takes ~2.057e25 Planck times to complete one orbit. Dividing the orbital period by the rotational period, it appears that an electron completes ~137.0609927 rotations per orbit. This is very close to the value of the fine structure constant (which I do not understand).

A remarkable result follows. By taking the formula E=hf and applying it to a proton and an electron (as though they were massless particles, which I assumed this formula was meant to describe), using the E of a proton and electron as a known in electron volts (without regard to the c^2) converted to Joules per second, I calculated the frequency of the proton as ~2.269e23 Hz and the electron ~1.2357e20 Hz. Then taking the mass in kg of the proton and electron I calculated in a post above a force necessary to accelerate (rotate) them at a fraction of c which at that time I assumed they would have in this scenario. However, as I noted, it would be possible that the speeds of rotation could be the same with different circumferences for the proton and electron. Taking the speeds as c (299792458 m/s), returning to the F=ma formula, I found a force in Newtons necessary to accelerate them, which converts to an energy in Joules necessary to produce the force. The energy/force is different for each particle, but by dividing this number by the frequency I found an energy per rotation: 2.73e-22 / 1.2357e20 for the electron and 5.014e-19 / 2.259e23 for the proton. This number turns out to be 2.209e-42 Joules per rotation. The remarkable thing (to me at least) is that when this number is multiplied by the speed of light, the result is ~6.6224e-34 Joules, which to me is close enough to Planck’s constant to actually be Planck’s constant accounting for error or calculation rounding or both. So I have to wonder how Planck’s constant was actually found, i.e. whether it is empirically derived or theoretical. I don’t know whether I have made a circular calculation or whether mass and frequency have been connected in this way before, but it is certainly astounding in the scenario I am working on. I would appreciate a comment from someone who might be able to clear this up. Regardless, I am putting it here for the record.

In the post above, multiplying mass by c, I found numbers representing (I think) the force necessary to accelerate a proton and electron. (However, I neglected to square c.) Dividing by the frequency I found a single number which, when multiplied by c, equals Planck’s constant. In other words, mc / f = h / c. In other words, mc^2 = hf. So what astounded me turns out to be a natural result, if kilograms of mass can be expressed in terms of c, frequency, and Planck’s constant. And as I read from “Physics Today” of March 2001 (“Adjusting the Values of the Fundamental Constants“, Peter J. Mohr and Barry N. Taylor), I believe they can (although maybe not as I found them). Quoting from Page 6 of that article, “This last remaining material definition of an SI unit could be eliminated by redefining the kilogram to be the mass corresponding to a specified frequency (v_k), according to the Einstein and Planck relations E=mc^2 and E=hv” I believe v_k refers to the Josephson constant but I am not sure how that works.

So, rearranging the formula, mass (in kilograms) is equal to hf / c^2. But Planck’s formula gives the energy of objects which have no inertial mass (i.e. which always move at c), while Einstein’s formula gives the “rest energy” of bodies which have inertial mass. According to Wikipedia, “…the quantity m … is the inertial mass of the object as measured in its rest frame, the frame of reference in which its velocity is zero.”

Leaving aside the semantics of absolute rest versus perpetual motion, the larger question (for me) is, “What is mass?” Commonly the idea of mass is combined with the idea of an ‘object’, or a ‘body’, or a ‘particle’, etc. In other words, the question asked is "what is the mass of an object", and the answer is - the amount of matter it contains! Then what is matter? (In the old days, that would be whatever has weight and occupies space. I don’t know what a scientist would answer today.) As the article above seems tacitly to acknowledge, a ‘kilogram’ of mass, having a certain weight under a certain gravitational force, may become a ‘kilogram’ of the electromagnetic equivalent of that certain weight (even though it would still be measured against the standard of a weight under a certain gravitational force). This would not be surprising since the official kilogram bar residing in Paris appears to have lost some of its mass. The transformation of a kilogram from a (theoretically) directly measured unit into a unit derived electromagnetically may point to some enlightenment in the understanding of matter (and energy). That is, rather than being a somewhat isolated object having certain properties (inertial mass, gravitational mass, electric charge, etc.), a body of matter may someday (and may already) be seen as part of a larger system, a system of motion, through which energy is transferred. In such an energy system, matter becomes a form - a particular pattern or system of repeated paths. Or it could be said that matter in such a system becomes a kind of medium for the transfer of energy, or a kind of container - a container whose contents are identical to what is outside the container, and identical to the container itself! The only difference being, in a system of motion, the particular kind of motion that distinguishes a ‘body of matter’ from what is inside and outside it.

Returning to the formula m = hf / c^2, which is a simple way of looking at what appears to be a very complicated mathematical procedure involving other physical constants, there is a number on the left which is arrived at by multiplying numbers on the right. The number on the left represents an undefined (or self-referential) mass. But the numbers on the right represent a potential for acceleration or change in motion; a frequency, or repeating motion; and the speed, i.e. motion, of light. In other words, all the numbers on the right refer to motion - distance over time, or time over distance, or space-time. So it makes sense to define the number on the left by the numbers on the right. This would be in Joules (per second), cycles (per second), and meters (per second) squared.

So I interpret this formula, reduced to a single rotation for each particle, to mean that the ‘mass’ of a proton or an electron is somehow related to ~7.3724e-51 Joules per rotation. I take ~7.3724e-51 Joules to represent the ’rest energy’ of the space which when accelerated (rotated) forms a particle. Since the field exists both inside and outside the radius of the particle, the particle may be seen as a rotational shell accelerated from both inside and outside. This space is rotated and impressed onto the surface area of a particle, to cause one rotation.

If the electric charge of a proton and electron are identical, that is 1.602176492e-19 Coulombs (Amperes per second), then in this scenario a proton will have a current per rotation of ~7.0615686e-43 amps, and an electron of ~1.2965e-39 amps. A Joule being measurable as Watts, it should be possible to determine the electric potential of a single rotation, since the energy of the particle per rotation is ~6.626e-34 Joules. Dividing this number by the current, the potential of a proton per rotation is ~938318435.4 Volts, and of an electron ~511039.0923 Volts. The Josephson constant indicates a frequency of 4.835979e14 Hz per Volt. This gives a proton frequency of ~4.528305e23 Hz, and an electron frequency of ~2.466e20 Hz, which are approximately twice the values used in this scenario (and which may be a result of the two-axis rotation of this scenario).

In other words, in this scenario, the energy of a particle being its electromagnetic energy, this energy is the result of the acceleration (rotation) of a spatial field energy of ~7.3724e-51 Joules at c^2 onto a specific surface area.

Returning to the question of mass, using the interpretation of mass which I gave in the post above in the formula for gravitational force gives an interesting result. F = G x m1 x m2 (leaving aside the radius). If the masses are calculated as hf / c^2, then the formula becomes F = G x (hf/c^2) x (hf/c^2). The only variants in this formula are the frequencies of the two particles. In other words, it is the frequency of each particle which gives the gravitational force. And the frequencies turn out to depend on the radius - and by extension the surface area - of each particle.

In other words, the gravitational force supposedly exerted by a particle on another particle derives from a spatial field energy of ~7.3724e-51 Joules being impressed onto the surface of the particle, with its strength determined by the specific surface area of the particle.

So the ‘force’ of gravity is as much a creature of the field as the ‘force’ of electromagnetism. Both these ‘fundamental forces’ are effects of constant universal spatial expansion.

As in the above post, if the terms hf / c^2 are substituted for mass in the equation for gravitational force, the result is ~1.01701e-67, while the result using kilogram-mass is ~1.01686e-67 - in other words, the “hf / c^2” value is ~1.00024 of the kilogram-mass value.

If Planck units are used, the relation between (h, frequency and c) becomes (h divided by the circumference of each particle), frequency being the inverse of circumference and c being 1. Planck units incorporate the gravitational constant, and Planck’s constant becomes Dirac’s constant (h / 2*pi), Planck length being the root of (hbar x G) / c^3 and Planck time being the root of (hbar x G) / c^5.

Using a value of 8.1759e19 Planck lengths for the proton circumference and a value of 1.5013e23 Planck lengths for the electron circumference, an approximation to the gravitational force per second can be found if F = [h / (C1 x root 2*pi)] x [h / (C2 x root 2*pi)] x 1.8549e43. The result is ~1.055943e-67, which is ~1.0384 of the kilogram-mass value. This may be within the margin of uncertainty.

The electric or Coulomb force between proton and electron (again disregarding radius) is given by F = e1 x e2, each particle having a value of ~1.602307e-19 Coulombs. Translated into Planck units, the value of e per Planck time is equal to current in amps per rotation divided by circumference. So an approximation to the Coulomb force per second can be found if F = [(Amps1 / C1) x 1.8549e43] x [(Amps2 / C2 x 1.8549e43].

These two equations, for gravitational force and Coulomb force, give the opportunity to find a relationship between them, to be continued.

so, your theory in a nutshell is?

__________________

In a nutshell, this scenario is that the universe evolves as an expanding field, with energy as expansion energy. The force which creates the field continues to operate within the field it creates, producing pressure within the field. The pressure is absorbed by rotation. So particles of matter are formed which are, in essence, rotating space. A particle is a rotating shell or surface on which internal pressure from within the shell meets external pressure from outside the shell. The field does not expand in the region of matter, and space is continually drawn toward the particles to maintain their spin. This inward motion of space is perceived as gravitational attraction. When a particle completes a rotation, an electric current and magnetic flux is created, which is maintained by the field. Electromagnetic force between particles is then “gravitomagnetic” (that is a term already used which I do not understand, so I put it in quotes). The field can be depleted and replenished by change in the circumference of the electric current. Time delay causes depletion of the field. There seem to be many other potential features which I have not yet explored. The advantage of this scenario is that the universe expands at a constant rate, there is no pre-Big Bang singularity, no need for large-scale inflationary quantum fluctuations, no need to explain “dark energy” or “dark matter”, etc. Matter is continuously created as the field expands.
There is more to come.

As in the post above, a relationship between the electromagnetic and gravitational force can be found if common terms are used. It may be seen that already a relation emerges in that, while the gravitational force Fg is found using Planck lengths for the circumference of each particle, and then multiplying by 1.8549e43 Planck times to find the force per second, the electromagnetic force Fe is found by multiplying by 1.8549e43 Planck times x the current for each particle, thus squaring the Planck time. This gives a fairly accurate result, and I believe is valid because all three values - current, potential and frequency (circumference) - are present in the Fg calculation, while in the Fe calculation, potential is not present and I do not believe this value varies (nor, I believe, does the current in the circuit). The significance of this may become apparent.

Fg per second = [h / (Ce x root 2pi)] x [h / (Cp x root 2pi)] x 1.8549e43 = ~1.506e-67

Fe per second = [(Ae / Ce) x 1.8549e43] x [(Ap / Cp) x 1.8549e43] = ~2.566e-38

Fe / Fg = ~2.429789e29

T = 1.8549e43 Planck times (1 second)

Ve x Vp = ~ 4.795e14 (this number is the product of the voltage per rotation of the proton and the voltage per rotation of the electron as proposed in a previous post; however, it is less satisfactory than a “best figure” of ~4.88447e14 as seen below).

If common terms are removed, it is possible to find the relation between Fe and Fg. Since h is the value of volts x amps, it is possible to remove A from the relation, and a ratio between Fe and Fg can be found as follows:

Fe / (2pi x Fg) = T / (Ve x Vp)

Substituting the value of Fg:

Fe x Ve x Vp = 2pi x T x 4.11558e-30 Fe

2pi x T = 2.429789e29 x Ve x Vp

2pi x T = 2.429789e29 x 4.795e14 Volts

2pi x T = 1.1658e44 Volts

T = 1.85545e43 Volts

Which is approximately one volt per Planck time. I believe this is a striking result. Equally striking is that the value of the combined voltages of the proton and electron in this example, namely ~4.8e14, is approximately the cube root of the value of 2pi x T, and the square root of the difference in the Fe and Fg forces. In other words, a value of 4.884474501e14 volts squared gives a value of 2.385809115e29 volts for the Fe-Fg difference, and cubed, a value of 1.165342379e44 volts for 2pi x T; and thus a value of 1.8546999e43 volts for T. The calculated values are within approximately 3 percent of the “ideal” values. I believe this is significant and points to the possibility that the gravitational force is linear (I am not sure if that is the right word, but by it I mean acting in a straight line between two bodies) while the electromagnetic force is three dimensional (that is, it acts in a whole volume of space).

If t is taken to be one Planck time, and if the relationship of volts to time is valid, then the voltages of particles applied to their current per t can be seen as both an acceleration and a potential for further acceleration when combined. Then the G and E forces can be related using notation as follows:

v for each particle = (t) for each particle

(t) x (t) = t

t^3 = 2pi T (i.e. [(t)x(t)^3 = 2pi T]

a = current per t

Then [Fg = av x av x T / 2pi] becomes [Fg = a(t) x a(t) x t^3 / 4pi^2]

and [Fe = aT x aT] becomes [Fe = (a x t^3 / 2pi) x (a x t^3 / 2pi]

Fg = a^2 x t^4 / 4pi^2

Fe = a^2 x t^6 / 4pi^2

Fe = Fg x t^2

In the case of a proton and an electron, if t = ~4.795e14, then t^2 = ~2.299e29

Fe = 2.299e29 x Fg

In the post above, “e” somehow replaced “v” as the voltage for each particle. This has been edited.

From the above, it may be seen that the constants “h” and “q” can derive v and hence t in this scenario. Current per Planck time, that is “a“, is also a constant.

a = current per t = 8.6379^-63

h = 6.626^-34

q = 1.602307^-19

v = h / current per cycle

current per cycle = q / f

v = h / (q/f)

v = h/q x f

v = (t)

(t) = h/q x f

(t) x (t) = t

Fg = (a^2 x t^4) / 4pi^2

Fe = (a^2 x t^6) / 4pi^2

The term “a“, that is current per t, can be expressed in terms of q and T (one second in Planck units), which produces a result relating the two forces in terms of q, h, and frequency of the particles.

a = q / T

T = t^3 / 2pi

a = 2pi x q / t^3

t = (h^2 / q^2) x f1 x f2

a = 2pi x q / [(h^6 / q^6) x f1^3 x f2^3]

a = 2pi x q^7 / (h^6 x f1^3 x f2^3)

*Root Fg = (a x t^2) / 2pi *For ease of calculation

Root Fg = (q^7 x h^4 x f1^2 x f2^2) / (h^6 x f1^3 x f2^3 x q^4)

Root Fg = q^3 / (h^2 x f1 x f2)

Fg = q^6 / (h^4 x f1^2 x f2^2)

By this same method, Fe = q^2

Following on the post above, the simplest equations appear to be as follows:

Volts per particle v = hf / q

t = v1 x v2

Fg = (q1 x q2) / t^2

Fe = q1 x q2

Thus, as in the post above, Fg is directly related to Fe. When this system is applied to similar particles, i.e. two electrons or two protons, it becomes apparent that Fg is inversely proportional to t (and directly proportional to current), so that two electrons have a greater Fg than two protons. The gravitational force remains overwhelmed by the repulsion of the particles. If the system is extended to two hypothetical particles of frequency T, Fg becomes vanishingly small as t becomes extremely large. So in this scenario it appears that the gravitational force is related to the overall flow of current in the field. The total field energy used is the same for a proton as for an electron, but this energy is used to different effect in the two particles. (It also appears that the current per unit of surface area for a proton is greater than for an electron by the ratio of their respective frequencies.)

The use of t for similar particles, i.e. two protons or two electrons, leads to other interesting results, among which is the appearance of the fine structure constant in their relationship and the derivation of frequencies, voltage potentials, t, and T. The values vary slightly from those used in previous posts. In the following equations, “e” refers to electron, “p” to proton, “f” to frequency, and “v” to potential in volts, “a“ to the inverse of the fine structure constant, 137.035999, “h” to Planck’s constant 6.6260693 e-34, and “q” to the elementary charge 1.60217653 e-19 .

te = ve^2

tp = vp^2

1. fe / vp = te / 2

2. fp / ve = tp / 2

3. fe / tp = a

4. fp = 2fe^2 / ve^3

5. fe = 2fp^2 / vp^3

6. ve = (h x fe) / q; vp = (h x fp) / q

7. q / h = fe / ve; fe = (q x ve) / h

8. From (6)
tp = [(h x fp) / q]^2

9. From (3) and (8)
fe / a = [(h x fp) / q]^2

10. From (4) and (9)
fe / a = [(h / q) x (2fe^2 / ve^3)]^2

11. q^2 / h^2 = (fe^3 x 4a) / te^3

12. From (6)
q^2 / h^2 = fe^2 / te

13. From (11) and (12)
(fe^3 x 4a) / te^3 = fe^2 / te

fe = te^2 / 4a

14. From (7) and (13)
te^2 / 4a = (ve x q) / h

15. Then

ve^3 = (4a x q) / h

ve = 509858.5241

te = 2.599557146 e11

fe = 1.232832504 e20 Hz

vp = 948494251.2

tp = 8.996413446 e17

fp = 2.293449041 e23 Hz

proton current per cycle = 6.985882404 e-43

electron current per cycle = 1.299589786 e-39

fp / fe = 1860.308707

2pi T = t^3 = 1.13097541 e44

T = 1.80000327 e43

T = 2(fp x fe) / pi

The relationships in equations 1 to 5 were discovered by searching for patterns. The result in which fp is ~1860 fe has further implications for the relationship of the electron and proton magnetic moments. The electron magnetic moment appears to be smaller, by approximately the root of 8 (~2.828), than it would be if it were directly related to the electron circumference.

Applying the Josephson constant to the voltages above, the result is again twice that found above.

With regard to (15) above, the values are arrived at by inserting the inverse of the fine structure constant as the value of fe / tp.

A most interesting result of this is that the electron potential, ve, multiplied by the proton potential, vp, is 4.835978791 e14, which is exactly the value of the Josephson constant (2q/h) giving hertz per volt.