## Gravity as Separational Insufficiency

This is not an everything goes forum, but rather a place to ask questions and request help for developing your ideas.  ### Gravity as Separational Insufficiency

Below I address questions relating to my article "A Simple Spin on Gravity" which is admittedly fast paced as it builds on two brief prior articles, ALPHA: Applying a Light Touch? and Spin½ 'Plane' & Simple. Associated animations (avg. 6 min.) are found here.

I'll start here with first principles. These are a set of foundational assumptions upon which any model rests. Occam's razor prefers simplicity. "Phyxed" (physics-fixed, better than real) is the model I use to solve many mysteries of the Standard Model, including gravity.

"The Standard Model of particle physics is the theory describing three of the four known fundamental forces (the electromagnetic, weak, and strong interactions, and not including the gravitational force)…"

Phyxed derives the standard model from just 3 first principles to which I'll refer.
Details follow (to facilitate post-specific replies).

Exceedingly Simple First Principles:
1. One kind of dimension:
2. One kind of object:
3. One kind of behavior: Active Member

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Location: Times Square (T2)    ### Re: Outward Bound

1. One kind of dimension: Physics uses the same term "dimension" for two different things, space and time. Space offers back and forth (bidirectional) translational freedom in each of three dimensions. Time offers forward-only (unidirectional) translational freedom in one dimension. Aging is observed at different rates, but even non-aging light can't travel backward in time.

Space is depicted as a line with arrows at both ends. Time is shown as a ray with an arrow extending away from an origin. Our continuum fundamentally provides 4D of potential separation, allowing 4D "events" to be different. Thus, four coordinates are needed to distinguish one event from another. Both space and time offer equivalent separation but typically in different, proportional units.

Phyxed models all four dimensions as temporal. With origins collected at a single point a radial temporal 4-field arises from what would be the singularity of the Big Bang. Since a 4-ball is enclosed by a 3-sphere, that 3-sphere constitutes the 3D "space" of the cosmos, expanding as it ages. An n-dimensional ball is enclosed by an (n-1)-dimensional sphere. Like known electric and magnetic fields but one dimension up, a radial temporal 4-field originates at a point and is unidirectional. The enclosing cosmos expands with age.

Rather than entropy giving time its arrow, it is unidirectional time which drives entropy. The expanding cosmos provides space for an ever-increasing number of random states (particle arrangements) compared to those which are ordered. Active Member

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Location: Times Square (T2)    ### Re: Hole Enchelada

2. One kind of object: The simplest object possible in a continuum is a discontinuity: a hole. It is the object from which all others in the cosmos arise. Informationally, it is a fundamental bit. Holes have no internal span (if they do they are "tubes"). Like hole in a piece of paper, a hole connects what's on one side with what's on the other. By convention, the dimension of a hole is given by the dimension of its enclosure. For a circular hole, the circumference is made from a 1D line, so that whole is considered a 1-hole. A massive black hole is enclosed by a 2-sphere (event horizon) so it's a 2-hole. A hole can have direction, which can, in principle, change by rotation about a hole's diameter.

"the sphere encloses a two-dimensional hole while the circle encloses a one-dimensional hole. However, because a hole is "not there", it is not immediately obvious how to define a hole or how to distinguish different types of hole.."

Phyxed asserts a "pinhole" (particle-interaction wormhole), a hole with a lightlike direction. It is thus, a speed c-dependent hole, accessible only to energy. In Special Relativity (SR), a lightlike trajectory has a slope of 1 in natural units. Lightlike intervals have magnitude zero, i.e. zero interval separation or "interval contact". So, a pinhole is a hole which acts as an energy conduit through space & time. Though a lightlike "worldline" appears to have length in spacetime diagrams, its zero magnitude implies that events A, B, C, & D are co-located, the same spacetime event with different coordinates. This is not uncommon on Euclidean maps of non-Euclidean geometry. A Mercader projection of the south pole similarly appears to have length, where A, B, C, & D are a single geographic location with different longitudinal coordinates. As shown, the south pole and a pinhole are both examples of projected contact. Active Member

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Location: Times Square (T2)    ### Re: On Best Behavior

3. One kind of behavior: The simplest of all behaviors is spin, from which all other behaviors may arise. It can represent motion without translation, spinning at a single spatial location, or with translation seen as rolling. All particles in the Standard Model have a property of "intrinsic spin" which has real, conserved units of angular momentum but for which a primary axis has never been identified. (see my Spin½ Plane & Simple).

Phyxed models intrinsic spin as "chronaxial", having a temporal primary spin axis. Such spin would then occur in a 3-plane as solid-angular spin. Time is never in the plane of rotation because unidirectionality prohibits the needed oscillatory freedom. But if time is robust enough to support translation (i.e. everything goes to the future), it can also serve as an axis of rotation.

Phyxed models curved-space, radial-time (see First Principle 1), where radial time is normal to space at all locations and the plane of rotation is an interval 3-plane. By definition, a spin vector has no projection on its plane of rotation. But on a spatial sphere chronaxial spin casts equal magnitude projections in every direction (half measured as negative), exactly as observed. Chronaxial spin has projections on curved space in every direction. Active Member

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Location: Times Square (T2)    ### phyti » May 13th, 2020, 2:05 pm wrote:If Einstein's invariant interval were rotated about its center in all directions, the ends would trace out a sphere. It's invariant since it doesn't change over time, events don't move. Thus no need of a 'time' coordinate, which is assigned by each observer according to their local clock, essentially for id purposes.
An event has no property labeled 'time'. If I eat lunch at the same place 5 days in a row, each lunch needs an identifier to distinguish it from the others. My cell phone assists me with a calendar. Active Member

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Location: Times Square (T2)    ### Travel Light, Go Far

Pinhole + Chronaxial Spin = Gravity

phyti wrote:If Einstein's invariant interval were rotated about its center in all directions, the ends would trace out a sphere.
Yes! Rims of a so-called light "cone" are such spheres. For clarity, it's often worth appending the dimension to an object. For example, the rim of a light cone can equivalently be called a "2-circle" or a "2-sphere", which are both the same as an ordinary sphere: the set of points equidistant from a central location in 3D. Light cone rims are actually spheres. The light "cone" is really a "3-cone" and a plane which cuts across any of its sections is a "3-plane".

phyti wrote:It's invariant since it doesn't change over time, events don't move.
"Invariance" does not usually refer to an interval being fixed. It refers to the fact that its magnitude (4D span) is the same to all inertial observers, though observers in different inertial frames will ascribe different spatial and temporal components to an interval.

Worldlines of ordinary objects are fixed in spacetime but we can imagine them moving. And there is no way to deny chronaxial spin of a null worldline (one having zero interval span) as is the case for those which are lightlike (my pinholes).

phyti wrote:Thus no need of a 'time' coordinate…
Fair point! A spin vector is an abstraction along a real or imagined axis, normal to the plane of rotation. Thus, a Flatlander has no need of an actual 3rd dimensional axis to rotate or orbit within its plane of existence.

What would you say however, about a hole in Flatland itself? What would it connect? A hole is meaningless unless it is from somewhere to somewhere. Thus, I fall back on the first principles of Phyxed.
1. Time comprises all dimensions as a radial 4-field emanating from the big Bang.
2. The one fundamental kind of object is a pinhole. It is a hole in a spatial simultaneity connecting a prior event to a later one. I'm not saying you have to believe this is "real" just that it is the model Phyxed. Because this model is the simplest possible, it will take you further than any other, in terms of explanatory power.

phyti wrote:An event has no property labeled 'time'
An event is a location in spacetime, which is identified by 3 spatial and one temporal coordinates. Their values depend on the coordinates specific to each inertial frame. I'm fine with not calling a relative label a property. But we do need four identifiers to distinguish one event from another. Even in a particular inertial frame, a single event can have more than one coordinate identity. Such co-located identities are "separated" by zero intervals. I'm asserting that every event on a light cone is the same event. Jorrie will be debating that with me in another thread. Active Member

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Location: Times Square (T2)    ### Re: Gravity as Separational Insufficiency

phyti » May 15th, 2020, 1:05 pm wrote:Read the paper a few times, see new concepts but don't understand what sustains them, source of energy, etc. How or why does a pinhole form? Is the 'rope' an extension of 'string theory'? Einstein already dealt with gravity as a field and mass as its energy source. True, the process needs elaboration, so why not work on that. Maybe space has a structure yet to be discovered, supporting Einstein's ether.
Overall the contents seem to be overly complicated.

Here is what can be extracted from existing SR theory.
On the left, a typical spacetime graphic, with the U-frame as a reference, observing anaut A in motion in direction x. A sends a light signal (blue) that reflects from the end of a stick (event R) and returns to A (event D). A assigns time of R as h, half of light transit time, per SR convention.
In 4D, things are moving in spacetime, the area contained by the Ut and Ux axes.

The spacetime graphic is very useful in simplifying cases to the essential elements and showing multiple relations visually, as in the 'picture is worth many words' adage.
My objections are the use of metaphorical interpretations, moving in time, 4-vectors, infinite mass, etc., as if they are the reality, when they are just the methods of analysis.

https://app.box.com/s/o1qpkjkt7ilklnz63no6itt9s0ceui1j

In reality, A and the light are moving as shown by the arrows at the bottom.
The red line indicates t', the time indicated on the A-clock. In transferring the interval t' to the At line or 'time line', the units would be expanded (dilated), as typically shown with tick marks. This means A and the A-clock are moving in one spatial dimension, in the x direction, leaving a 2D plane perpendicular to x, as shown on the right. The clock is generating its own local time (there is no universal time), so 'time' doesn't need a dimension.

https://app.box.com/s/somn42vezm5057knmpkdhv2hw22dku3t

Then there is perception space, represented in the light cone graphic, with observer U at the apex, which technically would be a small circle. For U the present is a brief interval of a few milliseconds of mental processing of sensory input. The 2D plane, with an object e in motion in the x direction, is projected onto the light cone, representing a history of e over time. Object e approaches from a distance, passes U with a minimum separation of d, then recedes to an increasing distance. The images of e require more light transit time to either side of P, the direction perpendicular to x. For U, the past is synonymous with distance, and e could move in the reverse direction. There is no future light cone since U can't have awareness of events that haven't happened.
Note the path of e is a hyperbola on the cone, and the only instance of distance varying in a linear mode is on the x axis. The typical case would be a hyperbola with hyperbolic time values. This was the case before SR.

https://app.box.com/s/52oddzqn3agfsgpxln5548rbx262qdmn

In addition to the t&x axes folding scissors style, the perceived world of the near light speed observer shrinks toward a limit of zero. Active Member

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Location: Times Square (T2)    ### Re: Heavy Reading

phyti wrote:…don't understand what sustains them, source of energy…
In Phyxed energy is precisely the chronaxial spin rate (excluding dark matter and dark energy to be addressed later.) Higher spin rate creates more instances of a gravitational field per unit time. Thus, energy and gravitational mass are inexorably linked. Think of each field instance as a light cone because gravity (as with all force) is lightlike. More cones on the timeline is higher gravity.

phyti wrote:How or why does a pinhole form?
Pinholes are the fundamental object of First Principle 2. It is a hole in our continuum pointing in a lightlike direction. It is the object from which all others arise, most notably by spinning to produce a field. Consider a pinhole as a "force object" which by spinning instantaneously about time creates a field of potential force (e.g. on a test particle).

phyti wrote:Is the 'rope' an extension of 'string theory'?
No, string theory needs far too many dimensions (most often 11) of inexplicably different types. I just meant an ordinary rope. Spin it fast and you create a field where average density falls off with radius. Of course, that's in an ordinary 2-plane of rotation.

If you could spin it around time, the density field would follow the inverse square law. What a coincidence! Almost too simple. Phyxed identifies mysterious intrinsic spin as chronaxial and it just so happens that it naturally provides the inverse square law for resulting fields. Every massive particle has them.

phyti wrote:Einstein … gravity as a field and mass as its energy source. True, the process needs elaboration, so why not work on that.
That's what Phyxed does. A pinhole is projected contact. Contact is the opposite of separation. Spinning the projection around time creates a field following the inverse square law where the separational capacity of the continuum is compromised. Things in the field can no longer maintain their separation from its source. That's all there is to it!

phyti wrote:Maybe space has a structure yet to be discovered
We don’t have to change the structure of space or even curve it. Instead we use a structural element, specifically a pinhole as a radial field element (like a rope) and give it chronaxial spin.

phyti wrote:Overall the contents seem to be overly complicated.
That may be because the article builds on two previous articles on pinholes and spin. The bottom line is exceedingly simple:
Gravity = Pinhole + Chronaxial Spin

phyti wrote:My objections are the use of metaphorical interpretations, moving in time
Chronaxial spin is most objectionable because it is instantaneous. Think about it. Any motion around a time axis takes no ∆t to accomplish. That would violate speed limit c! Except for two things: 1. a pinhole has no length so there is no circumferential speed. 2. a pinhole is a projection of contact and projections are exempt from speed limit c. (see Faster than light)

phyti wrote:there is no universal time
We do have a 'universal' time reference in the age of the cosmos. Aging is fastest in a rest frame, the cosmos can't move relative to itself, so it has always been in its rest frame. Nothing in the cosmos is older than the cosmos. The age of the cosmos can serve as a common maximally aged reference to all its inhabitants.

Aside from that, Phyxed employs time as the only kind of dimension in first principle 1. All four dimensions are filled by a radial temporal 4-field.

phyti wrote:There is no future light cone since U can't have awareness of events that haven't happened.
then we're not talking about SR which uses light cones to determine regions of causality. Phyxed strives to be compatible with SR. though photons are replaced by pinhole contact, the particle aspect of light (e.g. photoelectric effect) is perfectly maintained. A light cone is seen as the result of spinning a pinhole. It is an instance of a field. A pinhole as a lightlike radial field element generates a field when rotated about time

phyti wrote: n addition to the t&x axes folding scissors style, the perceived world of the near light speed observer shrinks toward a limit of zero.
Agreed. So does the interval separation between emitter and absorber. But for a light quantum it's not an asymptote, its actually zero interval separation (interval contact).  Active Member

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Location: Times Square (T2)    ### Re: Gravity as Separational Insufficiency

In reading and trying to understand this posting I read your viXra article titled Spin½ 'Plane' & Simple which seems to underpin the Phyxed approach. Possibly due to a combination of ignorance and complacency, I still fail to see the problem regarding spin.

Considering just one of the two possible electrons in an orbital, as shown in the provided figure, that appears on opposite sides of the nucleus at different times. Should it have spin ħ, and assuming that the electrons are moving at close to the speed of light, to human measurement of its spin component would be split in time, and measure at ħ/2 on either side. Even if there were 2 opposite spin electrons within the orbital (i.e. it was full), only one electron can be in any one location at the same time and thus the result would be the same for each electron.

So, assuming that the frequency (or probability) of an electron being at any one point within the 3D closed orbital is equal, then for a measurement of spin on either side a result of ħ/2 would be expected. Or, put another way, the measured spin of an orbital electron would be ħ/2 anywhere around the orbital shell.

For an atom with full orbitals, its net spin in any specified diagonal direction would be n x (ħ/2 + ħ/2) or nħ, where n = the number of full orbitals. Thus such an atom could be considered to be a boson.

Perhaps you could explain the errors of such logic.
Attachments Electron within an Orbital (2D projection)
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Pivot wrote:Spin½ 'Plane' & Simple …seems to underpin the Phyxed approach

Also known as "intrinsic spin", spin½ is one of three first principles in the Phyxed model. It's the basis of all action. It is the fundamental motion, to which all other actions can be reduced. Another first principle is time, which is ray-like, separator of events. Time, being fundamentally unidirectional, provides our continuum as a 4D temporal field emanating from the singularity of the central big bang event. The last first principle is the pinhole, the simplest possible object in the continuum. It is a discontinuity or hole in the continuum, which is most easily understood as the absence of separation. Holes have direction. In 4D, pinholes are lightlike, seen at 45° in a conventional spacetime diagram. If a pinhole stood still, it would also have an XYZ spatial direction, but a pinhole has intrinsic spin, which is essentially instantaneous about its temporal axis. So, a pinhole appears as a field pointing in all spatial directions at once.

Pivot wrote:I still fail to see the problem regarding spin. ...electrons in an orbital, as shown

Angular momentum, including intrinsic spin, is a conserved quantity. That means electrons retain precisely ħ/2 even when isolated outside orbitals. This is observed indirectly in particle colliders, as the sum of all particle intrinsic spins after a collision must equal that which existed prior to it.

In principle isolated electrons could have their spins quantized by a Stern-Gerlach device but in actuality it is far easier to implement with atoms having an odd number of electrons.

Pivot wrote:…assuming that the electrons are moving at close to the speed of light, to human measurement of its spin component would be split in time, and measure at ħ/2 on either side.

That's too much assumption. It's no longer good to model an electron moving around a nucleus. It's better to consider an electron spread out (i.e. distributed) probabilistically about the nucleus. The electron essentially exists in all orbital locations as once but with higher probabilities in some locations than others. Think of the electron spread like peanut butter rather than as a single peanut moving classically. The density of the peanut butter is higher in some regions than others. The highest density regions define the shape of an orbital.

Phyxed models an electron as a pinhole with chronaxial spin (spin about a temporal axis). That's just a more descriptive term for "intrinsic spin". As I described above, a gravitational field results. The electric field can be similarly modeled from the same field. An orbital is the inside out (i.e. "eversion") of the electron's field.

Picture spinning a rod about one end to create a field. We term the center of spin a “particle” from which the field arises. Now imagine the outside end of the rod catches on a heavy object. To conserve angular momentum the former inside end now spins about that object. That particle is now distributed in an "orbital" about the heavy object.

This is how I model an isolated electron distributing in an orbital about a nucleus. Importantly, to get 3D orbitals the axis of rotation is still time, but for an orbital the electron no longer has an internal temporal axis, rather it is distributed instantaneously about the temporal axis of the nucleus. A pinhole (green arrow) with chronaxial spin makes an electron’s field (left). When a pinhole alights on a nearby nucleus (maroon), its electron becomes captured (center), causing the electron to distribute instantaneously (and probabilistically) in an orbital about that nucleus (right).

Pivot wrote:So, assuming that the frequency (or probability) of an electron being at any one point within the 3D closed orbital is equal,
Orbitals aren't really closed. In principle, an electron in an atomic orbital has some probability of being anywhere in the universe about that nucleus. Orbital shapes however give the practical probabilities as observed. Also, the electron is not fully at any one orbital location, rather it is distributed probabilistically throughout the orbital as noted above. Active Member

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Location: Times Square (T2)    ### Re: Gravity as Separational Insufficiency

Also known as "intrinsic spin", spin½ is one of three first principles in the Phyxed model. It's the basis of all action. It is the fundamental motion, to which all other actions can be reduced.

And that is precisely why the concept of "intrinsic spin" needs to be proven to be an intrinsic property, rather than being a notional one based upon earlier assumptions. It needs to be 'proven' rather than be 'assumed', before building too much superstructure on top of it.

The assumption that an electron is a point-form charge particle would seem to be for mathematical expediency related to wave function and quantum mechanics theory. As a point-form entity an electron would have no bulk that could generate classical spin, and thus any associated spin (electron spin does exist and can be measured) has to be considered to be ‘intrinsic’ spin.

An electron represents energy that takes up a certain amount of 3D space, small as it may be. Sure you can argue about the physical size and form that the energy takes, but let’s not confuse mathematical license and reality: the point-source form of anything is dimensionless and is effectively nothing , with point-sources purely being mathematical or simulation modelling concepts. You may consider mathematically that the physical properties of something to be centred at a point (e.g. the centre of gravity of an object) without that object being considered to be a point source. So why pick on the poor little innocent electron?

Although ‘intrinsic’ spin might be an inexplicable attribute or property of electrons that defies explanation, it really looks far more likely that it simply represents collateral damage related to mathematical expediency. In effect the attribution of 'intrinsic' spin to electrons can be seen as a form of denial that the point-form based equations simply don't factor in or explain spin.

Angular momentum, including intrinsic spin, is a conserved quantity. That means electrons retain precisely ħ/2 even when isolated outside orbitals. This is observed indirectly in particle colliders, as the sum of all particle intrinsic spins after a collision must equal that which existed prior to it.

I agree that electron spin would retain their spin regardless of the circumstance: their conversion into photon might be a different issue however. I would be interested in the evidence that electrons isolated outside orbitals have ħ/2 spin: do you have links or references?

That's too much assumption. It's no longer good to model an electron moving around a nucleus. It's better to consider an electron spread out (i.e. distributed) probabilistically about the nucleus. The electron essentially exists in all orbital locations as once but with higher probabilities in some locations than others. Think of the electron spread like peanut butter rather than as a single peanut moving classically. The density of the peanut butter is higher in some regions than others. The highest density regions define the shape of an orbital.

I see a major problem with peanut butter analogy relating to the apparent ease at which electrons move from the valence band of an atom (where they act as peanut butter) to the conduction band (where they move and act as particles). It is pretty hard for peanut butter to reconstitute itself into a peanut. Consider the example of hole-movement: it is considered to be due to such to-and-throw transfer movement of electrons between silicon atoms within p-type semiconductor substrate at a rate to emulate the rapid random Brownian motion of electrons (particles) in n-type substrate. Such a process would involve a lot of nut cracking and reconstitution within the p-type.

Less energy and less mystique is involved should electrons be considered to maintain essentially the same physical form. Particle orbital motion might be able to be represented as a peanut butter probability smudge but that does not make it peanut butter or a smudge. And the movement of electrons as particles around the nucleus has a frequency that feeds nicely into wave functions without making them waves. Why must we assume that electrons transmogrify just to suit our mere-mortal equations or models? Thinking outside the box is great, but so is a little KISS (keep It Simple Science).

So when you say:
the electron is not fully at any one orbital location, rather it is distributed probabilistically throughout the orbital
it could just be a case of whether you prefer your peanut butter crunchy (electron 'particle' approach) or smooth (the smudge-transform approach).
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Joined: 14 Apr 2016    ### Re: Something from Nothing

Pivot wrote:It [intrinsic spin = chronaxial spin] needs to be 'proven' rather than be 'assumed', before building too much superstructure on top of it.
Actually, first principles are understood to be the basic building blocks (or postulates) upon which observed phenomena arise. Hopefully, some new falsifiable predictions arise as well to confirm or deny the foundation. But any proof requires some foundational premises. Phyxed has the simplest first principles you'll ever find.

Pivot wrote:As a point-form entity an electron would have no bulk that could generate classical spin … An electron represents energy that takes up a certain amount of 3D space, small as it may be. …the point-source form of anything ..is effectively nothing
Good point! (yeah, pun) It's common to mistake a particle as separate from its field. We consider earth’s size apart from its field. Quantum field theory (QFT) imagines particles as fairly localizable perturbations (like vibrations) of pre-existing fields.

Phyxed models a fundamental field created by a pinhole with chronaxial spin. A "particle" is simply the geometric center of that spin (the vertex of a light cone on a spacetime diagram). The field is what gives that point its identity. In terms of its field, an electron has infinite size (the reach of the field), same as earth.

Secondary rotation of the field (about a spatial axis) creates additional properties such as magnetism. When the spatial axis is central to an electron, you have the worlds smallest magnet. When the axis is external (as it is for electron current through a wire coil) you get bigger magnet.

What about rest mass? Gravitational mass is implied by the intensity of a particle's gravitational field. The equivalence of mass and energy arises by modeling chronaxial spin rate as the most fundamental expression of energy. Higher chronaxial spin rate means higher energy, while that also generates a more intense gravitational field (and implied mass).

Pivot wrote:'intrinsic' spin might be an inexplicable attribute or property of electrons that defies explanation, …related to mathematical expediency. …a form of denial that the point-form based equations simply don't factor in or explain spin.
Except that intrinsic spin is a conserved quantity. It has the same units of angular momentum of you spinning in an office chair. What science is missing is the primary axis and plane of rotation. Phyxed supplies these: axis = time, plane of rotation = XYZ spatial 3-plane.

Pivot wrote:I agree that electron spin would retain their spin regardless of the circumstance: their conversion into photon might be a different issue however.
Photons are attributed spin 1 (twice the spin magnitude of an electron), which works well as it is the difference between emitter and absorber (say +½ to -½). Though Phyxed views "photons" as 4D interval contact between emitter and absorber, spin difference works out the same.

Pivot wrote:I would be interested in the evidence that electrons isolated outside orbitals have ħ/2 spin
This is what particle physicists do for a living. They collide particles, such as free electrons, at very high energy and see what new particles come flying out. The rest masses of the "shower of particles" are covered by conservation of mass-energy. Their intrinsic spins are covered by conservation of angular momentum. Though calculated by computers, it all works out or there would be BIG headlines. Thus, each fermion exhibits characteristic spin½, bound or free.

Pivot wrote:It is pretty hard for peanut butter to reconstitute itself into a peanut.
It's no problem for an electron. I offered the example of a rod. Spin about one end creates a field for which the center can be termed a "particle". If the other end of the same rod is captured by a massive object, the first end will orbit that object if spin is conserved. The "particle" is now distributed by an everted field. If the rod breaks away from the object, spin can be seen as centered on the first end again. My diagram above is reversible.

Pivot wrote:Why must we assume that electrons transmogrify just to suit our mere-mortal equations or models?
Because the waves that are being discussed in orbitals and double slit experiments are probability waves.* That's a different thing altogether than what classical physics is used to. It requires the particle to be able to exist in (and to point to) many locations at once. This is equivalent to instantaneous motion. Only certain phenomena can accommodate such superluminal action. A projection, such as projected contact (i.e. a pinhole) is one of them. And chronaxial is inherently instantaneous.

*Actually, what’s waving is a "probability amplitude", which happens to equal the square root of the probability. Active Member

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Location: Times Square (T2)    ### Re: Gravity as Separational Insufficiency

each fermion exhibits characteristic spin½, bound or free

Provide the electron with finite 3D dimensions and the intrinsic spin associated with the point-form definition of the electron becomes ‘classical’ spin. Within an atomic orbita, the probability of the electron being in a particular place over time produces a spin estimate in terms of the reduced Planck constant ħ. As the electron has equal probability of being on opposite side of the nucleus, the spin energy is thus equal to (ħ/2)*f, where f= spin frequency of the electron.

When factored into Dirac theory, the spin energy of the orbital electron is reduced because the electron is only in the location associated with the direction of measurement for part of the time, which is factored into the reduced Planck constant. The spin energy of a free (i.e. non-orbital) electron could be expected to be of the order of h*f, where h = the un-adjusted or non-reduced Planck’s constant.

Now comes the problem of measuring the energy associated with spin for a free electron, This is not a straightforward matter, as first noted by Bohr. Garraway and Stenholm, when referring to the conclusions of Bohr, Pauli and Mott that it would not be possible, state that
the charge of the electron relates to its magnetic moment in such a manner that the separation of the spin components by the magnetic interaction is counteracted by the effect of the Lorentz force on the moving particle. The two effects are of the same order of magnitude, which can immediately be seen from the fact that the precession frequency (due to the magnetic moment) and the cyclotron frequency (bending the orbits) differ by only radiative corrections. Ultimately this state of affairs derives from the origin of the electron spin in the Dirac theory, where only one magnetic coupling term occurs.

Garraway and Stenholm suggest approaches that might make such measurement possible, but at this stage I do not think the problems have been overcome. Thus the measurement of the spin of a free electron would seem to be a work in progress. A lot could be riding upon the outcome.
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Joined: 14 Apr 2016    ### Re: Splitting Up is Hard to Do

Pivot wrote:Provide the electron with finite 3D dimensions… becomes 'classical' spin.
I'm not sure why you'd impose such a restriction. Classical spin (with orbital angular momentum) occurs about a spatial axis. Because the intrinsic spin of fermions has the same magnitude on every spatial axis measured, the primary spin vector can't be on any spatial axis. The primary spin vector thus relegated to a 4th axis (most simply, time), which would project equal magnitude components on every spatial axis – if space is spherically curved. In fact, such equal-magnitude spatial spin components should be considered strong evidence for a curved-space, radial-time model of our continuum. Chronaxial spin is solid-angular (encompassing 4pi steradians) and would make equal magnitude spin projections in every direction on curved space, with ± opposing pairs, exactly as observed.

That's a nice article. After it, the site recommends Hosein, who claims to have accomplished the measurement with a modified S-G device. Hosein's Fig. 6 shows the single electron beam (a) split in two (b) when an inhomogeneous magnetic field is applied.

A history of S-G by Sandip was also recommended. On page 5, Noble laureate Hans Dehmelt is recognized for using a Penning trap to very accurately measure the magnetic moment of stationary free electrons. As you note, this depends on the electron charge and intrinsic spin component. The results are notoriously close to those predicted for spin½. The only outstanding issue is the need for a conventional fudge factor of 2, which Phyxed relates to unwarranted classical reduction of h by 2pi when solid-angular chronaxial spin demands reduction by 4pi. Active Member

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