## Spin½ for Halfwits (like me)

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

### Spin½ for Halfwits (like me)

Hawking, via socrat44 wrote:particles have different properties of spin: 0, 1, 1/2, . . . etc. and
therefore they look different from different directions.

I specified fundamental fermions (e.g. electrons and quarks). Composite fermions, such as protons and neutrons, will exhibit a sum of spins, conserving angular momentum.

Hawking, via socrat44 wrote:A particle of spin 0 is like a dot: it looks the same from every direction. …'On the other hand, a particle of spin 1 is like an arrow: it looks different from different directions. Only if one turns it round a complete revolution (360 degrees) does the particle look the same.

"Virtual bosons" and "massless particles" model lightlike interactions, thus should be ignored as "particles". Lightlike interactions have zero-magnitude worldlines. No worldline, no particle. A better model is required for "force carriers". It is simpler to consider the force itself as an object, without inventing some other object to carry it. A ray-like (or "arrow") force object would be a component of the particle (i.e. the "thing" that is spinning), rather than yet-another sub-particle.

Hawking, via socrat44 wrote:A particles of spin 1/2 . . . looks the same ''if you turned it through two revolutions (720 degrees).

Yes! Hawking is naively referring to planar rotations, which have a spatial axis and encompass 2pi radians (i.e. spin in 3D). Chronaxial spin, which I personally attribute to "spin½" fermions, occurs in 4D (about time). It would thus, be solid angular spin encompassing 4pi steradians.
Like a Mobius strip (used to illustrate spinors), this requires two planar rotations to return the exact starting condition, exactly as observed.

The term "spin½" is absurd because there is no such thing as half a quantum! It arises because the measured spin of a fundamental fermion (such as an electron) is found to be half the expected quantum of angular momentum. Specifically, it is half of ħ. But ħ is the reduced Planck constant or h/2pi. Reducing by 2pi radians is fine for planar rotations but is incorrect for solid angular (4pi) rotations expected with chronaxial spin. With chronaxial spin, an electron should be expected to have spin = h/4pi, exactly as observed.

socrat44 wrote:Usually the form of electron seems as a ''ball''.

A ray-like force object, spinning about time, would describe a spherical (i.e. solid angular) field. The location central to that field at any moment is what we refer to as a "particle". Over time, that particle describes a worldline.

socrat44 wrote:So, it seems that Hawking is right: ''the particles DO NOT HAVE ANY WELL - DEFINED AXIS.''

Ha! Tell that to the electrons.

Jorrie wrote:FD, have you ever considered a 5th dimension for your "spin axis"? … "hyperaxial spin"

Yes. But less is more in models, and full 5D rotations would have greater* than the 4pi steradians, which so neatly fit above. "Hyperaxial spin" is rather nonspecific, as it could mean any spin in any plane greater than 2D. Chronaxial spin occurs in a 3-plane and might thus be specified as "3-spin". Rotation in a 4-plane (or an n-plane) might be specified as "4-spin" (or "n-spin").

Jorrie wrote:BTW, what you referred to as "interval-time coordinates" looks to me the same thing as standard space-propertime coordinates in SR.

"Interval-time coordinates" does refer to proper time but not to space. This is where Epstein coordinates get in trouble. They strive for Euclidean simplicity but fail to substitute interval coordinates for space. Thus, they can’t handle light. With interval coordinates, lightlike intervals define the origin, plain and simple.

Remote Contact: As interval goes to zero, space and time equate, regardless of the magnitude bypassed by a light quantum. Interval contact may thus be found to be spatially and temporally quite remote.

Einstein felt invariance (to all observers) to be the strongest argument for "reality". Thus, he might well have considered interval-time coordinates to be 75% more real than Minkowski's, which he was initially reluctant to accept.

"…a four-dimensional space-time… Indeed, Einstein himself was not sympathetic to this idea when he first encountered it. … The idea of space-time was not, in fact, Einstein's… It was…Herman Minkowski," - R. Penrose (forward to R. Feynman, p. xiv)

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### Re: the universe according to Emmy Noether

FD, your last few posts contain some very questionable physics (bordering on wishful thinking). I do not have the time to respond properly atm, but this may result them to be "dropped a level" - I think you will understand what I mean.

For now, let us just not mislead readers to think that your views represent mainstream physics in any way.

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### Re: Fair point

BurtJordaan wrote:let us just not mislead readers to think that your views represent mainstream physics in any way

I'm happy to clarify that anything I posted above which seems original is! I have been fairly vigilant and not found more than a faint hint here and there in mainstream literature.

I mistook your question about 5th dimensional spin as an encouragement toward non-mainstream ideas.

As good as it is, we need also recall that mainstream depictions of zero-magnitude, lightlike intervals are at least as untenable as the notion of "intrinsic spin". Transplant to a non-mainstream section would find no protest from me. (I favor the "Spin½ for Halfwits (like me)" title. ;o)

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### Re: Fair point

Faradave » 13 Aug 2017, 02:12 wrote:I mistook your question about 5th dimensional spin as an encouragement toward non-mainstream ideas.

But using the 5th dimension in relativity is mainstream. I was curious, as it should make no difference to your simplistic calculations of a zero-size object spinning, with spin components in each of the 3 spatial directions.

FD wrote:As good as it is, we need also recall that mainstream depictions of zero-magnitude, lightlike intervals are at least as untenable as the notion of "intrinsic spin".

If you refer to the "null interval", the spacetime path of light, the reality is that its scale is indeterminate on Minkowski diagrams, not "zero". It is like dividing zero by zero, where the result can be anything. There is never any scale along the light-cone, but it stretches to infinity.

And BTW, Epstein diagrams handle the null interval quite OK. I think you know it - the light-cone just 'morphs' into a light-sphere, so it handles space-intervals, time-intervals and null-intervals remarkably well.

This is all I have time for - more later.

PS. If you have not done so, I think you might benefit from reading David H. McIntyre's Spin and Quantum Measurement. Slightly mathematical, but with excellent prose all through the paper.

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### Re: Spin½ for Halfwits (like me)

Faradave » 12 Aug 2017, 20:02 wrote:Yes! Hawking is naively referring to planar rotations, which have a spatial axis and encompass 2pi radians (i.e. spin in 3D). Chronaxial spin, which I personally attribute to "spin½" fermions, occurs in 4D (about time). It would thus, be solid angular spin encompassing 4pi steradians.
Like a Mobius strip (used to illustrate spinors), this requires two planar rotations to return the exact starting condition, exactly as observed.

I hope you're not saying Hawking was naïve? He was simply using a naïve image for naïve persons reading the book! And BTW, the 4pi rotation was again just a naïve metaphor - AFAIK, no measurement of such an angle for particle spin has ever been made.

The term "spin½" is absurd because there is no such thing as half a quantum! It arises because the measured spin of a fundamental fermion (such as an electron) is found to be half the expected quantum of angular momentum.

You may be misunderstanding what quantum spin means. If you have read the David H. McIntyre's lecture that I have referred to above, you will find the real definition of Spin½.

"Interval-time coordinates" does refer to proper time but not to space. This is where Epstein coordinates get in trouble. They strive for Euclidean simplicity but fail to substitute interval coordinates for space. Thus, they can’t handle light. With interval coordinates, lightlike intervals define the origin, plain and simple.

I have already countered the Epstein part, but what I would like to know Dave, apart from the fanciful explanation for your "cronaxial spin", what other uses would your "interval coordinates" have? E.g. how would you plot the classical Alice and Bob sending greetings message to each other every year, say?

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### Re: the universe according to Emmy Noether

BurtJordaan » August 12th, 2017, 3:46 pm wrote:FD, your last few posts contain some very questionable physics
(bordering on wishful thinking). I do not have the time to respond properly atm,
but this may result them to be "dropped a level" - I think you will understand what I mean.

represent mainstream physics in any way.

I do not agree with what you have to say,
but I'll defend to the death your right to say it.
/ Evelyn Beatrice Hall /

Forum Moderator,
it seems, that you don't respect very much this point of view.
=================================.
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### Re: Spin½ for Halfwits (like me)

I do respect this p.o.v. of Evelyn. Just say it in the right Forum section and do not clutter a section dealing with mainstream physics with personal ideas that goes against it. We have plenty of sub-forums where people view their ideas all the time.

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### Re: Spin½ for Halfwits (like me)

BurtJordaan » August 14th, 2017, 3:46 am wrote:I do respect this p.o.v. of Evelyn.
Just say it in the right Forum section and do not clutter a section
dealing with mainstream physics with personal ideas that goes against it.
We have plenty of sub-forums where people view their ideas all the time.

In 1900 Max Planck presumed that the light wasn't really a continuous wave
as everyone assumed,
but perhaps could exist with only specific amounts, or "quanta," of energy.
=============
So, Planck was ''dealing with mainstream physics'' and solved it problem
''with personal ideas that goes against it.''
==================.
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### Re: Spin½ for Halfwits (like me)

Max Planck was a fully qualified professor in theoretical physics and was solving a unexplained experimental result. Ditto for Einstein. Simply in a different class ...

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### Pointed Argument

No rush with this. I know you're busy and I appreciate, as always, your thoughtful replies.

Jorrie wrote:the real definition of Spin½

"In applications where it is natural to use the angular frequency (i.e. …in terms of radians per second…) it is often useful to absorb a factor of 2pi into the Planck constant…called the reduced Planck constant…equal to the Planck constant divided by 2pi, and is denoted ħ (pronounced 'h-bar')" Wikipedia

Dividing by 2pi is fine for classical rotation, but if quantum spin is chronaxial, it must instead be reduced by the solid angular range of 4pi sr. In this way, fermion spin is not "½" but quite whole at h/4pi (i.e. ħ/2), exactly as measured, sans absurdity.

Jorrie wrote:But using the 5th dimension in relativity is mainstream. …should make no difference to your [quantum] spin components…

Interesting. I can readily understand taking a 5th dimensional perspective, in order to depict 4D regions, such as light cone sections. But modeling a 5th dimension, as part of the working manifold, requires selection of and adherence to type. Specifically, its unidirectional or bidirectional translational freedom.

Dimensionality gives more to consider than just spin components. Less dimensions reduce overall model complexity. A 3-plane of rotation is encompassed by 4pi steradians, which explains away the "half a quantum" oxymoron (above). There's also field intensity, as follows:

Spinning a rope overhead (about a spatial axis) sweeps out a radial 2-field (i.e. disk), for which average density falls directly with radius. I restrict my model to 4D because, given a temporal axis, a field element sweeps out a radial 3-field (i.e. a ball), for which intensity is consistent with the observed inverse square law. An element with a 4-plane of rotation, about a 5th D axis would have field intensity falling off with radius cubed.

Jorrie wrote:If you refer to the "null interval", the spacetime path of light, the reality is that its scale is indeterminate on Minkowski diagrams, not "zero". It is like dividing zero by zero, where the result can be anything. There is never any scale along the light-cone, but it stretches to infinity.

Mumbo jumbo (with all due respect). I'm referring specifically to the magnitude of a lightlike interval, which is defined as zero. This is geometry, not "wishful thinking." Forget scale. Zero is zero, regardless of scale. Besides, for interval magnitude, we're talking about a difference not a ratio (d² = r² -). The spatial (r) and temporal (t) spans (of any magnitude) are equal for a lightlike interval (d), which is thus, zero. And of course, this is invariant, agreed by all observers (even if they don't know it!)

"In relativity and in pseudo-Riemannian geometry, a null hypersurface is a hypersurface whose normal vector at every point is a null vector (has zero length with respect to the local metric tensor). A light cone is an example." Wikipedia

"Because of the minus sign, the spacetime interval between two distinct events can be zero. … Spacetime intervals are zero when x = ±ct. In other words, the spacetime interval between two events on the world line of something moving at the speed of light is zero. Such an interval is termed lightlike or null. A photon arriving in our eye from a distant star will not have aged, despite having (from our perspective) spent years in its passage." Wikipedia

"…the interval AB between two events can vanish even when the separations Δx, Δy, Δz in space and Δt in time between B and A are individually quite large. … The interval between two events is zero when they can be connected by a light ray." Taylor & Wheeler p. 37-38

"Where light goes from a given point is always a zero interval…to state that the propagation speed of light is invariant is the same as saying that the interval is zero." Feynman p. 99

"Minkowski space…necessarily distort metric relations and one has to learn to compensate for this distortion. …The simplest case [interval squared] Δs² = 0, which means precisely that [the events] are connectable by a light signal." Rindler p. 90-92

Jorrie wrote:BTW, what you referred to as "interval-time coordinates" looks to me the same thing as standard space-propertime coordinates in SR.

This is exceedingly clear with interval-time coordinates, and woefully distorted in Minkowski spacetime. If interval contact is not as clear to you in "space-propertime" coordinates (i.e. Epstein diagrams), they aren't the same.

Zero interval separation looks like contact (yellow dot), because it is! It is the embodiment of "locality" regardless of spatial and temporal remoteness.

Interval contact is as real and invariant as any other single event, regardless of having a multitude of space and time coordinate designations. Contact between point locations means they’re superimposed, just like all the longitudes of the south pole.

Jorrie wrote:how would you plot the classical Alice and Bob sending greetings message to each other every year, say [in interval-time coordinates]?

We need to be clear that lightlike interaction retains direction (always perpendicular to proper time), despite having zero magnitude. (Any zero-magnitude vector should do the same.) That direction may be drawn as a ray, much as it is in Minkowski diagrams (always 45° from proper time). It must not however, be erroneously interpreted as interval separation. It's interval contact. "See you!" = "Keep in touch!"

Presuming fixed spatial locations between A & B, annual, alternating, lightlike communications are shown as yellow lines (length = message duration). Communication should be interpreted as via pinholes (particle-interaction wormholes) in the desired direction. Dashed lines each indicate a single, representative quantum transmission.

Jorrie wrote:BTW, Epstein diagrams handle the null interval quite OK. I think you know it - the light-cone just 'morphs' into a light-sphere, so it handles space-intervals, time-intervals and null-intervals remarkably well.

I note that, "It is usual to make the radius 1 interval unit." Light, experiencing zero time might thus, define the origin, as with my interval-time coordinates. As you note, he refers to a growing "light-sphere" This could be seen as an observer's experience of a G or EM field but "we cannot put photons on the diagram - they do not carry clocks that tick, while massive particles have them built-in (decay times)". I wouldn't call that "handling the null interval remarkably well". Epstein needs to recognize lightlike interactions as mediated by interval contact (i.e. locality). Action-at-a-distance is an illusion perpetuated by brains hardwired for 3D.

Both coordinate systems employ the Pythagorean relation to great advantage. Interval-time coordinates (above) do so with less hand waving and no apologies. Lightlike intervals define the origin for fields and for transmission of individual quanta. Fields represent the potential for interaction, massless energy exchange is a single actual interaction.

Jorrie wrote:Spin and Quantum Measurement …BTW …the 4pi rotation was again just a naïve metaphor - AFAIK, no measurement of such an angle for particle spin has ever been made.

This seems to be a fine article. My own resources also make necessary use of various interferometers with multiple Stern-Gerlach devices (SGD), as well as the means to rotate particles. McIntyre's math is a challenge for me but his reported results are consistent with chronaxial spin (c-spin).

An important addition is that the solid angular range (4pi) of c-spin readily explains the Born rule. It mysteriously relates the probability of a prepared and subsequently measured fermion spin (by SGD) with the half-angle relation P = cos²(θ/2). This gives rise to the notion √P is "probability amplitude", which has QM flummoxed. What the heck is the square root of a probability??? QM just says, get used to "quantum weirdness." My point is that QM has naïvely overlooked the solid angle!

"There have been many attempts to derive the Born rule from the other assumptions of quantum mechanics, with inconclusive results. ... it is common to describe the Born rule as ... probability is equal to the amplitude-squared" Wikipedia

We can do better with c-spin. Consider an electron prepared with spin "up". At some angle (θ), a subsequent spin measure is made.
Left: Solid angle Ω is associated with an inscribed cone having base area A and planar apex angle θ.
Right: Opposing rays on the cone represent prepared and subsequently measured spin½ components.

A solid angle Ω describes a cone for which the planar projection has apex angle θ. Such projections easily neglect the relevance of the cone's base area A. With spin½ modeled as chronaxial, the solid angle between prepared and measured spins requires that area rather than arc will dictate their correlation. Prepared spin has 100% probability (P) of self-correlation (i.e. P = 1 when θ = 0), which diminishes as A increases. And area A varies with the square of its radius r, given by sin(θ/2). Thus:
P = 1 – sin²(θ/2) = cos²(θ/2).

The squared term indicates area, θ/2 indicates the area's associated solid angular range.

I call that proof!* What's in your pudding?

*allowing for a proportionality constant.

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### Re: Spin½ for Halfwits (like me)

Mainstream physics doesn't know what electron is.
Book " What is the Electron?"
By  Volodimir Simulik  Montreal, Canada. 2005. /
In this book:
‘ More than ten different models of the electron are presented here.
More than twenty models are discussed briefly.
Thus, the book gives a complete picture of contemporary theoretical

ftp://210.45.114.81/physics/%CA%E9%B...Simulik%20.pdf

And In the internet is possible to find 100 different models of electron.
All of these models of  electron are problematical.
==========================
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### Re: Pointed Argument

FD, all the quoted stuff in green are common knowledge and IMO, also have nothing to do with your definition of spin½. I do not dispute that you can draw an 'interval diagram', I'm actually just curious at what use it might have. What I do dispute is your definition of quantum spin number ½. Have you actually read the experiments in McIntyre?

David H. McIntyre wrote:If we assume that each electron has the same magnitude S of the intrinsic angular momentum or spin, then classically we would write the projection as Sz=
S cos θ, where θ is the angle between the z-axis and the direction of the spin S. In the thermal environment of the oven, we expect a random distribution of spin directions and hence all possible angles θ.

Thus we expect some continuous distribution (the details are not important) of spin projections from Sz = -|S| to Sz = +|S|, which would yield a continuous
spread in deflections of the silver atomic beam. Rather, the experimental result is that
there are only two deflections, indicating that there are only two possible values of the
spin projection of the electron.

This is the fundamental meaning of spin½, but do read the other text surrounding the math. And as Feynman, Hawking, etc. have stated, there is no classical (non-quantum) way to understand or describe this, surely not with classical relativity. Planck and Einstein tried hard in their later years and both have failed.

So, you feel that you can improve on that?

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### Re: Spin½ for Halfwits (like me)

Presuming fixed spatial locations between A & B, annual, alternating, lightlike communications are shown as yellow lines (length = message duration). Communication should be interpreted as via pinholes (particle-interaction wormholes) in the desired direction. Dashed lines each indicate a single, representative quantum transmission.

The question was really for Alice and Bob moving relative to each other, but this is quite a 'meta-scienctific' description. I have no idea what a "a single, representative quantum transmission" might mean. The diagram is actually quite incomprehensible to me. For your "pinholes", an extra dimension on the diagram would probably have made things a lot clearer...

But this (or Epstein diagrams) is not the issue here. It goes about particle spin, where the physics world patently disagrees with you.

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### Re: Mainstream Malfunction

Jorrie wrote:I have no idea what a "a single, representative quantum transmission" might mean.

It means "a single photon", in conventional parlance. I don't adhere to photons, referring instead transmission of energy quanta, via pinhole. I'm not surprised that it was unclear.

Jorrie wrote:…4pi rotation was again just a naïve metaphor - AFAIK, no measurement of such an angle for particle spin has ever been made.

The measurement is common knowledge in QM. Allow me. You're certainly familiar with wave-particle duality. When a particle beam (such a neutrons) is run through an interferometer (such as double slits), a characteristic interference pattern is observed, even when particles pass through individually on route to a detector surface. If one path through the interferometer has applied to it, a means for rotating the particle,* the accumulated interference pattern changes. The original pattern first returns only after applying 720° of rotation.

Thus:
"Electrons, protons and neutrons [i.e. fermions] see a 720° world." Schumacher guidebook p. 53. 2009, after describing the above experiment.

"Mathematically, quantum-mechanical spin states are described by vector-like objects known as spinors. There are subtle differences between the behavior of spinors and vectors under coordinate rotations. For example, rotating a spin-½ particle by 360 degrees does not bring it back to the same quantum state, but to the state with the opposite quantum phase; this is detectable, in principle, with interference experiments. To return the particle to its exact original state, one needs a 720-degree rotation." Spin (physics)

"In terms of more direct evidence, physical effects of the difference between the rotation of a spin-1/2 particle by 360° as compared with 720° have been experimentally observed in classic experiments in neutron interferometry. In particular, if a beam of spin-oriented spin-1/2 particles is split, and just one of the beams is rotated about the axis of its direction of motion and then recombined with the original beam, different interference effects are observed depending on the angle of rotation. In the case of rotation by 360°, cancellation effects are observed, whereas in the case of rotation by 720°, the beams are mutually reinforcing." Spin ½ citing: Rauch, Helmut; Werner, Samuel A. (2015). Neutron Interferometry: Lessons in Experimental Quantum Mechanics, Wave-Particle Duality, and Entanglement. USA: Oxford University Press

*applied weather a particle takes that path or not. That is, the rotation device does not act as a which-path detector. Recall that even neutrons have a very slight magnetic moment due to uneven quark charge distribution, so they can be precisely rotated with appropriate EM fields.

Jorrie wrote:You may be misunderstanding what quantum spin means …. McIntyre's lecture … you will find the real definition of Spin½. … What I do dispute is your definition of quantum spin number ½. Have you actually read the experiments in McIntyre?

I only browsed McIntyre because I find nothing there which is inconsistent with my other sources. It's nice but not news. Try this:

"However, the observed fine structure when the electron is observed along one axis, such as the z-axis, is quantized in terms of a magnetic quantum number, which can be viewed as a quantization of a vector component of this total angular momentum, which can have only the values of ±½." Spin ½

Whether fine splitting or twin beams emerging from an SG device, the measured spin magnitude is half of ħ. Which leads us to ask what is ħ? Given that the smallest quantum of angular momentum is the Planck constant h, as I provided:

"In applications where it is natural to use the angular frequency (i.e. …in terms of radians per second…) it is often useful to absorb a factor of 2pi into the Planck constant…called the reduced Planck constant…equal to the Planck constant divided by 2pi, and is denoted ħ (pronounced ‘h-bar)." Planck Constant

Thus no particle should have half of ħ! We can just say…"quantum weirdness" or we can realize that, for fermions, the classical reduction (by 2pi) is a mistake! It should be reduced by the solid angular range of 4pi, which is a geometric consequence of a temporal axis (i.e. spin½ = chronaxial spin). That's news!

Out of time, more later.

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### Re: Spin½ for Halfwits (like me)

https://en.wikipedia.org/wiki/Planck_constant wrote:In applications where it is natural to use the angular frequency (i.e. where the frequency is expressed in terms of radians per second instead of cycles per second or hertz) it is often useful to absorb a factor of 2π into the Planck constant. The resulting constant is called the reduced Planck constant or Dirac constant. It is equal to the Planck constant divided by 2π, and is denoted ħ (pronounced "h-bar"): ...

So, would you want to change the expression for frequency then to "steradians per second". Do you realize the implications of that?

I find that redifinion of standard terms, or making up own terms for existing concepts, to be very counterproductive. For one thing, very few scientists will take notice of what you write.

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### Re: Pointed Argument

Faradave » 14 Aug 2017, 22:29 wrote:As you note, he refers to a growing "light-sphere" This could be seen as an observer's experience of a G or EM field but "we cannot put photons on the diagram - they do not carry clocks that tick, while massive particles have them built-in (decay times)". I wouldn't call that "handling the null interval remarkably well"

Just not to leave a wrong impression with other readers, the null interval is actually quite straightaway on a space-propertime diagram. Also, not to detract from FD's Spin½ efforts, I will continue discussions on that on the Epstein Spacetime Diagrams thread under physics, direct link to be posted here later.

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### Re: Uncommon Knowledge

Jorrie wrote:FD, all the quoted stuff [about lightlike interval having zero magnitude] …are common knowledge

Good! So, we should be able to understand "zero interval separation" as interval contact.

And we should recognize that lightlike interaction occurs via interval contact, which has an intrinsic (i.e. unobservable) span of zero, while having non-zero extrinsic span (geodesic). that is lightlike interaction reveals a pinhole (particle-interaction wormhole).

And I should be able to refer to these ad lib in other science threads. Right?
Jorrie wrote:…do not clutter a section dealing with mainstream physics with personal ideas that goes against it. ... [by comparison,] Max Planck was a fully qualified professor in theoretical physics and was solving a unexplained experimental result.

A minor point: I believe "Phyxed" (physics-fixed, better than real) to be a different interpretation, entirely consistent with but simpler and deeper (more explanatory power & prediction) than the Standard Model of Particle Physics (SMoPP, i.e. "mainstream").

I also "explain unexplained experimental results" relating to intrinsic spin by giving a correct (i.e. 4pi) reduction of the Planck constant, as applied to fermions. This is not a trivial matter. For example:

"... one famous triumph of the Quantum Electrodynamics theory is the accurate prediction of the electron g-factor. The magnetic moment of an electron is approximately twice what it should be in classical mechanics. The factor of two [gs] implies that the electron appears to be twice as effective in producing a magnetic moment as the corresponding classical charged body. …a correction term [ae]… takes account of …interaction…with the magnetic field" - Magnetic Moment

The intrinsic spin magnetic moment for an electron (µs) is given by:
µs =– gsµBS/ħ,
where S is the electron spin angular momentum and µB the Bohr magneton. Both of those terms incorporate ħ/2 which, in that form, is fully reduced (i.e. h/4pi). However, in the denominator of µs, ħ is only half reduced, as h/2pi. If h had been reduced instead by the solid angular range of 4pi, it would be equivalent to having a factor of 2 in the numerator. Thus, gs would not mysteriously need to be "twice" that of the classical g-factor (gL). QED's anomalous magnetic moment (ae) is then accommodated at half the conventional value as gS = 1 + ae = 1.001159652181643.

Jorrie wrote:I do not dispute that you can draw an 'interval diagram', I'm actually just curious at what use it might have. [But spin½ is] where the physics world patently disagrees with you. … Feynman, Hawking, etc. have stated, there is no classical (non-quantum) way to understand or describe. So, you feel that you can improve on that?

I don’t think the mainstream disagrees so much as remains ignorant of chronaxial spin (i.e. about time). Recall:

"…Spin is an intrinsic property of a particle, unrelated to any sort of motion in space." - Angular Momentum Operator

"Physically, this means it is ill-defined what axis a particle [i.e. fermion] is spinning about." - Spin-½

Let "intrinsic" mean "unobservable". A temporal axis is unobservable. BTW, so are the classical spatial axes, if we mean space right now. We only intuit simultaneous space from light, which communicates energy and information from past locations.

But my point is that the mainstream is ignorant, having not even considered chronaxial spin. And who can blame them. By mapping Minkowski spacetime on a Euclidean plane, they get the mistaken impression that spin on a temporal axis would have no spatial components.

An angular momentum vector makes no projection on its orthogonal plane of rotation, regardless of dimensionality.

Importantly, supplying actual Euclidean coordinates (i.e. interval-time coordinates), reveals space in position to receive projections from a chronaxial spin vector, with equal magnitude in every direction, exactly as observed.

A 2D cross section revealing fermion spin in interval time coordinates. This provides for a spherically-symmetric, radial spin field about time. ±r = space, ±d = interval, t = proper time, σ = primary fermion spin vector, ±ħ/2 = "spin½" = measured spatial spin components

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### Re: Spin½ for Halfwits (like me)

I know of no physicist that will agree with you, so it remains a private theory with no support, AFAIK. So until you can drum up some reasonable support, I'll leave you to have fun...

BurtJordaan
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### Re: Gone Fishn'

Jorrie,

The trouble is, the few physicists I've encountered give even less substantive replies than that one! They quickly swim away to hide in the mainstream. (I do appreciate your prior efforts. Thanks!)

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### Re: Spin½ for Halfwits (like me)

We know electron by what it does, not by what it is.
Electron is not stable, solid, firm, steel  particle .
Electron's size, mass, energy  is dependent on its velocity.
Electron's size, mass, energy  is dependent on its spin / angular momentum.
The angular momentum can be different: 1/2, 3/2, 5/2, . . . . etc.
When angular moment is stronger, it size is smaller, the frequency is higher and
the energy is bigger: E=hf.

The orthodox style of thinking wouldn't open the door to understand what electron is.
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socrat44
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