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## Maxwell's Electromagnetism is a theory of knots

### Maxwell's Electromagnetism is a theory of knots

Physics Central wrote:See: Emptiness Tied in a Knot - Physics Central Physcis Buzz Blog - 1706-2017

Last month in the American Physical Society’s journal Physical Review A, a team of scientists from Leiden University in The Netherlands demonstrated just this. They used the mathematical theory of knots to explore electromagnetic fields. In doing so, they realized that some solutions to the fundamental equations of electromagnetism can be described as knotted structures.
[Click to enlarge]
Cable Knot Vortices in Electromagnetism - AJJM de Klerk etal - Fig1-17 Oct 2016.png (75.01 KiB) Viewed 357 times

The origin of knot theory dates back more than 125 years, to when Lord Kelvin suggested that atoms were swirling regions of the ether tied in knots (more on that here). The idea of ether was abandoned not long after, but it kicked off a field of study that has 1produced important results in many areas of physical science. About twenty years before knot theory was developed, James Clerk Maxwell developed a theory that describes how light, electricity, and magnetism behave and interact. He is the one that suggested light can be described as electromagnetic waves traveling through space. Maxwell’s groundbreaking work can be boiled down to a set of mathematically sophisticated equations—often called “Maxwell’s equations”—that are the foundation of classical electromagnetism, optics, and circuits. Recently, physicists realized that studying electromagnetic fields from a knot point-of-view leads to intriguing results. This new work focused on points in space called optical vortices, where the strength of an electromagnetic field is zero. Imagine a ray of light twisted like a corkscrew that is traveling toward the wall in front of you. The twisting causes the light to interfere in such a way that when it hits the wall, you see a ring of light surrounding a dark spot. The dark spot, where there is no light, is called an optical vortex. Like the calm in the eye of a hurricane, within that circle there is emptiness; the electromagnetic field is zero. In two dimensions, like on the wall, optical vortices are points. In three dimensions, they are lines.
This new work shows that optical vortices in real electromagnetic fields can be described as knotted electromagnetic field lines. Put another way, the researchers show that knotted structures can be exact solutions to Maxwell’s equations. In addition to this finding, the team mathematically describes how these structures emerge.

If you are interested in these knotty problems please look this paper up here at the preprint server:
Cable Knot Vortices in Electromagnetism
Albertus Johannes Jacobus Maria de Klerk, Roland Ivo van der Veen, Jan Willem Dalhuisen, Dirk Bouwmeester
(Submitted on 17 Oct 2016)

Knot-like structures, arising in several areas of physics, have received substantial interest for their topological properties over the preceding decades. In this letter we combine results from knot theory with Bateman variables for the electromagnetic Hopf field to construct a new family of finite energy null electromagnetic fields with stable optical vortices that are topologically equivalent to a given but arbitrary algebraic link. The class of algebraic links includes not only all torus knots and links thereof, but also cable knots which have thus far not been brought in connection to electromagnetism.

You may easily see by example that photon knots are also responsible for electrons... Williamson & van der Mark - Is the electron a photon with toroidal topology - 1997? First the "torus knot", then the "cable knot" views of the same "electron" which is actually a "particle".... or not.

A pair of these "knots" can be created from a pair of energetic photons nucleating electron and positrons in the process... functionally identical... matter from light virtually "ex nhilo". However this "electromagnetic smoke ring" does have a peculiar folding where the negative excursions of the field are all wrapped to the outside and all the positive excursions of the field are wrapped to the inside. The fields then become "static" and charged negative on the outside and positive on the inside... or as a connected "pair" an "electron" with a negative charge on the "outside" and a "positron" and a positive charge on the "inside".

Or even this recent development: Researchers develop magnetic switch to turn on and off a strange quantum property - Phys Org - 2505-2017 These "particles" are actually self trapping "waves" provided you have the "photonic energy" in these photons to create the electron-positron pair. It also suggests the source of the static charge in matter arising from the electric field of the "flying photon" constrained to a spherical compact knot. In that case the structure is the same as that of a Falaco Soliton but with a possible additional dimension. I would also add... subject to a "Page and Wootten" quantum time Mechanism. For details look here: Was Einstein Correct on Relativity and the Speed Of Light - John Duffield Site - 12 Jun 2017
Aa' menle nauva calen ar' ta hwesta e' ale'quenle

Good Elf

Posts: 471
Joined: Fri Oct 29, 2010 12:21 am
Location: Brisbane, Australia

### Re: Maxwell's Electromagnetism is a theory of knots

Do these knot theories connect with the proton/electron positive/negative charge model of the atom? Also, would the behavior of the knots somehow correspond with Schrodinger waves that define electron orbitals and chemical bonds? Or is this a parallel theory?
inertron

Posts: 835
Joined: Sat Aug 13, 2011 2:10 am

### Re: Maxwell's Electromagnetism is a theory of knots

Hi Inertron,
inertron wrote:Do these knot theories connect with the proton/electron positive/negative charge model of the atom? Also, would the behavior of the knots somehow correspond with Schrodinger waves that define electron orbitals and chemical bonds? Or is this a parallel theory?
Naturally if this picture corresponds to real electrons and real positrons it means that the electrostatic fields of charges is the result of a standing wave on both the inside and the outside of the particle. The wave of "charge" for an electromagnetic photon has both positive and negative phases as the electric field "oscillated" from positive through zero to negative and back through zero and all the way back to positive. If the dance of this wave is wrapped onto the surface of the toroid "with a twist" you end up with the twisted strip model of the electron which is negatively charged on the outside and if you pop it inside out the electron "becomes" a positron with a positive charge on the outside, it is all the result of the wrapping... see the paper Williamson & van der Mark - Is the electron a photon with toroidal topology - 1997
The two images are above in my previous post. I have made a "model" of the electron according to this schema, and an image is here:
[Click to enlarge]
Twisted Strip Electron_small.jpg (60.3 KiB) Viewed 209 times

This image corresponds directly with the drawing above at Figure 1B. Note this is the "arrow" convention for charge sign, the circle with a point is the positive tip of an arrow's shaft pointing at you, while the circle with a plus sign inside is the feathered end of the arrow and is positive (yeah, I know, I don't make these strange conventions). This is conventional current flow.

This monotype character indicates negative (feathers) on the left and positive (tip) on the right. In the image. As seen in this illustration the outside of the "electron" has the arrows pointing away from the "particle", while there are arrows on the inside directed inwards.

Popped inside out we have this "positron" (now positive on the outside and negative on the inside)...

[Click to enlarge]
Twisted Strip Positron_small.jpg (70.73 KiB) Viewed 209 times

Please note the red arrow (along the length of the strip) is the direction of propagation of light (in a folded figure eight). While the arrows all in the one direction upwards is the magnetic field threading it as in a solenoid.

You might be able to see that this is in accord with the right hand and left hand grip rule respectively. This matches the particle and antiparticle relationships in the one overall donut structure. This leads to the idea (for me) that the electron and positron are the one particle except that time is running in an opposite direction when compared with the positron (propagating backwards in time) for the positron (reversing the red arrow's relative direction compared with the direction of propagation for the electron) as noted by Richard Feynman leading to the Feynman-Stueckelberg Interpretation for Antiparticles as being the same particle but propagating backwards in time. Of course this apparent propagation direction is simply an artifact of the observer frame... the electron and positron are really the same particle. The center of the electron and the proton have no charge in it at all... it is hollowed out... a knot... which is a string wrapped around a core. There is a image that goes with these newer representations and papers and here it is...
[Click to enlarge] Details of related paper is included in the caption.
Researchers develop magnetic switch to turn on and off a strange quantum property - PhysOrg -2505-2017.jpg (56.92 KiB) Viewed 209 times

These multiple wrappings around the donut are called "winding numbers" and electrons with half integer spin have winding number 2 (reciprocal ½).
Recently another paper detailing a conference on just these issues on these phenomena related to electron fields has come up recently and brought to my attention by Kin99 on this Forum. See: Are electrons oscillating photons, oscillating “vacuum," or something else? The 2015 panel discussion. But since this conference a lot of actual experimental evidence has come up as indicated in my other post. The trick is to "naturally" wind a photon onto a torus just twice with one twist (winding number 2). That is the same for it's antiparticle... the positron. That happens at the creation energy of the electron positron pair.... about half a million electron volts. It's a neat quantum thing as you may very well imagine. Winding numbers 4, 6 are successively heavier versions of the electron... the muon and the Tau particles of the second and third generations of particles... ditto for protons and neutrons and their heavier counterparts. Don't ask how quarks come in except to say it will fit in there somewhere.

Now you wanted to know how these electric and magnetic fields and Schrodinger's Equation coincide... well just compare these two wave equations written in the same way...
You may have a look at this reference:
The resemblances in mathematical structures between the optical constants of artificial electromagnetic media and some physical phenomena in field theory: Jian Qi Shen - Submitted on 3 May 2004
This paper demonstrates that there is much similarity in the mathematical formalisms between the optical constants of artificial electromagnetic media (such as chiral media, left-handed media, photonic crystals and EIT media) and some physical phenomena in field theory, including general relativity, quantum mechanics, energy band theory, etc. The significance of such comparisons lies in that: (i) the unification in mathematical descriptions shows that many physical phenomena and effects, which seem to have no connections between them, actually share almost the same mathematical structures; (ii) it can provide clue to us on suggesting more new effects which is similar in mathematical descriptions to the familiar phenomena in other areas.
First the electromagnetic wave equation:

and now the quantum wave equation (one form of Schrödinger's Equation):

Notice the one to one comparison. Now there is no "exact" comparison of the properties of the electric field (E) and the the value of Psi (ψ) but there is a relationship relating the density of the wave function and the intensity of the field.
The relationship is not "one to one" because E is a measurable in electromagnetic theory, while normally psi is not a measurable at all but only a theoretical quantity representing the probability of the wave function that indicates at a certain position a real number for the position of a possible particle as a spatially normalized varying scale from zero to 1 if it were subjected to a measurement. Plotting this density function lead to maps of this normalized spatial density function as "shells" or "orbitals".

The theory of atomic orbitals and electron bonds is a kind of model based on the theory of overlapping bonds in shells and the ability to share paired electrons. There is no "exact science" for solving for complex many atom systems with even more electrons, only the hydrogen atom with (and without) one electron has been solved exactly. However in Physical Chemistry, according to some, the hydrogen bond theory works pretty well... up to a point. Schrodinger's Equation is all fine and dandy but it appears to follow the same structure as the harmonic solutions using Fourier Theory in three dimensions and time... or spherical harmonics... harmonic resonances on the surface of a sphere.
Here are spherical harmonics of an dipole oscillating sphere (technically nothing to do with atoms but to do with resonant electromagnetic systems)... here are the time independent solutions...

This bears an uncanny resemblance to Quantum Theory. Not surprisingly, the time dependent solutions are simply the simple harmonic solution. Many approaches deal with the time independent and time dependent parts to be separable... in reality nobody knows if this approach is truly correct. However it is an operational working model that seems to get valuable results. Underneath the very pretty solutions there are a number of unresolved assumptions.

There is an "uncanny" resemblance to the solutions of Schrodinger's Equation, S,P,D,F,G orbitals as an electromagnetic resonance : quantum shells"... while still not actually being Schrodinger's Equation at all. Schrodinger's Equation still cannot be derived entirely from first principles. It is still a very interesting theory, and it seems to work very well but the theory is never exact because electrons in orbitals are in quantum stationary states and the real theory of all that is still mathematically insoluble. A dynamic theory like Bohr had may not actually exist, the assumptions make that simple model of planetary electrons rotating around the central nucleus incorrect but it is an easy to understand concept for most people to grasp. The solutions of the Hydrogen atom without electrons is equivalent to this schema. We are all waiting for quantum computers that may be able to solve these "hard" problems exactly. Digital computers work for simple systems but not the more complex ones and it is all approximated using perturbation theory. The nucleus is another step in that general direction but because the simpler problems have no exact solutions these higher order theories take massive amounts of time to give even approximations to real world solutions. It's way beyond a fair treatment of your much simpler straightforward question above... OK. You deserve better, but I don't know how to make it so.

What we know is electrons do not spin and spiral around the atom, not in that simple sense. In the case of atoms this motion should cause radiation and the electron would spiral into the nucleus. It does not happen so the solution is the electron is that it is not in dynamic motion at all but in superposition of quantum states... stationary states. Until a property of the atom is measured or the electron are moving from one orbital to the next, the electron exist in a superposition of an infinity of possible states in the surrounding space and this is where the probability comes in rather than position vectors and electric fields. Since the atom cannot be measured without some kind of electromagnetic interaction, we only catch the atom between stationary states, while in a dynamic state, that is emitting or absorbing an electron or the electron changing orbitals, and this process is accompanied by absorption and emission of photons... but never exactly at the same time, so nobody can ever get actual data while it is in the true quantum stationary state. This is the state atoms are in for most of "our" time. Quantum Entanglement theory of time suggests that these stationary states are when any quantum state is in a state of quantum superposition, neither one state nor the other, and no recordable time is passing. The theory of the Wave function takes over from what is known and bridges that unknown part of quantum physics giving us probabilities about what an outcome might be if it is finally measured.

There is a special relationship with paired electrons or Cooper Pairs and these relate to the property of superconductivity in certain cold substances. It also relates possibly to the recently discovered "liquid light" or mix of photons and electrons at room temperature. I can't tell you much about it since this new property was only discovered very lately. Of course you can "imagine" that liquid light is a stationary quantum phase in electron shells and is facilitated by the emission and absorption of single quanta of specific frequency light that binds to the electrons. I have quite a few cautions with this interpretation... too far ahead of the curve to say for sure. Sorry that this might give you all a headache... it's pretty complicated and Nature is what it is and not what we might like it to be.
Aa' menle nauva calen ar' ta hwesta e' ale'quenle

Good Elf

Posts: 471
Joined: Fri Oct 29, 2010 12:21 am
Location: Brisbane, Australia

### Re: Maxwell's Electromagnetism is a theory of knots

Good Elf wrote:Hi Inertron,

Hi Good Elf, if it wasn't complicated, I would wonder if it was really you posting ;)
If the dance of this wave is wrapped onto the surface of the toroid "with a twist" you end up with the twisted strip model of the electron which is negatively charged on the outside and if you pop it inside out the electron "becomes" a positron with a positive charge on the outside,

You might be able to see that this is in accord with the right hand and left hand grip rule respectively. This matches the particle and antiparticle relationships in the one overall donut structure. This leads to the idea (for me) that the electron and positron are the one particle except that time is running in an opposite direction when compared with the positron (propagating backwards in time)

So all charged particles, including positrons, protons, and anti-protons would all have the same essential toroidal mobius strip charge oscillation/wrapping, and only the direction of time would determine whether they are measured as positive or negative charge? How is it that backward time, if that's possible, would cause the torus/strip to interact with forward-time (opposite charge) particles. E.g. how would a proton and electrons interact and bond due to opposite-direction torus/strip motion?

It's a neat quantum thing as you may very well imagine. Winding numbers 4, 6 are successively heavier versions of the electron... the muon and the Tau particles of the second and third generations of particles... ditto for protons and neutrons and their heavier counterparts. Don't ask how quarks come in except to say it will fit in there somewhere.

Quarks could be a model that has predictive power but fails to hold up relative to this other theory. Quarks basically explain how neutrons and protons have similar weights but different charge. Can this mobius torus theory explain charge neutrality? If a mobius strip only has two sides, that implies only two possibilities for charge, either positive or negative. How could the two sides of the strip neutralize each other? Some oscillatory geometry where the rotating strip configuration flips around causing its charge to oscillate and self-neutralize? What would cause the configuration to enter into this flipping pattern, then, interaction with a neutrino? What about the slight weight difference between neutron and proton? Energy difference between the flipping state and non-flipping state?

The theory of atomic orbitals and electron bonds is a kind of model based on the theory of overlapping bonds in shells and the ability to share paired electrons.

It seems like you'd need some kind of weaving geometry that accounts for electron shells as well as bonding characteristics.

There is no "exact science" for solving for complex many atom systems with even more electrons, only the hydrogen atom with (and without) one electron has been solved exactly. However in Physical Chemistry, according to some, the hydrogen bond theory works pretty well... up to a point. Schrodinger's Equation is all fine and dandy but it appears to follow the same structure as the harmonic solutions using Fourier Theory in three dimensions and time... or spherical harmonics... harmonic resonances on the surface of a sphere.

So these harmonic shape variations of spheres align to causing electron sharing and bonding? And how does a harmonic sphere correspond with the mobius torus?

Schrodinger's Equation still cannot be derived entirely from first principles. It is still a very interesting theory, and it seems to work very well but the theory is never exact because electrons in orbitals are in quantum stationary states and the real theory of all that is still mathematically insoluble.

The Schrodinger idea works to represent particles as dispersed waves that collapse into particles upon interaction. As for the shape of the orbitals, those don't make sense to me. I assume that the electron collapses into a particle when two different waves interact, and if not then they don't. In terms of why they bond, I assume it's because of particle-interaction dynamics like a negative point particle falls into orbit around a foreign ion, which in turn pulls the parent ion closer until that ion either repels away from the other ion due to same-charge repulsion, or because some electrons move to the outside of the molecule causing one ion to become more positively charged and thus pull electrons back away from the ion in whose direction the electrons migrated. This is a tedious explanation, but basically the electrons are sloshing back and forth between the two ions, which keeps the molecule bonded as a system. This is my way of understanding molecular bonding in terms of particles, and the Schrodinger wave-collapse just works because it converts the waves into particles for the sake of interaction with other particles as such.

I see how you could compare the equations and see the mobius torus idea fit with Schrodinger wave theory, but in terms of a mechanical explanation of how the toruses behave as Schrodinger waves, what could that be?

A dynamic theory like Bohr had may not actually exist, the assumptions make that simple model of planetary electrons rotating around the central nucleus incorrect but it is an easy to understand concept for most people to grasp.

Not only is it simple, it opens up the possibility that all configurations of energy/force operate in essentially the same way at different scales. So while we assume particles like electrons and protons to be so precisely quantized in their mass/energy and behavior that they couldn't possibly be organic bodies constituted of much tinier particles, the way a galaxy is constituted from stars, that would be the most logical explanation for everything. Planetary orbits are less eccentric than comets', and the precession of Mercury is considered exeptional, but in theory there is assymmetry in the orbital elipses of all orbiting bodies and if you were able to observe huge periods of time in fast-motion, you might see harmonic patterns in solar systems and galaxies similar to what you are envisioning at the subatomic level. Practically anything tends to normalize as a bell-curve given a large enough sample size, so all the variations we see in astronomical phenomena at our incredibly slow time rate could disappear if we could speed them up and see their oscillation patterns in terms of statistical normalization. So, likewise, we can imagine the same level of variation exists at the subatomic level if we could slow the oscillations down to a speed where we could take snapshots of successive states of the same electron or proton.

OK. You deserve better, but I don't know how to make it so.

Lol! I'm so deserving? I'll take the best shot at truth I can get, which is independent of how deserving or undeserving I might be :)

There is a special relationship with paired electrons or Cooper Pairs and these relate to the property of superconductivity in certain cold substances. It also relates possibly to the recently discovered "liquid light" or mix of photons and electrons at room temperature. I can't tell you much about it since this new property was only discovered very lately. Of course you can "imagine" that liquid light is a stationary quantum phase in electron shells and is facilitated by the emission and absorption of single quanta of specific frequency light that binds to the electrons. I have quite a few cautions with this interpretation... too far ahead of the curve to say for sure. Sorry that this might give you all a headache... it's pretty complicated and Nature is what it is and not what we might like it to be.

I suspect all electrons are always 'infused' with photons, except I would just say they contain energy. Orbiting planets also contain energy that would be released if, say, the Earth was able to drop down to Venus' orbit without accelerating to a speed that would send it hurling out far beyond our current solar-distance. Comets are, in a sense, in an excited state that will gradually 'ground' as they stabilize into a more circular orbit. Still, once stable they still contain energy, just not energy that is as likely to transfer elsewhere since the orbit is more contained in spatial terms.

So electrons could be similar to comets when they are excited, and be more prone to interacting with different objects at different distances from the sun. But when all energy transfers (i.e. collisions) have worked themselves out and things have stabilized into more circular orbits, energy is stably potentiated within the system. So grounded electrons could also be said to contain energy, as can excited electrons, and photonic transfers of energy can be likened to a wave of destabilizations radiating out from a stabilizing system. But how exactly are you saying that these 'liquid light' electrons are absorbing and holding energy in a way that's different from other states of matter?
inertron

Posts: 835
Joined: Sat Aug 13, 2011 2:10 am

### Re: Maxwell's Electromagnetism is a theory of knots

Hi Inertron,
There is a general reminder and a caution that these are not my ideas. I jut look at proposed analogies and see if they fit with experiment. The theories only have to fail in one place experimentally and I throw away the earlier theory replacing it with a more inclusive analogy. Many physicists say analogies are "c**p" but Feynman said they were an important part of his process and I will go with that analysis every time. I will also "resort" to "decomposition" when answering questions here... I am so very sorry about that. Philosophically it is sort of anathema to me. Basically there is a lot of evidence for the Universe being Holographic in nature... that is "As above, so below". The old concept that at some small scale or at some larger scale things (physics) all repeat again. In one sense they do but in another sense they don't. In the smaller scale there is a subatomic particle the heart of which is probably unknown and technically unreachable while on the larger scale something happens on the scale of Galaxies where our physics have some problems describing phenomena there and we also think on a far greater scale, the scale of the Universe, it is some kind of "bubble" and beyond "there be dragons". The edge of our maps. Old maps of the world had edges on them where they decorated the borders with fantastic beasts, the unknown. Well the edge of maps never really stopped there and the world was not flat and to describe the Universe lying beyond, you needed different kinds of maps. When I was told about these odd ideas and funny maps in school I quietly laughed at those who would have drawn them. I knew better than they did... how very smart I thought I was. Nowadays I suddenly realize we have similar problems... and we are coming up with similar solutions by inventing the borders on those new "maps" we have drawn... new kinds of fantastic beasts complete with the same old warning "There be dragons here". Only this is circumscribed by the infinity sign and "no go theorems" and covers to this maths and to preserve it's beautiful symmetry. The quantum/classical singularity at the heart of the sub-atomic particle/Black Hole. Science blushes at the sight of the naked singularity and tries to cover her in "mystery".

A scientist, Laurent Nottale has a kind of fractal theory of the Universe where, as scales become smaller and smaller, you really don't reduce down to a single point... your reach a factional dimension, a "seed" less than one, but certainly greater than zero, things (physics) continue to change but they don't converge down to a single central "point", or to something that solves everything (a Theory of Everything). I don't know if Nottale is right ore wrong, certainly it can be used to verify some known facts but this could be a contrivance. I think we don't know enough yet to be able to say exactly what is the right approach. While humans are cleaver, this is a disturbing thought and their desire for completion in all things drives them to propose solutions that cannot be questioned, remain beyond reproach forever yet provide all the answers to all the problems we propose. There is a branch of theoretical science that say just accept that what we say is right and your problems will all go away. Just recently in high energy physics doubly charmed subatomic particles have been discovered, others discoveries have particles with 5 quarks and so on and on, and the standard answer has been and seems to always be "Who ordered that?" No doubt these anomalies will be "stitched into" our current theories and some will want to forget that there was ever a problem at all. These combinations only make the Standard Model more and more complex. with more and more "free parameters" and none of these extensions were ever predicted.

I don't see a deconstruction solution coming out of these "mathematical woods" anytime soon. You know the old conundrum "How far can a dog run into the woods?" The answer is half way because after then... the dog begins to run out of the woods... that is what is at the heart of all woods and might lurk at the heart on every subatomic particle... absolutely nothing at all.... a kind of "Black Hole". If there is a tiny hole in the heart of the woods you might very well miss it entirely. In fact if it is smaller than the dog... much much smaller than the dog... the dog never actually sees the center of the woods and never actually reaches the center but misses it entirely... running right on past. If there were a "big black hole" at the center of the woods the dog could see it and peer down into it and say to himself that he had found it, the source of his quest. However the dog will never find any black hole at the heart of a woods even though these central things exist in all things and in all of nature and are everywhere in all subatomic matter. It is not that we forbid the dog to go there, the dog can't go there because it is just too small a place to visit. Humans have a similar problem, we can't see into the heart of matter so we use instruments to surrogately "visit" them. In the end our instruments, like ourselves, are built with materials we can manipulate and there are limits of size to this process (well so far anyway). So we can't really "see" infinity small things.

Most mathematical approaches try to understand forces and fields as arising from proposed "point sources" such as the negative charge on an electron is the result of a source of charge -q coulomb (finite electronic charge) concentrated at a single ideal point (having zero volume). In protons and in neutrons there are three interior "point sources" of fractional charge (in the first case sum to the unit one while in the second case sum to zero). If what is being learned recently is true, then at the heart of everything like sub-atomic particles and even Black Holes is absolutely "nothing"... Everything is somewhat like a donut... with a hole in the middle rather than some infinitely tiny point with no dimension where everything goes to infinity. If there were such an entity as a "point charge" the field at the center would rise to infinity and explode due to mutual repulsion where the infinite field values become concentrated at a point somewhat like the big bang itself. The Universe is not exploding around us so this is a false assumption. Unfortunately the maths for describing this kind of object is not something we have developed. All theoretical work since the realization all maths fail at this "Infinity" has been to set up artificial states which avoid discovering what is truly at the "heart of matter". There are two approaches... the first is "String Theory" where you place an undiscoverable almost infinitely small source of particle there at the tiniest range .... the Planck Length. Why? No special reason it was a "good number" to pick so that you can avoid conversion factors such the speed of light, Pi, the Gravitational Constant and Planck's Constant. Gosh it's pretty! Notice I don't have to explain why all those constants are there at all... they just are... it's a postulate. This length was:
${\displaystyle \ell _{\mathrm {P} }={\sqrt {\frac {\hbar G}{c^{3}}}}\approx 1.616\;229(38)\times 10^{-35}\ \mathrm {m} }$
Everybody understands that this length is so small there will never be any direct experimental proof that this theory is unrealistic. I mean never ever ever, even if our civilization persisted for a Billion years. This is paradoxically "small" is actually "big"... the produce the smallest particles in the Universe we make the biggest machine in the world to explore them. The scale in energy is off the charts. The next step may be to make a machine ten times bigger. Well I am not sure the world is prepared to spend that much money for only incremental increases in our understanding. In bangs for buck, the quantum physics of condensed matter is showing far greater theoretical payoffs than that and you can do this research on a benchtop. IMHO what we are doing is to get bigger and bigger "hammers" to crack open smaller and smaller "nuts". All we are making is "nut mash"... or quark-gluon plasma or quark "soup". You have to discover the motives behind this frenetic path of discovery and examine if our money is being spent in the best possible way. My intuition tells me we can't answer the problems being posed in particle physics using more and more energy... that deconstructionist approach. No matter how small a particle is (no matter how great the energy), it is not telling us anything about the fundamental "hole" in the "donut".

inertron wrote:
Good Elf wrote:Hi Inertron,

Hi Good Elf, if it wasn't complicated, I would wonder if it was really you posting ;)

You unfortunately know me very well... at least in that matter.
inertron wrote:
Good Elf wrote:If the dance of this wave is wrapped onto the surface of the toroid "with a twist" you end up with the twisted strip model of the electron which is negatively charged on the outside and if you pop it inside out the electron "becomes" a positron with a positive charge on the outside,

You might be able to see that this is in accord with the right hand and left hand grip rule respectively. This matches the particle and antiparticle relationships in the one overall donut structure. This leads to the idea (for me) that the electron and positron are the one particle except that time is running in an opposite direction when compared with the positron (propagating backwards in time)

So all charged particles, including positrons, protons, and anti-protons would all have the same essential toroidal mobius strip charge oscillation/wrapping, and only the direction of time would determine whether they are measured as positive or negative charge? How is it that backward time, if that's possible, would cause the torus/strip to interact with forward-time (opposite charge) particles. E.g. how would a proton and electrons interact and bond due to opposite-direction torus/strip motion?

It is not a physical wrapping any more than Special Relativity rules out the existence of different kinds of external observations which led to very strange optical features such as relativistic optical aberration. "Time running backwards" is an observation made from within a "relativistic frame of reference". The electron and positron are actually the one particle seen from two different vantage points centered around the speed of light. When particle and antiparticle are created in a high energy accelerator the direction of time is supposed to increase away from the source of that event. Feynman said while his Fenyman diagrams are very useful they are not fully representative of all ways to interpret it. That interpretation of particle creation events led to his famous Bombardier Analogy. You may read more about that in the thread Time and it role in quantum theory.
Inertron wrote:
Good Elf wrote:It's a neat quantum thing as you may very well imagine. Winding numbers 4, 6 are successively heavier versions of the electron... the muon and the Tau particles of the second and third generations of particles... ditto for protons and neutrons and their heavier counterparts. Don't ask how quarks come in except to say it will fit in there somewhere.

Quarks could be a model that has predictive power but fails to hold up relative to this other theory. Quarks basically explain how neutrons and protons have similar weights but different charge. Can this mobius torus theory explain charge neutrality? If a mobius strip only has two sides, that implies only two possibilities for charge, either positive or negative. How could the two sides of the strip neutralize each other? Some oscillatory geometry where the rotating strip configuration flips around causing its charge to oscillate and self-neutralize? What would cause the configuration to enter into this flipping pattern, then, interaction with a neutrino? What about the slight weight difference between neutron and proton? Energy difference between the flipping state and non-flipping state?
I have read only theories about electrons. Quarks are another kind of event. On the way the nucleus affects the electronic behavior of atoms there is considerable evidence that the astute placement of nanoparticles can cause the expression or repression of the properties of the atomic shells independent of any electrons that may be appearing to form them. If you consider the electron shells of atoms to be the "antenna" property of the sub-atomic radiating parameters inside the nucleus then the sub-nuclear dipole oscillators "generate" the electronic shells by way of their Spherical Harmonics in the "near-field" or "evanescent field".

This relates to an article: New Path For Designing Novel Nanomaterials Discovered - Science Daily - 13 Oct 2007.
What is simulated by this image are the effect of nearby nanoparticles on the dz2 orbital (far left) being altered through the interposing of nanoparticle shells (center) into a dyz orbital (far right). It would seem to be a subnuclear resonance with the nuclear charged quarks.

While "electrons" are captured by these radiant shells generated in the nucleus, they are in no part the result of the electrons outside the nucleus and it's charge but the effect of the charge in the nucleus originating in the quark constituents. I like the mobius idea but this does not strictly apply to the electron or any other particles that I know because the winding number is 2 (or spin ½). This is a whole "twist" in the twisted strip model according to Williamson and van der Mark, not a half twist as is the case in a mobius strip. This means as it is rotated it only undergoes a half flip for each full rotation and only returns to it's original state after two full rotations.The twisted strip is a double loop with one full twist. The orbitals beyond the nucleus are related to the "inner orbitals" of the quark nucleus not any independent property "generated" by the electrons outside that nucleus by themselves. The reality of Fourier generated extra nuclear "shells" are the result of the evanescent electromagnetic field central nuclear dipole sources. It is "frozen" in place due to quantization phenomena. Quick examination of the symmetry of Fourier theory shows that "electron shells" are related to central nuclear symmetry and not outer electron symmetry. It is also interesting to note the shells (which are evanescent EM fields) are not generated by electrons which is the way all other EM fields, such as radio antennas, humans use to generate electromagnetic effects. This following illustration show all d orbitals in nuclear theory however in a particular target material (above) the sub-nuclear resonance has been shifted to generate different kinds radiation lobes in the dz2 orbital, in the near field that now appear to be deemphasized in this particular material now emphasized as dyz orbital.

This is related to recent theory and experiments developed regarding stationary states called (paradoxically) Anapole radiation. I will just put a link to that topic here. New theory leads to radiationless revolution - PhysOrg - 1509-2015

On the other hand quantum states are not "flipping around" all over the place, they are stationary states. Quantum states only "flip" when they are not stationary. At that instant they are no longer sitting quietly in a quantum state. In general there are no really consistent solutions for these states. When electrons or photons are going someplace another theory is in place, the Universe is a kind of open waveguide. Neither electrons nor photons will emit or "jump" unless they have individually negotiated (transacted) a site to be absorbed. When an electron "jumps" it is called wave mechanical barrier penetration or quantum tunneling. Both electrons and protons "jump" or "tunnel" while the photons are emitted or absorbed but do not tunnel but "escape" confinement through propagation. The jumping behavior is related to protons and electrons (or fermions) being particles while the photons propagating behavior is related to bosons being light-like. We know that at it's core particles are actually waves too and we have spoken about this earlier in the thread. The behavior of electrons and photons are not exactly the same, the electron obeys Fermi-Dirac Rules while photons obey Bose-Einstein Rules and that depends on the winding number. For example electrons "jumping" physically from orbital to orbital are doing so in full integer steps but the intrinsic properties of the electron such as spin are in half integer steps. It is as though the nucleus and the electrons are half integer quantities while the structure they are all jumping around in is a full interger boson resonant structure. Indeed it is because the orbitals of the atom (minus the electrons) is a solution to the Spherical Harmonics Equations. The strong hunch here is the nucleus is partnering those boson shells outside the nucleus. The differences between these two different types of steps seem to force "space quantization". The electrons are half integer waves or fermions, while the structure they resonate in (electronic shells) are integer waves not caused by electrons themselves but caused by the nucleus(fermions), and those external shells are resonating as bosons in their interior nature.
Inertron wrote:
Good Elf wrote:The theory of atomic orbitals and electron bonds is a kind of model based on the theory of overlapping bonds in shells and the ability to share paired electrons.

It seems like you'd need some kind of weaving geometry that accounts for electron shells as well as bonding characteristics.
The interaction of electrons inside those shells is described by the way pairs of electrons can magnetically pair up over somewhat long distances as Cooper Pairs. This pairing is like this ↑↓. Such pairing also occur in particles and antiparticles created from the same source. However the former electron-electron (--) interaction is a repulsion while the electron-positron (-+) interaction is attraction and eventually to annihilation. Regarding electrons only, these "pairs" occur in liquid (and solid) superconductors and these mutually repelling yet mutually confining electrons lead to ideal friction-less electric conduction which is what is being sought. Currents which can circulate forever. What is probably eventually required to create room temperature superconductors is an externally penetrating field to align the pairs. These fields may be seen in part in the "liquid-light" example, which is a kind of room temperature superconductor or Bose-Einstein Condensate already, where the plasmons align near the boundary of the containing surface where there is a topological insulator. See: ‘Liquid Light’ Can Bend Around Objects in a Frictionless Flow - Seeker - 08 June 2017.

Inertron wrote:
Good Elf wrote:There is no "exact science" for solving for complex many atom systems with even more electrons, only the hydrogen atom with (and without) one electron has been solved exactly. However in Physical Chemistry, according to some, the hydrogen bond theory works pretty well... up to a point. Schrodinger's Equation is all fine and dandy but it appears to follow the same structure as the harmonic solutions using Fourier Theory in three dimensions and time... or spherical harmonics... harmonic resonances on the surface of a sphere.

So these harmonic shape variations of spheres align to causing electron sharing and bonding?The electron is the perfect "smoke ring" or torus, the nucleus is the source of that harmonic shell structure. The resonances on the surface of the Fourier Harmonic sphere are due to the central symmetry of the non-radiating nucleus. The electrons are attracted to the positive "charge" on the nucleus but cannot approach it due to space quantization. And how does a harmonic sphere correspond with the mobius torus?
Well it is not strictly a mobius torus but ignoring that, this spherical resonance the electrons are captured in is coming from the spherical harmonics of radiators embedded in the nucleus just like in a tiny non-radiating superconducting radio antenna that is indicative of several elementary dipole radiators in the nucleus which are embedded inside of and coming from the protons and neutrons themselves... which are actually charged as we all know but are superconductors... even the neutrons at that quark level have a vestigial radiation pattern. While materials like a bar of steel or copper exhibit some resistivity at room temperature, these individual sub-atomic particles in the nucleus of those atoms are individually superconductors, even at room temperature, and it is just through their mutual interaction they lose that ideal property due to externally introduced thermal bonding noise. If you liker the temperature enough, the bar of metal eventually will be come a superconductor at close to absolute zero degrees Kelvin when that sub-atomic superconductivity "spreads" to the adjoining quantum states and forms growing "puddles" of superconductivity.

Inertron wrote:
Good Elf wrote:Schrodinger's Equation still cannot be derived entirely from first principles. It is still a very interesting theory, and it seems to work very well but the theory is never exact because electrons in orbitals are in quantum stationary states and the real theory of all that is still mathematically insoluble.

The Schrodinger idea works to represent particles as dispersed waves that collapse into particles upon interaction. As for the shape of the orbitals, those don't make sense to me. I assume that the electron collapses into a particle when two different waves interact, and if not then they don't. In terms of why they bond, I assume it's because of particle-interaction dynamics like a negative point particle falls into orbit around a foreign ion, which in turn pulls the parent ion closer until that ion either repels away from the other ion due to same-charge repulsion, or because some electrons move to the outside of the molecule causing one ion to become more positively charged and thus pull electrons back away from the ion in whose direction the electrons migrated. This is a tedious explanation, but basically the electrons are sloshing back and forth between the two ions, which keeps the molecule bonded as a system. This is my way of understanding molecular bonding in terms of particles, and the Schrodinger wave-collapse just works because it converts the waves into particles for the sake of interaction with other particles as such.

I see how you could compare the equations and see the mobius torus idea fit with Schrodinger wave theory, but in terms of a mechanical explanation of how the toruses behave as Schrodinger waves, what could that be?
Complicated question but Schrodinger's Equation is a special case of the wave equation which is only an equation that shows how to minimize energy in a system for how to solve for atoms not how to solve primarily for electrons. Solving for electrons is a secondary property that the electrons solve among themselves.

Note that after knowing the potential and kinetic energy of a system the main purpose is to find time independent solutions to the equation which are "energy eigenvalues"... or in plain speaking... stationary states... states which do not change. As noted previously the dynamics of the system obey other rules such as the tunneling of protons or neutrons or electrons or the emission and propagation and finally the absorption of the photons. These are the stationary aspects (non-dissipative) character of the atom which neither loses or gains energy but simply moves it around the boundary states. This is similar to the solutions of standing sound waves on a resonant plate (Chladni Plate) as applied the science of cymatics... similar wave equation differnet physics... in this case sound and how it entraps particles such as grains of sand.

Figure 3—Notes on a Piano as Cymatic Images (cymascope.com)
These are the notes on a piano acting on the scattering of light by fine particles in a CymaScope or sand on a plates of various shapes (in this case they are all circular). Similar problem in quantum physics only the boundary is not a plate but a 3D spherical barrier and the arrangements of electrons inside that boundary is determined not by the electrons themselves but primarily by the spherical harmonics generated from the nucleus confined by that "3D spherical quantum well". The electrons only form stationary patterns in it through a mutual resonance and attractive repulsions. For atoms it is a very complicated 3D problem.
See:How Sound Affects You: Cymatics, An Emerging Science - Ask Audio - 2311-2014

Inertron wrote:
Good Elf wrote:A dynamic theory like Bohr had may not actually exist, the assumptions make that simple model of planetary electrons rotating around the central nucleus incorrect but it is an easy to understand concept for most people to grasp.

Not only is it simple, it opens up the possibility that all configurations of energy/force operate in essentially the same way at different scales. So while we assume particles like electrons and protons to be so precisely quantized in their mass/energy and behavior that they couldn't possibly be organic bodies constituted of much tinier particles, the way a galaxy is constituted from stars, that would be the most logical explanation for everything. Planetary orbits are less eccentric than comets', and the precession of Mercury is considered exceptional, but in theory there is asymmetry in the orbital ellipses of all orbiting bodies and if you were able to observe huge periods of time in fast-motion, you might see harmonic patterns in solar systems and galaxies similar to what you are envisioning at the subatomic level. Practically anything tends to normalize as a bell-curve given a large enough sample size, so all the variations we see in astronomical phenomena at our incredibly slow time rate could disappear if we could speed them up and see their oscillation patterns in terms of statistical normalization. So, likewise, we can imagine the same level of variation exists at the subatomic level if we could slow the oscillations down to a speed where we could take snapshots of successive states of the same electron or proton.
Well the rigid harmonic relationships of all the known planets in the "potentially habitable star system" called Trappist 1. But I cannot comment on that because it is a dynamic system and behaves classically not "quantumly". The wave function only describes the quantum stationary states.

Inertron wrote:
Good Elf wrote:OK. You deserve better, but I don't know how to make it so.

Lol! I'm so deserving? I'll take the best shot at truth I can get, which is independent of how deserving or undeserving I might be :)
Good Elf wrote:There is a special relationship with paired electrons or Cooper Pairs and these relate to the property of superconductivity in certain cold substances. It also relates possibly to the recently discovered "liquid light" or mix of photons and electrons at room temperature. I can't tell you much about it since this new property was only discovered very lately. Of course you can "imagine" that liquid light is a stationary quantum phase in electron shells and is facilitated by the emission and absorption of single quanta of specific frequency light that binds to the electrons. I have quite a few cautions with this interpretation... too far ahead of the curve to say for sure. Sorry that this might give you all a headache... it's pretty complicated and Nature is what it is and not what we might like it to be.

I suspect all electrons are always 'infused' with photons, except I would just say they contain energy. Orbiting planets also contain energy that would be released if, say, the Earth was able to drop down to Venus' orbit without accelerating to a speed that would send it hurling out far beyond our current solar-distance. Comets are, in a sense, in an excited state that will gradually 'ground' as they stabilize into a more circular orbit. Still, once stable they still contain energy, just not energy that is as likely to transfer elsewhere since the orbit is more contained in spatial terms.

So electrons could be similar to comets when they are excited, and be more prone to interacting with different objects at different distances from the sun. But when all energy transfers (i.e. collisions) have worked themselves out and things have stabilized into more circular orbits, energy is stably potentiated within the system. So grounded electrons could also be said to contain energy, as can excited electrons, and photonic transfers of energy can be likened to a wave of destabilizations radiating out from a stabilizing system. But how exactly are you saying that these 'liquid light' electrons are absorbing and holding energy in a way that's different from other states of matter?
I take that as comment. Good for you. I think that is the Electric Universe concept. For me the scale is not quite right. For example the scale of a quantum on the size of a galaxy is huge. It has little hope of dissipating and little hope of being emitted or absorbed. But it seems to affect it's motion on that scale, it behaves like a rigid rotating object like a wagon wheel, with embedded smaller scale semi-classical objects like us for example. At even smaller scale there is an even more striking quantum process that we see there and we are currently studying that right now. Time on the vastly larger scale and the infinitely smaller scale is different to the time on our quantum scale. Quantum entanglement play their role at each quantum level. Some photons created at the big bang are easily as big as galaxies and remain attached to their sources. The galaxy is "dragging it's feet" pulling all this entanglement baggage behind it as "quantum spacetime". We all exist at different scales but immersed in these various interpenetrating quantum phases, some superconducting and others not so much. Quantum Theory will always relate to just the stationary states and emission and absorption of photons are the dynamic states like in an open wave guide Universe where the source and sinks pre-negotiate the balancing of the transmitter load to the sink complex impedance. These are the results of Absorber Theory, The Transactional Interpretation of quantum theory or Feynman's Pet Theory. This is a block Universe where the retrocausality and causality interact in their wavefronts forming the illusion of particles. On the other hand Black Holes are something else and so are sub-atomic particles. There is far too much here. It is like trying to assemble a huge jigsaw puzzle, one small piece at a time. That is just an opinion of course Inertron.

Cheers... and thanks again for the questions.
Aa' menle nauva calen ar' ta hwesta e' ale'quenle

Good Elf

Posts: 471
Joined: Fri Oct 29, 2010 12:21 am
Location: Brisbane, Australia

### Re: Maxwell's Electromagnetism is a theory of knots

Good Elf wrote:Hi Inertron,
There is a general reminder and a caution that these are not my ideas. I jut look at proposed analogies and see if they fit with experiment. The theories only have to fail in one place experimentally and I throw away the earlier theory replacing it with a more inclusive analogy. Many physicists say analogies are "c**p" but Feynman said they were an important part of his process and I will go with that analysis every time. I will also "resort" to "decomposition" when answering questions here... I am so very sorry about that. Philosophically it is sort of anathema to me. Basically there is a lot of evidence for the Universe being Holographic in nature... that is "As above, so below". The old concept that at some small scale or at some larger scale things (physics) all repeat again. In one sense they do but in another sense they don't. In the smaller scale there is a subatomic particle the heart of which is probably unknown and technically unreachable while on the larger scale something happens on the scale of Galaxies where our physics have some problems describing phenomena there and we also think on a far greater scale, the scale of the Universe, it is some kind of "bubble" and beyond "there be dragons". The edge of our maps. Old maps of the world had edges on them where they decorated the borders with fantastic beasts, the unknown. Well the edge of maps never really stopped there and the world was not flat and to describe the Universe lying beyond, you needed different kinds of maps. When I was told about these odd ideas and funny maps in school I quietly laughed at those who would have drawn them. I knew better than they did... how very smart I thought I was. Nowadays I suddenly realize we have similar problems... and we are coming up with similar solutions by inventing the borders on those new "maps" we have drawn... new kinds of fantastic beasts complete with the same old warning "There be dragons here". Only this is circumscribed by the infinity sign and "no go theorems" and covers to this maths and to preserve it's beautiful symmetry. The quantum/classical singularity at the heart of the sub-atomic particle/Black Hole. Science blushes at the sight of the naked singularity and tries to cover her in "mystery".

Maybe one day people will look back on mathematical ideas like infinity and singularities and view them the way we view the idea of dragons today.

A scientist, Laurent Nottale has a kind of fractal theory of the Universe where, as scales become smaller and smaller, you really don't reduce down to a single point... your reach a factional dimension, a "seed" less than one, but certainly greater than zero, things (physics) continue to change but they don't converge down to a single central "point", or to something that solves everything (a Theory of Everything). I don't know if Nottale is right ore wrong, certainly it can be used to verify some known facts but this could be a contrivance. I think we don't know enough yet to be able to say exactly what is the right approach. While humans are cleaver, this is a disturbing thought and their desire for completion in all things drives them to propose solutions that cannot be questioned, remain beyond reproach forever yet provide all the answers to all the problems we propose. There is a branch of theoretical science that say just accept that what we say is right and your problems will all go away. Just recently in high energy physics doubly charmed subatomic particles have been discovered, others discoveries have particles with 5 quarks and so on and on, and the standard answer has been and seems to always be "Who ordered that?" No doubt these anomalies will be "stitched into" our current theories and some will want to forget that there was ever a problem at all. These combinations only make the Standard Model more and more complex. with more and more "free parameters" and none of these extensions were ever predicted.

I saw that news about a particle with double charge and quadruple weight, and I wondered how it was different from helium4. It does seem analogous to the way a neutron looks like a compressed hydrogen atom, though, doesn't it? Maybe we will discover that there is a type of quantum state where electrons and protons can be compressed into a much smaller dimension, and this state can be achieve with any atom of any size, effectively rendering it a neutronic elemental particle. There could be a whole periodic table of neutrons; a 'shadow' periodic table you could say, for dramatic effect.

I don't see a deconstruction solution coming out of these "mathematical woods" anytime soon. You know the old conundrum "How far can a dog run into the woods?" The answer is half way because after then... the dog begins to run out of the woods... that is what is at the heart of all woods and might lurk at the heart on every subatomic particle... absolutely nothing at all.... a kind of "Black Hole". If there is a tiny hole in the heart of the woods you might very well miss it entirely. In fact if it is smaller than the dog... much much smaller than the dog... the dog never actually sees the center of the woods and never actually reaches the center but misses it entirely... running right on past. If there were a "big black hole" at the center of the woods the dog could see it and peer down into it and say to himself that he had found it, the source of his quest. However the dog will never find any black hole at the heart of a woods even though these central things exist in all things and in all of nature and are everywhere in all subatomic matter. It is not that we forbid the dog to go there, the dog can't go there because it is just too small a place to visit. Humans have a similar problem, we can't see into the heart of matter so we use instruments to surrogately "visit" them. In the end our instruments, like ourselves, are built with materials we can manipulate and there are limits of size to this process (well so far anyway). So we can't really "see" infinity small things.

What interests me about black holes these days isn't the black hole itself, but the material surrounding it and how that material behaves differently because it surrounds a black hole instead of another gravitational body of like mass. Presumably there should be some turbulence lost as material disappears within the event horizon, while outside the horizon, turbulence affects both the capture rate of the hole as well as the energy-transfer rate away from the hole. If black holes anchored particles at their centers, I would want a theory that addresses how aspects of macro-sized black holes and the behaviors surrounding them are analogous to the tiny black hole phenomena. Otherwise, I wouldn't see the point of considering them as black holes in the first place.

Everybody understands that this length is so small there will never be any direct experimental proof that this theory is unrealistic. I mean never ever ever, even if our civilization persisted for a Billion years. This is paradoxically "small" is actually "big"... the produce the smallest particles in the Universe we make the biggest machine in the world to explore them. The scale in energy is off the charts. The next step may be to make a machine ten times bigger. Well I am not sure the world is prepared to spend that much money for only incremental increases in our understanding. In bangs for buck, the quantum physics of condensed matter is showing far greater theoretical payoffs than that and you can do this research on a benchtop. IMHO what we are doing is to get bigger and bigger "hammers" to crack open smaller and smaller "nuts". All we are making is "nut mash"... or quark-gluon plasma or quark "soup". You have to discover the motives behind this frenetic path of discovery and examine if our money is being spent in the best possible way. My intuition tells me we can't answer the problems being posed in particle physics using more and more energy... that deconstructionist approach. No matter how small a particle is (no matter how great the energy), it is not telling us anything about the fundamental "hole" in the "donut".

The funding is geared toward controlling the engineering/industrial resources that have the capacity to build these things, because some people want to be masters of such technology. The physics that comes out of them is interesting data (isn't all fresh data interesting, after all?) but the really good science, imo, comes when micro-scale mechanics are linked to observable phenomena they 'build up' to influence. So, with neutrinos, for example; they interested me very little before I considered that they could play some critical formative role in transmitting information/energy between the sun and planets. So the fact that neutrino observatories can be built is neither here nor there; except to the extent those observatories provide a glimpse of what kind of neutrino chemistry could be happening elsewhere in the core/mantle. If and when we can connect neutrinos to observable aspects of planetary geology, and differentiate how planets would behave in the absence of neutrino reactions from how they behave in dialogue with neutrinos, that is when neutrino science really comes to fruition. All the experiments, reactors, detectors, etc. are all amazing feats of engineering as well as theory, methodology, etc. but they are all really just stepping stones to the holy grail that emerges when their findings culminate in a new model of reality, or revision to an existing model that shows how something tiny impacts the universe broadly at other scales.

I have read only theories about electrons. Quarks are another kind of event. On the way the nucleus affects the electronic behavior of atoms there is considerable evidence that the astute placement of nanoparticles can cause the expression or repression of the properties of the atomic shells independent of any electrons that may be appearing to form them. If you consider the electron shells of atoms to be the "antenna" property of the sub-atomic radiating parameters inside the nucleus then the sub-nuclear dipole oscillators "generate" the electronic shells by way of their Spherical Harmonics in the "near-field" or "evanescent field".

Yes, I agree that the electron orbitals are really the guide-fields produced by the nucleus for the electrons to inhabit and not the electrons themselves. But to the extent that the shapes of these guide fields define the ion's parameters for interactions and relationships/bonds with other ions via electrons, they are significant. When you say they are stationary states, I have a problem with that because I don't see how two ions with separate orbitals can interlink via shared electrons without moving relative to each other. I supposed you could say that the orbitals overlap and that as long as they do, there is a probability that the shared electron will occupy the intersection between them and thus hold the ions together. But is this possible, or would the electron's charge neutralize the positive charge of one ion/orbital and thus be unavailable for the other ion/orbital to do the same, and so the un-neutralized ion would be pulled toward other electrons elsewhere?

While "electrons" are captured by these radiant shells generated in the nucleus, they are in no part the result of the electrons outside the nucleus and it's charge but the effect of the charge in the nucleus originating in the quark constituents.

It seems like the electrons should have their own patterns of charge-density that occur separately from the protonic guide fields of the ions/orbitals. If two ionized nuclei overlap orbitals in a plasma state, for example, their orbitals should repel each other because of same-charge repulsion. If, however, the plasma cools enough for the electrons to condense around the ions, some electrons should enter into the situation and fall into an orbital pattern within/between the overlapping orbital guide-fields of the adjacent ions, causing them to bond. So when the electrons are outside the shells, as per plasma, they should organize into some kind of pattern and not just fly around the universe randomly in all directions. Maybe we have to understand that all space consists of magnetic fields that guide charged particles, including electrons along field lines in such a way that none can ever really escape the magnetic topography of the particular region of space they are in.

I like the mobius idea but this does not strictly apply to the electron or any other particles that I know because the winding number is 2 (or spin ½). This is a whole "twist" in the twisted strip model according to Williamson and van der Mark, not a half twist as is the case in a mobius strip. This means as it is rotated it only undergoes a half flip for each full rotation and only returns to it's original state after two full rotations.The twisted strip is a double loop with one full twist. The orbitals beyond the nucleus are related to the "inner orbitals" of the quark nucleus not any independent property "generated" by the electrons outside that nucleus by themselves. The reality of Fourier generated extra nuclear "shells" are the result of the evanescent electromagnetic field central nuclear dipole sources. It is "frozen" in place due to quantization phenomena. Quick examination of the symmetry of Fourier theory shows that "electron shells" are related to central nuclear symmetry and not outer electron symmetry. It is also interesting to note the shells (which are evanescent EM fields) are not generated by electrons which is the way all other EM fields, such as radio antennas, humans use to generate electromagnetic effects. This following illustration show all d orbitals in nuclear theory however in a particular target material (above) the sub-nuclear resonance has been shifted to generate different kinds radiation lobes in the dz2 orbital, in the near field that now appear to be deemphasized in this particular material now emphasized as dyz orbital.

The mobius strip math is an interesting aside but I still don't see how it explains anything about the sub-atomic behaviors.

On the other hand quantum states are not "flipping around" all over the place, they are stationary states. Quantum states only "flip" when they are not stationary. At that instant they are no longer sitting quietly in a quantum state. In general there are no really consistent solutions for these states. When electrons or photons are going someplace another theory is in place, the Universe is a kind of open waveguide. Neither electrons nor photons will emit or "jump" unless they have individually negotiated (transacted) a site to be absorbed. When an electron "jumps" it is called wave mechanical barrier penetration or quantum tunneling. Both electrons and protons "jump" or "tunnel" while the photons are emitted or absorbed but do not tunnel but "escape" confinement through propagation. The jumping behavior is related to protons and electrons (or fermions) being particles while the photons propagating behavior is related to bosons being light-like.

I think there has to be something about the wave-collapse that allows light/photons to propagate more smoothly than the fermions. Ion trajectories in plasma get very curly very quickly as temperature falls and allows the electrons and protons to capture each other. The extremely tight curvature of the charged fields within the de-ionized atom would seem to be responsible for the ability of the photon to be captured and absorbed as an excited state within the atomic electron. It is as if the photon jumps into and out of the atom when it is absorbed and re-emitted, but its smooth motion outside of atomic electron capture would seem to be possible by virtue of the presence of uncollapsed charge-fields whose uncollapsed state allows the photon to proceed smoothly without jumping the way does into and out of atomic electrons.

The differences between these two different types of steps seem to force "space quantization". The electrons are half integer waves or fermions, while the structure they resonate in (electronic shells) are integer waves not caused by electrons themselves but caused by the nucleus(fermions), and those external shells are resonating as bosons in their interior nature.

This sounds mathematically interesting, but I don't exactly understand how the half and whole integer spaces interact, and why it is relevant that they are different.

Regarding electrons only, these "pairs" occur in liquid (and solid) superconductors and these mutually repelling yet mutually confining electrons lead to ideal friction-less electric conduction which is what is being sought. Currents which can circulate forever. What is probably eventually required to create room temperature superconductors is an externally penetrating field to align the pairs.

Conductivity grows more efficient as the ions/nucle within the conductor are frozen against motion, and thus against usurping energy from the current flowing through the electrons. Metals all have surplus 'loose' electrons that weakly bond their outer shells together, and so those electrons can oscillate relatively independently of the nuclei that anchor them. When you say that an 'externally penetrating field' will 'align the pairs,' I don't understand what difference it makes for pairs of electrons to be 'aligned' or not. Is there some reason they are more likely to transfer energy to the nuclei when they are not aligned?

That's all I have time for right now. Nice discussion. More later.
inertron

Posts: 835
Joined: Sat Aug 13, 2011 2:10 am

### Re: Maxwell's Electromagnetism is a theory of knots

Hi Inertron,

Inertron wrote:That's all I have time for right now. Nice discussion. More later.

Some very interesting comments there. I don't disagree with most of them so there is no need for any further comment from me. There are a couple of points that I may have glossed over and you seem to have found them. Naturally I am not an expert on everything so I will try and be brief... if that is at all possible for me.

Inertron wrote:What interests me about black holes these days isn't the black hole itself, but the material surrounding it and how that material behaves differently because it surrounds a black hole instead of another gravitational body of like mass.
Some speculation is necessary. The mass of a Black Hole is not concentrated at it's center. What I mean by that is the effect of the mass of every object has it's greatest deforming effect at the surface where the acceleration due to gravity is a maximum. If a Black Hole is going to form, it must form at a point at which the gravitational stress is a maximum. An object that is in the last state of gravitational collapse begins by shrinking in radius. If you treat a Black Hole as a point source then it's mass is concentrated at it's center. However it is clear that a Black Hole starts as a massive body like a cooling star in which the density of the body is collapsing under it's own mass and the radius of the body is becoming less over time. It does not shrink to a point but at a critical size approximately equivalent 3.8 times the mass of our sun (minimum) and it's "final" radius will be 12 Km radius (or 24 Km diameter). Assuming the acceleration due to gravity increases at the surface the acceleration due to gravity decreases as you enter the surface of the sphere and move towards the exact geometric center, where the acceleration due to gravity is identically zero at all times. This is because the aceleration due to gravity is the same from all directions and as a vector quantity it will cancel out. It is a well known Geophysical Result:
Tutor for Physics site wrote:Formula: Acceleration due to gravity inside the Earth

Here let r represent the radius of the point inside the earth. The formula for finding out the acceleration due to gravity at this point becomes:

g' = ( r / re )g

In both the above formulas, as expected, g' becomes equal to g when r = re.

The formula is not only appropriate for inside the earth but any solid. It's no that different for a star while it remains sub-critical. There are also hydrostatic effects as well, effects due solely to the overlying (fluid?) material. For the same reasons at the center of a star, those hydrostatic pressures are from all sides directed to the center, hence they all cancel at that center as well.
If the star is hot enough it may turn into a white dwarf before it collapses into a Black Hole. The electrons will be squeezed out of the electronic shells and it will form a surface conduction layer of electrons at the surface of the star while the interior will become a compressed fluid composed of charged nucleii a nearly degenerate superfluid surrounding a degenerate supersolid core. This nucleus at the core of a star will be self repelling (composed of all mostly positively charged particles) and so will not be being forced any further together (assuming almost all the nuclear fuel is used up). So at the center of a star, for the same reasons given for the other two forces, this force too will approach zero at the center as well. Everything zero at center but the acceleration due to gravity is a maximum at the surface. Not certain what modifying effects those other pressures will have, perhaps these pressures add to the overall stress energy density and move the critical stress into the surface... but it can't reach a maximum at the center where all the forces are cancelled out. My "intuition" suggests this forms a kind of "cookie cutter" punching out a hole near the radius of the star as it approaches the critical density.and the star collapses into the hole punching out a wormhole, the surface of the star is replaced by the new surface of spacetime which is like a pipe with nothing in it's interior. Since it has punched out spacetime itself the center of the hole contains absolutely nothing.... no surface of spacetime.... the surface of spacetime is now formed around the walls of the hole. This is a two dimensional surface or more accurately a two plus a small fractional dimensional surface or a spacetime defect and a source of a fractal spacetime, not three dimensional space at all. Regarding time, others have suggested that the role of space and time are at least partially exchanged.... perhaps not.

Some figures for the smallest stable Black Hole are here: Smallest Black Hole Found - Space - 0104-2008

Inertron wrote:I think there has to be something about the wave-collapse that allows light/photons to propagate more smoothly than the fermions.
Wavefunction-collapse is an odd concept. If you accept that Quantum Field Theory is correct there is a wavefunction for all classes of particles individually. For example there would be a wavefunction for photons but this wavefunction is a global property ... it covers the entire Universe. So a more realistic assumption is the entire Universe does not collapse for every quantum event that happens, but perhaps the wavefunction collapses is local to a smaller region after an event and within a short time "recovers" to the undiscovered state which is the wavefunction in quantum superposition. On the other hand there is a difference between the wavefunction of photons and the wavefunction of particles like electrons, protons and neutrons. The photon can be created without numerical conservation laws and are "on demand". They are also destroyed "on demand". IMHO these creation and destruction events are related to the initiation of the Advanced and Retarded wavefronts at sink and source respectively. The particle (photon) is detectable at the confluence of these two waves (there is some experimental justification for this nowadays as "whirling waves" and as a Dynamic Casimir Effect).... Two-State Vector Formalism -treatments by Lev Vaidman, Yakir Aharonov and originally proposed in 1942 as Wheeler–Feynman absorber theory. Today it's main proponent is Ruth Kastner. An imaginative picture of this analogy would be...

However a detection of the photon there virtually "creates" the photon "by observation".

Alternatively particles like the wavefunction of photons and the wavefunction of particles like electrons, protons and neutrons, while still global, are subject to conservation laws, they cannot be singly destroyed nor created. While in other respects they are the same these waves are "knotted" ... but don't take this analogy too far just now... is it an actual granny knot, I don't know. I just don't want to say that the knot is unravelable without an "antiknot"... it's matching antiparticle. So, since the Big Bang these are all these permanent knots in the electromagnetic field hanging about without any "antiknot" to mate up with. I prefer to think of this as dynamic standing wave rather than a stationary "charged" entity... which is what I think is the correct answer. So a quantum "jump" is all that is available to a particle which are subject to Emmy Noether's Conservation Laws or Noether's Theorem which states: "If a system has a continuous symmetry property, then there are corresponding quantities whose values are conserved in time." So you can get a hint as to what is conserved globally... all the properties we usually call "particles".

Inertron wrote:When you say that an 'externally penetrating field' will 'align the pairs,' I don't understand what difference it makes for pairs of electrons to be 'aligned' or not. Is there some reason they are more likely to transfer energy to the nuclei when they are not aligned?
A pair of electrons, which are both half integer fermion quantum states, will form a even quantum state when they team up and form a boson. The principle occurs everywhere in nature. Actually in the bulk of a superconductor all electrons are paired as "Cooper Pairs", but because they are of a similar charge polarity they also repel.... they form structures similar to "vortex tunnels" spanning the superfluid interface and pairs of electrons create a very high mutual surface tension. Type II Superconductors align these vortices vertically in a rotating disk of liquid Helium for example. Helium is an inert gas and does not conduct electricity... it also doesn't form ions. Electrons are also forming these structures in the outer shell structures of atoms as discussed above. With liquid Helium it formed the very first known Bose-Einstein Condensate which is a superfluid and a single macro quantum state and it can act like a viscous liquid having a kind of internal "perpetual motion" and also having virtually a very large surface tension and allow Helium to become entangled and to climb out of a vessel and over it's lip... "If you march in unison, you don't collide with each other," that marching in unison is quantum entanglement. See the article in Scientific American here:Strange but True: Superfluid Helium Can Climb Walls - Sci Am - 2002-2009. The superfluid is very closely related to the properties of the nucleus.... while it is not the actual properties of an actual nucleus, there are many "parallels" with it, electrons and the nucleus of atoms being superfluids themselves. In some respects at the heart of all matter are "black hole" like structures or Electromagnetic Black Holes.... these tunneling vortices between opposing aligned electrons and also between entangled protons and neutrons too. Condensed Matter processes, in the form of Bose Einstein Condensates (BEC), convert half integer Fermion matter waves into whole integer Bosons which are single macroscopic quantum states are all occupying the same volume as just one of them alone. Materials can have differing phases whose components can be Bosons and Fermions at the one time depending on the treatment. All Bosons have light-like properties and all Fermions have matter-like properties but pairs of identical matter particles, or even numbers of matter-wave particles form "Cooper Pairs" of their own kind too and form single quantum states with light-like properties. Both half integer and whole integer states can be excited in a BEC simultaneously as different coexisting phases. Look at the YouTube video on liquid Helium linked in the Scientific American page. As I have mentioned previously these "liquids" have been made, even at room temperature, with the most interesting "fluid" of all... light itself .... liquid light.

Cheers from GE
Aa' menle nauva calen ar' ta hwesta e' ale'quenle

Good Elf

Posts: 471
Joined: Fri Oct 29, 2010 12:21 am
Location: Brisbane, Australia

### Re: Maxwell's Electromagnetism is a theory of knots

Good Elf wrote:What interests me about black holes these days isn't the black hole itself, but the material surrounding it and how that material behaves differently because it surrounds a black hole instead of another gravitational body of like mass.
Some speculation is necessary. The mass of a Black Hole is not concentrated at it's center. What I mean by that is the effect of the mass of every object has it's greatest deforming effect at the surface where the acceleration due to gravity is a maximum. If a Black Hole is going to form, it must form at a point at which the gravitational stress is a maximum. An object that is in the last state of gravitational collapse begins by shrinking in radius. If you treat a Black Hole as a point source then it's mass is concentrated at it's center. However it is clear that a Black Hole starts as a massive body like a cooling star in which the density of the body is collapsing under it's own mass and the radius of the body is becoming less over time. It does not shrink to a point but at a critical size approximately equivalent 3.8 times the mass of our sun (minimum) and it's "final" radius will be 12 Km radius (or 24 Km diameter). Assuming the acceleration due to gravity increases at the surface the acceleration due to gravity decreases as you enter the surface of the sphere and move towards the exact geometric center, where the acceleration due to gravity is identically zero at all times. This is because the aceleration due to gravity is the same from all directions and as a vector quantity it will cancel out. It is a well known Geophysical Result:
Tutor for Physics site wrote:Formula: Acceleration due to gravity inside the Earth

Here let r represent the radius of the point inside the earth. The formula for finding out the acceleration due to gravity at this point becomes:

g' = ( r / re )g

In both the above formulas, as expected, g' becomes equal to g when r = re.

The formula is not only appropriate for inside the earth but any solid. It's no that different for a star while it remains sub-critical. There are also hydrostatic effects as well, effects due solely to the overlying (fluid?) material. For the same reasons at the center of a star, those hydrostatic pressures are from all sides directed to the center, hence they all cancel at that center as well.[/quote]
Is it insufficient to just say that at the event horizon, the speed of gravity in a centripetal direction must be the speed of light? I guess this could be problematic since matter can't reach the speed of light, but maybe that's where you encounter relativistic effects from the perspective of the matter accelerating into the black hole vs. what an outside observer sees.

If you are falling into a black hole, you are accelerating to ever-higher percentages of the speed of light, and so your mass would be increasing from the perspective of an outside observer, but from your perspective your mass may well be measured as constant and it is just the clock of the outside observer that appears to be slowing, as you appear to be receding into what would seem to be a much deeper hole to you than you would have estimated based on the volume of the black hole from the outside. At least this is how I understand the convergence of space/time dilation, mass-increase with relativistic speed, and perspectival differences altered by the black hole.

In terms of time speeding up from the outside perspective, that implies that physical processes happening in the accretion cloud surrounding the black hole would be happening faster, but what does that mean? What would it mean to look at the sun and say that ion motion and fusion are going faster because space/time is dilated via relativistic effects? From our perspective, it's just normal astrophysical fusion but maybe we fail to take into account that there are relativistic effects going on for the matter fusing in the sun, and from 'their' perspective, those ions are moving at a slower speed in a more voluminous space.

If the star is hot enough it may turn into a white dwarf before it collapses into a Black Hole.

But is there really a radical change that happens from the perspective of the 'white hot' ions of the star as it transitions into a BH, or are we as outside observers just observing the white-hot density as such because time and space appear compressed from our perspective?

The electrons will be squeezed out of the electronic shells and it will form a surface conduction layer of electrons at the surface of the star while the interior will become a compressed fluid composed of charged nucleii a nearly degenerate superfluid surrounding a degenerate supersolid core.

Aren't the electrons stripped from the ions in all fusioning stars?

This nucleus at the core of a star will be self repelling (composed of all mostly positively charged particles) and so will not be being forced any further together (assuming almost all the nuclear fuel is used up). So at the center of a star, for the same reasons given for the other two forces, this force too will approach zero at the center as well. Everything zero at center but the acceleration due to gravity is a maximum at the surface. Not certain what modifying effects those other pressures will have, perhaps these pressures add to the overall stress energy density and move the critical stress into the surface... but it can't reach a maximum at the center where all the forces are cancelled out. My "intuition" suggests this forms a kind of "cookie cutter" punching out a hole near the radius of the star as it approaches the critical density.and the star collapses into the hole punching out a wormhole, the surface of the star is replaced by the new surface of spacetime which is like a pipe with nothing in it's interior. Since it has punched out spacetime itself the center of the hole contains absolutely nothing.... no surface of spacetime.... the surface of spacetime is now formed around the walls of the hole. This is a two dimensional surface or more accurately a two plus a small fractional dimensional surface or a spacetime defect and a source of a fractal spacetime, not three dimensional space at all. Regarding time, others have suggested that the role of space and time are at least partially exchanged.... perhaps not.

I think you can re-interpolate all these bizarre effects in terms of changes in the appearance of matter/space outside the hole. WIthin the hole, the dimensions of space may be expanding, e.g. worm-holizing, but what would a worm-hole look like from the inside except normal space in which you rapidly approach objects that you didn't observe from outside the hole?

Wavefunction-collapse is an odd concept. If you accept that Quantum Field Theory is correct there is a wavefunction for all classes of particles individually. For example there would be a wavefunction for photons but this wavefunction is a global property ... it covers the entire Universe. So a more realistic assumption is the entire Universe does not collapse for every quantum event that happens, but perhaps the wavefunction collapses is local to a smaller region after an event and within a short time "recovers" to the undiscovered state which is the wavefunction in quantum superposition. On the other hand there is a difference between the wavefunction of photons and the wavefunction of particles like electrons, protons and neutrons. The photon can be created without numerical conservation laws and are "on demand". They are also destroyed "on demand". IMHO these creation and destruction events are related to the initiation of the Advanced and Retarded wavefronts at sink and source respectively. The particle (photon) is detectable at the confluence of these two waves (there is some experimental justification for this nowadays as "whirling waves" and as a Dynamic Casimir Effect).... Two-State Vector Formalism -treatments by Lev Vaidman, Yakir Aharonov and originally proposed in 1942 as Wheeler–Feynman absorber theory. Today it's main proponent is Ruth Kastner. An imaginative picture of this analogy would be...

However a detection of the photon there virtually "creates" the photon "by observation".

I don't see why a photon wave would coincide with the entire universe. A radio wave may be the size of a stadium until it collapses into the electron of an antenna that absorbs it, but it is not infinitely large unless it continues to redshift ad infinitum. Electron waves are more confusing, because they do one thing when they are free electrons and something different when they are anchored in orbit around a nucleus. I think it would clarify a lot if there was a single model for free electrons in inter-atomic space and within the orbitals of the atom. This makes intuitive sense to me considering the presence of electromagnetic fields and charge outside of atoms, but it seems that 'extra-molecular space' is typically viewed as charge-neutral, as if the electron escapes positive charge by ionization until it gets re-captured into some other ion's orbital space.

Wave collapse and space/time dilation seem like related concepts to me, so I think it would possible to view the electron wave's transition from a free electron to an atomic electron as 'wave-shrinkage' without it totally collapsing. Then, the interaction of the orbital wave with other such waves would cause collapse into what seems to be a point-particle, but even that could just be another, more radically 'shrunk' wave. The shrinkage of electromagnetic patterns due to interaction is a logical extension of the lorentz force displacement of a charged particle's trajectory from a straight line to a spiral pattern surrounding a magnetic field line. Add energy to plasma and accelerate the ions generating the magnetic field with their motion, and the electrons spiraling around them respond by tightening their spiral. The net effect is to contract/shrink the plasma, so in this sense the plasma/space is dilating or contracting depending on the speed/energy of particles moving within it.

A pair of electrons, which are both half integer fermion quantum states, will form a even quantum state when they team up and form a boson. The principle occurs everywhere in nature. Actually in the bulk of a superconductor all electrons are paired as "Cooper Pairs", but because they are of a similar charge polarity they also repel.... they form structures similar to "vortex tunnels" spanning the superfluid interface and pairs of electrons create a very high mutual surface tension. Type II Superconductors align these vortices vertically in a rotating disk of liquid Helium for example. Helium is an inert gas and does not conduct electricity... it also doesn't form ions.

I think I've read that helium has an ionization energy, albeit a very high one. How else would it fuse in a star? I still don't understand how a pair of electrons form a boson. Do you mean they form a photon or some other boson? In what sense do they function as a boson? I.e. what energy do they transmit and from where to where?

Electrons are also forming these structures in the outer shell structures of atoms as discussed above. With liquid Helium it formed the very first known Bose-Einstein Condensate which is a superfluid and a single macro quantum state and it can act like a viscous liquid having a kind of internal "perpetual motion" and also having virtually a very large surface tension and allow Helium to become entangled and to climb out of a vessel and over it's lip... "If you march in unison, you don't collide with each other," that marching in unison is quantum entanglement.

I suppose if the particles in a fluid were all entangled and thus magnetically aligned in a sense, they could move as a liquid without friction, but there has to be some potential for friction or the liquid would never heat up and evaporate, would it?

See the article in Scientific American here:Strange but True: Superfluid Helium Can Climb Walls - Sci Am - 2002-2009. The superfluid is very closely related to the properties of the nucleus.... while it is not the actual properties of an actual nucleus, there are many "parallels" with it, electrons and the nucleus of atoms being superfluids themselves. In some respects at the heart of all matter are "black hole" like structures or Electromagnetic Black Holes.... these tunneling vortices between opposing aligned electrons and also between entangled protons and neutrons too. Condensed Matter processes, in the form of Bose Einstein Condensates (BEC), convert half integer Fermion matter waves into whole integer Bosons which are single macroscopic quantum states are all occupying the same volume as just one of them alone. Materials can have differing phases whose components can be Bosons and Fermions at the one time depending on the treatment. All Bosons have light-like properties and all Fermions have matter-like properties but pairs of identical matter particles, or even numbers of matter-wave particles form "Cooper Pairs" of their own kind too and form single quantum states with light-like properties. Both half integer and whole integer states can be excited in a BEC simultaneously as different coexisting phases. Look at the YouTube video on liquid Helium linked in the Scientific American page. As I have mentioned previously these "liquids" have been made, even at room temperature, with the most interesting "fluid" of all... light itself .... liquid light.

Ok, I am seeing how this entangled superfluidity could relate to condensation of particles into denser, neutral superparticles. I guess the supercooling allows the particles to get close enough together for their electromagnetic entanglement potential to fully express itself, like bringing ferromagnets close enough together that magnetism takes over and snaps them together completely. But why would you call such bonded superparticles 'bosons?' Is a neutron a boson or a fermion? I thought neutrons were fermions, but are they bosons because they combine the half-integer charge numbers of a proton and electron to make a whole integer?

Cheers from GE

Thanks, as always, for your insights.
inertron

Posts: 835
Joined: Sat Aug 13, 2011 2:10 am

### Re: Maxwell's Electromagnetism is a theory of knots

Warning: This is becoming more speculative. This is because there are no calculations that are known to work inside a wormhole because of the need to apply Tensor Mathematics and then Spinor Mathematics, so in highly curved spacetime the "philosophy" of small distortions of "Minkowski Flatspace" rapidly becomes an invalid methodology. On the other hand the methodology of quantum physics takes over inside Wormholes. It is a case of "You can't get there from here." But you can try... a tad.
_______________________________________________________________________________________________________________________________________________________
Hi Inertron,
Quite a lot of questions...
Inertron wrote:Is it insufficient to just say that at the event horizon, the speed of gravity in a centripetal direction must be the speed of light? I guess this could be problematic since matter can't reach the speed of light, but maybe that's where you encounter relativistic effects from the perspective of the matter accelerating into the black hole vs. what an outside observer sees.
There comes a point at which the curvature of spacetime exceeds regions over which the underlying linear tensor theory fails. It just happens that if you simply look at the overall spatial relationships it bends the otherwise flat linear manifold into an orthogonal space... that space is still three dimensional with respect to our space but is oriented perpendicularly. Assuming time retains some kind of continuity over this boundary I think of this as orthogonal space ad existing in a reciprocal lattice. Of course Physics still exists there but the projection into our flatspace does not carry across... most particularly at the two dimensional spatial boundary surrounding the Black Hole where the apparent third dimension is being pinched off inside normal "outer space". The optical effects of this boundary would act like a caustic and Special Relativity is a projected optical effect for most physics. Look at this object such as a cube moving at a significant fraction of the speed of light. Light and Gravity propagate at the same speed ... that is C. That does not change. Nevertheless on the boundary the direction of motion is to move into the orthogonal space whose projection into our 3D space has no "shadow". In Fourier Theory terms we have moved from de Sitter Space into Anti-de Sitter Space. One description is optical and the other is mathematical. This latter space is a Reciprocal Space and Reciprocal Time which is a Frequency.... a holographic boundary.
Inertron wrote:If you are falling into a black hole, you are accelerating to ever-higher percentages of the speed of light, and so your mass would be increasing from the perspective of an outside observer, but from your perspective your mass may well be measured as constant and it is just the clock of the outside observer that appears to be slowing, as you appear to be receding into what would seem to be a much deeper hole to you than you would have estimated based on the volume of the black hole from the outside. At least this is how I understand the convergence of space/time dilation, mass-increase with relativistic speed, and perspective differences altered by the black hole.
Einstein wrote:"When forced to summarize the general theory of relativity in one sentence: Time and space and gravitation have no separate existence from matter. ... Physical objects are not in space, but these objects are spatially extended ... thus the concept of particles cannot play a fundamental part, ... and can only appear as a limited region in space in which the field strength or energy density are particularly high."
(Albert Einstein, Metaphysics of Relativity, 1950)

Einstein wrote:In a 1948 letter to Lincoln Barnett, Einstein wrote in German (translated): "It is not good to introduce the concept of the mass $M = \frac{m}{\\sqrt{1-v^2/c^2}}$ of a body for which no clear definition can be given. It is better to introduce no other mass than 'the rest mass' m. Instead of introducing M, it is better to mention the expression for the momentum and energy of a body in motion."
M is the fictitious "relativistic mass". Mass of sub-nuclear particles is a function of this "mass" M. The effect on all sub-atomic particles is a kind of inertia that is similar to attempting to move a bag full of gyroscopes around, it resists acceleration in all directions. The electrons, neutrons and protons and all particles (such as those that compose a space ship) exhibit this spin to relativistic mass conversion due to deBroglie matter wave confinement... their inner constituent photons of the sub-atomic particles behave like tiny gyroscopes, confined to move (spin) around in their individual vortex doughnut spaces.
$\lambda ={\frac {h}{p}}.$ where $p = mv$ and m is it's mass.
The inertial mass remains "m" in it's own "Inertial Frame" as determined and testable on board the freely falling space ship by noting the mutual reaction through a spring on an internal test mass moving with the space ship. So this should be very unsurprising. In the rest frame of the space ship, nothing is changing or happening whatsoever (ignoring the optical effects seen outside). However there is an external view that could be made by other theoretical observers not moving along the same trajectory. The ship is conforming to the geodesic surface into which it is moving, it is solenoidal, passing from de Sitter Space to Anti-de Sitter space and time becomes a quantum jump, a discontinuity in space... nothing more. Has there been any elapsed time... I dunno? There is an "elapsed space"... the ship will be at the remote end of the wormhole instantly, not through any "speed" but by connection, quantum entanglement, because a single quantum state existing at both ends of the external hull of the space ship now exists wholly resident at the remote end, plus some quantum settling time. The space ship became an intact complete matter wave in response to the near dimensional discontinuity on the boundary, and deformed optically and harmonically as a Spherical Harmonic on the surface of the "Black Hole" - "White Hole" pair. As the instanton connecting the two regions of spacetime conveys the ship to it's remote end instantly through a process of linear frame dragging leading to the situation in which any emitted light would behaves as a caustic. But the space ship internally will not undergo any deformation "in it's own rest frame", but (mainly fictitious) hypothetical observers in nearby reference frames might see it undergo extreme optical deformation as it moves across the fractal optical boundary. Movie goers have seen this all before in the movie "Interstellar". But all the special effect of turbulent motion may not actually exist at all.It's an optical caustic and Fourier transform on the surface of the deSitter and Anti-deSitter space of a two dimensional sphere, in space and time. Nothing happens to the ship as it is flung out of the other end of the "Black Hole"... now acting as a "White Hole". The wormhole may also be polarized for other reasons and may not be two way traversible... I dunno.

The issue of "spin" depends on other matters that the "space ship" may have had. Any residual spin may be an impediment to wormhole travel because it would induce trapping quantum states into the "Black Hole". Without a means to lose that residual spin, the space ship may be trapped in a quantum orbit surrounding the Black Hole forever.
Inertron wrote:In terms of time speeding up from the outside perspective, that implies that physical processes happening in the accretion cloud surrounding the black hole would be happening faster, but what does that mean?
Well it means that time in our observation vantage point on the entry side of the Wormhole appears to proceed slower and slower for the observed space ship until it stops and eventually disappears into the infra-red end of the spectrum at the Wormhole's Event Horizon. From a vantage point on the other side of the same Wormhole, the exit port, time for the space ship starts from zero and "speeds up" as the ship moves towards another fortunate observer that may happen to be waiting there at that time. A judicious use of energy and momentum may allow the ship to stop right next to the second observers spaceship where both clocks would now run in lock step. But the clocks have come from a different points in our Universe and have different synchronizations, maybe having different acceleration histories so don't expect them to agree on their zero's, just tick off similar seconds when brought close enough together in the same inertial frame. Unlike motion through space at near the speed of light, there is no Twin Paradox, the actual distance the clocks, the space ship and the travelers have moved is only a few kilometers across the quantum boundary. This is how relativistic time and quantum time differ. One is an application of Special and General Relativity and is the result of high speed "space travel", while the other is an application of the Page & Wootters Mechanism and is due to a "quantum jump". Does a quantum "jump"... maybe not... if the tunnel can be kept open, it is possibly a simple juxtaposition of the space on either side of an optically and mechanically short tunnel. Whatever quantum entanglement means this portal is a true "short cut" through space without many or most of the problems of time dilation. Time on either side depends not on Relativity but on Quantum Physics. If the Wormhole happens to be two way traversible, and that is a really big big "if", "bobbing back and forth" will restore the conditions of symmetry on either side without time dilation except for some small distortions near the two dimensional event horizon boundary. A clock would be carried across that boundary with minimal fuss. Compare and contrast actual propagation (motion through space) to the other side of the Universe to the other end of the Wormhole by conventional means... to do that in a "short time" would require a speed very close to the speed of light so that the occupants have not died and crumbled to dust while also exposing the crew to intense radiation through moving through the interstellar medium, however a trip back to the source of the Wormhole would cast the travelers into the far future. Maybe the Earth will be gone, consumed in it's own Nova.
Inertron wrote:
Good Elf wrote:If the star is hot enough it may turn into a white dwarf before it collapses into a Black Hole.

But is there really a radical change that happens from the perspective of the 'white hot' ions of the star as it transitions into a BH, or are we as outside observers just observing the white-hot density as such because time and space appear compressed from our perspective?
I wouldn't worry about that yet. It is so hypothetical it would need a full rework.
Inertron wrote:
Good Elf wrote:The electrons will be squeezed out of the electronic shells and it will form a surface conduction layer of electrons at the surface of the star while the interior will become a compressed fluid composed of charged nucleii a nearly degenerate superfluid surrounding a degenerate supersolid core.

Aren't the electrons stripped from the ions in all fusioning stars?
I am so very sorry to have even mentioned these topics here... they were said as throwaway lines, like that Guy singing and tap dancing the Universe Song atg the end of Monty Python's "The Meaning of Life", I just need to harvest your organs.

Inertron wrote:I don't see why a photon wave would coincide with the entire universe.... Wave collapse and space/time dilation seem like related concepts to me, so I think it would possible to view the electron wave's transition from a free electron to an atomic electron as 'wave-shrinkage' without it totally collapsing.
I cut out the bit I thought I did not need and harvested the bit that is most illustrative. This bit is correct. Photons in proximity of electrons enter into plasmon states and their wavelength are at least 1000 times shorter than the equivalent electromagnetic wavelength. Devices have already been fabricated to generate and utilize plasmon states to make such devices as on-chip lasers whose actual size in the optical range is too large to fit on a chip and are benchtop devices. They are called Spazers. Here are real dimensional shrinking of optical frequencies and available at a shop near you. You already know about the TARDIS, you know... it's bigger on the inside than on the outside. Well this is one of those things. While quantum field theory suggests the re is only one universal wavefunction for each of the primary "particles"... a quantum state collapse doesn't collapse the entire Universe , only the state itself... a very local collapse... a quantum non-demolition event that eventually "heals" back to a superposition of multiple quantum states.
Inertron wrote:I think I've read that helium has an ionization energy, albeit a very high one. How else would it fuse in a star? I still don't understand how a pair of electrons form a boson. Do you mean they form a photon or some other boson? In what sense do they function as a boson? I.e. what energy do they transmit and from where to where?
Helium does not fuse inside stars except in supernovas. It is hydrogen you need to know does most of hte fusion. Any two identical particles in close proximity will form a Boson. Fermion's are composed of half integer quantum states while a boson is an interger quantum state... any even number of identical fermions is equal to a boson.... it is the bases of how the Universe works when described as a series of multiple quantum phases (such as in Cold Condensed Matter Physics)... human beings are "part and parcel" among those phases.
Inertron wrote:I suppose if the particles in a fluid were all entangled and thus magnetically aligned in a sense, they could move as a liquid without friction, but there has to be some potential for friction or the liquid would never heat up and evaporate, would it?
Forget magnetism for now... it is all about quantum entanglement. Quantum phases are in lock step when they are "frozen" and as the state"thaws" the states gain independent degrees of freedom. We warm bodies have a great deal of freedom but there is a lot of cold matter in space and also hot matter in stars, and inside a single atom the individual quantum states such as Cooper Pairs in atomic orbitals have very few degrees of freedom since they are piecemeal "superconductors".... thus "cold" (by convention). High temperatures and low temperatures are a matter of relative scale and the way scales exchange energy.
Inertron wrote:I thought neutrons were fermions, but are they bosons because they combine the half-integer charge numbers of a proton and electron to make a whole integer?
Yes they are but in combination they are paired as bosons. Some atoms due to the pairing of all states can also be a boson. Lower the temperature and some states pair up more easily.
Inertron wrote:Thanks, as always, for your insights.

You are welcome Inertron.
Aa' menle nauva calen ar' ta hwesta e' ale'quenle

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