NTuft
-
Posts
286 -
Joined
-
Last visited
-
Days Won
1
Content Type
Profiles
Forums
Events
Posts posted by NTuft
-
-
2 hours ago, swansont said:
And?
The relative motion doesn’t create the interaction. You could transform into a frame where v = 0. You would have an electrostatic interaction that accounted for everything.
There may be something brought to bear on this here, A novel equivalence relation in relativity (+1 @studiot),
Quote[...] But standard special relativity cannot tell us directly that lightspeed objects do not exist in spacetime because it does not contain any concept of existence. Embedding it via the existence criterion makes this explicit and gives meaning to features of special relativity which could previously only be regarded as meaningless curiosities. Sometimes, paradigm changes happen precisely when seemingly meaningless curiosities in a model of reality are recognized to carry novel significance, and arguably, the birth of special relativity itself was due to such a development [2].
• The ontic equivalence relation establishes a novel classical geometric correspondence.
Because of dimensional reduction, lightspeed objects must by the ontic equivalence relation exist in a 2 + 1 dimensional spacetime. The mathematics of special relativity gives hints of this: As an object approaches the speed of light, its direction of motion and its time direction are both observed to approach the lightlike direction. In the limit of c, they both become lightlike [3]. But that means that in a lightspeed frame, our spacetime is a vector space with a linearly dependent set of vectors, which in turn implies that in a lightspeed frame, 3 + 1 spacetime has too many dimensions. Also, special relativity is clear that in such a frame there are only two independent spacelike directions.
The existence of lightspeed objects in 2 + 1- dimensional spacetime can be interpreted in terms of a classical and a quantum picture.
The classical picture is that as a lightspeed object traverses a null geodesic in spacetime, it defines a rest frame on a null-plane, so that what is in 2 + 1 dimensions the passage of proper time corresponds in 3 + 1 dimensions to motion in space. Since the rest frame in a null-plane has to be represented in 3 + 1 dimensions necessarily in an atemporal manner (due to the connection between existence in a spacetime and timelike proper time), it suggests a novel interpretation of the fact that the stabilizer subgroup of the Poincar´e group (‘Wigner’s little group’) for massless objects is isomorphic to E(2), the group of isometries in the Euclidean plane [4]. As the correspondence involves analogous quantities associated with spaces of different dimensionality, we will for clarity use left subscripts to indicate the total number of dimensions of the space with which the quantity is associated. Let 3d ∶ E 3 → [0,∞) be the distance function for three-dimensional Euclidean space, and 3τ∗ ∶ M3 → [0,∞) be the timelike plus zero (indicated by adding *) interval function [5] for three-dimensional Minkowski spacetime, then C ∶ 3τ∗ → 3d (3) will be called the classical τ ∗ −d duality. It reflects the fact that, unlike certain other relations such as set membership, existence in a spacetime is not inherited by a one-dimension higher embedding spacetime, an immediate consequence of the ontic equivalence relation.
In [6], it was implicitly shown that classical electrodynamics obeys the classical τ ∗ −d duality, as the magnetic force field of an infinite line current can be reinterpreted as the line integral of a two dimensional Coulomb force field such that a spatial distance covered by the line integral corresponds to the worldline of a Coulomb source in a twodimensional leaf of a foliation of space normal to the direction of the current (i.e. really a worldline in 2 + 1 dimensions). This reconceptualization permits the recognition of geometric relationships between Maxwell’s equations not evident in the standard formulation.[Ed.: Excuse bad formatting, see link]
1 hour ago, joigus said:The Lorentz force does have a time component, though. When you write down the complete --covariant-- form of the equation it gives,
fμ=quνFνμas a 4-vector equation. Where Fνμ produces all the components of E and B . These equations decouple into,
f0=qv⋅Efk=q(E+v×B)and where I think I may be missing a gamma factor. The 0-th Lorentz equation gives you the power gain or loss, and the spatial equation is the conventional Lorentz equation.
So the f0 is the 0-th and fk is the conventional. I don't have a handle on co-variant, contra-variant, vector indices or tensors here, I'd barely made a start on what I think is Einstein's vector convention. is the power gain/loss a boost? I ought to go through the sections I pointed at to get the details, but if you could explicate what this is saying I'd appreciate it; I don't even know what questions to ask.
Referring to the equivalence relation in relativity cite, does it make sense that the E and B fields are conceptually lightlike objects? I think it's such that they're thought of as the medium in which it propagates. What about the dimensionality? When swansont said that it could be reverted to a v=0 frame and electrostatics could describe it I was thinking that was like going from 3-D to 2-D spacelike dimensions, and then lo-and-behold the next section I read goes into classical electrodynamics... Which is not correct, as electrostatics can be 3-D, but as soon as it is, I think there is the additional degree of freedom for rotation, which again is a relative motion that can induce the B field.
And? I think that there was some back-and-forth about whether an interaction hinges on a relative motion, and I think magnetism does. I highly recommend the reading on equivalence relation in relativity, I don't have a good handle on relativity, and several readings of the initial pages are necessary.5 hours ago, NTuft said:I don't see physics as "made up""...everything in physics is made up to make the math work out.
...in the end, everything we do is to make the math work out."0 -
47 minutes ago, studiot said:
Since I first mentioned Lorenz I should point out that I was talking about the Lorenz Transformation, not the Lorenz force , which is an entirely different phenomenon.
They're not entirely unrelated, though. Searching the respective wiki articles for the other's terms, "transformation" or "Lorentz force", has details [Transformation of other quantities; Relativistic form of the Lorentz force]. The E and B fields defined by Lorentz force do not have a timelike quantity so I think you're correct to say they're different from Lorentz transformation including time.
8 minutes ago, swansont said:[...]
That’s qE + qv X B
There’s only a force if there’s a charge. The interaction is electromagnetic, not the relative velocity.
Yes, the corrected distribution got in there with the edit. However, also from the wiki's, the Lorentz transformation can illustrate that what appears as a static electric charge and E field in a rest frame appears to be a moving charge with consequent current flow and induced B field from another frame in relative movement--it only becomes an electro-magnetic interaction with some relative velocity, either of the charge or the observer thereof.
0 -
On 3/6/2023 at 2:18 PM, MigL said:
Markus Hanke ""
I would have no problem taking that step also.
I only mention 'things' because the questions are always"But what is an electron, really ?" or "What is a photon ?" or possibly your favorite "But what is gravity, really ?".
TheVat ""How would it make a difference ?
Everything we see ( contingent ) affects us through interactions.
That which is not contingent does not affect us through interactions.
IOW, whether it is there or not makes absolutely no difference to us, or the world around us.Why is it needed in our models, and, by Occam, why is it needed at all ?
( argument applies to religion/mysticism as well )I can see the utilitarian argument, but if there were some non-contingent, non-interacting "field" isn't it possible that our observations or reality is contingent in a way that couldn't necessarily be measured? I know that's a mushy, philosophical-religio-mystical question, but I don't see physics as "made up", rather that it's trying to develop a description.. To me, the explanatory power for theory is deficient if it's not encompassing reality, even if utility wouldn't require a complete understanding.
On 3/7/2023 at 8:44 AM, studiot said:Why not ?
They have a relative velocity, isn't that a physical interaction between two distinct entities ?
On 3/7/2023 at 8:57 AM, Genady said:I don't think that having relative velocity constitutes a physical interaction. Maybe it does in some sense, but I am not familiar with such sense. In every meaning of physical interaction that I am familiar with, such a relation is excluded. E.g., interacting particles in QFT.
Lorentz force,
Quote[...]For any charged particle q in more general situations moving in the presence of electric and magnetic fields the interaction is usually given by the Lorentz force:
In general, field theory and Maxwell’s equations are a ‘macroscopic’ approach as they were developed from a continuous medium model (the ether). However, as we will see in the following section, Weber’s force is ‘microscopic’ in that sense as it describes the interaction between two charged particles in its standard form. For a better comparison between Maxwell’s and Weber’s theory, Assis shows the derived force between two point charges from field theory [24] up to second order in v/c based on the work of Liénard, Wiechert and Schwarzschild, which was first obtained by O’Rahilly [25] as
In this formula q1 is the test charge and q2 is the source charge generating the fieldsand
, where according to Assis time retardation, radiation and relativistic effects have been included. The constant c is the speed of light and
denotes the acceleration of the point charge. It is apparent that the expression depends on the square of the source charge velocity and on its acceleration, whereas Weber’s force depends on the relative velocity and acceleration, as will be seen in Section 3.1.2.[...]
[...]Both the Schwarzschild force (24) and Lorentz force (23) have been criticised as violating conservation of linear and angular momentum. To restore conservation it is usually argued that the energy is lost or gained by the electromagnetic field generated by the charges or that self force needs to be taken into account [29,30]. However, a system of two point charges seems extremely difficult to test. The general applicability (or non-applicability) of Newton’s third law to the Lorentz force and generally in electrodynamics has been discussed in [31–33]. Cornille [32] also claims that if the electrodynamic force laws indeed violate Newton’s third law, then it inevitably leads to the conclusion that energy can be extracted from the ether, as the ether exerts a force that is responsible for the violation.
It has further been criticised that the velocityin the Lorentz force formula (23) is not clearly defined, that is what it is defined with respect to, was not even given by Lorentz himself [6,34]. It thus remains ambiguous if the definition is w.r.t a coordinate system or a source charge, which might itself be moving, although there seems to be support to the idea that Lorentz viewed the velocity as relative to the ether [6,34]. However, in relativistic treatments this is usually resolved by a chosen inertial frame of reference and regarding the velocity relative to the measuring device or observer.
In an interesting review about Maxwell’s equations and the field approach Tran [35] concludes that there are only few experiments supporting the Maxwell-Ampère and Maxwell-Faraday equation, at least not to the same degree of accuracy that the continuity equation and the magnetic law are supported. There is further discussion about conceptual problems in classic electromagnetism and modern particle-field theories in the literature [36,37]. This mainly focuses on the problem of point charges and their diverging self-energy, as the calculated energy of an electron with its own field tends to infinity based on classic electromagnetism. One solution is the renormalisation approach in the quantum theory of Dirac where the point charge is treated as a singularity and the infinite energy is subtracted as a constant from the problem to renormalise the energy content. The other solution is the extended particle model, where elementary charges are not treated as pointlike anymore and consequently the divergence in the singularity disappears. Pietsch [36] discusses both approaches and the associated cost of the proposed solutions, and for an interesting discussion of these approaches including a mathematical perspective, see [38], on which Pietsch bases their arguments. Pietsch then argues that both approaches are incompatible at a fundamental level and a better solution is needed, in which direct-action theories are proposed. Lazarovici [37] also discusses the self-energy problem and the Lorentz-Dirac as well as the extended particle solutions as unsatisfactory, but also involves free fields, among other philosophical, mathematical and physical arguments, and proposes the Wheeler-Feynman direct-action theory in particular as a solution to those problems. The renormalisation approach has also been criticised by other authors [39], including Feynman [40] and Dirac [41]. A similar argument has been made by Kastner about the Wheeler-Feynman direct-action theory, not only does it avoid self-energy problems, it is also not subject to Haag’s theorem and the consequent problems of free and interacting fields in quantum field theory (QFT) [42]. [...]
Foundations of Electromagnetism: A Review of Wilhelm Weber's Electrodynamic Force Law , pgs. 954-955, emphasis added.0 -
Injuries to diplomats is a limited hangout, a cover for two-way signals surveillance or injection technology.
0 -
53 minutes ago, CharonY said:
Chylomicrons are lipoproteins and they are produced in enterocyte. So in terms of distribution of lipids, they are basically at the source of dietary lipids, which get mobilized to adipose and muscle tissue. Cholesterol seems to be directed to the liver.
Yes, thank you.
53 minutes ago, CharonY said:I assume that was a typo (as the next sentence says the opposite), but reducing SFA content increases expression of LDL receptors. The assumption here is that LDL receptors are involved in LDL-cholesterol clearance from blood. I.e. reducing SFA increases LDL-receptors, which in turn reduce circulating LDL-cholesterol.
Yes, should say increases expression. Certainly yes there is the assumption that LDL receptors are involved in LDL-C clearance. The interpretation to end the abstract from the authors is like what you suggest. It could be decreased production VLDL->IDL->LDL is sensed and signals upregulation of expression of receptors, seeing that the diets step down both fat% and SFA%: 34%(15%)[0,0], 29%(9%)[-5%,-6%], 25%(6%)[-9%,-9%]. I presume both numbers are % of total energy, and the latter not a %SFA of total fat, as that seems implausible.
0 -
On 2/14/2023 at 4:52 PM, CharonY said:
I thin it should be added that there is (AFAIK) no gold standard with regard to these tests. While NMR does work at least as well as the other methods, it is not clear which one is the best. And best is defined here as yielding a measurement that is clinically predictive. It is also important to note that there is more work looking into LDL subclasses as the category is rather overly broad and fluent. And there is at least some suggestion that certain smaller types of LDL might be more diagnostic, but the measurements are even trickier, as higher specificity is needed.
[postulated +SFA=+LDL]
That is actually also rather complicated. Early on, there were already suggestions that the link between saturated fat and LDL cholesterol (or specifically LDL/HDL cholesterol ratio) is not straightforward. Some studies for example suggest that reducing saturated fat in the diet hat less effect than exchanging saturated with unsaturated fat, especially cis-PUFA. There is certainly a connection somewhere but as metabolism goes, it is likely again indirect. Some data suggests that the issue with saturated fat is perhaps not really only in the realm of LDL/HDL cholesterol ratio, but perhaps by increasing the very small LDL cholesterol particles, which might be more likely to cause cardiovascular events.
Edit: I have not read the paper referenced above, but the graph shows a slight increase in LDL-cholesterol but a shift of the most problematic (small) species from 45.2 nmol/dL to 39.6. It is unclear to me whether those changes are actually clinically relevant, but I suppose that would require a study on its own.
Indeed this is a complicated topic. I did not read the paper either, and should have and parsed it, instead of posting the "rah-rah" blog write-up. This was a feeding study on humans, which is important as I think the usual rodent studies want to draw a parallel between a small-bodied herbivore and a large-bodied omnivore with a large gallbladder and a large brain-body ratio which brain is a cholesterol dependent construction. I don't think most any conlcusions on mechanisms of metabolism can be extended to humans, but the basic results may point toward what are conserved mechanisms.
It looks to me that the Lipoproteins work alongside chylomicrons in the distribution and metabolism of fats. This is complicated by fats being both structural components and energetic substrates. Lipoproteins go from Very-Low Density packages distributed by the liver to Intermediate-Density, to Low-Density as they unload fatty acid cargo at peripheral tissue, dependent on binding of the Lipoprotein receptors. There is data that reducing SFA content in the diet reduces expression of LDL receptors (Reducing saturated fat intake is associated with increased levels of LDL receptors on mononuclear cells in healthy men and women).
Some knowledgeable people have taken evidence that the LDL receptor is saturated at very low levels as license to start statins without real indications. Again, there ought to be due diligence and it's lacking on my part here as well, but for one the materials and methods would need an investigation as to whether this saturation level is an in vitro type of tissue study or in the context of connected running metabolism. It's noteworthy that the study linked above looked at mononuclear cells, since I'm rather certain there are human population studies that show a decrease in all cause mortality and in particular suicides and infectious disease death correlating with higher levels of LDL.
I suppose what I find most interesting about the 3 egg/day result is that estimates are that cholesterol is metabolized on the order of 1g generated by the liver per day(Ed.: with losses, I'd bet, as bile salts of cholesterol+taurine/glycine excreted]. Usual estimates are that 20% of that may come from diet, but I would speculate that that may largely be tied to average egg intake. Going from 0 eggs/d to 3/day, with a conservative estimate of 200mg cholesterol per egg, shifts the burden on the liver from ~1g/day production to .4g/day, yet there is what looks like a non-significant increase in total cholesterol; it looks like the metabolism simply shifted to acommodate the increased ingestion (assuming 100% assimilation and utilization).
There is increasing evidence (especially if you buy into the write-ups, hook-line-and-sinker) that would exonerate SFA intake from causative in CVD. It seems to have been scapegoated in the context of metabolic syndrome or metabolic disease. I would just point out the French paradox as an entry into the topic.On 2/15/2023 at 4:17 PM, CharonY said:The way I tend to think about food and health is that a) one should have limit of regular calorie intake. We do have too easy access to food and overeating clearly is associated with a wide range. From there b) the food should cover all the necessary nutrients (hence the common recommendation to have somewhat broad diet) within that rough calorie limit.
So in this context the question would be whether you would just cut off excess olive oil and not replace it with anything else (i.e. reducing total calorie intake) which likely would have some net benefit. Conversely, if you would eat something else that contains e.g. saturated fats or instead increased carbohydrate intake, chances are that it would be more likely to be detrimental.
In other words, I am skeptical of claims that adding something to the diet (on top) has benefits, I think it is more about the composition while eating a healthy amount.
Energy balance, the interplay between intake and expenditure, is probably more important than trying to leverage metabolic mechanisms, which are complex and seemingly geared to account for and accomodate just about any diet. You seem to point at Calorie-Restricted-Optimal-Nutrition, which I second has merit; studies on monkeys are even by visible appearance alarming in comparing overfeeding to CR. That said, the Optimal-Nutrition end requires some knowledge and application: being wary of anti-nutrients (say trans-fats, and likely some lectins or phytochemicals) and saturating would be bottlenecks(chokepoints) on metabolism by finding adequate mineral, vitamin, and vitamin-like substance sources.
On 2/16/2023 at 1:19 AM, exchemist said:(I don't have a problem with my weight, which has been stable for years at: 66 +/-1 kg and 1.76m in height.)
Ok now you're "trolling" for a free online physical! J/k
I'm skeptical of the "Lipid hypothesis", but I know it still holds by and large in the mainstream. Which is preferred out on the science boards here at SF.net. Going into these details does seem somewhat natural from the context of the OP, but it's also a generalization of a specific question... Anyway perhaps welcome to SF, OP; not much context on what you want assessed and expecting readers to watch a video is a forlorn hope, and diverging into related topics is almost a given if you cease any follow-up or specifications on the topic at hand.
0 -
15 hours ago, sethoflagos said:
Some of you familiar with my posting style probably realise that my understanding of psychology is close to zero. Perhaps you can help raise it a notch or two.
I'm sure all of us at some point or other have read a post that exposed our ignorance. @Mordred and @Markus Hanke for example frequently leave me feeling exposed as an idiot without seeming to pause for breath. But I do exit that thread a little less of an idiot.
So why do a number of us seem to automatically assume that such exposure of our ignorance was intentional and malicious? No names no pack drill. Just curious.
I wonder if it matters if it's intentional or malicious. A stoic line would be that one can only control their responses, or that one can stifle any unreasonable emotional reaction, if there is self-mastery. Nonetheless, if something "gets your goat" I think it helps you see yourself--why or how am I identified with this point of contention that leads to negative emotion or reaction?
I agree with a line of argument that says the truth hurts. That dis-confirming information is interpreted by the brain as physical injury. I don't know how scientifically founded that is, but I do think there are studies on cognitive biases in political opinion where people presented with information dis-confirmatory to their belief have pain centers light up. I also think the issue of whether you're thinking with your adipose or your blood is at play.
I'm not so sure we can really control what impressions we make on others. Being able to be externally considerate always and internally considerate never is an equation for happiness. Being able to control the impressions we make on others would be quite a skill...
But is there a need for it? Perhaps stepping on people's corns can create a friction, create some difficulty to make a change that wouldn't be possible another way. It only make sense and is reasonable I think to be respectful here, I think we'd hope we understand each other and are working on things together. Yet if you think it's necessary to correct with dis-confirming information, it's going to bring the pain, and oftentimes I think it's done with a flair or presentation that might be taken personally, or as an insult, when in reality it's done in good humor (at least for the rest of the readers).1 -
On 2/3/2023 at 7:44 AM, Willem F Esterhuyse said:
Abstract
[...]"The model predicts that 16 should also be a magic number for stability."
"We will later prove that some nucleons go into the extra dimensions."[.pdf pg#1]"Figure 1.4: Li(3,3)'s structure. Since the orbitals in layer Q have a unit of OAM each we have: J = 1 + 0 = 1, and the isotope has odd neutrons, so P = (-1) so parity agrees. I count only unsymmetrical filled orbitals since the rest cancel. The next level (labeled as R) has 6x2 orbitals so they are arranged in a hexagon."[pg#4]
"The neutron in brackets resides in the extra dimensions and does not contribute OAM or parity, it's spin pairs.
Theorem 3
Some neutrons go into the extra dimensions.
Proof: From Figure 1.6 we see Li(3, 4) has JP = 3/2+ without the extra dimensions (ED) filling. The second diagram shows that one neutron of (Li(3, 4) JP = 3/2- ) goes to the ED. If the theorem wasn't so we have that Li(3,4) with JP = 3/2+ would be stable and it is not. QED.
We will see that neutrons fill so that Z = N in the ordinary dimensions, with more neutrons filling ED orbitals."[pg#5]
"The stability rules are as follows: 1. A nucleus is unstable if one or more protons in a ring are unbalanced. 2. A nucleus is unstable if two or more neutrons are unbalanced. 3. A nucleus is unstable if its OAM is 6 or more."[pg#6]
"Figure 1.19: Structure of Na(11, 12). J = 1 + 1 - 1 + 1/2 = 3/2 and parity is positive: agrees with the data. The next layer (T) is again a hexagon with its L values as previously (Figure 1.5 of ref. [13])." [pg#10]
"Ar(18, 22) is also stable with JP = 0+, therefore there must be two more extra-dimensional neutron orbitals (see figure 1.28). These two orbitals are just activated if all the orbitals of level T are filled. The next layer is two decagons plus two orbitals in the center of each. See figure 1.29."[pg#14]Can you explain more about the extra dimensions? It seems as though some results did not fit, so you postulate these ED orbitals.
Does your geometric model remain planar? You mention that P level is stacked on the z-axis(coming out of the page), PL over PR, one over another -- so is it more like
PL - QL
PL \ QL \
\ PR \ QR
PR QLonce you get to P+Q level? Not sure I understand your diagrams...
Then you on to hexagrams and decagons (plus two orbitals in the center). Is the geometry planar??
I think this is interesting. I think the shell model can accomodate geometric nucleus structure. You start with a 4 (2 proton-2 neutron), add 6s or 8s, then 10s or 12s.. I think you could really gain something (and maybe lose the extra dimensions) from reading this write-up on another geometrical model for nuclear structure:
Quote...
Professor Moon's Hypothesis
The existing dogma of nuclear physics requires us to believe that protons, being all of positive charge, will repel each other up to a certain very close distance corresponding to the approximat size of the nucleus. At that point, the theory goes, a binding force takes hold, and forces the little particles to stick together, until they get too close, at which point they repel again. Thus is the holding together of the protons in the nucelus accounted for.
Disdaining such arbitrary notions of "forces", and preferring to view the cause of such phenomenon as resulting from a certain characteristic of physical space-time, Moon and the author demanded a different view. Considerations of "least-action" suggested to Moon a symmetric arrangements of the charges on a sphere, while the number of such charges (protons), and the existence of shells and orbitals beyond the nucleus (electrons) suggested a nested arrangement of such spheres. Our belief that the universe must be organized according to one set of laws, applying as well to the very large and the very small, suggested that the harmonic proportions which the astronomer Johannes Kepler found in the ordering of the solar system would also be evident in the microcosmic realm, so we looked for this also in the arrangement of the nucleus.
We were led immediately to the five regular or Platonic solids, the tetrahedron, cube, octahedron, icosahedron, and dodecahedron. Moon developed a nested model, using the Platonic solids to deifne the atomic nucleus in much the same way that Kepler determined the orbits of the planets of the solar system. In Moon's "Keplerian atom", the 92 protons of the naturally occuring elements are determined by the vertices of two identical pairs of nested solids. Before elaborating the construction of this model, let us review the properties of the Platonic solids.... How the Model Works
In Moon's "Keplerian atom", the 92 protons of the naturally occuring elemnts are determined by two identical sets of nested solids each containing 46 vertices. Moon's proposed arrangement is as follows: Two pairs of regular Platonic solids, the cube-octahedron pair and the icosahedron-dodecahedron pair, may be called duals: one will fit inside the other such that its vertices fit centrally on the faces of the other, each fitting perfectly inside a sphere whose surface isthus perfectly and symmetrically divided by the vertices. The tetrahedron is dual unto itself and therefore plays a different role....The four dual solids my be arranged in a nested sequence--cube, octahedron, icoshedron, dodecahedron--such that the sum of the vertices is 46: cube=8 +Octahedron=6 +Icosahedron=12 +Dodecahedron=20 =46
...Building the Nucleus If we now take the vertices of the solids so arranged to be the singularities in space where the protons are found, a remarkable structure to the nucleus appears. First we see a sort of periodicity in the nucleus, formed by the completion of each of the "shells", as we might call the circumspheres of the cube, octahedron, icosahedron, and dodecahedron. Let us first look at which unique elements correspond to the completed "shells":
Oxygen(8)=completed cube
Silicon(14)=completed octahedron
Iron(26)=completed icosahedron
Palladium(46)=completed dodecahedron
...
Uranium(92)=completed twin nested figures....Fission of the Nucleus
Moon's model beautifully accounts for the process of fission. Filling out with protons the outermost figure, the dodecahedron, brings us to palladium, atomic number 46, an element that has an unusually symmetric character. First, a look at the table of electron configurations shows palladium to be the only element in which an outer electron shell, previously occupied, is completely abandoned by the extra-nuclear electrons. Second, palladium is a singularity in the fission process, falling at a minimum on the table of distribution of fission products. Palladium also marks the boundary point for the sort of fission that occurs with very high energy (for example, protons of billion-electron-volt energies), when nuclei are split up into two parts of similar size. Silver, atomic number 47, is the lightest of the elements that may split up this way.
To go beyond palladium in our model, a twin structure joins at one of the faces of the dodecahedron and begins to fill up its vertex positions with protons, beginning on the outermost figure. (Silver, atomic number 47, is the first.) Six positions are unavailable to it--the five vertex positions on the binding face of the second figure and the one at the face center where a vertex of the inscribed icosahedron pokes through.
Thus on the second nested dodecahedron figure, 15 out of 20 of the dodecahedral vertices are availabled, and 11 out of 12 of the icosahedral vertices. We now fill 11 of the available dodecahedral vertices, thus creating 47-silver and continuing through 57-lanthanum. At this point, one face of the dodecahedron remains open to allow filling of the inner figures. The cube and octahedron fill next, producing the 14 elements of the lanthanide, or rare earth series (58-cerium to 71-luterium). Placing the proton charges on the inner solids causes a corresponding inward pulling of the electron orbitals. Thus, the otherwise unaccounted for filling of the previously unfilled 4-f orbitals and the mystery of the period of 14 for the rare earths are explained.... The structure begins with a helium nucleus, or alpha particle-- a tetrahedron conttaining two protons and two neutrons at its four vertices. To go on to the third element, lithium, the protons must move outward to start building up their first shell on the vertices of a cube. The two neutrons that were on the vertices of the alpha particle have no need to leave. However, any additional neutrons will place themselves at the center faces of the cube, which is the same place as the midpoints of the edges of the large tetrahedron. (The smaller tetrahedron is called the alpha particle.) Thus,at 6-carbon-12, there are two neutrons on the alpha particle an four on the faces of the cube. For clarity, here is another example: the proton structure of 8-oxygen-16. Of the eight neutrons, two are on the inner alpha particle and six on the midpoints of the six edges of the large tetrahedron(or, the same thing, the face centers of the cube), marking the completion of this shell. The eight protons locate on the eight vertices of the cube. Thus, not only is oxygen highly symmetrical with respect to proton configuration, but also one of its neutron shells is complete. ...
emphasis added. Attached .pdf: 13pgs.
I'll try to get through the rest.
0 -
6 minutes ago, exchemist said:
I can still cycle to Wimbledon and back, up and down the hills, to buy bread, as I did before I went on statins, so I'm not worried about muscle weakness. And don't worry, I like olive oil too much to cut it back a great deal.
Very well, and that can be a metric. It'd be an issue of myopathy, broadly speaking, over time, but overall I think it is a low-incidence reported side effect.
0 -
Here's a link to a blog post discussing a controlled feeding study (2017) looking at effects of egg consumption on blood cholesterol:
Quote...HDL function may be more important than HDL concentration...
...conducted a study to confirm and quantify the previously observed increases in HDL and LDL particle size, LCATactivity, and plasma apoAII...
...Before the dietary intervention began, the participants underwent a 2-wk washout period, during which 0 eggs/d were consumed. This baseline period was followed up by sequentially increasing intake of 1, 2, and then 3 eggs/d (large, grade A, white purchased at local supermarkets) for 4 wk each...
..."Overall, intake of ≲3 eggs/d favored a less atherogenic LDL particle profile, improved HDL function, and increased plasma antioxidants in young, healthy adults"...
@Nutrition4Health, I did not watch the video; would you clarify about what the claims are that are being made? Is he claiming that eating eggs leads to cholesterol absorption and then sustained, circulating high cholesterol levels? Because I think that is bogus.
From what I understand, the number of particles, which relates to whether LDL and HDL are small and dense vs. large and fluffy, is an issue--it can be differentiated by an NMR lipid profile. Per Cleveland (U.S.) Clinic recommendations I believe an [Ed.: NMR profile for particle quantifying/sizing should be added], an ApoB level [and also see cited study re:ApoAII], and of course circulating triglycerides are recommended to get a good picture (check recommendations, this is not advice). The cholesterol intake from egg consumption is in my opinion offset by the choline (or lecithin) content of eggs facilitating healthy fat metabolism.
What seems to be more well established is that dietary saturated fat intake leads to increased LDL levels, which for some people may be problematic. The cholesterol hypothesis, roughly speaking, is that (LDL) cholesterol becoming oxidized and deposited in the endothelium is the mechanism of development for atherosclerosis. I do not think it is still held that dietary cholesterol is the main part of the mechanism, rather that the interplay between dietary fat and endogenous cholesterol metabolism can lead to oxidation and deposition of cholesterol plaques. The susceptibility to oxidation/inappropriate deposition I think is tied to the particle size...
As an aside, @exchemist, I do not think olive oil should be eschewed, as I think MUFA and PUFA are not shown to increase LDL "cholesterol". But yes perhaps control total fat intake--although Mediterranean ratio of <=30-40% total kCal I think is good... Again, IMO, traditional statins are very problematic in interrupting mevalonate->cholesterol, because it's then interferring with everything downstream in the steroid pathways (and muscle pain, weakness, and atrophy are underreported), let alone that cholesterol is a structural component in animal cell membranes. Perhaps look into psyllium husk, berberine, niacin (nicotinic acid) for cholesterol lowering? And do address choline/lecithin via eggs, liver, or perhaps a lecithin supplement for various things; or if you want to take statins for their anti-inflammatory and CVD protective effects it may be worthwhile investigating increasing dietary cholesterol. You may want an NMR lipid profile before even concluding that your levels are telling the tale, because the particle size/density may be more important. Friendly advice, not medical, and I should re-acquaint myself with the current literature, or any new evidence on the matter.
0 -
5 minutes ago, studiot said:
All I see is a yellow (ish) box with a date and time popping up.
But if you really have found a numbering system that would be marvelous.
chromebook Shenanigans displays url on webpage lower left-hand side on my end. Perhaps right-click, copy link address, paste it and it'll be at end of url.
0 -
On 2/13/2023 at 11:59 AM, studiot said:
Please quote the passage since this forum insists on not numbering the posts.
couldn't add edit to #1229842, so for what it's worth here, if you hover over the time stamp on a post the last # in the url (e.g. in your post above #1229844) looks like the post number over the whole forum.
0 -
23 hours ago, studiot said:
Did I ?
Please quote the passage since this forum insists on not numbering the posts.
In order to show that some set S constitutes a mathematical Field it is necessary to prove that S and its elements satisfy each and every one of the 11 Field axioms.
https://www2.math.upenn.edu/~kazdan/202F13/notes/FieldAxioms.pdf
If it is a field with extra properties these are extra axioms that will also need proof.
But remember each and every axiom must be proven satisfied.
I suppose I quibbled,
"Accept this definition from wikipedia."
And your stance is,
"That is unacceptable."
It was on the issue that I'd missed a point you were emphasizing about Fields, but I didn't see the point, and wanted to wave it away and make do with a "group", though I didn't define the group operation well, either.I grant your recent echoed point. I am out walking the dog in the... p-1ark!... and uncertain on which end is the wiener, in natural casing, and which end is gauging the walking. So I think it is a confusion of the mathematical theory and matematical modeling, which is nuanced, but I think it is good.
I had premised that I wanted to take as granted the sets and their field axioms. In going in to describe the problem in situ, I think there needs to be a failure of the commutator. My work-up is not formally acceptable or explicit.
I think that commutative multiplication can describe energy being added to a particle. I think the failure of the commutator to allow addition can describe the phenomena discussed. I do not think it is too far afield to have your wiener and walk it, too, if on a lattice gauge the spacing in the physics field is bringing together the interactions that are described by the operations that characterize the mathematical field.
The
book recommended Thursday is in the mail. +1 over there. Ought to walk before you run, and a group is more basic than a field, so maybe start there? Perhaps you have some thoughts on the set
to generate a group?
On 2/13/2023 at 6:16 AM, joigus said:I'm OK with that. Every time mathematicians publish a proof, there's a time period during which the jury is still out.
Another caveat on terminology though. Mathematically-minded people like to say 'QFT is a functor' --thereby 'functorial.' This is a concept in category theory. People also say 'action is a 'functional' --a function of function that produces a number. Those are very different concepts with very similar terms, so it's necessary to tread carefully.
I need to study the Lagrangian formalism, among other things. And be more precise in my terms and work-up to be taken seriously... Tread carefully.
0 -
9 hours ago, joigus said:
Sorry I can't comment much on that. I know next to nothing about Polyakov loops. From what I gather, those are Wilson loops applied to a QFT upon which you've performed a Wick rotation. I suppose they give you topological invariants of the corresponding thermal theory?
In TQFT, for Wilson loops the expectation value does not change under smooth deformations..They are gauge invariant.
By Wick rotations obects from thermal physics, exp(βH), are related to quantum physics, exp(−iH T).. Polyakov loop is "thermal analogue" to Wilson loop..
An imaginary temporal compactification, length of β=1/T(emp.), leads to topologically nontrivial loops around the compact direction known as Polyakov loops. Those loops (assuming the group center change of basis is not trivial) are gauge dependent,6 hours ago, joigus said:Here. I didn't remember very well. Mathematicians seem to have proved it's unsolvable, on account of incompleteness theorems:
Ok. I read your questions on TQFT, and those and the leads to "functorials", etc., look interesting. Interesting formulation. Thanks for this, article, too, but they make statements with caveats, so I wouldn't conclude it's unsolvable.
0 -
59 minutes ago, studiot said:
That's why I have given up on this thread a long time ago. +1
I'll repeat the distinction between the two.
QuoteIn mathematics, a field is a set on which addition, subtraction, multiplication, and division are defined and behave as the corresponding operations on rational and real numbers do. A field is thus a fundamental algebraic structure [...]
Most importantly for algebraic purposes, any field may be used as the scalars for a vector space, which is the standard general context for linear algebra. [...]
Fields can also be defined in different, but equivalent ways. One can alternatively define a field by four binary operations (addition, subtraction, multiplication, and division) and their required properties. Division by zero is, by definition, excluded.[2] In order to avoid existential quantifiers, fields can be defined by two binary operations (addition and multiplication), two unary operations (yielding the additive and multiplicative inverses respectively), and two nullary operations (the constants 0 and 1). These operations are then subject to the conditions above. Avoiding existential quantifiers is important in constructive mathematics and computing.[3] One may equivalently define a field by the same two binary operations, one unary operation (the multiplicative inverse), and two constants 1 and −1, since 0 = 1 + (−1) and −a = (−1)a.[nb 1]
[...]So addition and multiplication, multiplicative inverse, and effectively two nullary operations would be an equivalent way to define the field. I think I posited those, though I called addition non-commutative for the reasons I explained.
Quote----
In physics, a field is a physical quantity, represented by a scalar, vector, or tensor, that has a value for each point in space and time.[1][2][3You seemed to argue earlier that
wasn't a field--was it a problem with the operations I was proposing?
Feel free to give up. -10 -
1 hour ago, joigus said:
Sorry I can't comment much on that. I know next to nothing about Polyakov loops. From what I gather, those are Wilson loops applied to a QFT upon which you've performed a Wick rotation. I suppose they give you topological invariants of the corresponding thermal theory?
What I had in mind was a discrepancy in the trace -- a Wilson loop is functional if the perimeter measure is correct, whereas a Polyakov loop implies the area between confined states is what's needed (fuzzy re-hash). I think it's related to confinement and chiral symmetry breaking. I'll follow up on what you've mentioned.
I shouldn't have asked the last leading question, Glueballs. Would you explain what about it makes you think it "is considered to be the toughest problem around concerning physics?" I thought it was the conceptual or theoretical mathematical description of what has been pretty well established physically. So the back and forth between Physico-Mathematics, Mathematical-Physics; it does exist!
0 -
Quote
"We conjecture that in Yang–Mills theories the ratio between the ground-state glueball mass squared and the string tension is proportional to the ratio of the eigenvalues of quadratic Casimir operators in the adjoint and the fundamental representations. The proportionality constant depends on the dimension of the space-time only, and is henceforth universal. We argue that this universality, which is supported by available lattice results, is a direct consequence of area-law confinement. In order to explain this universal behavior, we provide three analytical arguments, based respectively on a Bethe–Salpeter analysis, on the saturation of the scale anomaly by the lightest scalar glueball and on QCD sum rules, commenting on the underlying assumptions that they entail and on their physical implications."
Emphasis addedSo does area-law confinement imply Polyakov loops to you? As opposed to Wilson loops being based on perimeter? Is the issue that glueballs need to have a prediction made about their lower mass bound?
0 -
-1 to 1st Lt post.
On 2/11/2023 at 12:01 AM, exchemist said:@toucanamentioned that. We know it seems important to them. We don’t know why, though. What does it do that satellites don’t, for instance?
+1 @TheVat's response. Antenna/transceiver in the near-field vs. far-field for a satellite?
On 2/11/2023 at 8:07 AM, iNow said:[...]
In truth, they’re still watching us right now today. Threads like this, what are people saying and speculating about. Which memes are rising to the top across social media platforms. What commentary is taking hold in chat rooms and engagement channels, which narratives are being pushed by influencers and aggregators. It really never ends.
Two-way street--this is a function of supercomputing power, and the U.S. and PRC lead the world, and are close competitors as far as I know. At least the mass of data is analyzed and distilled before intel assessment I reckon. FBI can hack back TOR layers and are dismissing cases without prejudice to not disclose the method.
21 hours ago, Genady said:@Alex_Krycek,
"I want to believe." Tic-tac shape noted. Cf. orb over Mosul.0 -
To clarify,
I'll say that the square root operation is a non-linear operation and cannot be performed at what I want to be the linear level so it functions as a place-holder, for the quark-antiquark here. I do not mean that -M is an anti-meson, but rather as though it's been rotated 180degrees.
Proton and anti-proton. Analagous to neutron, but the electron needs a work-up. So massive particles here, and there needs to be accounting for mass-energy equivalence. I think particle-antiparticle meeting can bring the annihilation, crossing the zero limit to produce massless emissions.
23 hours ago, joigus said:I think you're still confused as concerns 'fields' in algebra vs 'fields' in physics. Very different things.
It's like 'dog' in 'hot dog' vs 'dog' in 'I'm walking my dog.'
The mathematical field gives scalars for a vector space. I think the physics field is quantifying x at points in space. We then can build up these vector spaces to the description of physical fields. This is out of order, but you know more about it than I do, Chief; there's a need to get to
, and I believe you know about projective spaces to get to more complexity.
I'm looking at how an algebraic number field could build up a description. I think it can be extended to a quadratic form if we take it that theis the variables of energy-momentum or mass. I don't know about the co-efficients yet or where it goes from linear to non-linear though I think that could help, but I'm not hot-dogging it anymore, I know I don't know enough.
I still hold that this quadratic field may be the real basis for the complex field...0 -
On 2/9/2023 at 3:10 PM, MigL said:
The F-35 is a very good interdictor/strike aircraft, but its networking capabilities give it great situational awareness and make it a good BVR ( beyond visual range ) figter also.
Shooting a sidewinder, or any other type of missile, from well below, will destroy the suspended payload, yielding no intelligence.
Better to attck it at similar altitude and taget the balloon.Yes, and thank you. I need to catch up on the thread --
but of course I was joking, a little... hypothetically, Frank Luke continues flying the plane, AEGIS could guide the hook shot:
?0 -
@studiot, @joigus, @swansont, @uncool, @Genady, @dimreepr, @StringJunky, @Markus Hanke, @Mordred, et al.,
https://www.claymath.org/sites/default/files/yangmills.pdf
I take for granted the standard construction of
sets and operations to generate their number fields.
There exists the set p of prime numbers from the set of integers. Given the square root operation, generate the set of all
for a set called p'. With elements of p'={a,b,c...} restriction conditions:
: the confinement conditions.
The idea here is to create a mathematical description of the physical situation. The math logic is that the square root operation cannot be performed on the set element, imposing non-commutativity on addition here when not considering annihilation--so what would be mathematical additive inverses do not cancel to zero. The description of a hadron (characterized above by capital letters M,P,N) jet (M) or gluon cloud (P,N), with different values for different energy levels (and other n-tuples for exotic forms). I don't know how to treat multiplicative associativity/commutativity here.A second condition:
: the gap condition.
This creates an identity element, and multiplicative inverses define 0. Additive inverses (or symmetric counter magnitudes) exist, but the operation is barred for the unaltered elements in the interests of creating certain 2-tuples and 3-tuples corresponding to confined hadrons. These confined n-tuples are then incorporated into an extended set.
The set then extends to a group. The group operation consists in generating these groups, though this seems redundant; now +q-q pairs or +u+u+d, +d+d+u can be equated as symmetries under rotation. Normal multiplicative associative rule and left- and right-distributive rules are posited (d/t need for non-commutative multiplication now in force as), applying any p'p'=p un-bars the radicand allowing commutative addition and subtraction (e.g. p2=1, p2+p2=n (n=2,3,...) which can be used to reconstruct the number sets
Let
be the quadratic fields available, complex and real. Using constructions analogous to references below I would like to construct a vector space with p' elements. In basic terms the elements are analogous to the real vector space, being that p' is intuitively mappable over the real line with magnitude and direction. It may be possible to extend these constructions to a Hilbert space. I do not know how to conceive this as a quadratic form, which may be necessary.
Noting the constructions and developments in references, the construction may be able to move from
to G3 to what should exist (within a subset of) 
4, and then a formulated Hilbert vector space with needed conditions. The aim is what can function as a compact gauge group that encodes the physical situation and can work to generate the gauge symmetry groups of the Standard model, provide for logical gauge transformations and account for renormalization (e.g. see exponentiations as equating to divergences in loop diagrams) or gauge fixing, and account for the mass gap. I do not know enough, I ask for your help, inputs, critique; I have gotten through 2 papers referenced and limited on 2 others.
Ref. 1: A. Jadczyk; On the bundle of Clifford algebras over the space of quadratic forms; Paper presented at the 12th International Conference on Clifford Algebras and their Applications in Mathematical Physics.; incomplete. For each quadratic form Q∈Quad(V) over a given vector space over a field K we have the Clifford algebra Cl(V,Q) defined as the quotient T(V)/I(Q) of the tensor algebra T(V) over the two-sided ideal generated by expressions of the form
Ref. 2: D. Hestenes; Oersted Medal Lecture 2002: Reforming the mathematical language of physics, Am. J. Phys. 71 (2), February 2003, pp. 104--121. ; complete. Geometric Algebra vector space construction, G3, "The rules for multiplying vectors are the basic grammar rules for GA, and they can be applied to vector spaces of any dimension."
Ref. 3: Ibid.; Spacetime Physics with Geometric Algebra, Am. J. Phys. 71 (6), June 2003, pp. 1--24) ; incomplete. extends GA to GR 4-D spacetime; clarifications of Dirac's theory/equation, QM implications.
Ref. 4: Kumar, K.N.P.; Yang–Mills Existence and Mass Gap(Unsolved Problem): Aufklärung La Altagsgeschichte: Enlightenment of a Micro History; International Journal of Scientific and Research Publications, Volume 3, Issue 10, October 2013.; 231pgs.; complete. Dense with formalism and repetitions--apparently Category Theory construction of Yang-Mills problem propositions from CMI or slightly less official source. Again, very repetitive--and I'm not sure this actually is anything-- but it is a categorizing of propositions, each one split three ways (G1,2,3, T1,2,3) the author then looks to transform by logic to lambda (calculus?) addition, reaching the conclusion, "And as one sees, all the coefficients are positive. It follows that all the roots have negative real part, and this proves the theorem." I do not believe the conclusion: this could just be an even worse attempt at proving Y-M existence &than what I put above. Possibly most value found at Ref. 3: Reifler, F.; Morris, R."Conditions for exact equivalence of Kaluza-Klein and Yang-Mills theories", Lockheed Martin Corporation MS2 137−205. Cited file (Kumar,231pgs.) too large: see https://www.ijsrp.org/research-paper-1013/ijsrp-p2248.pdf
For further research: Yukalov, Yukalova; self-similar approximation theory e.g. From asymptotic series to self-similar approximants.
P.s. I still need the Foundations of Mathematics by Stewart and Tall.
0 -
On 2/6/2023 at 1:08 PM, swansont said:
[...]
* it can’t, according to https://www.lockheedmartin.com/en-us/news/features/history/f-22.html
They say ~10 miles, which is ~52,000 feet. But I would imagine the actual value is classified
[...]22 hours ago, MigL said:[...]
Incidentally, Canadian CF-18, or even the future F-35, could not bring it down, even had they tried.Cool beans. I wonder if all the pooh-poohing about the shit can the F-35 is is an Art of War tactic. "Oh, this thing can't fly. Oh, we can't figure out it's HUD or radar." You tellin' me I can't fly right below that there baloon and fire off me sidewinder, set my jet on autopilot, and fly that missile by wire straight up into that balloon? What, I need some extra propellant?
On 2/6/2023 at 10:49 AM, TheVat said:[...]Our next step is clear: obtain a Macy's Thanksgiving Day parade float and release it from an allied nation that's upwind of China. Mickey Mouse would get my vote.
On 2/6/2023 at 11:46 AM, geordief said:Oh no Micky sounds like President MiXi.They would surely take offense.Donald Duck may have more legs.
But filled with agricultural fertiliser by all means.
..It's got to be Pooh.. that last part is a Pooh reference! Peter Pan is probably most offensive, especially if we use the Wuhite verion.
0 -
Well... "interpretations of QM", or, what sort of "spin" are they putting on it?
My own bête noire in physics, I'd thought it a mere phantasm, I've found still lurks in the math. I recommend this introductory paper on Geometric Algebra(GA): Oersted Medal Lecture 2002: Reforming the Mathematical Language of Physics, by David Hestenes, Department of Physics and Astronomy Arizona State University (.pdf, attached)
In the Schrödinger wave equation, in developing the operator formalism I couldn't understand the treatment of the -iħ term; I still don't. I'd seen i was treated differently in matrix mechanics, and read it was regarded as the phase angle of the wave. After Hestenes's initial math work-up, he goes on to demonstrate that -iħ is actually encoding spin.
The GA formalism builds up vector multiplication differently as the geometric product: a sum of a symmetric inner product and an antisymmetric outer product. There is an absence of commutative rule, but left and right distributivity are given seperately, and there is a contraction rule peculiar to GA. The outer, "wedge", product is related to the traditional cross product by a ∧ b = i a × b, and so the geometric product of vectors a and b can be stated as ab = a ·b + i a × b .
The multivector form, M = α + a + ib + iβ (30), is comprised of a scalar, vector, bivector, and pseudoscalar, so "the Geometric Algebra G3 is a linear space of dimension 1 + 3 + 3 + 1 = 23 = 8. The expansion (30) has the formal algebraic structure of a “complex scalar” α + iβ added to a “complex vector” a + ib, but any physical interpretation attributed to this structure hinges on the geometric meaning of i...".
He develops some natural facility for reflections and rotations, which given a normal basis are co-ordinate free, and develops "rotors", which are equatable to quaternions. From my basic understand, a Clifford algebra is a combination of the Grassman algebra and Hamilton's quaternion algebra; Clifford had called it geometric algebra and Hestenes seems to have been devoted to developing this math formalism that Grassman had started.
QuoteThis is a good place to summarize with a list of the advantages of the GA approach to rotations, including some to be explained in subsequent Sections:
1. Coordinate-free formulation and computation.
2. Simple algebraic composition.
3. Geometric depiction of rotors as directed arcs.
4. Rotor products depicted as addition of directed arcs.
5. Integration of rotations and reflections in a single method.
6. Efficient parameterizations (see ref.16 for details).
7. Smooth articulation with matrix methods.
8. Rotational kinematics without matrices.
Moreover, the approach generalizes directly to Lorentz transformations, as will be demonstrated in a subsequent paper.
Pg. 23QuoteThe point of all this is that GA reduces the set of three vectorial equations (57) to the single rotor equation (55), which is easier to solve and analyze for given
[Ed.:where
,
is te angular(rotational) velocity]. Specific solutions for problems in rigid body mechanics are discussed elsewhere.16 However, the main reason for introducing the classical rotor equation of motion in this lecture is to show its equivalence to equations in quantum mechanics given below.
Pg. 24 Emphasis, clarification addedQuoteVII. Real Quantum Mechanics
Schroedinger’s version of quantum mechanics requires that the state of an electron be represented by a complex wave function ψ = ψ(x, t), and Born added that the real bilinear function ρ = ψψ† (70) should be interpreted as a probability density for finding the electron at point x at time t. This mysterious relation between probability and a complex wave
Pg. 26
function has stimulated a veritable orgy of philosophical speculation about the nature of matter and our knowledge of it. Curiously, virtually all philosophizing about the interpretation of quantum mechanics has been based on Schroedinger theory, despite the fact that electrons, like all other fermions, are known to have intrinsic spin. We shall see that that is a serious mistake, for it is only in a theory with electron spin that one can see why the wave function is complex. You may wonder why this fact is not common knowledge. The reason is that the geometric meaning of the wave function lies buried in the standard matrix version of the Pauli theory. We shall exhume it by translating the matrix wave function Ψ into a real spinor ψ in GA where, as we have seen, every
has a geometric meaning. We discover then that the
[...]
In particular, we find that the spinor wave function operates as a rotor in essentially the same way as rotors in classical mechanics. This suggests that the bilinear dependence of observables on the wave function is not unique to quantum mechanics — it is equally natural in classical mechanics for geometrical reasons. Though the relation of spin to the unit imaginary was first discovered in the Dirac theory,21, 22 it is easiest to see in the Pauli theory. The resulting real spinor wave equation leads to the surprising conclusion that spin was inadvertently incorporated into the original Schroedinger equation in the guise of the distinctive factor
Pg. 27
QuoteThus,
is the eigenvalue of the “spin operator” S. Otherwise said, the factor
in the Pauli matrix equation (75) is a representation of the spin bivector by its eigenvalue. The eigenvalue is imaginary because the spin tensor Sij = −Sji is skewsymmetric. We can conclude, therefore, that spin was originally introduced into quantum mechanics with the factor
Pg. 32
This is identical to the classical expression for the rotational kinetic energy of a rigid body with angular momentum 2s. 16 All this suggests that the rotor U describes continuous kinematics of electron motion rather than a probabilistic combination of spin-up and spin-down states as asserted in conventional Pauli theory. The most surprising thing about the energy expression (104) is that it applies to any solution of the Schroedinger equation, where
. But, according to (102), e1 and e2 are spinning about the spin axis with angular velocity ω, and (104) associates energy with the rotation rate. The big question is, “What is the physical meaning of this spinning?”
Pg. 33
There is also the paper Spacetime Physics with Geometric Algebra (.pdf attached), the sequel to the Ørsted medal lecture paper, with Section VIII: Interpretations of Quantum Mechanics.
1 -
Sika Technology AG Comprehensive understanding of grinding aids
Quote[Pg.4] [...]On the other hand, commercial grinding aids consist of nonpolar hydrocarbon skeletons as well as polar functional groups. The latter interact readily with clinker. The majority of active compounds are alcohols, i.e. they have polar organic hydroxide groups (R-OH). Triethanolamine (TEA) is a trialcohol and diethylene glycol (DEG) is a di-alcohol. Very good grinding performance is also achieved using some mono-alcohols, such as isopropanol. However, these are not used in commercial cement production because of their low boiling points (< 100 °C)[...]
[Pg.6-7][...]4.2 Agglomeration energy of C3 S and C3 A
Agglomeration energy can be understood as follows: the release of stored energy when two parallel relaxed cleaved surfaces come together or equally the required energy to separate them. Dry and hydroxylated tricalcium silicate surfaces (“C3 S”, “HC”) without and with various grinding aids were simulated in analogy with Figures 9-13. Figures 16 and 17 show a monomolecular layer of glycerine in the confined and separated states between cleaved C3 S surfaces. The difference between the two calculated energy levels is the agglomeration energy.The distribution of the glycerine molecules in the separated state does not play a crucial role [2].
An example with equal distribution is shown in Figure 18. The agglomeration energy (Fig. 19, data in mJ/m2 of surface) correlates at 90°C inversely with the grinding performance of clinker in the laboratory trials [2].
Agglomeration energy: C3 S > HC > HC-glycerine > HC-TEA > HC-TIPA > HC-MDIPA
Grinding performance: Clinker < HC < HC-glycerine < HC-TEA < HC-TIPA < HC-MDIPA
Not all clinker phases behave the same. In case of tricalcium aluminate (C3 A), the agglomeration energies and their ranking are partially quite different as is shown in Figure 20 (data in mJ/m2 of surface) [11].
Agglomeration energy: C3 A > HC > HC-TIPA > HC-glycerine > HC-TEA > HC-MDIPA
C3 A surfaces covered with TIPA have higher agglomeration energy than C3 S surfaces covered with TIPA, while the opposite behaviour is obtained with all other organic molecules. And, even more important, the agglomeration energies of dry and hydroxylated C3 A are almost double those of the corresponding values for C3 S. The beneficial effect of grinding aids is therefore substantially more marked with C3 A than with C3 S. This means that grinding aids can equalize to some extent the different grindabilities of the clinker phases and thus also of clinkers with different compositions.It doesn't sound like you're sintering to clinker, which is the focus of the above paper. From there,
Reference [16] Sohoni, S., Sridhar, R., Mandal, G.: The effect of grinding aids on the fine grinding of limestone, quartz and Portland cement clinker, Powder Technology 67 (1991), pp. 277–286 Science Direct.comQuoteAbstract
The effectiveness of seven grinding aids, namely triethanolamine, mono- and diethylene glycols, oleic acid, sodium oleate, sulphite waste liquor and dodecylbenzene sulphonic acid on the batch grinding of Portland cement clinker, limestone and quartz was investigated in a laboratory ball mill.
The initial stages of grinding of the materials studied, without the use of grinding aids, were found to depend on their Moh's hardness. Excessive shell and ball coatings led to virtual stoppage of fine grinding of cement clinker and limestone. Quartz, which did not exhibit this property, continued to grind finer.
All the grinding aids studied have been found to be effective in variable degrees. While the grinding aids had only a marginal effect on the grinding of quartz, they had a significantly beneficial effect on the grinding of limestone and cement clinker. Triethanolamine appeared to be the most effective of all the aids studied. In the grinding of cement clinker, gypsum also acted as a very effective grinding aid. The action of these additives has been attributed to their ability to prevent agglomeration and ball and mill coatings of the powder.Pubchem Triethanolamine BP 335-350°C
1
Number theory derivation from infinity; speculations on equations that are derived in terms of the Field
in Speculations
Posted · Edited by NTuft
style correction, added address
@swansont,
Using Weber's electrodynamics we can substitute masses for charges to get a description of gravitational force. By my read, it wouldn't need monopoles or point charges then -- the masses act like point charges. It does reduce to Newtonian gravity, and with Mach's principle the system is extended as Relational Dynamics by A.K.T. Assis.
Any thoughts on that? I'm pro-particle. You want to discuss the science I brought up on that? It was an overture to your particle leanings, I thought you'd like to discuss the cosmology development and why we can't find magnetic monopoles.
@studiot,
I think you had the technical issue explained to you by someone else, too? You have it figured now? Thanks to you and @joigus for more input here, and keywords.. I'll try to follow up. You guys all sure know a lot.