scholarly journals The Exact Theory of the Stern–Gerlach Experiment and Why it Does Not Imply that a Fermion Can Only Have Its Spin Up or Down

Symmetry ◽  
2021 ◽  
Vol 13 (1) ◽  
pp. 134
Author(s):  
Gerrit Coddens
Keyword(s):  
Magnetic Field ◽  
Paradigm Shift ◽  
Reference Frames ◽  
Euclidean Geometry ◽  
Pauli Principle ◽  
Left Handed ◽  
Energy States ◽  
The Many ◽  
The Magnetic Field ◽  
The Continuum

The Stern–Gerlach experiment is notoriously counter-intuitive. The official theory is that the spin of a fermion remains always aligned with the magnetic field. Its directions are thus quantized: It can only be spin-up or spin-down. However, that theory is based on mathematical errors in the way it (mis)treats spinors and group theory. We present here a mathematically rigorous theory for a fermion in a magnetic field, which is no longer counter-intuitive. It is based on an understanding of spinors in SU(2) which is only Euclidean geometry. Contrary to what Pauli has been reading into the Stern–Gerlach experiment, the spin directions are not quantized. The new corrected paradigm, which solves all conceptual problems, is that the fermions precess around the magnetic-field just as Einstein and Ehrenfest had conjectured. Surprisingly, this leads to only two energy states, which should be qualified as precession-up and precession-down rather than spin-up and spin-down. Indeed, despite the presence of the many different possible angles θ between the spin axis s and the magnetic field B, the fermions can only have two possible energies m0c2±μB. The values ±μB thus do not correspond to the continuum of values −μ·B Einstein and Ehrenfest had conjectured. The energy term V=−μ·B is a macroscopic quantity. It is a statistical average over a large ensemble of fermions distributed over the two microscopic states with energies ±μB, and as such not valid for individual fermions. The two fermion states with energy ±μB are not potential-energy states. We also explain the mathematically rigorous meaning of the up and down spinors. They represent left-handed and right-handed reference frames, such that now everything is intuitively clear and understandable in simple geometrical terms. The paradigm shift does not affect the Pauli principle.

Humanity Imperiled by the Geomagnetic Field and Human Corruption

2021 ◽  
Vol 8 (1) ◽  
pp. 456-478
Author(s):  
J. Marvin Herndon
Keyword(s):  
Magnetic Field ◽  
Solar Wind ◽  
Charged Particle ◽  
Geomagnetic Field ◽  
Paradigm Shift ◽  
Government Officials ◽  
The Public ◽  
Person Perspective ◽  
First Person Perspective ◽  
The Many

Earth’s magnetic field acts as a shield, protecting life and our electrically-based infrastructure from the rampaging, charged-particle solar wind. In the geologic past, the geomagnetic field has collapsed, with or without polarity reversal, and inevitably it will again. The potential consequences of geomagnetic collapse have not only been greatly underestimated, but governments, scientists, and the public have been deceived as to the underlying science. Instead of trying to refute or advance a paradigm shift that occurred in 1979, global geoscientists, individuals and institutions, chose to function as a cartel and continued to promote their very-flawed concepts that had their origin in the 1930s and 1940s, consequently wasting vast amounts of taxpayer-provided research money, and making no meaningful advances or understanding. Here, from a first person perspective, I describe the logical progression of understanding from that paradigm shift, review the advances made and their concomitant implications, and touch upon a few of the many efforts that were made to deceive government officials, scientists, and the public. It is worrisome that geoscientists almost universally have engaged in suppressing or ignoring sound scientific advances, including those with potentially adverse implications for humanity. All of this suggests that the entire institutional structure of the geophysical sciences, funding, institutions, and bureaucracies should be radically reformed.

scholarly journals Properties of the Solar Filigree Structure

1974 ◽  
Vol 56 ◽  
pp. 45-47
Author(s):  
R. B. Dunn ◽  
J. B. Zirker ◽  
J. M. Beckers
Keyword(s):  
Magnetic Field ◽  
Fine Structure ◽  
Solar Physics ◽  
List Type ◽  
Blue Wing ◽  
One To One ◽  
Granulation Pattern ◽  
Network Patterns ◽  
The Magnetic Field ◽  
The Continuum

A number of observers have noted the presence of bright structures near the cores of the chromospheric rosettes when observed in the far wings of the Hα line (eg Hα ±7/8 Å). Dunn and Zirker observed these bright structures with the highest possible resolution using the Sacramento Peak vacuum solar telescope. They find that these bright regions exhibit a very intricate fine structure which can be followed out much further into the Hα line wing (eg Hα + 2 Å) and even into the continuum. They called this fine structure ‘solar filigree’, the name referring mainly to the collective appearance of the fine structure elements. The elements themselves appear as dot-like structures and frequently also as small wiggly structures called ‘crinkles’. The properties of the filigree structure are summarized as follows: (i)Size: Measured diameter of the crinkles and dots equals 0.25, 0.40 and 0.60″ at Hα + 2 Å, Hα ± 7/8 Å and Hα ±5/8 Å respectively. The telescope resolution equals 0.22″ so that at Hα + 2 Å the structure is extremely small. The drawings in Figure 1 show typical sizes of the crinkles and network patterns in the filigree.(ii)Contrast: Filigree is enhanced in the blue wing of the Hα line. Measured contrast, uncorrected for seeing, equals 5–10%.(iii)Relation to the Granulation: The filigree structures tend to lie between the granules. This is, however, not a strict rule. It seems that in the course of their lifetime the granules move the filigree structures around with velocities of about 1.5 km s-1. Some of the crinkles also seem to wash out temporarily until compressed again by a new granule. The detailed structure of the filigree, therefore, changes significantly over times comparable to the granule lifetime. The overall structure is, however, preserved over much longer periods of time. The granulation pattern when observed in the continuum well outside the Hα line appears very peculiar in that it has substantially decreased in contrast. It appears ‘soft’ similar to granulation washed-out by seeing. This abnormal granulation can be traced over long times (> 30 min) and coincides in location to the filigree location. It is, therefore, definitely real.(iv)Relation to the spicules: The filigree structure falls near the center of the Hα chromospheric rosettes. These rosettes consist of dark elongated mottles which should probably be identified with spicules. There is, therefore, at least a coarse relation between the occurrence of spicules and the filigree. There is no clear evidence that variations in the filigree pattern are related to the generation of spicules. Some spicules seem to originate from the spaces between the crinkles. Too few, however, to conclude a definite relation.(v)Relation to the magnetic field: Beckers studied the filigree with the Universal Birefringent Filter in the magnesium b1 and b2 lines. It is very well visible in the far wing of the lines (eg. b1 ±0.8 Å). When traced into the line core the structures increase somewhat in size, as they do in Hα, and form structures similar to, and perhaps identical with, the so-called photospheric network. In the magnetically sensitive b2 line one sees a one-to-one correspondence between these network structures and the magnetic field so that, at least in the layers seen near the core of the b2 line, there is a one-to-one correspondence between the filigree structures and the enhancements in the magnetic field. Simon and Zirker (Solar Physics, submitted for publication) using a spectrograph also found that the filigree occurs in regions of enhanced magnetic field. However, in contrast to the filter observations, they found the magnetic field regions to be much more diffuse (2–3″) so that there is not a one-to-one spatial correspondence between filigree and magnetic field structure.

scholarly journals XIII.—The Strains Produced in Iron, Steel, and Nickel Tubes in the Magnetic Field. Part I.

1897 ◽  
Vol 38 (3) ◽  
pp. 527-555 ◽  
Author(s):  
C. G. Knott
Keyword(s):  
Magnetic Field ◽  
Short Note ◽  
Interesting Phenomenon ◽  
Senior Student ◽  
Sources Of Error ◽  
Physical Laboratory ◽  
The Many ◽  
Many Sources ◽  
The Magnetic Field ◽  
Interior Volume

On July 20th, 1891, I communicated to the Society a short note on the effect of longitudinal magnetisation on the interior volume of iron and nickel tubes (see Proceedings, 1890–91, pp. 315–7). These earliest results of observation of a new and interesting phenomenon in magnetic strains were obtained during my last few months' residence in Japan. In following out the lines of research therein suggested, I have been fortunate in having had placed at my disposal by Professor Tait the resources of the Physical Laboratory of Edinburgh University. I desire here to record my great indebtedness to him for the interest he has taken in the work, and for his many helpful suggestions. In surmounting the many experimental difficulties met with at every turn, I had the invaluable co-operation of Mr A. Shand, a senior student in the Physical Laboratory. Various results obtained since 1892 have been communicated in short notes from time to time (see Proceedings, 1891–2, pp. 85–88, 249–252; 1893–4, pp. 295–7; 1894–5, pp. 334–5; see also B. A. Reports, 1892 and 1893); but it was not possible to regard these as altogether satisfactory. It was only in May of last year (1895) that the many sources of error were finally got rid of, and the apparatus perfected. The present paper deals entirely with the results obtained since then. In these later experiments I was ably assisted by Mr A. C. Smith, a student in the Physical Laboratory.

scholarly journals Comparing extrapolations of the coronal magnetic field structure at 2.5R⊙with multi-viewpoint coronagraphic observations

2019 ◽  
Vol 627 ◽  
pp. A9 ◽  
Author(s):  
C. Sasso ◽  
R. F. Pinto ◽  
V. Andretta ◽  
R. A. Howard ◽  
A. Vourlidas ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Solar Corona ◽  
Large Scale ◽  
Solar Rotation ◽  
Coronal Holes ◽  
Coronal Magnetic Field ◽  
Central Meridian ◽  
Fast Method ◽  
The Many ◽  
The Magnetic Field

The magnetic field shapes the structure of the solar corona, but we still know little about the interrelationships between the coronal magnetic field configurations and the resulting quasi-stationary structures observed in coronagraphic images (such as streamers, plumes, and coronal holes). One way to obtain information on the large-scale structure of the coronal magnetic field is to extrapolate it from photospheric data and compare the results with coronagraphic images. Our aim is to verify whether this comparison can be a fast method to systematically determine the reliability of the many methods that are available for modeling the coronal magnetic field. Coronal fields are usually extrapolated from photospheric measurements that are typically obtained in a region close to the central meridian on the solar disk and are then compared with coronagraphic images at the limbs, acquired at least seven days before or after to account for solar rotation. This implicitly assumes that no significant changes occurred in the corona during that period. In this work, we combine images from three coronagraphs (SOHO/LASCO-C2 and the two STEREO/SECCHI-COR1) that observe the Sun from different viewing angles to build Carrington maps that cover the entire corona to reduce the effect of temporal evolution to about five days. We then compare the position of the observed streamers in these Carrington maps with that of the neutral lines obtained from four different magnetic field extrapolations to evaluate the performances of the latter in the solar corona. Our results show that the location of coronal streamers can provide important indications to distinguish between different magnetic field extrapolations.

scholarly journals An experiment on the origin of the earth's magnetic field

1923 ◽  
Vol 104 (727) ◽  
pp. 451-455 ◽  
Keyword(s):  
Magnetic Field ◽  
Slight Modification ◽  
Residual Effects ◽  
Earth’S Magnetic Field ◽  
Gravitational Action ◽  
Earth's Magnetic Field ◽  
Intimate Mixture ◽  
The Many ◽  
The Magnetic Field ◽  
Accepted Form

Of the many suggestions which have been made as to the origin of the earth’s magnetic field, perhaps the most promising is that it may be due to a slight modification of the laws of electrodynamics from the commonly accepted form. Electrically neutral matter is believed to consist of an intimate mixture of enormous amounts of positive and negative electricities, the electric and magnetic effects of which are usually supposed to balance each other. If the balance were not quite exact then small residual effects would be expected, among which gravitation and the earth’s magnetic field might be included. On such an hypothesis we might expect moving matter to produce a magnetic field similar to the field due to moving electricity, and we should expect some relation between the magnetic field due to moving matter and its gravitational action.

scholarly journals Continuum sensitivity and design optimization of superconducting systems under critical current densities with magnetic field dependence

2021 ◽  
Author(s):  
Kyungsik Seo ◽  
Tim Coombs ◽  
Il Han Park
Keyword(s):  
Magnetic Field ◽  
Design Optimization ◽  
Critical Current ◽  
Current Density ◽  
State Equation ◽  
Design Sensitivity ◽  
Continuum Sensitivity ◽  
Current Densities ◽  
The Magnetic Field ◽  
The Continuum

AbstractThis paper presents an approach for deriving the continuum sensitivity of superconducting systems operating at critical current densities and an optimization method based on the continuum sensitivity. In the sensitivity problem, the superconducting systems is represented by a variational state equation, wherein the magnetic permeability depends on the magnetic field, which is transformed from a state equation with a field-dependent source. The design sensitivity is derived using the material derivative concept of continuum mechanics and the adjoint variable method. The adjoint system has a material property represented as a symmetric tensor that contains the sensitivity of the current density with respect to the magnetic field. The design sensitivity is represented in the analytical form of a surface integral on the interface between the superconducting material and its surroundings, which depends on the sensitivity of the current density. The optimization scheme is constructed based on the continuum design sensitivity. In the design optimization, the level set method is used to express the shape variation of the superconducting materials. The numerical example of infinite solenoids demonstrates that the design sensitivity provides an accurate design solution considering the critical current condition. In addition, the design example of a magnetic resonance imaging solenoid shows that the derived design sensitivity has the inherent ability for attaining the compact design by treating the input current of a superconducting system as a critical condition.

WHITE NOISE PATH INTEGRAL TREATMENT OF THE PROBABILITY DISTRIBUTION FOR THE AREA ENCLOSED BY A POLYMER LOOP IN CROSSED ELECTRIC-MAGNETIC FIELDS

2012 ◽  
Vol 17 ◽  
pp. 77-82
Author(s):  
BEVERLY V. GEMAO ◽  
JINKY B. BORNALES
Keyword(s):  
Magnetic Field ◽  
Brownian Motion ◽  
Probability Distribution ◽  
Magnetic Fields ◽  
White Noise ◽  
Probability Density ◽  
Path Integral ◽  
Integral Treatment ◽  
The Many ◽  
The Magnetic Field

The probability density for the area A enclosed by a polymer loop in crossed electric-magnetic fields is evaluated using the Hida-Streit formulation. In this approach, the many possible conformations of the polymer, x(v) and y(v), are represented by paths and are parametrized in terms Brownian motion. When the magnetic field is switched off, results agree with the works of Khandekar and Wiegel5

scholarly journals The analysis of beams of moving charged particles by a magnetic field

1927 ◽  
Vol 114 (769) ◽  
pp. 729-744 ◽  
Keyword(s):  
Magnetic Field ◽  
Velocity Distribution ◽  
Charged Particles ◽  
Thin Layers ◽  
Homogeneous Groups ◽  
The Many ◽  
The Masses ◽  
Slow Electrons ◽  
Physical Quantities ◽  
The Magnetic Field

The practice of analysing beams of charged particles moving with different velocities by means of the magnetic field is now well established. Among the many important physical quantities which have been determined in this way must be included the value of e/m , the velocities, intensities and charge carried by the homogeneous β-ray groups of radioactive elements, the masses of iso­topes, and, recently, it has been applied to the analysis of very slow electrons. In most of this work it has only been necessary to find the energies of the various groups of charged particles, and for this purpose no detailed consideration of the focussing action of the magnetic field was necessary. Problems relating to the relative numbers of particles in the homogeneous groups cannot, however, be solved without more accurate knowledge of the action of the magnetic field, and it was in connection with the relative intensities of the β-ray groups of radium B and radium C that the work here described was started. In carrying out these calculations, it soon became evident that they had a much wider application than simply to the problem to which they owed their origin. In addition to furnishing a method of obtaining the structure of the line produced by the focussing action of the magnetic field for any kind of source of charged particles, these calculations indicate the best design for the apparatus containing the source of charged particles. Further, when applied to particles which have traversed thin layers of stopping material, the analysis leads to a knowledge of the velocity distribution of the retarded particles, Up to the present no method has been devised of finding this velocity distribution experimentally, and although the results obtained are only approximate, yet they show definitely that the method indicated here is quite practicable.

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