Stern Gerlach experiment 1922

In the original 1922 Stern Gerlach experiment the single horizontally propagating incident beam was split into two ‘up’ or ‘down’ diverging beams. An observation not consistent with predictions of the time which were that the path deflection angles in a classical model should be deflected up or down in only an even range of angles. Here it is proposed that net translational forces on a dipole in an inhomogeneous field can correctly model the observed split paths for a classical model. In that the dipoles will initially experience a range of very small path deflections via the up or down net translational forces on them as they enter the apparatus. A deflection force dependent upon the specific angle of the N-S axis of polarity of each incident dipole relative to the applied external N-S field in the apparatus. This separation of the beam into 2 paths, one up and one down is effectively a classical version of the “space quantisation” often referred to in QT. After entering the field, the dipoles will then have been sorted into two up and down paths as well as each path having a range of these very small different angled path deflections from the horizontal incident path. They will then all each experience an additional amount of net translational forces applied equally on all aligned dipoles as they propagate through the 3.2 cm length of the external field. Separating the 2 up and down sets into two distinct paths.

Introduction

Spin is a theoretical construct that seems to be preventing Quantum theorists from finding simpler solutions to experiments based on classical models only. Here it is proposed that if atoms are treated as magnetic dipoles subject to inhomogeneous magnetic fields, then the Stern Gerlach experiment can be explained sufficiently by a classical model.

We know in the experiment that the incident beam must consist of all angles of dipole polarisations. And so it follows that statistically this must be a 50/50 split. That is half must have their N pole facing up from any angle between horizontal to perpendicular to the beam path. And the other half must have the same range of angles between 0-90 degrees but all with their N pole facing down. And we know separately from experimental observations that a dipole will be repelled if its N pole faces towards the N pole of an external field. Or attracted if its S pole faces the external field’s N Pole. Implying that in a classical model, as it is also expected to do in QT, half of the dipoles will be initially deflected upwards in a range of angles by the external field. And half deflected downwards. Separately there is also a statistical preference for a greater number of dipoles with their N-S dipoles fields facing parallel to the direction of motion of the dipole in a beam.

In accordance with well accepted classical models of net force on dipoles in inhomogeneous fields each atom in the incident beam will experience a path deflection upon entering an inhomogeneous magnetic field depending on each incident atom’s dipole field angle relative to the external field. This path deflection is proportional to the net translational force imposed on the dipole by the inhomogeneous external field of the S -G apparatus. As illustrated in Fig 1, a dipole whose field angle is closest to perpendicular to the inhomogeneous field will receive the least net force. And a dipole oriented with its field parallel to the external field will receive the greatest net up or down force. It is at this moment of entry into the external magnetic field of the apparatus that this range of positive or negative deflections on the dipole paths are effected. And once inside the field, all dipole fields are now aligned N-S with the external field. From which point on a net translational force is then applied equally to all the now aligned dipoles as they pass through the 3.2 cm length of the inhomogeneous magnetic field part of the apparatus. A net up or down translational force which pulls the two “quantised” north south beams of dipoles farther and farther apart in curved paths. With each dipole receiving the same amount of net force up or down as all of the other dipoles. Illustrated in Fig 1 as the curved paths showing the effect of the constant up or down net translational forces on the moving dipoles. This net force eventually separates the beam into 2 North and south paths at the image plane. As is observed in the original S-G experiment. This initial up down range of path splitting of the deflected beams atoms based on incident dipole angles is essentially what is usually referred to as space quantisation in QT.

Separately, it is worth pointing out here that currently no published experiments showing the multiple beam paths predicted for other elements in a S-G apparatus and predicted by Quantum theory has ever been successfully completed. All available reference show that all single element S-G style tests always gave only the same double humped split paths in the image plane as the silver atoms did in the original experiment. Casting serious doubts over the validity of Quantum theory and its failed ‘space quantisation’ multi path predictions for atomic elements other than silver.

Quantisation into Positive or negative paths in a classical model

It is important here to explain in more detail how the beam splitting can be explained classically. In that the even spread of angles of dipole fields in the experiment, as predicted by a Classical model in 1922, can still be made consistent with the observed split paths at the image plane without invoking space quantisation. The answer lies in the fact that after the dipoles have upon entry aligned themselves with the external field, the net translational force up or down on a dipole will be constant for all dipoles travelling in the horizontal beam equally as they pass through the rest of the 3.2 cm of external N-S field. Which means that all angles of paths with up (down) directions will now be pulled up (down) additionally by the same amount of force away from their original horizontal path. Take for example a dipole whose path angle away from the horizontal after entering the field will have been deflected upwards by a very small path deviation of an angle of only 0.00000001 degrees. If one calculates what path deflection that would give after travelling 3.2 cm it would not be measurable. This is also close enough to be statistically considered as zero dipoles in the beam at this angle for the purposes of modelling the experiment. But after it travels through the 3.2 cm of the beam this aligned dipole will also have been subjected to a total additional amount of net up translational force from the external field. And that total would have deflected the dipole up by an additional angle to its path to become measurable. That amount in the Stern Gerlach experiment was observed to be between a 0.1mm to 0.2mm path shift from the original horizontal path. Effectively creating the atom free empty middle band in the image plane in a classical model.

Stage 2 and 3 deflection paths modelled classically

To make stages 2 and 3 also consistent with a classical model one can then assume that after stage 1 as outlined above, all the silver atoms polarities have field directions that match the inhomogeneous field of stage 1. When travelling through the stage 2 inhomogeneous field, which is also in the same magnetic field orientation as stage 1, no splitting of the beam will occur in stage 2. As the beam of silver atoms polarities are now lined up with both the stage 1 and 2 external fields. The beam will only be deflected up towards the stronger N pole of the external field due to net translational forces on each dipole in the beam. And proceed as a single deflected beam to stage 3. In stage 3 the dipole alignment process resets and starts over again to repeat the same splitting process as seen in stage 1. Because the beam entering stage 3 has all its atoms polarities in the beam now aligned at right angles to the applied inhomogeneous field in stage 3. And therefore, all dipoles will have to have their polarities rotated and deflected up or down so as to be re-aligned again to the stage 3 external field. Unfortunately, this purely classical effect seen in stages 2 and 3 is also often misinterpreted in QT as space quantisation.

Summary and conclusion

Upon entry into the inhomogeneous field of the apparatus the incident dipoles experience an initial deflection proportional to the angle between the specific dipole field angle and the direction of the inhomogeneous external field. This sorts the incoming beam into two sets of paths. One up and one down. Each path has a range of deflection angles from the original beam path. Deflections which are still much too small to be measurable at the image plane in Stern Gerlach. It is important to note that at this point all the atoms have also had their dipole field angles re-aligned with the North South external field by rotational force.

What is remarkable is that Quantum theorists then and now have been unable to understand the basics of net translational magnetic effects on dipoles. In that they don’t seem to realise that net force initially separates the dipoles into either up or down paths upon their entry into the external field with a range of net forces proportional to the incident dipole angles. At which point the now aligned dipoles in each set all experience the same total of net translational force from the external field as they continue on through the 3.2 cm path in the apparatus. And it is this net force which further separates the up or down sets to become observable as two separate beams at the other end of the apparatus field. 

Reference

1. The Stern-Gerlach Experiment Translation of: “Der experimentelle Nachweis der Richtungsquantelung im Magnetfeld” 2023 Martin Bauer

Sunspot magnetic field modelled with a variable speed inner core solar dynamo

Current theory on solar magnetic fields posits that the overall solar and local sunspot magnetic fields are created by thermal convection heating in the convection zone. Which then creates the overall solar dipole magnetic field and also the observed Magnetic field loops at the photosphere which then drive the physical rotations of the plasma in sunspots.

The novel Variable speed core solar dynamo model described in this paper here proposes exactly the opposite. In that it is the differential rotation of the solar plasma in the convection zone due to the suns rotation, that is the mechanism that produces the dynamo that induces the observed solar magnetic field. A model where the suns dipole polarity reverses depending on whether the inner core rotates slower or faster than the plasma in the outer convection zone. A cycle of 11 year slower, then 11 year faster periods called the solar cycle. In each cycle this differential rotation also creates local eddy currents or vortices in the plasma. These vortices are observed at the photosphere as sunspots.

For sunspots, where the rotation axis of the plasma vortex of the sunspot is at right angles to the suns surface (pointing straight up from the suns surface), then the direction of the local induced dipole magnetic field of the sunspot predicted by the Variable speed core solar dynamo model will be parallel to the rotation axis of the plasma in the sunspot. The sunspot magnetic field in this model is thus predicted to be orthogonal to the suns surface. That is, it should point straight up from the suns surface. This is confirmed in Borrero et al 2014, where the authors found that there is also a further link between sunspot magnetic polarity and direction and the physical rotation of the plasma vortex that creates the sunspot. They observed that the polarity of the sunspot magnetic field is dictated by the direction of rotation of the sunspot vortex. Clockwise gives positive polarity, counter clockwise negative. This rotation direction/polarity relationship is also consistent with and predicted by the Variable speed core solar dynamo model. 

Borrero et al also confirm that the sunspot magnetic field is at it strongest and points directly outwards-upwards from the surface of the photosphere at the center of the the rotating sunspot, the umbra, and declines in strength and to more tangental directions relative to the suns surface the farther out from the center of the rotating sunspot one looks. Confirming the Variable speed core solar dynamo model’s predictions. Which propose that the differing velocity gradient across the rotating plasma of the sunspot produces a N-S magnetic field parallel to the axis of the rotating plasma that is also strongest at the center of the axis of rotation.

We also know from various studies including Yan et al, 2008 that not only do sunspots vortices rotate, they also have opposite sunspot rotations and magnetic polarities between the hemispheres. In that if in any solar cycle there are more positive magnetic polarities in the northern hemisphere then will always be more negative polarities in the Southern Hemisphere. And vice versa for subsequent cycles. This further confirms predictions made by the Variable speed core solar dynamo model which posits that differential  rotation of the plasma will induce, on average, opposite rotations of sunspots in opposite hemispheres. And in turn these rotational directions of the sunspot plasma will induce opposite polarities depending on whether the rotation is CW or CCW.

This relationship between rotational velocity of the sunspot plasma and its its induced magnetic field in the variable speed model is additionally confirmed in Li and Liu 2015 and Wang et al. 2016: “There is a direct relationship between rotations and the triggering of solar flares. Across all of the active regions examined, there are a number of commonalities observed in the rotational behaviour of sunspot groups. As expected, the higher-flaring regions show much higher average angular velocity values”.

Another study by Brown, Nightingale et al, found a connection between the increased activity of a coronal loop with a speeding up of the rotation of a sunspot. Further confirming that the physical rotational period of the dynamo of the rotating sunspot plasma dictates not only the direction of the induced field but its strength.

And in this following paper it is also found that sunspot rotations reverse rotational directions and polarities between solar cycles.  Consistent with the variable speed model where it is predicted that the slowing down or speeding up of the inner core relative to the convection zone between 11 year solar cycles will reverse the direction of the differential rotation every 11 years. In other words clockwise rotation of the plasma induces an opposite polarity to counter clockwise rotation. Further confirming that the physical rotation of the convection zone  plasma is the dynamo driver that induces the overall solar and local sunspot magnetic fields.

And in their 2016 paper Zheng et al also observed the following: “In the year of 2003, the α sunspot groups and the preceding sunspots tend to rotate counterclockwise and have positive magnetic polarity in the northern hemisphere. In the southern hemisphere, the magnetic polarity and rotational tendency of the α sunspot groups and the preceding sunspots are opposite to the northern hemisphere. From 2014 January to 2015 February, the α sunspot groups and the preceding sunspots tend to rotate clockwise and have negative magnetic polarity in the northern hemisphere. The patterns of rotation and magnetic polarity of the southern hemisphere are also opposite to those of the northern hemisphere.” Zheng et al, 2016.

These observations are also consistent with the Variable speed core solar dynamo model. In that not only are the polarities of sunspots dictated by the direction of sunspot rotation, but that the average overall direction of rotation of sunspots for each hemisphere reverses between each succesive solar cycle. 

Summary

These various data cited above confirm predictions made by a Variable speed core solar dynamo model that the more solid solar inner core rotates faster and then slower than the outer part of the convection zone at the photosphere. Producing an equatorial east west reversal* in the rotation direction of the convection zone plasma every 11 years. And in turn inducing local eddy currents in the plasma and observe as sunspots at the photosphere

*A reversal in the direction of the rotation of the convection zone in an observer frame that rotates with the suns mass around its axis. (Imagine hovering above a sunspot on the sun as it rotates around the suns axis of rotation.) 

This is not the same frame as the heliocentric frame where the sun rotates around its axis in the observer frame and the inner core is then said to be rotating faster then slower than the outer convection zone plasma.