The Bell Inequality

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote"><i>Originally posted by pshrodr</i>
<br />is what I wrote actually a synopsis of the experiment?<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">That might be one way to describe it.

<blockquote id="quote"><font size="2" face="Verdana, Arial, Helvetica" id="quote">quote:<hr height="1" noshade id="quote">If so, then it appears like someone devised a numerical illusion to play on someone else and the whole community fell for it.<hr height="1" noshade id="quote"></blockquote id="quote"></font id="quote">The debates between Bohr and Einstein had much at stake. Physicists tended to line up according to their professional and financial interests rather than according to the merit of the arguments.

If this sounds like the description of today's physicists and astronomers too, I would be hard-pressed to disagree. This phenomenon exists because, in the words of P.A.M. Dirac, "the number of physicists truly contributing to the advancement of the field is about ten, and that number has not been increasing with time." Put less tactfully, the rest are "sheep" in that they tend to pick experts to follow instead of making an independent assessment of the merit of the arguments, which requires more knowledge, experience, and guts to do. -|Tom|-

Rather than extend my analysis of the Bell inequality, I investigated the Stern Gerloch EPR puzzle yesterday and figured out the solution. Potentially the same readers of the other submission will be interested in this.


The Stern Gerlach Experiment/ EPR puzzle solution.

This is the explanation of why placing a filter tipped by 90 degrees between one at 0 degrees and one at 180 degrees allows electrons to pass through the 180 degree tipped box when no electrons pass without the inclusion of the 90 degree tipped box.

Electrons are shot from a gun at the first box, and are assumed to have any orientation. Box 1 is set up with magnets to remove electrons of the spin down state. Electrons are said to have only 2 states, spin up and spin down. However, within a state such as spin up there is a whole northern hemisphere in which the axis of the counterclockwise spin can be located.

The orientation is pictured by making a right hand fist with the thumb extended up. As just indicated, the concept of up means the thumb is pointed any direction above an assumed equator.
The fingers represent the direction of the spin and the tilt of their circles relative to the horizontal. We believe that any of these spin up arrangements of an electron are such that they will be attracted by the north pole of a magnet. Since the spin down electrons are repelled by the north pole or identically attracted by the south pole of the magnet, this property is used to remove them from passage through the box.

Now, the interaction between the magnet and the electron has another property which actually might be part of the attraction characteristic it applies to spin up particles such as electrons. This other property is that the magnet provides spin which is parallel to the direction in which it attracts these spin up ‘negative’ charge electrons. This new spin is than forced onto the electron. In this process it is merged with the existing spin of the electron. So, as an example, if we have an electron spinning with a north pole axis and the magnet adds a spin centered on the equator at longitude 0 degrees, A new net spin will be produced that redefines the spin of the electron. Assume the 2 spins are equal in magnitude. Then there will be a single new axis of rotation which is centered at 45 degrees north latitude, 0 degrees longitude.

We can then consider any point in the northern hemisphere as the original axis and with the magnetic spin added, the new center of spin will lie on the radian connecting the 2 centers and half way between them. Any and all of these new points will lie in the northern hemisphere so the electron remains spin up.

Simply as an aside, the situation gets more complicated if the 2 original spin rates vary. Essentially one can multiply the times to complete each of the two spins and imagine a spin life line extending around space and back almost to the original start point. As the spin rate difference is larger it becomes simpler to envision both rotations separately. We do something like this regarding earth’s daily spin separate from it’s annual sine wave type of relative spin. Although our relationship to the sun is not visualized as a spin of earth but rather a variation in angle of incidence caused by earth’s fixed tilt and its revolution. This motion causes us to experience and visualize 365 separate, slightly offset to each other, spin equators.

Continuing, we have all electrons exiting box 1 with spin up, as the spin down electrons have been eliminated.. If they immediately enter the upside down box rotated by180 degree then all will appear spin down relative to the magnet which is now in a relationship opposite the box 1 situation. Therefore all will behave as original spin down electrons and be eliminated. If instead we pass them through a box rotated by 90 degrees we must again analyze the effect of the magnets. Let’s assume that now the western hemisphere is related to the magnet as was the northern hemisphere in the first box. Then electrons with their axis of rotation in the western hemisphere appear spin up while those in the eastern hemisphere appear spin down. From the prior box, all electrons that exited do not have a spin axis in the southern hemisphere and so none do now either. Using the mechanisms above, the eastern hemisphere spin axis electrons will be removed. That leaves 25% of the original electrons to exit this box. The western hemisphere spin axis electrons will be the ones originally pulled toward the magnet. Additionally, the magnet will force it’s spin onto these electrons. We have not changed the orientation of the electron to it’s original discharge line, so we can identify the spin now being forced upon the electron as being centered at the original south pole just as we had defined the forced spin as at the zero longitude in the prior box. So we again merge the existing spin axis with the south pole. Doing so we still have no axis that ends up in the eastern hemisphere. However as we average the original spin axis with the new axis along their arc/radian of connection we end up with some electron’s new axis in the southern hemisphere while others end in the northern hemisphere. We are merging right hand spins so connecting arcs can be from 90 degrees to 270 degrees in length.

When we finally send the electron into the upside down box 3, the original location of spin axis has been relocated twice. The second relocation changes the apparent resulting effect of the spin blocking mechanism in box. As before, it wont block northern hemisphere electrons but now we have some there. So some electrons will survive that would not have done so without the action in 90 degree tipped box 2.

That is the solution. If you recognize the issue about the existence of both north and south magnets in the boxes, I can address how this doesn’t change the result. The multiple magnets are needed to ultimately return the path of travel to it’s original. With respect to relocating the spin axis, the positive magnet adds to and relocates the spin. The negative magnet reduces the spin. But it is centered where the positive magnet spin was centered. If it has any effect on location, it is to move the original spin axis further along the connecting arc. The only way to get the spin axis relocated into the spin down hemisphere is to reverse the spin. This would transfer the counterclockwise rotation axis by 180 degrees. But the spin slowdown caused by the negative magnet is exactly offset by the spin increase caused by the positive magnet so the spin will never become reversed.

Paul Schroeder

Ref. The Stern Gerlach experiment. David M. Harrison, U of Toronto. Web article.


paul schroeder