Lawrence,

I owe an apology both to you and to myself. I was preparing for a vacation at the time you posted this, and regretted that I was not able to engage your interesting and important argument. I made a promise to myself to get back to it, and forgot.

It's exactly the case that homotopically continuous functions require two distinct operations that prevents the analytical continuation from the initial condition, of a single function over the simply connected manifold of a unitary space.

Your comparison of the two-slit experiment to a homotopy-equivalent topology of genus 2 reduced to a torus of genus 1 is absolutely brilliant, in my opinion. I had never heard it expressed that way before. It's pinpoint accurate.

For continuous function physics on a topology of genus 0, analysis on the simply connected 3-sphere continues from every point to any other set of points, because all points are homotopy equivalent.

I would love to discuss the black hole case with you.

All best,

Tom

"You need to put more effort in to understand the propositions I've presented."

I would, if they didn't conflict with the physics we already know.

Since the universe is Fine-Tuned, then we have good reason to post the following message somewhere on the planet earth, in big letters.

Dear Creator of the Universe,

How are you. Hope you're fine. We're OK. Please communicate with us.

Love and respect,

Humanity

P.S. Can you tell us how to build a hyperdrive?

Dear Peter,

thank you again for your reply.

As i now understand it: when i need to draw just one line for each detector, then neccessarily the cones must be indentical at each side. In your fig. 3 the cones are such, that the two lines are perpendicular to each other. I had in mind what you said earlier, that one cone is for Alice, the other for Bob. So the two lines cannot always be perpendicular to each other. Because, say, at the left side of your fig. 3 (let's associate this side with what happens at the left detector) the left particle could be touched exactly at the pole. For this case the circumference (line of latitude) must shrink to zero. But what happens here should not influence what happens at the other detector, means the other cone in fig. 3 could well be the same and should not shrink.

For the case that at the left detector there is maximum angular momentum transfered, the circumference (line of latitude) must be at the maximum, means must be identical with the equatorial plane. This would automatically also rise the other cone's line of latitude to the maximum. Again, both setting angles are now identical again, which contradicts the independence of Alice and Bob.

So, how to draw just two lines to represent to different cones with two different lines of latitude? Or are the two lines perpendicular to each other the frame of reference for your further considerations?

I trust your cosine^2 and sine^2 functions. I only want to know how to systematically read out from fig. 3 the circumstances at Bob's and Alice's sides for EVERY case. Have the drawings to be changed for every run of the experiment? Or is it so, that the two axis standing perpendicular to each other automatically lead to the conclusion that the 'poles' are not a single point at the sphere, but are pole caps (like you suggest in your fig. 3)?

Can one read out of fig. 3 that for each one of two particles a different line of latitude has been touched?

I think that should it be for tonight.

Thanks again for replying!

Stefan

John,

I like what you said. A macroscopic example would be a set of Gimbals as used on ships and aircraft. "In inertial navigation, as applied to ships and submarines, a minimum of three gimbals are needed to allow an inertial navigation system (stable table) to remain fixed in inertial space, compensating for changes in the ship's yaw, pitch, and roll". .........."In turn, angular measurement devices called "resolvers" mounted on the three gimbals provide the nine cosine values for the direction cosine matrix needed to orient the ship.Similar sensing platforms are used on aircraft."Wikipedia, Gimbal. Which makes me think this analogy allows a better description of the roll motion I was trying to describe than a second axis on the flip plane, which I'm not sure is right.If you look at the picture of the early Modern dry compass suspended by gimbals it can be seen that three motions are possible; the inner ball can spin, the gimbal on which it is suspended allows what I called flip and the one suspending that gimbal allows what I have called roll.If orientation of observer can also be altered it can be seen that there is very much more variation in possible spin outcomes than might at first be imagined with simple spinning ball visualization.Another macroscopic example of extra degrees of freedom than one axis of rotation is a globe pivoted on the sides but also able to be spun with the pivots sliding around on the equator, and mounted on a rotating platform.

Describing how the electromagnetic wave is formed from the motion of the photon particle. The spin clockwise and anticlockwise (depends which pole is thought about) gives the magnetic field of the photon. The flip North to bottom, South to top and vice versa gives the oscillation of the magnetic field and the roll to left or right acting on the flip and consequently also the spins gives the two different polarizations. Its now moving simultaneously in 3 ways. If that motion from one exterior viewpoint over time, as the wave passes, is represented diagrammatically it looks like an electromagnetic wave in which the oscillation of magnetic field along the line of propagation is also turning about that line. The direction of turn being its polarization. The electric component is a consequence of the moving oscillating magnetic field.

This particle motion answers the double slit particle wave conundrum. The photon really is a particle and its motion is creating oscillating flux in the environment recognized as magnetic and electric fields. When reaching the double slit the particle can only go through one but its associated flux acts like the wave it is passing through both slits and interfering on the other side. The interference of the flux is then able to influence the path the particle takes. Even a single photon particle will produce the the regularly fluctuating flux which is able to interfere with itself on reaching the double slit apparatus.

As the same interference is found for other particles too it can be assumed that they too have oscillatory characteristics that set up environmental flux that will behave as waves too.

Hi Georgina,

the Gimbal is a fascinating thing, though i don't think that it can explain the double-slit epermiment's results. Imagine the delayed-choice experiment, measuring through which slit the photon came after it passed the slit.

By outlining a photographic plate at the measurement plane, there will be seen interference over time. Now do outline two detectors for each slit instead of the photographic plate (at points that correspond to the minima at the photographic plate).

Over time (the same time as needed to generate the interference pattern), there will be no more minima at the two detector positions, despite the detectors are in the same plane as the photographic plate was. This indicates, that there must be some 'nonlocal' influence form the detectors in the direction to the slits.

Is there a flaw in my lines of reasoning. Comments are welcome.

I found a 'quantum gyroscope', maybe this could be interesting for you.

http://en.wikipedia.org/wiki/Quantum_gyroscope

Best wishes,

Stefan

Stefan sorry I didn't really understand your explanation of the delayed choice experiment.

Quote" These experiments are attempts to decide whether light somehow "senses" the experimental apparatus in the double-slit experiment it will travel through and adjusts its behavior to fit by assuming the appropriate determinate state for it, or whether light remains in an indeterminate state, neither wave nor particle, and responds to the "questions" asked of it by responding in either a wave-consistent manner or a particle-consistent manner depending on the experimental arrangements that ask these "questions."End quote ,Wikipedia,Wheelers delayed choice experiment Notice the option it actually is a particle creating associated wave (as a result of the particles particular motion) is not an option, The electromagnetic nature of the photon has been ignored.

Quote"According to the complementary principle, a photon can manifest properties of a particle or of a wave, but not both at the same time. What characteristic is manifested depends on whether experimenters use a device intended to observe particles or to observe waves... When this statement is applied very strictly, one could argue that by determining the detector type one could force the photon to become manifest only as a particle or only as a wave."End quote.Wikipedia wheeler's delayed choice That is a measurement problem. The particle is creating a wave through its motion but both wave and particle can't be detected together. Not entirely true because even when just a single photon is detected as a particle it is still affected by wave interference because if lots are allowed through they show the interference pattern through the build up of their distribution over time.

Dear Georgina,

maybe i should explain it a little more in detail.

You assume the photon to be a particle with a certain electromagnetic flux around it.

As you know from the double-slit experiment with single photons, over time, there will be an interference pattern at the observation plane. This pattern consists (usually) of dark and light bars. The lightest bar of them is found approximately in the middle of the two slits (projected to the observation plane).

If we measure with two detectors in the area whe are used to find the lightest bar, we can 'deduce' 'which way' each photon went (slit one or slit two). The relative frequencies of particle impacts at detector 1 and 2 are different from what we could expect if we do not measure 'which way' information.

In other words: By measuring 'which way' information, the inferference pattern i spoke of above is altered over time at the areas where the the two detectors are situated: Statistically, much more photons do arrive there than in the case of a measurement method that does not extract which-way information at these two points in the observation plane.

Note that until the observation plane (with or without the two detectors standing there) is reached by every single photon, the conditions for the physical mechanisms described by you (two slits open, particle, flux) from the slits to the observation plane remain unchanged. This must also include the mechanism that is responsible for every single particle's path to contribute properly to the whole interference pattern.

But as i remarked, by observing several regions of the observation plane with a device capable of extracting 'which way' information, the expected interference pattern gets altered. Means, now there are more photons that find their ways to these measurement locations than without the two detectors.

The question therefore is, how the two detectors in sufficient distance to the action at the slits can alter this action by remote.

For an interesting discussion of the so called "separation fallacy" you may wish to take a look at this interesting paper:

The 'Past' and the 'Delayed-Choice' Double-Slit Experiment

Best wishes,

Stefan

Georgina,

Very interesting description of gimbaled navigation gyros, I always loved boats but inertial guidance is very different from dead reckoning on a 2-D surface. I'll have to follow up on that. Your own ponderings find better communication using the tri-gimbal analogy also, much gets confused (for me) trying to follow all the flip-flops when speaking in terms of 'this' rotation or 'that' rotation. The similar difficulty is encountered in the Maxwellian 'leap-frog' phenomenon of electric-magnetic inductance reactance.

Speaking of magnets; macroscopically if we take two quality uniform bar magnets and lay one flat on a table, and perch the other so that its opposing pole will 'float' a little above the pole end of the first, the one end of the second magnet will rest on the table while its other end is levitated. When initially positioning the inclined magnet its free end will briefly oscillate up and down and then settle to a stable attitude, hovering above the opposing end of the first magnet laying flat on the table. I go back to Faraday's concept, that the magnetic field is itself an extension physically of the substance of the magnet, not something else associated with the substance. So for me there is nothing weird about the idea of electromagnetic radiation having a particulate nature as well as a field-like nature. I think the double slit type experiments do in fact exhibit the inductance-reactance which you propose. And I believe that such types of experiments, as well as what QM asserts, provide clues to the actual real physical shape of the waveform.

So somebody tell me; how does QM explain what that levitated free end of the second magnet is doing? Oddly (for him), Einstein removed 'force' from his theorizing, but force is there on display. And force is the product of mass and motion; so what is it that is moving? Time? jrc

Dear Georgina,

sorry, i pasted the wrong content of my computer's cache.

Her the link:

http://jamesowenweatherall.com/SCPPRG/EllermanDavid2012Man_QuantumEraser2.pdf

Best wishes,

Stefan

Stefan,

"the cones are such that the two lines are perpendicular to each other." They can be anywhere (i.e. see alt pos'n for B).

As the cones use the same axis the angle between them is constant ALL ROUND the circumference.

Spin 1 and spin 1/2 particles actually behave differently by half the phase (as found). The cones may be on opposite OR the same sides of the sphere (that changes at 90^o difference) and one may indeed shrink to zero. Remember it's the angle BETWEEN THE TWO we're looking at, so one setting may be zero with no effect on the other.

But there are really two 'stages' in using the sphere, the second simplified to a circle. One way to understand how to get the final cos^2 distribution is to analyse my experiment in the essay 'end notes', or follow this;

Set 'zero' datum as EITHER the 'spin axis' or equatorial plane depending on which quality we want (momentum or direction). Now mark off the RELATIVE angle. Either the OAM or spin direction certainty distribution will change as the cosine of that relative angle. At 90 degrees from that datum position the uncertainty is at a maximum, then as the angle keeps increasing

Georgina,

The random 'tumbling axis' model hits Bell's Theorem head on. It was the commonly assumed model up to then. I'll quote some passages from Bell himself who assumed that model, from; "Bertlemann's Socks and the nature of Reality";

"Then, if the magnetic axis of each particle is randomly orientated...results in the 'ad hoc' model. ...does what's required of it..but not at intermediate angles." Then;

"of course this trivial model was just the first one we thought of, and it worked up to a point. Could we not be a little more clever, and devise a model which reproduces the quantum formulae completely? No. It cannot be done, so long as action at a distance is excluded. This point was realised only subsequently. neither EPR nor their contemporary opponents were aware of it."

Bell was right. Going that route is a very well trodden dead end. Don't be seduced into following it. My model only circumvents Bell's theorem because it does NOT use that assumption! It's not the propagating particles that use the y and z axis degrees of freedom, it's the detector field electrons. The WAVE is a result of the helical dynamic AROUND the polar propagation axis. The poles don't switch until the interaction. That is the unique attribute that unlocks the solution (and represents 'entanglement').

Bell anticipated this exact type of solution, approaching from a different angle though he never found it; "the solution, invisible from the front, may be seen from the back." (p.194).

Richard Gill insists Bell made no "assumptions", indeed he tried not to but the 'tumbling' model was an assumption, and, as I show, the critical wrong one.

GYRO's

The other action you wanted is "YAW". Spacecraft use 'Sagnac ring' gyro's as they're sensitive to motion in all three planes. There is a theoretical issue with the popular 'interpretation' of SR, but they work perfectly. The DFM resolves that issue, retaining the SR Postulates (the "entire theory" as AE's 1952 description).

Best wishes

Peter

Stefan,

Quick answers; Electrons, photons or neutrons. Yes, the detector electrons fill the space with spin oriented to the setting. I think I answer why they go different ways (one spins 'backwards' relatively).

And Yes; we may say they are 'new' particles, but it's the 'same' energy quanta.

Must dash for now

P

Dear Peter,

thanks again for your elucidating reply.

by looking at fig. 5 in your essay, the blue curve is the cos^2 distribution, means the spin correlation distribution for the Bohmian experiment.

But it could also be read as the OAM energy transfer for the different cones of a particle (sphere). For 90° the spin correlation of the particle pairs is lost, a particle is then touched at a pole. Does this imply that the other (twin) particle is also touched at a pole? If yes, that's spooky. If not, what are the reasons for the observed result, namely that at 90° the spin correlations are lost? (the answer perhaps would elucidate what constitutes the strong correlations at 0° and 180°).

As always, i ask for elucidating answers.

Best wishes,

Stefan

Dear Peter,

thank you for the reply.

I think it would be of enormous help to describe in detail one distinctive case, say the case for a pair of electrons with their respective magnets at a relative angle of 90°.

Especially what happens to *each* of the two electrons in the 90° case; And what happens in the magnetic field of the respective magnets to each of the two electrons - and later on in the respective detectors, again for each of the two electrons.

I think the reader (as well as me) would greatly appreciate such a step-by-step explanation.

Thank you very much!

Best wishes,

Stefan

John,

The continuous motion of the 3 rotations is easier to follow I should think than leap frogging which is taking interleaved samples of velocity and position over time. How about putting an equilateral triangle around each pole so the points are midway between pole and equator. Label N pole A and the three points B C D. Do the same the other end.S pole is E the points F G H. Twisted so that the points of Souths triangle are between the points of N's triangle not lined up. That gives a nice even distribution of points. The three motions could be split into single vectors for the motion of each point and the combination of the three vectors gives the resultant motion vector.Using different colours for each pole and point, plot the spatial separation of the points and poles at the start and then at regular time intervals plotting the new location calculated from the 3 vectors, shifting the new plots to the next time interval position along a time axis (running in the direction of propagation) and joining the points of same letter by the resultant vector line. I think that would draw a pretty illustration of the motion. Imagine that done for lets say 200 points on the Globe. I'd like to do that.

  • [deleted]

Re. SpinFrom the Stanford Encyclopedia of Philosophy, Bohemiam mechanics, Spin. ....problem is that there is no ordinary (nonquantum) quantity which, like the spin observable, is a 3-vector and which also is such that its components in all possible directions belong to the same discrete set. The problem, in other words, is that the usual vector relationships among the various components of the spin vector are incompatible with the quantization conditions on the values of these components...For a particle of spin-1 the problem is even more severe. The components of spin in different directions aren't simultaneously measurable. Thus, the impossible vector relationships for the spin components of a quantum particle are not observable. Bell (1966)End Quote (My bold and italic emphasis added) The part I have highlighted in bold appears to me to be a mistaken view. The illustration of the 3 gimbals in motion, Wikipedia shows that 3 different seemingly incompatible motions can occur simultaneously. Each gimbal gives a degree of freedom. The vector relationships are not impossible but can not be simultaneously measured. Using the gimbal terminology analogy. If you are measuring pitch alone you are not measuring roll or yaw, and so on with the different possibilities. IE measuring rotation just in one orientation precludes measuring the other rotations. What is actually happening is the outcome of the three motions that can be imagined spread along a time line that is also the line of propagation. For a photon it seems to me the motion might be thought of as a 4-vector because there is the pitch rotation vector (that I was calling spin) 1, roll rotation vector(that I was calling flip) 2, yaw rotation vector(that I was calling roll) 3 and movement along line of propagation vector 4. Imagining that in spherical space with time dimension is probably easier than projecting it onto a flat space.