[General] Albrecht Instantaneous gravity force

Albrecht Giese genmail at a-giese.de
Mon Feb 6 08:09:33 PST 2017


Wolf,

the solution to this apparent problem is not a property of the electric 
field but a consequence of special relativity. So applicable for all 
kinds of forces.  I have mentioned "retarded potential", and the 
according calculation has to take into account relativity. So, textbooks 
about special relativity which also treat retarded potential have the 
formal solution.

(If this would be a real problem or a real phenomenon in physics we 
would have a violation of angular momentum at many occasions.)

I shall try to explain this in the following in a way which can 
(hopefully) be a bit visualized.


Am 05.02.2017 um 21:47 schrieb Wolfgang Baer:
>
> Albrecht:
>
> I do not see how your example with electric forces applies to the 
> gravitational example.in van Flanders 1998 paper , or for that matter 
> to your model of an elementary particle. Has anyone ever seen positron 
> electron orbiting each other?
>
>
> Consider two particles instantly at 10 and 6 Oclock send out a force 
> that propagates radially from their instantaneous position
>
> A time of flight delay caused by field propagating spherically to 
> reach the other particle after it has moved around the orbit.
>
> This means there is an angle between the purely radial from orbit 
> center direction by an angleΘ
>
I am not so sure that I understand this description. So I try to 
describe the problem, as it appears initially, in my way. Hopefully 
correctly.

The apparent paradox is that the object at position 6 o'clock does not 
see the opposite object at 12 o'clock where it is at that moment, but at 
the past position 10 o'clock where it was when it has emitted the field 
of the force. So one may conclude that the force vector arriving at the 
position at 6 o'clock points to (or from) the 10 o'clock position.  And 
so there is a component in the tangential direction which affects the 
momentum of the object. Is this your concern?

But this conclusion, that it points to the 10 o'clock position, is not 
correct. The force vector points to (or from) the position 12 o'clock.

This does not seem logical at the first glance. But it is physically 
correct. Because with respect to the frame of the moving object in the 
opposite position the space is contracted (if following Einstein) or the 
fields are contracted (if following Lorentz). This contraction causes a 
turn of the direction of the force vector, visible if 
Lorentz-transformed into the frame of the observer at rest.

This now is only a qualitative description. Maybe not satisfying. But 
the precise determination has to be done by use of the according Lorentz 
transformations. It is too lengthy to do it here. So I have to refer to 
a description in a text book.

I have one which does it and which I find well understandable. It is:  
A.P. French, Special Relativity, Chapman & Hall.

Albrecht
>
> This angle will give a force vector along the orbit path would this 
> not change the momentum??
>
> The only way I know Bohr atom works is because the proton is at the 
> center of the electron orbit so no matter where the electron moves 
> around the orbit it will experience a radial only force.
>
> I believe van Flanders 1998 paper claims that ephemerus  data was 
> calculated assuming instantaneous gravity force projection and which 
> seem to match visual position when corrected for the time delay 
> between sources and observer. And if the time delay for gravity were 
> introduced it would show up in orbit corrections not actually seen.   
> Is he making a mistake?
>
> best,
>
> Wolf
>
> Dr. Wolfgang Baer
> Research Director
> Nascent Systems Inc.
> tel/fax 831-659-3120/0432
> E-mailwolf at NascentInc.com
> On 1/31/2017 1:35 PM, Albrecht Giese wrote:
>>
>> Wolf,
>>
>> regarding the /speed of gravitational influence/:
>>
>> I have looked into the mentioned paper of Van Flanders in 1998 and 
>> particularly his arguments why gravitational influences must 
>> propagate instantly, not at the speed of light. I do not follow his 
>> arguments because he has overlooked an important point.
>>
>> His argument (also that one cited from Eddington) is: If the speed of 
>> gravitational propagation is limited (e.g. to c) then in the case of 
>> two celestial bodies each body would not see the other one at its 
>> actual  position but at a past position. This would destroy the 
>> conservation of momentum. -  However, this is not the case.
>>
>> One simple example to see that this argument cannot be true. We can 
>> imagine a set up of two /massive /bodies which orbit each other and 
>> which are bound to each other by an electrical force; this is easily 
>> possible by putting an appropriate electrical charge of different 
>> sign onto both bodies. Also the electrical force is, as we know, 
>> restricted to the speed of light. But it is very clear that this set 
>> up would keep the momentum of both bodies and would steadily move in 
>> a stable way.
>>
>> How does this work? The phenomenon is the so called "retarded 
>> potential". It has the effect that, even though both charges are seen 
>> at a past position by the other charge, the force vector points to 
>> the /actual /position of the other one.
>>
>> If we now assume that gravity is a force (independent of what 
>> Einstein talks about curvature of space), then the same rules of 
>> retarded potential apply to gravity. And so there is no change of 
>> momentum even though the effect of gravity is limited to the speed of 
>> light.
>>
>> Does this provide some clarification?
>>
>> Albrecht
>>
>>
>> Am 22.01.2017 um 20:52 schrieb Wolfgang Baer:
>>>
>>> Al:
>>>
>>> I think the "where is the evidence" argument is no longer powerful 
>>> because so many things happening in physics have little or even 
>>> contradictory evidence. I'm just reading Van Flanders 1998 "the 
>>> speed of gravity" Physics Letters A250 1-11 which makes a good case 
>>> for gravity influences influences moving instantly - not at the 
>>> speed of light.
>>>
>>> However I like your idea of only interactions - in fact I'm 
>>> developing a theory along those lines by modeling nothing as an 
>>> empty page and requiring material formatting of the page as an 
>>> explicit field of space cells. This still allows fields as a 
>>> shortcut for calculating  interactions from multiple distant cells, 
>>> but nothing remains nothing, if there are no cells to host 
>>> interactions i.e. sources and sinks, then there is no influence 
>>> propagating. It takes some material to propagate influences.
>>>
>>> I would be very curious to read how your "one way out" formulates 
>>> this problem.
>>>
>>> One of my hang ups is that any visualization of material basis for 
>>> space implies a kind of permanent structural relationship between 
>>> sources and sinks - but objects do seem to move fairly fluidly from 
>>> place to place. Do sources and sinks move in your vision, If so what 
>>> do they move in?
>>>
>>> best,
>>>
>>> Wolf
>>>
>>> Dr. Wolfgang Baer
>>> Research Director
>>> Nascent Systems Inc.
>>> tel/fax 831-659-3120/0432
>>> E-mailwolf at NascentInc.com
>>> On 1/21/2017 10:20 PM, af.kracklauer at web.de wrote:
>>>> Challenge for proponents of fields (all kinds: E&M, Gravity, 
>>>> Tension, whatever):  If the universe is finite, then the field 
>>>> sources on the outer rind will be pumping field energy into the 
>>>> void, the material universe would be cooling down, etc. So, where 
>>>> is the evidence for such?  If the universe is finite but 
>>>> topologically closed, then it will have certain "Betti numbers" for 
>>>> various forms which will be closed, (see: algebraic topology 
>>>> texts), again there should be some observable consequence from the 
>>>> these closed forms.  So (again) where's the evidence?   Granted, 
>>>> current tech may not be up to the task; but that would imply that 
>>>> field theories have to be reduced in status to be virtually religion.
>>>> One way out:  there are no fields, but interactions between sources 
>>>> and sinks.  Where one is missing, there's nothing!  In particular 
>>>> nothing emminating from sources without regard for target-like 
>>>> sinks. Advantage: the math works out without internal 
>>>> contradictions (divergencies, etc.).  Another advantage: from this 
>>>> viewpoint, there are no waves, and associated divergencies.  They 
>>>> are just cocek the ptual Fourier components for the interactions. 
>>>> Useful, but strictly hypothetical.
>>>> For what it's worth, Al
>>>> *Gesendet:* Sonntag, 22. Januar 2017 um 04:19 Uhr
>>>> *Von:* "Roychoudhuri, Chandra" <chandra.roychoudhuri at uconn.edu>
>>>> *An:* "Nature of Light and Particles - General Discussion" 
>>>> <general at lists.natureoflightandparticles.org>
>>>> *Betreff:* Re: [General] light and particles group
>>>>
>>>> John M.
>>>>
>>>> I am not the right person to give you decisive answers as I have 
>>>> not followed the math relevant to the origin of Gravitational Wave 
>>>> (GW) and its spontaneous propagation.
>>>>
>>>>       First, you can find out the current state of technology in 
>>>> the measuring precision of (i) fringe fraction, F (i.e., 
>>>> 180-degree/F) vs. (i) polarization angle fraction F (90-degree/F). 
>>>> As I recall, much better than thousandth of a fringe-shift is now 
>>>> measurable. I do not know what is the current best value of F for 
>>>> polarization measurement. You can look up Gravitational Faraday 
>>>> Effect also. I did “poke my nose” there in the past; but could not 
>>>> find anything measurable.
>>>>
>>>>      Second, more fundamental physics. All material based waves and 
>>>> light waves require a continuous tension field that steadily gets 
>>>> pushed away from the original site of perturbation induced on the 
>>>> field; provided the perturbation does not exceed the restoration 
>>>> linearity condition (“Young’s Modulus”, or equivalent). For, 
>>>> stretched material string, the mechanical tension is T and the 
>>>> restoration force is the “inertial mass” “Sigma” per unit length; 
>>>> then string-wave v-squared =T/Sigma. For light, c-squared = 
>>>> Epsilon-inverse/Mu. Epsilon-inverse is the electric tension and Mu 
>>>> is the magnetic restoration force. These analogies are explained in 
>>>> some of my papers; I have sent earlier.
>>>>
>>>>       Now my very basic question for the experts in GW: */How do 
>>>> you define the GW-tension field?/* All spontaneously propagating 
>>>> waves require a steady and continuous tension field in which a 
>>>> suitable perturbation triggers the original wave. What is the 
>>>> velocity of GW and what are the corresponding tension and 
>>>> restoration parameters? If you say, it is the same velocity as “c”, 
>>>> for the EM wave; then */we have some serious confusion to 
>>>> resolve/*. Are the tension and restoration parameters same as those 
>>>> for EM waves? Then, why should we call it GW; instead of pulsed EM 
>>>> waves? Or, */are the two parameters really physically different for 
>>>> GW/*(should be); but GW-velocity number just happens to coincide 
>>>> with “c”?
>>>>
>>>>      I took Einstein’s explanation for the origin of Gravity as the 
>>>> “Curvature of Space” literally, as the Potential Gradient generated 
>>>> around any assembly of Baryonic Particles. So, a pair of rotating 
>>>> binary stars will generate a periodically oscillating potential 
>>>> gradient. Whatever the value of the effective gravity of a 
>>>> “stationary” binary star around earth is; it would be oscillating 
>>>> slightly when the “stationary” binary stars start rotating around 
>>>> themselves. But, this is not Gravity Wave to me. It is a phenomenon 
>>>> of “locally” changing value of the “curvature of space”; not a 
>>>> passing by wave. Imagine the typical “trampoline demo” for 
>>>> Einsteinian gravity with a heavy iron ball at the depressed center. 
>>>> If you periodically magnetically attract the iron ball to 
>>>> effectively reduce the trampoline curvature; we are not generating 
>>>> propagating GW; we are periodically changing the local “curvature”!
>>>>
>>>>      These comments should give you some pragmatic “food for thought”!
>>>>
>>>> Chandra.
>>>>
>>>> *From:*General 
>>>> [mailto:general-bounces+chandra.roychoudhuri=uconn.edu at lists.natureoflightandparticles.org] 
>>>> *On Behalf Of *John Macken
>>>> *Sent:* Saturday, January 21, 2017 4:14 PM
>>>> *To:* 'Nature of Light and Particles - General Discussion'
>>>> *Subject:* Re: [General] light and particles group
>>>>
>>>> Chandra,
>>>>
>>>> I have one quick question for you and the group to consider.  You 
>>>> mention that Maxwell connected the speed of light to the properties 
>>>> of space (epsilon and mu). To explain my question, I first have to 
>>>> give some background which is accomplished by quoting a short 
>>>> section of the previously attached paper.
>>>>
>>>> “Gravitational waves (GWs) propagate in the medium of spacetime. 
>>>> They are transverse quadrupole waves which slightly distort the 
>>>> “fabric of space”.  For example, a GW propagating in the “Z” 
>>>> direction would cause a sphere made from baryonic matter such as 
>>>> metal to become an oscillating ellipsoid.  When the sphere expands 
>>>> in the X direction it contracts in the Y direction and vice versa. 
>>>> The GW produces: 1) no change in the total volume of the 
>>>> oscillating sphere 2) no change in the rate of time, 3) no 
>>>> displacement of the center of mass of the oscillating sphere.
>>>>
>>>> Point #3 addresses an important point. If there are two isolated 
>>>> masses such as two LIGO interferometer mirrors suspended by wires 
>>>> [17], the passage of a GW does not move the mirror’s center of 
>>>> mass.  Instead of the mirrors physically moving, the GW changes the 
>>>> properties of spacetime producing a redshift and a blue shift on 
>>>> LIGO’s laser beams.  This difference in wavelength is detected by 
>>>> the interferometer as a fringe shift…”
>>>>
>>>> With this introduction, the questions are:
>>>>
>>>>  1. Should a GW effect the permeability and permittivity of free space?
>>>>  2. Should the two orthogonal  polarizations of a GW produce
>>>>     opposite effects on the permeability and permittivity of free
>>>>     space?
>>>>  3. Since epsilon and mu determine the speed of light, should a GW
>>>>     produce a different effect on the two orthogonal polarizations
>>>>     of light?
>>>>
>>>> If the answer to question #3 is yes, then this suggests that it 
>>>> should be possible to detect GWs by monitoring the polarization of 
>>>> a laser beam.  It is vastly simpler to detect a slight difference 
>>>> in the polarization of a single beam of light than it is to detect 
>>>> the same optical shift between two arms of an interferometer.  The 
>>>> interferometer encounters vibration noise to a much greater degree 
>>>> than is encountered in the polarization of a single laser beam. 
>>>>  Also, multiple laser beams could identify the direction of the GW 
>>>> much better than an interferometer.
>>>>
>>>> Perhaps this is off the subject of the discussion group. But it is 
>>>> an example of a subject which might be low hanging fruit that could 
>>>> make a historic contribution to physics.  In the past I have made 
>>>> the suggestion that GWs produce a polarization effect, but this 
>>>> suggestion is lacking additional insight and analysis to be taken 
>>>> seriously.  Is there anyone in this group with the expertise to 
>>>> contribute to this study?
>>>>
>>>> John M.
>>>>
>>>> *From:*General 
>>>> [mailto:general-bounces+john=macken.com at lists.natureoflightandparticles.org] 
>>>> *On Behalf Of *Roychoudhuri, Chandra
>>>> *Sent:* Saturday, January 21, 2017 11:56 AM
>>>> *To:* Nature of Light and Particles - General Discussion 
>>>> <general at lists.natureoflightandparticles.org 
>>>> <mailto:general at lists.natureoflightandparticles.org>>
>>>> *Subject:* Re: [General] light and particles group
>>>>
>>>> “Gravitational waves indicate vacuum energy exists”, paper by John 
>>>> Macken
>>>>
>>>> John M.: Thanks for attaching your paper. */The title clearly 
>>>> indicates that we really are in basic agreement. The cosmic space 
>>>> has physical properties./* I have expressed my views a bit 
>>>> differently, that the cosmic space is a */stationary /*Complex 
>>>> Tension Filed (CTF), */holding 100% of the cosmic energy/* in the 
>>>> attached papers and in my book, “Causal Physics”. */If the 
>>>> so-called vacuous cosmic space and the CTF were not inseparable, 
>>>> the velocity of light would have been different through different 
>>>> regions of the cosmic space/*!
>>>>
>>>>      I just do not like to continue to use the word “vacuum” 
>>>> because, in the English language, it has acquired a very different 
>>>> meaning (“nothing”) for absolute majority of people over many 
>>>> centuries. It is better not to confuse common people by asserting 
>>>> new meanings on very old and very well established words.
>>>>
>>>>      Further, in your support, the quantitative values of at least 
>>>> two physical properties, Epsilon & Mu, of the comic space have 
>>>> already presented as quantified properties by Maxwell around 1867 
>>>> through his wave equation. Recall (c-squared)=(1/Epsilon.Mu). These 
>>>> properties of the cosmic space were already quantified before 
>>>> Maxwell by the early developers of electrostatics and magneto statics.
>>>>
>>>>      I assume that you are suggesting us that we need to postulate 
>>>> and quantify other physical properties possessed by this cosmic 
>>>> space (*/Maxwellian or Faraday Tension Field/*?), so that the 
>>>> “emergent dynamic particles” out of this cosmic space would display 
>>>> all the properties we have already been measuring for well over a 
>>>> century.
>>>>
>>>> However, I disagree, as of now, that cosmic space is “space-time” 
>>>> four dimensional. Because, the “running time” is not a measurable 
>>>> physical parameter of any physical entity that we know of in this 
>>>> universe. So, I assert that the “running time” cannot be altered by 
>>>> any physical process. */Humans have smartly derived the concept of 
>>>> “running time” using various kinds of harmonic oscillators and/or 
>>>> periodic motions./* We can alter the frequency of a physical 
>>>> oscillator by changing its physical environment. Of course, this is 
>>>> my personal perception, */not supported by the entire group/*. But, 
>>>> that is precisely the purpose of this free and honest discussions 
>>>> so we can learn from each other. As my understanding evolves; I 
>>>> might change back my mind and accept space as four- or even 
>>>> thirteen-dimensional.
>>>>
>>>> Chandra.
>>>>
>>>> *From:*General 
>>>> [mailto:general-bounces+chandra.roychoudhuri=uconn.edu at lists.natureoflightandparticles.org] 
>>>> *On Behalf Of *John Macken
>>>> *Sent:* Saturday, January 21, 2017 1:37 PM
>>>> *To:* 'Nature of Light and Particles - General Discussion'; 'Andrew 
>>>> Worsley'
>>>> *Cc:* 'M.A.'
>>>> *Subject:* Re: [General] light and particles group
>>>>
>>>> Dear Chandra and All,
>>>>
>>>> You have said “We definitely have advanced our */collective 
>>>> understanding/* that */space is not empty and the particles are 
>>>> some form of emergent properties of this same universal cosmic 
>>>> field./*”  The idea that space is not an empty void has not been 
>>>> quantified in any model of spacetime proposed by members of  the 
>>>> group.
>>>>
>>>> I have concentrated in defining and quantifying the properties of 
>>>> the vacuum and the results are presented in the attached paper.  
>>>> This paper analyzes the properties of spacetime encountered by 
>>>> gravitational waves.  The conclusion is that spacetime is a sea of 
>>>> Planck length vacuum fluctuations that oscillate at Planck 
>>>> frequency. This model can be quantified, analyzed and tested.  It 
>>>> is shown that this model gives the correct energy for virtual 
>>>> particle formation.  It also gives the correct energy density for 
>>>> black holes, the correct zero point energy density of the universe 
>>>> (about 10^113 J/m^3 ) and generates the Friedmann equation for the 
>>>> critical density of the universe (about 10^-26 kg/m^3 =  10^-9 
>>>> J/m^3 ).
>>>>
>>>> The reason for mentioning this to a group interested in the 
>>>> structure of electrons,  photons and electric fields is that the 
>>>> quantifiable properties of spacetime must be incorporated into any 
>>>> particle or field  model.
>>>>
>>>> John  M.
>>>>
>>>> *From:*General 
>>>> [mailto:general-bounces+john=macken.com at lists.natureoflightandparticles.org] 
>>>> *On Behalf Of *Roychoudhuri, Chandra
>>>> *Sent:* Saturday, January 21, 2017 8:45 AM
>>>> *To:* Andrew Worsley <worsley333 at gmail.com 
>>>> <mailto:worsley333 at gmail.com>>; Light & particles. Web discussion 
>>>> <general at lists.natureoflightandparticles.org 
>>>> <mailto:general at lists.natureoflightandparticles.org>>
>>>> *Cc:* M.A. <ambroselli at phys.uconn.edu 
>>>> <mailto:ambroselli at phys.uconn.edu>>
>>>> *Subject:* Re: [General] light and particles group
>>>>
>>>> Dear Andrew Worsely:
>>>>
>>>>     This is a platform for ethical, serious and honest discussions 
>>>> on scientific issues that the prevailing mainstream platforms have 
>>>> been shunning. We definitely do not want to sow unsubstantiated 
>>>> distrust within this group. */This not a political forum where 
>>>> sophisticated deceptions are highly prized; which has been 
>>>> intellectualized as “post-truth”!/* This is not a “post-truth” forum.
>>>>
>>>>      So, please, */help us/*by getting help from computer 
>>>> professionals before repeating any further unsubstantiated accusations.
>>>>
>>>>      If you can definitively identify anybody within our group 
>>>> carrying out unethical and destructive activities; obviously, we 
>>>> would bar such persons from this group discussion.
>>>>
>>>> Chandra.
>>>>
>>>> Dear All Participants:
>>>>
>>>> Please be vigilant in maintaining the essential ethics behind this 
>>>> discussion forum – honestly accept or reject others’ opinions; 
>>>> preferably, */build upon them. This is the main objective of this 
>>>> forum as this would advance real progress in physics out of the 
>>>> currently stagnant culture/*. While we have not come to realize any 
>>>> broadly-acceptable major break-through out of this forum; we 
>>>> definitely have advanced our */collective understanding/* that 
>>>> */space is not empty and the particles are some form of emergent 
>>>> properties of this same universal cosmic field./* This, in itself, 
>>>> is significant; because the approach of this group to particle 
>>>> physics is significantly different from the mainstream. I 
>>>> definitely see a better future for physics out of this thinking: 
>>>> Space is a real physical field and observables are manifestation 
>>>> (different forms of excited states) of this field.
>>>>
>>>>       Most of you are aware that our SPIE conference series, which 
>>>> was continuing since 2005, has been abruptly shut down without 
>>>> serious valid justifications (complains from “knowledgeable people” 
>>>> that “bad apples” have joined in). We certainly do not want 
>>>> something similar happen to this web discussion forum due to 
>>>> internal dissentions and internal unethical behavior.
>>>>
>>>> Many thanks for your vigilance and support.
>>>>
>>>> Respectfully,
>>>>
>>>> Chandra.
>>>>
>>>> *From:*Andrew Worsley [mailto:worsley333 at gmail.com]
>>>> *Sent:* Saturday, January 21, 2017 4:49 AM
>>>> *To:* John Duffield
>>>> *Cc:* Roychoudhuri, Chandra; ANDREW WORSLEY
>>>> *Subject:* Re: Andrew Worsley, light and particles group
>>>>
>>>> Hi John,
>>>>
>>>> Could be a coincidence, but some damn troll from the discussion 
>>>> group (called Vladimir) has screwed up my email which I have had 
>>>> problem free for the last 20 years- and my computer is now going 
>>>> suspiciously slow.
>>>>
>>>> Andrew
>>>>
>>>> On Thu, Jan 19, 2017 at 7:44 PM, John Duffield 
>>>> <johnduffield at btconnect.com <mailto:johnduffield at btconnect.com>> wrote:
>>>>
>>>> Chandra:
>>>>
>>>> Please can you add Andrew Worsley to the nature of light and 
>>>> particles group. I’ve met him personally, and think he has a 
>>>> valuable contribution to make.
>>>>
>>>> Apologies if you’ve already done this, but Andrew tells me he’s 
>>>> received a /blocked by moderator/ message.
>>>>
>>>> Regards
>>>>
>>>> John Duffield
>>>>
>>>> 7 Gleneagles Avenue
>>>>
>>>> Poole
>>>>
>>>> BH14 9LJ
>>>>
>>>> UK
>>>>
>>>> *From:* John Duffield [mailto:johnduffield at btconnect.com 
>>>> <mailto:johnduffield at btconnect.com>]
>>>> *Sent:* 09 January 2017 08:34
>>>> *To:* 'Roychoudhuri, Chandra' <chandra.roychoudhuri at uconn.edu 
>>>> <mailto:chandra.roychoudhuri at uconn.edu>>
>>>> *Cc:* 'ANDREW WORSLEY' <member at aworsley.fsnet.co.uk 
>>>> <mailto:member at aworsley.fsnet.co.uk>>; 'John Williamson' 
>>>> <John.Williamson at glasgow.ac.uk 
>>>> <mailto:John.Williamson at glasgow.ac.uk>>; 'Martin Van Der Mark' 
>>>> <martinvandermark1 at gmail.com <mailto:martinvandermark1 at gmail.com>>
>>>> *Subject:* Andrew Worsley, light and particles group
>>>>
>>>> Chandra:
>>>>
>>>> Please can you add Andrew Worsley (worsley333 at gmail.com 
>>>> <mailto:worsley333 at gmail.com>) to the nature of light and particles 
>>>> group. I’ve met him personally, and think he has a valuable 
>>>> contribution to make. He has described the electron as being what 
>>>> you might call a quantum harmonic structure.  The electron in an 
>>>> orbital is described by spherical harmonics, the electron itself 
>>>> might be described by spherical (or toroidal) harmonics.
>>>>
>>>> Regards
>>>>
>>>> JohnD
>>>>
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