[General] STR twin Paradox

Chip Akins chipakins at gmail.com
Sun Jun 11 17:16:40 PDT 2017


Hi All

 

A question regarding what seems to be a Special Relativity paradox.

 

There are twins.  They are moving relative to each other in a very large circle.  The first twin observes the trajectory of the second twin and thinks the second twin is moving very fast in a huge circle, while he, the first twin, thinks he, the first twin, is not moving.  The second twin observes the first twin, who appears to be moving very fast and in a huge circle as well. The second twin thinks he, the second twin, is not moving, but feels the first twin is moving very fast and in a huge circle.

 

A third person, an observer, has measured the cosmic background radiation, and put himself at a position of “rest” in space relative to the cosmic background. The third person, observer, as it happens, is in the same frame as one of the twins. So he, the third person observer thinks one twin is not moving and the other is moving.

 

Once the huge circle is complete, the twins are in the same locale.  Each twin believes the other is moving relativistically for all this time, and therefore believes the other twin will not have aged near as much. They are very close in proximity after the circle is complete, and transmit their respective ages to each other.

 

Now the apparent paradox.

 

If all motion is relative then there is no solution to the actual age of the either of the twins. 

 

If all motion is not relative then the moving twin will appear younger.

 

This is another illustration of what Grahame has discussed.  There is no reciprocity, so all motion is not relative.

 

Thoughts?

 

Chip

 

From: General [mailto:general-bounces+chipakins=gmail.com at lists.natureoflightandparticles.org] On Behalf Of Albrecht Giese
Sent: Sunday, June 11, 2017 8:49 AM
To: general at lists.natureoflightandparticles.org
Subject: Re: [General] STR twin Paradox

 

Wolf,

I would feel better if our discussion would use detailed arguments and counter-arguments instead of pure repetitions of statements.

 

Am 10.06.2017 um 07:03 schrieb Wolfgang Baer:

WE all agree clocks slow down, but If I include the observer then I get an equation for the slow down that agrees with eperimetn but disagrees with Einstein in the higher order, so it should be testable

I disagree and I show the deviation in your calculations below. 



Lets look at this thing Historically:

In the 19’th century the hey day of Aristotelian Philosophy everyone was convinced Reality consisted of an external objective universe independent of subjective living beings. Electricity and Magnetism had largely been explored through empirical experiments which lead to basic laws  summarized by Maxwell’s equations. These equations are valid in a medium characterized by the permittivity ε0  and permeability μ0  of free space. URL: https://en.wikipedia.org/wiki/Maxwell’s_equations <https://en.wikipedia.org/wiki/Maxwell%E2%80%99s_equations> 
            These equations  are valid in a coordinate frame x,y,z,t and are identical in form when expressed in a different coordinate frame x’,y’,z’,t’. Unfortunat4ely I’ve never seen a substitution of the Lorentz formulas into Maxwell’s equations that will then give the same form only using ∂/∂x’, and d/dt’, to get E’ and B’ but it must exist. 

One thing has been done which is much more exciting. W.G.V. Rosser has shown that the complete theory of Maxwell can be deduced from two things: 1.) the Coulomb law; 2.) the Lorentz transformation. It is interesting because it shows that electromagnetism is a consequence of special relativity. (Book: W.G.V. Rosser, Classical Electromagnetism via Relativity, New York Plenum Press). Particularly magnetism is not a separate force but only a certain perspective of the electrical force. 



            In empty space Maxwell’s equations reduce to the wave equation and Maxwell’s field concept required an aether as a medium for them to propagate. It was postulated that space was filled with such a medium and that the earth was moving through it. Therefore it should be detectable with a Michelson –Morely experiment. But The Null result showed this to be wrong.

In the view of present physics aether is nothing more than the fact of an absolute frame. Nobody believes these days that aether is some kind of material. And also Maxwell's theory does not need it. 

An aether was not detected by the Michelson-Morely experiment which does however not mean that no aether existed. The only result is that it cannot be detected. This latter conclusion was also accepted by Einstein. 



Einstein’s Approach:

            Einstein came along and derived the Lorentz Transformations assuming the speed of light is constant, synchronization protocol of clocks, and rods, the invariance of Maxwell’s equations in all inertial frames, and the null result of Michelson-Morely experiments. Einstein went on to eliminate any absolute space and instead proposed that all frames and observers riding in them are equivalent and each such observer would measure another observers clocks slowing down when moving with constant relative velocity. This interpretation lead to the Twin Paradox. Since each observer according to Einstein, being in his own frame would according to his theory claim the other observer’s clocks would slow down. However both cannot be right.

No! This can be right as I have explained several times now. 



            Einstein found an answer to this paradox in his invention of general relativity where clocks speed up when in a higher gravity field i.e one that feels less strong like up on top of a mountain. Applied to the twin paradox: a stationary twin sees the moving twin at velocity “v” and thinks the moving twin’s clock slows down. The moving twin does not move relative to his clock but must accelerate  to make a round trip (using the equivalence principle calculated the being equivalent to a gravitational force). Feeling the acceleration as gravity and knowing that gravity slows her clocks she would also calculate her clocks would slow down. The paradox is resolved because in one case the explanation is velocity the other it is gravity.

This is wrong, completely wrong! General relativity has nothing to do with the twin situation, and so gravity or any equivalent to gravity has nothing to do with it. The twin situation is not a paradox but is clearly free of conflicts if special relativity, i.e. the Lorentz transformation, is properly applied. 



 

Lorentz Approach:

            Lorentz simply proposed that clocks being electromagnetic structures slow down and lengths in the direction of motion contract in the absolute aether of space according to his transformation and therefore the aether could not be detected. In other words Lorentz maintained the belief in an absolute aether filled space, but that electromagnetic objects relative to that space slow down and contract. Gravity and acceleration had nothing to do with it.

            This approach pursued by Max Van Laue argued that the observer subject to acceleration would know that he is no longer in the same inertial frame as before and therefore calculate that his clocks must be slowing down, even though he has no way of measuring such a slow down because all the clocks in his reference frame. Therefore does not consider gravity but only the knowledge that due to his acceleration he must be moving as well and knowing his clocks are slowed by motion he is not surprised that his clock has slowed down when he gets back to the stationary observer and therefore no paradox exists. 

 

Everyone agrees the moving clocks slow down but we have two different reasons. 

In Lorentz’s case the absolute fixed frame remains which in the completely symmetric twin paradox experiment described above implies that both observers have to calculate their own clock rates from the same initial start frame and therefore both calculate the same slow down. This introduces a disembodied 3d person observer which is reminiscent of a god like .

Also any third person who moves with some constant speed somewhere can make this calculation and has the same result. No specific frame like the god-like one is needed.

And formally the simple statement is not correct that moving clocks slow down. If we follow Einstein, also the synchronization of the clocks in different frames and different positions is essential. If this synchronization is omitted (as in most arguments of this discussion up to now) we will have conflicting results.



 

In Einstein’s case both observers would see the other moving at a relative velocity and calculate their clocks to run slower than their own when they calculate their own experience they would also calculate their own clocks to run slow. 

This is not Einstein's saying. But to be compliant with Einstein one has to take into account the synchronization state of the clocks. Clocks at different positions cannot be compared in a simple view. If someone wants to compare them he has e.g. to carry a "transport" clock from one clock to the other one. And the "transport" clock will also run differently when carried. This - again - is the problem of synchronization.



But because they know the other twin is also accelerating these effects cancel and all that is left is the velocity slow down. In other words the Einstein explanation that one twin explains the slow down as a velocity effect and the other as a gravity effect so both come to the same conclusion is inadequate. Einstein’s explanation would have to fall back on Lorentz’s and both twins calculate both the gravity effect and the velocity effect from a disembodied 3d person observer which is reminiscent of a god like .

No twin would explain any slow down in this process as a gravity effect.

Why do you again repeat a gravity effect. There is none, neither by Einstein nor by anyone else whom I know. Even if the equivalence between gravity and acceleration would be valid (which it is not) there are two problems. Even if the time would stand still during the whole process of backward acceleration so that delta t' would be 0, this would not at all explain the time difference experienced by the twins. And on the other hand the gravitational field would have, in order to have the desired effect here, to be greater by a factor of at least 20 orders of magnitude (so >> 1020) of the gravity field around the sun etc to achieve the time shift needed. So this approach has no argument at all. 



 

So both Lorentz’s and Einstein’s approaches are flawed because both require a disembodied 3d person observer who is observing that independent Aristotilian objective universe that must exist whether we look at it or not.

No, this 3rd person is definitely not required. The whole situation can be completely evaluated from the view of one of the twins or of the other twin or from the view of any other observer in the world who is in a defined frame. 

I have written this in my last mail, and if you object here you should give clear arguments, not mere repetitions of  your statement. 



Now Baer comes along and says the entire Aristotelian approach is wrong and the Platonic view must be taken. Einstein is right in claiming there is no independent of ourselves space however his derivation of Lorentz Transformations was conducted under the assumption that his own imagination provided the 3d person observer god like observer but he failed to recognize the significance of this fact. And therefore had to invent additional and incorrect assumptions that lead to false equations.

            When the observer is properly taken into account each observer generates his own observational display in which he creates the appearance of clocks. Those appearance are stationary relative to the observer’s supplied background space or they might be moving. But in either case some external stimulation has caused the two appearances. If two copies of the same external clock mechanism are involved and in both cases the clock ticks require a certain amount of action to complete a cycle of activity that is called a second i.e. the moving of the hand from line 1 to line 2 on the dial. Therefore the action required to complete the event between clock ticks is the invariant.

           The two clocks do not slow down because they appear to be moving relative to each other their rates are determined by their complete Lagrangian Energy L = T-V calculated inside the fixed mass underlying each observer’s universe. The potential gravitational energy of a mass inside the mass shell  is  

Eq. 1)                          V= -mc2 = -m∙Mu∙G/Ru. 

            Here Mu and Ru are the mass and radius of the mass shell and also the Schwarzchild radius of the black hole each of us is in. 

            A stationary clock interval is Δt its Lagrangian energy is L= m∙c2

            A moving clock interval is Δt’ its Lagrangian energy is L= ½∙m∙v2 +m∙c2

The kinetic energy is T = ½∙m∙v2 only in the non-relativistic case. But we discuss relativity here. So the correct equation has to be used which is T = m0c2 *( 1/(1-v2/c2)-1)



Comparing the two clock rates and assuming the Action is an invariant

Eq. 2)                          (m∙c2) ∙ Δt = A =  (½∙m∙v2 +m∙c2) ∙ Δt’

Dividing through by m∙c2 gives

Eq. 3)                          Δt = Δt’ ∙ (1 + ½∙v2/c2)

Which to first order approximation is equal to

Eq. 4)                          Δt = Δt’/(1 - v2/c2)1/2 

First order approximation is not usable as we are discussing relativity here.



Since the second order terms are on the order of v4/c4 I believe Einstein’s theory has not been tested to the second term accuracy. In both theories the moving clock interval is smaller when the clock moves with constant velocity in the space of an observer at rest.

Funny, you are using an approximation here which is a bit different from Einstein's solution. And then you say that Einstein's solution is an approximation. Then you ask that the approximation in Einstein's solution should be experimentally checked. No, the approximation is in your solution as you write it yourself earlier. -

Maybe I misunderstood something but a moving clock has longer time periods and so indicates a smaller time for a given process. And if you follow Einstein the equation                                    Δt = Δt’/(1 - v2/c2)1/2  is incomplete. It ignores the question of synchronization which is essential for all considerations about dilation. I repeat the correct equation here:  t' = 1/(1 - v2/c2)1/2*(t-vx/c2) . Without this dependency on the position the case ends up with logical conflicts. Just those conflicts which you have repeatedly mentioned here.  

And by the way: In particle accelerators Einstein's theory has been tested with v very close to c. Here in Hamburg at DESY up to v = 0.9999 c. So,  v4/c4 is 0.9996 as a term to be added to 0.9999 . That is clearly measurable and shows that this order of v4/c4 does not exist. You have introduced it here without any argument and any need. 



            Lorentz is right that there is an aether and Einstein is right that there is no absolute frame and everything is relative. But Baer resolve both these “rights” by identifying the aether as the personal background memory space of each observer who feels he is living in his own universe. We see and experience our own individual world of objects and incorrectly feel what we are looking at is an independent external universe.

Either Einstein is right or Lorentz is right if seen from an epistemological position. Only the measurement results are equal. Beyond that I do not see any need to resolve something. 
Which are the observers here? The observers in the different frames are in fact the measurement tools like clocks and rulers. The only human-related problem is that a human may read the indication of a clock in a wrong way. The clock itself is in this view independent of observer related facts. 



 

Dr. Wolfgang Baer
Research Director
Nascent Systems Inc.
tel/fax 831-659-3120/0432
E-mail wolf at NascentInc.com <mailto:wolf at NascentInc.com> 

On 6/7/2017 5:54 AM, Albrecht Giese wrote:

Wolf:

Am 06.06.2017 um 08:14 schrieb Wolfgang Baer:



Albrecht:

First there have been so many E-mails I do not know which one you want me to look at to understand your explanation. So please send me a copy of it again.

Sorry but I am not at home now and do not have this mail at hand. But you will find it by its contents:

My mail was about this apparent conflict if two moving observes say that the clock of the other one is slowed down compared to his own one. Which is not a contradiction if you look at the time related Lorentz transformation:
t' = gamma*(t-vx/c2) 
where you have to insert correct values for v and x. You will find it in a mail of last week.
This understanding is essential for any discussion of dilation.



Of course if there is some special to interpret Einstein's intent  that is not in Einstein's book then perhaps you are right , 

Which book of Einstein do you mean? As above, this is not a special interpretation of Einstein's intent but the correct use of the Lorentz transformation.



if you are telling me that the only valid inertial frame is the  frame of a third person god like observer who is stationary before the twins fire their rockets and in that frame both of the twins doing exactly the same thing would have exactly the same clock rates and therefore they will have the elapsed time when they meet.

No, you can take any frame you want. But for the whole process where you use the Lorentz transformation you have to refer to the same frame.



And further if you are telling me that both twins must realize that their own clock is slowing down and the other twin's clock is also slowing down because both twins must do their calculations in this special initial god like 3d person frame so both agree

No, it is not the condition that there is a god like person, but one has to stay with one frame whichever it is.




And further you are telling me that all the talk about there not being a special inertial frame, and everything is relative 
and neither twin  believes he is in his  own inertial frame because neither feels he is moving is a misinterpretation of SRT

whether someone feels that he is moving or not depends also on his choice of the reference frame.



and further that URL https://en.wikipedia.org/wiki/Twin_paradox


"Starting with Paul Langevin <https://en.wikipedia.org/wiki/Paul_Langevin>  in 1911, there have been various explanations of this paradox. These explanations "can be grouped into those that focus on the effect of different standards of simultaneity in different frames, and those that designate the acceleration [experienced by the travelling twin] as the main reason...".[5] <https://en.wikipedia.org/wiki/Twin_paradox#cite_note-Debs_Redhead-5>  Max von Laue <https://en.wikipedia.org/wiki/Max_von_Laue>  argued in 1913 that since the traveling twin must be in two separate inertial frames <https://en.wikipedia.org/wiki/Inertial_frames> , one on the way out and another on the way back, this frame switch is the reason for the aging difference, not the acceleration per se.[6] <https://en.wikipedia.org/wiki/Twin_paradox#cite_note-6>  Explanations put forth by Albert Einstein <https://en.wikipedia.org/wiki/Albert_Einstein>  and Max Born <https://en.wikipedia.org/wiki/Max_Born>  invoked gravitational time dilation <https://en.wikipedia.org/wiki/Gravitational_time_dilation>  to explain the aging as a direct effect of acceleration.[7] <https://en.wikipedia.org/wiki/Twin_paradox#cite_note-Jammer-7>  General relativity is not necessary to explain the twin paradox; special relativity alone can explain the phenomenon.[8] <https://en.wikipedia.org/wiki/Twin_paradox#cite_note-8> [9] <https://en.wikipedia.org/wiki/Twin_paradox#cite_note-9> .[10] <https://en.wikipedia.org/wiki/Twin_paradox#cite_note-10> "

Paul Langevin and Max von Laue are both correct with their explanation as I already wrote in the other mail. 




Einstein and Born explanation is bull shit because in fact there is a preferred inertial frame  i.e the frame in which both twins were initially at rest 

Albert Einstein and Max Born are according to Wikipedia cited by other books, but no contents are given. So, what shall I say? I know about Einstein that he has, when he was asked about the twin paradox, referred to acceleration in so far that in any case of acceleration the original frames are left and so the Lorentz transformation is no longer applicable. I have the facsimile of a letter which Einstein once wrote to a former member of our pre-Vigier group (i.e. PIRT) saying just this. 

I do not know and have never heard that Einstein referred the twin paradox to gravity. And to refer here to gravitational time dilation is so far from any logic that I cannot imagine that Einstein has mentioned something like that at any time. 




Then I agree with you.

But be careful what you wish for because this leads to my CAT theory that all objects are created in the obserer's space and the observer always provides the fundamental background in which both Einsteins theory and Lorenz theory and for that matter maxwell's equations are valid. I would love to have you agree with my object-subject integrated physics, which I am developing. Look at my Vigier 10 paper to see I argued that Einsteins imagination was he special background space in which his thought experiment occurred.

I am afraid that you will overload or over-interpret Einstein's theory if using it for any observer dependent theories. Einstein himself believed that there is an objective reality but that every inertial frame is an own world in some sense. Relativity exists according to Einstein completely independent of the existence of thinking humans.




PS: your explanation is like Max von Laue's only he did not use a symmetric experiment protocol and therefore requires four reference frame switches, which lead me to ask how is the frame change implemented if not through the gravitational time dilation explanation put forward by Einstein and Born. 

Why so complicated? As soon as some object changes its speed it leaves its original frame. That is simply the definition of a linear motion, nothing philosophical beyond that.
And the symmetric version of the twin paradox is your proposal, so neither Max von Laue nor somebody else will have used it. So only one change of the frame, not two or more changes.




 we are getting closer soon I'll show you that the speed with which your particles move is the speed of Now In CAT not the speed of light, which is always changing and not at all constant.

For Einstein the speed of light is constant everywhere. I personally do not agree to this because I follow the Lorentzian relativity, which I do because the Lorentzian SRT is based on physics whereas Einstein's relativity is based on abstract principles. In general I do not like principles as final solutions of open questions.

In a general view it is a big surprise for me that such a simple physical phenomenon like SRT can be made or seen so complicated as it appears in this discussion.



Dr. Wolfgang Baer
Research Director
Nascent Systems Inc.
tel/fax 831-659-3120/0432
E-mail wolf at NascentInc.com <mailto:wolf at NascentInc.com> 

On 6/5/2017 7:15 AM, Albrecht Giese wrote:

Wolf,

to summarize: Einstein's book is not wrong, but if you use it in a wrong way then the results are conflicting.

Am 05.06.2017 um 04:26 schrieb Wolfgang Baer: 

 

On 6/4/2017 9:40 AM, Albrecht Giese wrote:
Each twin has two choices

1.) He ignores physics. He travels forth and back and when he is back again, he meets twin 2 and can compare the clocks of both. They will indicate the same time. So he will not see any problem.

He does not ignore physics but ignores SRT. Both twins do exactly the same thing and physics tells them to expect to get the same result. 





2.) He knows physics SRT and particularly special relativity. And, to be close to your case, he may define after his start his frame of motion as the reference frame. So in this frame his clock will run with normal speed. 

His frame of reference is his spaceship outfitted with real meter sticks and real clocks. He looks outside and measures the doppler shift from a predefined signal frequency and so each one knows the other is moving away at velocity 'v' relative to himself

Any rod and any clock is according to Einstein related to one frame. If one changes his frame, anything is new. 

Then, when his retro rocket has started, he will notice the acceleration. He knows that compared to his previous state of motion he is now moving towards twin 2 with a speed which you have called v. 

His frame of reference is still his spaceship outfitted with real meter sticks and real clocks. He looks outside and measures the doppler shift from a predefined signal frequency and so each one knows the other is moving away at velocity 'v' relative to himself only now the velocity is toward each other.

If he still understands his spaceship as his frame after the retro rocket has started then he leaves the conditions for the validity of SRT.



And as he knows physics, he will be aware of the fact that now his own clock will run differently than before. 

No he reads a book on special relativity written by Einstein that tells him the other twins clock should run slow than his own.

If he reads and understands special relativity following Einstein then he knows that now also his own clock runs slower.



So if he wants to understand what is going on and if he still takes his original state of motion as his reference frame, he has to realize that his clock is now running slower. 

Why would he take his original state of motion as his reference frame? That would be some imaginaty space ship still moving away at velocity "v". His reference frame is his space ship, something may have effected its clocks and rods but his frame is his frame. You are making up a story about his own clocks that are obviously running exactly the way they always as far as his observations are concerned  in order to make the theory he read in the SRT book more valid than what he actually sees and can measure. 

The Lorentz transformation which we are talking about defines the transformation from one (inertial) frame to another one. If twin 1 takes his spaceship as his frame after the acceleration then any facts from the time before are no longer of relevance. 



- On the other hand, if he wants to understand the situation of twin 2 he has to realize that the speed of twin 2,  taking place with v in relation to his own original frame, causes a slow down of the clock of twin 2. But then, after twin 2 has fired his retro rocket, twin 2 will have speed = 0 with respect to the original frame of twin 1. So the clock of twin 2 will now run in the normal way. 

Compared with an imaginary frame. We and Einstein claimed to deals with real rods and clocks

Any rod and any clock is according to Einstein related to a frame and makes no sense without such reference. If one changes his frame, anything is new. The word "real" has a limited meaning in that case. 



- If you now add the different phases of both clocks, i.e. the phases of normal run and the phases of slow down, you will see that the result is the same for both twins. And this is what I have explained quantitatively in my last mail.

All one has to do is to add to the protocol that each twin should take a faximily of their own clocks and  compare them later by your own analysis ( see bold face above) each twin would believe his own Fax would run at the normal rate but the other would slow down.

Here you misunderstand how dilation works. I have tried to show you earlier that clock comparison is not so simple. If two observers move with respect to each other, then in a naive view the observer holding clock 1 would say that clock 2 runs slower and at the same time the observer holding clock 2 would say that clock 1 runs slower. This is as a fact logically not possible. I have explained in the other mail how this comparison works correctly so that the logical conflict does not occur. Please look at that mail again and we can continue our discussion on that basis. 




In other words the experiment gives the answer logic would expect, but the story in Einstain's book is wrong. It is not that mooving clocks do not slow down but the theory explaining it is different and must include the physics of the observer, which I'll describe next once we get this point straightened out.

Einstein is not wrong but you are using the Lorentz transformation in an incorrect way. Please read the other mail again and we can discuss on that basis. 




I must say that I have problems to understand where you have a difficulty to see this.





Dr. Wolfgang Baer
Research Director
Nascent Systems Inc.
tel/fax 831-659-3120/0432
E-mail wolf at NascentInc.com <mailto:wolf at NascentInc.com> 






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