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*Princeton Physicist Professor Russell Kulsrud*

[The first letter follows an emailed announcement distributed by me after the publication of my paper, Subject Title MISSED PHYSICS]

Subj: Re: MISSED PHYSICS...

Date: 1/3/2001 1:17:40 PM EST

From: rkulsrud(a)astro.Princeton.EDU (Russell Kulsrud)

To: TelesisSci(a)aol.com

CC: (Distribution)

I do not belive this. I was refereeing this paper and it looked flooky and wrong.

russell kulsrud

Subj: Re: MISSED PHYSICS...

Date: 1/3/2001 1:20:14 PM EST

From: rkulsrud(a)astro.Princeton.EDU (Russell Kulsrud)

To: TelesisSci(a)aol.com

CC: (Distribution)

Sorry. I refereed this last on nov 13 so he must have sent it in and got it accepted since then, so this is ok.

I still think it is wrong but sowhat.

russell kulsrud

Subj: MISSED PHYSICS

Date: 1/3/2001

To: rkulsrud(a)astro.Princeton.EDU

CC: Rdavidson(a)pppl.gov

Professor Russell Kulsrud

Princeton University

Dear Professor Kulsrud:

Thanks for your comments characterizing my findings, distributed over the internet. I do not know what "flooky" means, but I certainly understand "wrong".

May I respectfully invite you to refute the paper in the open literature with a signed commentary? Since you have already formulated your objection (while reviewing my paper for Professor Davidson), this should not require a great deal of time or effort on your part.

Sincerely yours,

Bibhas De

Subj: Re: MISSED PHYSICS

Date: 1/3/2001 6:18:17 PM EST

From: rkulsrud(a)astro.Princeton.EDU (Russell Kulsrud)

To: TelesisSci(a)aol.com

CC: rkulsrud(a)astro.Princeton.EDU, Rdavidson(a)pppl.gov

Dear Dr. De,

I really do appologize for my intemperate comment. If you could send me the list of people that were replied to I will apologize to them. I mixed your paper up with another paper I was refereeing and thought your paper was submitted before i submitted my comments. (Senility is setting in!) I should not have stated so openly my opinion although you never did reply to my comments.

Again I apologize. I do not care to openly write a paper on this topic as it would take more time than I conveniently

sincerely,

Russell Kulsrud

Subj: Re: MISSED PHYSICS...

Date: 1/4/2001 5:04:18 PM EST

From: rkulsrud(a)astro.Princeton.EDU (Russell Kulsrud)

To: TelesisSci(a)aol.com

CC: (Distribution)

I wish to apologize for making my remarks on the paper of De "The Missed Physics ..." to a wide audience on the internet. These remarks were meant to be only to the publisher and to him, and should not have benn made openly. (Through my inexperience I inadvertently pushed the wrong button when asked who the reply was to be to.) We will try to resolve our different opinions of this work in private.

Russell Kulsrud

Subj: GRACE NOTE

Date: 1/4/2001

To: rkulsrud(a)astro.Princeton.EDU

Dear Professor Kulsrud:

There really was nothing to apologize for, although this is very magnanimous of you. Everyone will see this as such.

My point was merely this: Your name carries a great deal of authority. If you feel strongly about the result being wrong, why not state it appropriately in a right forum - such as in a scientifically argued rebuttal in the literature? (You have already answered this).

But more to my liking, why not take another look at the scientific issue? I certainly would prefer to have you on my side.

Sincerely yours,

Bibhas De

Subj: Re: GRACE NOTE

Date: 1/5/2001 10:08:11 AM EST

From: rkulsrud(a)astro.Princeton.EDU (Russell Kulsrud)

To: TelesisSci(a)aol.com

Dear Dr. De,

Since this gaff of mine I have decided to look more closely at your paper then I did before. I find it is a good deal more elegant than i have previously thought. However, the problems at infinity are somewhat subtle and I am trying to resolve them in my mind. I did notice that for your first solution the flux through the boundary is of order sqrt(r) * an oscillatory function, namely J1(kr) and I am not sure how this reflects on currents far away. I am trying to see what happens if one tries to approach your solution over all space by currents out to some R for both solutions and then let R go to infinity. This seems tricky because of the large flux coming through the r=R surface. this flux is positive for z>0 and negative for z<0 (or vice versa) and if one only had this boundary condition and no other currents the field would be finite in the finite region. However, both solutions may have the same flux through r=R, and it could cancel. This depends on how one approaches the solutions through all space.

I will keep looking at this more carefully and let you know if I find anything. let me know what you think about this problem at infinity.

By the way the classical condition that a current free solution vanish in a finite region is that the magnetic potential \phi satisfies \phi \nab \phi dot dS integrated over the boundary vanish. This is really an interesting problem that you have presented even if it does not lead to a nonzero solution in the end it is pedagogically valuable.

Regards,

Russell Kulsrud

Subj: YOUR COMMENTS

Date: 1/5/2001

To: rkulsrud(a)astro.Princeton.EDU

Dear Professor Kulsrud:

Here is my consolidated response to the various issues you have raised:

The two potentials 1 and 2 I view as merely mathematical steps (scaffolding, say) towards constructing the final result. The potentials 1 and 2 here have no physical significance. If they did, they could indeed be criticized as infinite energy solutions. What I suggest is that their mathematical difference gets us to a finite energy, finite extent structure having physical significance.

Let us look at it another way. Suppose a computer were taught the rules of the game, and asked to arrive at the final result (if possible). Then the potentials 1 and 2 would not arise - and the related criticisms would not arise. Or, suppose a good mathematician arrives at the final solution along a different route.

In the end, as you must have sensed, it becomes an issue of numerical computations, or, an "engineering" problem. And this can be a substantial second step. Initially, I wanted to float the idea, and attract debate. Obviously, I feel there is something of substance here. But if not, as you say, the debate could be illuminating.

I am deeply grateful for whatever attention you are able to give to this problem

Sincerely yours,

Bibhas De

Subj: Re: YOUR COMMENTS

Date: 1/5/2001 3:16:15 PM EST

From: rkulsrud(a)astro.Princeton.EDU (Russell Kulsrud)

To: TelesisSci(a)aol.com

Dear Dr. De

I will look over your remarks this week end and get back to you on Monday. I do not have the time to inspect them this afternoon as it has started to snow hard and I have to go.

russell

Subj:

Date: 1/8/2001 3:16:41 PM EST

From: rmk(a)pppl.gov (Russell Kulsrud)

To: TelesisSci(a)aol.com

Dear Dr. De,

Thank you for your comments. I have read them now and see what you mean.

How would you actually go about setting up the magnetic fields as a thought experiment. I have been trying to arrive at a scheme.

What i would do is put in the currents for each potential 1 and 2 out to a certain fixed radius and then subtract these currents and let R go to infinity.

The trouble I found was that with these currents alone i would not get the first potential as i would need to add some flux through the surface r=R and z up to about 1/k. Then I would get your first potential.

Subj: Re: CALCULATIONS

Date: 4/27/2009

To: rmk(a)pppl.gov

Dear Professor Kulsrud:

In a numerical computation of the final structure, one needs the FIELDS due to the potentials 1 and 2. But the first of these field structures is already completely specified analytically at every point, including the z = 0 surface (no singularities). Therefore, no reference to the CURRENT needs to be made here at all. This non-reference is crucial - and is what separates 1 from 2. The second field structure should be calculated the way you describe - as a sum of the fields due to a number of single current loops of widening radius and changing currents. As you point out, there is here the problem of singularity at r = R. (But this is not specific to my paper. It is the same classical singularity of the fields due to a single current loop at the conductor itself.). The singularity can be avoided and yet the fields calculated completely using numerical methods (This is somewhat similar problem to calculating fields very close to a long solenoid.). I hope that this answer corresponds to the question you have asked.

If on the other hand, the question is: How would one actually produce this structure in the laboratory, then I have further thoughts I could submit for your consideration.

Sincerely yours,

Bibhas De

Subj: Re: CALCULATIONS

Date: 1/9/2001 1:39:03 PM EST

From: rkulsrud(a)astro.Princeton.EDU (Russell Kulsrud)

To: TelesisSci(a)aol.com

Dear Dr. De,

thanks for your message.

I am not unsympathetic with your views which are most interesting.

I am simply trying to cope with the behaviors at infinity. Are currents at infinity involved.

for example you say fields one are completely known and so do not need to be calculated from currents.

However, there must be currents that produce it, for example the currents in the z = 0 surface which you use to construct the second field.

The big question is are there any other currents around that do not cancel when you subtract the two fields. This is important as when you subtract them you claim the resulting field has no currents. But if there were currents at infinity this would not be the case as your difference field would not then be source free.

As a trivial example consider a field in the z direction uniform throughout all space. I has no currents in the finite part of space but I do not think you could consider this a source free field. There really is no such field but there could be on uniform over a very large region say generated by a very large solenoid. the currents in the solenoid are the source of this field.

It is just a good approximation to treat the field as everywhere uniform although in any limiting sense there are currents very far away.

My concern is that something analogous may be happening for your first field. I just am unable at the moment to decide if there should or should not be currents at infinity. For this we have to ask how to pass to the infinite limit of your field occupying a very large region as in the above trivial uniform case.

At the end of your email you say you have thoughts of how to actually produce field in the lab. I would certainly like to here them and to contrast them with the way one makes a "uniform field " in the lab.

I will keep pondering you field to see if I can reconcile it with my way of thinking.

Regards,

Russell

Subj: Re: CALCULATIONS

Date: 1/9/2001 2:55:22 PM EST

From: rkulsrud(a)astro.Princeton.EDU (Russell Kulsrud)

To: TelesisSci(a)aol.com

Dear Dr. De,

One way to produce your field 1 as a limit would be to set a wall at a R at which J1(a R) = 1 and put a surface current along this R and of magnitude equal to Bz(aR, z ) along this wall. then let the wall go to infinity.

Of course this current would vary in sign as the limit was taken, but there would still seem to be sources of this field in addition to those along z=0.

Can you think of a way to pass to the limit which would avoid such currents? by the way you are aware that the field 1 has infinite energy while I believe field 2 has finite energy so field 2 is easier to obtain.

Of course it would be nice to pass directly to field 1 minus field 2 by a limiting process but I am not sure how to do this.

Regards,

russell

Subj: Re: CALCULATIONS

Date: 4/28/2009

To: rkulsrud(a)astro.Princeton.EDU

Dear Professor Kulsrud:

I just received your two messages.

The potential 1 is being used strictly as a mathematical solution of the original equations. The equations are satisfied for this structure, and this is the property that is being carried over to the final structure. In other words, any currents that did not ener into the discussion as a mathematical term does not figure in the problem, even though this may be of interest as a separately standing problem of physics.

In the final structure, which we must now treat as a physical entity, fields go to zero at infinity in all directions, and hence there is no hint of any currents at infinity.

In sum, suppose that you did not know anything about the problem, and I suddenly gave you the final structure as a set of numbers ("I got this in a dream"), and told you that this is the solution for source-free magnetic field - as can be verified with a computer. Then the issue of potential 1, potential 2, currents etc. would not arise at all.

Please do not hesitate to let me know if the above is not satisfactory.

Sincerely yours,

Bibhas De

Subj: Re: CALCULATIONS

Date: 1/9/2001 5:24:18 PM EST

From: rkulsrud(a)astro.Princeton.EDU (Russell Kulsrud)

To: TelesisSci(a)aol.com

Dear Dr. De,

ok. the question is do the fields which you find by your scheme go to zero sufficiently fast. I think this must always have been the problem.

solution 2 goes to zero along z near zero at the rate 1/R^3 or faster the solution for a dipole.

Solution one however goes as 1/sqrt(r) like the bessel function although it does oscillate.

Do you agree with these estimates?

If you do than the big question is how fast should it go to zero to be of practical interest, i.e. realizable in the lab?

This is what I think we really disagree on.

For example the magnetic field about a line current is azimuthal and goes as 1/R. However, there must be a return current and this would truncate this field before it goes to infinity, so do you think such a 1/R field is realizable or must it be terminated.

this is where I stand at the moment and i admit I am puzzled by the question of the behavior at infinity and how one should address it.

regards

I look forward to your next comment because I think we may be approaching agreement.

russell

Subj: Re: CALCULATIONS

Date: 4/29/2009

To: rkulsrud(a)astro.Princeton.EDU

Dear Professor Kulsrud:

The fields at infinity can be studied as follows:

Solution 1: For z = 0 and r going to infinity, the fields clearly decline as 1/sqrt(r).

Solution 2: For z = 0 and r going to infinity, the fields are essentially determined by the local currents there, and therefore do not follow a dipole behavior (i.e. 1/r**3). (Consider this for a moment, aided by some sketches perhaps.) Rather, the fields follow the current distribution. I think that if the mathematical expression could be analytically taken to this limit (r >>z), this must be the result also. So I expect the fields to decline similarly to solution 1 above.

This would mean that going radially out, the fields will cancel towards infinity. Also, the fields clearly go to zero exponentially upwards and downwards. So I would expect that the problem of infinity would not carry over to the final structure.

I will try to collect my thoughts on the experiment.

Sincerely yours,

Bibhas

Subj: Re: CALCULATIONS

Date: 1/10/2001 11:44:51 AM EST

From: rkulsrud(a)astro.Princeton.EDU (Russell Kulsrud)

To: TelesisSci(a)aol.com

Dear Dr. De,

We are getting closer.

let me know if you are tired of these communications.

As I see it we disagree on the asymptotic behavior of field 2. I gave a hasty estimate based only on contributions for small R currents which gave the dipole estimate and you are correct the there could be important behavior for R \approx r. However, could you evaluate these contributions more explicitly since the current factor J1(R) oscillates rapidly compared to r for large r. it looks like one has to do a complex contour for r since the real contour in r has to be displaced into the complex plane by iz^2 due to a pole in r-R because of the factor multiplying the E elliptic integral. I have not had a chance to do this carefully as yet but will attempt it in a day or so.

I left my copy of your paper at home so cannot do anything today.

Our disagreement centers on whether field 1 and field 2 have the same large r behavior for z = 0+ or 0-.

If they do then the cancelled field probably the point of your paper valid and the fields are indeed peculiar but maybe correct.

if they do not agree then the question falls back to how fast fields must fall off to be of real practical interest.

by the way I can refer you to an integral formula in Gradshtein and Ryzsik on page 109, formula 6.565 that combines your three references to Abromvich and Stegen into one reference.

regards

russell

Subj: Re: CALCULATIONS

Date: 4/30/2009

To: rkulsrud(a)astro.Princeton.EDU

Dear Professor Kulsrud:

Short of a full-blown numerical computation project, I don't know how to address this question directly. There may, however, be indirect (loose) ways of looking at this.

Going out to infinite r, with z = +/- 0, you can imagine the currents in Case 2 to be linear, parallel strips. The contribution from the central region here is essentially zero. Also, the nearby strips have essentially the same current. This leads to a field pattern that is in phase with Case 1. This has to mean that the functional dependence is also the same as Case 1. It would then be difficult to imagine why the amplitudes should be different.

Also, the conventional criticism against the paper has always been that the two potentials are exactly equal everywhere. I have shown that they are different for z >> r. Doesn't that leave equality elsewhere (I am being partly facetious here!).

What do you think?

Sincerely,

Bibhas

Subj: Re: CALCULATIONS

Date: 1/11/2001 1:35:23 PM EST

From: rkulsrud(a)astro.Princeton.EDU (Russell Kulsrud)

To: TelesisSci(a)aol.com

Dear Dr. De,

I am trying to do the asymptotic evaluation of the solution 2. My strategy is to take the vector potential from Jackson page 142, equ 5.36. I intend to multiply this integral by J1(\alpha a) and integrate over a. The double integral will then give the vector potential A2 for the second field. then I will replace r^2 by r^2 = z^2 (cylindrical coordinates) and r cos (\theta) by z and go to the limit of large \rho for fixed(and small) z. I will do this by first interchanging the \phi and a integrals. then I plan on using J1 = J0' and integrating by parts to bring down a factor of \rho. this is a standard way of getting the large harmonic fourier transform limit of a function. J1 or J0 are like sinusoidal functions for large arguments (with the extra factor of 1/sqrt(\alpha a) so this should work. there could be some trouble at phi equal zero which I plan to look at more closely. I should find the 1/\rho^n behavior this way and find out after a rho differentiation whether if it cancels the the B_z first field behavior.

If it does fine. We are finished.

If it does not then we have to discuss further how fast the field must vanish for an application and what application do one should have in mind.

I will let you know what I find.

I think it is very tricky to do numerically but this analytic approach might work.

Regards,

Russell

Subj: Re: CALCULATIONS

Date: 1/18/2001

To: rkulsrud(a)astro.Princeton.EDU

Dear Professor Kulsrud:

Many thanks for these labors. I think, however, that I had better wait till you have reviewed your calculations and seen if the factor 3/4 emerges. I would also like to know how the factor alpha has carried through in the new term. Please note also that at any given point in space, there can be an infinite number of solutions that are curl-free. So, one should not probably insist on the 3/4 emerging on this ground alone. In other words, I would not question your 1/8 for this reason alone. Please note also that even though r << z, r is free to be much larger than zero.

I look forward very much to your further findings. I am glad to see that all other matters are settled.

Sincerey yours,

Bibhas

Subj: Re: CALCULATIONS

Date: 1/19/2001

To: rkulsrud(a)astro.Princeton.EDU

Further to my latest note, my comment about infinite number of solutions is badly stated. Please disregard. But no reason to question 1/8 if that is what you continue to get.

B.

Subj: Re: CALCULATIONS

Date: 1/18/2001 5:08:01 PM EST

From: rkulsrud(a)astro.Princeton.EDU (Russell Kulsrud)

To: TelesisSci(a)aol.com

Dear Dr. De,

I have not forgotten your work. In fact I have been spending a lot of time verifying your calculations and statements.

All of them are true but one. both fields have the same currents so theredifference is current free. The fields have the same asymptotic behaviour at infinity and their difference approaches zero as 1/r^(3/2) or faster. then I finally rechecked your statement about the behavior of A2 when r << z, namely your equation 22 and I realized that such behavior is not curl free as it should be. I looked more carefully at the expansion for small r and found that when one goes to the third order in this expansion one picks up a term a constant times (b0/2) r^3 corresponding to the next term in the bessel series for J1. Unfortunately, I must have made an error in this since the constant that i got was 1/8 and it should be 3/4. However, because the field has got to be current free the constant should probably be 3/4 and I have to look closer at the expansion to get this term correct.

In conclusion, it looks like the fields have to agree in this region (r<

I enjoyed this exercise very much and frankly had trouble putting this down. it is a beautiful example in asymtotics and should provoke some interesting reactions since the form of these two (identical?) fields is so very different.

I look forward to hearing your comment on this remark

regards

russell

Subj: Re: CALCULATIONS

Date: 1/19/2001 12:25:29 PM EST

From: rkulsrud(a)astro.Princeton.EDU (Russell Kulsrud)

To: TelesisSci(a)aol.com

Dear Dr., De,

I made a mistake in the expansion of J1. it is r/2 - r^3/16 so the factorof 1/8 is indeed leads to the value that agrees with J1.

I took alpha = 1 by a choice of units.

I forgot to say i made use of 'gradshteyn and Ryzhik pages 709-710 formula 6.59 (1)-(4) in my expansion.

Maybe you should try to check the expansion in r<

I will contact you when I get back on Feb. 1

regards

russell

Subj CLARIFICATION

Date: 1/31/2001

To: rkulsrud(a)astro.Princeton.EDU

Dear Professor Kulsrud:

Welcome back! I am trying to reconcile your (beautiful) calculations with the conclusion that the two potentials are equal everywhere. Let me summarize first my understanding of these calculations:

(1) BEHAVIOR AT INFINITY: You have shown that for r>>z, and r going to infinity, the two potentials converge. This confirms that the final structure is a finite energy structure, even though the intermediate structures are not.

(2) BEHAVIOR ON-AXIS: You have shown that for r<

AN EXAMPLE TO ILLUSTRATE THE QUESTIONS: Consider two potentials B1 and B2 due to two current loops carrying the same current but differing slightly in diameter. These potentials (1) converge for r going to infinity, (2) converge towards the axis, reaching 0 on-axis, and (3) agree at an infinite number of intermediate points (r,z) [with r >> a or z >> a ( a = mean radius of the loops)]. Based on your curl-free argument, one would then conclude that the two potentials B1 and B2 are equal everywhere. But this is clearly not the case.

I wait to hear your thoughts - perhaps I have missed you logic.

Best regards,

Bibhas

Subj: Re: CLARIFICATION

Date: 2/1/2001 2:45:23 PM EST

From: rkulsrud(a)astro.Princeton.EDU (Russell Kulsrud)

To: TelesisSci(a)aol.com

CC: rkulsrud(a)astro.Princeton.EDU

Dear Bibhas,

Everything you say about my conclusions is correct.

What I meant to imply is that if one does an expansion in r than we expect the coefficients of the powers of r to disagree. You showed that the linear term agreed. The r^2 term is zero in both cases. I found by going to third order in the expansion of field 2 that the r^3 term was the r^3 term of the Bessel function. this is as far as I went so at the moment there is no direct evidence that the fields differ.

One could of course go to fourth and fifth order andsee if the expansions disagreed or not. I did not have time of energy for this but since field 2 was curl free I would be very surprised if it did not give the next terms in the series for the Bessel function. Your example would have slightly different z dependences which of course does not matter on the axis since they vanish but slightly off the z axis they differ and I do not believe they agree. Of course they do agree at an infinite number of points and do differ so perhaps my argument is too strong and too intuitive. However, if the z dependence was a pure exponential then there would be only the Bessel solution( I think).

Anyway to show the fields differ one has to find at least one point at which they differ. If they agree up to a certain power of r and then differ then subtraction gets rid of the powers that agree and taking the limit of this difference, say for example, if they differ in the r^5 term, then for small enough r the difference must be non zero. This of course assumes that the series converge in r.

In other words, where we stand is that I claim that you have not succeeded in proving that the difference is not zero, but I have not really proved that it is zero. You showed that the second field goes as r for very small r but so does field 2. You imply that the first field differs from r for r not too small but so does the second field and the difference is the same in r^3 as one would expect if they agreed.

I hope this is not too confusing.

all the best

russell

Subj: Re: THANK YOU!

Date: 2/5/2001

To: rkulsrud(a)astro.Princeton.EDU

Dear Russell:

Many thanks for the nice note. Yes, your conclusions and opinions are quite clear to me. However, I leave any public exposition of these views to you. I quite welcome your documenting of your beautiful calculations in some form. The most logical form would be a rebuttal of my paper upon its publication.

For myself, I feel that the problem merits publication.

Take care!

Bibhas

Subj: Re: THANK YOU!

Date: 2/6/2001 10:17:49 AM EST

From: rkulsrud(a)astro.Princeton.EDU (Russell Kulsrud)

To: TelesisSci(a)aol.com

Dear Bibhas,

I don't feel it is necessary to publish any rebuttal. i just wanted to know what was going on. I love such mysteries.

If you have fax available I could fax a handwritten version of my last calculation of the r^3 term to you if you wish. Send me the fax no if you have it.

It was really fun to do some analysis for a change.

Regards,

Russell

ps. by the way I did not use the eliptic integrals but worked with the directly with the \phi integral of Jackson

Subj: Re: THANK YOU!

Date: 2/7/2001

To: rkulsrud(a)astro.Princeton.EDU

Dear Russell:

Thank you for your generosity in sharing your work. I would love to see the calculations. I am somewhat more interested in your demonstration that the fields decline rapidly enough towards infinity at the z = 0 plane.

The fax number is .

Hope to keep in touch!

Bibhas

Subj: Re: THANK YOU!

Date: 2/7/2001 11:03:52 AM EST

From: rkulsrud(a)astro.Princeton.EDU (Russell Kulsrud)

To: TelesisSci(a)aol.com

Bibhas,

I will try to send this in a day or two as soon as I scribble something down.

I think that you thought the expansion is in r/z but there are some strictly (alpha r)^n/ z where only one power of z occurs and this is the discrepancy between us. You will see how this works.

Regards

Russell

thanks for the fax no.

Subj: Re: THANK YOU!

Date: 2/16/2001

To: rkulsrud(a)astro.Princeton.EDU

Dear Russell:

I have been away for a few days. Just a note to say that you have faxed anything, I have not received it. If you have not, please disregard this note.

Bibhas

Subj: Re: THANK YOU!

Date: 2/19/2001 5:17:46 PM EST

From: rkulsrud(a)astro.Princeton.EDU (Russell Kulsrud)

To: TelesisSci(a)aol.com

bibhas,

I am afraid I have not had a chance to send it but I certainly will soon. thanks for being patient.

Regards

Russell

Subj: Re: FYI: MISSED PHYSICS

Date: 6/4/2001 10:40:05 AM EST

From: rkulsrud(a)astro.Princeton.EDU (Russell Kulsrud)

To: BibhasDe(a)aol.com

Sorry I did not send my calculation to you yet be will shortly. We had a tragedy in our family (a death) which took me out of action for some time.

regards

russell

Subj: Re: FYI: MISSED PHYSICS...

Date: 6/4/2001

To: rkulsrud(a)astro.Princeton.EDU

Dear Russell:

I am very sorry to hear of your loss. Please give me no mind until you are ready.

Best regards,

Bibhas

Subj: CORROBORATION?

Date: 7/10/2001

To: rkulsrud(a)astro.Princeton.EDU

Dear Russell:

I don't mean to intrude at this time, but I am sending the following message for you to consider when you are able to do so.

I have had a chance to reread our email correspondence. I spotted something amazing that I earlier missed. Let me pose the problem first. The issues we were debating were:

(1) Are there any problems of infinity and singularity? (2) Are the two potentials (fields) equal or unequal (paper is wrong if equal)?

You have beautifully resolved (1), your independent calculations showing that no such problems exist.

On (2), the last conclusion you gave me was that the issue remains unresolved. However, I now find at least two independent results of your calculations that prove mathematically that the two potentials are UNEQUAL! These two results are (I simply quote from your letters so you can recognize them readily):

A. "The fields have the same asymptotic behaviour at infinity and their difference approaches zero as 1/r^(3/2) or faster."

B. "I think that you thought the expansion is in r/z but there are some strictly (alpha r)^n/z where only one power of z occurs and this is the discrepancy between us."

If you agree that these results prove the potentials to be unequal, then in fact you have provided complete and independent corroboration of the result of the paper.

Best regards,

Bibhas

Subj: Re: CORROBORATION?

Date: 7/12/2001 1:59:36 PM EST

From: rkulsrud(a)astro.Princeton.EDU (Russell Kulsrud)

To: BibhasDe(a)aol.com

Dear Dr. De,

thanks for your note and kind remarks. I apologize I never got around to sending more details of my calculation, but serious events intervened. At the moment I confess i do no remember the details without looking them up.

My impression was that we or you had not succeeded in showing that the two anyalytic expressions for the field were different. I believe I was able to show that the next term in the expansion of the expression in terms of elliptic integrals in terms of r agreed with the same next term of the expansion of the bessel function expression. Originally I did not have the constant in front of r^3 correct but on a closer look it turned out to also be the same. Thus there was not yet any difference between the two expression that had emerged.

I will try to get this calculation to you shortly.

All the best,

Russell

Subj: Re: CORROBORATION?

Date: 7/12/2001

To: rkulsrud(a)astro.Princeton.EDU

Thank you for your response.

As and when you write up your calculations, this would be a good time to ponder in parallel my earlier comment: The term by term agreement that you are testing, although interesting, does not shed any light on the issue of equality. Since the two potentials asymptotically approach agreement at r = 0, you can make as many terms agree as you wish by making r arbitrarily small. After all, aren't you simply establishing that an asymptote is an asymptote?

This is why I think your other calculations testing singularity and infinity problems are of interest. It seems that they also show the inequality. Therefore, I think, your calculation corroborate the paper.

So as to avoid the lack of clarity of fax, why not send your calculations by mail (when you are ready) to my home address:

Best regards,

Bibhas

Subj: Re: CORROBORATION?

Date: 7/12/2001 5:02:16 PM EST

From: rkulsrud(a)astro.Princeton.EDU (Russell Kulsrud)

To: BibhasDe(a)aol.com

Dear Dr. De,

I think that the two expressions actually agreed at infinity although I should check this. The point is that so far assumption that the two expressions are identical if of different form has not yet been contradicted by any hard results if they in fact do agree at infinity.

They have not yet diverged on the axis.

this is really a quite interesting analytic problem

regards

russell

Subj: PERMISSION TO CITE?

Date: 8/2/2001

To: rkulsrud(a)astro.Princeton.EDU

Dear Russell:

I am working on a draft of a "white paper" examining the ramifications of my idea. With your permission, I would like to include the following section (or a version thereof that is acceptable to you):

<<<<<<< V. EVALUATION OF THE IDEA IN THE SCIENTIFIC COMMUNITY

To this author's knowledge, the only sincere and objective attempt to examine the paper has been conducted by R. M. Kulsrud of Princeton University (Kulsrud, 2001; personal communication), a recognized authority in EM Theory. However, in spite of a detailed and lengthy study, he has been unable to reach any definitive conclusions. His current opinion, quoted here with his permission, is that neither he has been able to disprove the idea nor has this author been able to prove it. >>>>>>>

I don't know where, or if, this paper will be published. Right now, it's just a work in progress.

Sincerely yours,

Bibhas

Subj: Re: PERMISSION TO CITE?

Date: 8/2/2001 1:53:22 PM EST

From: rkulsrud(a)astro.Princeton.EDU (Russell Kulsrud)

To: BibhasDe(a)aol.com

Dear Dr. De,

I think you are going too far with this.

My opinion is that the two fields are identical. However, it is indeed difficult to show this. Since all the background on such fields namely that they should be unique is for the identity i think it is a burden on you to show that they actually differ if you are convinced that they are.

I have checked the expansion you suggest to second order and find to these two orders they do agree and since this is unlikely if they are truly different i have a strong feeling that they are identical.

There is always the outside chance that mathematically they are different but then this contradicts the mathematical proof that they should be the same.

I think that you should go to another order on the r expansion and see if you can find some difference.

You should not make such a big deal until you have definite proof that there is a difference.

Your quotation that I have not been able to find a difference seems mild enough that I would not object if you insist on going on to try to challenge the scientific community. I thought I had been doing a pretty good job of showing that these two fields are very likely identical.

Perhaps a numerical test might be warranted.

Sincerely your and no hard feelings.

Russell

PS it is still a very good mathematical challenge that you pose to check whether these two fields really could differ.

Subj: Re: PERMISSION TO CITE?

Date: 8/2/2001

To: rkulsrud(a)astro.Princeton.EDU

Dear Professor Kulsrud:

Thank you for your response. Under the circumstances, I will not include that section or your name.

Instead, I urge you again to take a public position on the issue. Since you have already done the research, this would be a more productive way to add your expert voice to the issue than to privately admonish me.

Indeed, to this late date I have not seen a single line of your calculations. Therefore, I am at a disadvantage with regard to your assertion that they favor the existing theory. From your description of your calculations, it is quite clear to me that this is not the case. I have explained this comment before.

Sincerely yours,

Bibhas De

Subj: Re: FYI Missed Physics II

Date: 10/29/2001 10:58:07 AM EST

From: rkulsrud(a)astro.Princeton.EDU (Russell Kulsrud)

To: BibhasDe(a)aol.com

Dr. De,

I feel very badly that I have been so lazy about sending you my calculations.

I thought I should do a numerical check about whether your two expressions in series form differ or not.

I will try to do this shortly.

Regards and good luck with your paper.

Russell

Subj: Re: FYI Missed Physics II

Date: 10/30/2001

To: rkulsrud(a)astro.Princeton.EDU

Dear Professor Kulsrud:

Thank you for the message. I will look forward to your final conclusions.

Bibhas De

On Sun, 28 Oct 2001 BibhasDe(a)aol.com wrote:

SOURCE-FREE MAGNETIC STRUCTURES

by

Bibhas R. De

P. O. Box 21141

Castro Valley, California 94546, USA

Email: BibhasDe(a)aol.com

Abstract

A seminal discovery shaping science and technology thus far is that of electromagnetic wave by James Clerk Maxwell in the 1860s, based on what is today known as Maxwell's equations. It is possible that misinterpretations of these equations by his immediate successors have been promulgated ever since, preempting a concomitant development: The source-free static magnetic field structure as a co-equal consequence of the same equations. The entire concept of magnets and magnetic field - one of the oldest chapters of physics - may now need reconsideration, with broad and deep implications for both science and technology. The new result may bring to confluence a number of disparate concepts of physics.

KEY WORDS: magnetic field; string theory; fusion energy; dark matter; dark energy; gravitation; empty space; cosmology; future technology.

Full article at: http://www.journaloftheoretics.com/Links/Papers/BibhasDe.pdf

Subj: Re: FYI Missed Physics II

Date: 1/14/2002

To: rkulsrud(a)astro.Princeton.EDU

In a message dated 10/29/2001 10:58:07 AM EST, rkulsrud(a)astro.Princeton.EDU writes:

<< I thought I should do a numerical check about whether your two expressions in series form differ or not. >>

Dear Professor Kulsrud:

I wonder if your study is still ongoing, concluded, in the back burner, or abandoned. Thanks in advance for an update.

Sincerely,

Bibhas De

Subj: Re: FYI Missed Physics II

Date: 1/16/2002 2:38:13 PM EST

From: rkulsrud(a)astro.Princeton.EDU (Russell Kulsrud)

To: BibhasDe(a)aol.com

Dear Dr. De,

I still have the calculation but at the moment I would say it is on the back burner. I still have your fax and when I get a moment I will send the raw calculations to you. A more reasoned treatment will have to wait a bit longer. sorry. the reason I don't send them immediately is that a whole bunch of other stuff got dumped on them, refereeing and such so it will take a little time to dig them out.

Regards

Russell