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1994 Tesla Symposium at Colorado Springs
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1994 Tesla Symposium at Colorado Springs

TESIA'S EGG OF COUJMBUS, RADAR S1EAL1H, mE TORSION 1ENSOR,
AND 1HE ''PHII.ADElPHIA EXPFRIMENT'

by
KL. Corum"', J.F.

Co~

Ph.D."'"'

and

J.F.X Daum., Ph.D.......

"Can we learn to think in 4-dimensions? This, and negative time, mvolve dreaming of
the wildest sort, with no support whatsoever as yet from anything we see or record on
our delicate instruments."
Vannevar Bush,
:March 2, 1967····

Corum & Associates, Inc., P.O. Box 761, Campton, NH, 03323
... Battelle, 505 King Ave., Columbus, Ohio, 43201-2693
•••340 Leighton Ct., Westerville, OH 43081
····Bush, V., Science Is Not Enough, Morrow and Co., 1967, pg. 168.

"Gentlemen, ... we are facing a crises such as the world has never seen before [WWI], and until the
situation clears, the best thing we can do is to devise some scheme for overcoming the submarines,
and that is what I am doing now. (Applause)"
:Minutes of the ?11 AIEE Edison Medal
Presentation to Nikola Tesla, :May 18, 1917

ABS1RACT
In this paper we follow the thread leading from Tesla's spinning "Egg of Columbus"
demonstration, through his proposal of a large rectangular helix disposed about the hull of a ship for
U-boat detection, to Arnold Sommerfeld's discussion of magnetically biased ferrites creating .
electromagnetic stealth for WW-II submarines. By calculation, the required magnetic field to reduce a
ship's radar reflection to less than lo/o, at L-Band (1.5) GHz, is in excess of 15,000 Alm Fields this
order of magnitude would appear to fulfill the requirements of a "Philadelphia Experiment~. Such
intense fields. would create green mist and cavities in salt water, and magnetophosphenes aJ!.dPurkinje
patterns in humans, particularly if driven at frequenci~ in the range of 10 - 125 Hz, as Wc:lS_available
from the synchronous generators on WW-II electric drive ships. We conclude that ·with the knowledge
available, the DSRB (under Vannevar Bush) would have been derelict not to have conducted such;  an
experiment.
Finally, we present speculation on temporal bifurcations. Assuming Hehl's hypothesis that
localized Cartan Torsion tensors are generated by ferromagnetic spin, we propose two physical
experiments which distinguish temporal anisotropy arising from anholonomity (the Sagnac effect) from
that arising in the torsion of the 1929 version of the unified field (Eddington's "crinkled rnariifold").
Disclaimer
This paper stands unique among our publications both on Tesla and on the conventional
aspects of electromagnetism and relativity. In this regard it is partly speculative. (And, only partially
at that, since we report on some of our experimental findings that can be verified by independent
laboratory examination). Before wading too deep into a controversial subject like that before us, it is
coin.Luon for respectable folk to acknowledge their limitations. We need to make some kind of
professional "disclaimer". Let us express it this way: we offer this little study in the spirit of an
engineer and some physicists having some fun [in the sense of Arthur Eddington,< 1X2> Joseph
Slepian.,<3>'" Jearl Walker,<4>'"* Edwin Abbot,<5> George Gamow,<6> or even Arthur C. Clark], looking at
published statements, attempting to stay within the bounds of engineering technical propriety, and
saying, "What if ·... ?" Since the theoretical analyses make specific physical predictions, it follows that
our assertions can be experimentally examined by disinterested (but technically qualified) third parties,
and that we haven't strayed too far from the scientific method in our amusing pastime. Taken in that
spirit, our passing entertainment should also provide recreational diversion for skeptics, grad stildents,
the lunatic fringe, engineers, and men of honor.

·s1epian wrote a delightful series of "Electrical Es8ays" for engineers. Start with the one cited and
read either forward or backward several years.
**Walker wrote about physics problems, "I am not so interested in how many you can answer as I
am in getting you to worry over them"

PARf I - RADAR AND ROfATING FIElDS

Introduction
During the 1992 International Tesla Symposium, the authors took the opportunity to once
again visit the site of Tesla's Colorado Springs laboratory and nearby Prospect Lake, where many of
Tesla's experiments were conducted in 1899. While vvalking armmd the Monmnent in War Memorial
Park our conversation turned to the book by William Moore and Charles Berlitz on the Philadelphia
Experiment. A colleague at Battelle had introduced us to the story in fall of 1989. One of the
presentations at the last ITS S)'IlllX>sium concerned the topic, and as we walked we began to JX)nder
out loud how we might rationally explain such an experiment. The following is the result of our
reveries.
The world of magnetics, today is extremely complex. During the 1940's and SO's h!gh field
magnetics became "big physics", and it would be impossible for the authors in this small space to even
attempt a modem analysis of this topic. Instead, we believe that there is some merit to erfiPloying the
sort of physicci arguments, both classicd and relativistic, that wo'U!.d have been available by scientists
of the deca:le preceding the Philadelphia Experiment. This is not a discussion of anything even

remotely like the Navy's new "Sea Shadow".(7)
It has been asserted that the initial Philadelphia Experiment took place "sometime between
July 20 and.August 20, 1943."<8> Simply put: in the experiment(s) a big coil of wire was v.rapped
around a large ship, the ship became invisible in a foggy green mist, and a lot of people on board
were hurt. (Some thought they went through a rip in the fabric of the space-time continumn, were
teleported from the Philadelphia shipyards to Norfolk, Vrrginia, and saw alien humanoids). The
respected names identified with with the experiment include Albert Einstein (1879-1955),· Rudolph
Ladenburg (1882-1952), John Von Neumann (1903-1957) [and his Gottingen dissertation advisor,
David Hilbert (1862-1943)], Nikola Tesla (1856-January 7, 1943), Oswald Veblin (1880-1960),
Burtrand Russell (1872-1970), Gabriel Kron (1901-1968), Vannevar Bush (1890-1974) and a host of
other recognized men of renown whose common interest seems to include, among other things, an
historjcal association with things of interest to the Navy, and submarine detection in particular. The
Department of the Navy has officially identified the experiment as mythical, having its genesis in a
1955 book on UFO's,<9> not Naval science.00> Perhaps the story really was mythological. However, if
*Einstein served as a consultant for the R&D Division of the US Navy Bureau of Ordnance from
rvfay 31,1943-Jtme 30,1946. Interestingly, according to the FBI Einstein file [QC 16 ESU55; OCLC
#13720407; Title #3892869], EinStein vvas in Philadelphia during the time of the alleged Philadelphia
Experiment. (On the evening. of August 10, 1943 he spoke before the Philadelphia section of the
"Friends of Soviet Russia".)

3

that's the case, then our hats are off to the brilliant scientists that spun this gossamer web of fantasy for no ordinary laymen could have done it.
\\by Tesla?

It is now common knowledge that Tesla had attempted to market his radio controlled craft (the
"telautomaton"; Patent• 613,809) to the US Navy.··< 11 X12> Tesla was the first to advocate the electric
drive for naval vessels.<1 3) He was the first to suggest that electric drive war ships could be used in
peacetime to supply shore power during emergencies. <14> (They were, of course. See the comments
below). And, as is evident from Tesla's quote at the top of this article, he was again dealing with the
Navy during World War I. It was during this time that he met in Washington with Assistant Secretary
of the Navy Franklin Delano Roosevelt. Roosevelt's mentor, Josephus Daniels, was

Secre~

of the

Navy..... (It was also during this time that university professor and future Director of OSRQ (Office of
Scientific Research and Development), Vannevar Bush, vvas just starting research on submarine
detection for the Navy.) From Tesla's files, we know that a few years later, during the 1920's, the
Navy in Philadelphia (specifically John B. Flowers, Electrical Engineer), was examining.Tesla's work
Anderson has noted that, "Tesla vvas engaged. .. at the E.G. Budd Mfg. Co. in Philadelphia from 19251926."05> And, we also know that when Tesla died in 1943, Naval Intelligence officers accompanied
I\!llT EE Professor John G. Trump (a Bush colleague also in the employ of OSRD) as he secretly

examined Tesla's papers.
We think that not only can the Philadelphia Experiment be tracked to statements which Tesla
published during World War I, and were grasped by men like Bush, but that the physics of the
experiment can actually be traCed back to Tesla's invention of the rotating magnetic field
Furthermore, to us to there appears be a legitimate link between Tesla's rotating fields and the Torsion
tensor which appears in Einstein's 1927-29 Unified Field Theory publications. This connection was
first identified and published by Gabriel Kron at GE (Schenectady) during the 1930's. Return with us
·For which Tesla has been identified as the Father of robotics.
0

In 1916 Tesla said, "I vainly attempted to persuade them to accept. I perfected the machine in
1898, and tried everything in my power to have it adopted. .. After the patent expired a few months
ago Congress appropriated [$750,000] and I have now the pleasure of simply looking on while others
are using my inventions, which I could not persuade people to adopt. This is usually so." [Anderson,
1992, pg. 19.] "I tried to persuade the Navy... it was absolutely impossible to find listeners... "
[Anderson, 1992, pg. 158.]

...Both Daniels and FDR advocated absolute legal control of the electromagnetic spectnun by the
Navy.

now to 1887 and Tesla's first rotating field patent (#381,968; Applied for October 12,1887; Issued

l\1ay 1, 1888).
Polyplme Currents and Rotating Fields

The creation of the rotating magnetic field was "ptn-ely the work of scientific imagination". It
has been identified as the greatest creation of the human mind since the invention of the wheel.
Tesla's discovery of polyphase currents and "an invisible wheel made of nothing but a magnetic field"
(the phrase is due to Reginald Kapp)< 16> was the turning point from the past into the 20th century.
Tesla stands at the focal point of the important electrical discoveries of the 20th century. At the
conferral of the AlEE's highest award of honor, B.A Behrend remarked,
-

"Were we to seize and to eliminate from otn- industrial world the results of l\.1r. Tesfas work,
the wheels of industry would cease to tum, our electric cars and trains would stop,_Qtn- towns
would be dark, our mills would be dead and idle."< 17>
When Tesla died in 1943, Yale University EE professor Charles F. Scott observed,
"The evolution of electric power from the discovery of Faraday in 1831 to the initial great
installation of the Tesla polyphase system in 1896 is 'undoubtedly the most tremendous event
in all engineering history'. n(lS)
.
And, the connection to the relativity of rotation (an issue still not put to rest today) was not

overlooked: Yale physicist Leigh Page once said,
"The rotating armatures of every generator ·and every motor in this age of electricity are
steadily proclaiming the truth of the relativity theory to all who have ears to hear. "0 9>
Let us follow ~s central thread that runs through Tesla's professional career back to its origin.
While Tesla had constructed the first rotating field apparatus in the summer of 1883 (one year
before both he, and the Statue of Liberty, arrived from France), it was not until 1887 that a company
was formed to exploit the phenomenon. However, Tesla was unable to raise capital to commercially

introduce his invention. (The enterprise was lll1dercapitalized'.) He finally found a skeptical Wall
1

Street lawyer that was somewhat interested, and this is the conversation as Tesla retells it.
Tesla: "Do you know the story of the Egg of Cohnnbus? ...Well, what if I could make
an egg stand on the pointed end without cracking the shell?". "If you could do this

·As Columbus had done when getting Queen Isabella to pawn her jewels for three ships to sail in.

we would admit that you had gone Columbus one better." "And would you be willing
to go out of your way as much as Isabella?" "We have no cro'M1jewels to pawn,"
said the lawyer, who was a wit, "but there are a few ducats in our buckskins and we
might help you to an extent. <20>
11

Tesla arranged for a demonstration the next day. He placed a copper-plated egg on a w~en plate
above his rotating magnetic field (there is a photograph of the apparatus in the Secor article). As soon

as the windings were energized the egg began to spin. [Tesla's spirining egg is, in fact, a macroscopic
analog of the Einstein-de Haas effect

~vestigated'almost thirty

years later. The materials in Einstein's

WWI experiments spin because of m~lecular 'amperian currents' (although later Einstein did suggest
using high frequency 'rotating magnetic fields' to Barnett). In Tesla's experiments they spin because of
induced eddy currents. See part V below.]
"... to their astonishment, it stood on end, but when they found that it was rapidly spinning their stupefaction was complete·... No sooner had they regained their
composure than Tesla was delighted with their question: 'Do you want~ money?' ...
That started the ball rolling. Tens of ·millions of horsepower of Tesla induction motors
are now in use all over the world and their production is rising like a flood .. Rotating
fields of 15,000 horsepower are now being turned out... and ship propulsion by Tesla's ·
electric drive whic~ according to Secretary of the Navy Daniels' statement, has proved
a great success. n<21 >
The electrical circuit which Tesla employed for the egg of Columbus used two phase AC energizing
the coils in quadrature and the source frequency was varied from 25 to 300 cycles, "the best results

being obtained with currents from 35 to 40 cycles..... The story was also mentioned in Flemings
P11Jnov
'Tieg1a(12)
_.......,,,.,,OJ nf"
'"'".L
JL

A

In 1893, 6 years after demonstrating the egg of Columbus to the attorneys and business
investors in New Yor~ a large egg demonstration was constructed for Tesla by Albert Schmid and
Charles H Scott, at the time both of Westinghouse. (Scott, subsequently an EE professor at Yale,
served as President of both the AIEE and, later, the IRE.) The egg occupied part of the Westinghouse
exhibit in the Electricity Building at the great Chicago World's Fair.· The 1893 Fair celebrated the

sooth anniversary of Columbus' discovery of the new world and, ostensibly, it was intended to launch

*The language used to describe the striking effect his 1892 lecture-demonstration had on the Royal
Institution in London, was, "The scientists simply did· not know where they were when they saw it."
(Anderson, 1992, pg. 95)
**Note that Tesla ~ recognized that he can characterize different sPnning eggs widi certain
gyromagnetic resonance frequencies!! This was in 1887.

society into the 20th century. There is a photograph of Tesla's exhibit in the 1\1artin book. <23) This was
only a few months before Lord Kelvin was to choose the Tesla polyphase system for Niagfil-a Falls,
and 3 years before the first Niagara Falls plant was turned on
\Vhile Tesla had been active in RF generation in the early 1890's, the close of the decade saw

him making great strides in the realm of high voltage RF power processing. These experiments
culminated in a cluster of patent applications and the construction of the Wardenclyffe laboratory.
Mention should also be made of his turbine development and intense engineering consulting practice
just prior to WWI. From the comments above it is clear that he \vaS actively promoting his patented
ideas.
Tesla's Reflections on Radar and Ships Wmpped in Coils of \\ire

-

Just after receiving the AIEE's Edison medal (May 18, 1917), Nikola Tesla grantedjil
interview to H W. Secor of the Electrical Experimenter magazine. (Secor's article was published in
August of 1917.) The topic of discussion ttnned to the detection of Gennan U-boats (U-boat =
Unterseeboot = submarine), which had caused so much distress to the

allies~·

The US had entered the

war in April of 1917. Tesla's concerns centered armmd the detection of submarines, in particular the
possibility of non-ferrous hull detection Listen as, filtered by the pen of a journalist, Tesla narrates
the electrical preparation of the ship:
"Now, suppose that we erect on a vessel, a large rectangular helix or an inductance
coil of insulated wire. Actual experiments in my laboratory at Houston Street (New
York City), have proven that the presence of a local iron mass, such as the ship's hull,
would not interfere with the actions of this device. To this coil of wire, measuring
perhaps 400 feet in length by 70 feet in width (the length and breadth of the ship*) we
connect a source of extremely high frequency and very powerful oscillating ctnTent. <24>
11

We think that Vannevar Bush was aware of this suggestion, and it is our thesis that these words are
the seed that later blossomed as the "Philadelphia Experiment". The article then goes on to describe
an RF technique which subsequently became quite popular (though not on such a grand scale) for
metal detectors and for tuning the reactance of RF coils in transmitters and receivers. Upon further
prodding by Secor, Tesla discussed a high peak power microwave raiar for operation at wavelengths
"... of but a few millimeters". (X-Band radar at 10 GHz has a wavelength of 30 mm.)
Tesla desired that the ship be able to provide sufficient electrical power, and he states this in
"According to Jane's Fighting Ships (1967-68, pg. 408), the Eldridge (DE-173) was 306 feet long
by 37 feet at the beam, and had a draft of 14 feet. Its main engines were GM diesels, electric drive, 2
shafts, 4.5 Mw.

the interview.
"The average ship has available from say 10,000 to 15,000 HP. ... The electric energy
would be taken from the ship's plant for a fraction of a minute only, being absorbed at
a tremendous rate by suitable condemeIS and other apparatus, from which it could be
liberated at any rate desired."
Clearly, Tesla was contemplating the use of pulsed ctnTents· in the coils around the ship. Remarkably,
vessels wrapped in coils were observed during WW-II (perhaps for mine sweeping or even degaussing
studies). [According to Moore, Francis Bitter, of ivfIT, recalled witnessing "a relatively large ship
carrying ... a bar magnet going from the bow ... vvay aft. This bar magnet had coils wolllld around it
which passed ctnTent produced by big motor generators."<25)] By the way, the Eldridge's generator was
rated at 4,600 kVA and could deliver 6,000 HP. Two generators, as described in the book, could
deliver more than 12,000 HP (almost 9 Mw).

-

-

It is not clear that l\1r. Secor even fathomed vvhat Dr. Tesla was speaking about. Mow much
of what was published in the article were

T~la's

ideas and what was added (or deleted) by Secor is

not transparent. (We have the same problem with O'Neill's colorful biography.) After Tesla's brief
discussion of sonar, Secor mixes together the RF magnetic detection process and the "electric ray"
radar technique. While Secor's version of Tesla's disclosures might solllld, today, like oversimplified
impractical popularizations, Secor was quick to conclude his 1917 article with the disclaimer, "...
several important electrical war schemes will shortly be laid before the War and Navy Departments by
Dr. Tesla, the details of which we naturally cannot now publish. 11<26> Margaret Cheney has observed
that, at the time, Thomas Edison

"... had been named to direct the new Naval Consulting Board in Washington, with the
primary job offinding a w01 of spotting U-boats. Tesla's idea, if even brought to Edison's
attention, would almost certainly have been discounted. "(27)

*'~I will tell you the secret of all these wonderful displays. ... Consider a large gun which hurls a
projectile of a ton a distance of 18 or 20 miles. If you figure the horsepower at which the gun
delivers energy, you will find that it amollllts to from 6 to 12 or 15 million horsepower.... With the
methods which I have devised, with my transformer, it is not at all difficult to get rates of energy
many times that. ... in the plant on Long Island, if I wanted to operate, I could have just reached a rate
of 1 billion horsepower. ~ .. That wonderful thing can be accomplished through a condenser. The
condenser is the most wonderful electrical instrument ... You store less energy in the condenser than in
the gun, but whereas a gun will discharge ... in 1150 of a second, a condenser can discharge the energy
in 1 millionth of this time. ... all these effects which elicited great wonderment of the profession, were
always produced by damped waves, because with the undamped waves it would not have been
possible· to attain any such activities." [Tesla on His Work With Alternating Currents, by L.I.
Anderson, 1992, pp. 112-113.]

It should also be noted that Vannevar Bush was involved in the same endeavor:
"During 1917-18 [Bush] was engaged in research on submarine detection in connection
with the United States Navy special board on submarine devices. <28>
11

In 1917, Bush, fresh out of graduate school,* was a newly appointed assistant professor of electrical
engineering at Tufts College in Medford, JVIassachusetts and consulting for the American Radio and
Research Corporation. [AI\1RAD was a J.P. Morgan venture, built on the Tufts campus, which
manufactured "thousands of transmitters and receivers" during WWI.<29>] Bush was one of the guiding
lights for a spin-off company which, in 1925, was renamed Raytheon.** (In 1941 Raytheon became
the prime source for the new Navy Search Radar.<30>) Bush joined the IvfiT EE Department faculty
(his specialty, initially, was electrical power and subsequently operational calculus and analog
computers (the famous network analyzer)) and became Dean, and then Vice-President of~ in
1931.:·· He accepted the position of President of the Carnegie Institution of Washington m1938 (~d
held the position tmtil 1955). He was Science Advisor to the President and was appointed by
Roosevelt as chainnan of the National Defense Research Committee (July, 1940),···· as director of

9sRD - the Office of Scientific Research and Development (1941), and as Chairman of the Joint
Committee on New Weapons and F.quipment of the Joint United States Chiefs of Staff (1942).<31 >

*Bush received a BS and an MS from Tufts College (1913), Doctor of Engineering jointly from
l\1IT and Harvard (1916), and eventually 10 honorary doctorates from various colleges and
universities. During his remarkable career, he was science advisor to several Presidents. He was
Vice-President and Dean of Engineering at l\1IT in 1931, the year that he wrote to Tesla
*"'Raytheon, in fact, (with 25% of the EE department invoived) came to be known by the grad
students at :MIT in the late 1920's as "an extension of the Electrical Engineering Department.!' (See
Reference 29.)
***Ever the entrepreneur, when Bush heard AF. Joffe of the Polytechnic Institute of Leningrad
present his ideas on a new super-dielectric for HV insulation, he rallied his investor friends and went
to Leningrad and Moscow. (As described in his autobiography, Pieces of the Action (Morrow, 1970),
the enterprise resulted in failure.)
.......Recall that John G. Trump, accompanied by three Naval personnel, examined Tesla's personal
papers when he died in January of 1943. Trump was Secretary of the Mcrowave Committee of the
National Defense Research Committee from 1942 lllltil 1944 when, as a member of General C.A
Spaatz's Advisory Special Group on Radar, he·went to· Europe as the Director of the British Branch of
the (MT) Radiation Laboratory. (See Electrical Engineering, Vol. 80, No. 5, ivfay, 1961, pp. 364365.) [General Spaatz, by the way, was Air Force Chief of Staff and headed the "very secret"
committee on UFOs. According to Irving Langmuir, (Physics Today, October, 1989, pg. 48) Spaatz
had confided, "You know it's very serious. It really looks as though there is something there." (Also
see Physics Today, March 1990, pg. 13 and April, 1990, pg. 13.]

(

Vannevar Bush guided much of the Nation's weapons research during WWII. According to Frank B.
Jewet( (President of the National Academy of Sciences), as head of OSRD Bush
"... directed the mobilization of the entire civilian scientific and technical power of the nation
and welded it together into the military establishment in the greatest industrial research and
development man has ever known "<32>
Recall that Vannevar Bush, while

Vi~

President of MIT, had sent Tesla birthday greetings in 1931:

"Dear Dr. Tesla ... I wish to join to my own tribute of admiration for your unique
career the congratulations of the :Massachusetts Institute of Technology, where the
contribution which your original genius has made for the benefit of mankind is fully
appreciated. "<33>
In 1943, Bush, like Tesla in 1917, received the AIEE's highest honor (at that time the B:lison Award).

Bush held about 50 US patents for various inventions. Let us move ahead from Tesla's

s~gestion,

to

place coils of wire on a ship, to radar and radar counter-measures (stealth).
Radar
It seems to be broadly recognized that, although Heinrich Hertz had observed RF standing
waves resulting from metallic reflections, it was Nikola Tesla, in 1900, who was the first to propose
the concept of radar.<34> According to NRL radar pioneer RM Page, it was Tesla who first" ...
suggested the use of electromagnetic waves to determine the relative position, speed, and course of a
moving object. "<35> The earliest patent issuing for radar appears to have been the British patent granted
to Gennan engineer Christian Hulsmeyer.<36>· Certainly, Tesla's Lnterview with H W. Secor appears as
an added note in the radar lore.<37) The acronym raiar was an official code word adopted by the US
Navy in November of 1940, the same month that the MIT Radiation Laboratory was organized for the
exploitation of the microwave region for radar.
Sommerfeld on Electromagnetic Stealth During \VW-Il
In his authoritative two volume radar cross section handbook, George Ruck has pointed out the
desirable features of radar absorbers.
"The search for suitable radar absorbing materials (RAM) was initiated in the early 1940's both
in the United states and Germany. Ideally, the optimum RAM would be a paint-like material
effective at all polarizations over a broad range of frequencies and angles of incidence.

·Edison Medalist. in 1928. (Eleven years after Tesla)

Unfortunately, such a material does not exist and the probability of its being developed is
rather remote. "<33>
Arnold Sommerfeld ( 1868-1951) presents a surprising discussion of German war research ~n
stealth and radar absorbing materials in the optics volume of his famous Lectures on Theoretical
Physics.<39) He relates that the case where the magnetic penneabilities_ between two media (air and
target) are unequal (µ 1 :t ~ is "of some historical interest".
~ a counter measure against allied radar, a
largely nonreflecting ("black") surface layer of small thickness. This layer was to be
particularly non-reflecting for perpendicular or almost perpendicular incidence of the
radar wave. In this case the angle of incidence and the angle of transmission are both
almost equal to zero. The problem is solved by making the ratio of the two wave
impedances equal to unity.

"During the war die problem arose to find,

m

Ei/H

i2

= -1 =
E/H

1

(1)

2 . 2

The criterion is, thus, not the index of refraction but the ratio of wave impedances."
Sommerfeld's suggestion is similar to the idea of making the radar target stnface a "conjugate match"
to eliminate radar reflections. If one could make the impedance of the second medium be the same as
free-space, the target would become radar invisible. He continues:
"In order to 'camotefl,age' an object against ra1ar waves, one must cover it with a layer
for vvhich this ratio of wave resistances has the value 1 in the region of centimeter
waves. According to [the law of refraction and the boundary conditions] this means
that if we call the constants of the desired material E and µ and those of air E0 and µ0 ,
then
(2)

Hence, the problem concerns not only the dielectric constant but also the relationship
between the dielectric constant and the permeability. A substance must be formed
whose relative permeability J.1r = µ/µ 0 is of the same magnitude as its relative dielectric
constant Vf;,.
This case is discussed by Ridenour in Volume 1 of the famous l\tllT Rad Lab series,<40> and in a well
known analytical reference by Weston.<41 ) Sommerfeld continues,
But the problem is not yet solved. For at its back surface the layer borders on
the object (metal) which is to be camouflaged, and this second surface still reflects
strongly. Hence, the ftnther condition must be imposed that the layer should absorb
sefficiently strongly. This requires a complex rather than a real dielectric constant and
because of the requirement (Eq. 2) a corresponding complex penneability. 'The
material must, therefore, be ferromagnetic and must possess a strong hysteresis or a

!

t

structural relaxation that acts correspondingly. Thus, a difficult technological problem
was posed which, though not unsolvable, required extemive preparatory work.
·
Because of the urgent war situation, the solution which ha:f to be used resulted
from the following considerations ... "
Sommerfeld then changes the course of his ideas. He proceeds to describe the reduction in radar
reflection by a rather conventional means that does not build t.qx>n the requirement of Equation (2).
Instead, what he discusses next is covering the surface \Vith layers of lossy dielectric material, each
strata being less than Y4 wavelength thick, neglecting entirely any effects attributable to µ. ("In this

manner the reflected intensity could be reduced to 1% of the value given by Fresnel's formula ... "<42>)
After the war, a number of papers were published by Sommerfel~'s colleagues at Gottingen and
Munich, in l.eitschrift firr Angewandte Physik, on the topic of radar absorption (Just scan the
magazine's

annuru index for 1956-1959.)

Presumably, after the 'War the Gennan workers \Wre less

constrained in publishing their research on the topic of RAM than Allied scientists.· Even.....~t this late
date most significant western RAM publications are classified, particularly those related to the stealth
bomber technology.
Jn his 1947 MT Rad Lab Volume, Ridenour comments that,

"Absorbent materials have been produced in Germany for the radar camouflage of Uboats. The type of absorber that was actually put into service was of the interface kind The
dielectric constant and permeability were produced by a high concentration of spheroidal metal
particles (carbonyl iron). The concentration of metal was 800/o by weight, and values of
dielectric constant and permeability were E = 7, andµ= 3.5.
An absorber of the second kind was also developed in Gennany. It consisted of a
series of layers whose conductivity regularly increased \Vith depth. The layers were separated
by foam-type plastic whose dielectric constant was close to 1. The absoxption was excellent
from 4 to 13 cm [2.3-7.5 GHz]. However, the complete absorber was a rigid structure 2.5
inches thick, and it was never actually used. "<43>
Is there any connection between the remarks of Sommerfeld and the supposed GeID1al1 version
~f the

"Philadelphia Experiment", which has been rumored to have occurred at the Kiel Shipyards in

Germany during World 'War II? Surprisingly, after hinting at ferromagnetic materials, Sommerfeld did
not tell us how to produce magnetic radar camouflage. We \\!ill try our hand at supplying the missing
details below. But first, we review conventional linear RAM
Ferromagnetic Radar Absotbing l\1aterial

The more-or-less conventional approach to radar stealth is to either employ "shaping" of the

*The American scientist of Getman origin, quoted by Dr. Rinehart in the Moore-Berlitz book (pp.
202-203) was clearly mistaken in his ~sment of Gemlail military spirit.

target (use GID to greatly reduce the RCS), or to utilize the microwave absorption properties of the
complex dielectric constant and complex permeability constant. In lossy dielectric and ferromagnetic ..
matter

µ(<.i.>)

=

e 1(<.i.>) - je 11(<.i.>)

(3)

µ'(<.i.>) - jµ"(w)

(4)

and from Poynting's Theorem, the time average power dissipated is given by44>
(5)

The imaginary components of E and µ arise from hysteretic losses and appear in a standing-Similar to
frictional dissipation."'"' The one-way propagation attenuation in lossy simple media can be~fmmd from
a

=

Re { y } = Re { /jwµa - w2 µe }

(6)

which would occur in the use of an imperfect conductor that is thick enough to sufficiently attenuate
any reflections from its back surface at the frequencies in question l\1aking use of the conductivity
term gives the dissipation mechanism for "space cloth" (which has a wave impedance of 377
ohms/square) and carbon/graphite composite materials. The real part of E andµ lead to reactive
fields, and to capacitive bypass and inductive choking, respectively. Ferromagnetic loading dissipation
occurs in the imaginary component of the magnetic terms. Modeling targets as distributed
transmission lines and resonators demonstrates that material impedance loading of RF "hot spots"
detunes the target structure and decreases RF reflections significantly.
Ferromagnetic materials with very low conductivity are called ferrodielectrics, or ferrites.
Kraus notes that,
"A lossy mixture of high-µ (ferrite) material and a high-E (barium titanate) material can be
used effectively for wave absorption with bothµ and E being complex and with ratio µIE
equal to that for free space (µ/f;.= 1). Although the mixture constitutes a physical

·Ferromagnetic substances are those, which when immersed in an external magnetic field, become
strongly magnetized in the direction of the impressed field, and which exhibit retentivity and hysteresis.
Iron, nickel, cobalt and gadolinium are the only ferromagnetic elements at room temperature.
**In ferromagnetic materials µ is a nonlinear fimction of the applied magnetic field strength, H

discontinuity, an incident wave enters it without reflection. The velocity of the wave is
reduced, and large attenuation can occ~ in a short distance."<45>
As an example, Kraus considers a solid ferrite-titanium slab, for which ~ = c;. = 60(2-j 1) at 100
J\1Hz, and finds that the wave impedance Z = '1<_µ/E)

free space, and the attenuation constant is a

=

= Z which is the characteristic impedance of
0

126 Np/m = 1092 dB/m A 10 mm thick slab of this

material, backed by a perfectly conducting sheet, attenuates the propagating signal 11 dB each way
and reduces the radar backscatter by 22 dB. ("The reflected power is less than 11100 of the incident
power.")
Let us now tum to the situation where a magnetic bias is applied to a ferromagnetic material
in order to "tune" the reflectivity of the meditnn to be a minimtnn for centimeter 'Wavelength radar
signals.
l\fagnetically-Bi~ed Radar Camouflage

"You want camoiifl,age, gentlemen! Give me a ship and I'll show you peifect camoiifl,age." (p. 125"').
Returning to Equation (1 ), we ask if there exists any phenomenon by which power line
ctnTents in a large coil around a steel (or ferromagnetic) body could somehow bring about a reduction
in the reflection of microwave energy from the steel body. Is there a phenomenological. principle that
mcy have appeded to those that conceived and designed the Phila:lelphia experimenJ? (Where were
the JASONs in those days?) It turns out that there is an interesting candidate which may, indeed,
explain the motivalion for the experiment.

In Appendix I, we detennine the surface impedance of a ferromagnetic slab that is immersed
in a constant magnetic field oriented parallel its the surface. This would simulate the situation of a ·
destroyer escort, with coils wrapped around it, illtnninated broadside by microwave radar pulses. The
normally incident, monochromatic, horiz.ontally polarized,.... plane wave reflection from the target's
surface can then be calculated by using the surface impedance
(7)

'"The Philadelphia Experiment, by William L. Moore and Charles Berlitz, Ballantine Books, 1979.
'"*Horizontally polarized for an 'L-coil' helix about the ship, and vertically polarized for an 'M-coil'
helix about the ship. See the comments on degaussing below.

,i.f

(see Appendix I) in the expression for the field complex reflection coefficient at the interface

re cu)

::

Ere.fleeted

Zu(cu) - Z 0

Eincident

Z44(cu)

+

(8)

Z0

where the characteristic iropedance of free space is taken as Z0 = 377 Q What is of interest is that the
reflection coefficient can be tuned to make the radar reflected power drop below 11100 of the incident
power by varying the current in the wires around the ship. Finally, we determine the magnetic biasing
required to make the radar reflection, discussed by Sommerfeld, vanish at centimeter (radar)
wavelengths.
In Figures 1 through 7 we calculate and plot the set of parameters derived in Appendix I, and

the target reflection coefficient r(ro) for various physical constants. A wide range of assurnOO physical
constants are listed in Table I for the variety of examples which we ran analytically. Th~ $1ectrical
conductivity of steel is typically on the order of 1ff mhos/m at OC, and in Examples 1 and 2 we have
assumed an RF value somevvhat less. The applied field strengths are those necessary to raise the
ferromagnetic resonances to the L and X Bands. With the substantial values of ~ involved for
microwave resonances, we suppose that significant physical nonlinearities come into play. As a result,
we must say that the assumed values of Xt, are open to question [However, there seems to be some
latitude here. We found that the theory predicted similar resonances if, in the model, we employed
conductivities as low as 70 rnhos/rn, but in that case Xt,'s of 1620 (L-Band) and 11 (X-Band) would be
required for radar reflection elimination.] Figure 8 is .a plot of the radar reflection coefficient of
Example 6 verses frequency as the bias magnetic field strength is "tuned".
TABLE I ELECTRICAL SPECIFICATIONS

pARMv1ETER

o:,(Q

~

(l)r

(mhos/m)

(ArnpTurns/m)

rad/s

1. L-Band

0.5xlQ6

15,000

3x1()9

l.15xl07

2. X-Band

0.5xlQ6

271,000

5x109

7.9lx1()4

3. L-Band

70

15,000

3x109

1620

4. X-Band

70

271,000'.

5x109

11

5. L-Band

45

50,000

3x109

1000

6. X-Band

6400

271,000

Sx109

1000

7. UHF

103

15,000

2.7xl()9

2200

~

.J.EXAMPLE

/

1.S

~

'\\!

-20

'

\

I

I

\./
-so'--~~~~...&....~~~~__._~~~~---'"--~~~~..A.-~~--....__--1

1.5

0.5

3.5

2.5

5.5

4.5

Example I of Table I: L-Band Plot of Equation (8) in dB vs fin GHz.

Figure 1.

0

I

··10
--20

-30

\

40

'

\

--so

I
'

-60

-70
·:-80
8.8

Figure 2.

8.9

9

9.1

9.2

9.3

9.4

9.5

9.6

9.7

9.8

9.9

10

10.l

10.2

10.3 10.4

Example 2 of Table I: X-Band Plot of :Equation (8) in dB vs f in GHz.

. -10
-15
-20
-25
-30
-35
-40
45

-so
Figure 3.

I.

0.8

l.4

l.2

2

1.8

1.6

2.2

2.4

2.6

Example 3 of Table I: X-Band. Plot of Equation (8) in dB vs f in GHz.

-20
-25

-30
-35

--40
-45

·--so
Figure 4.

8.8 8.9

9

9.l

9.2

9.3

9.4

9.5

9.6

9.7

9.8

9.9

IO

10.l

10.2

10.3 10.4

Example 4 of Table I: X-Band. Plot of Equation (8) in· dB vs fin GHz.

'\,'

2000--y-..-,----.....--..

4000

1200

3200

400

i

I

/'\.,_

'

\

2400
µ" (f)

µ' (f)

-40

1600
800
2

3

4

0

0

2

3

Real and imaginary parts of the permeability vs f in GHz for Example

Figure 5.1

R (f) 400
8

2ol

350

100

300
250
200

4

s.:_

I ..'

~\

\

0

\\
\

150

\~

100

----

50
0
0

Figure 5.2

2

4

Surface resistance Rs and reactance

0

2

Xs vs f in GHz for Example 5.

3

4

0
-10
-20
I

-30

I

i

I

.

i

\

i

\ i

-40

: i

\ i

-so

I/
\!
~

-60
0.5

Figure 5.3

1

1.5

2

2.5

3

Plot of Equation (8) in dB vs fin GHz for Example 5: L-Band ·

3.5

1·10

4

I.5•10

6000

·,.

~

2000

µ' ( f)

:

µ .. ( f)

-2000

5

10

/

\

j
I

I

3000

4

0

9000
6000

\/

-6000
-1·10

l.2• 104

/\

/

4

20

15

0

5

0

10

20

15

--

-

Real and imaginary parts of the complex permeability vs freqtiency in Gf;:Iz for
Example 6 of Table I: X-Band

Flgure 6.1

RS(f)

400---------(\

350
300

/\

/

50

250

\

200
150

~

I
____ ,,,,_.,/

/'

-~t·

-10

100

'

I

\___,__,.-

--15
-2or+-·
_ _____.._ _....___-'--_......

50
0

0

Figure 6.2

200~
150
100

·,

5

10

15

20

Surface resistance Rs and reactance

.o

5

IO

15

20

Xs vs frequency in GHz for Example 6 of

Table I: X-Band.

,..
d

-10
-15
-:20
-:25
-30
-35

\
-40

\

\I

-45

-so

J

v

8.8 8.9

9

9.1

9.2

9.3

9.4

9.5

9.6

9.7

9.8

9.9

10

10.l

10.2

10.3 10.4

Plot of equation (8) in dB vs frequency in GHz for Example 6 of Table I:
X-Band

Figure 6.3

-10

·20

-30

·50'-------'--__.__ ___.__ _~-----'-----'---_.._----""-----"
0.2
0.4
0.6
0.8
1.2
1.4
1.6
1.8
2

Figure 7.

Plot of Equation (8) in dB vs frequency in GHz for Example 7 of Table I: UHF.

--·
...,

r

"A man went to the Navy and sai<:L 'You want camouflage, gentlemen!
Give me a ship and I'll give you camouflage.' " (Moore and Berlitz, pg. 125.)

~§~

"'"'---=2so

-----275
-so'----...!.-----'------'----=...i.---""-----'------------.,;.w.::;
8.8

Figure 8.

9

9.2

9.4

9.6

9.8

10

10.2

Plot of f(t) in dB for Example 6 as H;, is varied from 255 to 290 kA/m

l0.4

The bottom line on all this is that, the smface impedance has a parallel resonance character,
with the effective permeability and the surface impedance both peaking at resonance frequencies
determined by the selected values of the current in the helical coil strrrotmd.ing the ship. The

magnitude of r(co) and the gyromagnetic resonant frequency can be "tuned" by varying the IX bias
field~!!

In particular, at least for the fanciful .values which we assumed for the ship's hull, one can

bring the surface impedance to equal the characteristic impedance of free space, and thus significantly
reduce radar reflection over a useful band of frequencies. One can notch out a depression in the radar
retmn in excess of 20 dB, 500 :MHz (or more) wide at either L-Band (UHF-2 GHz) or X-Band (8-12.5
GHz). :More than probable, a 1943 Philadelphia experiment would have been carried out at L-Band
Equation (2) above can be satisfied at L-Band if I\, is "tuned" to 15,000 Alm That is to say,
if there is 1 turn/m around the ship carrying a current of 15,000 amperes, the ship's radar r~flection
will drop to a :fraction of its zero current value at 1.5 GHz. This would seem to fulfill the _
requirements for a "Philadelphia" experiment. (Surprisingly, there also seems to be another-modest
resonance in the upper infrared, although this may possibly be a glitch in our computer code.) To be
sure, we do not claim that any material is capable of such deep nulls in the radar reflection, or is
tunable over such broad bandwidths. However, the evidence, meager though it is, appears to indicate
that the radar reflection can be minimized and the use of electronic camouflage would probably have
been studied experimentally. Surely these things were taken llllder consideration at that time.
Small Scale Laboratory Experimental Verification
Anned with this theoretical knowledge, we thought it might be circumspect to attempt a small
scale laboratory experiment to verify the effect of Hon r(ro) at X-Band for ordinary steel. (From the
book it appears that the Navy also conducted scale model experiments.)· In fact, we performed two
experiments with our "egg of Columbus" apparatus,"''" which we think have bearing upon our
Philadelphia Experiment discussion. In the final Part of this paper, we will propose two more
experiments.
1) RCS Modification. In order to attain very large currents from a modest supply we took our
'egg of Columbus' toroidal steel core (as a radar target simulating the ship's hull) and used an 8 kV 10
µF capacitor discharge pulse through the windings, which were arranged in series. [The surge current
'"[Dr. RF. Rinehart], "I recall some computations aoout this in relation to a model experiment
which ~ in view at the time." (P. 187)
'""'Our core was made of spiral wound steel strap, giving a core 10" ID, 14" OD, and2" thick. There
were four coils , each 120 turns of# 12 enameled copper wire.

would appear to have been on the order of
I0

=

8,000
21t x 72 x .5

= 35 amps

(9)

which would imply a peak magnetic field strength on the order of <f~> ~ (120 Tums/quadrant)(4
quadrants)(35 amps/Tmn)/(27t x 6"/39.37) = 17.5 kA-T/m] The transfonner steel was illuminated
broadside to the doughnut with a small pyramidal horn-mmmted Raytheon CK-109 X-Band klystron
(100-250 mW at 9.98-11.98 GHz), and the radar backscatter was observed with an HP X-Band crystal
detector, as shown in Figure 9. It would not be unreasonable to suppose that this is the sort of
experiment that Tesla could easily have performed during, or even well before, the 1930's. (He
probably would have used UHF or L-Band, With a somewhat lower power level.) In /act, [rwowd be
swprising if he. had not examined this corifigwation.

A distinct difference between the magnetic bias-on and bias-off target backscatter was
obseived. Clearly Tesla would have observed this phenomenon!
2) Brine Displacement· We immersed the 'egg of Columbus coil' in the bottom of a plastic
tub of water and rocksalt. When the coil was energized, the water 'flew out of the tub' (literally)! At
lower power and the apparatus placed outside and mder the tub, the salt water in the tub swirls
around (One of the authors (KLC) saw a version of this, with a 'pickle jar' about 113 full of mercury,
demonstrated at the Serbian Academy of Sciences and Arts' 1993 Tesla Symposium last September at
Novi Saad
Cl~_rly,

\Vi.th up to 4.5

~

available, eddy currents in salt vvater would not only btnTow out a

hull-shaped hole in the water, but would probably levitate the ship somewhat. As a homework
assignment, the reader is invited to perform the calculation for his amusement.
Initial C.Onclmion

The analysis would appear to lend credence to the hypothesis that something more than
mythology is involved, and it renders plausible the conclusion that sufficient motivation existed to
actually conduct a "Philadelphia Experiment" to examine radar

steal~

on ships with electric drives.

Independent of whether our assmned values are practical or not, the analysis, which uses no
phenomenology that wasnt known subsequent .to 1938; would probably have brought WWII Naval
investigators to the point of radar stealth experimentation. In fact, it would have bee~ derelict
behavior for the Defense Science Research Board not to have conducted such .experiments if it were
aware of this phenomenology (as it must have been) in 1943. Such an approach to stealth, however, is

. ·--··· ·- ........ - ... . . .
··- ..... ·-···--- .. -· ..
.

. ... - . ·--. ··-- - ..

... ---··· ··r----·. ·-- ........ •...

.. ···-·

0

.

.

------ ·- .......... ·------·- --- --· - - --···--···-·· .. ··-·
...

Bias off

Bias on
200 µs/div

Oscilloscope Display

2" Thic""k
10 .. rn~14" OD
L=0.5 H.

9.98 GHz

CK-109
Klystron
(100-250 mw)

~

~

Figure 9.

HP

')__

_j_

~

6

c

:=

10 uF

v

=

8 kV

X - Band

Xta L Detector

Experimental setup for radar backscatter from an 'egg of Columbus' apparatus.

impractical and certainly would be of little interest, as such, to the military today.
PART Il - 1HE EXPERIMENTAL PIATFORM:
There probably exists a technical discussion of the "Bostwick" Class-of Destroyer Escorts
some place in the engineering literature. From Janes Fighting Ships we lmow that the Bostwick class,
of which the DE-173 (the Eldridge) was a member, had the following properties:<46)
Practical Infonnation About Destroyer Escons

Displacement, tons
Length, feet (meters)
Beam, feet (meters)
Draft, feet (meters)
Guns, dual purpose
Guns,AA
A/S

J\1ain Engines
Speed, lmots
Radius, miles
Oil fuel (tons)
Compliment

1240 standard; 1900* full load
306 (93.3) .
37 (11.3)
14 (4.3)
3-3 in (76 mm) 50 cal.

2-40 mm
Fixed hedgehog; OCT
GM diesels, electric drive
6 ooo·bhp; 2 shafts (4.5 MW)
19
1,500 at 11 lmots
300
150 (accommodation 220)

And, it was transferred to Greece in 1951. Several photographs of other Destroyer Escorts of the same
class are also provided Interestingly, there does exist a descriptive level discussion of the use of
destroyer escorts for providing shore power from their propulsion generators.
In a remarkable 1948 paper for engineers, Anderson and Fifer describe how electric propulsion
ships were pressed into service to supply electric power to areas where the retreating enemy had
destroyed existing shore plants. "fuing World -war II, there were constructed a large number of AC
turbine electric propelled vessels which had possibilities for supplying shore power."<47) (The DE's
delivered substantial power and, according to F.M Starr of GE Schenectady, "were best suited to
small diversified loads"<4&) because they could be operated in parallel at a number of nominal output
voltages at 50/60 Hz.) This is consistent with Tesla's 1917 suggestion for peacetime uses, as referred
to above.
Anderson and Fifer even show photographs of two Destroyer escorts, tied up side by side at a

"According to Moore and Berlitz, "The Eldridge was laid down on February 22,1943, at Federal
Shipbuilding and Dry Docks, Newark, NJ, and had a displacement of 1,240 tons standard and 1,520
tons full load." (pg. 158)

dock, delivering power to Portland, :Maine (instead of to a third ship between them, as occurred in one
"Philadelphia Experiment" reported by More and Berlitz) during harvest-time after a severe drought

had left the city without hydroelectric power in fall of 1947.
Their photographs show details of the method used to connect power between the vessels and
land, the cable gantries required because of the high tides at Portland, and even the propulsion controls
and the power controls which were located in the forward engine room and the after engine room.
(This is better than the movie!.) There is a close-up view of the side of a Destroyer Escort showing
the cable reels and tmit substation. If would seem reasonable to assume that the Philadelphia
Experiment would have used huge power cables much like those shown in these pictures. Anderson
and Fifer tell us that the destroyer escort propulsion generators operated at 1,500 volts, 25-135 Hz,
and, "The power output from the two vessels was about 9,000 kW."<49> This would seem to imply
RMS generator ctnTents on the order of 3,000 Amps - slightly below the 104 - 1OS order of ~gnitude
required for the experiment. (See "Resonance" comments below.)
Sbipbomd Degaussing lmtallatiom

During the time of the Philadelphia Experiment, in late summer of 1943, the Naval Ordinance
Laboratory had only two civilian scientists retailed on contract, Jolm Kraus and Albert Einstein.
Kraus was heavily engaged in ~hip degaussing. ("To reduce the ship's magnetic field we wrapped

several. tons of very heavy insulated copper wires around the ship. "<50>)
The same issue of the A.IEE Transactions discussing supplying shore power also has an
introduction to WW-II ship degaussing technology.<51 > What is of special interest are the coil
configurations on the ship. There were basically five different types of coil systems used on a ship.
One of them, the "L-coil" was a helical solenoid with its axis parallel to the axis of the ship. "It was
composed of a series loops in vertical planes perpendicular to the centerline of the ship. The loops

(:txh ran inside the hu/1 from the keel to the underside of the weatherdeck... The instaUations, with few
exceptions were plcxed inside of the vessels. "<52l (Early on, it vvas not fully appreciated that coils
placed inside the hulls could give effective protection, and so the first installations were actually made
with the wires clamped outside and encircling the ship. Later, the coils were placed inside the steel
hulls, the effect being reduced by about 30%, but the savings in maintenance justified the move.)
Another coil configuration, the 'M-coil' "encircled the ship just inside the hull in a horizontal plane

*" ... it concerned three ships. When they rolled the film, it showed two other ships feeding some
sort of energy to the central ship... After a time the central ship, a destroyer, disappeared slowly into a
transparent fog... " Moore and Berlitz, P. 240.

approximately at the water line. "<53 > (Again, early on these were placed outside the ship.)
Kraus says, "The wires in each coil might make a blllldle as big as a man's wrist. Tons of
copper were used on every ship, and degaussing coils became number one in ot.rr country's use of
copper. "C54 > (About 12,000 American naval and merchant ships were fitted with a shipboard
degaussing installation in early WW-II - no wonder we went to a "silver penny" one year.) :Michel
reports that it was not uncommon to use a multiconductor wire bundle composed of 19 conductors of
40,000 circular mill area.· Some cables were "up to five inches in diameter and racked three and four
cables together. "<55 >
Within this context of coil construction, one wonders, "How much current could such coils
carry if pressed to the limit?" Not counting the presence of a heat sink (the hull of the ship and the

sea), the maximum current carrying capacity of a wire is limited. by the so called "fuzing current",
which is the OC current at which a wire will melt. For copper wire,<56>
. (10)

(A l" diameter copper wire melts at 10 kA, and a 5" diameter wire at 114.5 kA.) So, it appears that
the standard bundles could probably handle quite some current if pressed to the limit.
Mchel reports that degaussing installations operated off the ships 240 volt OC supply bus
through rheostats (the M-coil operated directly off a motor-generator pair) and the coils typically
"produced 1,500 ampere turns". "Since the degaussing coils must produce fields extending rather long
distances, the strength of the coil fields in the immediate vicinity of the cables is sufficiently high
under some conditions to adversely ai"'fect the operation of other equipment. "<57) Apparently even
electric arc welders could be affected by the degaussing coils. ("Noticeable irregularities in the welding
operation will occur. "<58>)
PARf ill - CORRElATION" \VIlH 1HE :MOORE-BERI.IIZ BOOK
The Philadelphia Experiment

[All of Benjamin Franklin's electrical experiments were known abroad as "Philadelphia Experiments".
However, he himself referred to the famous 1752 demonstration of the equivalence of lightning and
frictional electricity as "the" Philadelphia Experiment.<9 >]

*This would be about 3.8 inches in diameter. C~n = O.OOl °'1AcM_)

The book by Moore and Berlitz<60> is a source of surprising descriptive infonnation Recently,
one critic<61 > examined the book and concluded, ''Not only does the information presented by Moore
and Berlitz in The Philadelphia Experiment fail the most fundamental test of verification, but the
massive amount of evidence available has demonstrated the thesis patently invalid

11

<62>

We think the

contrary to be true. Not only is the phenomenology supplied, but the independent statements of
various witnesses corroborate the basic technical. issues.
Moore declares that he is not atrained scientist, and it is understandable that technical
testimony is often garbled Take, for example, the interview with Dr. Rinehart (pp. 178-205).
Reading between the lines, Moore (although frantically trying to record what he was being told)
clearly didn't understand what Reinhart was saying. Further, given the tmorthodox manner of C.M
Allen's disclosures, it is a wonder that any meaning can be distilled. This much makes sense:
Carl M Allan
"Electronic camouflage... Some sort of electronic camouflage produced by pulsating energy
fields." (p. 19)
"The Navy did not know that there would be men die from odd effects of hyperfield vvithin or
upon field" (p. 46)
We think the first statement is consistent vvith om presentation above. The second is consistent with
the idea of incident RF interactions with the a low frequency magnetically biased medhnn [fields (RF)
on fields (DC)], just as given in Appendix I.
Commander X
(A scientist in the WW-II Navy radar program)
"I heard they did some testing both along the [Delaware] river and off the coast, especially
with regard to the effects of a strong magnetic force field on radar detection apparatus." (p.
169)
Though hearsay evidence, this is also consistent with the idea of a magnetically biased radar absorber.
We have much more to quote, but will present it with discussion, below.
~onant

:Magnification

One of the issues raised above was how could they step up the ctnTent from the generator by
an order of magnitude. The large ~ required for magnetic biasing vvill result from ~ large ctnTent in
the coils. Obviously, they could use a JX>Wer transfonner to step the current up (and voltage down).
They could, in fact, run high current with a low duty cycle and pulse the coils at very low frequencies.

(Not so good for power transformers.) Or, they might employ the resonant rise in circulating currents
which occurs in a parallel resonant tank circuit. Although DC magnetic biasing was assumed for the

Ho field in Appendix I, this was not necessary, and low frequency pulsations may even be employed.
It is only required that the frequency of the magnetic bias field (I-\,) be much, much less than the radar
carrier frequency (adiabatic. invariance), but low enough for saturation to occm.

Dr. RF. Rinehart
"I think that the conversation had turned at this point to the principles of resonance and how
the intense fields \Vhich would be required., for such an experiment, might be achieved lising
this principle." (p. 191)
"I feel confident that the idea of producing the necesSary electromagnetic field for
experimental purposes by means of the principles of resonance was also initially suggested by
Kent• - possibly as a result of these discussions with Professor Allen··." (p. 187) -

Dr. Valentine
"The experiment [Dr. JesSup] said had been accomplished by using naval-type magnetic
generators, known as degaussers, Vvhich were 'pulsed' at resonant frequencies so as to create a
tremendous magnetic field on and around a docked vessel." (p. 130)
In Appendix II of our took on Vacuum Tube Tesla Coils<63> and in Appendix II below, we
show that if they had placed a capacitor in parallel with the ship's coils (as Tesla suggested in the
1917 interview above) and brought the system to parallel resonance at the ship's generator frequency,
then the circulating current in the coils would be stepped up by the Q of the parallel resonant system
That is, the AC current circulating in the tank circuit coil is larger than the input current by the
amount
(11)

where IT is the terminal point input current (the generator current in this case),

Or= coJ.JR, R =

CRcoii+ I\:oup1oo), and ~upied is the effective load resistance coupled in (due to eddy current loss in the

ship and sea water). In the older literature this is called a "current amplifier" or "current magnifier".<64)
The circulating reactive kVA in the tank circuit is Q times the real component of the generator power
into the tank. (Power is conserved of course, there is no magic going on.) By the way, "pulsing" a
tank circuit is the fundamental idea behind the original· class C oscillator. At full power, a tank circuit

'"Robert Hanington Kent.
'"'"Professor Charles Metcalf Allen of Worcester Polytechnic Institute.

could provide a resonant rise of the ctrrrent to levels sufficient to support the L-Band experiment
discussed above. (A higher Q or pulse power processing might support the X-Band experiment.)
The use of low frequency AC pulsations for biasing is similar to the use of raw AC for class
C oscillator driven Tesla coils. In the optical case it would, more than likely, lead to the
"shimmering" situation discussed by Dr. Rinehart (pp'. 198-199).
PARf IV-· OBSERVABIE RAMIFICATIONS
Next, we would like to examine the collateral effects that one would not be surprised to
observe accompanying such an intense magnetic experiment. There would be phenomenological
effects and physiological consequences.
Phenomenological Effects

Low Frequency Iv.fagnetohydrodynamics in Salt Water:
l.

Green fog and mist
"After a time the central. ship, a destroyer, disappeared slowly into a transparent fog until al.I
that could be seen was an imprint of that ship in the water. Then, when the field, or whatever
it was, was- twned off, the ship reappeared slowly out of thin fog." (p. 240).

"I saw, cfter a few minutes, a foggy green mist arise like a thin cloud" (p. 110).
"suddenly, the green fog returned..." (p. 249).

2.

A cavity in the water:
"The men on the ship were apparently able to see one another vaguely, but al1 that could be
seen by anyone outside of the field was 'the clearly defined shape of the ship's hull in the
water. " (p. 88).
"I watched as the DE 173 became rapidly invisible to human eyes. And yet, the precise shape
of the keel and underhul.l of the ship remained impressed into the ocean water as it and my
own ship sped dong somewhat side by side and close to inboards." (p. 110-111).
"The field was effective in an oblate spheroidd shape, extending one hundred yards out from
ecrh beClln .. of the ship... Any person outside that cozdd see nothing save the clearly defined
shape of the ship's hul.l in the water."(p. 41).

To be sure sea vvater (~Ulm at ELF) is no superconductor. However, a time varying magnetic
field, via Faraday's law, generates eddy ctnTents in salt water, which in turn react back on the

.. A ship's "beam" is its width at the widest point.

magnetic source opposing any changes in the source field Consider the following description due to
Feynman.
"If we have a sheet of a perfect conductor and put an electromagnet next to it, when
we tlnn on the current in the magnet, currents called 'eddy currents' appear in the sheet, so that
no magnetic flux enters. The same thing happens if we bring a bar magnet near a perfect
conductor. This makes it possible to suspend a bar magnet in air above a sheet of perfect
conductor... If the conductor i~ not quite perfect there will be some resistance to flow of the
eddy currents. The. cmTents will tend to die out and the magnet will slowly settle down. The
eddy currents in an imperfect conductor need an emf to keep them going, and to have an emf
the flux must keep changing. The flux of the magnetic field gradually penetrates the
conductor... In a nonnal conductor, there are not only repulsive forces from eddy ClUTents, but
there can also be sideways [drag] forces [which prevent lateral motion]."<65 )

The circulating AC eddy currents woUld agitate the sea -water, at acoustical frequencies, {plJillPing the
salt water, rriaking steam, mist and fog) and, in all probability, hollow out a cavity tmder the magnet.
(Consider what happens "With a high current AC electromagnet in a plastic tub of salt water~) [It's
even more exciting with polyphase AC and a rotating magnetic field!
"If, instead of dragging a conductor past a magnet, we try to rotate it in a magnetic field, there

vvill be a resistive torque from the same effects. Alternatively, if we rotate a magnet near a
conducting plate or ring [or conducting egg!], the ring [or egg] will be dragged arolllld;
currents in the latter will create a torque that tends to rotate it armmd .. A field like that of a
rotating magnet can be made with an arrangement of coils [on an iron torus] ... we have a
'rotating' magnetic field .. The [rotary drag] torque produced on a conductor by such a rotating
field is easily shown by standing a metal ring oh an insulating table just above the torus.
[Feynman here shows a ring hanging by a string over a table above a three phase toroidal
transformer.] The rotating field causes the ring to spin about a vertical axis. <66)
0

Feynman has just described the Egg of Columbus to his Cal Tech students, - without ever mentioning
its inventor. It's too bad - for the students, that is. (They're the actual loosers.) Tesla didn't even
have to use a string to hold up the egg, like Fe)TII11al1 (80 years later) does!]
Well, how much green fog and mist could you make with a nine megawatt AC generator?
How big a cavity could you funnel out of the sea? It would be fascinating to calculate this out as
another appendix.
3.

Unsettled Conditions:

"... a boiling of the water, ionization of the swrounding air, and even a 'Zeemanizing' of the
atoms... The ionization created by the field tended to cause an wzeven refroction of the light...
The result would not be a steady mirage effect, but rather a moving ba:k and fonh
displocement caused by cerlain inherent tendencies of the AC field.. We felt that with proper
effort some of these problems could be overcome and that a resonant frequency could probably
be found that would possibly control the visual apparent internal oscillation so that the

shimmering would be at a much slower rate... " (pp. 198-199).

One might expect power dissipation in the water, due to circulating eddy ctnTents in the sea, to heat
the water, perhaps to the level of steam Also, the sea would be a heat sink for any heating of the
hull. 'Zeemanizing' is discussed elsewhere. There would be a good deal of turbulence near the ship
(as demonstrated by the second of our experiments described above).
Ionization in the air could result as follmvs. Large magnetic fields rapidly changing in time
can cause an ionizing breakdown of aii.C67) The idea stems from Joseph Slepian's pioneering patent<68>
which resulted in D.W. Kerst's creation of the Betatron accelerator in 1941.<69>
If a nonsinusoidal waveform were used to drive the ship's bias coils, 8ay a low duty-cycle

pulse train (as in a class C oscillator), or a capacitive discharge directly into the coil, then large spikes

in Eel> would result from the rapid CHja (make/break). In the language of lumped circuits,

ycoil= L

di/dt has spikes. For a cylindrical solenoid, Faraday's I.aw gives:
(12)

If E should rise to near 200 kV/m (well below air breakdown at 3 MV/m) incipient atmospheric

Trichel pulses would be emitted from every sharp object on the ship and extensive corona would
ensue. Clearly, a fast rising pulse would not be a good choice of waveform.
4.

Acoustic whine and hum:
"!felt the push of that force field against the solidness of my amz and hand outstretched into
its humming, pushing, propelling flow. " (p~ 110).
"In trying to describe the sounds that the force field made as it circled arowui the DE 173... it
began as a humming whispering sound, and then increased to a strongly sizzling buzz, like a
rushing tolfent." (p.111).
"A special. series of electrical. power cables ha:J been lai.d from a nearby power house to the
ship. When the order was given and the switches thrown, 'the reszdting whine was dlmost
unbearable. ' " (p. 248).

It would seem reasonable to assume that the media immersed in the bias coil's low frequency magnetic
fields (the ship and the sea water) would respond "Yith mechanical vibrations, much like the acoustical
hum of conventional power transformers for example. (The ship and sea water have become the output
of an acoustical transducer,

drive~

by the bias coils.) More than likely, the power content of hannonic

spectra would be substantial well into the ultrasonic region, (think of all the electrical, mechanical, and

physiological nonlinearities present), accounting for the perception of 'unbearable whine'.
Biological (Physiological) Effects
While on earth our physical OOdies move about in relatively weak backgrotmd magnetostatic
(Y4 gauss), fair weather electrostatic (100 V/m), acoustical pressure (Yz dyne/cm2), RF, and gravitational
fields. This experiment would have meant total immersion in an unusual set of electromagnetic and
acoustical fields. While people have been subjected to fairly large OC magnetic fields, <70> the
Philadelphia Experiment probably used intense low frequency pulsating fields, which could lead to a
novel set of recognized perceptual phenomena
One might expect peculiar responses from the nervous system, visual system, auditory system,
and respiratory system, as well as general mental and perceptual confusion.

• "We coul.dn't stand the effects of the energy field they were using. .. It effected us in different
w07s. Some only saw double, others began to laugh and stagger like they were drunk, and a
few pc:Esed o'Ut. Some even claimed that they ha:J pc:Esed into another world and had seen and
tdked to dien beings." (p. 19).
"A ey person within that sphere became vague in fonn b'Ut he too observed those persons
aboard the ship as though they were of the same state, yet were walking upon nothing. " (p.
41).

"As he stood there trying to comprehend what ha:J happened, and looking for his ship, he
watched indistinct figwes in motion whom he could not identify as sailors and some other
shapes 'that did not seem to belong on the dock, if that is where I was.' " (p. 248).
Let us zero i.. r1 on perceptual effects wtiich we would expect llllder such circUiT..StaI1ces:
l\1agnetophosphenes and Purkinji figures. A phosphene is a sensation of light produced by physical
stimuli other than light. A rnagnetophosphene is one stimulated by time-varying magnetic fields.
What about Purkinji patterns?
Johannes Purkinji, the renowned Czech physiologist of the 19th century once said, "Deceptions
of the senses are the truths of perception." By this he meant that, "Illusions call our attention to the
workings of the visual system, whereas normal perception fails to do so. "C7 I) Purkinji was famous for
studying a number of variously shaped, subjective optical patterns that can be excited by electrical
stimulation. In 1819, he put a circuit intenupter (a chain) in series with a battery and electrodes
across the face, and saw different shaped geometrical patterns when he wiggled the chain. (The
phenomenon goes back (again) to Benjamin Franklin and to Allesandro Volta)
Following on the clue that a low frequency electromagnetic pulse spectrum was involved,
Knoll and Kugler, in Germany (at Munich), investigated the excitation of 'Purkinji pattems'.<72>

(Apparently, similar patterns have been observed during brain surgery by direct electrical stimulation
of the visual cortex at 60 Hz. <73>)
"It has been found that (besides flicker), a whole 'spectrum' of subjective abstract light patterns
can be excited in the brain by using temporal electrodes and pulses of a few volts within the
encephalographic fr~uency range... While shapeless flicker covers a large frequency range,
patterns are excitable mostly within the range of 5-35 pulses/second The number of
subjective patterns excitable in each individual wa.s longer for mental patients tl1fill for
techniCal students.... Most patients with beta-encephalographic activity showed pattern
excitation frequencies greater than 50 pulses/second .. <14>
11

They observed many light patterns such as stars, wheels, asterisks, bright dot patterns, moons, 'smiley
faces' and other geometrical shapes.
Fascinating surveys have been published by Becker, who specifically reports on 'magnetophosphenes' (magnetically stimulated phosphenes),<75> and by Oster.<76> Becker relates that, :··
"The intensity is greatest between 20 and 30 Hz... Above 90 Hz the phenomenon becomes less
evident... As the field strength is ~creased, the luminosity appears to involve more and more
of the visual field .. No subjective sensations of~ type were noted during stecdy field
applications, but phosphenes were experienced during 'make' and 'break' of the coil cwrent. ".(77)
(Apparently the original data were obtained by placing the subject's head in a large solenoidal coil.)
The results would seem to illustrate the importance of an intense low frequency time varying magnetic
field
Oster suggests that Phosphenes "may well constitute the fact behind reports of phantoms and
ghosts. "<7&> He points out that alcohol and hallucinogenic drugs can induce phosphenes, however,
"Pulses in the same frequency range as brain waves (from 5 to 40 H'z) were most effective in
producing phosphenes.

11

79

< >

Oster did something else that was particularly interesting. He looked for beats.
"Using two electrically independent generators and four electrodes, we have applied pulses of
two different frequencies at the same time. Each is just above the critical point [upper cutoff
frequency] and would therefore produce no phosphenes by itself Together they generate
beats, which are seen as undulating phosphenes, that move slowly across the field of view. It
would appear that some neural mechanism mixes the two signals, which interact periodically
to produce a beat. "( 80)
(A phosphene superheterodyne, no less: use one generator as a signal, link couple the other into the
head as an injected Local Oscillator, and let the brain do the IF filtering, processing and detection!
They could probably have searched for third order intermodulation distortion products, gotten the
image frequency rejection ratio, and a host of other radio characterizations.)

The medical industry, at one time, thought that electrically stimulated phosphenes might bring
about artificial vision for the blind<SIXB2) Jearl Walker83) discusses phosphenes and states that not only
are they poorly understood ("There has been al.most no work published on modeling the

phenomenon."), but also the physical source has not even been identified
We think that visual distortion, magneto-phosphenes and Purkinji patterns (whether they were
the alien humanoids reported as being seen by some sailors, or not) would certainly have accompanied
the experiment. Such cerebral cortex stimulation (time varying magnetic flux producing induced
electrical voltage stimuli along the visual and nervous systems) would probably also play a role in the
"blanking out" experienced by some participants, even after the fields had been tum~ off. The
"blanking out" and "frozen" episodes may have followed as a result of simple nonlinear responses of
the nervous system. Ftnthermore, because the pennitivity for brain tissue is complex (E=E'-jE"), with
an effective conductivity (cre= ill€"), one would expect AC (diathenny or 'diatheretic') dielec_!fic
heating of the tissue, with ensuing mental and neurological complications.
Summmy RelllaM Leading To Another Question

All this leads to a relatively tmpretentious question If the physics of the experiment is so
easy to explain, and the physiological symptoms so easy to rationalize, then why would there be such
a shroud of mystery in the Navy, and such unwillingness to aclmowledge it? (Surely, with the
National debt the size it is, they must have figured this all out years ago.) The military have
conducted many experiments that went awry and where people were seriously injured. Why cover up
this one?
The reluctance implies deeper issues. It would seem to suggest that something of an unusual
nature occurred during the experiment. What was it?
PARf V - TORSION 1ENSOR CONJECTURE
"The views of space and time which I wish to lay before you. .. are radical.
Henceforth space by itself, and time by itself, are doomed to fade away into mere
shadows, and only a kind of union of the two will preserve an independent reality."
Hermann Mnkowski, Cologne, 1908*<84 )
At this point, not only are the authors going to go out on a limb but, metaphorically speaking,
we also will saw the tree off. Listen to the bizarre testimony presented by those involved in the

*An English translation, accompanied by Arnold Sommerfeld's notes and commentary, is
referenced

experiment.

"The experimental ship also somehow mysteriously disappeared from its Philadelphia dock and
showed up only minutes later in the Noifolk area It then subsequently vanished again only to
reappear at its Philadelphia dock. Total. elapsed time - a mater of minutes. " (p. 89).
"Suddenly, the deep fog 'flashed off,' leaving Silvennan in a very corifused state and wondering, 'what
in the world I was doing in Noifolk.' fie said he had recognized the pla:e as Noifolk 'because I ha1
been there before to the ship's other dock there.' Then, just as suddenly, the green fog retwned; it
lifted again and Silvennan fowui himself bcxk at dockside in the Philalelphia Navy Yard" (p. 249).
"One day, looking at the harbor from the dock, {five British merchant seamen in Noifolk, VA] were
understandably amazed to see a sea-level cloud suddenly fonn in the harbor, and dmost immediately
dissipate, leaving a destroyer escort in full view, which stayed but a few moments before it was
covered by a cloud and vanished again." (p. 250).
_
These quotes sound like the unmitigated blabberings of some science fiction vvriter:,---Look, you
can't do a macroscopic job" like this with quantum mechanics, or even general relativity. Nme
megawatts is one bodacious rate of energy delivery, but (worm holes, black holes· and 'zitterbewegung'
notwithstanding) it's not enough to distort Schwarzschild's metric, or Kerr's metric, or anylxxly else's
solution, to the extent that something like this could happen, even in a small locality. The obvious
rational explanation would be 1;hat some people that saw it were confused or intoxicated. Certainly
one might expect the former to be the case for those sailors immersed in the intense fields of the
experiment. But still, one wonders ...
Now we ask, "What about time-travel and teleportation?" How could these topics become part
of the associated lore? [To this point, we've been having fun at the Joseph Slepian - Jearl Walker
level. Now we'll have to join Edwin Abbott, Sir Arthur Stanley Eddington,<S5> and George Gamow, or
Philip (teleportation)<86> and King Hezekiah (time travel)<87).] Let us have some history, and attempt
speculative conjecture on these topics while striving to maintain mathematical sensibility.
SPIN, 10RSION, AND CRINKLED SPACE-lIME
"I do not think it is too extravagant to claim that the method of the tensor calculus is the only possible
means of studying the conditions of the world which are at the basis of physical phenomenon."
Sir Arthur Stanley Eddington**
*To make a black hole with a null surface (absolute event horizon) the size of the ship's

= (2GM)/c2 = 5.5 meters] would require an energy of 3.34x1044 Joules.
**The Mathematical Theory of Relativity, Cambridge U. Pr., 1923, pg. 49.

beam~

Relation of Gyromagnetic Phenomena to the Production of Torsion
During the course of our investigation of the Philadelphia experiment we examined the
hypothesis that quantum mechanical. spin, such as found in ferromagnetic materials, may affect the
structure of space-time. We were intrigued by a remark that Friedreich Hehl and his colleagues
published,
"One finds that distant observers, who measure only the metric field, cannot distinguish
between a (fenomagnetically) polarized source of spinning matter (which causes torsion
locally) and a rotating distribution of matter with the same total angular momentum (which
nmvhere causes torsion). "<88> .
What was meant by ferromagnetic generation of localized torsion? This, and the fact that torsion
pennits temporal displacements of magnitude

_
(13)

drove us to pursue even wil~er musings than presented above. Could it be possible that, as a result of
magnetically biasing the ship to radar stealth, torsion defonnations were excited in the fabric of spacetime itself? (We told you that we were going out on a limb, in this section.) Were that possible, then
there might be teleportation and time-travel without the crushing effects of gravitational ctnVature, or
squeezing through the Schwarzschild radius down the throat of a black-hole, or thoughts of bubbling
out through a white-hole at some unknown place in the universe, or ID44 joules required to make the
machine run. The torsion technique might even be within reach of pre-WWII electrical engineering.
If the spin were right, one might leap ahead along his world line (or perhaps even backWards) without

travelling all the distance in between What an enchanting idea!
In the pursuit of this hypothesis, we came across a very extensive literature on the relationship
between quantum mechanical spin and space-time torsion. (This seems to be the present employment
of Einstein's 1929 UFf space with torsion.) Based on this research, we provide below an heuristic and
speculative account of the affect of quantum mechanical spin on the structure of space-time and also
propose a new theory of the Aharonov-Bohm effect with an outline for an experiment to verify our
theory. We also propose a classical experiment utilizing the conventional Sagnac Effect and photon
gyros to distinguish between temporal jumps due to 'Anholonomity' and jumps due to 'Torsion'.
Since the concepts of anholonomity and torsion are central to our discussion, we will begin by
illustrating what these tenns mean

T01sion and the Anholonomic Object
In a considerable volume of the literature, the concepts of torsion and anholonomity are

mingled and confused They are distinctly different, anholonomity being frame dependent and torsion
being a true tensor field quantity. Imagine a reference system of coordinates that you carry around
with you to make measurements. This reference system consists of a field of orthogonal basis vectors
that span three space dimensions e1,

e:z, ~'and time e4•

(We use boldface for vectors.) These are

Einstein's 'n-Bein', or tetrad, fields. Now, using this reference field of frames, you can make
measurements which can be transmitted to a second observer, who, can transform your measurements
into his reference field of frames using his own set of orthogonal basis vectors (er',

~ ', ~ ',

e4'). (We

could say this much more elegantly, but for the present audience and the limitations of space, please
permit us to be vigorous instead of rigorous. Those that understand the fonnalism can supply their
own rigor.)

• In flat space-time (where the Riemann curvature tensor is zero), each observer cari~elate his
reference frames (determined by his set of orthogonal basis vectors) to another observer's reference

frames via a simple Lorentz transfonnation, provided that no forces are acting on the observers
(observers are moving inertially).
In the case when observers are not moving inertially, relating the reference frames of the

observers can be greatly facilitated by employing the mathematical machinery of torsion and the
anholonomic object as we show in the following.
Now imagine two separated observers (observer 1 and observer 2) who wish to compare
measurements (we do not assume the observers are moving inertially). In order to do.this they must
determine how their reference frames differ. The only way to compare reference frames is to transport
observer one's set of basis vectors to the same location as observer 2 and

s~

how they differ \\'hen

compared with each other at the same location. See Figure I 0.
Let ei be one of observer one's basis vectors at P0 and let ei' be one of observer two's basis
vectors at P1 (we will use latin indices throughout this paper "With values 1,2,3, for the spatial
dimensions and 4 for time).

ei(P0~ 1 )

is the value of observer one's ei basis vector after it has been

parallely transported to P1 (to parallel transport a vector means to move it without changing its length
or angle). Dei is the difference between observer one's parallely transported basis vector and observer
two's basis vector. lbis gap defect Dei between the two basis vectors is due either to a change in the
coordinate basis between observer 1 and observer 2, in which case it can be mathematically
transformed away, or it was due to defonnations in the path it took between P0 and P 1, in which case
the gap defect cannot be transformed away, or a combination of both.

Figure 10.

Parallel transport of a vector from P0 to P1•

To see this more clearly, let us move observer one's set of basis vectors over two different
paths. Parallel displacing an incremental vector cfxb(\ from the point P0 along the basis vector ea over

an infinitesimal distance dxi to the point P1 = P0 + dxi gives the vector
(14)

Similarly, parallel displacing the increrpental vector dxie2 from the point Po along the basis vector eb
over an infinitesimal distance dx.1' to the point P2 = P0 + dx.1' gives the vector
(15)

The gap defect between the parallely t.ransJX>rted vector at P1 and the actual value of the vector cfxbeb

(16)

Likewise, the gap defect between the parallely t.ransJX>rted vector at P2 and the actual value of the
vector dx3e2 at P2 is
(17)

The total gap defect between the two vectors is

where the commutation and anholonomic object are given by89X90>
(19)

As Eddington and Schouten recognized in the l 920's, parallelograms (composed of parallel transported

vectors) don't necessarily close (either because of anholonomity or because of torsion).<91 x92x93 x94>
"Einstein's world geometry may be briefly described as a geometry in which there are parallels
but not parallelograms. Thus he admits the existence, even at great distances, of a line CD
equal and parallel to AB; but the line through B parallel to AC fails to cut CD. (We are
dealing with at least three dimensions, so that lines are not necessarily coplanar.) The

geometrical. idea of an abortive parallelogram which fails to close up at its fourth comer, does
not carry us very far, and it is necessary to proceed analytically."<95 )
This is not an effect attributable to curvature. Furthermore, while the anholonomic object can be
transformed away by a coordinate transfonnation, this is not the case for torsion
One interpretation of a coordinate transfonnation is that it simply means to relabel the
coordinate basis of one frame into that of another. For example, the point P is located in one
coordinate system by the points x, y. In another coordinate system, which we will call the prime
coordinate system, the same point is located by the points x', y'. If the coordinate transformation (the
relabeling process) between the two is holonomic then

dx

1

= ( ~)dx

and

dy'

= (

t}iy

(20)

and the coordinate differentials are integrable into coordinate curves. If the coordinate transformation
is non-holonomic then the above relations do not hold (this is lmown as Pfa:ff's problem) and the prime
system uses basis vectors which are not tangent to the coordinate cmves of any coordinate system.
The anholonomic object, as we have seen, measures the discrepancy between the basis vectors of two
different coordinate systems that have been caused solely by the mathematical machinery (the
coordinate transformation) that relates the two coordinate systems; remember the commutation
operation [ea,

~]

from above. Consequently, what luJs been created mathematically can be dissolved

mathematically and the anholonomic object can be transformed away by an appropriate change in the

choice of coordinates.
We do not wish ~o imply that the anholonomic object is a mathematical artifact with no
physical consequences. Failure to take into account the anholonomity inherent in the twisting of the
tetrads in some reference systems can hpve drconatic consequences. <96X97)(9SX99) (Thomas precession, the

Sagnac effect, the Oppenheimer-Schiff paradox, the Fe)'TIIIlan Paradox, etc., are all classic examples of
the effects of anholonomity.) In relativistic rotation one desires to describe what's happening in the
rotating (anholonomic) frame, not in the holonomic (non-rotating) frame!
The Components Of the torsion tensor scab are obtained from(!OO)(!Ol)(IOZXIOJ)(I04)
tJ.

-

re

[ab]

(21)

Torsion, unlike anholonomity, is due to changes in the properties of the llllderlying manifold and
cannot be transformed awqv by a change in the coordi.nate basis. Torsion is a measure of how much

P4

/£,.a~=
.

[ea,eJ =
- 2 ocabec

Figure 11.

The non-closure of the outside quadrilateral depends upon Anholonomity. The
non-closure of the inner pentagon depends on the Torsion of the manifold

~:

:

the manifold is crinkled or folded, and such geometries can be made anholonomic Riemannian by
tearing, as discussed in great detail in the publications of Gabriel Kron It should also be noted that
the principle of equivalence does not hold in spaces with torsion cios)
A simple picture might help to illustrate torsion: imagine a folded towel. Start at a point

underneath the fold and trace a circle so that you cross over the fold The point 'Where you return
after tracing the circle is on the fold above the point where you started If there were no torsion, i.e.,
no fold, you would have returned to the same point where you started (Do not confuse this with
curvature. What we are discussing is distinctly different from Riemannian ctnVature!) The torsion
component
(22)
measures the gap across the fold from 'Where you started to where you finished The distinction
between gap defects arising from anholonomity and from torsion is shown in Figure 11, which is self
explanatory. (Look, for c = 4 we're talking about a 'time machine'.)
Perhaps one more sketch will help clarify all this analytical machinery. Consider the 'crinkled'
manifold represented in Figme 12. The affine connection is asymmetric:

P ab:;t: I\a· Consequently,

parallel transporting the two vectors at Po(t=O) leads to the discrepancy, or gap defect vector shown

In spaces \Vi.th torsion, an observer in space can be transported forward in time by the ammmt
(23)

c dt = dx4

e =
~

4
ab dfili]

2[S

e

~

Similarly, as shown on the left, an observer may jump through the space gap d<J> (\Vi.th dt =O), the gap
being given by

(24)
3

dcp = dx e_,

=

3
ab dfili] e<i>

2[S

In spaces \Vi.th anholonomity (but no torsion), the gaps are actually measured as the Sagnac effect and
Thomas precession, respectively. The former is of considerable interest to GPS receivers and photon
rate gyros.
As we have seen, anholonomity is a mathematical creation caused by a choice in coordinates

or resulting from noninertial motion It's a twisting of the coordinate smfaces used an observer.
Torsion, however is caused by a folding of the space-time manifold itself. What cozdd cause a folding

cdt

Figure 12.

A 'crinkled' space modeled as a pleated fabric. The jumps are due to Torsion if
scab :;t:Q and due to Anholonomity if Qab :;t:O.

or crinkling of the space-time manifold and so create torsion? Is there a way that we could actually
build such a 'time machine' out of magnets and coils and capacitors and stuff? We look at one answer
to this question in the next section

Spin and Torsion
Spi.I\ the angular rotation of an object about one of its axis is a concept for which we are all
familiar. Quantum mechanical spin, the internal angular momentum of a quantum mechanical particle
is a more elusive concept. Recent work< 106>, however, has brought to light an old suggestion< 107) that
quantum mechanical spin may be regarded as an angular momentum generated by a circulating flow of
energy in the wave field of the quantum mechanical particle. With this concept of quantum
mechanical spin in mind, we will proceed to discuss how quantum mechanical spin may create torsion
in the space-time manifold
In the previous section where we heuristically demonstrated the concepts of torsion1:lnd the
anholonomic object using parallely transported basis vectors, we fmmd that when we compared the
parallely transported basis vector to their actual values at a point some infinitesimal distance away,
there was a gap defect due to the misalignment of the respective basis vectors. This misalignment can
be corrected by simply rotating the parallely transported vector lllltil it aligns with the actual value of

the vector at the destination point. The rotation that caused the misalignment of the basis vectors
consists of two parts: one part proportional to the anholonornic object which can rotate the transported
basis vector on a Riemannian (torsion-free) manifold, and the other part due to torsion which provides
another independent rotational degree of freedom Now let us see how the extra degree of rotational

freedom associated wit11 torsion can be related to quanttun mecr..an.ical spin
Assume that a material system can be described in tenns of a Lagrangian density L. Then the
energy-momentum tensor Tj of the material system can be described by

(25)

where gj is the metric of the underlying manifold and g is its determinant.
Metric specifies the scaler product between two basis vectors which lie in the tangent space
above the manifold and is used to determine distance and angle on the manifold Because metric is
used to defme distance, a variation in the metric 8gj detennines a variation in the distance on the
'manifold

Analogous to the definition of the energy momentwn tensor stated above, it has ~n shown
that a dynamical definition of spin can be related to variations in the contortions of space-time
"t' ji

(26)

k

where -rJi is the spin angular momentum and K;jk is the contortion tensor 108>.
The contortion tensor is related to the torsion tensor by 109>
(27)

Consequently, a .variation in the contortion tensor implies a variation in the torsion and in~e affine
connection We can see tl:ris more clearly by defining an affine connection for spaces with torsion in
anholonomic coordinates as<n°>
(28)

and in holonomic coordinates as<lll>
{ .k} _ K ..k
'j

I}

(29)

where Lk) is Christoffel's symbol of the second kind As mentioned above, this idea can actually be
traced back to Schouten and Cartan in the 1920's.
Thus, we see that a variation in the contortion tensor K;j k, varies the torsion space-time
·connection and leads to a twisting of the parallely transferred orthogonal basis vectors.
We have passed through some rather subtle mathematics here, and lest the reader think that
this is, to quote some anonymous wag, the product of the leisme of the theory class, let us state in the

strongest tenns ]XJSsible that what we have just said lies at the bedrock fotmdation of electrical
engineering! Perhaps some history would be in order before proceeding.
A Short Histoiy of S1£cessful Unified Field 'lbeoiy Applicatiom
Historically, the idea of an tmSymmetric affme connection was first discussed in a 1921
footnote by Arthm Eddington <112) He conceived that such a manifold would be "infinitely crinkled'.

This can be visualized as a geometrical manifold constructed as a folded or pleated sheet of cloth as
mentioned above. Any attempt to ext:rafX>late out away from the contact point of reference P0 will
lead to unanticipated results. Infinitesimal parallelograms are discontinuous as one approaches a pleat
from above the fold or from under the fold If the discontinuity is due to actual folds in the manifold,
the resulting pentagon is due to torsion and the discontinuity is of magnitude scabcbedX'ec. If, however
the jtunp discontinuity is due to folds in the choice of coordinate swfa:es, the resulting pentagon is
due to anholonomity and the coordinated time correction required is of magnitude 20 cabmadX'ec. This
is the case for the Sagnac effect and it is clearly observed with the GPS (Global Positioning Satellite)
system, and especially with global time dissemination.
The torsion tensor was introduced almost simultaneously in 1922 by Eli Cartan< 113> (1859-1951)
and in 1923 by Jan Schouten< 114> (1883-1971). Subsequently, from 1925 to 1931 Einstein e1!1Ployed
affine connection asymmetry in speculative generalizations of relativity th~ry.(1 15X 116X 11 7X 118X~9x 120> He
had hoped to link the four vector potential

{AJ to a contracted torsion tensor field (SbiJ. Re seems to

have had difficulty recognizing the distinction between anholonomity, which depends on the
commutation of the basis vectors, and torsion, which depends solely on the asymmetry of the affine
connection.
Norbert Wiener was the first to recognize that Einstein's distant parallelism gave the possibility
of comparing 'spins' at different points.
"The notion of a parallelism valid for the whole of space and of Einstein's n-uples enables us
to carry over the Dirac theory into general relativity almost without alteration... the quadruples
need not be integrable so as to fmnish us with a co-ordinate system throughout space... This
seems to us the most important aspect of Einstein's rec,ent work. .. <121 >
11

Wiener saw the tetrad approach of Einstein's as providing a bridge between the macroscopic world of
mechanical bodies and the microscopic world of quantwn mechanics, and a way to compare the distant
interaction of spins. Perhaps the curious issues which Dr. Eric Laithwaite• has raised concerning "spin
radiation" from gyros may be resolved in this manner.
".. .it should be possible to cause one force-precessed wheel to transmit a torque through space
to another spinning wheel. If that be true it is extremely likely that this kind of [nonelectromagnetic] radiation is bombarding the earth from outer space and should be capable of
collection. <122)
11

Modem work on unified field theories is concerned more with the identification of torsion with spin,

0

1984 IEEE Tesla Medalist, and Professor at Imperial College, London.

which was not Einstein's stated purpose in the l 920's versions of the UFf. •
Einstein's laoors with unsymmetric connections were again taken up after 1945.< 123X124X125 ) In
the latter reference he points out, in fact, that
"... at first the Riernannian metric was considered the fundamental concept on which the
general theory of relativity, and thus the avoidance of the inemal system, was based Later,
however, Levi-Civita rightly pointed out that the element of the theory that makes it possible
to avoid the inertial system is rather the infinitesimal displacement field rbac • The metric, or
the symmetric tensor field gk which defines it, is only indirectly connected with the avoidance
of the inertial system in so far as it determines a displacement field <126>
11

(The "at first" that Einstein uses refers to the 1916 classical general relativity, now so familiar. The
"later, ... Levi-Civita" comment refers to a famous 1930 paper.< 127)) Apparently during the late 1920's
Einstein was somevvhat touchy about Cartan's priority with the torsion tensor, as can be seen in his 21
-

letters to Cartan on the topic of "Femparallelismus".< 128> It should be clear that Einstein hac_r
independently created a Riemannian geometry with torsion.<129>
Perhaps the most unexpected application of Anholonomity and the Torsion tensor is in the area
of electrical machinery and electrical circuit theory (dating, in fact, back to Tesla's 'egg of Columbus'
and his creation of the rotating magnetic field). With the appearance of Einstein's unified field work
of the late 1920's, Gabriel Kron discovered a remarkable unifying role for these concepts in the
generaliz.ed theory of electrical machines.< 130> During his lengthy career at General Electric, Kron
published a _long series of contributions formally employing geometrical concepts from Einstein's socalled "unsyrnmetric unified field theory" to successfully explain complex mutual interconnections of
electrical networks and machinery in tenns of tensors.< 131 >< 132X133XI 34Xt 35x136> Nominated for his
pioneering contributions by Paul Langevin (who first recognized the importance of de Broglie's work),
Kron received the Montifiore Prize in 1936. l\1IT mathematics professors St:ruik< 137) and Wienet 138)
were both interested in Kron's application of Einstein's Unified Field Theory to electrical machinery.
The application to electrical systems should not be surprising since the unified field theories were
framed to describe situations which involve physical coordinates (space and time), gravitation, and
electrodynamics. Kron's approach, however, was to employ the same mathematics to describe
interconnected systems with physical coordinates, mechanical energy, and electrical energy. (This

*As a side note, it was also during this time in the 1920's that Einstein and Dr. Leo Szilard (18981964) filed 16 joint patent applications (ostensibly for an electrodynamic pwnp). Einstein patented a
gyrocompass. And, with Rudolph Goldschmidt ( 1876-1950), Einstein received a joint 'hearing aid' patent.
Goldschmidt is famoils in radio history as the inventor of the high frequency RF generator utilizing groups
of rotating coils for harmonic generation, and resonance for CW production. Goldschmidt's apparatus was
used in the first wireless link between Gennany and the US in 1914.

application has enjoyed remarkable success in industry and, presently, it is extensively employed by
electrical utilities and heavy electrical equipment. manufacturers around the world in the analysis of
interconnected power systems.) Kron's approach is a tensor theory and consequently invariant. [The
popular state variable approach is not, and therefore it is doomed to failure in the general case. It
cannot be a fundamental electrical theory. (Try it on a curved manifold, or even one with torsion!) It
is a matter of invariance: sooner or later, the geometers will even win the political battle being waged
by the algebraic topologists in the fight over electrical circuit pedagogy!]
The mathematical analogy to Einstein's work is only fonnal, of course, since, as Kron points
out, mechanical energy is not the same as gravitational energy.< 139> However, the practical utility,

success (the actual words used by Banesh Hoffmann* were "experimental confirmation" <t<W)), and the
wide-spread use of the 1929 Einstein unsymmetric Unified field theory in electrical power systems
usudly comes as quite a surprise to most ph