KHAN: A New Superluminal Signaling Scheme

Kublai Khan: character sketch for Marco Polo by Jose Lopez

KHAN: A New Superluminal Signaling Scheme

A few years ago CCNY graduate Demetrios Kalamidas proposed a clever FTL signaling scheme that was refuted both in general and in its very specifics by an international team of quantum opticians. Details here, here and here. At the heart of the Kalamidas scheme is his original method of which-path info erasure that would seem to merit closer attention. Before Kalamidas, the conventional method of erasing information about which of two paths a photon took was to confuse the observer by combining those two paths, either by directly bringing the two beams together with a positive lens or with a wedge-shaped mirror, mixing the two paths in a 4-port optical beam splitter, or overlapping the two diffraction patterns resulting from each path being sent through one of two closely-spaced double slits. The most beautiful feature of his new scheme is that Kalamidas is able to erase which-path info from two paths without actually having to combine the two paths.

FIG A.  1. Path-entangled photon possessing full which-path info; 2. Erasing which-path info using diffraction at a double slit;  3. Erasing which-path info by combing paths in a beam splitter.

 EQ 1 in FIG A displays the wave function for a typical path-entangled photon. In the same quantum way that Schrödinger's infamous cat can be both dead and alive, a single photon can travel two paths at the same time. The difference is that humans lack the ability to form quantum superpositions of cats but anyone can produce path-entangled photons by the trillions. (It happens naturally at every window pane -- if quantum physics is correct, each photon until it's actually observed exists for an instant in a superposition of both being reflected and being transmitted thru the glass: a mundane example of one photon temporarily traveling two paths at once.)

FIG A1. illustrates the case where which path the photon takes can be decided by merely placing one photon detector in each beam. Examples 2. and 3. show two ways that which-path info can be erased thru combining the two paths. In these two cases the photon can be coaxed into showing off its wave nature by "taking both paths at the same time" and "interfering with itself" with the result that large numbers of identical photons will produce a diffraction pattern or some other periodic behavior that is characteristic of waves of a certain wavelength.

Which-path info erasure leads inevitably to the possibility of forming interference patterns, so a brand-new erasure method (such as that proposed by Kalamidas) can be expected to lead to a brand-new way of forming interference patterns.

FIG B. Which-path info erasure via the Kalamidas Option

FIG B illustrates the development of the Kalamidas Option in three steps. Step 1 shows the path-entangled photon traveling unhindered along both paths. Detectors A and B unambiguously decide along which path the photon actually went and which path was untraveled. In Step 2, Kalamidas puts a 50/50 beam splitter into both path A and path B. Now there are four possible detection events corresponding to the four different detectors [A1 A2 | B1 B2]. I will use the symbol [10|00] to indicate the case where the photon triggers detector A1. And symbol [00|01] indicates that the photon has triggered detector B2. At this stage which-path info is still intact: it is always possible to infer from the detector response which path the photon took. And hence no wave phenomena will be observed.

However the fun begins at Step 3. Here at each beam splitter we introduce a new kind of light which I call "Gray Light" whose photon number is uncertain. Gray Light consists of an equal superposition of one photon |1> and zero photons |0>. Such a number-uncertain beam is not difficult to produce. Its quantum wave function is written:

Ψ = s |0> + s |1>     where s = 1/√2

This use of Gray Light is due to Nick Herbert. In his original FTL proposal, Kalamidas used weak coherent light as his photon-number-uncertain source. The math is more complicated for Kalamidas's original scheme than for Gray Light.

Even with the addition of Gray Light to the mix, photon which-path info is still largely preserved. There are two cases to consider:  Either the photon is in the path (which I call FULL) or the photon is not in the path (which I call EMPTY). 

In the case where path A path is FULL, the addition of gray light leads to FIVE different outcomes [10], [01], [11], [20] and [02]. If path A is FULL, then path B must be EMPTY and the addition of Gray Light to an EMPTY path results in THREE different outcomes for path B, namely [00], [10] and [01]. The number of different outcomes for A FULL/B EMPTY is just FIVE x THREE = 15. Similarly the number of different outcomes for B FULL/A EMPTY is also 15. But four of these outcomes (the so-called "Kalamidas Outcomes") are identical so the addition of Gray Light leads to a total of only 26 different detector outcomes rather than 30.

For most of these outcomes, which-path info is strictly preserved. For instance, outcomes of the form [11]. [20] and [02] can only occur in a FULL path. And outcome [00] can only occur in an EMPTY PATH.

The only outcomes which could have been produced by either a FULL or an EMPTY path are the FOUR Kalamidas Outcomes:

[10|10], [10|01], [01|10], [01|01]    The Four Kalamidas Outcomes

If only one photon is detected in each path, there is no way of knowing whether this was a Gray Light photon added to an EMPTY PATH or a FULL PATH unaltered by Gray Light. The rules of quantum mechanics say that if two processes can lead to the same output, then you must add the amplitudes of these two processes coherently. Coherent addition leads to interference effects. So Kalamidas's trick of adding number-uncertain light can lead to the interference of two beams of light without having to actually combine the two beams. To observe this interference we place a variable phase delay expQ in path B. 

When the input to the Kalamidas Machine is given by EQ 1, namely an equal-amplitude coherent superposition of  FULL A/ EMPTY B and FULL B/ EMPTY A beams, the probability of observing the four Kalamidas Outcomes is:

[10|10] = 1/16 (1 + cosQ)  [10|01] = 1/16 (1 - cosQ) 

[01|10] = 1/16 (1 - cosQ)  [01|01] = 1/16 (1 + cosQ)

COHERENT SUPERPOSITION

The presence of the cosQ term is a sure sign of wave behavior: the two beams, though physically separate are interfering with each other in a periodic way. Only the four Kalamidas Outputs show this wavelike behavior; the other twenty-two outcomes (for whom which-path info is still intact) remain constant while the phase angle Q is varied, rather than oscillating like the KO terms.

If, instead of a coherent superposition, our input to the Kalamidas Machine is an incoherent superposition, then the interference terms vanish. In other words, when the single photon takes BOTH PATHS (coherent superposition), the Kalamidas outputs show waves. When the single photon takes EITHER path A OR path B (incoherent superposition), wave behavior vanishes. For incoherent superposition, the probability for the Kalamidas Outputs becomes:

[10|10] = 1/16    [10|01] = 1/16

[01|10] = 1/16    [01|01] = 1/16 

INCOHERENT SUPERPOSITION

For incoherent superposition input, the Kalamidas outputs are constant. Note that the sum of the probabilities of each of these cases is 1/4, indicating that in a long experimental run, a Kalamidas output can be expected to occur 25% of the time.

The fact that the Kalamidas Machine seems able to detect the difference between a coherent and an incoherent single photon two path superposition is the inspiration for a new faster-than-light signaling scheme I call KHAN (for Kalamidas-Herbert Augmented Nearness).

FIG C. KHAN superluminal signaling scheme

To achieve FTL signaling we need a source of TWO path entangled photons, one photon going to ALICE (along two paths C and D) and one going to BOB (along two paths A and B). The entanglement is such that BOB's path A photon is always linked to ALICE's path C photon. And BOB's path B photon is always linked to ALICE's path D photon. Each pulse of light produces TWO PHOTONS -- one which goes to ALICE and one which goes to BOB. But each of these photons can take two paths at once. Not so easy to explain in words. FIG C explains it better and even includes an equation.

In the KHAN scheme ALICE is the sender and BOB the receiver. ALICE attempts to signal BOB by switching her photon from an INCOHERENT MIXTURE to a COHERENT MIXTURE of paths. Since the Kalamidas Machine responds differently to these two types of light, success would seem to be assured.

ALICE possesses a beam splitter whose transparency she can change from 100% to 50/50 transmission/reflection. When ALICE chooses Option A (100% transmission) her detectors reveal which-path info (Alice's photon takes either path C or path D): Mutual entanglement forces BOB's photon to likewise take a definite path, so the Kalamidas Machine indicates INCOHERENT SUPERPOSITION (no wavelike behavior: no dependence on phase angle Q).

On the other hand when ALICE chooses Option B (50/50 beam splitter) she erases all path information both at her site (and by mutual entanglement) at BOB's site as well. When ALICE chooses Option B, the input to the Kalamidas Machine is COHERENT PATH SUPERPOSITION, so BOB should observe wavelike behavior: periodic dependence on phase angle Q.

For ALICE's Option A: the ALICE/BOB entanglement takes the form:

Ψ (ABCD) = s ( |A0>|C0> + |B0>|D0>)  ALICE's Option A

For ALICE's Option B, the ALICE/BOB entanglement takes the form:

Ψ (ABCD) =S { (|A0> + i |B0>) |C0> + ( i |A0> + |B0>) |D0>}  ALICE's Option B

where S = √2 and s = 1/√2. For ALICE's beam splitter I have used the symmetric convention where both reflections are multiplied by i.

 

When you do the calculation for the KHAN scheme, there is a sense in which both of these things happen -- 1. no waves at BOB's site for ALICE's Option A and 2. waves at BOB's site for ALICE's Option B. But in spite of this marvelous seemingly instant change at a distance from no-wave to yes-wave, this process cannot be used for superluminal signaling.

INCOHERENT: When Alice chooses Option A and measures a photon in her path C, all four output of the Kalamidas Machine have the same constant probability: No wave behavior. Same when Alice measures a photon in path D.

[10|10] = 1/32    [10|01] = 1/32

[01|10] = 1/32    [01|01] = 1/32

OPTION A: ALICE MEASURES PHOTONS AT C

[10|10] = 1/32    [10|01] = 1/32

[01|10] = 1/32    [01|01] = 1/32

OPTION A: ALICE MEASURES PHOTONS AT D

[10|10] = 1/16    [10|01] = 1/16

[01|10] = 1/16    [01|01] = 1/16

OPTION A: ALICE MEASURES PHOTONS AT BOTH C AND D

COHERENT: When Alice chooses Option B and measures a photon in her path C, all four outputs of the Kalamidas Machine show wave behavior of the form [M + N sin Q] where M and N are constant. If we limit our observations only to the case where ALICE observes a photon in path C, then the Kalamidas Machine shows undeniable wave behavior at all four output ports.

This looks good but the worst is still to come. When Alice measures a photon in her path D, all four outputs of the Kalamidas Machine now show wave behavior of the form [M - N sin Q].

Since both these ALICE outputs (C and D) happen at random with equal probability, the total probability of the Kalamidas Outputs is 2M. All wave effects vanish.

[10|10] = 1/32 (1 + sin Q)    [10|01] = 1/32 (1 - sin Q)

[01|10] = 1/32 1 - sin Q)    [01|01] = 1/32 (1 + sin Q)

OPTION B: ALICE MEASURES PHOTONS AT C

[10|10] = 1/32 (1 - sin Q)    [10|01] = 1/32 (1+ sin Q)

[01|10] = 1/32 1 + sin Q)    [01|01] = 1/32 (1 - sin Q)

OPTION B: ALICE MEASURES PHOTONS AT C

[10|10] = 1/16    [10|01] = 1/16

[01|10] = 1/16    [01|01] = 1/16

OPTION B: ALICE MEASURES PHOTONS AT BOTH C AND D

We can see from this explicit calculation of the results of the KHAN scheme, that each INTERFERENCE EFFECT linked to ALICE's path C is exactly canceled by an equal and opposite ANTI-INTERFERENCE EFFECT linked to ALICE's path D. This kind of mutually canceling wave behavior is experienced over and over again by presumptive FTL signaling engineers. Wave behavior undoubtedly appears at BOB's site when ALICE erases her which-path information -- as can be verified by looking at all of BOB's outputs while triggering only on one of ALICE's outputs. But when both of ALICE'S outputs are taken into account -- as is the case in any FTL signaling scheme -- the waveness at BOB's site tied to one of Alice's outputs is EXACTLY CANCELED by the waveness tied to the other of Alice's outputs.   I have dealt with this (seemingly inevitable) phenomenon in a previous post.

So farewell to the KHAN scheme for superluminal signaling. Even though the effort failed, it was fun learning how to carry out the calculations using Kalamidas's clever new method of path erasure. Something imaginative and new like this almost never fails to excite me. Thanks, Demetrios.

Northern Hemisphere Spring 2016: Irish Tantra

William Butler Yeats (1865 - 1939): Nobel Laureate 1923

CRAZY JANE
TALKS TO THE BISHOP

I met the Bishop on the road
And much said he and I.
"Those breasts are flat and fallen now,
Those veins must soon be dry;
Live in a heavenly mansion,
Not in some foul sty."

"Fair and foul are near of kin,
And fair needs foul," I cried.
"My friends are gone, but that's a truth
Nor grave nor bed denied,
Learned in bodily lowliness
And in the heart's pride.

A woman can be proud and stiff
When on love intent;
But Love has pitched his mansion in
The place of excrement;
For nothing can be hale or whole
That has not been rent."

---William Butler Yeats (1933)

Arago Spot: Green

St Paddy's Day 2016

SONG OF THE IRISH WHISTLE
with apologies to Joanie Madden

Sure, it's a holy instrument
Like everything that comes from God
You must learn to hold her reverently
Like Father Kelly's Holy Wafer
Or a patch of Irish sod.

Close your lips around her fipple
And thru her narrow airway
Blow a prayer across that tilted floor
Called "labium" when there's one of them
And "labia" when there's more.

Now the noise she makes is frightful
Like a pack o' banshees wailin'
The men are rising from their seats
And now your life depends
On the music you can coax from her
With your fancy fingerin'

Sure breathin' (and tonguin') have to be mastered
But they're just a part o' the thing
For it's how ye move yer flesh
Across the openings, laddie,
That makes the Irish whistle sing.

You may play in a grove
You may play in a pub
You may play with a maid in the spring
But playing the Irish whistle
You must mind your fingering
For it's how ye move yer flesh
Across the openings
That makes the Irish whistle sing.

Sure, it's how ye move yer flesh
Across the openings
That makes the Irish whistle sing.

Sol Entangler

Circular Diffraction: Arago's Spot

 I want to woo Her not view Her

Pet Reality until She purrs

Longing to merge with Dame Nature bodily

Yearning to mingle my substance with hers

And them content with merely observing

Are nothing but Nature's voyeurs.

The goal of quantum tantra is to discover a new way of connecting with Nature that involves both mind and quantum mechanics. An early interview by Abu Ben Nooma, author of Red-Light Bardo captures some of the spirit of this quest as does Rudy Rucker's short fiction Panpsychism Proved recently published in Nature magazine. 

While searching for that all-important clue to a quantum-tantric breakthrough, Nick has been amusing himself by writing dozens of QT-inspired poems and designing/building a handful of "Preposterous Devices" that attempt to capture some of the flavor of this new science. Since these devices possess no theoretical basis (the science they pretend to demonstrate does not yet exist), they are mere guesses, shots in the dark, desperate premonitions and hardwired petitions to my Muse to grant me fresh inspiration for quantum-tantric gadgets that will actually work and for a new vision of Nature that will change the world.

My first preposterous device was called "The METAPHASE TYPEWRITER" after the hypothetical "metaphase membrane" that separates matter and mind. The MT uses a quantum-random radioactive source and Geiger counter to drive an English-language biased text generator. The MT was conceived of as an "empty channel" that might be possessed by living beings, by discarnate entities, by angels, devils or spirits of any variety. The Metaphase Machine was operated during the 1970s in a great variety of high psychic energy situations without any noticeable success.

Metaphase Typewriter: Yellow plastic tube houses radioactive source and Geiger counter

 Later with the help of Richard Shoup, who then worked at Xerox PARC in Palo Alto, I devised the QUANTUM METAPHONE which converted the metaphase device into a quantum-driven voice box, a kind of supernatural "Siri" designed to let spooks speak. None deigned to talk to us.

Metaphase Sound Machine by Dmitry Morosov, Moscow. This project was commissioned by Future Everything (Manchester) and Laboratoria Art & Science Space (Moscow)

 Recently a few artists have been inspired by the MT to produce quantum-driven devices of their own design. Lynden Stone, working at Queensland University in Australia instigated the Metaphase Typewriter Revival Project producing a quantum text generator using modern physics hardware and computer interfaces that was exhibited in both Australia and America. Lynden's doctoral thesis explored some of the history of art inspired by modern physics which includes her lovely painting Schrödinger's Puss featured at the bottom of this post. Meanwhile, in the former Soviet Union, prolific Moscow multi-media artist Dmitry Morosov (who goes by the name "::vtol::") produced a sound and motion machine driven by quantum-random nuclear decay which ::vtol:: claims was inspired by the Metaphase Typewriter.

The biggest flaw in the metaphase class of quantum mind-matter devices (Quantum Answering Machines) seems to be the assumption that spirits can alter radioactive decay to send messages to the living. A promising direction for further QUAM research might be to seek different sources of quantum "randomness" to drive the communication channel, for instance the recent device of Shi et al at the University of Singapore that derives random numbers from fluctuations in the quantum vacuum.

Dr & Mrs Future testing the Stellerator

 Another class of preposterous device (hoping to connect minds together using quantum theory) works on the notion of linking two people's consciousnesses together by, loosely speaking, arranging for them "both to attempt to observe the same photon". This purported quantum linkage is achieved by having both participants view light whose "radius of coherence" extends across both of their retinas. This kind of device might be called a Quantum Intimacy Machine (QUIM).

The first quantum intimacy machine (called the STELLERATOR) exploits the fact that the "lateral coherence radius" of light from distant stars is huge. The star with the smallest lateral coherence radius is Betelgeuse in the Orion constellation. This star's LCR is eight feet wide; every other star in the sky has a larger value of LCR.

The value of the LCR, loosely speaking, is a measure of the width of the photon wavefunction, an indication of the extent to which a single photon can "be in two places at once" while still maintaining its integrity (oneness).

There is a sense in which light from Betelgeuse is made up of a collection of eight-foot wide pancakes of light, each representing a single photon. These photon pancakes are very thin (the longitudinal coherence length is comparable to the wavelength (a fraction of a micron)) so that these stellar discs are less like flapjacks and more like very thin crepes. And each of these single-photon crepes is hurtling down from every star in the sky at the speed of light.

The stellerator is a simple hollow tube which allows two observers to focus their attention on a single star and to compete as to who will "collapse the crepe-shaped photon wave functions" from that star. The guess/hope/conjecture is that this simple activity of constrained star gazing will link the minds of the participants in a new and notable way.

One big flaw in Stellerator theory is that the photon pancake is so large that every object inside an 8 ft radius (in the case of Betelguese) is competing for the same photon. Thus the participation of two human retinas in "collapsing the photon wave function" is minimal compared to the grass, the rocks, the dirt around you. What's needed is a coherent source made of smaller pancakes, pancakes the same size or smaller than the dark-adapted human iris (about 3 mm).

The Lunerator uses reflection to produce two coherent beams.

 Enter the LUNERATOR, a purported quantum intimacy machine that uses the Moon as a source of coherent light. The size of the coherence disk is inversely proportional to the apparent size of the heavenly body. Stars appear very small so their coherence disks are large. On the other hand, both the Moon and the Sun loom large in the sky (apparent diameter of about 1/2 a degree) so their lateral coherence radii are correspondingly small, approximately 0.1mm (about 10 times the size of a red blood corpuscle), hence able to shoot comfortably thru the iris-hole of any human being.

The Lunerator takes a stream of moonlight (which consists of tiny amoeba-sized wafers of elemental light) and, using a half-silvered mirror, splits this photon stream in two and directs each half stream to a different observer. Now according to quantum theory, each photon wafer TAKES BOTH PATHS, so each observer in theory can compete to collapse the wave function of the same photon with God-only-knows-what effect on the subjective experiences of the participants in this peculiar new way of sharing lunar light.

A brand new improvement on the Lunerator is the SOLARATOR (called by some a Sol Entangler) which is similar in many respects to the Lunerator (same lateral coherence radius, for instance) with the added advantage of higher intensity and spectral separation. (Spectral purity increases the longitudinal coherence length, thereby making the photon pancakes thicker). Instead of using a half-silvered mirror to split the beam in two, the Solarator employs a mirrored diffraction grating provided by a blank DVD disk masked down to a working diameter of a few millimeters. As with the Lunerator, the two beams (now each a pure spectral color rather than cream-colored moonlight) are sent to two observers who compete to collapse the same photon's two-part wave function.

The Solarator uses diffraction to produce two coherent beams

Solarator in action.

 When I first conceived these various photon-sharing-based quantum intimacy machines, I believed that they were each an example of quantum entanglement. But that is not the case. Each of the photon wave functions in all of these three examples is factorable, hence not entangled. The only non-locality which these devices possess is a kind noted by Einstein early in the quantum game when he noticed that light from a single atom is supposed to emit a wave function which travels to all parts of the universe where at every moment it represents the probability of a photon being observed.

But when that photon is actually observed at one single place, the probability of it being observed somewhere else instantly drops to zero, seemingly violating the relativity rule that nothing can travel faster than light. It's this kind of non-locality that's operating in these three putative quantum intimacy machines. However, hundreds of labs all over the world daily produce truly entangled photon beams which might be utilized for the next generation of truly entangled preposterous devices. For example, Nicolas Gisin and his buddies at the University of Geneva are already experimenting with ways of entangling human retinas using entangled light. Perhaps the next quantum tantra breakthrough will occur accidentally tomorrow in some optics lab in Switzerland.

[After this post was published, Lynden Stone reminded me of conceptual artist Jonathon Keats's Quantum Marriage in which a committed couple ceremonially bath themelves in TRULY ENTANGLED LIGHT produced by sunlight passing thru a non-linear crystal. Thanks, Lynden.]

We hold these truths to be self-evident --

This direct, non-symbolic experience of Nature-from-inside

That the Universe is filled with billions of invisible conscious beings

That every sentient creature lives equally near to the mystery

That deep reality is waiting for us to ask the right question.

Erwin's Puss by Lynden Stone, housed at Centre for Quantum Dynamics, Griffith University, Queensland, Australia

Thousand Science

Happy Valentine's Day 2016

HAPPY VALENTINE'S DAY 

 

ELEMENTS OF TANTRA

Love every one of My Elements

Caress My Paradox

Embrace each phase-entangled photon

Hug My Molecules; kiss My Quarks.

The Universe is My Body

From every eye, the glance is Mine

Down every river flow My Fluids

In every thing resides My Mind.

I loved you inside your mother's womb

Your every atom have I kissed

I made you everything you are:

You treat Me like I don't exist.

When you open your eyes you gaze on My Body

You taste My Flesh with your lips

Every smell is My Sexual Attractant

Every touch is My Kiss.

Come open your sensors to Nature's flirtations

Come lend your step to My Dance

I'm only fourteen (billion) years old

But I'm eager and ripe for romance.

Love every one of My Elements

Caress My Paradox

Embrace each phase-entangled photon

Hug My Molecules; kiss My Quarks. 

Smiling Whale: Khola Shou Herbert

 

The Life of Gia-fu Feng

Gia-fu Feng, teacher, translator and Taoist rogue

In 1970, I was working at Memorex and driving every day "over the hill" from Boulder Creek to Santa Clara. Some evenings I would stop at the very top of Bear Creek Road at Stillpoint, a Taoist community founded by Gia-fu Feng. Sipping tea, enjoying the hot tub and conversing with Gia-fu and his companions was a pleasant contrast to my role as a physicist overseeing research into the technical details of making better magnetic tape.

On one of my many trips to Esalen Institute in Big Sur in the '60s, I had heard that if you got up early (not easy for me), you could learn Tai Chi from a crazy-wisdom master from China. As long as I was there I showed up for Gia-fu's classes which seemed to be an original recipe of classic Chinese forms plus Esalen-inspired sensory awareness techniques. Outside of Esalen our paths would sometimes cross due to Gia-fu's friendship with Elizabeth Kent Gay, "the lady from Vermont" who introduced me to SF dancer Betsy who eventually became my wife. I liked Gia-fu. He was cheerful, smart and unpredictable.

I recently discovered that Carol Ann Wilson, the sister of the woman to whom Gia-fu left his estate (including a stream-of-consciousness story of his life) has written a biography called Still Point of the Turning World.

published by Amber Lotus, Portland, Oregon

Since Carol had never met Gia-fu and was merely carrying out her sister's legacy, I expected a fact-filled book without much spirit. I was pleasantly surprised by Carol Ann Wilson's ability to capture the essence of this unusual man. Reading her book (it is written in the present tense) feels like following Gia-fu himself (and his thoughts) through the daily adventures of his extraordinary life.

Born in 1919 as the third son of a successful Shanghai banker, Gia-fu and his eight siblings were well-educated in both modern and classical Chinese subjects. Near the end of his career, the father's greatest pride was a wall in his house displaying his children's many academic degrees.

The Feng family's life is soon disrupted by the Japanese invasion and occupation of China. With her ability to put the reader into the thick of things, Carol Wilson brings to life (thru Gia-fu's eyes) the chaos in China caused by the strife between three warring factions, the Japanese, Chiang Kai-shek's corrupt but US-backed Free China army plus the growing Communist forces led by Mao Tse-tung. Shortly after the war ends Gia-fu and his younger brother Chao-hua board a ship for America, the first intending to study international finance, the other engineering. Thirty years pass before Gia-fu is able to return home. Meanwhile Carol Wilson relates the fate of the formerly wealthy Feng family under the new Communist government -- an intimate look at modern history through its effect on people whom you have come to care for.

Gia-fu enrolls at the Wharton school in Philadelphia but, becoming increasingly disoriented by American culture, he "hops in an old jalopy" and wanders across the United States, a trek which eventually leads him to San Francisco where he finds a position with Alan Watts at the American Academy of Asian Studies both as student and translator. Arriving in the midst of the San Francisco Renaissance, Gai-fu becomes friends with writers Alan Watts and Jack Kerouac, poets Lew Welch, Gary Snyder and Lawrence Ferlinghetti, and other talents, among them fellow student at the Academy and future cofounder of Esalen Institute, Dick Price.

When Mike Murphy and Dick Price tentatively began their "human potential center" in Big Sur, Gia-fu showed up as Esalen's accountant (using an abacus), Tai Chi teacher, and "keeper of the baths".

Gia-fu eventually finds Esalen too hectic for his tastes and starts his own center called Stillpoint on Bear Creek Road high above Silicon Valley. There he meets Jane English, a physicist from Berkeley, and they begin a life together and collaborate on two books: Gia-fu's translations of the Tao Te Ching -- the most translated book outside the Bible -- and Chuang Tzu's Inner Chapters. Jane produces stark black-and-white photographs reminiscent of Chinese paintings which Gia-fu decorates with calligraphy. Their Tao Te Ching is an immediate success and has gone through innumerable printings.

Gia-fu's Bear Creek neighbors however are not happy living next to a Taoist tea house and Gia-fu is pressured to leave, eventually settling in Colorado where Stillpoint finds a more congenial home. His Tai Chi lessons become popular in Europe where he and Jane travel to give workshops. Eventually they separate, Jane moving to Mt. Shasta and Gia-fu remaining in Colorado. As a physicist I find their union fascinating -- the energetic meeting of yin and yang. Also notable from the science and mysticism perspective is the fact that Gia-fu and Jane helped Fritjof Capra find a publisher for his ground-breaking Tao of Physics. And that Gia-fu and Jane were also able to meet with Joseph Needham, author of the multivolume work Science and Civilization in China.

Nearing the conclusion of this engaging and well-researched biography, I am reminded of my last meeting with Gia-fu. My wife and I had just birthed a son in Boulder Creek, whom we called Khola (a short form of Nicholas) and Betsy felt that he should be christened and given a middle name. Neither of us belonged to a conventional religion so we decided that the "most sacred person" we knew was Gia-fu Feng up at Stillpont. (I can hear Gia-fu laughing in his grave at being called "most sacred person"). So we hard-boiled a bunch of eggs, decorated them in Ukrainian pysanky style and the three of us drove the few miles up winding Bear Creek Road to Gia-fu's community in the hills.

Gia-fu was pleased by our visit and improvised an appropriate christening ceremony. We had not yet chosen a name so Gia-fu opened a drawer and pulled out a Chinese character carved from wood. "This is the character 'shou'," he said, "which means 'long life'. And it's also the name of my brother who is a banker in Hong Kong." So that's how Khola got his middle name. How Khola himself came to become a San Diego banker is another story.

Thank you, Gia-fu Feng, for being such an unforgettable part of my life. And thank you, Carol Ann Wilson, for the immense care you took in producing this remarkable book about a most remarkable man. 

Nature is my teacher: Gia-fu Feng: Photo by Jane English

Doctor Hofmann's Diagnosis

FIRST ACID TEST: 50th Anniversary

DOCTOR HOFMANN'S DIAGNOSIS

Jawohl, mein Herr. 
This substance can only be
truly appreciated
by smart, sophisticated
Europeans like you and like me
who both possess advanced degrees
And strong intellectual presence.

Jawohl, mein Schatz. 
And after last night's
mind-expanding spree
I must confess I fully agree:
Lysergic Acid Diethylamide
is much too good for the peasants.

Numbers: Natural and Unnatural

Nick spots an Unnatural Number: Graphic by August O'Connor

God made the integers; all else is the work of man.
  Leopold Kronecker (1823-1891)

It's customary to call the "counting numbers" 1, 2, 3, 4, 5 ... the NATURAL NUMBERS which somehow implies that all the other numbers are (as Kronecker suggested) artificial or unnatural.

Some thinkers include zero in the set of natural numbers and others do not. The Roman numeral system had no symbol for zero (Romans used the word nulla instead. On the other hand, in the Arabic numerals that we use today, zero plays an essential role.

In the 6th century BC, Greek philosopher Pythagorus and his followers declared that All is Number, an opinion largely echoed by today's theoretical physicists. To the NATURAL NUMBERS, Pythagorus added fractions, numbers that can be expressed as the ratio a/b of two natural numbers. Derived from primordial integers, these so-called RATIONAL NUMBERS were considered by the Pythagoreans to be the basic building blocks of the physical world.

An impressive triumph of the Pythagorean view was a discovery that linked RATIONAL NUMBERS to the human mind. The Pythagoreans discovered by experiment that the human sense of musical concordance was stimulated most strongly by pairs of tones whose wavelength ratios are the rations of small natural numbers. The musical unison is a 2/1 ratio of tones; the perfect fifth is a 3/2 ratio, the perfect fourth is the ratio of 4 to 3 and so on. In the intervening 8 centuries, humans have made no further discovery comparable to the remarkable Pythagorean musical scale that solidly links human subjectivity to the properties of rational numbers.

This ideal Pythagorean paradise was shattered by the discovery of IRRATIONAL NUMBERS, such as the square root of 2, which cannot be expressed as the ratio of two integers. Rumor has it that revealing the fact that the SQUARE ROOT OF TWO is irrational (a proof that is taught today in every high school) was punishable by death. A mathematician named Hippasus was supposed by some to have been drowned at sea by the Pythagorean Mafia for sharing this dark mathematical secret.

I'm currently reading An Imaginary Tale by Paul Nahin which tells the story of the IMAGINARY NUMBER "i" defined as the SQUARE ROOT OF -1. Physicists routinely use "i" in their calculations but few are aware of how long and difficult was the process involved in bringing this bizarre new number into the charmed circle of conventional math.

Nahin's tale involves dozens of famous and not so famous mathematicians who were baffled by the concept of the square root of a negative number. Judging from his recountings of obscure mathematical contests, long forgotten rivalries and obscure misunderstandings, Nahin has done a lot of research for this book. One of the facts that impressed me was that even at the time of Newton and beyond, mathematicians were not entirely comfortable with the notion of a NEGATIVE NUMBER. What is the true meaning of a number that is "less than nothing"?

When the NEGATIVE NUMBERS (both rational and irrational) are added to the POSITIVE NUMBERS plus ZERO, the result is called the REAL NUMBERS. The REAL NUMBERS can be considered to lie on a REAL LINE that stretches from minus infinity at the far left to plus infinity at the far right. For a very long time, it was believed that the REAL NUMBERS were the only numbers that existed -- hence the term "real"

The concept of the negative square root occurs in the theory of algebraic equations, most starkly as the solution to the simple equation: x^2 +1 = 0. The names that various mathematicians gave to the alleged solutions to such an equation are indicative of their attitude to the existence of the negative square root. They called it "unacceptable", "sophistic", "impossible" or just plain "wrong". To the French philosopher Rene' Descartes goes the honor of calling such numbers "imaginary" but he meant it in a dismissive way. Later when such numbers were finally welcomed into the canon, Swiss mathematician Leonard Euler resurrected Descartes' slur and christened these numbers IMAGINARY NUMBERS with no harm intended.

The crucial breakthrough towards making sense of IMAGINARY NUMBERS was achieved not by a mathematician but by a Danish surveyor Caspar Wessel (1745-1818) who postulated that imaginary numbers represented a distance at right angles to the REAL LINE. If the REAL LINE represents locations in the East/West direction, then according to Wessel the IMAGINARY LINE can represent locations in the North/South direction. No doubt from his experience in making maps, Caspar Wessel had invented what we today call "the complex plane", the mathematical country where real and imaginary numbers can dwell together in perfect harmony

Complex Plane: Red Line maps the Reals; Green Line maps the Imaginaries

Wessel's new geometric scheme literally put IMAGINARY NUMBERS on the map and opened up a flood of research into these previously dubious and mysterious quantities. Once IMAGINARY NUMBERS had been tamed, amazing calculations could be carried out and previously impossible tasks became easy.

For instance, what is the value of i to the ith power? Turns out this is a REAL NUMBER with the value of 0.2078... And easily calculated from equations derived from Wessel's construction.

With the introduction of Wessel's map (also called the Argand plane after a Parisian book-keeper who independently made the same discovery) one more kind of number has to be added to the list of man-made UNNATURAL NUMBERS. When one adds a REAL NUMBER (such as 2) to an IMAGINARY NUMBER such as 2i) one obtains a new number which is neither real nor imaginary. Numbers such as z = 2 + 2i have been given the name COMPLEX NUMBER. And the flat map on which COMPLEX NUMBERS enjoy their existence is accordingly called the complex plane.

Many remarkable discoveries have been made in the COMPLEX NUMBER realm. The theory of quantum mechanics uses COMPLEX POSSIBILITIES to represent Nature rather than REAL PROBABILITIES, a situation which still puzzles most physicists. And in Einstein's relativity, time can be viewed as an IMAGINARY quantity in contrast to the three REAL spatial dimensions.

Dozens of new mathematical formulas emerged from the study of the complex plane, including Euler's Identity which connects the sine and cosine function with the number e, the base of the natural logarithms.

e^ix = sin x + i cos x       Euler's Identity

This equation is enormously useful in many fields, especially in electrical engineering where the author Paul Nahin made his mark. When x = π, the Euler Identity reduces to:

e^iπ +1 = 0

This impressive little equation brings together in one simple statement 5 of the most important constants in mathematics. At age 15, the physicist Richard Feynman wrote this formula into his notebook with the caption: THE MOST REMARKABLE FORMULA IN MATH.

Since his specialty is electrical engineering, Nahin gives an example of the usefulness of COMPLEX NUMBERS in the analysis of electrical circuits. In the space of a few pages headed "A Famous Electronic Circuit That Works Because of Square Root of -1" Nahin describes the inner workings of a device called the phase-shift oscillator.  

Why is this device so famous? Turns out it was the first product manufactured in the legendary Palo Alto garage of William Hewlett and David Packard. Their variable-frequency audio oscillator became the basis of a billion-dollar industry. That's a lot of bang for a purely imaginary buck.

Hewlett-Packard 200A Audio Oscillator

QuantumTantra 2015

Happy New Year 2016 from Quantum Tantra blog

On the longest night of the year, it seems appropriate to summarize the old year's notable happenings.

This year witnessed the deaths of Don Joyce, Terry Pratchett and my brother Tom. The world is poorer and much less funny with their passing.

I've read a lot of books this year but three in particular stuck in my mind: 1. Victor L. Wooten's The Music Lesson: a Search for Spiritual Growth Through Music. Wooten is a virtuoso bass player (review of the book and video of Wooten jamming here,) Wooten's writing has been compared to Carlos Casteneda's as he describes meeting up with various unlikely musical shamans who trick and tease Wooten into seeing more deeply into the magic that hides behind all the notes and the practice.

2. Jasper Fforde's Shades of Grey is a science-fiction portrayal of a society in which one's rank is determined by the range of one's color perception ("greys", who perceive only in black-and-white, live at the bottom of the heap.)  In Fforde's fictitious Chromatacia, color possesses extraordinary power -- it can be used to damage and to heal. A particular shade called "Lincoln", available only to doctors, is a powerful painkiller and if stared at for more than 10 seconds causes hallucinations. On his blog, Fforde actually displays some of the more stunning shades (including Lincoln) that play a big part in his story.  But don't expect to get high off these tints -- we humans just aren't put together that way.

3. Charles Seife's Proofiness: The Dark Arts of Mathematical Deception shows how easily people can be impressed by a number no matter how fictitious or meaningless that number might be. Seife uses mostly examples from politics, showing how the numbers from polls and elections are almost always misleading. He analyzes in great detail a few famous close political races and as a bonus explains who actually won the recent Gore/Bush presidential election. (It's not whom you think.) Seife's book deserves a place on the shelf next to Darell Huff's classic How to Lie with Statistics which covers much the same ground. Cuts through numeric bull shit like a hot scalpel. The biggest message I took away from Seife's book is this: 73% of all statistics are made up on the spot.

This blog's main concern is quantum physics, poetry, and more recently, music.

On the physics front there appeared Some Notes on Quantum Entanglement in which I present a simple and informative new way to describe the classic double-slit experiment. For reasons unknown, this post has accumulated a comparatively large number of hits. In The JJCCTT Device I analyze a new FTL signaling scheme proposed by a student from Jerusalem Center for Technology. The main advantage of the JJCCTT proposal is that the correlation between Alice and Bob consists of 2 bits rather than the usual 1 bit. After some calculations we find, as might have been expected, that this doubling of possible outcome patterns does not allow FTL signaling. Thanks, Omer!

Following up on our early invention and investigation of Sirag Numbers, we define the notion of Sirag Triangles and discover a surprisingly elegant solution that generates all Sirag Triangles with integer sides.

In The Quantum Olympics we look at recent attempts to experimentally discover the largest material object that displays clear quantum effects.

And in Six Optical Miracles we describe the remarkable yet little known Ewald-Oseen Extinction Theorem that explains why a pane of glass is transparent rather than behaving like a dense fog.

See also Does Earth Possess a Second Season? my small contribution to the Catastrophic Anthropogenic Global Warming conversation.

On the poetry front, the world of letters has been enriched by a dozen mostly new poems cooked up inside the frenzied minds of Nick Herbert and his alter ego Doctor Jabir 'abd al-Khaliq. These poems include: Is Jack a Tacit Muslim?, Church of the Origin, Esalen Institute (written to honor founder Michael Murphy's 85th birthday), Jabir's Proof, The Philosopher's Bone, Thirteen Unnatural Acts, Kiss My Bare Art, Ninety-nine Names of Goddess, Reading Readiness, Altered State, Dangerous Candy, No Torture Please.

And lastly Abduction by Aliens, a videoed performance at the Grand Conclave of Glad Scientists convened at a secret Pacific beach front location by Dr and Mrs Future.

In this little collection, even the most jaded reader will find something that will please, educate, amuse, mystify, enlighten and offend.

Finally, this years achievements on the music front in both composition and performance.

For the celebration of the 50th anniversary of Bell's Theorem, the museum at Queen's University in Belfast asked to exhibit my song "Bell's Theorem Blues" as an example of art inspired by this famous result in physics. I persuaded a trio of musicians in Boulder Creek to perform the song and sent lyrics, sound and video recording to the month-long Bell Fest.

Then our little Irish band Blarney was asked to play at the Santa Cruz Art League's theater on Broadway Avenue: Blarney on Broadway. For two hours the four of us performed for an enthusiastic and responsive audience and here is one of our tunes.

All in all, a very good year.

On this, the season's longest night, may your New Year be brightened by the coming of the light.

Matt, August, Kim and Nick are Blarney