Quantum Ansible

Nikolai Nikitin and Konstantin Toms

QUANTUM ANSIBLE

A few days ago a paper appeared in the physics arXiv that described a clever new faster-than-light signaling scheme. The authors are a pair of Russians from the Lomonosov State University in Moscow, Nikolai Nikitin and Konstantin Toms, who is currently a postdoc at the University of New Mexico after spending time at the ATLAS experiment at CERN. N&T called their paper "Quantum Ansible" after a fictional FTL signaling device in the novels of Ursula LeGuin.

N&T's Quantum Ansible is a more sophisticated realization of my early (1982) FLASH FTL signaling scheme which imagined a universal quantum copying device that could exactly duplicate any unknown quantum state. My FLASH proposal was quickly refuted by Wootters, Zurek and others and led to the discovery/invention of the quantum no-cloning rule which plays an important part in the field of quantum computing.

Any classical datum can be easily copied, as simple as pushing the "Duplicate" command in your computer menu. But Nature outlaws such a duplicate command for quantum data. The best you can do, given an unknown quantum state, as was shown by Leonard Mandel, is to duplicate that state with 5/6 (= 83.3%) accuracy. As noise-free as this might seem, this small degree of copying imperfection was precisely sufficient to render my FLASH FTL communication scheme kaput.

The field of quantum computing has developed immensely since the discovery of the no-cloning rule. We know, for instance, that it is possible to perfectly clone any known quantum state. And thanks to the field of quantum computing, there is an easy way to do so: the so-called CNOT gate (or Feynman gate, as it is sometimes called).

The four possible operations of the CNOT gate.

The CNOT gate has two inputs and two outputs. The top input traverses the gate unchanged; the bottom input flips its sign if the top input is |1>. If the top input is |0>, the bottom output remains the same. CNOT stands for "Controlled NOT": the top input controls whether the bottom input will remain the same or will be subjected to the NOT operation, which changes a one to a zero.

As simple as this gate seems to be, the CNOT gate plays an important role in quantum computing. It can, for instance, be used to clone a known quantum state, without the use of lasers.

In a classical computer the inputs and outputs of the CNOT gate are simple binary bits, symbolized by zeros and ones. In a quantum computer, the inputs and outputs are quantum states, symbolized (in Dirac notation) by |0>s and |1>s. In the case of the quantum ansible, |0> represents the spin-down state of Alice's electron in the z-direction, a quantum state which could also be symbolized as:

|0> ----> | minus z--Alice>

|1> ----> |plus z -- Alice>

With this re-interpretation of the operation of the CNOT gate, it is easy to see how this simple gate can be used as a cloning tool for an orthogonal pair of quantum states.

We consider only the gate operations labeled A and B. In these two cases the bottom input is always |0> which in the physical situation represents Alice's electron having spin down in the z direction). In these two special cases, we note that the CNOT gate will clone either the |0> or the |1> state if it is presented to the upper input. Simply put in a |0> and two |0>s come out. Put in a |1> and two |1>s come out. In this special situation the CNOT gate can be used as a simple cloning tool for one particular known quantum state.

The importance of cloning in faster-than-light signaling schemes cannot be overestimated. In the usual measurement situation you get just one chance to measure the spin state of a single photon or electron. With a cloning device you can get two or more chances to measure different physical properties of a single quantum entity.

The designers of the quantum ansible imagine Bob located 4 light-years away on Alpha Centauri sending a spin-entangled sequence of electrons to Alice on Earth. Bob measures one electron spin and sends the other partner of the pair to Alice. If Bob measures spin along the z axis, Alice's distant electron will immediately (!) acquire a z-direction spin (either up or down); if Bob measures along the x axis Alice's distant electron will instantly acquire an x-axis spin.

If Alice can detect the difference between a random sequence of z-polarized electrons and a random sequence of x-polarized photons at her detector on Earth, then she can decode Bob's message (sent faster than light) which is encoded by his conscious decision at Alpha Centauri to switch his electron spin detector between the z-direction and the x-direction.

Given this situation, Nikitin & Toms make a clever move: they actually attempt to exploit the no-cloning rule in their favor. You can clone one known state (says Nature). So N&T choose to clone Alice's electron spin in the z-direction. But you are forbidden, says Nature, to clone any other spin direction.

That's fine, say Nikitin and Toms: we'll get great results measuring z-spin, because we can use a z-cloner. And we'll get terrible results when Bob sends x-polarized electrons. And from the difference between our good results and our terrible results, we'll be able to decode Bob's signal.

Ha. Ha, Nature. We Russians have finally fooled you.

Good results means an accurately measured z-spin of every electron. Terrible results mean a completely unpolarized beam of electrons with no directional preference whatsoever.

CRITIQUE

So far I have sketched the alleged operation of N&T's quantum ansible as it appears in their eight-page paper. Now I add my own comments.

This ansible scheme would actually work if everything behaved as they described it. But the weak point is N&T's assumption of a completely depolarized beam at Alice's site when Bob chooses to measure x-polarization. In a truly unpolarized beam, at the very least, Alice's cloner would refuse to work (because it's operating on an unknown state) and would not only produce two electrons of the same polarization all of the time but two electrons of different polarizations some of the time. The math (correct in my estimation) shows that this never happens. In fact, Alice's cloner continues to produce pairs of z-polarized photons, despite the alleged total polarization scrambling expected to occur due to Bob's choice to measure another polarization orthogonal to the direction that Alice's cloner is tuned to. In fact, from N&T's math alone, one can see that the physical situation at Alice's site seems to change when Bob decides to measure one spin direction rather than another, but the statistical outcome at Alice's site remains exactly the same.

Here's an analogy to what seems to be happening in the quantum ansible expeiment.

In my right-hand pocket I have a bunch of fake coins: either heads on both sides or tails on both sides. I pull one out and flip it. The result is known for sure. But I pick the coins at random from my pocket. The result is a random sequence of heads and tails. This physical situation (I claim) is analogous to Bob choosing to measure his electrons in the z-direction, the direction in which Alice happens to possess a perfect cloner.

In my left-hand pocket I have a bunch of fair coins: heads on one side, tails on the other. I pick a coin at random and flip it on the table. The result is a random sequence of heads and tails. This physical situation (I claim) is analogous to Bob choosing to measure his electrons in the x-directions, at a right angle to the direction in which Alice possesses a perfect cloner.

In both the coin analogy and the ansible experiment the actual physical situation seems to change depending on which pocket I select and which spin direction Bob selects (the math describing Alice's situation is certainly different for Bob's two choices). But although the physical situation seems to be different in both cases, the statistical predictions for the outcomes is exactly the same both for the coins and for Alice's measurements.

The quantum ansible is a gallant and clever attempt to exploit quantum entanglement to overcome Einstein's famous light-speed barrier to human information transfer. But despite its ingenuity, I do not believe it will work. Thank you, Nikitin and Toms, for an amusing physics puzzle.

At the conclusion of their quantum ansible paper, Nikolai Nikitin and Konstantin Toms thank a certain C. Aleister (Saint Genis-Pouilly, France) for creating a warm and friendly working atmosphere for discussion between the authors. With a bit of searching, I was able, on Facebook, to find a picture of these two Russian scientists' mysterious benefactor.

Aleister the cat illustrates the SO(3) rotation group

TEN YEARS OLD: QUANTUM TANTRA BLOG

Ten Years Old

Quantum Tantra Blog is now 10 years old. Happy Birthday, old friend!

During its life QTB has published 495 posts which have received more than 500,000 views. The blog is mainly a kind of diary of the major concerns and accomplishments of Nick Herbert and his alter ego Doctor Jabir 'abd al-Khaliq.

Nick's primary goal is to father a brand new physics (Quantum Tantra) which will connect us all with Nature in a more direct and intimate way. This quest has generated dozens of pages of quirky quantum tantric poetry but no concrete physical results as yet. But I continue to pursue this "impossible dream".

The quest begins with quantum mechanics, the most successful theory of the physical world ever devised, which comes at the price of physicists not knowing what this theory actually means: the "quantum reality problem" -- about which I wrote my first book Quantum Reality: Beyond the New Physics.

One of the important milestones in quantum reality research is Bell's Theorem in which Irish physicist John Stewart Bell proved that although the quantum facts are everywhere "local", the quantum reality underlying these fact must be "non-local". The term "non-local" essentially means "faster-than-light", which Albert Einstein declared verboten in physics.

John Stewart Bell: Reality is Non-local

But, in a truly peculiar twist of logic, Bell's faster-than-light proof applies only to REALITY not to the FACTS. Einstein's prohibition still holds for the world we can see; only the invisible reality behind these facts must be faster-than-light.

Bell's Theorem has led to many clever attempts to move FTL REALITY into FTL FACT. One of my hobbies is superluminal signaling schemes, many of which are described in my book Faster-Than-Light: Superluminal Loophole in Physics and in quite a few of my QTB blog posts.

In fact, exactly ten years ago, as I was just beginning this blog, I had just published, in the physics arXiv, a FTL communication scheme called ETCALLHOME which was refuted within 24 hours by Israeli physicist Lev Vaidman.

Demetrios Kalamidas: inventor of KISS

The most exciting FTL scheme reported in QTB was the KISS proposal of Demetrios Kalamidas which uses a kind of "fake news" effect to exploit quantum path entanglement to send superluminal signals. Six prominent physicists, including one of Kalamidas's former optics professors, were involved in KISS's eventual refutation.

KISS: A New Superluminal Commication Scheme
Demetrios: the Opera
The Kalamidas Experiment
FTL Signaling Made Easy
Kalamidas Refuted
The Kalamidas Experiment: Easy Pickings

The refutation by Wootters and Zurek of one of my own FTL schemes, called FLASH, led directly to the quantum no-cloning rule, a result important in the field of quantum computing since it proves that, unlike classical information, such as a jpg of your cat, which can be exactly copied, perfect cloning of quantum information violates the laws of Nature. The story of the discovery of the no-cloning rule is the centerpiece of David Kaiser's recent book How the Hippies Saved Physics which also recounts the adventures of some of my disreputable physics friends.

David Kaiser and some hippies who "saved physics"

Kaiser describes the Esalen Seminars on the Nature of Reality, hosted by myself and eccentric mathematician Saul-Paul Sirag, where for eight years prominent physicists were invited to discuss Bell's Theorem along the Big Sur cliffs and in the Esalen sulfur baths. Through the good graces of Fed Ex philanthropist Charles Brandon we were able to award, in Esalen's Big House, the Reality Prize to John Bell (theory) and John Clauser (experiment) for their decisive demonstration of quantum reality's necessary non-locality, possibly the first time these guys's important achievements were publicly recognized.

Esalen Reality Prize Day. Left to Right: Charles Brandon, Nick Herbert, Adriana Chernovska, John Clauser, Saul-Paul Sirag, Bernard D'Espagnat (John Bell's proxy), Henry Stapp. Nick's son Khola in front holding wine glass

Also in QTB, I describe my collaboration with Saul-Paul Sirag in elucidating the nature of the Sirag Numbers, a sequence of integers indirectly related to the quantum theory of angular momentum. Later, I give a brief biography of Saul-Paul (who was born in a concentration camp) as preface to a review of his new math book ADEX Theory: How the ADE Coxeter Graphs Unify Mathematics and Physics.

Saul-Paul Sirag, eccentric mathematician

In 2014, the city of Belfast celebrated the 50th anniversary of Bell's Theorem by naming a street in its Titanic district after his theorem and by hosting a museum exhibit of works of art inspired by Belfast-born John Bell. My song Bell's Theorem Blues was chosen as one of the exhibits and was performed by local (Boulder Creek) vocalist Joy Rush, pianist Jack Bowers with George Galt on harmonica. The festival could not afford to pay our fares to Ireland but you can listen to the recording we sent and read the lyrics here.

BC Blues Trio: George Galt, Jack Bowers, Joy Rush

In this blog I also recall my two meetings with John Stewart Bell at the home of Stanford physics professor Pierre Noyes.

In the spirit of our old quantum physics seminars, Esalen has been hosting invitational meetings on the more general topic of human Superpowers, initiated by one of its founders Michael Murphy and expanded by extraordinary religious scholar Jeffrey Kripal. Most of these superpowers are considered IMPOSSIBLE so they thought it might be fun to have a few physicists on board. I was invited to two of these seminars including one devoted to the extraordinary levitations of St Joseph of Copertino, chronicled in the recent book by Michael Grosso The Man Who Could Fly. This seminar inspired my own levitation project, a subset of my quantum tantra urge to learn to relate to Nature in radical new ways.

Jeff Kripal & Nick Herbert: Old Esalen Lodge

As part of my project to relate to Nature in brand new ways, I invented the Metaphase Typewriter, a quantum-random putative mechanical spirit medium. In common with all of Nick's efforts so far, this project seemed to utterly fail. But recently the Metaphase Typewriter was revived as an art project by Lynden Stone in Queensland, Australia and by Dmitry Morosov in Moscow.

Lynden Stone's Erwin's Puss

While Nick was waiting for the Messiah to come (a play on the name of the wonderful picture book about Esalen by Bernie Gunther : What to Do Till the Messiah Comes), he fell in with a bunch of rowdy Irish musicians in Santa Cruz, learned to play the Irish whistle, and became part of a band called Blarney which plays at private parties and (a few times) on stage. My biggest achievement as member of the wonderful Blarney band was the composition of a patter song, 32 Irish County Jig, that recites each of Ireland's 32 counties. I am really surprised that no one else had ever done this before.

Blarney Band: Matt Johnson, August O'Connor, Kim Fulton-Bennett, Nick Herbert

Then there is my poetry ("the kiss of death" according to my literary agent John Brockman). In Boulder Creek, for a dozen or so years, there arose a remarkably fertile poetry movement, which I call the Bistroscene after Conrad Santos's Boulder Creek Bistro where a majority of the action took place and where I premiered my quantum tantric poems and many others. Many of these performances were videoed by Alan and Sun Lundell (aka Dr and Mrs Future) and are still being rediscovered as Al and Sun transfer their ancient video formats to archival hard drive.

Kiss My Bare Art
The New Sex Robot
He Did Not Die
Harlot Nature
ZAM
2000-year-old Pickup Line
The Aphrodite Award
Los Gatos Apple Store
Maya

Celebrating the Irises
Mayday Play

Regarding weird literary output, it would be impossible to ignore my friend Rudy Rucker, the Lawrence Ferlinghetti of cyberspace. Rudy conceived and published Flurb, an online magazine of radically trippy inventions, including some of my own stuff and the most imaginative alien psychedelic I have even encountered -- James Worrad's Eye-High.

Since quantum tantra (the search for new doorways into Nature) is still in its embryonic stage, there is very little concrete accomplishments to which I can point. Here however are a few teasers:

Abu Asks About Quantum Tantra
No More Safe Science
Opening Night
Happy Doomsday
Greatest Pleasure
Elements of Tantra

Urge: A Short Opera about Reality
Tantric Jihad: the Video
Quantum Tantra Stripped Bare

In this short post, I cannot cover completely all ten years of my blog: I have decided to exclude the numerous book reviews and friends' obituaries (except for my two younger brothers Tom and Duke and my cat Onyx). Please click the tags for topics and people that interest you. My apologies to everyone I have left out. Although concrete quantum tantric research seems at an absolute standstill, I can at least briefly brag about six minor accomplishments:

Nick Herbert aka Dr. Jabir

I self-published two books of verse: Physics on All Fours and Harlot Nature;
I invented 99 new chakras: 99 Nick Chakras;
I invented a new (Ukrainian) holiday: YIDD;
I invented a new (imaginary) element: Khaliqium;
I invented a new (psychic) currency: Khlit Coin;
I devised a new proof that classical and quantum ESP powers must be precisely equal: Nick's Proof.

The quantum tantra posts with the most views ares:
1. Schrödinger's Proof for the Existence of God
2: Does Consciousness Create Reality?
3. Jailbait

Many thanks to all my viewers.

Happy 10th Birthday, dear Quantum Tantra Blog!

TKO TKOED

Demetrios Kalamidas, creator of the TKO superluminal signaling scheme.

Page 1 of Kalamidas's TKO FTL proposal

Page 5 of Kalamidas's TKO FTL proposal

A few days ago I received 6 or 7 hand-written notes from Demetrios Kalamidas outlining a new faster-than-light (FTL) signaling scheme that he had devised. Three years ago, Kalamidas had proposed (and even published in a major optics journal!) an FTL scheme which was so devilishly clever that it occupied the time of several smart physicists before his scheme (which I irreverently called KISS for Kalamidas's Instant Signaling Scheme) was finally wrestled to the ground and definitively defeated.

Not one to give up so easily, Kalamidas has now come up with another FTL scheme (which I christened TKO, for The Kalamidas Option). "Refute this one, Nick," he challenged.

Well, before I could refute TKO, I had to understand it. So I made a little sketch, which Kalamidas agreed captured the gist of his new scheme.

Kalamidas's TKO Superluminal Signaling Scheme

In the TKO scheme a single photon |1> is divided by a beam splitter into two equal paths |a> and |b> and recombined at ALICE's beam splitter into two other paths |c> and |d>. This simple photon divide-and-recombine scheme is called a Mach-Zehnder (MZ) interferometer which has found numerous uses in the field of optical physics. Before the |b> photon enters her beam recombiner, ALICE has the option to add a phase Q to the |b> beam, altho in the TKO scheme ALICE does not exercise this option.

In BOB's |a> beam is placed a photon up-conversion crystal (symbolized by the blue circle labeled XTL which, with 100% efficiency, converts two incident photons to one photon with twice the energy. This double-energy photon (which Kalamidas calls OMEGA) exits the scene along path |H>.

In the simple MZ configuration the up-conversion crystal XTL is never triggered, since there is never more than one photon |a> in BOB's beam.

But then BOB adds a second pulsed source of light |G> that is timed to strike the XTL at the same time as each of the |a> photons. If |G> were a simple pulsed source of single photons |1>, then this XTL would remove every |a> photon from BOB's beam by transforming |1> + |a> into an OMEGA. No |a> photons would ever be sent to ALICE who would receive only |b> photons. No interference (between photon path |a> and path |b> would ever occur. The resulting situation would be utterly boring.

So instead of letting |G> be a boring source of single photons, Kalamidas makes |G> a more interesting source of "Gray Light" which is a coherent superposition of the zero-photon vacuum state |0> and the single photon state |1>:

|G> = X |0> + Y |1>         EQ 1

where X^2 + Y^2 = 1

So now whenever the Gray Light contains a single photon |1> (which happens with probability Y^2), this photon combines with BOB's photon |a> and is removed from the |B> beam by the up-converting XTL in the form of a doubled-frequency OMEGA photon.

Whenever the Gray Light contains the zero-photon vacuum state |0> which happens with probability X^2, then photon |a> remains unmolested and travels to ALICE's beam combiner where it's mixed with ALICE's photon |b>.

Given this physical setup, how does ALICE send a signal to BOB?  In Kalamidas's scheme, ALICE has two options which I call YES and NO. In the YES option she sets her beam combiner to 50/50 and maximally mixes photons |a> and |b> into her outputs |c> and |d>.

Choosing the NO option, ALICE removes her beam combiner (or equivalently sets its transparency to 100%) so the |a> and |b> photons do not mix. Photon |a> goes directly into counter |c> and photon |b> goes directly into counter |d>.

ALICE's choice amounts to a decision whether to mix photons |a> and |b> (YES) or not to mix the photons (NO). If BOB observes any difference in his results when ALICE switches between YES and NO, then this difference can be used to send a signal faster than light.

If BOB's experience is always the same, then no signaling occurs.

I looked at TKO and came up with an immediate refutation.

Let's suppose that the Gray Light is equally divided into NOTHING (the vacuum state |0>) and SOMETHING (the one-photon state |1>). This means that half the time there is a Gray-Light photon hitting the crystal and half the time there is not.

1. Whenever there is not a Gray Light photon, BOB will see nothing = 50% of the time.

2. Whenever there is a Gray Light photon but no |a> photon, BOB will see 1 photon. This happens 25% of the time since the photon takes path |b> 1/2 the time and Gray light emits a photon 1/2 the time: 1/2 x 1/2 = 1/4 = 25%

3. By the same reasoning whenever there is a Gray Light photon that meets an |a> photon, BOB will see nothing, because the Gray Light photon will be converted into an OMEGA.

By adding up all possibilities we see that 50% of the time BOB sees NOTHING, 25% of the time he sees an OMEGA and 25% of the time he sees ONE PHOTON.

Furthermore this 50/25/25 behavior is completely independent of any action on ALICE's part. Therefore no signaling ever takes place. 

I considered this refutation particularly simple and obvious. So I sent my result to Kalamidas.

"No, no, no, no, Nick! You did not even look at what I have written (his seven pages of hand-inscribed notes). Your calculation is much too simple. IT IGNORES ALL THE PHASES!"

"Phases?"

"Yes, Nick, phases." BOB does not just get either SOMETHING or NOTHING at his detectors, He gets SOMETHING and NOTHING between which there exists a definite phase relationship. And that phase relationship depends on ALICE's choice of YES and NO."

"Phases, Demetri? Phases between SOMETHING and NOTHING?"

"Yes, Nick, phases between SOMETHING and NOTHING. That's what makes Gray Light so special. Gray Light's not a mere incoherent mixture of SOMETHING and NOTHING. Gray Light is a coherent superposition (like Schrodinger's Cat) -- a superposition of two possibilities that are linked by a definite phase relationship, a relationship between two objects that only makes sense in quantum mechanics. "

"Yeah, buddy. I know about phases. Phases are the meat and potatoes of every quantum calculation. But in my way of thinking, phases only exist between actual possibilities of something happening. How can NOTHING possibly possess a phase?"

"It can, it does. And that fact is the secret ingredient of my TKO scheme. Check it out, dude. If you include phases in your calculation for what BOB sees (including the phase of the vacuum state |0>) you'll discover (just like I did) that BOB sees something when ALICE makes her YES choice and BOB sees something different when ALICE makes her NO choice. I don't have to tell you, Nick, that if my result is correct, then FTL signaling is a done deed, hence signaling backwards in time, hence breakdown in causality and hence AN END TO THE WORLD AS WE KNOW IT!"

"Ummph! I gotta sit down and think a bit about whether NOTHING can possess a phase. Let me get back to you, man."

So Nick gets out his optics books and several cups of coffee and generates a little essay called: "Can NOTHING have a phase? And he decides YES. So the Kalamidas TKO proposal must be taken seriously.

Paying attention to vacuum phases, Nick calculates what BOB will see for ALICE's two choices of 1. inserting a beam splitter -- a choice I call YES. and 2. taking out her beam splitter and observing the |a> and |b> photons separately -- a choice I've called NO.

And here are the results: here is what BOB sees when ALICE makes her two choices:

YES ===> [ |G(1)> ] + 1/2 Y [ |1> ] + sY [ |0> ]           EQ 2

NO ===> s [ |G(2)> ] + sX [ |0> ] + sY [ |0> ]               EQ 3

where |G(1)> and |G(2)> are two different kinds of Gray Light given by:

|G(1)> = X |0> + Y/2 |1>  and |G (2)> = X |0> + Y|1>    EQ 4

where the square brackets [ ...  ] indicate a quantity that has "lost its phase" and must be added incoherently. Inside the square bracket, phases still must be taken into account. I have found this unconventional square bracket notation useful in dealing with entangled systems which routinely destroy the phases of entangled sub-systems while preserving the phases of the system as a whole

These results express the quantum amplitudes that appear in BOB's observation channel |B>. To obtain probabilities these amplitudes must be squared. But squaring these raw amplitudes will destroy the phase relations and merely reproduce the results that Nick obtained earlier -- if phases are not important then BOB's results don't depend on ALICE's two choices so no signaling can occur.

But BOB is not restricted to merely passively observing the output of his |B> channel. Instead he has the option to deploy a phase-sensitive detector at |B> that might be able, in principle, to detect the two different forms of Gray Light that appear in EQ 2 and EQ 3. Such a detector might be realized by optical homodyne experiments -- subtle kinds of experiment that have produced such peculiar phenomena as the famous "squeezed vacuum state". Both Demetrios and I begin to look into the homodyne literature for some clue as to how BOB might effectively carry out a phase sensitive measurement.

Our literature search went nowhere. Homodyne experiments seemed designed for tasks far removed from our concerns. At this point Kalamidas and I were stuck. Our search for a REAL MACHINE that could measure the phase between NOTHING and SOMETHING had come up empty handed.

But then came the crucial breakthrough. We both realized this: "We don't got to show you no steenking measuring device". At this early stage the TKO proposal is only a thought experiment, which meant that Demetrios and I had unrestricted access to the vast warehouses of the ACME thought experiment Super Store. The fabled ACME warehouse contains all conceivable measuring devices provided only that they don't violate the laws of physics. The ACME shelves, for instance, are empty of perpetual motion devices and quantum-state Xerox machines. Who supplied that box-on-a-spring which could weigh a single photon, that Einstein used in his famous debate with Bohr? ACME, of course. Or its European equivalent.

Before we raid the ACME shelves, let's take a closer look at BOB's two results. On the surface his YES and NO results look completely different, with the exception of the last zero-photon event sY [ |0> ] which occurs only when an OMEGA is created. This OMEGA term is common to both of ALICE's choices. On the other hand the fact that BOB's two remaining terms seem distinctly different (the same result Kalamidas obtained on page 5 of his hand-written manuscript) gives us hope that, equipped with a 100% sensitive phase-discriminating device, BOB might be able to detect a difference between ALICE's YES and ALICE's NO choices. Hence, given an appropriate device from the ACME store, the TKO proposal might actually work as an FTL signaling machine. Such was our optimistic expectation.

So this is what I ordered from ACME -- a device (called GL (MAX) that splits reality into two orthogonal kinds of Gray Light which I call |S> and |D>:

|S> = s ( |0> + |1> )     And |D> = s ( |0> - |1> )      EQ 5

  

where s = 1/SQRT (2)

The detector GL (MAX) is maximally sensitive to the phase angle between NOTHING |0> and SOMETHING |1>. If this phase angle is positive, the photon ends up in detector |S>. If this phase angle is negative, the photon ends up in detector |D>. In the general case where the phase angle (and amplitude) can be anything, the photon has a definite (and calculatable) probability of ending up either in detector |S> or detector |D>. How the detector GL (MAX) might be physically realized is not our concern. If there were a way to make tons of money from this kind of photon phase detection, a detector of the type GL (MAX) would soon be realized.

Lacking a plausible real way to measure photon phases, Kalamidas and I resort to the ACME thought-experiment warehouse. The price is certainly right: this "ACME Miracle Detector" costs absolutely nothing.

The first thing to notice about the ACME Miracle Detector is that BOB's basis states NOTHING |0> and SOMETHING |1> can be conveniently expressed in terms of AMD states |S> and |D> as:

|0> = s ( |S> + |D> )      |1> = s ( |S> - |D> )                EQ 6

These two expressions will be especially useful for expressing EQ 2 and EQ 3 in terms of phase-sensitive quantum states |S> and |D>. And also useful for calculating the probabilities of the responses of our two orthogonal miracle-detector results <S|S> and <D|D>

Expressing EQ 2 and EQ 3 in terms of the miracle detector bases |S> and |D>, we easily obtain:

YES => s { [ (X + 1/2 Y) |S> + (X - 1/2 Y) |D>]  + 1/2 Y [ |S> - |D> ]}
+ 1/2 Y [|S> - |D>]

NO => s^2 { [(X +Y) |S> + (X-Y) |D>] + X [ |S> + |D>]}
+ 1/2 Y [ |S> - |D> ]

EQ 7 & EQ 8

where the square brackets [... ] indicate no external phase -- inside the brackets, amplitudes do coherently combine, but each bracketed quantity as a whole must be added incoherently to each of its bracketed fellows.

EQ 7 & EQ 8 represent the quantum amplitudes at BOB's |S> and |D> phase-sensitive detectors for each of ALICE's choices.

To determine the quantum probabilities at BOB's |S> and |D> phase-sensitive detectors, we calculate the absolute squares of EQ 7 & EQ 8.

YES PROB ==> 1/2 {(X^2 + XY + Y^2) <S|S>
+ (X^2 - XY + Y^2) <D|D> }

NO PROB ==> 1/2 {(X^2 + XY + Y^2) <S|S>
 + (X^2 - XY + Y^2) <D|D> }

EQ 9 & EQ 10

The final result is that both of these probabilities are exactly the same for all values of the Gray Light parameters X and Y. Thus what happens at BOB's |B> channel, even if BOB is able to deploy perfect miracle phase-sensitive detectors from ACME,  is completely independent of ALICE's actions. ALICE can send no signal, superluminal or otherwise, to BOB.  The exact equality of EQ 9 and EQ 10 means that the TKO proposal totally fails. This result was initially obtained using unconventional square bracket notation, but Kalamidas has independently reached the same conclusion using a standard density matrix calculation.

Although, in common with all previous FTL schemes, the TKO proposal ultimately failed, its detailed refutation led me to places I'd never been before. Highly rewarding was the journey. Thanks much, Demetrios, for taking me along on your trip.

Omega Centauri, the sky's brightest globular cluster

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.

JJCCTT Device for FTL Signaling

Omer and Nick's JJCCTT Device for FTL Signaling

JJCCTT Device for FTL Signaling

Bell's Theorem proves that quantum reality must be non-local.

Belfast-born physicist John Stewart Bell based his important proof about reality on the EPR Device (named after Einstein, Podolsky and Rosen) which uses TWO ENTANGLED PHOTONS whose wave function ψ can be written:

ψ (EPR) = 1/√2 ( |HH> + |VV> )          (EQ1)

Bell showed (and John Clauser subsequently measured) that this quantum wave function's statistical predictions exceed any result that any merely local reality is able to muster. Thus quantum reality is non-local.

Later Greenberger, Horne and Zeilinger used THREE ENTANGLED PHOTONS described by the GHZ wave function:

ψ (GHZ) = 1/√2 ( |HHH> + |VVV> )        (EQ2)

to prove a "Bell's Theorem without Inequalities". GHZ showed from EQ 2 that a local reality predicts a certain result will never happen, while quantum mechanics says that this same result must always happen. Since quantum mechanics gives the correct prediction, one measurement suffices to prove that quantum reality is non-local.

In recognition of GHZ's concise proof, the quantum state described by EQ 2 is usually called a "GHZ state".

Recently, Omer Dickstein, a physics student at Jerusalem College of Technology, proposed to exploit the non-locality exhibited by FOUR ENTANGLED PHOTONS for faster-than-light signaling. His wave function just adds one more photon to the GHZ state:

ψ (GHZ + 1) = 1/√2 ( |HHHH> + |VVVV> )        (EQ3)

As a place holder I have tentatively called EQ 3 the "GHZ plus one" state. How this state will eventually be designated will depend on what we learn from temporarily construing it as the core ingredient of an FTL signaling machine -- the so-called JJCCTT Device where JJCCTT stands for "Joint Jerusalem-California Collaboration on Transluminal Telecommunication".

The state |HHHH> represents the simultaneous emission of FOUR Horizontally-polarized photons, two of which are measured by Alice, and two of which are measured by Bob, each of whom possess two detectors that register "H" when accepting a Horizontal photon and "V" when accepting a Vertical photon.

The state |VVVV> represents the simultaneous emission of FOUR Vertically-polarized photons, two of which go to Alice, and two of which go to Bob.

One nice thing about the JJCCTT situation is that, unlike the EPR situation where Alice and Bob possess only one detector each (hence can obtain only ONE BIT of information), in the JJCCTT situation both particles possess two detectors (hence each can potentially obtain TWO BITS of digital information. The JJCCTT Device represents, information-wise, a more broad-band channel than its EPR competitor.

One might naively imagine that EQ 3 represents a situation in which the 4-photon source emits EITHER a pulse of 4 H-photons OR a pulse of 4 V-photons but that is not the case at all. In this peculiar process (called "polarization entanglement") illegal for all except quantum systems, the source emits BOTH a quadruple of H-photons and a quadruple of V-photons AT THE SAME TIME.

You might think of EQ 3 as describing a kind of "four-photon Schrödinger Cat state". When unlooked-at, "this cat" is in a superposition of both a 4H-cat and 4V-cat. (4H-cat has four Hazel (yellowish-brown) feet and 4V-cat has four Vermilion (yellowish-red) feet). Each foot simultaneously is both colors. That's when not looked at. But whenever it's looked at, whoever looks will always see this cat with each foot having the same color -- either four Hazel-colored feet or four Vermilion-colored feet -- no matter how far apart the cat's feet are. Bob and Alice might be 100 light-years apart and this feet-coloring process will happen exactly the same way.

According to quantum mechanics, when this ambiguous pulse of 4-light (quantum cat) encounters a detector, the detector "flips a coin" and randomly decides which one of these two possible polarizations it will "make real". Will it be the all-H-state or the all-V-state? It is important to understand that quantum theory tells us that this choice of what polarization will be recorded is made at the detector, not at the source.

Once this decision is made by one detector (we can never really identify which one), the other 3 detectors follow suit, so that each detector, no matter how far it might be separated from all the others, immediately comes to the same conclusion concerning which possible polarization state (H or V) it will also make real.

It is easy to see how this apparent instantaneous conspiracy between far-distant detectors to always record the same polarization, when up until the moment of choice both polarizations were actively possible, might embolden some physicists to attempt to exploit this system to send signals faster than light.

The configuration pictured above won't work as an FTL channel between Alice (the traditional sender) and Bob (the inevitable recipient), because EQ 3 allows only two elemental events to happen, either HHHH or VVVV, none of which are under the control of either Alice or Bob.

But here's how Omer from JCT in Jerusalem plans to change all that. We note that in the START STATE (pictured below), only two things ever happen to Alice and Bob. They either both receive 4 H-photons. Or both receive 4 V-photons. Bob always registers HH or VV in his two polarization detectors. And so does Alice. Never anything else.

START STATE: Only two events can happen, either HHHH or VVVV.

In particular Bob never observes a "cross term" such as HV or VH, where one of his two detectors counts a H-photon and the other counts a V-photon.

If there were something Alice could do with her photons that would produce "cross terms" in Bob's results, then Alice would be able to send a message to Bob at superluminal speed.

The essence of the JJCCTT Project is to examine all the things that Alice can do to her 2 photons, while looking for effects that Alice's actions might have on Bob's 2-photon cross terms.

Here's a hint about what Alice might do to induce cross-terms into Bob's detectors.

Alice might decide, for instance, to "make real" states of Right and Left Circularly polarized light rather than H and V polarized light as in the START STATE. Alice can easily configure her two detectors (using a phase plate and a beam combiner) to register R and L light rather than H and V light.

If Alice's R-and-L-making action causes any amount of R and L light to appear at either one of Bob's detectors, this will have drastic consequences. Because R light incident on an H/V detector (the kind Bob has deployed) will always produce a random mixture of H and V counts -- that will certainly lead to cross terms in Bob's data. Likewise L light incident on Bob's detectors will inevitably produce cross terms via the same procedure.

The 2-photon EPR situation offers some hope that this could happen, via a process that Irwin Schrödinger dubbed "steering". Starting with EQ 1, which represents a perfect correlation of H and V photons between Alice and Bob, Alice can transform her detectors from the Plane-Polarized basis H/V to the Circularly-Polarized Basis R/L, where R and L are Right- and Left-circularly polarized photons. This transformation turns EQ 1 into:

ψ (EPR) = 1/√2 ( |RL> + |LR> )          (EQ4)

One interpretation of EQ 4 is that by Alice's choice to measure R/L polarization rather than H/V polarization, she was able to "steer" Bob's distant photons from a mixture of the H/V eigenstates into a mixture of the R/L eigenstates.

Can the same "steering mechanism" that works for the EPR state work its magic on the GHZ +1 state? If Alice can steer even the tiniest fraction of Bob's H/V photons into a R state and/or a L state, then transluminal signaling will be accomplished via the instant appearance of cross terms {of the form HV or VH) in Bob's two HV detectors.

Any physicist familiar with purported FTL signaling schemes will reflexively credit such a vaguely plausible argument as no more than a hopeful conjecture. And will suspend judgement until seeing some actual calculations. Omer at Jerusalem Center for Technology and Nick at Quantum Tantra Ashram in California are currently calculating the 16-term quantum correlation matrix that encodes the full behavior of the JJCCTT device for whatever detector choices Alice can make to try to signal Bob. These are very elementary calculations. But it is easy to make mistakes.

For the record: It was Omer who suggested that the GHZ + 1 system might be a promising candidate for FTL signaling. And it was Omer who proposed that Alice-controllable cross-terms in Bob's HV detectors might function as an FTL signal. And it was Nick who suggested that Alice might use Schrödinger "steering" to remotely create cross-terms in Bob's HV detectors. And Nick did the graphics.

RESULTS: Omer calculated the correlation matrix for the case where Alice chooses to measure R and L photons rather than H and V photons:

Now eight events can happen, but none produces Bob's HV or VH cross terms.

Next Omer considered rotating both Alice's detectors by 45 degrees so that Alice registers Diagonal (D) and Slant (S) polarized photons instead of H and V.

Again eight events can happen, but none produces Bob's HV or VH cross terms.

Neither of these two efforts on Alice's part succeeds in producing cross terms in Bob's detectors. And indeed a more general calculation that allows Alice to effect any possible combination of rotation and phase change in her detectors gives the same result. Nothing that Alice can do will produce an FTL signal in Bob's detector.

So the JJCCTT proposal fails as an FTL signaling device.

"Science is great, but it’s low-yield. Most experiments fail. That doesn’t mean the challenge isn’t worth it, but we can’t expect every dollar to turn a positive result. Most of the things you try don’t work out — that’s just the nature of the process. Rather than merely avoiding failure, we need to court truth." -- Ferric Fang, microbiologist

Citing the FTL signaling Impossibility proofs of Philippe Eberhard and many others, it would be easy to have anticipated our negative result, These well-known impossibility proofs state, in essence, that 1. YES, quantum Theory is non-local (by inspection); 2. YES, quantum Reality is non-local (proved by John Bell) but; 3. NO, the quantum Facts are as local as can be.

Despite the FTL nature of the Theory that represents the World, despite the FTL nature of the Reality which underlies the World, the World Herself displays not a speck of evidence for any FTL connections.

I wish to thank Omer at JCT for proposing this project and I appreciate the fun we had doing these calculations. But now, as in so many other encounters with quantum reality, we end up where we started, back home again at Physics for Beginners.

Omer and Nick: two collaborators separated by 10 time zones.