Stellerator: A Quantum Intimacy Machine
by Nick Herbert

 

ABSTRACT: I describe the operation of the naked-eye stellerator and its purported use for enhancing empathy between two people by quantum-entangling their minds via mutually coherent stimulation of their separated retinal tissues. This discussion of a rudimentary quantum intimacy machine is intended to stimulate the development of more sophisticated devices of a similar kind.

 

 

Nick Herbert
Box 261
Boulder Creek, CA 95006
quanta@cruzio.com
January 2006


STELLERATOR: A QUANTUM INTIMACY MACHINE

BRAND NEW KINDS OF UNION?
Quantum theory in principle describes the world as an unbroken wholeness that privileges no parts or partitions of the whole. Yet in practice quantum measurements appear no different from classical measurements—neither the measuring apparatus nor the scientists who design and observe them are ever seen to merge with the measured phenomena. Despite the theoretical inseparability of the quantum world, the clean separation of observer and observed remains a surprisingly stubborn fact that characterizes all physical measurements whether of gross material objects (the fall of an apple) or tiny quantum wavicles (the momentum of an electron).

A speculative venture I call “quantum tantra” aims to change all that. By taking advantage of the theoretical quantum inseparability of observer and observed, quantum tantra seeks a more direct unmediated union with nature than conventional measurements can provide. Perhaps such union will take place as a communion of human minds with heretofore undetectable minds inside inanimate objects. Once such intimate new channels into reality are opened, the fundamental physical variables of energy and entropy may be supplemented by the equally fundamental quantity of something resembling empathy.

Since union with non-human minds is bound to be confusing and disorienting, the first attempts at opening up new connections to nature will probably involve using the apparatus of quantum theory to link ordinary human minds in some novel and unexpected way—to, in effect, exploit some particularly quantum aspect of the world to build a “quantum-mechanical empathy machine”. This paper describes the motivations behind the design of one such putative quantum empathy machine—the naked-eye stellerator.

COHERENT LIGHT FROM STARS
The apparent angular size of the sun and the moon as viewed from Earth is about half a degree. The angular sizes of the planets, asteroids and moons in our solar system are smaller but are still resolvable with modest telescopes. On the other hand, the angular size of even the closest star is too small to be directly resolved by even the best terrestrial telescopes. For all practical purposes every star in the sky looks like a point of light.

The first measurement of the diameter of a star was not carried out directly but measured instead the “coherence radius” of the light from a particular star. The coherence radius is inversely related to the star’s angular size—the smaller the star, the larger the coherence radius of its light.

When one looks out over the ocean, one sees patches of water waves that are obviously travelling together as well as other patches that are travelling in some other direction. Within each patch the waves are said to be “coherent”, every part of the wave bears some definite phase relationship to every other part of the wave in the same patch. On the other hand, the phase relations between waves in different patches are random. Waves belonging to different patches are said to be “incoherent”.

The “coherence width” of a water-wave patch is the distance across the wave front—a distance measured perpendicular to the wave’s travel direction. The “coherence length” of a patch is the distance that the patch extends along its direction of travel.

It is the same with light from the stars. Every star produces patches of coherent light that travel to Earth (at light speed) with a particular coherence width and coherence length. The coherence width of starlight depends in a simple manner on the star’s apparent angular diameter. The relationship between a star’s angular diameter and its coherence width is derived from an elegant mathematical relationship called the Van Cittert-Zernike Theorem.

THE VAN CITTERT-ZERNIKE THEOREM
Light emitted from a laser is completely coherent. Light emitted from a star is completely incoherent. Yet by the time that starlight reaches the Earth it has somehow in its long journey organized itself into co-ordinated patches of waviness similar to the patches of coherent water waves in the ocean. How does initially incoherent starlight become coherent simply by travelling from there to here?

One of the most characteristic features of coherent light is that it is all travelling in one direction—hence the use of laser light as a pointer or surveying tool. A laser achieves this feat by only amplifying light that’s travelling in one particular direction. A star manages to get all its light travelling in a single direction by throwing away all light that isn’t headed towards your eye on Earth. A star, in a way, is a very inefficient laser.
Once the starlight is travelling in a particular direction the laws of wave motion will cause it to cohere for a particular distance across its wave front. Because of the simple filtering provided by its great distance all the starlight is travelling in almost the same direction and possesses a particular width of coherence.

The Van Cittert-Zernike Theorem allows you to calculate that coherence width. Here’s how.

Van Cittert and Zernike (two Dutch physicists) say this. Imagine, as did some ancient astronomers, that the sky is an opaque black sphere with holes punched in it through which shines some external fire. Now look at one of those holes. In reality that hole is a star emitting incoherent light but we are going to replace that star (in our imagination) with a completely coherent light source shining through the hole (same size as the star) in the black celestial sphere.

Because the light shining through the (circular) hole is coherent, it will produce a diffraction pattern on Earth of a well-known shape and size. The diffraction pattern from a circular hole is called the Airy pattern (after George Airy, British Astronomer Royal 1835) and looks like a central disk where most of the light is concentrated—a central disk surrounded by concentric rings of light and dark. It is a very familiar pattern. The same Airy pattern is produced in your eye by light diffracted by small particles on your cornea or in the eyeball’s fluids (so-called “floaters”). The radius R of Airy’s central disc depends only on the wavelength λ of the light and the angular diameter α (measured in radians) of the star as viewed from Earth. The formula for the Airy radius R is this:

AIRY RADIUS R = 1.22 λ/α

Now comes the good part. This calculation was carried out for a completely imaginary situation and gives the dimensions (on Earth) of a purely hypothetical diffraction pattern that would occur if completely coherent light (of wavelength λ) would happen to shine though a hole in the sky of angular dimensions α. What Van Cittert and Zernike showed mathematically is that the size and shape of this DIFFRACTION PATTERN is EXACTLY EQUAL to the size and shape of the COHERENCE PATTERN of light emitted incoherently from a disk the same size as the hypothetical hole in the sky.

In other words, Van Cittert and Zernike showed how to replace one problem—the calculation of a coherence width—with an easier problem—the calculation of a diffraction pattern—that gives the same numerical result. We can now use the above formula to calculate the coherence width of light from various stars—if we could measure the star’s apparent angular size. Which we can’t. The stars are too small.

Or we could measure the coherence width and use the above formula to calculate the angular diameter of the star. But how do you measure the coherence of starlight?

STELLAR INTERFEROMETERS
When light is coherent, parts of it can be made to “interfere” with other parts of the same light and produce (what else?) an “interference pattern”. Bringing together parts of incoherent light results in “no interference” or a random pattern of light. Interference patterns often take the form of rows of light and dark fringes and the contrast between these fringes is called the visibility V. Perfectly coherent light produces highly contrasting fringes with a visibility of 1.0. For incoherent light the visibility drops to zero.

The apparatus that brings different parts of a light wave together is called an interferometer. The first stellar interferometer consisted of a steel beam mounted crosswise across the opening of a large telescope. The beam carried two small mirrors that captured two chunks of starlight from the same star and deflected them into the telescope where they were combined to form an interference pattern. When the two mirrors are close together, they are both within the coherence radius of light from the star, but as they are moved apart the coherence lessens (according to Airy’s formula) and consequently the fringe visibility decreases. When the two mirrors are separated by the distance R (the radius of coherence), the coherence is zero and fringe visibility vanishes. In this manner the radius of coherence of a few very large stars was determined and for the first time the angular size of a star was (indirectly) measured.

Combining this angular size with the star's distance from Earth (obtained by astronomers using well-known methods) we obtain the star's physical diameter. Using this roundabout method we find that some stars are similar in size to Earth's sun while others are catagorized as "giants" and "dwarfs".

Only a few star diameters could be measured this way because most stars have coherence diameters larger than 10 feet and the physical difficulty of mounting large mirror frames stable to within a wavelength of light on the front of a big telescope soon placed a practical limit on this method of doing interferometry. Recall that measuring the coherence radius requires that your interferometer be large enough to detect the loss of coherence as the mirrors are separated. If the interferometer is significantly smaller than the star's radius of coherence, the fringe visibility will not measurably change as the mirrors are separated.

Conventional interferometry (so-called “amplitude interferometry”) combines the light beams before they are detected but another type of interferometry (called “intensity interferometry”) detects the light first and then looks for correlations between the resulting electronic signals from the light detectors. Intensity Interferometry was pioneered in the 1950s by Robert Hanbury Brown and Richard Twiss who mounted separate optical telescopes on railway cars in the Australian outback near Narrabri, New South Wales. The advantage of Intensity Interferometry is that it can achieve wide separations (and hence measure smaller stars) plus the fact that it is much easier to synchronize two electronic signals to nanosecond precision than it is to align two separate mirrors to within a wavelength of light. The disadvantage of intensity interferometry is that it only works for very bright stars and that (at first) some physicists believed that it was impossible in principle to observe the interference of intensities rather than amplitudes.

In spite of their critics, Hanbury Brown and Twiss were able to measure the coherence widths (hence the angular diameters) of a dozen or so of the brightest stars visible from Narrabri. (See following Table 1) Their work has inspired the use of intensity interferometry in many other fields including elementary particle physics and has led to the establishment of an active stellar interferometry group (Sydney University Stellar Interferometer--SUSI) at Narrabri in the Australian outback.

 

 

 

 

THE HANBURY BROWN-TWISS INTENSITY INTERFEROMETER AT NARRABRI, NEW SOUTH WALES, AUSTRALIA

 

 

TABLE 1: Angular Diameter and Coherence Radius of 12 Celestial Bodies
STAR NAME

MAGNITUDE

DISTANCE

(Light Years)

ANGULAR DIAMETER

(milli arc seconds)

COHERENCE RADIUS

(Feet)

The Sun -26.7 nearby 1/2 degree 0.08 mm
The Full Moon -12.7 nearby 1/2 degree 0.08 mm
Betelgeuse 0.41v 520 ly 50 mas 8 ft
Antares 0.92v 520 ly 40 mas 10 ft
Aldebaran 0.86v 68 ly 25 mas 16 ft
Arcturus 0.06 36 ly 22 mas 18 ft
Sirius -1.42 8.7 5.6 mas 70 ft
Canopus -0.72 98 ly 6.2 mas 65 ft
Procyon 0.37 11.3 ly 5.5 mas 70 ft
Vega 0.04 26.5 ly 3.1 mas 139 ft
Spica 0.91v 220 ly 0.80 mas 500 ft
Bellatrix 1.64 470 0.75 mas 530 ft

v = variable star
Adapted from “The Intensity Interferometer” Robert Hanbury Brown, Halsted Press (1974)


The usefulness of the Hanbury Brown-Twiss work for my purposes is their definitive determination of the coherence radiuses for a number of different bright stars. As shown in the above chart, these coherence radiuses range from a minimum of 8 ft (Betelgeuse) to more than 500 ft (Bellatrix). Note that the Sun and the Moon are so large that their coherence radiuses are less than a tenth of a millimeter. Light from these nearby bodies is not very coherent.

QUANTUM POSSIBILITY PANCAKES
Quantum theory describes light as a wave (of possibility) when it’s not being observed and a particle (of actuality) called the photon when it’s detected.

The coherence radius (8 ft in the case of Betelgeuse) is in some sense a measure of the width of the quantum possibility wave as it travels at the speed of light towards your eye. As this invisible quantum wave passes past your head, part of it enters into your open eyes, and represents a certain possibility that a molecule in your retina will be excited. If this happens the wave function is said to “collapse” and you see a flash of light. (Not quite correct. A single retinal cell can indeed be excited by a single photon of light but it actually takes about six roughly simultaneous retinal stimulations to create a perceived flash). When a dark-adapted eye (area about 1 square centimeter) is viewing a first magnitude star, the eye’s retina is being excited by about one trillion photons per second.

The width of one of these quantum waves in the case of Betelgeuse is 16 ft (twice the coherence radius) but how thick is this wave? The coherence length L of a light wave depends on its spectral purity—the narrower the band of optical frequencies, the longer the coherence length. The frequency range of starlight is determined by the human eye’s color response. For the human eye, the coherence length of starlight is about 1 micron (1 millionth of a meter). For comparison the diameter of a human hair is about 100 microns. If the star is viewed through a narrow-band filter, the coherence length could perhaps be increased by a factor of 100, resulting in a coherence thickness about the size of a human hair.

On a dark starry night, when you look up at Betelgeuse, from the point of view of quantum physics, what happens is this. Hurling down from the sky at the speed of light are trillions upon trillions of invisible “probability pancakes” each about 16 feet across and less than a hair’s breadth thick. Did I mention that each of these hair-thin optical pancakes is vibrating too?—buzzing at a frequency of about 1000 GHz.

A portion of one of these huge fast buzzy disks strikes the cornea of your eye, is refracted by its lenses, enters the optical fluid and strikes the retina, offering it one chance to absorb one photon. Most of these offers the retina refuses, but somewhere, something else contacted by the same possibility pancake accepts the offer by collapsing the 16-foot-wide disk of light into one tiny location. And in this manner the giant star Betelgeuse succeeds in having one photon of its light absorbed by some little bit of Earthly matter. In a few cases one of these pancakes collapses inside your eye and if these collapses happen often enough you are rewarded with the experience of a bright reddish star in the shoulder of the constellation of Orion, the Hunter.

THE NAKED-EYE STELLERATOR
Starlight is described by quantum theory as wide but very thin disk-shaped possibility waves travelling at the speed of light. When two detectors are illuminated by the same probability wave they are both in a sense competing for the same quantum of light. This quantum correlation (sometimes called “entanglement”) binds the two detectors together in a particularly quantum way. The fact that two optical detectors inside a star’s coherence width are quantum-connected is the basis for the operation of the intensity interferometer. Inside the coherence width all detectors are in a sense being dealt cards from the same deck. Detectors outside the coherence width are not quantum connected and are being dealt cards (photons) from different decks.

When two creatures (Kitty-chan and Keroppi, for example) are observing the same star while inside that star’s radius of coherence, their retinas are, in some sense “mutually entangled”. The (entirely speculative) premise underlying the quantum intimacy machine is that mutually entangled retinas produce mutually entangled minds. MERs => MEMs.

The retina is, after all, an extension of the brain. And the brain’s actions, in some mysterious way, are correlated with the mind. So, it’s not entirely implausible that quantum-correlated retinas could lead to quantum-correlated minds. It’s a hypothesis that’s never been tested and is now within reach of experimental verification. The operation of the naked-eye stellerator, the first proposed quantum intimacy machine, depends on this assumption—that entangled retinas produce entangled minds.

When two of you go out under the dark night sky, you are assailed by starlight from every direction, leading no doubt, to confusing messages at your retinas. The purpose of the stellerator is to reduce interstellar confusion by isolating one bright star in the visual field. I have found that a 1/4” diameter plastic tube about 1 foot long reduces the visual field to about 2.5 degrees, which is quite sufficient to isolate and center the same star’s image on the retinas of two different individuals.

The operation of the stellerator is as simple as its design. Prepare yourselves for intimacy in whatever manner seems appropriate. Go out under the night sky. Look at the same star through your individual plastic tubes. Pay attention to the star and to your state of mind. Take a deep breath and think about quantum theory.

Most of the possibility pancakes that pass through your two retinas will not trigger a response. But even without interaction each pancake is entangling your two retinas. Quantum mechanics is like that. The mere possibility that something could happen is effective in changing the actual world. As Henry Stapp, a physics professor at UC Berkeley puts it: “(Quantum) events which could have happened but did not, influence the world that does happen.”

As each disk of possibility passes through your retina—trillions and trillions every second—your retinas (and perhaps your minds as well) become more and more entangled. No one really knows what this means. We are at the very beginning of our investigation into the workings of quantum intimacy machines. The naked-eye stellerator is a primitive device whose intention is not really to fuse minds but merely to demonstrate the principle by which future, more sophisticated quantum intimacy machines might actually operate.

One problem with the stellerator, as presently realized, is that not only is your retina entangled with the retina of your mate, but with every light-absorbing object inside the same radius of coherence. Every chlorophyll molecule in every blade of grass, every stick, stone, flower or grain of sand within an 8-foot circle (in the case of the star Betelgeuse) is also becoming part of your intimate quantum unity as you look through your two little tubes at the same star. If quantum intimacy were so easy to achieve, you might possibly be in danger of falling into mystical union with every material object inside the magical circle of coherence. No two people who’ve every tested the naked-eye stellerator (Sun & Allen, for instance, pictured at the right) has ever reported this happening to them. But as with any new science, it is well to be aware of possible dangers so as not to be caught by surprise.

I am pleased to acknowledge the help and inspiration of Michael Murphy who invited physicists to Esalen Institute, Big Sur to explore the edges of reality, where the idea for the stellerator first arose and was light-heartedly tested in the hot tubs and on the cliffs near the Big House by many daring explorers including Ralph Abraham, Terence McKenna, Saul-Paul Sirag, Mary-Minn Peet, Beverly Rubik and Charles MacDermed, among others.

Nick Herbert
Box 261
Boulder Creek, California 95006
quanta@cruzio.com
January 2006