Tracking photons through the classic double-slit experiment

Jan 27, 2012 | Metaphysics

By Chris Lee | Published 7 months ago
Tracking photons through the classic double-slit experiment

This week, an exciting new experiment has been published in Science. Funnily enough, it repeats an experiment that is over 200 years old, and I am not certain that it teaches us anything new about the world. But it puts the weirdness of quantum mechanics on display for all to see. And it allows me to get sidetracked by history and generally ignore the work in question except in passing.

A bit of history
In 1803, Thomas Young published a paper on an experiment that has not just become famous, but is, in fact, the workhorse paper of quantum mechanics. In his experiment, light was passed through two closely spaced and narrow slits. Some distance after the slits, the light hit a screen so that the resulting intensity pattern could be observed.

Instead of two fuzzy stripes, a banded pattern was observed, one that could only be explained by assuming that light had a wave nature. With light assumed to be a wave, the waves’ amplitudes could sum to provide dark bands and light bands. This publication was the final salvo in the battle between physicists who believed that light was a particle and physicists who believed that light was a wave. Shortly after the publication of Young’s paper, the “wave physicists” accepted the surrender of the “particle physicists” at a secret ceremony at Cambridge, where the losing side handed over their tables of integrals and agreed never to use calculus again.

And there the story might have ended. In fact, for many such stories in physics, it does end there. But in 1924, a young physicist called de Broglie published the results of his work on the emerging theory of quantum mechanics. In his work, he posited that all particles had a wave-like nature—and, conversely, every wave has some particle-like properties. This was a revelation, and what better way to test it than with versions of Young’s double slit experiment?

Since then, physicists have used double-slit-style experiments to observe the wave-like properties of electrons, neutrons, whole atoms, and entire conglomerates of atoms in the form of Bose Einstein condensates. Clearly, matter has both particle-like and wave-like properties. De Broglie did not celebrate—instead he gave up on quantum mechanics as we know it today in disgust. Why?

The main reason boils down to this: the interference pattern can be built up from photons that are sent through the slits one at a time. They have no chance of interfering with each other, so the only way for the pattern to build up is for each photon to interfere with itself. And the only way for that to occur is if the photon somehow passes through both slits at the same time.

Once you add in a few other considerations, like when and how an experimenter chooses to make a measurement, you are left with an unsettling degree of non-locality and a sort of spooky instantaneous propagation of the wavefunction. It was enough to make a small group of physicists turn in their slide-rules and resign themselves to watching from the sidelines.

Back to the present experiment
The current experiment can be described as a physicist hearing that the photon went through both slits, agreeing, but then saying, “No, seriously, which slit did the photon go through?” Yes, there remains a visceral and fundamental discomfort with the realities of quantum mechanics. Nevertheless, this discomfort has led to a very clever experiment that comes as close as is possible to answering this question.

Any experiment that tells you with certainty which slit the photon passed through will not allow an interference pattern to build up. Even if the experiment doesn’t absorb the photon, it modifies its properties enough that it cannot interfere with itself; because we know that it went through just one of the slits, it shouldn’t interfere with itself. But what if we made a probabilistic measurement? One that just said something along the lines of “this photon went through the left slit with 75 percent probability.”

To do this, the researchers constructed a double slit experiment, but instead of placing a screen after it, they placed a crystal that has a different refractive index depending on how the light is polarized. Depending on the angle with which the photon passes through the crystal, its polarization gets a small rotation. After that, an optical element tries to set the polarization to a particular state, and, depending on where the photon originated from, will fail to a greater or lesser extent. Following that, the photon is deflected at some angle that depends on its polarization, allowing a simultaneous measurement of part of the photon’s momentum and where it hits on a screen (which is governed by the interference pattern).

Because all of these measurements are probabilistic, you never know which photon came from where, but over time you can build statistics that tell you where photons are most likely to be found. If you do this repeatedly, with the second half of the detection apparatus moved closer to and further away from the slits, you can build up photon trajectories.

It’s important to realize that these are not the trajectories of individual photons—instead they are more like probability clouds that tell you where photons are most likely to be found. And what do you know? Half the photons appear to have gone through one slit and half go through the other.

But, in fact, this is a lie. That photon still has to have gone through both slits. It is important to realize that a measurement has to produce a result. It is always going to find that the photon is somewhere, and that tells us very little about where it came from or where it is going to.

With that knowledge, it is hard to say what this experiment tells us that we didn’t know before. The only difference is that now we have both data and theory saying the same thing, which is important. But, there was so much data from so many different experiments that would have had to have been wrong for this experiment to turn up any other result that it is hard to be surprised.

That said, this demonstrates another aspect of control. These weak measurements only give partial information and are limited to statistical inferences. But they also result in measurements that cannot otherwise be made, making them an important new tool in the development of quantum apparatus.

http://arstechnica.com/science/news/2011/06/an-experiment-that-just-keeps-on-giving.ars

Tunnel-Realities and Imprints

Jan 27, 2012 | Metaphysics

Let’s try Dr. Leary‘s perspective on these mysteries.

To understand neurological space, Dr. Leary assumes that the nervous system consists of eight potential circuits, or “gears,” or mini-brains. Four of these brains are in the usually active left lobe and are concerned with our terrestrial survival; four are extraterrestrial, reside in the “silent” or inactive right lobe, and are for use in our future evolution. This explains why the right lobe is usually inactive at this stage of our development, and why it becomes active when the person ingests psychedelics.

We will explain each of the eight “brains” briefly.

I. THE BIO-SURVIVAL CIRCUIT

This invertebrate brain was the first to evolve (2 to 3 billion years ago) and is the first activated when a human infant is born. It programs perception onto an either-or grid divided into nurturing-helpful Things (which it approaches) and noxious-dangerous Things (which it flees, or attacks). The imprinting of this circuit sets up the basic attitude of trust or suspicion which will ever after trigger approach or avoidance.

II. THE EMOTIONAL CIRCUIT

This second, more advanced bio-computer formed when vertebrates appeared and began to compete for territory (perhaps 500,000,000 B.C.). In the individual, this bigger tunnel-reality is activated when the DNA master-tape triggers the metamorphosis from crawling to walking. As every parent knows, the toddler is no longer a passive (bio-survival) infant but a mammalian politician, full of physical (and psychic) territorial demands, quick to meddle in family business and decision-making. Again the first imprint on this circuit remains constant for life (unless brainwashed) and identifies the stimuli which will automatically trigger dominant, aggressive behavior or submissive, cooperative behavior. When we say that a person is behaving emotionally, egotistically or ‘like a two-year-old,’ we mean that s/he is blindly following one of the tunnel-realities imprinted on this circuit.

III. THE DEXTERITY-SYMBOLISM CIRCUIT

This third brain was formed when hominid types began to differentiate from other primate stock (circa 4-5 million B.C.) and is activated for the linear left-lobe functions of the brain, determines our normal modes of artifact-manufacture and conceptual thought, i.e., third circuit ‘mind.’

It is no accident, then, that our logic (and our computer-design) follows either-or, binary structure of these circuits. Nor is it an accident that our geometry, until the last century, has been Euclidean. Euclid’s geometry, Aristotle’s logic and Newton’s physics are meta-programs synthesizing and generalizing first brain forward-back, second brain up-down and third brain right-left programs.

IV. THE SOCIAL-SEXUAL CIRCUIT

The fourth brain, dealing with the transmission of tribal or ethnic culture across generations, introduces the fourth dimension, time.

Since each of these tunnel-realities consists of biochemical imprints or matrices in the nervous system, each of them is specifically triggered by neuro-transmitters and other drugs.

To activate the first braintake an opiate. Mother Opium and Sister Morphine bring you down to cellular intelligence, bio-survival passivity, the floating consciousness of the newborn. (This is why Freudians identify opiate addiction with the desire to return to infancy.)To activate the second tunnel-reality, take an abundant quantity of alcohol. Vertebrate territorial patterns and mammalian emotional politics immediately appear when the booze flows, as Thomas Nashe intuitively realized when he characterized the various alcohol states by animal labels: “ass drunk,” “goat drunk,” “swine drunk,” “bear drunk,” etc.

To activate the third circuit, try coffee or tea, a high-protein diet, speed or cocaine.

The specific neurotransmitter for circuit four has not been synthesized yet, but it is generated by the glands after pubescence and flows volcanically through the bloodstreams of adolescents.

NONE OF THESE TERRESTRIAL DRUGS CHANGE BASIC BIOCHEMICAL IMPRINTS. The behaviors which they trigger are those which were wired into the nervous system during the first stages of imprint vulnerability. The circuit II drunk exhibits the emotional games or cons learned from parents in infancy. The circuit III “mind” never gets beyond the permutations and combinations of those tunnel-realities originally imprinted, or abstractions associated with the imprints through later conditioning. And so forth.

But all this Pavlovian-Skinnerian robotism changes drastically and dramatically when we turn to the right lobe, the future circuits and extraterrestrial chemicals.

The four evolving future ‘brains’ are:

V. THE NEUROSOMATIC CIRCUIT

When this fifth “body-brain” is activated, flat Euclidean figure-ground configurations explode multi-dimensionally. Gestalts shift, in McLuhan‘s terms, from linear VISUAL SPACE to all-encompassing SENSORY SPACE.A hedonic turn-on occurs, a rapturous amusement, a detachment from the previously compulsive mechanism of the first four circuits. I turned this circuit on with pot and Tantra.

This fifth brain began to appear about 4,000 years ago in the first leisure-class civilizations and has been increasing statistically in recent centuries (even before the Drug Revolution), a fact demonstrated by the hedonic art of India, China, Rome and other affluent societies. More recently, Ornstein and his school have demonstrated with electroencephalograms that this circuit represents the first jump from the linear left lobe of the brain to the analogical right lobe.

The opening and imprinting of this circuit has been the preoccupation of “technicians of the occult”—Tantric shamans and hatha yogis. While the fifth tunnel-reality can be achieved by sensory deprivation, social isolation, physiological stress or severe shock (ceremonial terror tactics, as practiced by such rascal-gurus as Don Juan Matus or Aleister Crowley), it has traditionally been reserved to the educated aristocracy of leisure societies who have solved the four terrestrial survival problems.

About 20,000 years ago, the specific fifth brain neurotransmitter was discovered by shamans in the Caspian Sea area of Asia and quickly spread to other wizards throughout Eurasia and Africa. It is, of course, cannabis. Weed. Mother Mary Jane.

It is no accident that the pot-head generally refers to his neural state as “high” or “spaced-out.” The transcendence of gravitational, digital, linear, either-or, Aristotelian, Newtonian, Euclidean, planetary orientations (circuits I-IV) is, in evolutionary perspective, part of our neurological preparation for the inevitable migration off our home planet, now beginning. This is why so many pot-heads are STAR TREK freaks and science fiction adepts. (Berkeley, California, certainly the Cannabis Capital of the U.S., has a Federation Trading Post on Telegraph Avenue, where the well-heeled can easily spend $500 or more in a single day, buying STAR TREK novels, magazines, newsletters, bumper stickers, photographs, posters, tapes, etc., including even complete blueprints for the starship ENTERPRISE.)

The extraterrestrial meaning of being “high” is confirmed by astronauts themselves; 85% of those who have entered the free-fall zero gravity describe “mystic experiences” or rapture states typical of the neurosomatic circuit. “No photo can show how beautiful Earth looked,” raves Captain Ed Mitchell, describing his Illumination in free-fall. He sounds like any successful yogi or pot-head. No camera can show this experience because it is inside the nervous system.

FREE-FALL, AT THE PROPER EVOLUTIONARY TIME, TRIGGERS THE NEUROSOMATIC MUTATION, Leary believes. Previously this mutation has been achieved “artificially” by yogic or shamanic training or by the fifth circuit stimulant, cannabis. Surfing, skiing, skin-diving and the new sexual culture (sensuous massage, vibrators, imported Tantric arts, etc.) have evolved at the same time as part of the hedonic conquest of gravity. The Turn-On state is always described as “floating,” or, in the Zen metaphor, “one foot above the ground.”

VI. THE NEUROELECTRIC CIRCUIT

The sixth brain consists of the nervous system becoming aware of itself apart from imprinted gravitational reality-maps (circuits I-IV) and even apart from body-rapture (circuit V). Count Korzybski, the semanticist, called this state “consciousness of abstracting.” Dr. John Lilly calls it “metaprogramming,” i.e., awareness of programming one’s programming. This Einsteinian, relativistic contelligence (consciousness-intelligence) recognizes, for instance, that the Euclidean, Newtonian and Aristotelian reality-maps are just three among billions of possible programs or models for experience. I turned this circuit on with Peyote, LSD and Crowley’s “magick” metaprograms.

This level of brain-functioning seems to have been reported first around 500 B.C. among various “occult” groups connected by the Silk Route (Rome-North India). It is so far beyond the terrestrial tunnel-realities that those who have achieved it can barely communicate about it to ordinary humanity (circuits I-IV) and can hardly be understood even by fifth circuit Rapture Engineers.

The characteristics of the neuroelectric circuit are high velocity, multiple choice, relativity, and the fission-fusion of all perceptions into parallel science-fiction universes of alternate possibilities.

The mammalian politics which monitor power struggles among terrestrial humanity are here transcended, i.e., seen as static, artificial, an elaborate charade. One is neither coercively manipulated into another’s territorial reality nor forced to struggle against it with reciprocal emotional game-playing (the usual soap-opera dramatics). One simply elects, consciously, whether or not to share the other’s reality-model.

Tactics for opening and imprinting the sixth circuit are described and rarely experienced in advanced rajah yoga, and in the hermetic (coded) manuals of the medieval-Renaissance alchemists and Illuminati.

No specific sixth circuit chemical is yet available, but strong psychedelics like mescaline (from my 1962-63 “sacred cactus,” peyotl) and psilocybin (from the Mexican “magic mushroom,” teonactl) open the nervous system to a mixed-media series of circuit V and circuit VI channels. This is appropriately called “tripping,” as distinguished from straight-forward fifth circuit “turning on” or “getting high.”

The suppression of scientific research in this area has had the unfortunate result of turning the outlaw drug culture back toward fifth circuit hedonics and pre-scientific tunnel-realities (the occult revival, solipsism, Pop Orientalism). Without scientific discipline and methodology, few can successfully decode the often-frightening (but philosophically crucial) sixth circuit metaprogramming signals. Such scientists as do continue to study this subject dare not publish their results (which are illegal) and record ever-wider tunnel-realities only in private conversations—like the scholars of the Inquisitorial era. (Voltaire announced the Age of Reason two centuries too soon. We are still in the Dark Ages.) Most underground alchemists have given up on such challenging and risky self-work and restrict their trips to fifth circuit erotic tunnels.

The evolutionary function of the sixth circuit is to enable us to communicate at Einsteinian relativities and neuro-electric accelerations, not using third circuit laryngeal-manual symbols but directly via feedback, telepathy and computer link-up. Neuro-electric signals will increasingly replace “speech” (hominid grunts) after space migration.

When humans have climbed out of the atmosphere-gravity well of planetary life, accelerated sixth circuit contelligence will make possible high-energy communication with “Higher Intelligences,” i.e., ourselves-in-the-future and other post-terrestrial races.

It is charmingly simple and obvious, once we realize that the spaced-out neural experiences really are extraterrestrial, that getting high and spacing out are accurate metaphors. Circuit V neurosomatic rapture is preparation for the next step in our evolution, migration off the planet. Circuit VI is preparation for the step after that, interspecies communication with advanced entities possessing electronic (post-verbal) tunnel-realities.

Circuit VI is the “universal translator” often imagined by science-fiction writers, already built into our brains by the DNA tape. Just as the circuits of the future butterfly are already built into the caterpillar.

VII. THE NEUROGENETIC CIRCUIT

The seventh brain kicks into action when the nervous system begins to receive signals from WITHIN THE INDIVIDUAL NEURON, from the DNA-RNA dialogue. The first to achieve this mutation spoke of “memories of past lives,” “reincarnation,” “immortality,” etc. That these adepts were recording something real is indicated by the fact that many of them (especially Hindu and Sufis) gave marvelously accurately poetic vistas of evolution 1,000 or 2,000 years before Darwin, and foresaw Superhumanity before Nietzsche.

The “akashic records” of Theosophy, the “collective unconscious” of Jung, the “phylogenetic unconscious” of Grof and Ring, are three modern metaphors for this circuit. The visions of past and future evolution described by those who have had “out-of-body” experiences during close-to-death episodes also describes the trans-time circuit VII tunnel-reality.

Specific exercises to trigger circuit VII are not to be found in yogic teaching; it usually happens, if at all, after several years of the kind of advanced rajah yoga that develops circuit VI facility.

The specific circuit VII neurotransmitter is, of course LSD. (Peyote and psilocybin produce some circuit VII experiences also.)

Circuit VII is best considered, in terms of 1977 science, as the genetic archives, activated by anti-histone proteins. The DNA memory coiling back to the dawn of life. A sense of the inevitability of immortality and interspecies symbiosis comes to all circuit VII mutants; we now see that this, also, is an evolutionary forecast, since WE STAND RIGHT NOW ON THE DOOR-STEP OF EXTENDED LONGEVITY LEADING TO IMMORTALITY.

The exact role of the right-lobe circuits and the reason for their activation in the 1960s cultural revolution now becomes clear. As sociologist F.M. Esfandiary writes in UPWINGERS, “Today when we speak of immortality and of going to another world we no longer mean these in a theological or metaphysical sense. People are now traveling to other worlds. People are now striving for immortality. Transcendence is no longer a metaphysical concept. It has become reality.”

The evolutionary function of the seventh circuit and its evolutionary, aeon-spanning tunnel-reality is to prepare us for conscious immortality and interspecies symbiosis.

VIII. THE NEURO-ATOMIC CIRCUIT

Hold on to your hats and breathe deeply—this is the farthest-out that human intelligence has yet ventured.

Consciousness probably precedes the biological unit or DNA tape-loop. “Out-of-body experiences,” “astral projection,” contact with alien (extraterrestrial?) “entities” or with a galactic Overmind, etc., such as I’ve experienced, have all been reported for thousands of years, not merely by the ignorant, the superstitious, the gullible, but often by the finest minds among us (Socrates, Giordano Bruno, Edison, Buckminster Fuller, etc.). Such experiences are reported daily to parapsychologists and have been experienced by such scientists as Dr. John Lilly and Carlos Castaneda. Dr. Kenneth Ring has attributed these phenomena to what he calls, very appropriately, “the extraterrestrial unconscious.”

Dr. Leary suggests that circuit VIII is literally neuro-atomic—infra, supra and meta-physiological—a quantum model of consciousness and/or a conscious model of quantum mechanics by the turned-on physicists discussed previously (Prof. John Archibald Wheeler, Saul-Paul Sirag, Dr. Fritjof Capra, Dr. Jack Sarfatti, etc.) indicates strongly that the “atomic consciousness” first suggested by Leary in “The Seven Tongues of God” (1962) is the explanatory link which will unite parapsychology and paraphysics into the first scientific empirical experimental theology in history.

When the nervous system is turned on to this quantum-level circuit, space-time is obliterated. Einstein’s speed-of-light barrier is transcended; in Dr. Sarfatti’s metaphor, we escape “electromagnetic chauvinism.” The contelligence within the quantum projection booth IS the entire cosmic “brain,” just as the micro-miniaturized DNA helix IS the local brain guiding planetary evolution. As Lao-tse said from his own Circuit VIII perspective, “The greatest is within the smallest.”

Circuit VIII is triggered by Ketamine, a neuro-chemical researched by Dr. John Lilly, which is also (according to a wide-spread but unconfirmed rumor) given to astronauts to prepare them for space. High doses of LSD also produce some circuit VIII quantum awareness.

This neuro-atomic contelligence is four mutations beyond terrestrial domesticity. (The current ideological struggle is between circuit IV tribal moralists-or-collectivists and circuit V hedonic individualists.) When our need for higher intelligence, richer involvement in the cosmic script, further transcendence, will no longer be satisfied by physical bodies, not even by immortal bodies hopping across space-time at Warp 9, circuit VIII will open a further frontier. New universes and realities. “Beyond theology: the science and art of Godmanship,” as Alan Watts once wrote.

It is therefore possible that the mysterious “entities” (angels and extraterrestrials) monotonously reported by circuit VIII visionaries are members or races already evolved to this level. But it is also possible, as Leary and Sarfatti more recently suggest, that They are ourselves-in-the-future.

The left-lobe terrestrial circuits contain the learned lessons of our evolutionary past (and present). The right-lobe extraterrestrial circuits are the evolutionary script for out future.

Thus far, there have been two alternative explanations of why the Drug Revolution happened. The first is presented in a sophisticated way by anthropologist Weston LaBarre, and in an ignorant, moralistic way by most anti-drug propaganda in the schools and mass media. This explanation says, in essence, that millions have turned away from the legal DOWN drugs to illegal HIGH drugs because we are living in troubled times and many are seeking escape into fantasy.

This theory, at its best, only partially explains the ugliest and most publicized aspect of the revolution—the reckless drug abuse characteristic of the immature. It says nothing about the millions of respectable doctors, lawyers, engineers, etc., who have turned away from second circuit intoxication with booze to fifth circuit rapture with weed.

Nor does it account at all for the thoughtful, philosophical sixth circuit investigations of persons of high intelligence and deep sensibility, such as Aldous Huxley, Dr. Stanley Grof, Masters-Houston, Alan W. Watts, Carlos Castaneda, Dr. John Lilly and thousands of scientific and lay researchers on consciousness.

A more plausible theory, devised by psychiatrist Norman Zinberg out of the work of Marshall McLuhan, holds that modern electronic media have so shifted the nervous system’s parameters that young people no longer enjoy “linear” drugs like alcohol and find meaning only in “non-linear” weed and psychedelics.

This is certainly part of the truth, but it is too narrow and overstresses TV and computers without sufficiently stressing the general technological picture—the ongoing Science-Fiction Revolution of which the most significant aspects are Space Migration, Increased Intelligence and Life Extension, which Leary has condensed into his SMI²LE formula.

Space Migration plus Increased Intelligence plus Life Extension means expansion of humanity into all space-time. SM + I² + LE = infinity.

Without totally endorsing Charles Fort’s technological mysticism (“It steam-engines when it comes steam-engine time”), it is obvious that the DNA metaprogram for planetary evolution is far wiser than any of our individual nervous systems—which are, in a sense, giant robots or sensors for DNA. Early science-fiction of brilliant writers like Stapledon, Clarke, Heinlein; Kubrick’s 2001—all were increasingly clear DNA signals transmitted through the intuitive right lobe of sensitive artists, preparing us for the extraterrestrial mutation.

It is scarcely coincidental that mainstream “literary” intellectuals—the heir of the Platonic-aristocratic tradition that a gentleman never uses his hands, monkeys with tools or learns a manual craft—despise both science-fiction and the dope culture. Nor is it coincidental that the WHOLE EARTH CATALOGS – created by Stewart Brand, a graduate of Ken Kesey’s Merry Pranksters—are the New Testament of the rural drop-out culture, each issue bulging with tons of eco-technological information about all the manual, dextrous, gadgety know-how that Plato and his heirs consider fit only for slaves. Not surprisingly, Brand’s latest publication, CO-EVOLUTION QUATERLY, has been devoted to publicizing Prof. Gerard O’Neill’s space-habitat, L5.

Nor is it an accident that dopers seem to prefer science-fiction to any other reading, even including the extraterrestrial-flavored Hindu scriptures and occult-shamanic circuit VI-VIII trip-poets like Crowley and Hesse.

The circuit VI drugs may have contributed much to the metaprogramming consciousness that has led to sudden awareness of “male chauvinism” (women’s liberationists), “species chauvinism” (ecology, Lilly’s dolphin studies), “type-G star chauvinism” (Carl Sagan), even “oxygen chauvinism” (the CETI conference), etc. The imprinted tunnel-realities which identify one as “white-male-American-earthian” etc. or “black-female-Cuban” etc. are no longer big enough to enclose our exploding contelligence.

As TIME magazine said on November 26, 1973, “Within ten years, according to pharmacologists, they will have perfected pills and cranial electrodes of providing life-long bliss for everyone on Earth.” The 1960s hysteria about weed and acid was just the overture to this fifth circuit break-through. Nathan S. Kline, M.D., predicts real aphrodisiacs, drugs to speed up learning, drugs to foster or terminate any behavior. … Those who were jailed or beaten by cops in the 1960s were forerunners of the Revolution of Inner Technology.

STAR TREK is a better guide to the emerging reality than anything in the NEW YORK REVIEW OF BOOKS. The life-support and defense-system engineer, Scotty (circuit I), the emotional-sentimental Dr. McCoy (circuit II), the logical science officer Mr. Spock (circuit III) and the alternately paternalistic and romantic Captain Kirk (circuit IV) are perpetually voyaging through our future neurological history and encountering circuit V, VI, VII, and VIII intelligences, however crudely presented.

In short, the various levels of consciousness and circuits we have been discussing, and illustrating, are all biochemical imprints in the evolution of the nervous system. Each imprint creates a bigger tunnel-reality. In the Sufi metaphor, the donkey on the which we ride becomes a different donkey after each imprint. The metaprogrammer continually learns more and is increasingly able to be aware of itself operating. We are thus evolving to intelligence-studying-intelligence (the nervous system studying the nervous system) and are more and more capable of accelerating our own evolution.

Leary now symbolizes intelligence-studying-intelligence by the mark, I². On the lower levels, you see with one “I”, so to speak. On the higher levels, you see with many “I”s, and space-time shifts from three Euclidean dimensions to non-Euclidean multi-dimensionality.

By Robert Anton Wilson
The Eightfold Model of Human Consciousness

http://deoxy.org/8circuit.htm

Flash Animations for Physics

Jan 27, 2012 | Metaphysics

We have been increasingly using Flash animations for illustrating Physics content. This page provides access to those animations which may be of general interest. The animations will appear in a separate window.

The animations are sorted by category, and the file size of each animation is included in the listing. Also included is the minimum version of the Flash player that is required; the player is available free from http://get.adobe.com/flashplayer/. The categories are:

• Chaos
• Classical Mechanics
• Electricity and Magnetism
• Fluid Mechanics
• Micrometer Caliper
• Miscellaneous
• Nuclear
• Optics
• Oscilloscope
• Quantum Mechanics
• Relativity
• Sound Waves
• Vectors
• Waves

In addition, I have prepared a small tutorial in using Flash to do Physics animations. It contains screen shots and embedded Flash animations, so the file size is a 173k. You may view it in a separate window at http://faraday.physics.utoronto.ca/PVB/Harrison/Flash/Tutorial/FlashPhysics.html.

LInks to versions of these animations in other languages, other links, and license information appear towards the bottom of this page.

The Animations

There are 99 animations listed below. Some are simple; others are more complex. The most recent animations added to the list are identified.

Category	Title	Description/Comment
Chaos	Bunimovich Stadium	Illustrating the chaotic Bunimovich Stadium. Requires Flash 6; file size is 17k.	View
Chaos	Logistic Map	The logistic map, which demonstrates the bifurcations of the population levels preceding the transition to chaos. Requires Flash 6; file size is 15k.	View
Chaos	Lorenz Attractor	Looking at the Lorenz Attractor in a chaotic regime, allowing the attractor to be rotated. Requires Flash 6; file size is 550k.	View
Chaos	Three-body Gravitational Interaction	2 fixed suns and 1 planet. Initial conditions are controllable, and up to 4 different independent planets may be displayed. Requires Flash 6 and a computer with reasonable power; file size is 50k.	View
Classical Mechanics	Displacement and Distance	A simple animation showing the difference between the distance and the displacement. Requires Flash 5; file size is 5k.	View
Classical Mechanics	Constant Acceleration	1-dimensional kinematics of a body undergoing constant acceleration. Includes visually integrating the acceleration and velocity graphs, and visually differentiating the position and velocity graphs. Requires Flash 6; file size is 30k.	View
Classical Mechanics	Motion Animation	A car with a non-zero initial speed has a constant acceleration whose value can be controlled by the user. Requires Flash 6; file size is 27k.	View
Classical Mechanics	Dropping Two Balls Near the Earth’s Surface	Two balls falling near the Earth’s surface under the influence of gravity. The initial horizontal speed of one of the balls may be varied. Requires Flash 6; file size is 11k.	View
Classical Mechanics	Galilean Relativity	Illustrating Galilean relativity using his example of dropping a ball from the top of the mast of a sailboat. Requires Flash 6; file size is 22k.	View
Classical Mechanics	Foucault Pendulum	A simple snimation viewing a Foulcault Pendulum at the North Pole from an inertial frame above the Earth. See also the Foucault Pendulum animation in the Relativity section. Requires Flash 7 and ActionScript 2; file size is 1.3 M .	View
Classical Mechanics	Projectile Motion	Firing a projectile when air resistance is negligible. The initial height and angle may be adjusted. Requires Flash 6; file size is 36k.	View
Classical Mechanics	Kinematics of Projectile Motion	A visualisation exploration of the kinematics of projectile motion. Requires Flash 6; file size is 9k.	View
Classical Mechanics	The Monkey and the Hunter	An animation of the classic lecture demonstration. The actual demonstration is preferable if possible; then this animation can be given to the students for later review. Requires Flash 6; file size is 21k.	View
Classical Mechanics	Racing Balls	Two balls roll down two different low-friction tracks near the Earth’s surface. The user is invited to predict which ball will reach the end of the track first. This problem is difficult for many beginning Physics students. Requires Flash 6 Release 79; file size is 140k.	View
Classical Mechanics	Racing Skiers	The “Racing Balls” animation which is accessed via the above line sometimes triggers cognitive dissonance and rejection in beginning students. For some of these, changing the balls to skiers helps to clarify the situation, and that is what this animation does. The “Racing Balls” one should be used with students first. Requires Flash 6 Release 79; file size is 145k.	View
Classical Mechanics	Air Track Collisions	Elastic and inelastic collisions on an air track, with different masses for the target cart. Requires Flash 6; file size is 70k.	View
Classical Mechanics	Newton’s Cradle	A small animation of Newton’s Cradle, sometimes known as Newton’s Balls. Requires Flash 6; file size is 1k.	View
Classical Mechanics	Hooke’s Law	A simple animation illustrating Hooke’s Law. Requires Flash 6; file size is 13k.	View
Classical Mechanics	Coordinate System for Circular Motion	An unusual coordinate system for describing circular motion. Requires Flash 6; file size is 94k.	View
Classical Mechanics	Vertical Circular Motion	A mass is in circular motion in the vertical plane. We show the weight and force exerted by the tension in the string. Requires Flash 6; file size is 7k.	View
Classical Mechanics	Forces on a Pendulum	The weight, force due to tension, and total force exerted on the bob of a pendulum are shown. Requires Flash 6; file size is 8k.	View
Classical Mechanics	Motion in a Noninertial Frame	The motion of a ball in uniform circular motion is viewed by an observer in a rotating reference frame. Requires Flash 6; file size is 12j,	View
Classical Mechanics	Rolling Disc	A simple animation that traces the motion of a point on a rolling disc. Requires Flash 6; file size is 31k.	View
Classical Mechanics	Right-Hand Screw Rule	The direction of the angular velocity vector given by a right-hand screw rule. Requires Flash 6; file size is 196k. Also linked to from the Vectors section.	View
Classical Mechanics	Direction of the Angular Velocity Vector	A simple animation of the direction of the angular velocity vector. Requires Flash 6; file size is 125k.	View
Classical Mechanics	Curling	Curling rocks and tori sliding across surfaces. Requires Flash 6; file size is 601k.	View
Classical Mechanics	How Does a Cat Land on its Feet?	The saying is that cats always land on their feet. This animation explains how they do this. Requires Flash 6; file size is 81k.	View
Classical Mechanics	Precession of a Spinning Top	A simple animaiton of a spinning top which precesses. Requires Flash 5; file size is 739k.	View
Classical Mechanics	Simple Harmonic Motion I	Demonstrating that one component of uniform circular motion is simple harmonic motion. Requires Flash 6; file size is 10k.	View
Classical Mechanics	Simple Harmonic Motion II	Illustrating and comparing Simple Harmonic Motion for a spring-mass system and for a oscillating hollow cylinder. Requires Flash 5; file size is 20k.	View
Classical Mechanics	Damped Simple Harmonic Motion	The damping factor may be controlled with a slider. The maximum available damping factor of 100 corresponds to critical damping. Requires Flash 6; file size is 12k.	View
Classical Mechanics	Driven Simple Harmonic Motion	A harmonic oscillator driven by a harmonic force. The frequency and damping factor of the oscillator may be varied. Requires Flash 6; file size is 199k.	View
Classical Mechanics	Coupled Harmonic Oscillators	Two simple pendulums connected by a spring. The mass of one of the pendulums may be varied. Within mathematical rounding errors, the resolution on the screen of one pixel, and a frame rate of 12 frames per second the animation is correct, not an approximation. Requires Flash 6; file size is 47k.	View
Electricity and Magnetism	Coulomb’s Law	A simulation of an experiment to determine the dependence of the electrostatic force on distance. Requires Flash 6; file size is 15k.	View
Electricity and Magnetism	Comparing a DC circuit to the flow of water.	A simple DC circuit has a DC voltage source lighting a light bulb.Also shown is a hydraulic system in which water drives a turbine. The two systems are shown to be similar. Requires Flash 6; file size is 51k.	View
Electricity and Magnetism	A Light Switch	A simple animation of how a common light Switch works. Requires Flash 6; file size is 4kb.	View
Electricity and Magnetism	Field Lines	Illustrating representing an electric field with field lines. Requires Flash 5; file size is 22k.	View
Electricity and Magnetism	A Simple Buzzer	A simple buzzer consisting of a battery, a flexibile metal strip, a piece of iron, and some wire. Requires Flash 6; file size is 20k.	View
Electricity and Magnetism	Electric Field of an Oscillating Charge	An electric charge is executing simple harmonic motion, and the animation shows the electric field lines around it. Requires Flash 6 and a computer with reasonable power; file size is 40k.	View
Electricity and Magnetism	Electric and Magnetic Fields of an Oscillating Charge	A 3 dimensional animation of the “far” fields of an oscillating charge. Requires Flash 6; file size is 120k.	View
Electricity and Magnetism	Circular Polarisation	Circular polarisation generated from a linearly polarised electromagnetic wave by a quarter-wave plate. Requires Flash 6; file size is 785k.	View
Electricity and Magnetism	Spinning Charges and an Inhomogeneous Magnetic Field 1	A spinning charged object passes through an inhomogeneous magnetic field. This animation is also used in a discussion of the Stern-Gerlach experiment. Requires Flash 6; file size is 74k.	View
Electricity and Magnetism	Spinning Charges and an Inhomogeneous Magnetic Field 2	A spinning charged object passes through an array of 3 magnets each producing an inhomogeneous magnetic field. This animation is also used in a discussion of the Stern-Gerlach experiment. Requires Flash 6; file size is 79k.	View
Fluid Mechanics	Viscous Motion	Dropping a ball in a viscous liquid. The densities, liquid viscosity, and size of the ball are controllable. Requies Flash 6; file size is 55k.	View
Fluid Mechanics	Dropping a Ball From the CN Tower	A ball is dropped through the air from 350 m above the ground. The ball may be a billiard ball, a 5-pin bowling ball or a 10-pin bowling ball. The 5-pin bowling ball clearly shows the drag crisis. Requires Flash 7; file size is 133k.	View
Micrometer Caliper	Measuring with a Micrometer	A simple animation of using a micrometer to measure the width of a pencil. Requires Flash 5; file size is 13k.	View
Micrometer Caliper	An Exercise in Reading a Micrometer	Provides controls to position the micrometer, and when a button is clicked displays the reading. Requires Flash 5; file size is 30k	View
Miscellaneous	A Simple Piston and Boyle’s Law	A small animation showing a piston compressing a sample of gas. As the volume of the gas goes down, the density and therefore the pressure goes up. Requires Flash 5; file size is 3.9k.	View
Miscellaneous	Derivative of the Sine Function	An animation illustrating that the derivative of a sine function is a cosine. Requires Flash 6, file size is 20k.	View
Miscellaneous	Area of a Circle As a Limit	Illustrating that the area of a circle is a limit of the sum of the areas of interior triangles as the number of triangles goes to infinity. Requires Flash 5; file size is 12k.	View
Miscellaneous	Integration	Illustrating the meaning of the integral sign, including an example. Requires Flash 5; file size is 124k.	View
Nuclear	Scattering	Simulating nuclear scattering experiments by scattering ball bearings off targets. This is based on an experiment in the First Year Physics Laboratory at the University of Toronto. Requires Flash 6 Release 79; file size is 182k.	View
Nuclear	Nuclear Decays	The decay of 500 atoms of the fictional element Balonium. Uses a proper Monte Carlo engine to simulate real decays. Requires Flash 6, file size is 27k.	View
Nuclear	Pair Production	A simple illustration of electron-positron production and annihilation. Requires Flash 5, file size is 21k.	View
Nuclear	The Interaction of X-rays With Matter	Illustrating the 3 principle modes by which X-rays interact with matter. Requires Flash 6; file size is 47k.	View
Optics	Rotating a Mirror and the Reflected Ray	Illustrating that when a mirror is rotated by an angle, the reflected ray is rotated by twice that angle. Requires Flash 6; file size is 20k.	View
Optics	Reflection and Refraction	Illustrating reflection and refraction, including total internal reflection. Requires Flash 6; file size is 33k.	View
Optics	Object-Image Relationships	Ray tracing for a thin lens showing the formation of a real image of an object. Requires Flash 5; file size is 17k.	View
Optics	Using an Optical Bench	A simulation of an optical bench with a light source, object, thin lens and an image. The screen that displays the image is moved. Requires Flash 5, file size is 14k.	View
Oscilloscope	The Time Base Control 1	Shows the effect of changing the time base control on the display of an oscilloscope. There is no input voltage. Requires Flash 5; file size is 10k.	View
Oscilloscope	The Time Base Control 2	Shows the effect of changing the time base control on the display when there is an input voltage varying in time. Requires Flash 5; file size is 12k.	View
Oscilloscope	The Time Base Control 3	Shows the effect of changing the time base control on the display when there is an input voltage varying in time when the frequency of the voltage is high. Requires Flash 5; file size is 17k.	View
Oscilloscope	The Voltage Control	Shows the effect of changing the voltage control on the display. Requires Flash 5; file size is 10k.	View
Oscilloscope	The Trigger	Shows the effect of changing the trigger level on the display. Requires Flash 5; file size is 5.9k	View
Quantum Mechanics	The Bohr Model	The photon excitation and photon emission of the electron in a Hydrogen atom as described by the Bohr model. Requires Flash 6: file size is 77k.	View
Quantum Mechanics	Circular Standing Waves	Illustrating how thinking about the electron as a de Broglie wave “explains” the Bohr model.	View
Quantum Mechanics	Complementarity	Here we visualise a hydrogen atom, which consists of an electron in orbit around a proton. In one view the electron is a particle and in the other view it is a probability distribution. The reality is neither view by itself, but a composite of the two. Requires Flash 5; file size is 15k.	View
Quantum Mechanics	The Double Slit Experiment 1	The famous “Feynman Double Slit Experiment” for electrons. Here we fire one electron at a time from the electron gun, and observe the build-up of electron positions on the screen. Requires Flash 5; file size is 15k.	View
Quantum Mechanics	The Double Slit Experiment 2	Here we illustrate Complementarity using the double slit experiment. We view the path of the electron from the gun to the observing screen as a particle and as a wave. Requires Flash 5; file size is 33k.	View
Quantum Mechanics	Stern-Gelach Filters	Up to three Stern-Gerlach filters with user-controlled orientations are placed in an electron beam. Requires Flash 7; file size is 130k.	View
Quantum Mechanics	Bell’s Theorem	Based on an analysis by Mermin, this animation explores correlation measurements of entangled pairs. Requires Flash 6; file size is 38k.	View
Relativity	Michelson-Morley Experiment	A simple analogy involving two swimmers that sets up the Michelson-Morley Experiment. Requires Flash 6; file size is 15k.	View
Relativity	Time Dilation	A demonstration that the phenomenon of time dilation from the special theory of relativity necessarily follows from the idea that the speed of light is the same value for all observers. Requires Flash 6; file size is 55k.	View
Relativity	Deriving Length Contraction	A tutorial that shows how relativistic length contraction must follow from the existence of time dilation. Requires Flash 5; file size is 37k.	View
Relativity	Length Contraction is Invisible	This series of animations demonstrates that the relativistic length contraction is invisible. Requires Flash 5; file size is 90k.	View
Relativity	Deriving the Relativity of Simultaneity	A tutorial that shows how the relative nature of the simultaneity of two events must follow from the existence of length contraction. Requires Flash 5; file size is 39k.	View
Relativity	Twin Paradox	There are many ways of approaching this classic “paradox”. Here we discuss it as an example of the relativistic Doppler effect. Requires Flash 6; file size is 116k.	View
Relativity	Foucault Pendulum and Mach’s Principle	This began as an animation of the Foucault Pendulum, but then I generalised it to illustrate Mach’s Principle. See also the simple Foucault Pendulum in the Classical Mechanics section. Requires Flash 6, file size is 1.5M.	View
Relativity	Advance of the Perihelion	A simple animation showing Newton’s and Einstein’s predictions for the orbit of Mercury. Requires Flash 6; file size is 7.0k.	View
Sound Waves	Beats	Illustrating beats between 2 oscillators of nearly identical frequencies. Requires Flash 6; file size is 215k.	View
Sound Waves	Doppler Effect: Wave Fronts	Illustrating the wave fronts of a wave for a moving source. There are a few similar animations on the web: this is my re-invention of that wheel. Requires Flash 6; file size is 11k	View
Sound Waves	Doppler Effect	Illustrating the classical Doppler Effect for sound waves. Requires Flash 6; file size is 43k.	View
Sound Waves	Tuning Fork	A small animation of a vibrating tuning fork producing a sound wave. Requires Flash 5; file size is 2.7k.	View
Sound Waves	Pressure and Displacement Waves	This animation shows air molecules vibrating, with each molecule “driving” its neighbour to the right. It is used to illustrate that when the displacement wave is at a maximum then the density of the molecules, and thus the pressure wave, is at a minimum and vice versa. Requires Flash 5; file size is 30k	View
Sound Waves	Temperament	A very brief introduction to the physics and psychophysics of music, with an emphasis on temperament, the relationship between notes. Requires Flash 6 and sound; file size is 151k.	View
Vectors	Adding 2 Vectors	A simple demonstration of adding 2 vectors graphically. Also demonstrates that vector addition is commutative. Requires Flash 5; file size is 7k.	View
Vectors	Adding 3 Vectors	A simple demonstration of adding 3 vectors graphically. Also demonstrates that vector addition is associative. Requires Flash 5; file size is 10k.	View
Vectors	Subtracting 2 Vectors	A simple demonstration that subtracting 2 vectors graphically is the same as adding the first one to the negative of the second one. Requires Flash 5; file size is 4.5k.	View
Vectors	Component Addition	A simple demonstration that to add 2 vectors numerically, just add the cartesian components. Requires Flash 5; file size is 16k.	View
Vectors	Unit Vectors	A simple animation of unit vectors and vector addition. Requires Flash 6; file size is 12k.	View
Vectors	Dot Product	A simple demonstration of the relation between the dot product of 2 vectors and the angle between them. Requires Flash 6; file size is 8k.	View
Vectors	Right-Hand Screw Rule	The direction of the angular velocity vector given by a right-hand screw rule. Requires Flash 6; file size is 196k. Also linked to from the Classical Mechanics section.	View
Vectors	Cross Product	The direction of the cross product of 2 vectors is demonstrated. The magnitude shown is correct but not discused. Requires Flash 6; file size is 44k.	View
Waves	Traveling Waves	Illustrating the sign of the time term for traveling waves moving from left to right or right to left. Requires Flash 6; file size is 42k.	View
Waves	A Plane Wave Travelling Through Two Mediums	Illustrating the relation between wavelengths and frequencies of a wave when it travels from one medium to another. Requires Flash 6; file size is 5.4k.	View
Waves	Refraction	The previous animation shows wave fronts entering the mediums with a zero angle of inciddence. Here the angle of incidence is not zero. Requires Flash 6; file size is 11kb	View
Waves	Reflections From a Barrier	A wave is reflected from a barrier with a phase reversal. This is the behaviour for transverse waves and the displacement aspect of a longitudinal wave. Requires Flash 5; file size is 42k.	View
Waves	Reflections From Two Barriers	A wave is reflected back and forth between two barriers, setting up a standing wave. Requires Flash 5; file size is 41k.	View
Waves	Standing Waves With a Node on Both Ends	The first three standing waves for nodes at both ends. The frequencies of the waves are proportional to one over the wavelength. Requires Flash 5; file size is 11k.	View
Waves	Standing Waves With a Node on One End	The first three standing waves for a node at one end and an antinode at the other. The frequencies are proportional to one over the wavelength. Requires Flash 5; file size is 18k.	View

Other Languages and Links

These animations have been translated into Catalan, Spanish and Basque:

En aquest enllaç http://www.meet-physics.net/David-Harrison podeu trobar la versió al català de les animacions Flash de Física.

Las animaciones Flash de Física se han traducido al español, y están disponibles en esta dirección:
http://www.meet-physics.net/David-Harrison

Fisikako Flash animazioak euskeratu dira eta helbide honetan eskura daitezke
http://www.meet-physics.net/David-Harrison

Many animations have been translated into Greek by Vangelis Koltsakis. The web site is: http://users.sch.gr/ekoltsakis/nt/harrison/harrison.htm

Many animations have been translated into Dutch by Jacques Bijvoet, Dalton Lyceum Barendrecht. http://www.xs4all.nl/~jafrma/Harrison/

Most animations have been translated into Hungarian by Sandor Nagy, Eötvös Loránd University. Üdv a magyar látogatónak! Nagy Sándor egyik gyűjteményében (http://nasa.web.elte.hu/Harrisonia/) 68 magyarított animációmat találja meg magyar szövegkörnyezetben.

This “master index” page to my animations turns out to be linked to from a number of other sites. This surprises and delights me. A few of those sites are:

http://www.upscale.utoronto.ca/GeneralInterest/Harrison/Flash/

Zero-point energy

Jan 27, 2012 | Metaphysics

Zero-point energy is the lowest possible energy that a quantum mechanical physical system may have; it is the energy of its ground state. All quantum mechanical systems undergo fluctuations even in their ground state and have an associated zero-point energy, a consequence of their wave-like nature. The uncertainty principle requires every physical system to have a zero-point energy greater than the minimum of its classical potential well, even at absolute zero. For example, liquid helium does not freeze under atmospheric pressure at any temperature because of its zero-point energy.

The concept of zero-point energy was developed in Germany by Albert Einstein and Otto Stern in 1913, using a formula developed by Max Planck in 1900.^[1][2] The term zero-point energy originates from the German Nullpunktsenergie.^[1][2] The German name is also spelled Nullpunktenergie (without the “s”).

Vacuum energy is the zero-point energy of all the fields in space, which in the Standard Model includes the electromagnetic field, other gauge fields, fermionic fields, and the Higgs field. It is the energy of the vacuum, which in quantum field theory is defined not as empty space but as the ground state of the fields. In cosmology, the vacuum energy is one possible explanation for the cosmological constant.^[3] A related term is zero-point field, which is the lowest energy state of a particular field.^[4]

[edit] History

In 1900, Max Planck derived the formula for the energy of a single energy radiator, e.g. a vibrating atomic unit:^[5]

where h is Planck’s constant, ν is the frequency, k is Boltzmann’s constant, and T is the absolute temperature.

Then in 1913, using this formula as a basis, Albert Einstein and Otto Stern published a paper of great significance in which they suggested for the first time the existence of a residual energy that all oscillators have at absolute zero. They called this residual energy Nullpunktsenergie (German), later translated as zero-point energy. They carried out an analysis of the specific heat of hydrogen gas at low temperature, and concluded that the data are best represented if the vibrational energy is^[1][2]

According to this expression, an atomic system at absolute zero retains an energy of ½hν.

In 1916 Walther Nernst postulated that the vacuum of space is filled with zero-point electromagnetic radiation.^{[citation needed]}

[edit] Relation to the uncertainty principle

Zero-point energy is fundamentally related to the Heisenberg uncertainty principle. Roughly speaking, the uncertainty principle states that complementary variables (such as a particle’s position and momentum, or a field’s value and derivative at a point in space) cannot simultaneously be defined precisely by any given quantum state. In particular, there cannot be a state in which the system sits motionless at the bottom of its potential well, for then its position and momentum would both be completely determined to arbitrarily great precision. Therefore, the lowest-energy state (the ground state) of the system must have a distribution in position and momentum that satisfies the uncertainty principle, which implies its energy must be greater than the minimum of the potential well.

Near the bottom of a potential well, the Hamiltonian of a system (the quantum-mechanical operator giving its energy) can be approximated as

where E₀ is the minimum of the classical potential well. The uncertainty principle tells us that

making the expectation values of the kinetic and potential terms above satisfy

The expectation value of the energy must therefore be at least

where is the angular frequency at which the system oscillates.

A more thorough treatment, showing that the energy of the ground state actually is requires solving for the ground state of the system. See quantum harmonic oscillator for details.

[edit] Varieties

The concept of zero-point energy occurs in a number of situations.

In ordinary quantum mechanics, the zero-point energy is the energy associated with the ground state of the system. The professional physics literature tends to measure frequency, as denoted by ν above, using angular frequency, denoted with ω and defined by ω = 2πν. This leads to a convention of writing Planck’s constant h with a bar through its top to denote the quantity h/2π. In those terms, the most famous such example of zero-point energy is associated with the ground state of the quantum harmonic oscillator. In quantum mechanical terms, the zero-point energy is the expectation value of the Hamiltonian of the system in the ground state.

In quantum field theory, the fabric of space is visualized as consisting of fields, with the field at every point in space and time being a quantum harmonic oscillator, with neighboring oscillators interacting. In this case, one has a contribution of from every point in space, resulting in a calculation of infinite zero-point energy in any finite volume; this is one reason renormalization is needed to make sense of quantum field theories. The zero-point energy is again the expectation value of the Hamiltonian; here, however, the phrase vacuum expectation value is more commonly used, and the energy is called the vacuum energy.

In quantum perturbation theory, it is sometimes said that the contribution of one-loop and multi-loop Feynman diagrams to elementary particle propagators are the contribution of vacuum fluctuations or the zero-point energy to the particle masses.

[edit] Experimental observations

A phenomenon that is commonly presented as evidence for the existence of zero-point energy in vacuum is the Casimir effect, proposed in 1948 by Dutch physicist Hendrik B. G. Casimir (Philips Research), who considered the quantized electromagnetic field between a pair of grounded, neutral metal plates. The vacuum energy contains contributions from all wavelengths, except those excluded by the spacing between plates. As the plates draw together, more wavelengths are excluded and the vacuum energy decreases. The decrease in energy means there must be a force doing work on the plates as they move. This force has been measured and found to be in good agreement with the theory. However, there is still some debate on whether vacuum energy is necessary to explain the Casimir effect. Robert Jaffe of MIT argues that the Casimir force should not be considered evidence for vacuum energy, since it can be derived in QED without reference to vacuum energy by considering charge-current interactions (the radiation-reaction picture).^[6]

The experimentally measured Lamb shift has been argued to be, in part, a zero-point energy effect.^[7]

[edit] Gravitation and cosmology

Unsolved problems in physics

Why doesn’t the zero-point energy density of the vacuum change with changes in the volume of the universe? And related to that, why doesn’t the large constant zero-point energy density of the vacuum cause a large cosmological constant? What cancels it out?

In cosmology, the zero-point energy offers an intriguing possibility for explaining the speculative positive values of the proposed cosmological constant. In brief, if the energy is “really there”, then it should exert a gravitational force.^[8] In general relativity, mass and energy are equivalent; both produce a gravitational field. One obvious difficulty with this association is that the zero-point energy of the vacuum is absurdly large. Naively, it is infinite, because it includes the energy of waves with arbitrarily short wavelengths. But since only differences in energy are physically measurable, the infinity can be removed by renormalization. In all practical calculations, this is how the infinity is handled. It is also arguable that undiscovered physics relevant at the Planck scale reduces or eliminates the energy of waves shorter than the Planck length, making the total zero-point energy finite.

[edit] Free-energy devices

As a scientific concept, the existence of zero-point energy is not controversial although the ability to harness it is. In particular, perpetual motion machines and other power generating devices supposedly based on zero-point energy are highly controversial and, in many cases, in violation of some of the fundamental laws of physics.^{[citation needed]} However, many engineers claim to have invented such over-unity devices.

Thus, current claims to zero-point-energy-based power generation systems have the status of pseudoscience.^[9]

The discovery of zero-point energy did not alter the implausibility of perpetual motion machines. Much attention has been given to reputable science suggesting that zero-point-energy density is infinite, but in quantum theory, zero-point energy is a minimum energy below which a thermodynamic system can never go. Thus according to the standard quantum-theoretic viewpoint, none of this energy can be withdrawn without altering the system to a different form in which the system has a lower zero-point energy.

It is possible that the discovery of new physics will alter this conclusion. For example, in stochastic electrodynamics, the zero-point field is viewed as simply a classical background isotropic noise wave field which excites all systems present in the vacuum and thus is responsible for their minimum-energy or “ground” states. The requirement of Lorentz invariance at a statistical level then implies that the energy density spectrum must increase with the third power of frequency, implying infinite energy density when integrated over all frequencies.^[10] If this theory is correct, there is no reason that energy, or for that matter, momentum, could not be extracted, and would of course still leave infinite energy density and infinite momentum density, isotropic in all directions simultaneously, remaining in the wave field.

According to NASA, “the concept of accessing a significant amount of useful energy from the ZPE gained much credibility when a major article on this topic was recently [March 1st, 2004] published in Aviation Week & Space Technology, a leading aerospace industry magazine”.^[11]

The calculation that underlies the Casimir experiment, a calculation based on the formula predicting infinite vacuum energy, shows the zero-point energy of a system consisting of a vacuum between two plates will decrease at a finite rate as the two plates are drawn together. The vacuum energies are predicted to be infinite, but the changes are predicted to be finite. Casimir combined the projected rate of change in zero-point energy with the principle of conservation of energy to predict a force on the plates. The predicted force, which is very small and was experimentally measured to be within 5% of its predicted value, is finite.^[12] Even though the zero-point energy is theoretically infinite, there is as yet no practical evidence to suggest that infinite amounts of zero-point energy are available for use, that zero-point energy can be withdrawn for free, or that zero-point energy can be used in violation of conservation of energy.^[13]

http://en.wikipedia.org/wiki/Zero-point_energy