David Bohm's theory

His theory turned out to be so attractive that many felt: the Universe cannot be different than Bohm described it.

John Briggs, David PeetMirror Universe

Inseparable unity

One of the main creators of the amazing idea that the Universe is like a giant hologram is a student of Einstein - a professor at the University of London, one of the most prominent specialists in the field of quantum physics, David Bohm. As a graduate student, Bohm wrote his Ph.D. thesis under the supervision of Robert Oppenheimer.

After graduating from Pennsylvania State College, Bohm went to the University of California at Berkeley and worked at the Lawrence Radiation Laboratory in 1943, doing plasma research, before receiving his Ph.D.

There he encountered one striking example of quantum interconnection. Plasma is a partially or fully ionized gas in which the densities of positive and negative charges are almost the same (4). To his surprise, Bohm found that, once in the plasma, the electrons stopped behaving as separate particles and became part of the collective whole. While the individual motions of the electrons were random, a large number of electrons led to effects that were remarkably organized. Like some kind of amoeba, plasma constantly regenerated itself and surrounded all foreign bodies with a shell - it behaved similarly to a living organism when a foreign substance enters its cell. Bohm was so impressed with the organic properties of plasma that he often imagined the electron sea as a "living being" (5).

In 1947, Bohm accepted an offer of an assistantship at Princeton University (which was a recognition of his merits) and continued the study of the behavior of electrons in metals that had begun at Berkeley. Time and time again he found that the seemingly chaotic movement of individual electron-particles was capable of collectively producing a highly organized movement. Like the plasma he studied at Berkeley, he was faced with a situation where not only two particles coordinate their behavior: he saw a whole ocean of particles, each of which seemed to know what the other trillions of particles were doing. Bohm called such collective motions of particles plasmons, and their discovery brought him fame as an outstanding physicist.

Later, in 1951, when Oppenheimer came under intense pressure from Senator McCarthy's Un-American Activities Commission, Bohm was called in for questioning and refused to testify, causing him to lose his job at Princeton University and no longer teach in the United States, moving first to Brazil and then to London (5).

quantum potential . The collective movement of plasmons and the presence of a strange relationship between seemingly unrelated events at the intra-atomic level haunted Bohm. To answer this question, Bohm suggested that, firstly, elementary particles, contrary to Bohr's assertion, exist in the absence of observers and, secondly, beyond Bohr's reality, there is a deeper reality at the subquantum level, not yet discovered by science.

Based on these hypotheses, Bohm found that many obscure phenomena in quantum physics can be explained by postulating the existence of some hypothetical field that, like gravity, pervades all space. However, unlike gravitational, magnetic and other fields, the action of the new field does not weaken with distance, and its force is distributed evenly throughout space. Bohm named this field quantum potential and postulated it as a wave information field controlling electrons.

The collective activity of the electrons in the plasma can be explained by the coordinating action of the quantum potential, which provides the electrons with information so that they know about everything that happens around them.

Such an understanding is analogous to the movement of a ship in the ocean, controlled from the shore using a radio signal. The ship moves due to its own energy, but receives instructions for maneuvering with the help of radio waves, which carry only information. Similarly, the quantum potential provides the "course change instructions" required for an electron to interact with its environment.

As Bohm points out, such “electrons do not scatter, because thanks to the action of the quantum potential, the entire system acquires a coordinated movement - this can be compared to a ballet in which the dancers move synchronously, unlike a disorganized crowd ... Such quantum whole states are more like the organized behavior of the parts of a living being than the functioning of individual parts of the machine” (5).

A close study of the properties of the quantum potential led him to an even more radical departure from orthodox thinking. Contrary to classical science, which has always considered a system as a simple addition of the behavior of its individual parts, the quantum potential hypothesis defined the behavior of the parts as a derivative of the whole. Moreover, it not only confirmed Bohr's statements that elementary particles are not independent "particles of matter", but also postulated the whole as the primary reality.

Even more surprising was the fact that at the level of quantum potential there is no localization at all, all space becomes one and it becomes meaningless to talk about spatial separation. This explains such a property of space as non-locality.

The non-local aspect of the quantum potential allowed Bohm to explain the connection between paired particles without violating the special theory of relativity, which prohibits exceeding the speed of light. To clarify, he offered the following example: imagine a fish swimming in an aquarium. Imagine also that you have never seen a fish or an aquarium before and that the only information about them you get through two television cameras, one of which is directed at the end of the aquarium, and the other looks from the side. If you look at two television screens, you can mistakenly assume that the fish on the screens are different. Indeed, since the cameras are placed at different angles, each of the images will be slightly different. But as you continue to watch the fish, you eventually realize that there is some connection between them. If one fish turns, the other makes a slightly different, but synchronous turn. If one fish is shown frontally, another is shown in profile, etc. If you are not familiar with the general situation, you may mistakenly conclude that the fish coordinate their movements instantly, but this is not the case. There is no instant connection between them, because at a deeper level of reality - the reality of the aquarium - there is one, not two fish (5).

According to Bohm, elementary particles are connected in the same way as images of one fish in two sides of an aquarium. Although particles like electrons appear to be separate from each other, at a deeper level of reality - the reality of an aquarium - they are only two aspects of a deep cosmic unity.

Thus, Bohm sees non-local connections as an essential part of some kind of unity, believing that deeper than the level of probability there is a deeper “level of non-manifestation” that is inherent in the cosmic network of relationships (3).

Bohm's views on "an inseparable unity" contradicted the mechanistic point of view of scientists who viewed the universe as a universal machine. The world was reduced to a set of basic elements, which are particles (electrons, protons, quarks, atoms, etc.) and various types of fields continuously extending through space. All these elements are fundamentally external to each other, and not only in that they are separated in space, but also in that the fundamental nature of each is independent of the fundamental nature of the neighbor, and the forces of interaction do not affect the deeply internal nature of the elements. . Such a structure is more likely to be compared with a machine than with a single organism.

Of course, the mechanistic approach allows for the existence of a biological organism (for it is obvious) in which parts can profoundly influence the very nature of other parts and the whole organism, since they are fundamentally related both to each other and to the whole. But even in this case, everything ultimately comes down to molecules, such as DNA, RNA, proteins, etc. Even if some new properties and qualities arise in the body, they are always implied in molecules. So in the end the organism is just a convenient way to talk about a large number of molecules.

The fact that modern science does not have a language for describing the integral world was discussed at the conference "Scientific results of the second millennium: a view from Russia", which was held at the end of 2000 in St. Petersburg. The scientists summarized:

Science has decomposed the world into elementary bricks. Studying the organism, she descended to the cell. However, current data in the field of molecular biology show that in order to describe only one single organic cell, it will take a whole human life, with the expectation that a person will describe it 24 hours a day. It turns out that the cell represents the Universe, and the way of crushing the world into bricks for the purpose of its knowledge is a dead end. The world, broken into pieces, has become as incomprehensible as a master's masterpiece cut into millions of pieces. The process of cognition has stopped (6).

The quantum potential hypothesis postulated the existence of the whole and its parts, which are correlative categories: speaking of one, one should mean the other. Something can only be a part if there is a whole of which it can be a part.

Bohm published his alternative vision of quantum theory in print in 1952.

Reaction to his work was mostly negative. Some physicists believed so strongly that no alternatives were possible that they dismissed his theory without consideration. Others hurled violent attacks at her. In the end, all objections were reduced to philosophical disagreements: Bohr's point of view was so rooted in physics that Bohm's alternative approach seemed more than heresy.

Despite the sharpness of the attacks, Bohm believed that there was a deeper reality than Bohr admits, and he calmly continued to polish his alternative approach to quantum physics.

However, the more than restrained reaction of the scientific community to his ideas regarding unity and nonlocality, as well as the uncertainty of further research in this direction, forced him to switch to another topic. In the 1960s, he took up a close study of order.

About order. In classical science, all objects were usually divided into two categories: objects that have order in their parts, and objects whose parts are in a disordered, or random, state. Snowflakes, computers, and living beings are all examples of ordered objects. Scattered coffee beans on the floor, debris after an explosion, numbers generated by a tape measure are examples of disordered objects.

The question arises: what is order? Generally speaking, almost everyone has some idea of ​​the order. We are all familiar with the order of numbers, the order of points in a line, the order of the functioning of an organism, the many orders of tones in music, the order of time, the order of language, the order of thinking, etc. However, according to Bohm, it is impossible to give a generalized and intelligible concept of order ( 7).

As Bohm delved more and more into the subject he was studying, he began to realize that there were various degrees of order. Some things are more ordered than others, and the hierarchy of order is infinite in the universe. From this, Bohm concluded that what seems disordered to us may not be such at all. Perhaps the order of these things is "of such an infinite magnitude" that they only seem to be disordered, chaotic. Today, many scientists share a similar point of view on chaos. For example, the American scientist B. Williams writes: “Chaos is a higher form of order, where randomness and unsystematic impulses become an organizing principle rather than more traditional cause-and-effect relationships in the theories of Newton and Euclid” (8).

While immersed in these thoughts, Bohm once saw a device in a BBC television program that further developed his ideas. The device was a specially designed vessel containing a large rotating cylinder. The space of the vessel was filled with glycerine - a dense, transparent liquid - with a drop of ink floating motionlessly in it. Bohm was interested in the following: when the handle of the cylinder was turned, the ink drop spread over the glycerin and seemed to be dissolved. But as soon as the pen was turned in the opposite direction, the weak ink trajectory slowly disappeared and turned into the original drop (5).

Bohm later wrote:

This experience amazed me because it corresponded exactly to my idea of ​​order, that is, when the ink spot spread, it still had a “hidden” (that is, unmanifested) order, which appeared as soon as the drop was restored. On the other hand, in our ordinary language, we would say that the ink was in a state of "disarray", having dissolved in glycerin. This experience led me to a new definition of order (5).

This discovery greatly encouraged Bohm. Finally, he found a metaphor for understanding order, which not only allowed him to bring together all his disparate thoughts over many years, but also provided a powerful analytical apparatus at his disposal. That metaphor was the hologram.

Bohm became an adherent of the holographic theory of the Universe after being disappointed with the generally accepted theories, which were unable to provide a satisfactory explanation for the phenomena of quantum physics.

Hologram and its properties

Holography is a method of recording and restoring a wave field, based on the registration of an interference pattern, which is formed by two waves: a wave reflected by an object illuminated by a light source (object wave), and a wave coherent with it, coming directly from the source (reference wave). The registered interference pattern is called a hologram (4).

The foundations of holography were laid by the physicist Denis Gabor (later a Nobel laureate) in 1948. When Gabor first came up with the idea of ​​holography, he didn't think about lasers. His goal was to improve the electron microscope, at that time a rather simple and imperfect device. Gabor proposed to record information not only about the amplitudes, but also about the phases of electron waves by superimposing a coherent (synchronous) reference wave on the object wave. He used a purely mathematical approach based on the calculus invented in the 18th century by the French mathematician Jean Fourier.

Mathematical support of the hologram. J. Fourier developed a mathematical method for translating a pattern of any complexity into the language of simple waves and showed how these waveforms can be transformed into an original pattern. To understand the essence of such a transformation, let us recall that a television camera, for example, translates a visual image into a set of electromagnetic waves of different frequencies. And the TV with the help of an antenna perceives this packet of waves and translates them into a visual image. Like the processes in a television camera and television, the mathematical apparatus developed by Fourier transforms patterns. The equations used to convert patterns to waveforms and back are known as Fourier transforms. It was they who allowed Gabor to translate the image of an object into an interference “spot” on a holographic film, and also to invent a way to convert interference patterns back into the original image.

However, the lack of powerful sources of coherent light did not allow Gabor to obtain a high-quality holographic image.

Holography experienced a second birth in 1962–1963, when the American physicists E. Leith and Y. Upanieks used a laser as a source and developed a scheme with an inclined reference beam (4).

Let's take a closer look at what a hologram is. A hologram is based on interference, that is, a pattern resulting from the superposition of two or more waves. If, for example, a pebble is thrown into a pond, it will produce a series of concentric, divergent waves. If we throw two pebbles, we will see, respectively, two rows of waves, which, diverging, are superimposed on each other. The resulting complex configuration of intersecting peaks and valleys is known as an interference pattern.

Any wave phenomenon, including light and radio waves, can create such a picture. The laser beam is especially effective in this case, since it is an exceptionally pure, coherent light source. The laser beam creates, so to speak, a perfect pebble and a perfect pond. Therefore, only with the invention of the laser was it possible to obtain artificial holograms.

Two beams of light are directed from the laser source: at the object and at the mirror. The waves reflected from the object (subject) and from the mirror (reference) are directed onto a photographic plate with a light-sensitive surface, where they are superimposed on each other. The resulting complex interference pattern, containing information about the object, is a holographic photograph, which outwardly has no resemblance to the object being photographed. It can be a system of alternating light or dark rings, straight or wavy stripes, and also have a spotted pattern (9).

Hologram Properties . If the hologram is illuminated by a reference wave from the source, then as a result of light diffraction on the interference structure of the hologram, a copy of the object wave is restored in the diffraction beam, and at some distance an imaginary volumetric (wave) image of the object appears, which is difficult to distinguish from the original (4). The three-dimensionality of the image of such objects is surprisingly real. You can walk around the holographic image and see it from different angles, as if it were a real object. However, when you try to touch the hologram, your hand will simply pass through the air and you will not detect anything, just as, for example, you do not detect radio waves in space with your hand.

Three-dimensionality is not the only remarkable property of a hologram. If you cut off half of the holographic film and then illuminate it with a laser, the image that appears not far away will still be intact. Even if only a small piece of holographic film remains, then from it, with appropriate lighting, a complete image of the object will appear. True, the smaller the piece, the worse the image quality. Unlike ordinary photographs, each small piece of holographic film contains all the information of the whole.

In addition to a three-dimensional image, a hologram has another unique property: several images can be sequentially recorded on one photographic plate only by changing the angle at which two lasers irradiate this plate. And any image recorded in this way can be restored by simply illuminating this plate with a laser directed at the same angle at which the two beams were originally located. The researchers calculated that using this method, one square centimeter of film could hold as much information as ten Bibles!

Thus, holograms have a fantastic ability to store information. Holographic coding of information is amazingly effective. None of the existing means of storing information can be compared with the amount of information that can be recorded by a hologram. The efficiency of information coding using a hologram is so great that it can be compared with the efficiency of information storage in human memory (10).

If two coherent waves are superimposed on each other in space (and not on a photographic plate), a so-called information matrix, or interferogram, containing information in an encoded form, is formed.

Hidden Order and Revealed Reality

As soon as Bohm began to carefully study the hologram, he saw that it represented a new way of explaining order. The interference patterns recorded on a piece of holographic film appear chaotic to the naked eye, like an ink drop spread in glycerin, which, however, has a hidden (implicit) order. According to Bohm, the film also contains a hidden order, for the image encoded in the interference patterns is a hidden plenitude folded in space. And the hologram projected by the film has an expanded order, because it represents an unfolded and visible version of the image. Both phenomena have a hidden, or coiled, order, reminiscent of the order of a plasma composed of seemingly random individual behavior of electrons. Since each part of the holographic film contains the entirety of information, then, therefore, this information is distributed non-locally. And that wasn't the only brilliant guess the hologram produced.

The more Bohm thought about this phenomenon, the more he became convinced that the universe actually uses the holographic principle in its work. It is permeated with countless different waves of different levels of vibration - from low-frequency electromagnetic to high-frequency torsion. Each wave of the same kind forms an interferogram with a coherent wave of the same kind. Thus, the Universe is a huge floating hologram, at any point of which information about the entire World is contained, but it is encoded in holographic interference microstructures (5).

And if the Universe is organized in accordance with the holographic principle, it must naturally have non-local properties. This holographic universe eventually allowed Bohm to create a coherent and strikingly radical theory.

The hypothesis of the scientist, according to which our Universe is like a giant hologram, can be assessed as stunning. After all, this means that the world in which we live can actually be a subtle and complex illusion like a holographic image (7). Beneath it is a deeper order of being - an infinite and primordial level of reality - from which all objects are born, including the visibility of our physical world, just as a hologram is born from a piece of holographic film.

In the VI century BC, the great Egyptian priest Hermes Trismegistus, telling his son Tatu about God, said:

... every appearance is created, for it is manifested; but the invisible is always there, needing no manifestation. He is always there, and He makes all things manifest. Invisible, because eternal, He, without showing Himself, causes everything to appear. Uncreated, He manifests all things in appearance; appearance, however, is inherent only in created things, it is nothing other than birth. He begets, Himself being unbegotten; It does not appear to us in a sensible image, but it gives sensible images to all things. Only born beings appear in sensual images: indeed, coming into life is nothing else than appearing in sensations... Only thought sees the invisible, for it itself is also invisible (11).

Isn't it true that there is much in common between the explanations of Trismegistus and the modern physicist Bohm?

Today, there is already a lot of evidence to suggest that our world and everything in it, from electrons and snowflakes to comets and shooting stars, are just ghostly projection pictures projected from some deep level of reality that is far beyond our own. the ordinary world - so far away that the very concepts of time and space disappear there. The Universe, and this is confirmed by a number of serious studies, is a giant hologram, where even the tiniest part of the image carries information about the general picture of being (Everything in Everything!) and where everything, from small to large, is interconnected and interdependent. According to many modern scientists and thinkers, the holographic model of the Universe is one of the most promising pictures of reality that we have at our disposal today.

Bohm published his first articles on the holographic nature of the universe in the early 1970s, and in 1980 he published a completed work entitled Completeness and Implicative Order. The book not only brings together a myriad of ideas, it gives a radically new picture of the universe.

Since everything in the cosmos consists of a continuous holographic fabric imbued with an implicative (hidden) order, it is meaningless to talk about the Universe consisting of “parts”. The universe, according to Bohm, is a single whole!

It is the inviolable integrity of the Universe that unites two great theories - the theory of relativity and the theory of quantum physics, although their basic physical concepts are rather contradictory. Relativity requires strong continuity, strong determinism, and strong locality. In quantum mechanics, the exact opposite is asserted: discontinuity, indeterminism, nonlocality. But the inviolable integrity of the universe underlies both theories.

Holodynamics or holomotion . Since the term "hologram" usually refers to a static image and does not convey the dynamics and active nature of the endless folding and unfolding that continuously creates our Universe, Bohm prefers to define the Universe not as a hologram, but as "holodynamics" or "holomotion".

The photographic plate example was about the static recording of light, which is the movement of waves. However, reality, according to Bohm, is the movement itself, in which information about the whole object is dynamically folded in every part of space, and then unfolded in the image. A similar principle of enfoldment and unfoldment can be observed in a wide range of experiences. For example, light from all parts of a room contains information about the entire room and actually wraps it up in that tiny beam that passes through the pupil of our eye. And the brain and somehow consciousness unfold this information so that we get the feeling of a whole room. Similarly, light entering a telescope wraps up information about the entire universe of space-time. In other words, the movements of all kinds of waves roll up the whole in every part of the Universe (7).

A simpler example of folding and expanding information can be seen in the operation of a television camera and television. So, the camera, which the operator uses to shoot any object, convolves information about the object, translating the image into a system of electromagnetic waves of various frequencies. The television receiver expands this information on the screen. In old TVs, there was even such an image adjustment as “sweep”: when the setting went astray and the image in the full sense of the word collapsed “to a point”, the “sweep” adjustment brought the image back to normal, and it unfolded literally before our eyes in full screen.

Unmanifested or total potentiality is an infinite number of possibilities for the manifestation of experiences, tendencies that are realized in the process of movement of the energy of the Universe, aimed at realizing oneself as a whole. In fact, this movement (holomotion) is a dynamic phenomenon, on the basis of which all forms of the material Universe are formed, and is the process of awareness itself (7).

According to Bohm, it is the movement of folding and unfolding, which he called “holomotion”, that represents the original reality, and objects, essences and forms are relatively stable independent and autonomous features of holomotion, in exactly the same degree as, for example, a whirlpool - a similar feature of current fluid motion.

By coining the term holomotion, Bohm showed that reality is structured like a hologram. He argues that the visible reality that we know and feel is a holographic projection of a hologram formed in an invisible, hidden sphere - a coiled order of higher space. The folded order takes on a concrete form or unfolds into what we know as reality, which Bohm calls the expanded order.

With this approach, the electron is no longer a separate object, but a set that has arisen as a result of the folding of space. When an instrument detects the presence of a single electron, it means that only one aspect of the electron set is manifesting at a given moment, similar to how an ink drop is detected from a glycerin stain. If an electron appears to be moving, it is caused by a continuous series of such folds and unfolds.

Thus the electron and all other particles, like a geyser spouting from the earth, are sustained by a continuous influx from the hidden order. It is easy to imagine how an electron unfolds from this background in some particular position, then coils into it again, and another nearby unfolds and coils again, and another, and another - and gradually it begins to look like the trace of one electron. You can see the discontinuity here, as the deployment sites don't have to be continuous. It becomes clear how discontinuity and continuity, undulating qualities, can come from deployment. It is the constant and dynamic exchange between the two orders that explains how particles can change from one type to another, how a quantum appears now as a particle, now as a wave. In a word, elementary particles, like everything in the Universe, exist no more independently of each other than the elements of an ornament on a carpet.

Both aspects are always present in a collapsed form in the entire quantum set, and only the way the observer interacts with this set determines which aspect will appear and which will remain hidden (7).

In his general theory of relativity, Einstein literally stunned the world by declaring that space and time are not separate, but smoothly connected entities, flowing as parts of a whole, which he called the space-time continuum. Bom takes another giant step forward. He says that everything in the universe is part of a continuum. This is a very profound conclusion.

“Despite the seeming separation of things at the explicative level, everything is a continuously distributed reality, eventually ending with the implicative and explicit (hidden and open) orders merging with each other. Let's dwell on this for a moment. Look at your hand. Now look at the light coming from the lamp behind you. And the dog sitting at your feet. You are not just made of the same entity: you are the same entity. One entity. Indivisible. A huge Something that stretched out its countless arms and appendages into apparent objects, atoms, restless oceans and twinkling stars of space” (5).

Parts and fragments . Indeed, if all elementary particles are interconnected at a deeper level, then the electrons of every cell of our body are connected with the electrons of every animal, every fish, every heart that beats, every star that twinkles in the sky. Everything interpenetrates everything, and although human nature tends to divide everything, dismember, sort out all the phenomena of nature, all divisions are artificial, nature, in the final analysis, is an inseparable web.

As human beings, we are all part of a whole that we externally perceive as the universe. But the stiffness and limitations of our ordinary perceptual systems delude us into believing that we are separate. We perceive ourselves as separate not only from other human beings, but also see ourselves as different from all sentient life forms. We have trapped ourselves in imagining that space and time are the only coordinates in which we can define our existence.

But time and space in the holographic world cannot be taken as a basis, because such a characteristic as position does not make sense in the Universe, in which nothing is separated from each other. And since the past, present and future exist simultaneously in the holographic world, with the help of appropriate tools it is possible to penetrate into the depths of this superhologram and see pictures of the distant past or look into the future.

The general habit of breaking the world apart and ignoring the dynamic interrelationship of all things gives rise to all our problems, not only in science, but also in personal and social life. For example, the division between the observer and the observed, or the division between mind and matter, has led to serious difficulties in understanding the world as a whole. Thinking about the integrity of the world, we distinguish ourselves as an observer looking at this integrity. And we involuntarily split this whole, identifying ourselves with only one of its parts. Several observers, each of which is an external object in relation to all the others, split this whole even more. However, the whole set of parts formed in this way is interconnected.

Unfortunately, we humans divide the whole not even into parts, but into fragments. There is a fundamental difference between a part and a fragment. As the Latin root indicates, and as seen from the related English word fragile ("fragile"), "fragment" is to break or break.

For example, to hit a clock with a hammer is not to produce parts, but fragments, divided so that they cease to be meaningfully connected with the whole. Of course, there are areas where fragmentation is needed. For example, to prepare concrete, you need to crush stones. This is fine.

From Bohm's point of view, the problem of humanity is that we humans have a fragmented way of thinking that produces breakdowns and fragments and does not see the proper parts in their connection with the whole. This leads to a general tendency to "break apart being" in an improper way according to our thoughts. For example, all parts of humanity are fundamentally interdependent and interconnected. However, the original and dominant importance given to differences between people, families, professions, nations, races, religions, ideologies, etc., does not allow human beings to work together for the common good, or even for survival.

When a person thinks of himself in such a fragmentary way, he inevitably tends to see himself first, his own person, his own family, in a word, "his own shirt, which is closer to the body." He does not think of himself as inwardly connected with the whole of humanity and, therefore, with the rest of the people. In the same way, he separates body and mind so that he can treat them separately. Physically it is unhealthy, but mentally it is unfavorable for the mind.

“For example, if we are talking about the fact that there are two nations, then the same problem exists here. You see, people in two nations may not be very different from each other, as in France and Germany. However, they insist that they are completely different. Some say: Deutschland über Alles, others: Vive la France, and then they say: “We must set hard boundaries; we must put up giant fences along these borders; we have to destroy anything just to protect them” – and now we have the First World War… Although, if you cross the border, no division is noticeable; people are not very different, and if by historical chance it happened that two were one, then such a thing would not happen ... And if you think that there are two parts, then you will begin to impose them ...

But, of course, before things actually start to change because of this - because of the fact that we begin to think differently - this thought must be deeply embedded in our intentions, actions, and so on, in our whole being ”(7).

So, according to Bohm, the fragmented thinking that humanity has today contributes to the emergence of a reality that is constantly breaking down into disorderly, disharmonic and destructive activity. And this at a time when the world is a single whole, which can be divided into parts (and they are natural), but cannot be broken into unrelated fragments. Division into parts can only be applied to a certain limit - it should always be remembered that each part depends on every other part. Chernobyl is a good example of this. An atomic explosion occurred in Ukraine, and sick children are born in Belarus, Russia and other countries.

Unfortunately, we believe, for example, that we can extract valuable materials from the Earth without affecting the rest of it. We believe that we can solve various problems of society, such as crime, poverty, addiction to drugs, ignoring society as a whole, etc. We even believe that we can defeat terrorism in a single country, such as Iraq.

The existing way of fragmenting the world not only does not work, but may even be fatal (7).

However, Bohm warns that this does not mean that the universe is a gigantic indistinguishable mass. Things can be part of an indivisible whole and at the same time have unique qualities. To illustrate this point, he draws our attention to the small whirlpools and whirlpools that often form in a river. At first glance, such whirlpools seem to be independent and have individual characteristics, such as magnitude, speed and direction of rotation, etc. But upon closer examination, it turns out to be impossible to determine where a given whirlpool ends and a river begins. Thus, Bohm does not consider it meaningless to talk about the difference between "things". He just wants us to be constantly aware that the various aspects of holodynamics, that is, the so-called "things", are just an abstraction, the way in which our consciousness highlights these aspects.

Consciousness as a subtle form of matter . Bohm's Holographic Universe explains many other mysteries. One of these mysteries is the influence that consciousness has on the intra-atomic world. As we have seen, Bohm rejects the idea that particles do not exist until they are in the field of view of the observer. And he insists on bringing consciousness and physics together. However, he believes that most physicists are on the wrong path, trying to divide reality into parts and declaring that one independent entity - consciousness - interacts with another independent entity - an elementary particle.

Since all things are aspects of holodynamics, Bohm believes that it makes no sense to talk about interacting consciousness and matter. In a sense, the observer is the observed itself. The observer is also a measuring device, experimental results, a laboratory, and a breeze blowing outside the walls of the laboratory. In fact, Bohm believes that consciousness is a more subtle form of matter, and the basis for its interaction with other forms of matter lies not in our level of reality, but in a deep implicative order. Consciousness is present in various degrees of folding and unfolding in all matter - this is why plasma, for example, has some of the characteristics of a living being. As Bohm says, “The ability of a form to be dynamic is the most characteristic feature of consciousness, and we already see something conscious in the behavior of an electron” (5).

In a word, consciousness and matter, according to Bohm, are projections of a higher reality nested in each other, which is neither consciousness nor matter in its pure form. True, Bohm does not call this higher reality the Creator.

Similarly, he believes that the division of the universe into living and non-living objects does not make sense. Animate matter and inanimate matter are inextricably linked with each other, and life is in a latent state throughout the universe. Even stone is in some sense alive, Bohm says, since life and intelligence are present not only in matter, but also in "energy", "space", "time", "the whole fabric of the universe" and everything else that we abstractly highlight. from holodynamics and are erroneously considered as independently existing objects. Bohm states: “You can equally call the implicative area the Ideal, the Spirit, the Consciousness. The separation of two concepts - matter and spirit - is an abstraction. They have the same basis.

In a Universe where all things are infinitely interconnected, the consciousnesses of all people are also interconnected. Despite the seeming outer limits, we are creatures without boundaries. The idea that consciousness and life (and, in fact, everything in the universe) are multiples rolled up in the universe has startling implications. Just as each piece of a hologram contains an image of the whole, each part of the universe contains the entire universe.

Therefore, every cell of our body also contains the entire folded cosmos. Every leaf, every raindrop, and every speck of dust possesses the same property, giving new meaning to the famous lines of William Blake:

See eternity in one moment
The vast world is in a grain of sand,
In a single handful - infinity
And the sky is in a cup of a flower.

If our universe is but a pale shadow of a deeper order, what lies at the primordial basis of our reality?

Bohm suggests the following. According to the modern understanding of physics, each section of space is permeated with various types of fields, consisting of waves of various lengths. Each wave has some energy. When physicists calculated the minimum amount of energy a wave could carry, they found that each cubic centimeter of vacuum contains more energy than all the energy of all matter in the entire observable universe!

Some physicists refuse to take these calculations seriously and believe that there is an error hidden somewhere. However, Bohm believes that this endless ocean of energy does exist. And scientists, like fish who do not see the water in which they swim, ignore the existence of a vast ocean of energy, because they are concentrated only on the objects floating in this ocean, that is, on matter.

A good confirmation of Bohm's point of view is the work on the study of the physical vacuum, about which the academician of the EAN G. I. Naan says: "Vacuum is everything, and everything is vacuum." According to J. Wheeler, the Planck energy density of the physical vacuum is 10 95 g/cm 3 , while the density of nuclear matter is 10 14 g/cm 3 . Other estimates of the energy of vacuum fluctuations are also known, but all of them are much larger than Wheeler's estimate (2).

According to Bohm, matter does not exist independently of this ocean of energy, from the so-called "empty" space. “Space is not empty. It is filled, as opposed to a vacuum, and is the basis for the existence of all things, including me and you. The universe is inseparable from this cosmic ocean of energy and appears as a ripple on its surface, a comparatively insignificant "excitation pattern" in the midst of an unimaginably vast ocean" (5).

This means that, despite its apparent materiality and huge size, the Universe does not exist by itself, but only the offspring of something that is immeasurably larger and more mysterious than it. Moreover, the Universe, according to Bohm, is not even a derivative of this immeasurable Something, it is only a fleeting shadow, a distant echo of a grander reality.

Bohm's statements are confirmed by the statement of the director of the Main Astronomical Observatory of Ukraine, a member of the Ukrainian Academy of Sciences and many foreign academies, Yaroslav Yatskiv: “Recent astronomical discoveries have proved the presence in the Cosmos of an energy inaccessible to instruments that controls the course of the development of the Universe” (12). Academician Yatskiv is one of the founders of the highest and second largest observatory in Russia at the Terskol peak in the Elbrus region. The observatory operates as part of the International Center for Astronomical and Medical-Ecological Research, established by the Academies of Sciences of Russia, Ukraine and the government of Kabardino-Balkaria in 1992.

According to Yatskiv, today only 7% of the world's available matter is available for observation. These are the Moon, Earth, planets, galaxies, stars. About 16% of matter is dark matter, the existence of which has been reliably proven, but they have not yet been investigated. Perhaps this is a mass of neutrinos, or particles unknown to science, or galaxies. “The rest,” Yatskiv said, “is some kind of mysterious dark energy… The latest observations in open space have discovered antigravity and fluctuations in the electrocosmic background, which indicate that there is Something in the Universe that is responsible for the scenario of the development of the Universe,” the academician noted. He emphasized that he was far from mysticism and would not call the mysterious energy the Universal Mind, the Absolute or God.

“This is a property of the Cosmos unknown to science,” Yatskiv said. He recalled that even Einstein introduced the conditional lambda term into his equations, but considered it his mistake. “And now we know that he is responsible for dark energy,” said Yatskiv (12).

We considered it appropriate to cite a small excerpt from the dialogue between D. Bohm and D. Krishnamurti, concerning their reflections on order, the Universe and some kind of energy (13). Jiddu Krishnamurti (1896-1986) is one of the most prominent spiritual teachers of our time. Discovered by Theosophists as a boy in India, he was groomed by them as the new Messiah, a role he abandoned when he independently pursued his own spiritual quest. Traveling the world with his students, giving lectures, he gained many supporters, including prominent statesmen and intellectuals.

Acquaintance with the works of J. Krishnamurti prompted Bohm to seek a direct meeting with the author. Their first meeting took place in 1960 and proved to be extremely fruitful for Bohm. In the future, their meetings and conversations became regular, and acquaintance over time grew into friendship. Krishnamurti's ideas served as a powerful impetus for D. Bohm's further scientific work. They are clearly traced in the book by D. Bohm "Integrity and its inherent order" (London, 1980), in his approach to the problem of a holistic vision of the world, as well as the nature of consciousness. Particularly interesting in this regard is the book “Disclosure of Meaning. Conversations with David Bohm”, in which the scientist and his interlocutors find out how the ideas arising from a holistic perception of the world can be put into practice.

“In our conversations with Krishnamurti,” D. Bom later recalled, “many issues related to my scientific work were considered. We talked about space and time, about the universe and the connections of external nature with the internal structure of the human spirit. We discussed the confusion and confusion that conditions human consciousness."

Bohm: We can assume that there is some order of the universe, some kind of law.

Krishnamurti: I agree. The universe functions, and it has its own order.

Bohm: Yes, and the fact that a single mechanism can go wrong is part of the order of the universe. If the machine breaks down, then this does not mean disorder in the universe, it is part of the order of the universe.

Krishnamurti: Yes. There is disorder in the order of the universe, where it concerns a person.

Bohm: It's not a disorder at the level of the universe.

Krishnamurti: No. This is at a much lower level.

Bohm: On a human level, it's a mess.

Krishnamurti: But why does man live in this disorder from the very beginning?

Bohm: Because he lives in ignorance, he still has not seen the main thing.

Krishnamurti: Although man is part of the whole, he still lives in a tiny corner and lives in disorder. And this huge knowing mind does not have ...

Bohm: Yes, you could say that the possibility of creativity is also the possibility of disorder. So, if a person had the opportunity to create, then there was also the opportunity to make mistakes. He could not be fixed, like a machine, to always act in perfect order. This mind would not want to turn him into a machine that is incapable of creating disorder. Do you agree that the universe, the mind that created nature with order, does not operate everywhere simply mechanically? Is there any deep meaning in his work?

Krishnamurti: Yes. We said "emptiness", this emptiness is everything, and therefore it is that which is absolute energy. It is completely pure, undistorted energy. Is there something behind her? I feel like we can't touch it, I feel like there's something behind this energy.

Bohm: Can we say that this Something is the basis, the essence of everything? Are you saying that everything arises from an inner basis?

Krishnamurti: Yes, there is another. You know, here one must be extremely careful not to lose the sense of the real, not to fall into an illusion, not to be carried away by desire or even by the desire for research and search. It has to happen. Do you understand what I mean? There is Something beyond this. How can we talk about it? You see, energy is only there when there is emptiness. They are together.

Bohm: This pure energy you speak of is emptiness. Do you believe that there is Something beyond this emptiness, the basis of this emptiness?

Krishnamurti: Yes (13).

In our opinion, when talking about a certain Something that is the basis of everything, the interlocutors involuntarily touch upon the Creator.

So, the fundamental feature of Bohm's cosmology is the assertion that reality is ONE, that it is an indivisible integrity underlying the entire Universe, at the basis of matter and consciousness. The whole world model informs us that we are part of an indivisible reality that has an innate ability to formulate ideas about itself. "Biological systems, the living matter of the planet and the surrounding space can be represented as a single physically organized system, somewhat similar to a single giant near-Earth hologram."

In a conversation with journalist R. Weber, Bohm said: “The replacement of previous ideas is a clear paradigm of a unified field of being, a self-conscious universe that perceives itself as integral and interconnected. By analogy with physics, this reality can be called the field of Consciousness. This unified field is neither neutral nor meaningless, as required by the existing scientific canon; it is an orderly and beneficent energy manifesting itself in that new realm in which physics, psychology and religion are immersed” (14).

Professor of the Institute of Theoretical Physics of the University of Oregon (USA) Amit Goswami in his book “The Universe that Creates Itself” with the subtitle “How Consciousness Creates the Material World” writes the following about this: “Consciousness is the fundamental principle on which everything that exists is based, and hence, the Universe we observe” (15). In an effort to give a precise definition of Consciousness, Gosvami identifies four circumstances.

1. There is a field of Consciousness (or an all-encompassing ocean of Consciousness) which is sometimes referred to as a psychic field.

2. There are objects of Consciousness, such as thoughts and feelings, that rise from this field and sink into it.

3. There is a subject of Consciousness - one who feels and / or is a witness.

4. Consciousness is the basis of existence.

A similar point of view is shared by Russian scientists, academicians A.E. Akimov and G.I. Shipov, stating: “It is difficult to consider the evolution of the Universe without such a factor as the Consciousness of the Universe, a fragment of which is the consciousness of Man” (16).

To date, Bohm's theory is still in its infancy. Until recently, D. Bohm was engaged in the development of the mathematical basis of his theory, which uses such mathematical concepts as the "matrix" and such branches of mathematics as topology. There is a promising similarity between his implicit order theory and the bootstrap theory. Both of these concepts come from understanding the world as a dynamic network of relationships and put forward the concept of order to the central place, use matrices as a means of describing change and transformation, and topology as a means of more precisely defining categories of order. Finally, both of these approaches recognize that consciousness is an integral component of the universe, which in the future should be included in a new theory of physical phenomena.

Such a theory may arise from the combination of Bohm's and Chu's theories, which are two of the most inventive and philosophically profound approaches to describing physical reality. However, explicit elements of consciousness cannot be introduced into them. Hopes are pinned on the unification of these two theories with the theory of torsion fields (TFT). It is this association that represents today the most successful description of unity, stability and harmony in the relationship between the components of physical reality.

Nobel Prize winners in physics have proven that, without a doubt, the physical world is a single ocean of energy that appears and disappears after milliseconds, pulsing again and again.
There is nothing solid and solid. Such is the world of quantum physics.
It has been proven that only thought allows us to collect and hold together those "objects" that we see in this constantly changing field of energy.

So why do we see a person, and not a flashing bundle of energy?
Imagine a film reel. A movie is a set of frames at approximately 24 frames per second. The frames are separated by a time interval. However, due to the speed with which one frame succeeds another, an optical illusion occurs, and we think that we see a continuous and moving image.

Now think about television.
The cathode ray tube of a TV is just a tube with many electrons that hit the screen in a certain way and thus create the illusion of shape and movement.

That's what all objects are anyway.
You have 5 PHYSICAL SENSES (sight, hearing, touch, smell and taste). Each of these senses has a specific spectrum (for example, a dog hears sound on a different spectrum than you; a snake sees light on a different spectrum than you, and so on).

In other words, your set of senses perceives the surrounding sea of ​​energy from a certain LIMITED point of view and, based on this, builds an image. This is not a complete and by no means an accurate picture. This is just an interpretation. All our interpretations are based solely on the "internal map" of reality that we have formed, and not on objective truth. Our “map” is the result of experience accumulated over a lifetime. Our thoughts are connected to this invisible energy, and they determine what this energy forms. Thoughts literally go through the universe particle by particle in order to create physical life.

Take a look around. Everything you see in our physical world began as an idea, an idea that grew as it was shared and expressed until it grew enough to become a physical object in a few steps. You literally become what you think about the most. Your life becomes what you believe in the most. The world is literally your mirror, allowing you to physically experience what you believe to be true for you...until you change your perspective.

Quantum physics shows us that the world around us is not something rigid and unchanging, as it might seem. On the contrary, it is something constantly changing, built on our individual and collective thoughts.

What we think is true is actually an illusion, almost a circus trick. Fortunately, we have already begun to uncover this illusion and, most importantly, look for ways to change it.
What is your body made of? The human body is made up of nine systems including the circulatory system, digestion, endocrine system, muscular system, nervous system, reproductive system, respiratory system, skeletal system, and urinary tract.

And what do they consist of?
from tissues and organs.
What are tissues and organs made of?
From cells.
What are cells made of?
From molecules.
What are molecules made of?
From atoms.
What are atoms made of?
from subatomic particles.
What are subatomic particles made of?
From energy!

You and I are pure energy-light at its most beautiful and intelligent. An energy constantly shifting beneath the surface, but under the control of your powerful intellect. You are one big starry and powerful Human Being.

If you could see yourself under a powerful electron microscope and perform other experiments on yourself, you would be convinced that you are composed of a bunch of constantly changing energy in the form of electrons, neutrons, photons, and so on.

The same is true of everything that surrounds you. Quantum physics tells us that it is the act of observing an object that causes it to be where and how we see it. An object does not exist independently of its observer! So, as you can see, your observations, your attention to something, and your intention, literally creates this object.

This has been proven by science. Your world is made up of spirit, mind and body. Each of these three elements, spirit, mind and body, performs a function that is unique to it and not available to the others. What your eyes see and your body feels is the physical world, which we will call the Body. The body is an effect created for a cause.

This reason is Thought. The body cannot create. It can only feel and be felt... that is its unique function. Thought cannot feel... it can only invent, create and explain. It needs the world of relativity (the physical world, the Body) in order to feel itself.

Spirit is All That Is, that which gives Life to Thought and Body. The body does not have the power to create, although it gives such an illusion. This illusion is the cause of many disappointments. The body is just a result, and it has no power to cause or create anything.

The key to all this information is the opportunity for you to learn to see the universe differently, in order to bring into being all that is your true desire.

Nobel Prize winners in physics have proven that, without a doubt, the physical world is a single ocean of energy that appears and disappears after milliseconds, pulsing again and again. There is nothing solid and solid. Such is the world of quantum physics. It has been proven that only thought allows us to collect and hold together those "objects" that we see in this constantly changing field of energy.

So why do we see a person, and not a flashing bundle of energy?

Imagine a film reel.

A movie is a set of frames at approximately 24 frames per second. The frames are separated by a time interval. However, due to the speed with which one frame succeeds another, an optical illusion occurs, and we think that we see a continuous and moving image.

Now think about television.

The cathode ray tube of a TV is just a tube with many electrons that hit the screen in a certain way and thus create the illusion of shape and movement.

That's what all objects are anyway. You have 5 physical senses (sight, hearing, touch, smell and taste).

Each of these senses has a specific spectrum (for example, a dog hears sound on a different spectrum than you; a snake sees light on a different spectrum than you, and so on).

In other words, your set of senses perceives the surrounding sea of ​​energy from a certain limited point of view and, based on this, builds an image. This is not a complete and by no means an accurate picture. This is just an interpretation.

All our interpretations are based solely on the "internal map" of reality that we have formed, and not on objective truth. Our “map” is the result of experience accumulated over a lifetime.

Our thoughts are connected to this invisible energy, and they determine what this energy forms. Thoughts literally go through the universe particle by particle in order to create physical life.

Take a look around.

Everything you see in our physical world began as an idea, an idea that grew as it was shared and expressed until it grew enough to become a physical object in a few steps.

You literally become what you think about the most.

Your life becomes what you believe in the most.

The world is literally your mirror, allowing you to physically experience what you believe to be true for you...until you change your perspective.

Quantum physics shows us that the world around us is not something rigid and unchanging, as it might seem. On the contrary, it is something constantly changing, built on our individual and collective thoughts.

What we think is true is actually an illusion, almost a circus trick.

Fortunately, we have already begun to uncover this illusion and, most importantly, look for ways to change it.

What is your body made of?

The human body is made up of nine systems including the circulatory system, digestion, endocrine system, muscular system, nervous system, reproductive system, respiratory system, skeletal system, and urinary tract.

And what do they consist of?

from tissues and organs.

What are tissues and organs made of?

From cells.

What are cells made of?

From molecules.

What are molecules made of?

From atoms.

What are atoms made of?

from subatomic particles.

What are subatomic particles made of?

From energy!

You and I are pure energy-light at its most beautiful and intelligent. An energy constantly shifting beneath the surface, but under the control of your powerful intellect.

You are one big starry and powerful Human Being.

If you could see yourself under a powerful electron microscope and perform other experiments on yourself, you would be convinced that you are composed of a bunch of constantly changing energy in the form of electrons, neutrons, photons, and so on.

The same is true of everything that surrounds you. Quantum physics tells us that it is the act of observing an object that causes it to be where and how we see it.

An object does not exist independently of its observer! So, as you can see, your observations, your attention to something, and your intention, literally creates this object.

This has been proven by science.

Your world is made up of spirit, mind and body.

Each of these three elements, spirit, mind and body, performs a function that is unique to it and not available to the others. What your eyes see and your body feels is the physical world, which we will call the Body. The body is an effect created for a cause.

This reason is Thought.

The body cannot create. It can only feel and be felt... that is its unique function.

Thought cannot feel... it can only invent, create and explain. It needs the world of relativity (the physical world, the Body) in order to feel itself.

Spirit is All That Is, that which gives Life to Thought and Body.

The body does not have the power to create, although it gives such an illusion. This illusion is the cause of many disappointments. The body is just a result, and it has no power to cause or create anything.

The key to all this information is the opportunity for you to learn to see the Universe differently, in order to bring to life all that is your true desire.

When we move from classical to quantum mechanics, our ideas about the importance of certain concepts change in many ways. (We have already considered some of these concepts before.) In particular, the concept of force is gradually fading away, and the concepts of energy and momentum are becoming of paramount importance. Instead of the movement of particles, as you remember, we are now talking about the amplitudes of probabilities that change in space and time. These amplitudes include wavelengths associated with impulses and frequencies associated with energies. Momenta and energies determine the phases of wave functions and for this reason they are important for quantum mechanics. Instead of force, it is now about how the interaction changes the wavelength. The notion of strength becomes secondary, if it is worth talking about at all. Even when, for example, they mention nuclear forces, in fact, as a rule, they still work with the interaction energies of two nucleons, and not with the force of their interaction. It never occurs to anyone to differentiate energy in order to see what the force is. In this section, we want to describe how vector and scalar potentials arise in quantum mechanics. It turns out that precisely because momentum and energy play the main role in quantum mechanics, the most direct way to introduce electromagnetic effects into the quantum description is to do this with and .

We must first briefly recall how quantum mechanics works. We will return to what was described in vol. 3, ch. 37, an imaginary experiment in which electrons were diffracted by two slits. In FIG. 15.5 shows the same device. The electrons (they all have approximately the same energy) leave the source and move towards the wall with two narrow slits. Behind the wall is a "protective" shaft - an absorber with a movable detector. This detector is designed to measure the frequency at which electrons enter a small area of ​​the absorber at a distance from the axis of symmetry. This frequency is proportional to the probability that an individual electron emitted from the source will reach this part of the "roll". The probability has a complex distribution (shown in the figure), which is explained by the interference of two amplitudes, one from each slot. The interference of two amplitudes depends on their phase difference. In other words, when the amplitudes are equal to and , the phase difference determines the interference pattern [see. issue 3, ch. 29, equation (29.12)]. If the distance from the slits to the screen is , and the difference in the lengths of the paths of the electrons passing through the two slits is (as shown in the figure), then the phase difference of the two waves is given by the ratio

As usual, we assume , where is the wavelength corresponding to the spatial variation of the probability amplitude. For simplicity, we consider only those values ​​that are much less than ; then you can accept

When equal to zero, then equal to zero; the waves are in phase, and the probability has a maximum. When equal to , the waves are out of phase, interfering destructively, and the probability reaches a minimum. Thus, the electronic intensity takes on a wave-like form.

Fig. 15.5. Interference experiment with electrons.

Now we want to formulate the law that replaces the law of force in quantum mechanics. This law will determine the behavior of quantum mechanical particles in an electromagnetic field. Since everything that happens is determined by the amplitudes, then the law will have to explain how the influence of the magnetic field affects the amplitudes; we will have nothing more to do with particle accelerations. This law is as follows: the phase with which the amplitude reaches the detector, moving along some trajectory, the presence of a magnetic field changes by a value equal to the integral of the vector potential along this trajectory, multiplied by the ratio of the particle charge to Planck's constant. I.e

If there were no magnetic field, then some definite phase of arrival would be observed. If a magnetic field appears somewhere, then the arrival phase increases by the value of the integral in (15.29).

Although this is not necessary for our present reasoning, we note nevertheless that the influence of the electrostatic field is also expressed in a phase change equal to the time integral of the scalar potential with a minus sign:

These two expressions are valid only for static fields, but by combining them, we get the correct result for any, static or dynamic, electromagnetic field. It is this law that replaces the formula . For now, however, we will only talk about a static magnetic field.

Let us assume that the experiment with two slits is carried out in a magnetic field. We want to find out with what phase two waves reach the screen, the paths of which lie through two different slits. Their interference determines the place where the maximum probability will be. We will call the phase of the wave traveling along the trajectory (1) , and denote by the phase when there is no magnetic field. Then, after switching on the field, the phase reaches the value

. (15.30)

Similarly, the phase for trajectory (2) is

. (15.31)

Wave interference in the detector depends on the phase difference

The phase difference in the absence of a field will be denoted by ; this is the same difference that we calculated in equation (15.28). In addition, we notice that from two integrals one can make one going forward along the path (1), and backward along the path (2); this closed path will be denoted by (1-2). So what happens

. (15.33)

This equation tells us how a magnetic field changes the motion of an electron; with its help we can find new positions of intensity maxima and minima.

Before we do this, however, we want to pose one interesting and important question. You remember that there is some arbitrariness in the vector-potential function. Two different potential vector functions and , differing by the gradient of some scalar function, represent the same magnetic field (because the curl of the gradient is zero). They therefore lead to the same classical force. If in quantum mechanics all effects depend on a vector potential, then which of the many possible -functions is correct?

The answer is that the same arbitrariness continues to exist in quantum mechanics. If in equation (15.33) we replace by , then the integral of will turn into

.

The integral of is calculated along a closed path (1-2); but the integral of the tangent component of the closed path gradient is always zero (by Stokes' theorem). Therefore, both lead to the same phase differences and to the same quantum mechanical interference effects. In both classical and quantum theory, only the curl is important; any function for which the curl is as it should lead to the correct theory.

The same conclusion becomes obvious if we use the results presented in Chap. 14, § 1. There we showed that the contour integral of over a closed path is equal to the flow through the contour, in this case the flow between paths (1) and (2). Equation (15.33) can, if we wish, be written as

where the flux , as usual, means the surface integral of the normal component . The result depends only on , i.e. only on the rotor.

But since the result can be expressed both in terms of and in terms of , it may give the impression that it holds its positions in the “real” field, but still looks like an artificial formation. But the definition of a "real" field that we first proposed was based on the idea that a "real" field could not act on a particle at a distance. We undertake to give an example in which it is equal to zero (or at least an arbitrarily small number) in any place where the particles may be, so that it is impossible to imagine what directly affects them.

You remember that if there is a long solenoid through which an electric current flows, then the field exists inside it, but there is no field outside, while many vectors circulate outside the solenoid (Fig. 15.6). If we create such conditions that the electrons will pass only outside the solenoid (only where there is), then, according to equation (15.33), the solenoid will still affect their movement. According to classical views, this is impossible. According to classical concepts, the force depends only on . To know if current is flowing through a solenoid, a particle must pass through it. And quantum mechanics claims that the presence of a magnetic field in a solenoid can be established by simply bypassing it, without even coming close to it!

Fig. 15.6. Magnetic field and vector potential of a long solenoid.

Imagine that we placed a very long small diameter solenoid right there behind the wall between two slots (Fig. 15.7). The diameter of the solenoid must be much smaller than the distance between the slots. Under these circumstances, the diffraction of electrons by the slit will not lead to appreciable probabilities that the electrons will slip somewhere near the solenoid. How will all this affect our interference experiment?

Fig. 15.7. A magnetic field can influence the motion of electrons even when it exists only in a region where the probability of finding an electron is negligible.

Let's compare two cases: when current flows through the solenoid and when there is no current. If there is no current, then there is neither , and the initial pattern of electronic intensities along the absorber is obtained. If we turn on the current and create a magnetic field inside the solenoid, then a field will appear outside. There will be a shift in the phase difference proportional to the circulation outside the solenoid, which means that the pattern of maxima and minima will shift to a different place. Indeed, since the flow between any two paths is constant, the circulation is just as constant. For any point of arrival, the phase changes in the same way; this corresponds to the fact that the whole picture is shifted along by a constant value, say, by . This value is easy to calculate. The maximum intensity occurs where the phase difference of the two waves is zero. Substituting instead of the expression (15.32) or (15.33), and instead of the expression (15.28), we get

, (15.35)

The picture in the presence of a solenoid will look as shown in Fig. 15.7. At least that's what quantum mechanics predicts.

Just the same experiment was done recently. This is an extremely difficult experience. The wavelength of electrons is extremely small, so the device must be miniature, otherwise you will not notice the interference. The slots must lie close together, which means that an unusually thin solenoid is needed. It turns out that, under certain circumstances, iron crystals grow in the form of very long and microscopically thin filaments. If these iron threads are magnetized, they form a small solenoid that has no external magnetic field (it only appears at the ends). So, an experiment was done on the interference of electrons with an iron thread placed between two slits, and the predicted shift of the electronic picture was confirmed.

And then the field in our sense is already “real”. You can object: "But there is a magnetic field there." Yes, there is, but remember our original idea - "real" is only such a field, which, in order to determine the motion of a particle, must be set in the place where it is located. The field in the thread acts at a distance. If we do not want its influence to look like action at a distance, we must use the vector potential.

This problem has an interesting history. The theory that we have outlined has been known since the very beginning of quantum mechanics, since 1926. The very fact that the vector potential appears in the wave equation of quantum mechanics (the so-called Schrödinger equation) has been obvious from the moment it was written. The fact that it cannot be replaced by a magnetic field was convinced by everyone who tried to do it; one after another, everyone was convinced that there was no simple way for this. This is also clear from our example, when an electron moves through a region where there is no field, and yet is affected. But, since in classical mechanics, apparently, it did not have a direct, important meaning, and, further, due to the fact that it could be changed by adding a gradient, people repeated again and again that the vector potential does not have a direct physical meaning, that even in quantum mechanics only electric and magnetic fields have "rights". In retrospect, it seems strange that no one thought to discuss this experience until 1956, when Bohm and Aronov first proposed it and made the whole question crystal clear. All this was always implied, but no one paid any attention to it. And many were simply shocked when this question came up. For this reason, some people thought it necessary to experiment and make sure that all this is really so, although quantum mechanics, in which we all believe for so many years, gave a completely unambiguous answer. It is interesting that such things can be in the public eye for thirty years, but due to certain prejudices about what is essential and what is not, they can be ignored by everyone.

Now we want to continue our analysis a bit. We will demonstrate the relationship between the quantum mechanical and classical formulas to show why it turns out that, in a macroscopic view of things, everything looks as if the particles are controlled by a force equal to the product of the curl. To derive classical mechanics from quantum mechanics, we need to consider cases where all wavelengths are small compared to distances over which external conditions (such as fields) change noticeably. We will not pursue the generality of the proof, but will only show everything with a very simple example. Let us turn again to the same experiment with slits. But now, instead of cramming the entire magnetic field into a narrow gap between the slits, let's imagine a magnetic field that spreads out behind the slits in a wide band (Fig. 15.8). Let's take an idealized case when the magnetic field is uniform in a narrow strip with a width much smaller than . (This is easy to do, you just need to move the absorber farther away.) To calculate the phase shift, we must take two integrals of along two trajectories (1) and (2). As we have seen, they differ simply by the flow between these paths. In our approximation, the flow is . The phase difference for the two paths is therefore

From this analysis we see how it turns out that the vector potential, which appears explicitly in quantum mechanics, gives rise to a classical force that depends only on its derivatives. In quantum mechanics, only interference between adjacent paths is essential; in it it always turns out that the effect depends only on how much the field varies from point to point, and therefore only on derivatives, and not on itself. Despite this, the vector potential (along with the accompanying scalar potential) seems to lead to a more direct description of physical processes. The deeper we penetrate into quantum theory, the clearer and more transparent it becomes to us. In the general theory - quantum electrodynamics - in the system of equations that replace Maxwell's equations, vector and scalar potentials are already considered fundamental quantities. Vectors and are gradually disappearing from the modern record of physical laws: they are being replaced by and .

The quantum potential field provides the system with information, not energy. This understanding is analogous to a ship in the ocean, controlled from the shore using a radio signal.

The ship moves on its own energy, but the instructions for maneuvering are sent using radio waves. Radio waves don't carry the energy needed to change a ship's course, they only carry information! The same happens in the case of the behavior of an electron. The quantum potential provides the course-changing instructions required for the electron to interact with its environment. From the quantum potential, electrons receive information immediately and everywhere in space. The intensity of the potential does not matter, only its form !

JOURNEY OUTSIDE

Physicist Jack Sarfatti, like William Teller, takes us on a different journey beyond conventional thinking. Sarfatti developed a new discipline of thinking, which he called Fast-Quantum theory. Its ideas are characterized by the fact that they extend beyond the traditional concepts of quantum theory. Simply put, Sarfatti seeks to explain the interaction of mind and matter! This interaction takes place in the realm above the quantum world.

Mind and matter interact with the help of intermediate information waves that influence and organize matter. Information waves managed conscious intent!

In the Sarfatti model, the Bohm quantum potential becomes the carrier q-bits of information in pilot waves that actually originate in mental wavefields! It is these waves that are responsible for the coordination of the complex and dynamic self-organization of matter. Sarfatti establishes a connection between the mental wave field and the field of quantum potential, which provides the electron with guiding information! According to Sarfatti, conscious awareness in the physical body is connected to non-local consciousness outside the physical body via an electronic matrix in the brain. Electrons form “ coherent-phase matrix of a tiny nano-antenna in the form of an electric dipole” . Such a matrix can be considered as a kind of coherently tuned network structure. Its task is to enter information into microtubules brain. At the same time, the matrix links the physical body to the mental wave fields.

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INTENTION DRIVES PILOT WAVES

What controls the carriers q-bit information pilot waves? Sarfatti explains: “ conscious INTENTION” . Quantum pilot waves are like information patterns. These are thought forms that organize matter. They operate outside of space and time - they are non-local. Thought forms do not work on the basis of intensity. They govern the energy of solid things. At the quantum level, their action is very large, despite the low intensity of the information wave. Active information carries potential everywhere, but becomes activated only where it acquires meaning. Activated information is the form.

REVERSE ACTION - SPIRIT INTERVENTION

The post-quantum theory of Sarfatti contains characteristic features. The key concept of his theory is what he calls reverse action. Reverse action involves the interaction of mind and matter, where matter is forced to interact with mind. It is a process of two-way communication. A two-way process creates and activates a feedback loop connecting mind and matter into an indivisible whole! Sarfatti explains that the result of the reverse action is that the high-level control structure of the brain works minute by minute with its control information. There is an ongoing recovery process in the form of a consistent process. Interaction " pumped by external messages from the past, future and everywhere, bypassing the moment here and now of the light cone of the brain. According to Sarfatti, reverse action “ breathes life into the equations of physics. It's the Holy Spirit."