home Makeup Energy can take a negative value. Abstract: Can energy be negative? Negative beings in the aura

Energy can take a negative value. Abstract: Can energy be negative? Negative beings in the aura

In our bustling world, it is almost impossible to maintain a harmonious aura, constantly entering into an exchange of subtle matters with people and objects.

Negative energy in a person appears due to the destruction of positive vibrations, incorrect thinking, or the influence of people and objects of the other world. But do not be afraid of problems in the biofield, because negativity can be displaced or transformed, and then resort to methods of protecting subtle matters.

Why does a person lose energy?

In most cases, the outflow of vitality is associated with the individual’s extreme attachment to the events of the past. We are talking about the so-called bindings created by the energy of other people, significant for the subject, and also constantly supported by negative emotions.

Typically, a person often returns to stressful situations and negative circumstances in his life. Obsessive worries and doubts are feelings that require a lot of energy, so the biofield weakens. The main types of the most energy-consuming states are:

Feeling sorry for yourself and others

The desire not to betray others and constantly take care of them, as well as the desire to protect oneself in any situation, lead to the loss of enormous vitality.

Pity is not love, so it does not replenish the aura with fresh and pure energy. Sacrifice and the constant desire to help are simply a form of unequal energy exchange.

Resentment

Memories associated with events that are unfair to the person himself most often disturb the soul and mind. Constantly thinking about situations takes a lot of time and energy.

In addition, projecting negative emotions onto your offender is a sure way to receive the same thing in return, and even in an increased volume. The same applies to the thirst for revenge, when a person spends energy on developing a plan for retaliatory evil.

Feelings of shame, guilt or humiliation

Memories of being used or done wrong are associated with the irreparability of the situation, it is frightening and annoying.

A person is angry with himself, so he not only kills positive energy flows, but also fills the biofield with negative matters.

Envy

This emotion not only prevents you from enjoying the joys of life, but also spoils the energy of another person who has become an object of envy. As a result, the law of karma comes into play, and the person drowns in his own negativity and experiences. Time is wasted on empty dreams rather than real goals.

Some of the emotions that arise are not so much related to real people, how many with objects of the material world. Very often a person is forced to part with some objects, valuables, money. When he constantly thinks about his losses, gets angry at himself and others, he wastes energy 24 hours a day. At the same time, his thoughts do not leave him even in his sleep, so the biofield does not update at night.

There are several other reasons why a person lacks energy.

Firstly, lifestyle plays a role, because if an individual does something that his heart is not in, he constantly suffers.
Secondly, suppressing one’s emotional experiences in the bud has a negative impact on the biofield. Sometimes energy can flow away due to the fact that a person’s boundaries of interpersonal communication are shifted. Some people can become chronic carriers of a heavy aura because they have many psychological traumas, including those that originate from childhood and relationships with parents.

Classification of energy outflow

Some esotericists classify the reasons for the outflow of energy according to what level of the human body they affect:

Energy from the physical shell is stolen by stooped and hunched postures, strong looseness of movements, external imitation of other people, as well as illnesses, muscle tension, sudden and spontaneous movements, and aggressive dancing.
The ethereal double lacks vitality due to improper breathing, lack of communication with nature, and decreased general tone.
The astral body loses energy due to negative emotions, pessimism and depression. Internal conflicts, conflicting desires, dependencies and attachments, and sleep disorders also influence here.
The outflow of vital forces at the level of the mental layer of the aura occurs due to a chaotic flow of thoughts, frequent immersion in the world of dreams and useless chatter.

Why does a bad aura appear in rooms? Subtle matters of previous owners of apartments, as well as energy traces of death and illness, can influence here. Any space retains a negative message evil people and energy vampires. It makes sense to cleanse the biofield of a home or office space after major scandals and conflicts.

Negative beings in the aura

Among the evil entities that choose a weakened aura or a clot of negativity as their habitat, there is their own classification.

The presence of such a formation in the biofield can be judged by the appearance of growths and tumors not only in the energy body, but also in the physical body.

Any small entity attracts similar thought forms, which leads to the complete filling of the shell with negativity, a change in human behavior and the destruction of organs. It is noteworthy that these creatures have the custom of settling not only in people, but also in residential premises. Because of them, the atmosphere at home sharply deteriorates, a bad aura is observed in the office, and accidents occur at work.

The main alien energy-information structures from the subtle world are:

Lying Spirit- an entity that leads to serious depression and is dangerous due to the appearance of false thoughts and emotions. Often clings to the aura of those who communicate with people who are prone to risks. These are, for example, drug addicts, avid casino gamblers, and betting enthusiasts.
Lucifer- the formation of an otherworldly world of unearthly origin. Most often it appears in the biofield during the full moon or new moon. Signs of the essence are attacks of rage, strong lust, thirst for arguments, violence and sex. These vibrations can pose as another formation, a false entity. To get rid of the creature, you need to repent of sins from past lives.
Archimania- structures of greed and power. For the owner of such an essence, the level of spiritual values falls due to the desire for material wealth.
UFO- an energy structure of obsession that arises in the biofield at the moment of a dream about traveling on a spaceship. Carriers of this formation have strange marks on their bodies, scars and wounds. You can get rid of the essence only in 75-80 aura cleansing sessions.
Anti-religious entity- an alien structure that interferes with attending religious ceremonies. At the same time, the most incredible reasons arise in a person’s head why he cannot go to church or communicate with a clergyman.
Nerve blocker- an energetic essence that enhances the consequences of any stressful situation. A person’s neck or back begins to hurt, migraines and constant facial tics are also observed. If an individual has suffered a deep personal tragedy, the “Grief” program can become attached to him.
Self-programming- this is an entity that is formed on its own, without guidance by external influence. Usually this structure is attracted by a constant thought stream of a negative type. This could be due to financial difficulties, problems in your personal life, etc. According to the criterion of the mechanism of formation, there is also an alien structure, consciously created by other people and introduced into the biofield by a magical ritual. At the same time, it is necessary to separately highlight those entities that come from sorcerers or witches.
Fire or air structure- destructive human energy caused by frequent contact with the elements of fire or air. Usually found in heavy smokers. The entity attacks during the full moon, and is especially attracted to the injured thin shell. The main signs are overexcitement and angry attacks.
Leech- an alien neoplasm attracted by low vibrational radiations of human thoughts. Usually they penetrate due to the eternal desire to be rich and successful, because the personality at the same time slows down in spiritual development.
Earth sign Cancer is an external entity caused by gluttony and excessive sexual intercourse. During the full moon, it attacks those who do not know how to deal with life, and leads to emotional imbalance, feelings of fear and physical weakness. If this structure overpowers the aura, the person will be pale or have an earthy complexion. Vibrations of this type tend to provoke cancer.
Reptile- energy generation generated bad thoughts, vile desires. Causes depression, agitation, tearfulness, sleep disturbances, aggression, and suicidal thoughts. The most common type of such creature is the larva, which strives to strengthen its bad habits, for example, delusions of grandeur.
Larvae in the heart cause jealousy and envy, and larvae on the right side are attracted from the so-called 13th brown world, and they are considered the most dangerous due to the development of unknown diseases in the human body.

Under the ceiling in the room there are small flyers and films that rarely communicate with the individual, but feed on the energy of his affairs. Energy seals can be found in any blind space without direct sunlight or ventilation. They hide at a height of 2-3 meters.

Some flyers enter the openings of the apartment during renovation. From the point of view of real harm, the most dangerous ones in the room seem to be striped energy creatures without heads, which are sources of infectious diseases.

Negative energies affecting humans

In some cases, the aura becomes severely deformed and energy begins to flow away when a conscious magical influence has been exerted on the individual’s biofield. Also, energy entities from the other world can adhere to a weakened thin shell. Negative information that people convey to each other can be divided into several types:

Evil eye

The procedure for filling the astral body of the aura with negative information from the outside. At the same time, the new energy has an emotional connotation, usually destructive. The evil eye disrupts the functioning of the astral layer, while blocking the etheric body.

This exposure is especially dangerous for young children who do not know how to defend themselves.

As a result, they develop stomach infections and skin diseases. As for adults, the unpleasant consequences of the evil eye appear after a few months. These are unreasonable fears, uncertainty, nightmares, pain in the heart and lower back.

Damage

This is a negative information and energy influence using a special spell. Here the mental body receives a clot in the form of negative thought forms.

Damage can be caused due to envy, but not to a close relative. This is also done by sorcerers, psychics, and witches.

Love spell or conspiracy

This is an energy flow that leads to various physical illnesses and mental disorders. These information flows are of no use unless the cause of the problem is addressed. Otherwise, a person simply becomes irritated or tired, he suffers from hysterics and persecution mania, shows aggressiveness, and does not want to live.

Any potential diseases are driven even deeper into the vital processes of the body.

Damn

The most destructive energy with a negative message. This form of influence affects the causal body - the most subtle matter responsible for karma. The curse is very powerful and evil because it wants to destroy a person by breaking his connection with cosmic forces. In this case, even the physical shell and mental body are destroyed.

There is also a generational curse - hereditary information in the subconscious with a sharply negative attitude and emotional stress. As many as 7 generations may suffer from this energy and have hereditary diseases. The ancestral curse damages the True Self and the astral field.

Release of negative energy on a person

Energy disruption as a result of accidental or purposeful human influence can always be felt not only at the initial stage, but also at the moment of transmission of negative flows. In this case, the source of negativity does not necessarily have to be in direct contact with the bearer of the aura. Therefore, it is so important to listen to your inner feelings and intuition.

It is worth noting that the transfer of negative energy is not always an end in itself, sometimes it is simply by-effect one-way energy exchange.

In particular, energy vampires or people whose life force channels are blocked due to damage, strive to receive healthy energy from others. As a result, they automatically give them part of their deformed energy.

But one way or another, dumping bad clots is an unpleasant procedure, and it is better to prevent it in advance.

How to determine that negative signals are being transmitted to you in the biofield

A person imposes himself in a conversation

He talks about his problems, demands pity and compassion. Sometimes, for the sake of attention, he may begin to behave defiantly or even aggressively. Wanting to get rid of his negativity, the individual cries into his vest and wants to get advice. A person wants to involve his future donor in difficulties and troubles.

A boring monologue and complaints can pour in not only during personal meetings, but also over the phone. Sometimes people may speak in a sing-song voice or, conversely, whisper and hiss to appear threatening.

Disengaged critic

The opposite strategy also happens - this is the position of a detached critic. Usually such a person is at a distance from you, but then he begins to find fault, his calm is disrupted by an emotional storm.

Some of these people seek to irritate their victims deliberately, using those channels of influence to which the person will react more sensitively. For example, you can yell at an auditory learner, and make comments to a visual learner about their appearance.

A personal meeting

If the meeting is personal, when conveying negativity, the person will definitely accept threatening pose. Direct visual contact also serves as a very important energy bridge.

Such people like to slam doors and constantly touch their own clothes, especially if they are dressed provocatively to attract visual attention.

Entering into body contact

An important part of relieving negative flows if the victim and the bearer of negativity are kinesthetics. A person can not only touch his arms, face, shoulders, but also step on his leg and push. Throwing objects towards the future donor is also likely.

If you encounter, for example, a gypsy, she may even pull out a hair from you or put any small object in your hands and then take it back.

How to resist the transfer of negative energy and not become a donor of healthy vitality against your will? It is best not to listen to the person, interrupt the conversation, sit away and always remain calm. Sometimes it makes sense to change your image so as not to attract the attention of energy vampires. It is also helpful to imagine an imaginary mirror protection around the body. During forced communication, you can mentally distance yourself from a dangerous interlocutor, going into the world of your fantasies.

If you yourself have a need to dump negative energy, do not direct it to a living object, rather use the power of the elements. You can look at the flow of the river, dissolving your thoughts in it, at the rain and the flame of a candle. It is useful to take salt baths, charm stones, burn wood chips in a fire, imagine funnels with negativity going into the ground.

How does a heavy aura affect the interlocutor?

The bearer of a negative biofield greatly exhausts everyone around him, even with fleeting and sweet communication. If communication is prolonged, then a feeling of melancholy, melancholy, depression, and lack of faith in one’s strength arises.

There may be a feeling of loneliness, groundless aggression, and thoughts of suicide. At night the person will be tormented by nightmares.

The worst thing about the influence of heavy energy is that it attracts all sorts of minor failures and major troubles to the interlocutor. Therefore, many people immediately begin to feel inexplicable fear, anxiety, and approaching danger at the moment of communication.

At the physical level, the heavy energy of the interlocutor also makes itself felt. Usually a person begins to feel a headache, strange pressure and tingling in different parts of the body. The chest becomes compressed and the heart ache. Sometimes you feel like you have a cold with fever and sweat on your forehead. Asthmatic attacks, shortness of breath, and surges in blood pressure often begin. The consequence of a sudden loss of strength due to the energy pressure of someone else's aura is drowsiness, hiccups and yawning.

Negative energy in a person often becomes a cause of discomfort for himself and the people around him. Therefore, it is worth regularly diagnosing your own aura for negative clots and trying to look at the world with a positive outlook, sending only good intentions and thoughts to the world.

N.K. Gladysheva, IOSO RAO, school No. 548, Moscow

This issue has never been specifically discussed in detail in the so-called stable textbooks. It was considered too difficult for high school students. At the same time, “by default” students (and often teachers) believe that energy can only be a positive quantity. This leads to misunderstandings when analyzing energy conversion in various processes. For example, how to explain that when water is boiled, all the energy imparted to the substance goes to evaporation, while the average kinetic energy the motion of particles does not change, but the energy of interaction of particles becomes equal to zero? Where does the energy coming from the heater disappear? Many such examples can be given. But it is more expedient not to remain silent that the energy of interaction between bodies can be both positive and negative. The difficulties in understanding this provision are far-fetched. After all, even the students primary classes understand that ambient temperature can be either positive or negative! Moreover, schoolchildren quite easily perceive the existence, along with the Kelvin scale, of other temperature scales (Celsius, Fahrenheit, Reaumur). Thus, the idea that the numerical value of some physical quantity depends on a conventionally chosen origin of its reference is not incomprehensible to a high school student.

Selecting the potential energy reference point

We will show how to explain to students that when studying mechanical phenomena, in many cases it is convenient to choose the level of reference for potential energy so that it will have a negative value.

Analysis of energy transformation implies a more detailed familiarization of students with its forms. Any textbook reports that a body of mass m, moving relative to a chosen reference frame with some speed v, has kinetic energy Ekin = mv2/2 in this frame. If in some frame of reference the body is motionless, then its kinetic energy is equal to zero. Therefore, the kinetic energy of a body is called the energy of motion. Unlike other characteristics of motion, such as speed v or momentum p = mv, kinetic energy is not related to the direction of motion. It is a scalar quantity. It is advisable to invite students to independently show that the kinetic energy of a body and a system of bodies cannot be a negative quantity.

The nature of potential energy can be completely different. In the case of a mathematical pendulum (a material point of mass m suspended on a weightless inextensible thread of length l), it is associated with the attraction of the pendulum’s load by the Earth. It is this gravitational interaction that reduces the speed of the load as it moves upward. In the case of a tennis ball hitting a wall, potential energy is associated with the deformation of the ball. What the energy of interaction of the load with the Earth and the energy of deformation have in common is that such energy can be converted into kinetic energy and vice versa.

However, not all processes are reversible. For example, when a hammer hits a piece of lead, the kinetic energy of the hammer seems to disappear without a trace - the hammer almost does not bounce back after the impact. In this case, the kinetic energy of the hammer is converted into heat and its subsequent irreversible dissipation.

Let's take a closer look at the concept of potential energy. The nature of potential energy is different, so there is no single formula for calculating it. Of all types of interaction, we most often encounter the gravitational interaction of the Earth and bodies located near its surface, so first of all we should dwell on the discussion of the features of gravitational interaction.

What is the formula for calculating the potential energy of interaction of the Earth with bodies located near its surface? The answer is suggested by the oscillations of the pendulum. Please note (Fig. 1): points B, at which kinetic energy is completely converted into latent (potential) form, and point A,

where the kinetic energy of the pendulum is completely restored, lie at different heights above the Earth's surface. Huygens also found out that the height h of the pendulum's rise to point B is proportional to the square of its speed v2max at the bottom point A. Leibniz estimated the amount of latent (potential) energy at points B by the mass m of the pendulum's load and the height h of its rise during oscillations. Accurate measurements of the maximum speed vmax and height h show that the equality is always satisfied:

where g  10 N/kg = 10 m/s2. If, in accordance with the law of conservation of energy, we assume that all the kinetic energy of the pendulum is converted at points B into the energy of gravitational interaction of its load with the Earth, then the energy of this interaction must be calculated using the formula:

This formula hides a conditional agreement: the position of the interacting bodies, at which the energy of their interaction En is conventionally considered equal to zero (zero level), is chosen so that in this position the height h = 0. But when choosing the zero level, physicists are guided only by the desire to simplify the solution to the limit tasks. If for some reason it is convenient to assume that the potential energy is equal to zero at a point at a height h0  0, then the formula for potential energy takes the form:

Ep = mg(h – h0).

Consider a stone falling from a cliff (Fig. 2). It is necessary to determine how the kinetic energy Ek of the stone and the potential energy En of its interaction with the Earth changes as it falls. Suppose that at the edge of the cliff (point A) the speed of the stone is zero.

When a stone falls, its friction with the air is small, so we can assume that there is no dissipation of energy and its transformation into heat. Consequently, according to the law of conservation of energy, when a stone falls, the sum of the kinetic and potential energy of the system of bodies Earth + stone does not change, i.e.

(Ek + Ep)|B = (Ek+E0)|A.

Let us note the following.

1. According to the conditions of the problem at point A, the speed of the stone is zero, therefore Ek| A = 0.

2. It is convenient to choose the zero level of potential energy of interaction between the stone and the Earth in such a way as to simplify the solution of the problem to the utmost. Since only one fixed point is indicated - the edge of rock A - it is reasonable to take it as the origin and put Ep| A = 0. Then the total energy (Ek + Ep)|A = 0. Consequently, by virtue of the law of conservation of energy, the sum of the kinetic and potential energies of the stone and the Earth remains equal to zero at all points of the trajectory:

(Ek + Ep)|B = 0.

The sum of two non-zero numbers is equal to zero only if one of them is negative and the other is positive. We have already noted that kinetic energy cannot be negative. Therefore, from the equality (Ek + Ep)|B = 0 it follows that the potential energy of interaction of a falling stone with the Earth is a negative quantity. This is due to the choice of the zero potential energy level. We took the edge of the rock as the zero reference point for the coordinate h of the stone. All points through which the stone flies lie below the edge of the cliff, and the values of the h coordinates of these points lie below zero, i.e. they are negative. Consequently, according to the formula En = mgh, the energy En of the interaction of a falling stone with the Earth must also be negative.

From the equation of the law of conservation of energy Ek + En = 0 it follows that at any height h down from the edge of the rock, the kinetic energy of the stone is equal to its potential energy taken with the opposite sign:

Ek = –En = –mgh

(It should be remembered that h is a negative value). Graphs of the dependence of potential energy Ep and kinetic energy Ek on coordinate h are shown in Fig. 3.

It is also useful to immediately examine the case when a stone is thrown upward at point A with a certain vertical speed v0. At the initial moment, the kinetic energy of the stone is Ek = mv02/2, and the potential energy, by convention, is zero. At an arbitrary point in the trajectory, the total energy is equal to the sum of the kinetic and potential energies mv2/2 + mgh. The law of conservation of energy is written as:

mv02/2 = mv2/2 + mgh.

Here h can have both positive and negative values, which corresponds to the stone moving upward from the throwing point or falling below point A. Thus, for certain values of h the potential energy is positive, and for others it is negative. This example should show the student the convention of assigning potential energy a certain sign.

After familiarizing students with the above material, it is advisable to discuss the following questions with them:

1. Under what condition is the kinetic energy of a body equal to zero? potential energy of the body?

2. Explain whether the graph in Fig. 1 corresponds to the law of conservation of energy of the system of bodies Earth + stone. 3.

3. How does the kinetic energy of a thrown ball change? When does it decrease? is it increasing?

4. Why, when a stone falls, its potential energy turns out to be negative, but when a boy rolls down a hill, it is considered positive?

Potential energy of a body in a gravitational field

The next step involves introducing students to the potential energy of a body in a gravitational field. The energy of interaction of a body with the gravitational field of the Earth is described by the formula En = mgh only if the gravitational field of the Earth can be considered uniform, independent of coordinates. The gravitational field is determined by the law of universal gravitation.

N.K. Gladysheva, IOSO RAO, school No. 548, Moscow

This issue has never been specifically discussed in detail in the so-called stable textbooks. It was considered too difficult for high school students. At the same time, “by default” students (and often teachers) believe that energy can only be a positive quantity. This leads to misunderstandings when analyzing energy conversion in various processes. For example, how can we explain that when water is boiled, all the energy imparted to the substance goes to evaporation, while the average kinetic energy of particle motion does not change, and the interaction energy of particles becomes equal to zero? Where does the energy coming from the heater disappear? Many such examples can be given. But it is more expedient not to remain silent that the energy of interaction between bodies can be both positive and negative. The difficulties in understanding this provision are far-fetched. After all, even primary school students understand that the ambient temperature can be both positive and negative! Moreover, schoolchildren quite easily perceive the existence, along with the Kelvin scale, of other temperature scales (Celsius, Fahrenheit, Reaumur). Thus, the idea that the numerical value of some physical quantity depends on a conventionally chosen origin of its reference is not incomprehensible to a high school student.

Selecting the potential energy reference point

Ep = mg(h – h0).

(Ek + Ep)|B = (Ek+E0)|A.

Let us note the following.

1. According to the conditions of the problem at point A, the speed of the stone is zero, therefore Ek| A = 0.

(Ek + Ep)|B = 0.

Ek = –En = –mgh

(It should be remembered that h is a negative value). Graphs of the dependence of potential energy Ep and kinetic energy Ek on coordinate h are shown in Fig. 3.

mv02/2 = mv2/2 + mgh.

After familiarizing students with the above material, it is advisable to discuss the following questions with them:

1. Under what condition is the kinetic energy of a body equal to zero? potential energy of the body?

2. Explain whether the graph in Fig. 1 corresponds to the law of conservation of energy of the system of bodies Earth + stone. 3.

3. How does the kinetic energy of a thrown ball change? When does it decrease? is it increasing?

4. Why, when a stone falls, its potential energy turns out to be negative, but when a boy rolls down a hill, it is considered positive?

Potential energy of a body in a gravitational field

where R is the radius vector drawn from the center of mass of the Earth (taken as the origin) to a given point (recall that in the law of gravity, bodies are considered point-like and motionless). By analogy with electrostatics, this formula can be written as:

and call it the vector of the gravitational field intensity at a given point. It is clear that this field changes with distance from the body creating the field. When can a gravitational field be considered homogeneous with sufficient accuracy? Obviously, this is possible in a region of space whose dimensions h are much smaller than the distance to the center of the field R. In other words, if you are considering a stone falling from the top floor of a house, you can safely ignore the difference in the value of the gravitational field on the top and bottom floors. However, when studying the movement of planets around the Sun, one cannot assume that the planet is moving in a uniform field, and one should use the general law of gravitation.

You can derive a general formula for the potential energy of gravitational interaction between bodies (but do not ask students to reproduce this conclusion, although they, of course, should know the final formula). For example, let's consider two stationary point bodies of masses m1 and m2, located at a distance R0 from each other (Fig. 4). Let us denote the energy of gravitational interaction of these bodies by En0. Let us further assume that the bodies have moved slightly closer to the distance R1. The energy of interaction of these bodies became En1. According to the law of conservation of energy:

Ep = Ep1 – Ep0 = Fthrust. avg s,

where Fthrust cр – the value of the average gravitational force in the section s = R1 – R0 of the body moving in the direction of the force. According to the law of universal gravitation, the magnitude of the force is:

If the distances R1 and R0 differ little from each other, then the distance Rav2 can be replaced by the product R1R0. Then:

In this equality En1 corresponds to corresponds . Thus:

We have obtained a formula that indicates two features of the potential energy of gravitational interaction (it is also called gravitational energy):

1. The formula itself already contains the choice of the zero level of potential gravitational energy, namely: the energy of gravitational interaction of bodies becomes zero when the distance between the bodies in question is infinitely large. Please note that this choice of zero value of the energy of gravitational interaction of bodies has a clear physical interpretation: when the bodies move infinitely far from each other, they practically cease to interact gravitationally.

2. Since any real distance, for example between the Earth and a rocket, of course, the energy of gravitational interaction with such a choice of reference point is always negative.

In Fig. Figure 5 shows a graph of the dependence of the energy of gravitational interaction of the rocket with the Earth on the distance between the center of the Earth and the rocket. It reflects both features of gravitational energy that we talked about: it shows that this energy is negative and increases towards zero as the distance between the Earth and the rocket increases.

Communication energy

The knowledge acquired by students that energy can be both positive and negative quantities should find its application in the study of the binding energy of particles of a substance in its various states of aggregation. For example, students can be offered the following qualitative reasoning.

We have already seen that particles of matter always move chaotically. It was by endowing particles with the ability to move in this way that we were able to explain a number of natural phenomena. But then why don’t tables and pencils, walls of houses and ourselves scatter into separate particles?

We have to assume that particles of matter interact and are attracted to each other. Only a sufficiently strong mutual attraction of particles can hold them near each other in liquids and solids and prevent them from quickly scattering in different directions. But why then do the particles in gases not stay close to each other, why do they fly apart? Apparently, in gases the interconnection of particles is not sufficient to retain them.

In mechanics, to evaluate the interaction (connection) of bodies, we used such a physical quantity as the potential energy of interaction. In the kinetic theory of matter, the connection between particles of matter is characterized by the energy of their interaction Ec (this energy is not always potential). The fact that particles in liquids and solids hold each other, but not in gases, suggests that the binding energy of particles with each other in these media is different.

Gas. In a gas, the distance between particles is large and their connection is weak. The particles occasionally collide with each other and with the walls of the vessel. The collisions are elastic in nature, i.e. total energy and total momentum are conserved. In the intervals between collisions, particles move freely, i.e. do not interact. It is reasonable to assume that the interaction (bond) energy of particles in a gas is approximately zero.

Liquid. In a liquid, particles are brought closer together and partially touch. Their mutual attraction is strong and is characterized by the binding energy Ecw (water). To tear off one molecule from the bulk of the liquid, it is necessary to perform work A > 0. As a result, the molecule will become free, as in a gas, i.e. its binding energy can be considered equal to zero. According to the law of conservation of energy, Ecw (water) + A = 0, from which Ecw (water) = –A< 0.

To determine the numerical value of the energy Eb(water) of particles in water, let us turn to experiment. Already everyday observations suggest: in order to evaporate water boiling in a kettle, you need to burn a certain amount of wood or gas. In other words, work needs to be done. Using a thermometer, you can make sure that the temperature of boiling water and the temperature of the steam above it are the same. Consequently, the average energy of particle motion in boiling water and in steam is the same. The thermal energy transferred to boiling water from the fuel is converted into the interaction energy of particles of evaporating water. This means that the energy Eb of particles in boiling water is less than in water vapor. But in a pair Ec(pair) = 0, therefore, the energy of interaction of particles in a liquid is less than zero, i.e. negative.

Measurements using calorimeters show that to evaporate 1 kg of boiling water at normal atmospheric pressure, about 2.3  106 J of energy must be transferred to it. Part of this energy (approximately 0.2  106 J) is spent so that the resulting water vapor can displace air particles from a thin layer above the surface of the liquid. The rest of the energy (2.1  106 J) goes to increase the binding energy of water particles during their transition from liquid to vapor (Fig. 6). Calculations show that 1 kg of water contains 3.2  1025 particles. Dividing the energy 2.1  106 J by 3.2  1025, we obtain: the binding energy Eb of each water particle with other particles during its transition from liquid to vapor increases by 6.6  10–20 J.

Solid. To melt and turn ice into water, you need to do work or transfer a certain amount of heat to the ice. Binding energy of water molecules in the solid phase Eb< 0, причем эта энергия по модулю больше, чем энергия связи молекул воды в жидкой phase. When ice melts, its temperature remains 0 °C; The water formed during melting has the same temperature. Therefore, in order to transfer a substance from a solid to a liquid state, it is necessary to increase the interaction energy of its particles. To melt 1 kg of ice that has already begun to melt, you need to expend 3.3  105 J of energy (Fig. 7). Almost all of this energy is used to increase the binding energy of particles during their transition from ice to water. Sharing energy

3.3  105 J per number of 3.2  1025 particles contained in 1 kg of ice, we find that the interaction energy Eb of ice particles is 10–20 J less than in water.

So, the interaction energy of vapor particles is zero. In water, the binding energy of each of its particles with other particles is approximately 6.6  10–20 J less than in steam, i.e. Eb(water) = –6.6  10–20 J. In ice, the binding energy of each particle with all other ice particles is 1.0  10–20 J less than in water (and accordingly 6.6  10– 20 J + 1.0  10–20 J = 7.6  10–20 J less than in water vapor). This means that in ice Ec(ice) = –7.6  10–20 J.

Consideration of the features of the interaction energy of particles of a substance in various states of aggregation is important for understanding the transformation of energy during transitions of a substance from one state of aggregation to another.

Let us give, in particular, examples of questions that students can now answer without much difficulty.

1. Water boils at a constant temperature, absorbing energy from the flame of a gas burner. What happens when this happens?

A) The energy of movement of water molecules increases;

B) the interaction energy of water molecules increases;

C) the energy of movement of water molecules decreases;

D) the interaction energy of water molecules decreases.

(Answer: B.)

2.When melting ice:

A) the kinetic energy of a piece of ice increases;

B) the internal energy of ice increases;

C) the potential energy of a piece of ice decreases;

D) the internal energy of ice decreases.

(Answer: B.)

Until now, we have considered the energy of interaction between bodies attracting each other. When studying electrostatics, it is useful to discuss with students the question of whether the interaction energy of particles is positive or negative when they repel each other. When particles repel each other, there is no need to impart energy to them in order to move far away from each other. The interaction energy is converted into the energy of motion of flying particles and decreases to zero as the distance between particles increases. In this case, the interaction energy is a positive quantity. The identified features of interaction energy can be consolidated when discussing the following issues:

1. Is the energy of interaction between two oppositely charged balls positive or negative? Justify your answer.

2. Is the energy of interaction between two similarly charged balls positive or negative? Justify your answer.

3. Two magnets approach each other with like poles. Does the energy of their interaction increase or decrease?

Communication energy in the microcosm

According to the concepts of quantum mechanics, an atom consists of a nucleus surrounded by electrons. In the reference frame associated with the nucleus, the total energy of the atom is the sum of the energy of electron motion around the nucleus, the energy of the Coulomb interaction of electrons with a positively charged nucleus, and the energy of the Coulomb interaction of electrons with each other. Let's consider the simplest of atoms - the hydrogen atom.

It is believed that the total energy of an electron is equal to the sum of the kinetic energy and the potential energy of the Coulomb interaction with the nucleus. According to Bohr's model, the total energy of an electron in a hydrogen atom can only take on a certain set of values:

where E0 is expressed in terms of world constants and the mass of the electron. It is more convenient to measure the numerical values of E(n) not in joules, but in electron volts. The first allowed values are:

E(1) = –13.6 eV (energy of the ground, most stable state of the electron);

E(2) = –3.4 eV;

E(3) = –1.52 eV.

It is convenient to mark the entire series of allowed values of the total energy of a hydrogen atom with dashes on the vertical energy axis (Fig. 8). Formulas for calculating possible values of electron energy for atoms of other chemical elements are complex, because Atoms have many electrons that interact not only with the nucleus, but also with each other.

Atoms combine to form molecules. In molecules, the picture of the movement and interaction of electrons and atomic nuclei is much more complex than in atoms. Accordingly, the set of possible values of internal energy changes and becomes more complex. The possible values of the internal energy of any atom and molecule have some features.

We have already clarified the first feature: the energy of an atom is quantized, i.e. can only take a discrete set of values. The atoms of each substance have their own set of energy values.

The second feature is that all possible values E(n) of the total energy of electrons in atoms and molecules are negative. This feature is associated with the choice of the zero level of interaction energy between the electrons of an atom and its nucleus. It is generally accepted that the interaction energy of an electron with a nucleus is zero when the electron is removed at a large distance and the Coulomb attraction of the electron to the nucleus is negligible. But in order to completely tear an electron away from the nucleus, you need to expend some work and transfer it to the nucleus + electron system. In other words, in order for the energy of interaction between an electron and a nucleus to become zero, it must be increased. And this means that the initial energy of interaction between the electron and the nucleus is less than zero, i.e. negative.

The third feature is that those made in Fig. 8, the marks of possible values of the internal energy of an atom are terminated at E = 0. This does not mean that the energy of the electron + nucleus system cannot, in principle, be positive. But when it reaches zero, the system ceases to be an atom. Indeed, at the value E = 0, the electron is removed from the nucleus, and instead of a hydrogen atom, there is an electron and a nucleus that are not connected to each other.

If the detached electron continues to move with kinetic energy Ek, then the total energy of the system of no longer interacting particles ion + electron can take on any positive values E = 0 + Ek.

Issues for discussion

1. What components make up the internal energy of an atom?

2. Why did we consider the energy of an atom only using the example of the hydrogen atom?

3. What conclusions about the features of the internal energy of an atom follow from its quantum mechanical model?

4. Why do we consider the internal energy of an atom or molecule to be negative?

5. Can the energy of an ion + electron group be positive?

Familiarity with the internal energy of an atom will not only consolidate knowledge about the possibility of negative values of potential energy, but also explain a number of phenomena, for example, the phenomenon of the photoelectric effect or the emission of light by atoms. Finally, the knowledge gained will allow you to discuss very interest Ask about the interaction of nucleons in the nucleus.

It has been established that the atomic nucleus consists of nucleons (protons and neutrons). A proton is a particle with a mass 2000 times greater than the mass of an electron, carrying a positive electrical charge (+1). As is known from electrodynamics, charges of the same sign repel each other. Therefore, electromagnetic interaction pushes protons apart. Why doesn't the core fall apart into its component parts? Back in 1919, while bombarding nuclei with α-particles, E. Rutherford found out that in order to knock a proton out of the nucleus, the α-particle must have an energy of about 7 MeV. This is several hundred thousand times more energy than is required to remove an electron from an atom!

As a result of numerous experiments, it was established that particles inside the nucleus are connected by a fundamentally new type of interaction. Its intensity is hundreds of times greater than the intensity of the electromagnetic interaction, which is why it was called the strong interaction. This interaction has an important feature: it has a short range and “turns on” only when the distance between nucleons does not exceed 10–15 m. This explains the small size of all atomic nuclei (no more than 10–14 m).

The proton-neutron model of the nucleus allows one to calculate the binding energy of nucleons in the nucleus. Let us recall that according to measurements it is approximately equal to –7 MeV. Let's imagine that 4 protons and 4 neutrons combined to form a beryllium nucleus. The mass of each neutron is mn = 939.57 MeV, and the mass of each proton is mp = 938.28 MeV (here we use the system of units accepted in nuclear physics, in which mass is measured not in kilograms, but in equivalent energy units, recalculated using Einstein’s relation E0 = mc2). Consequently, the total rest energy of 4 protons and 4 neutrons before they combine into a nucleus is 7511.4 MeV. The rest energy of the Be nucleus is 7454.7 MeV. It can be represented as the sum of the rest energy of the nucleons themselves (7511.4 MeV) and the binding energy of nucleons with each other Eb. That's why:

7454.7 MeV = 7511.4 MeV + Ev.

From here we get:

Ep = 7454.7 MeV –7511.4 MeV = –56.7 MeV.

This energy is distributed over all 8 nucleons of the beryllium nucleus. Consequently, each of them accounts for approximately –7 MeV, as follows from the experiments. We again found that the binding energy of mutually attracted particles is a negative quantity.

5. States with negative energy. Positive electron

The equations of Dirac theory exhibit special properties, allowing solutions corresponding to the states of a particle whose energy can be negative. An electron in one of these states must have some rather strange properties. To increase his speed, energy must be taken away from him. And, on the contrary, to stop him, you need to give him some energy. In an experiment, an electron has never behaved so strangely. Therefore, it was quite legitimate to believe that states with negative energy, the existence of which is allowed by Dirac’s theory, are not actually realized in nature. One might say that in this sense the theory gives too much, at least at first glance.

The fact that Dirac's equations allow for the possibility of the existence of states with negative energy is undoubtedly a result of their relativistic nature. Indeed, even in relativistic dynamics electron, developed by Einstein within the framework of the special theory of relativity, reveals the possibility of motion with negative energy. However, at that time the difficulty in Einstein's dynamics was not very serious, because it, like all previous theories, assumed that all physical processes were continuous. And since the electron’s own mass is finite, it always has finite internal energy in accordance with the relativistic principle of equivalence of mass and energy. Since this internal energy cannot disappear, we cannot continuously move from a state with positive to a state with negative energy. Thus, the assumption of continuity of physical processes completely excludes this kind of transition.

Therefore, it is enough to assume that at the initial moment of time all electrons are in states with positive energy to see that the state always remains the same. The difficulty becomes much more serious in Dirac mechanics, for it is quantum mechanics, allowing for the existence of discrete transitions in physical phenomena. It can be easily seen that transitions between states with positive and negative energy are not only possible, but should also occur quite often. Klein gave an interesting example of how an electron with positive energy, entering a region where a rapidly changing field operates, can leave this region in a state with negative energy. Consequently, the fact that an electron with negative energy had never been discovered experimentally turned out to be very dangerous for Dirac’s theory.

To get around this difficulty, Dirac came up with a very ingenious idea. Noting that, according to the Pauli principle, which we will talk about in the next chapter, there cannot be more than one electron in one state, he assumed that in the normal state of the surrounding world, all states with negative energy are occupied by electrons. It follows that the density of electrons with negative energy is the same everywhere. Dirac hypothesized that this uniform density could not be observed. At the same time, there are more electrons than are needed to fill all states with negative energy.

This excess is represented by electrons with positive energy, which is what we can observe in our experiments. In exceptional cases, an electron with negative energy can, under the influence of an external force, transform into a state with positive energy. In this case, an observed electron instantly appears and at the same time a hole, an empty space, is formed in the distribution of electrons with negative energy. Dirac showed that such a hole can be observed experimentally and should behave like a particle with a mass equal to the mass of the electron and a charge equal to it, but of opposite sign. We will think of it as an anti-electron, a positive electron. This unexpectedly formed hole cannot exist for long. It will be filled with an electron with positive energy, which will undergo a spontaneous transition to an empty state with negative energy, accompanied by radiation. So, Dirac explained the unobservability of states with negative energy and at the same time predicted the possibility, albeit rare and ephemeral existence, of positive electrons.

Undoubtedly, Dirac's hypothesis was very simple, but at first glance it seemed somewhat artificial. It is possible that a large number of physicists would remain somewhat skeptical in this regard if experiment did not immediately prove the existence of positive electrons, the characteristic properties of which Dirac had just predicted.

Indeed, in 1932, first the subtle experiments of Anderson, and then Blackett and Occhialini, discovered that the decay of atoms under the influence of cosmic rays produces particles that behave exactly like positive electrons. Although it was still impossible to state absolutely strictly that the mass of the new particles was equal to the mass of the electron, and their electric charge was equal and opposite in sign to the charge of the electron, subsequent experiments made this coincidence more and more likely. Further, it turned out that positive electrons tend to quickly disappear (annihilate) when they come into contact with matter, and annihilation is accompanied by radiation. The experiments of Thibault and Joliot-Curie seemed to leave no doubt on this issue.

The exceptional circumstances under which positive electrons appear and their ability to annihilate, shortening their lifetime, are precisely the properties that Dirac foresaw. Thus, the situation turned out to be the opposite: the existence of solutions to the Dirac equations with negative energy not only does not call them into question, but, on the contrary, shows that these equations predicted the existence and described the properties of positive electrons.

Nevertheless, we must admit that Dirac's ideas about holes lead to serious difficulties regarding the electromagnetic properties of the vacuum. It is likely that Dirac's theory will be reformed and establish greater symmetry between both types of electrons, with the result that the idea of holes, together with the difficulties associated with it, will be abandoned. At the same time, there is no doubt that the experimental discovery of positive electrons (now called positrons) represents a new and remarkable confirmation of the ideas underlying Dirac mechanics. The symmetry between both types of electrons, which is established as a result of a more thorough study of some analytical features of the Dirac equations, is of great interest and undoubtedly will play an important role in the further development of physical theories.

From the book Physical Chemistry: Lecture Notes author Berezovchuk A V

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Many problems consider the one-dimensional motion of a body, the potential energy of which is a function of only one variable (for example, the coordinates X), i.e. P=P(x). A graph of potential energy versus some argument is called potential curve. Analysis of potential curves allows us to determine the nature of body movement.

We will consider only conservative systems, i.e. systems in which there are no mutual conversions of mechanical energy into other types.

Then the energy conservation law in the form (13.3) is valid. Let's consider a graphical representation of potential energy for a body in a uniform gravitational field and for an elastically deformed body.

Potential energy of a body of mass T, raised to a height h above the Earth's surface, according to (12.7), P(h) = mgh. The graph of this dependence P = P( h) - a straight line passing through the origin of coordinates (Fig. 15), the angle of inclination of which to the axis h the greater the greater the body weight (since tg = mg).

Let the total energy of the body be E(its graph is a straight line parallel to the axis h). On high h the body has potential energy P, which is determined by the vertical segment enclosed between the point h on the x-axis and graph P( h). Naturally, the kinetic energy T is given by the ordinate between the graph P(h) and the horizontal line HER. From Fig. 15 it follows that if h=h max , then T= 0 and P = E= mgh max, i.e. the potential energy becomes maximum and equal to the total energy.

From the graph below you can find the speed of the body at altitude h:

mv 2 /2=mgh max -mgh, where

v = 2g(h max -h).

Dependence of potential energy of elastic deformation P =kx 2 /2 from deformation X has the form of a parabola (Fig. 16), where the graph of the given total energy of the body E - straight, parallel to the axis

abscissa x, a values T and P are determined in the same way as in Fig. 15. From Fig. 16 it follows that with increasing deformation X The potential energy of the body increases, and the kinetic energy decreases. The abscissa x max determines the maximum possible tensile deformation of the body, and -x max determines the maximum possible compression deformation of the body. If x=±x max, then T=0 and П=E = kx 2 max /2, i.e. the potential energy becomes maximum and equal to the total energy.

From the analysis of the graph in Fig. 16 it follows that with the total energy of the body equal to E, the body cannot move to the right x max and to the left -x max, since kinetic energy cannot be a negative quantity and, therefore, potential energy cannot be greater than the total. In this case, they say that the body is in potential hole with coordinates

X max xx max .

In the general case, the potential curve can have a rather complex form, for example, with several alternating maxima and minima (Fig. 17). Let's analyze this potential curve.

If E is the given total energy of the particle, then the particle can only be located where P(x) E, i.e. in areas I and III. The particle cannot move from region I to III and back, since it is prevented potential barrierCDG, whose width is equal to the range of values X, for which E<П, а его высота определяется разностью П max -E. In order for a particle to overcome a potential barrier, it must be provided with additional energy equal to or greater than the height of the barrier. In area 1 particle with total energy E finds itself “locked” in a potential hole ABC and oscillates between points with coordinates x a And X C .

At the point IN with coordinate x 0 (Fig. 17) the potential energy of the particle is minimal. Since the force acting on the particle (see §12) F X =-d P / d x (P is a function of only one coordinate), and the condition for the minimum potential energy d P/ d x=0, then at the point INF x = 0. When a particle is displaced from position x 0 (both left and right) it experiences a restoring force, so position x 0 is position stable equilibrium. The specified conditions are also satisfied for the point X" 0 (for P max). However, this point corresponds to the position unstable balance, since when a particle is displaced from position X" 0 a force appears that seeks to remove her from this position.

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