Additional Information
Tachyon engine
Scientific progress is often achieved this way: first an invention appears, and then efforts are made to find out what was actually invented. Joanita Estevez built a tachyon engine five years before she realized the essence of her discovery.
Her achievement was evidence that it is possible to design and build a tachyon engine, knowing only hearsay about tachyons. When Estevez finally figured out how her invention worked, she named the effect, and then the engine, “tachyon,” after particles moving faster than light in a vacuum. Obviously, tachyons have nothing to do with it, but the name nevertheless stuck. A century after a new invention made it possible for a deep-space ship to travel through hyperspace for the first time and return safely to Earth, the engine was still called a tachyon engine.
Of course, Dr. Juanita Estevez was a genius, although, according to some of her colleagues, “with great regards.”
The device, which eventually turned out to be a prototype of a tachyon engine, was designed by her as a “matter separator.” Objects placed in its field disappeared, “split” into their constituent particles and, presumably, dissipated into the atmosphere. Caring most of all about her own safety, the doctor was in no hurry to share the intermediate results of her work. On the contrary, Estevets threw herself into it headlong, focusing on research in two directions: firstly, she wanted to measure the intensity of radiation of the “separated” particles into the atmosphere, and secondly, she tried to determine the power of the “separator” itself, experimenting with objects from various materials and different weights.
The doctor was unable to determine the “power of radiation,” but experiments with objects with different physical characteristics yielded unexpected results.
But even then chance intervened. In the meantime, Dr. Estevets had no idea that the tested objects were still moving somewhere, and not “separated”, but entirely. She also did not know that the location of the moved object depends on the mutual influence of the field magnitude, the mass of the object, as well as the direction and speed given to the object when exposed to the field (during these experiments, the rotation of the Laboratory Station provided both direction and speed).
One fine day, Dr. Estevets placed a titanium blank in the field of her device. Almost at the same moment, the Laboratory Station was rocked by an explosion that tore apart one of its bulkheads. The cause of the explosion became clear when a titanium block was found stuck in the bulkhead. The blank, having passed through hyperspace, entered the physical space already occupied by the bulkhead. Since the blank turned out to be harder than the bulkhead, the latter could not stand it and burst.
Naturally, no one attached any significance to this incident until Dr. Estevets rather timidly admitted that the blank belonged to her.
Continuation of research was in question. Dr. Estevez herself, embarrassed by her lack of understanding of her own experiments, became even more withdrawn and suspicious. The station's scientific director was torn between the desire to continue the experiments begun by Dr. Estevez and the temptation to remove her from research. The station's economic administrator opposed the entire project, arguing that the entire station was at risk of suffering from destruction.
But Dr. Estevez's research has gone too far to be stopped. Over time, the benefits they could bring became obvious. New models of the “matter separator” were built. Experiments on moving objects through hyperspace have resumed. The results of the experiments were processed by computers. Based on the results obtained, hypotheses were built, which, in turn, were tested by subsequent experiments.
So, the tachyon engine eventually found itself in the service of people. With its help, the transition from one dimension to another became possible as soon as the main characteristics of the hyperspatial field (mass, speed, hysteresis) were calculated, which happened long before the understanding of hyperspace itself by the scientific community of the Earth.
As always, humanity first took a step, and only then thought about its consequences.
Is time travel possible? And how to technically send messages to the past? How to talk to your future self? These questions have long been the subject of the most heated debates and the most passionate searches in the scientific community.
“Time is a dimension, but in this sense it is so unusual that we can only allow ourselves to move forward, with the flow, for as long as our existence in the Universe is possible. We are trying to find a way into the past, but in doing so we will be influencing a very important part of our physical universe called causation. If we want to travel back in time, we have to find a way to prevent causality from breaking,” says Charles Liu, a professor of astrophysics at the City University of New York College of Staten Island.
Free movement in the space-time continuum is a rather controversial topic due to the lack of a sufficient evidence base. No facts to rely on. Not a single clue. Nevertheless, the topic is very worthy and requires non-standard solutions. What if, instead of looking for a way to travel to the past or future, we do something more realistic - intertemporal communication, for example?
Dr. John Kramer, professor emeritus of physics at the University of Washington, believes that in addressing this global issue, we must learn the art of small, baby steps. If we have not yet learned how to move through time ourselves, then why not start with simpler things. After all, instead of people, we can send a message. The professor is currently working on the ability to receive a text message a millisecond before it was sent. He conducts his research in university laboratories using laser beams. Cramer really hopes to one day make ends meet with Einstein’s assumption of “ghostly action at a distance” (instantaneous nonlocal collapse of the wave function), finally getting out of the logical labyrinth of mutual substitution of the concepts of dynamic and kinematic principles of relativity. To this noble goal, he is attempting to split photons using a series of semiconductor nanocrystals to demonstrate that quantum nonlocality is quite suitable for communication between times.
“We must admit that we can send and receive the same letter at the same time,” says the now familiar authoritative nuclear physicist Kramer, who even dealt with the Large Hadron Collider in Switzerland.
For those who have never studied physics in high school, we will try to explain this in simpler and more understandable words. If you take a pair of photons created at the same time and try to change one of them, it will cause a corresponding instantaneous change in the second. Even if they are separated by a distance equal to a galaxy. This means that you can communicate at speeds exceeding the speed of light and send your messages over unimaginable distances.
Of course, this does not agree with the basic postulate of the theory of relativity, which states that no interaction can occur at a speed exceeding the speed of light in a vacuum. It is for this reason that Einstein called such entanglement “ghostly action at a distance.”
Even Einstein did not submit and seems somehow implausible, such an interaction is theoretically possible. Physicists call it “nonlocal quantum communication.”
"You'll be able to communicate with other planets in real time," says John Kramer. - “Wear a virtual helmet and drive your buggy along the distant dunes of Mars.”
In other words, it would give the world's space agencies the ability to communicate with their aircraft in real time. Unfortunately, due to insufficient funding, the fate of the project currently hangs in the balance. But the scientist does not lose heart.
“We will first need to develop a way to most efficiently detect the photons needed for the experiment,” he says. - “otherwise no further measurements can be made.”
Based on the famous “string theory” (ultramicroscopic filaments, the thinnest one-dimensional objects that can perform an infinite number of resonant vibrations and, when combined, create microparticles in ten dimensions), boson string theory speaks of an elementary particle that has no mass, which is called a tachyon and can move faster than light. But do tachyons exist in reality? And will they allow messages to travel in space and time? Nobody knows this yet. The presence of a tachyon in this theory only indicates its instability. This instability in string theory is explained by supersymmetry, which, in turn, leads to the emergence of the superstring theory - a hypothetical cosmic structure that holds the primary matter of the Universe.
Visualization of the tachyon
Tachyons so far only reveal the inconsistency of traditional mathematical calculations. It is believed that this question is tough only for physicists, who insist on one thing: the fact that no one has ever seen tachyons does not mean at all that they do not exist. Perhaps scientists have not yet been born who can create necessary tools. After all, the lion's share of success depends on this.
And if the tachyon exists, then it would theoretically be possible to send messages at superluminal speeds. These particles could easily travel into the past and leave their traces there. To avoid this problem (after all, time travel can destroy all existing laws of the physical world!) back in 1967, the American theoretical physicist Gerald Feinberg presented his principle of reinterpretation: a tachyon traveling into the past, in the antiworld - a logical consequence of the future theory of loop quantum gravity - is a tachyon traveling into the future. In other words, as strange as it may seem, sending and receiving tachyon is the same action, combining two sides of the same coin.
“There is no other way to explain the difference that would make it possible to send and receive such messages,” wrote Andrew Zimmerman Jones and Daniel Robbins in their book String Theory for Dummies.
If Kramer manages to take the first step, then the second may turn out to be truly fateful in the history of mankind. “I’m a little scared because the consequences can be unpredictable,” says the professor.
Tachyons are in stock call 8 916 916 16 16
Ether, prana and tachyon energy are one and the same; they spread everywhere and are located at any point in space-time-dimension.
This is the great secret of zero point technology.
(Drunvalo Melchizedek)
Tachyons are elementary particles moving faster than light, carriers of universal cosmic energy that precedes the energy of light. (Greek “Takhi” - fast, ion - particle). The energy of Tachyons has always existed; it is a spectrum of certain vibrations of the Universe. This energy has pure, high-level consciousness. Tachyons have incredible healing powers. The Tachyon energy - being in the human field - harmonizes, balances and supports all human systems, both on the physical and energetic levels. It rejuvenates the entire body. This energy comes where it is needed. It will help you remember the mechanisms of self-regulation and regeneration, in the restoration of all cellular structures. Using Tachyons, you will much more easily realize your true inner potential and realize it in your life. On an energetic level, it is the balancing and restoration of the chakras to their natural, original state of verticality, as a result of which you turn into a superconductor and transmitter of universal energy. And on a spiritual level, this energy will help us to be active creators of our reality. If you are very interested in something and would like to reveal some talent or ability, Tachyons will help you.
The energy of Tachyons cannot be used to harm any person, because this energy has a very high level of consciousness that understands what is happening in all dimensions of reality. It is polar, which means that there is no opposite energy of tachyons, and it does not have the properties of ordinary minerals that need to be energetically “purified”. On top of this, this energy is very rarely “attached” to any individual, i.e. Any tachyonized item can be freely used by several people in a row. If these products need to be cleaned, it will only be from elementary dust. Even if these products are partially destroyed (in case of careless handling), they will still retain the tachyon energy field.
Tachyons can be used different ways- for example, as a decoration - a pendant - to harmonize the level of your physical and emotional activity during the day, and will also serve as your guide in meditation and will prove to be an indispensable assistant for supporting any work with your energy fields. Tachyons affect the physical aspects of our body, as well as plants, food and animals.
Tachyon energy helps to maintain a high level of awareness of your life, confidence in your strengths and in your truth, without manipulation and pressure, with respect for your own path. All this happens due to the fact that you become a spiritual teacher for yourself.
These products are from the Terra Tachyon series.
The colors of tachyons have their own meanings.
Red: color of earthly and physical strength (first Chakra)
Abundance of energy and stability. Red is associated with the earth and is grounding, as well as the first or root chakra and its corresponding organs - the lower pelvis, legs, knees and spine. If you feel low on energy, it is recommended to wear one of the red tachyonized products.
Orange: the color of creative awareness, sexual expression and joy (second Chakra)
Creativity, sexuality, joy and strength. Like red, orange is useful for grounding, as well as for skin problems and depression.
Yellow: color of mood and misunderstood emotions, associated with the solar plexus (third Chakra)
Balance of emotions and support of internal organs. Yellow is associated with all emotional manifestations - with a feeling of strength and energy, and their lack. Yellow is very useful when you need to harmonize your emotions.
Green: the color of emotional awareness, kindness and heart balance. Also good for all kinds of relaxation (fourth Chakra). Balancing heart energy, relieving tension, stress, peace and opening the heart. Green is associated with both physical and evolutionary development, and is useful when we need to make decisions based on the dictates of the heart. Green has a calming effect in stressful situations.
Light blue: the color of easy self-expression and self-knowledge. Energy balance (fifth Chakra) - neck and shoulders. Communication and self-expression. The color blue symbolizes all types of creativity and all methods of oral communication. Blue - useful when you find it difficult to explain something.
Sapphire Blue: the color of inner peace, freedom and awareness. Associated with increased brain activity in order to balance it.
(sixth Chakra). Expanded perception and inner peace. Blue color is associated with the expansion of consciousness, intuition, insight, and the formation of internal space. This color protects against the tendency to absorb the emotions and moods of other people.
Amethyst: the color of consciousness, and the path to awareness of consciousness in everything (seventh Chakra). Color promotes the transition from the material and physical plane to spiritual knowledge. Helps activate thought processes.
Golden-Topaz: the color of abundance, which manifests itself in the possibility of manifesting various situations and goals.
Abundance, happiness, balance of various forces. Golden Topaz is the color of the sun and balanced energy. Also called “enlightened yellow,” this color strengthens the solar plexus, preventing simmering emotions from taking over, so you can make decisions based on pure intuition. The color Topaz, which represents abundance, can be important when you need to 'bundle' a variety of energies and put them into one 'container'.
Pink: the color of heaven on earth, or manifestations of divinity in everyday life. Associated with the unification of soul, mind and matter.
The color of Unconditional love, the cosmic Heart. Pink is the color of love and has beneficial effects for the heart. Pink is also the color that guides us to the original cosmic force, i.e. cosmic heart.
Aqua: the color of curiosity, awareness and deepening connections on a global scale. Associated with the unification of heart and brain qualities.
Expanded communication with the outside world; overcoming manipulation and the color of the Age of Aquarius. The color aqua is associated with communication in the broadest sense of the word. Sea green tachyonized products provide you with optimal support when making telephone calls, writing letters, giving lectures, selling products and services, and writing books.
Opal: color to delve into the invisible, to perceive its essence and make it visible. Associated with the beginning of the creative process.
Self-realization, the ability to see and realize things and situations that may be hidden from you. Opal is the color of the moon and reflected energy. It is associated with the perception of structures that move between visible and invisible spheres. Opal can be a disturbing color because it is not always easy to look for what is yet unknown within yourself that is ready to be revealed.
White: the color of action energy to react and respond accordingly. Associated with the conscious process of being an observer.
The color of actions, ideas and their practical application. White color is associated with the discovery of ideas or the initial stage of action, and with their implementation.
Crystal Clean: the color of clearing, clearing and letting go of shadows and chronic problems. Associated with the purity of diamonds and therefore the purity of Self.
Self-confidence, the understanding that comes with actions. Crystal clear is the most significant “color” among tachyonized products. It represents clarity and understanding on all levels and is a "color" that is extremely useful for working with all issues, both body and mind. Promotes self-confidence and self-awareness. Useful for all types of chronic diseases.
Lilac: color for new opportunities, opportunities, probabilities and discoveries. Associated with joyful changes on various levels.
The color of growth and new beginnings, like the arrival of Spring after a long Winter. Lilac is a typical spring color that supports growth processes and the experience of “personal rebirth”. It is also the color of alertness towards the world and untapped opportunities, the color of the joy of feeling when, after a long and difficult winter, we feel the first warm rays of the Sun.
Star Ring Red-Gold: color to activate the subconscious power in everyone - to be recognized and purposeful in order to evolve into a multidimensional creation (Star Ring only).
Unity of material and spiritual forces (Star Ring only). The red-gold color helps to unite your own strengths.
Black: the color of conscious transformation and creativity. Associated with filling the voids of the meaning of birth.
Transformation, primordial feminine energy Universe. The color black represents the original woman and the formless nothingness that allows the coming of life to be formed. Black also represents abundance, which appears empty and hidden at the same time.
Small Tree of Life
Supports you in working towards your own potential. Despite its smaller size compared to the others, its energy is more intense. The Small Tree of Life can be used to resolve worries or to work in meditation, as well as for energetic work on the chakras.
Advice: A small but intense Tree of Life will stimulate your meditation, work on visions, and reflections.
Small donat
A great pendant and an easy way to support and energize your body every day. The small donat has a triple helix on one side to concentrate energy.
Tip: due to its size and weight, the small donation is perfect for wearing directly on the skin for focused nourishment of the body.
Average donation
The middle donut is a fashionable pendant that carries the charm of modest elegance. Supports you by helping you find personal balance. An average donation gives energy and creates an atmosphere - even after a hard day.
Big donation
A large donation creates a powerful energy field and very effectively supports you throughout the day. To concentrate energy, a seven-pointed spiral is located on one side.
Tip: To effectively exchange energy with the earth, place a large red donut under your feet.
star ring
The soul is a form of universal consciousness. She is not tied to the earth. She loves to visit Earth and other systems in the Universe and even other universes and realms. Often the soul loses memories of its wanderings or cannot realize them, since it is not trained for this.
The star ring clarifies the experience of communicating with the energies of other planets and other systems. It also reminds us that we are not just human beings, but soul travelers.
This is the name given to particles whose speed exceeds the speed of light in a vacuum. Let us immediately make a reservation that we are talking about hypothetical particles: experimental attempts to detect such particles have not been successful. But the very assumption of their existence seems paradoxical: SRT is based on the limited speed of signal transmission, and the limit is precisely the speed c. Of course, there are no restrictions on speed “in general” (see § 8.1), but signal transmission is the spread of energy and momentum. The movement of particles that we are accustomed to can certainly serve as a signal. In addition, for ordinary particles with a finite rest mass, the existence of which we have become accustomed to, the speed of light is simply unattainable. From the relativistic equation of motion for such particles it follows that the speed of light can only be achieved over an infinitely long time (not to mention the fact that in order for them to reach the speed of light, infinitely more energy is required). Thus, the question of superluminal speed of particles of our ordinary world disappears immediately.
It is possible, however, to assume the existence of a special group of particles, the transition from which to ordinary particles or vice versa is impossible. These particles could be generated in some kind of nuclear transformations immediately at superluminal speeds. The assumption about the emergence of tachyons is inspired by the picture of the generation of photons: photons are immediately generated at the speed of light,
but do not arise “dynamically” at all during the acceleration of ordinary particles.
In exactly the same way as in § 3.5, it can be shown that if in one ISO the particle velocity is greater than c, then this is also true in any other ISO. Consequently, ordinary particles (photons) and tachyons form independent groups of particles in the sense that transitions from one group to another due to the acceleration of particles are impossible and that the transition from one ISO to another leaves the particle in the same group in which it was located and in the original ISO.
Let us assume the existence of such particles and consider the kinematic consequences of this assumption.
So, we assume that the tachyon speed (determined in the usual way) is greater than c, i.e. . Then for the interval between two events - the positions of the tachyon at two points in space at two moments in time - we, as usual, obtain (one-dimensional movement along the axis
For a tachyon (as opposed to ordinary particles), that is, the interval is spacelike; We saw in § 3.4 that in this case the concepts of “later” and “earlier” for two events are no longer absolute. Consequently, there are frames of reference where the tachyon moves in one direction, and those where it moves in the opposite direction. It is possible to find a condition imposed on the tachyon speed so that in some system K its motion is “reverse”. In the K system for the tachyon
We believe (for any time interval will differ in sign from (which means a change in the sequence of events in time), if From here the desired condition is found, it is clear that Differences in the description of the tachyon motion in systems are clearly visible in Fig. 8.7, a. The lines of simultaneity in K are parallel axis, drawing them further and further along the positive axis, we mark the position of the tachyon more and more to the right - the tachyon is moving to the right. The lines of simultaneity in K are parallel to the x-axis. If we draw these lines so that they intersect the axis further and further along the positive direction of the axis we find the tachyon more and more to the left - the tachyon is moving to the left.
The same result can be presented even more dramatically (Fig. 8.7, b). Let in the K system a tachyon leave point O and arrive at the world point P. In the K system, as can be seen in the figure, the tachyon was “emitted” at the moment (“earlier”) and arrived
to point P at the moment i.e. “later”. The same diagram shows the spatial and temporal axes of the K system (the lines of simultaneity in K are parallel to the axis. The figure shows that the tachyon in the K system was previously at point P (at the moment), then it moved to point 0, where it was absorbed (at moment ) Thus, only by choosing a reference frame can one obtain the movement of a tachyon in the opposite direction in space and detect absorption of a tachyon instead of emission in one reference frame.
Rice. 8.7. a) Movement of a tachyon considered in two ISOs. In the K system the tachyon moves to the right, in the K system it moves to the left. The thick line is the world line of the tachyon, b) Reversal of the order of events in time for a moving tachyon.
Let us note in passing the curious picture of the observation of a “luminous tachyon,” i.e., a tachyon emitting light. From Fig. 8.8 it is clear that an observer at rest in the K system will “see” two tachyons going in two opposite directions.
Let us now return to the reversal of the sequence of events in time, in particular the exchange of places of “emission” and “absorption”. At first glance, this situation contradicts the usual ideas about the relationship between cause and effect. Indeed, let it be known that in O there is a source of tachyons. The source is the "cause" of the tachyon. The movement of the tachyon towards P is a “consequence” of the generation of the tachyon. But observation in the K system shows that the tachyon comes from P and is absorbed into O. As unusual as this may be, we must still admit that the observed sequence does not contradict cause-and-effect relationships, if we clearly formulate what we mean by such relationships. You can reason, for example, like this.
We will assume that A is a cause, an effect, if the repetition of event A at moments of time chosen arbitrarily invariably leads to the occurrence of event B at the moment of time. Here, controlled repetitions of event A and their correlation with event B are essential. In this sense, cause-and-effect relationships do not depend on which event occurs “earlier” and which “later”.
Rice. 8.8. Observed picture of the motion of a luminous particle moving at superluminal speed.
The sequence of events over time is not part of the definition of causation and cannot serve to distinguish between cause and effect.
In our example in the K system, the controlled event is the absorption of a tachyon. This controlled absorption will always be preceded by the movement of the tachyon from P to O. We will have to recognize the absorption as the cause, and the movement of the tachyon as the effect. The above definition of cause and effect does not correspond to the usual statement that “the absolute meaning of the words “earlier” and “later”... is a necessary condition in order for the concepts of cause and effect to make sense.” Of course, if “cause” and “effect” occur at one point (in a given ISO), then the cause must be faster than the effect. But then the interval between events is obviously time-like and in any ISO the effect will be “later” than the cause. This cannot happen with tachyons. All “events” with tachyons occur, from our point of view, at different points. Sharing sequences of events is not scary.
So, a change in the temporal sequence of events does not violate the usual ideas of causality. But there is a condition that must be fulfilled unconditionally. It consists in the fact that one cannot influence the past from the present. A signal sent from a given point in space cannot appear there before it was sent.
If tachyons could serve as signals, then, as can be seen from the diagram in Fig. 8.9, they could be used to send a signal so that another signal caused by the first one would return to the point of sending the first signal (cause-and-effect cycle) before the first signal was emitted. In Fig. Figure 8.9 shows the world lines of two bodies I and II, which were initially at rest, then moving uniformly and rectilinearly with the same speeds, and then again at rest. World points A and A lie on the line of simultaneity, coinciding for both bodies in motion. World points C to C lie on the line of simultaneity, coinciding for both bodies at rest. The figure also shows the world lines of two superluminal signals and . By sending a signal and then (after receiving the signal) another signal, we will receive the signal at a point earlier than the signal from A was sent.
Rice. 8.9. A closed cause-and-effect cycle involving superluminal signals. Lines I, 11 - world lines of two systems of reference. The first superluminal signal is sent from point A - the line of simultaneity). From system II (point C) a reverse superluminal signal is sent which arrives at system I (point earlier than the first signal was sent (point A). Lines of simultaneity and world lines of superluminal signals are drawn in accordance with Fig. 2.6, b.
Thus, we have an example of a closed cause-and-effect cycle, when there is the possibility of influencing the past. Of course, this result applies to any superluminal signal, but when applied to tachyons, this means that tachyons themselves (unlike ordinary particles) can no longer serve as signals.
If we assume the possibility of the existence of tachyons and compliance with the requirements of the cause-and-effect cycle, then precisely the possibility of reversing the sequence of events in time for tachyons allows us to get rid of objections associated with the “dynamic” properties of these particles. If we consider the basic relations of SRT to be valid for tachyons, then from the transformation formulas for the velocity and energy of the particle
(see chapter 3, 5)
it follows that in those very reference systems in which the sequence of events for the tachyon changes its order (and in which the sign of the speed changes, which is due to the fact that the sign is different), the energy of the tachyon becomes negative. The negative energy of the tachyon is unacceptable because its presence would mean the possibility of unlimited energy production. Indeed, the joint generation of two tachyons - one with negative and the other with positive energy - would not require the expenditure of energy, and the resulting tachyon with positive energy could perform useful work.
But we have already seen (see Fig. 8.8) that if in the K frame the emission of a tachyon is observed, which is then absorbed, then in the K frame, in which the speed of the tachyon satisfies the condition, the same process can be described as an absorbed tachyon moving in the opposite direction direction, and the energy of the tachyon will already be positive. This circumstance allows us to bypass the difficulty associated with the appearance of negative energies.
Finally, a few comments regarding the momentum and energy of tachyons. It follows from STR (see Chapter 5), if we restrict ourselves to the one-dimensional case that
If we plot a graph, we get a hyperbola, and, as we saw (§ 5.5),
If a particle accelerates, then on the plane it moves along the hyperbola (8.11). The tangent slope is always less than c, regardless of how the energy of the particle increases - whether due to the acceleration of the particle or due to the transition to another frame of reference. Since the particle energy is positive, the lower branch of the hyperbola is not considered. Let us also pay attention to the fact that the asymptotes of the hyperbola, the equation of which will be, correspond to photons. If we assume that the basic formulas of relativistic mechanics are applicable to tachyons (see Chapter 5), then they become imaginary quantities, because where can we obtain real values of momentum and energy if we consider the quantity as mass? However, why is imaginary mass better than imaginary energy and momentum ? But the point is that
This is the imaginary proper mass of the tachyon, and there is no frame of reference where the tachyon would be at rest (the frame of reference consists of ordinary particles, and its speed is always less than c). Therefore, the tachyon’s own mass is unobservable and can be considered whatever it is.
But then on the plane we should consider two more hyperbolas corresponding to the imaginary own mass. Thus, on the plane we need to consider three hyperbolas (Fig. 8.10). The slope of the tangent to these hyperbolas is everywhere greater than c. Of course, the multiplier enters not only into the expressions for momentum and energy - it enters into the definitions of length through its own length and time intervals through its own time. But we can easily abandon the “own” quantities, considering them unobservable.
Rice. 8.10. Tachyons into ordinary particles depicted on a plane
Referring the reader to the literature for details, let us summarize some results.
Recently, attempts have been made - while remaining within the framework of STR - to find out the properties of particles whose speed exceeds c. From the point of view of SRT, velocities that do not correspond to the real physical distribution of anything can be anything. Ordinary particles always move at speeds less than c; any “signal” has a speed less than c. Consequently, the tachyon itself cannot serve as a signal, i.e. its interaction with our world is extremely limited. It is possible that it is possible to allow the interaction of tachyons with our world only through the exchange of electromagnetic signals.
If we proceed from the principle “everything that is not forbidden has the right to exist,” we should admit the possibility of the existence of tachyons. There is no direct theoretical ban on tachyons yet. However, it seems unlikely that such particles actually exist. The experiment has the last word.
§ 8.4. The clock paradox. This paradox - if there really is a paradox here - appears due to the repeatedly discussed differences in the timing of time intervals between events in different ISOs. Let us briefly recall the results needed further.
Let the body be at rest in the system K and, according to the clock moving with it and the system K, two events were noted at point x at the moments of time and The interval is a period of proper time, and it is natural to denote it by . Observers from K will mark these same two events at two points of the system K by two hours, these events are recorded at moments and The time interval between the same two events will be equal We know that
that is, the interval of proper time between events is less than the interval between those events, counted by the clock of the system relative to which the body moves (cf. § 3.3).
In formula (8.13) there is an obvious asymmetry in the timing. It would seem that one can reason like this. Since all clocks in K are synchronized, the time counted by different clocks in K can be equated to the counting of a period of time by one clock from K. Then it turns out that identical clocks in two ISOs K and K run differently. But SRT is based on the complete symmetry of inertial systems! And she really is! It’s just that our reasoning has missed an important detail. Since simultaneity is relative, clocks that are synchronized in one system are not synchronized at all from the point of view of another. Clock synchronization is relative! The quantity is not at all an interval of proper time for a clock from K. Let us make the corresponding calculation.
Let clock III be at rest at the beginning of system K, moving with speed V relative to K. Clock I, synchronized in system K and at rest in this system, is at point and clock II is at point
The variable coordinate of clock III in the K system is equal to Thus, the coordinates of clocks I, II, III in the K system will be
From the Lorentz transformation formula, one can obtain the dependence of the x coordinate in the K system on the time V in this system and the x coordinate in K, namely:
So we will find that it is obvious that Therefore,
As always, we believe that it is possible to compare clock readings from two systems when they are in the same location. Then it is actually possible to make the following comparisons. First, one can compare the readings of clock III with the readings of clock I as they pass each other; we will denote the corresponding clock readings by secondly, we can compare the readings of clocks III and II, when clock III passes by the clock we will denote these readings by (Fig. 8.11). When clock III coincides with I, then both clocks are at the point; therefore, according to (8.17), we will find the values of the moments of time and namely: . At the same time, from (8.16) we obtain . The readings are the readings of two different clocks synchronized in the K system.
Rice. 8.11. Explanation of the complete symmetry of two icercial reference systems in relation to the “slowdown” of time. In any reference system, the interval of proper time between two events will be less than the interval of time between the same two events, measured by two hours of any other ISO.
According to synchronization in this system, when clock II showed the moment, then clock I showed the same moment. The difference is the time elapsed in the K reference system, during which the reading of clock III changed to . From the point of view of system K, the course of clock III is determined by the relation
as it should be, since it is a period of proper time. Since the moving clocks observed from the K system are lagging behind. We know all this. Now we move on to the decisive step: we need to compare the progress of the clocks as it appears from the point of view of the K system. To judge the progress of the clocks, we need to follow the progress of some
hours, say hours II. But for these clocks there is only one direct indication: when they were opposite clock III, then clock III showed and clock II showed Another reading of clock II needs to be calculated (cf. § 2.4). We will find where clock II was and what it showed when clock I was opposite clock III. We will answer all the questions posed from the point of view of the K system. When clock III was opposite I, it showed the time. Clock II was located from clock I by distance But when clock I was opposite III, then their coordinates Therefore, this is the coordinate of clock II at the moment when clocks I and III coincide. But now it is not difficult to find the reading of clock II at the same moment in time. Into the formula
we will substitute the values (The value, due to the synchronization of the clocks in K, will coincide with the reading of the clock from K, located at the point so) As a result of the substitution, we will obtain the reading of clock II:
If clocks I and II were synchronized, they would show the same time. But they are synchronized only in K, but not in K. We see that from the point of view of K, the clocks of the K system are experiencing desynchronization, a difference in readings accumulates
increasing as the hours move away from each other. We already obtained this result in § 2.4. Since in the K system the distance is then the reading of clock II will be Comprising the difference between the marked time and the calculated one, we get
or, according to (8.20),
And this means that an observer in system K will find that the clock moving relative to him is lagging behind. Thus, the complete equality of systems is proven.
This result confirms the complete equality of the two considered inertial systems: if two ISOs have two
identical clocks, then the intervals of proper time counted by these clocks are identical. Of course, it cannot be otherwise, since one of the first principles of STR is the principle of relativity: if identical clocks ran differently in two ISOs, then this would be a physical way to distinguish these systems.
Although this clarification needed to be made, this is, of course, not the paradox of the clock. Suppose we compared the readings of two clocks: some from the K system, and the other from K. The clocks, naturally, will immediately diverge after the comparison and will move further and further away from each other. But if, nevertheless, one of them is somehow returned to the same point where the other clocks are located, and their readings are again compared, what will we discover then? The answer to this question is called the clock paradox. This answer is not at all simple, and the reader should be patient.
Rice. 8.12. World lines of two hours I and II. The world line corresponds to clock I, which is at rest in K. Clock II first moves uniformly from clock I (the line then, having changed its speed at exactly T to an equal but opposite direction, again approaches clock I. At a point they find themselves next to each other, and you can compare their readings again (the first comparison took place at point O). Comparison of clock readings is precisely what is called the clock paradox. In the inset: the world line of one clock returning to point
First of all, we note that all formulas of SRT refer to quantities considered within the framework of inertial reference systems. All time measurements that are made in the service station are carried out by a clock stationary in one or another ISO. Having compared two clocks once, we can no longer bring them together again at one point in space without taking them out of the frame of reference where they were at rest during the first comparison. Indeed, if the movement is rectilinear, it is necessary to first slow down one clock, and then give it a speed of the same value, but in the opposite direction. Then the clock, the direction of movement of which we changed, after some time will find itself in the same place with the clock with which the comparison was made. All this is clearly visible on the Minkowski diagram, which shows the world lines of two clocks - (Fig. 8.12).
It is very convenient to consider the “clock paradox” using the coefficient method (§ 3.7). We will use the space-time diagram in Fig. 8.12. Here the world lines of three clocks are depicted: some located at the beginning of K (line of others (II), resting at the beginning of K (line , finally, we can find the time interval between the reception of the light signal by clock I (point E) and the meeting of clocks I and III at point We saw in § 3.7 that when the sign of the relative speed of two reference systems changes, the coefficient k changes to Therefore, the time interval, which is depicted in Fig. 8.12 by a segment, is equal to From the symmetry of the thought experiment used, it is clear that Denoting the value of this time interval by we get, that the period of time measured by clock I between the meeting of clock I with clock II and clock III is equal to
But the total time counted by two observers (clocks II and III) is equal to . This value is always less than (8.22), because it immediately follows from the inequality that
This reasoning has the undoubted merit that all time readings are made by clocks at rest in inertial frames of reference. So, a shorter time interval between events is obtained when measured by two inertial observers compared to the time interval intended by one observer. Let us pay attention to the fact that here, in contrast to the case when the time interval measured by one clock was compared with the time interval between the same events on two hours of another ISO, the time intervals measured by the clocks of three ISOs are compared.
So, the use of two clocks (II and III) led us to the conclusion that time intervals are counted differently. It is sometimes proposed to use the same clocks in the K and K" reference systems: at point T, clock II is simply transferred to the system and appears
the opportunity to exhaust the period of time that interests us with just one watch. This proposal is worth dwelling on. Although we measure the time interval between events O and two clocks (I and II), these clocks in the proposed version are by no means equal. When clock II is transferred from it, it experiences acceleration and finds itself in a non-inertial frame. Their world line is already curved (see inset in Fig. 8.12). But inertial motion is by no means equivalent to non-inertial motion. It is quite possible that a clock that was constantly moving by inertia counts a longer period of time than a clock that participated in non-inertial motion. There is no contradiction here; Einstein's theory of gravity also leads to this conclusion.
We have already said (see § 3.3) that, in principle, any acceleration affects the clock. In principle, “correctly running” clocks are in inertial reference frames. Let the world line of the particle be curved (which means that the particle experiences acceleration). At any moment of time of motion with acceleration, one can find an inertial observer moving tangentially to the trajectory of the true motion with the instantaneous speed of the actual motion. A clock moving with acceleration moves “correctly” if its course exactly coincides with the course of a clock of the same design, moving in the indicated manner together with an inertial observer.
At what point on the world line does the difference in the readings of schnercial and non-inertial clocks occur? It follows from the principle of relativity that watches of the same design run in all ISOs in the same way. From here it is clear that the difference in the readings of two clocks that find themselves at the same point in space is due to the acceleration of the clock, i.e., the curved part of the world line. An objection often put forward is that the curved part of the world line can be made as small as desired, i.e., acceleration can be ensured in a very short time. And the accumulating difference in readings can be very large. Let us not forget, however, that acceleration over a short period of time means the appearance of colossal forces, and a reversal of relativistic speed is associated with significant acceleration. In addition, the difference between the length of a curved world line and the length of a straight world line connecting the same points is determined not by the length of its curved part, but by the fact that it is curved as a whole. This statement is perfectly illustrated in Fig. 8.13: although path II from city A to city L is “almost all the time straight,” it is certainly longer than the path from A to B but in a straight line I. If acceleration does not affect the clock, then the length of the world line of the particle determines the interval own time.
Shorter path Well, although path II differs from the direct one only in a small area. The difference in lengths is due not so much to the fact that there is a curved section, but to the fact that the entire path II as a whole is not straight.
This transition is responsible for the significant difference in the nocases of hours I and III. If we take two identical living organisms as two identical clocks, we will come to the “twin paradox”.
But the transition to living organisms entails a number of complications, and we will refer the reader to the literature.
