Philosophical experiments. Gravitational waves. Famous violinist Thomson

Gravitational waves - artist's rendering

Gravitational waves are disturbances of the space-time metric that break away from the source and propagate like waves (the so-called “space-time ripples”).

IN general theory relativity and in most others modern theories In gravity, gravitational waves are generated by the motion of massive bodies with variable acceleration. Gravitational waves propagate freely in space at the speed of light. Due to the relative weakness of gravitational forces (compared to others), these waves have a very small magnitude, which is difficult to register.

Polarized gravitational wave

Gravitational waves are predicted by the general theory of relativity (GR), and many others. They were first directly detected in September 2015 by two twin detectors, which detected gravitational waves, likely resulting from the merger of two and the formation of one more massive rotating black hole. Indirect evidence of their existence has been known since the 1970s - General Relativity predicts the rate of convergence of close systems due to the loss of energy due to the emission of gravitational waves, which coincides with observations. Direct registration of gravitational waves and their use to determine the parameters of astrophysical processes is an important task of modern physics and astronomy.

Within the framework of general relativity, gravitational waves are described by solutions of wave-type Einstein equations, which represent a perturbation of the space-time metric moving at the speed of light (in the linear approximation). The manifestation of this disturbance should be, in particular, a periodic change in the distance between two freely falling (that is, not influenced by any forces) test masses. Amplitude h gravitational wave is a dimensionless quantity - a relative change in distance. The predicted maximum amplitudes of gravitational waves from astrophysical objects (for example, compact binary systems) and phenomena (explosions, mergers, captures by black holes, etc.) when measured are very small ( h=10 −18 -10 −23). A weak (linear) gravitational wave, according to the general theory of relativity, transfers energy and momentum, moves at the speed of light, is transverse, quadrupole and is described by two independent components located at an angle of 45° to each other (has two directions of polarization).

Different theories predict the speed of propagation of gravitational waves differently. In general relativity, it is equal to the speed of light (in the linear approximation). In other theories of gravity, it can take any value, including infinity. According to the first registration of gravitational waves, their dispersion turned out to be compatible with a massless graviton, and the speed was estimated as equal to speed Sveta.

Generation of gravitational waves

A system of two neutron stars creates ripples in spacetime

A gravitational wave is emitted by any matter moving with asymmetric acceleration. For a wave of significant amplitude to occur, extremely large mass emitter and/or huge accelerations, the amplitude of the gravitational wave is directly proportional first derivative of acceleration and the mass of the generator, that is ~ . However, if an object is moving at an accelerated rate, this means that some force is acting on it from another object. In turn, this other object experiences the opposite effect (according to Newton’s 3rd law), and it turns out that m 1 a 1 = − m 2 a 2 . It turns out that two objects emit gravitational waves only in pairs, and as a result of interference they are mutually canceled out almost completely. Therefore, gravitational radiation in the general theory of relativity always has the multipole character of at least quadrupole radiation. In addition, for non-relativistic emitters in the expression for the radiation intensity there is a small parameter where is the gravitational radius of the emitter, r- its characteristic size, T- characteristic period of movement, c- speed of light in vacuum.

The strongest sources of gravitational waves are:

• colliding ( gigantic masses, very small accelerations),
• gravitational collapse of a binary system of compact objects (colossal accelerations with a fairly large mass). As private and most interesting case- merger neutron stars. In such a system, the gravitational-wave luminosity is close to the maximum Planck luminosity possible in nature.

Gravitational waves emitted by a two-body system

Two bodies moving in circular orbits around general center masses

Two gravitational bound body with the masses m 1 and m 2, moving non-relativistically ( v << c) in circular orbits around their common center of mass at a distance r from each other, emit gravitational waves of the following energy, on average over the period:

As a result, the system loses energy, which leads to the convergence of bodies, that is, to a decrease in the distance between them. Speed ​​of approach of bodies:

For the Solar System, for example, the greatest gravitational radiation is produced by the and subsystem. The power of this radiation is approximately 5 kilowatts. Thus, the energy lost by the Solar System to gravitational radiation per year is completely negligible compared to the characteristic kinetic energy of bodies.

Gravitational collapse of a binary system

Any double star, when its components rotate around a common center of mass, loses energy (as assumed - due to the emission of gravitational waves) and, in the end, merges together. But for ordinary, non-compact, double stars, this process takes a very long time, much longer than the present age. If a compact binary system consists of a pair of neutron stars, black holes, or a combination of both, then the merger can occur within several million years. First, the objects come closer together, and their period of revolution decreases. Then, at the final stage, a collision and asymmetric gravitational collapse occurs. This process lasts a fraction of a second, and during this time energy is lost into gravitational radiation, which, according to some estimates, amounts to more than 50% of the mass of the system.

Basic exact solutions of Einstein's equations for gravitational waves

Bondi-Pirani-Robinson body waves

These waves are described by a metric of the form . If we introduce a variable and a function, then from the general relativity equations we obtain the equation

Takeno Metric

has the form , -functions satisfy the same equation.

Rosen metric

Where to satisfy

Perez metric

Wherein

Cylindrical Einstein-Rosen waves

In cylindrical coordinates, such waves have the form and are executed

Registration of gravitational waves

Registration of gravitational waves is quite difficult due to the weakness of the latter (small distortion of the metric). The devices for registering them are gravitational wave detectors. Attempts to detect gravitational waves have been made since the late 1960s. Gravitational waves of detectable amplitude are born during the collapse of a binary. Similar events occur in the surrounding area approximately once a decade.

On the other hand, the general theory of relativity predicts the acceleration of the mutual rotation of binary stars due to the loss of energy in the emission of gravitational waves, and this effect is reliably recorded in several known systems of binary compact objects (in particular, pulsars with compact companions). In 1993, “for the discovery of a new type of pulsar, which provided new opportunities in the study of gravity” to the discoverers of the first double pulsar PSR B1913+16, Russell Hulse and Joseph Taylor Jr. was awarded the Nobel Prize in Physics. The acceleration of rotation observed in this system completely coincides with the predictions of general relativity for the emission of gravitational waves. The same phenomenon was recorded in several other cases: for the pulsars PSR J0737-3039, PSR J0437-4715, SDSS J065133.338+284423.37 (usually abbreviated J0651) and the system of binary RX J0806. For example, the distance between the two components A and B of the first binary star of the two pulsars PSR J0737-3039 decreases by about 2.5 inches (6.35 cm) per day due to energy loss to gravitational waves, and this occurs in agreement with general relativity . All these data are interpreted as indirect confirmation of the existence of gravitational waves.

According to estimates, the strongest and most frequent sources of gravitational waves for gravitational telescopes and antennas are catastrophes associated with the collapse of binary systems in nearby galaxies. It is expected that in the near future several similar events per year will be recorded on improved gravitational detectors, distorting the metric in the vicinity by 10 −21 -10 −23 . The first observations of an optical-metric parametric resonance signal, which makes it possible to detect the effect of gravitational waves from periodic sources such as a close binary on the radiation of cosmic masers, may have been obtained at the radio astronomical observatory of the Russian Academy of Sciences, Pushchino.

Another possibility of detecting the background of gravitational waves filling the Universe is high-precision timing of distant pulsars - analysis of the arrival time of their pulses, which characteristically changes under the influence of gravitational waves passing through the space between the Earth and the pulsar. Estimates for 2013 indicate that timing accuracy needs to be improved by about one order of magnitude to detect background waves from multiple sources in our Universe, a task that could be accomplished before the end of the decade.

According to modern concepts, our Universe is filled with relic gravitational waves that appeared in the first moments after. Their registration will make it possible to obtain information about the processes at the beginning of the birth of the Universe. On March 17, 2014 at 20:00 Moscow time at the Harvard-Smithsonian Center for Astrophysics, an American group of researchers working on the BICEP 2 project announced the detection of non-zero tensor disturbances in the early Universe by the polarization of the cosmic microwave background radiation, which is also the discovery of these relict gravitational waves . However, almost immediately this result was disputed, since, as it turned out, the contribution was not properly taken into account. One of the authors, J. M. Kovats ( Kovac J. M.), admitted that “the participants and science journalists were a bit hasty in interpreting and reporting the data from the BICEP2 experiment.”

Experimental confirmation of the existence

The first recorded gravitational wave signal. On the left is data from the detector in Hanford (H1), on the right - in Livingston (L1). Time is counted from September 14, 2015, 09:50:45 UTC. To visualize the signal, it is filtered with a frequency filter with a passband of 35-350 Hertz to suppress large fluctuations outside the high sensitivity range of the detectors; band-stop filters were also used to suppress the noise of the installations themselves. Top row: voltages h in the detectors. GW150914 first arrived at L1 and 6 9 +0 5 −0 4 ms later to H1; For visual comparison, data from H1 are shown in the L1 graph in reversed and time-shifted form (to account for the relative orientation of the detectors). Second row: voltages h from the gravitational wave signal, passed through the same 35-350 Hz bandpass filter. The solid line is the result of numerical relativity for a system with parameters compatible with those found based on the study of the GW150914 signal, obtained by two independent codes with a resulting match of 99.9. The gray thick lines are the 90% confidence regions of the waveform reconstructed from the detector data by two different methods. The dark gray line models the expected signals from the merger of black holes, the light gray line does not use astrophysical models, but represents the signal as a linear combination of sinusoidal-Gaussian wavelets. The reconstructions overlap by 94%. Third row: Residual errors after extracting the filtered prediction of the numerical relativity signal from the filtered signal of the detectors. Bottom row: A representation of the voltage frequency map, showing the increase in the dominant frequency of the signal over time.

February 11, 2016 by the LIGO and VIRGO collaborations. The merger signal of two black holes with an amplitude at maximum of about 10 −21 was recorded on September 14, 2015 at 9:51 UTC by two LIGO detectors in Hanford and Livingston, 7 milliseconds apart, in the region of maximum signal amplitude (0.2 seconds) combined the signal-to-noise ratio was 24:1. The signal was designated GW150914. The shape of the signal matches the prediction of general relativity for the merger of two black holes with masses of 36 and 29 solar masses; the resulting black hole should have a mass of 62 solar and a rotation parameter a= 0.67. The distance to the source is about 1.3 billion, the energy emitted in tenths of a second in the merger is the equivalent of about 3 solar masses.

Story

The history of the term “gravitational wave” itself, the theoretical and experimental search for these waves, as well as their use for studying phenomena inaccessible to other methods.

• 1900 - Lorentz suggested that gravity “...can spread at a speed no greater than the speed of light”;
• 1905 - Poincaré first introduced the term gravitational wave (onde gravifique). Poincaré, on a qualitative level, removed the established objections of Laplace and showed that the corrections associated with gravitational waves to the generally accepted Newtonian laws of gravity are canceled out, thus the assumption of the existence of gravitational waves does not contradict observations;
• 1916 - Einstein showed that, within the framework of general relativity, a mechanical system will transfer energy to gravitational waves and, roughly speaking, any rotation relative to fixed stars must sooner or later stop, although, of course, under normal conditions, energy losses of the order of magnitude are negligible and practically not measurable (in In this work, he also mistakenly believed that a mechanical system that constantly maintains spherical symmetry can emit gravitational waves);
• 1918 - Einstein derived a quadrupole formula in which the emission of gravitational waves turns out to be an effect of order , thereby correcting the error in his previous work (an error remained in the coefficient, the wave energy is 2 times less);
• 1923 - Eddington - questioned the physical reality of gravitational waves "...propagating...at the speed of thought." In 1934, when preparing the Russian translation of his monograph “The Theory of Relativity,” Eddington added several chapters, including chapters with two options for calculating energy losses by a rotating rod, but noted that the methods used for approximate calculations of general relativity, in his opinion, are not applicable to gravitationally bound systems , so doubts remain;
• 1937 - Einstein, together with Rosen, investigated cylindrical wave solutions to the exact equations of the gravitational field. During the course of these studies, they began to doubt that gravitational waves may be an artifact of approximate solutions of the general relativity equations (correspondence regarding a review of the article “Do gravitational waves exist?” by Einstein and Rosen is known). Later, he found an error in his reasoning; the final version of the article with fundamental changes was published in the Journal of the Franklin Institute;
• 1957 - Herman Bondi and Richard Feynman proposed the “beaded cane” thought experiment in which they substantiated the existence of physical consequences of gravitational waves in general relativity;
• 1962 - Vladislav Pustovoit and Mikhail Herzenstein described the principles of using interferometers to detect long-wave gravitational waves;
• 1964 - Philip Peters and John Matthew theoretically described gravitational waves emitted by binary systems;
• 1969 - Joseph Weber, founder of gravitational wave astronomy, reports the detection of gravitational waves using a resonant detector - a mechanical gravitational antenna. These reports give rise to a rapid growth of work in this direction, in particular, Rainier Weiss, one of the founders of the LIGO project, began experiments at that time. To date (2015), no one has been able to obtain reliable confirmation of these events;
• 1978 - Joseph Taylor reported the detection of gravitational radiation in the binary pulsar system PSR B1913+16. Joseph Taylor and Russell Hulse's research earned them the 1993 Nobel Prize in Physics. As of early 2015, three post-Keplerian parameters, including period reduction due to gravitational wave emission, had been measured for at least 8 such systems;
• 2002 - Sergey Kopeikin and Edward Fomalont used ultra-long-baseline radio wave interferometry to measure the deflection of light in the gravitational field of Jupiter in dynamics, which for a certain class of hypothetical extensions of general relativity makes it possible to estimate the speed of gravity - the difference from the speed of light should not exceed 20% (this interpretation does not generally accepted);
• 2006 - the international team of Martha Bourgay (Parkes Observatory, Australia) reported significantly more accurate confirmation of general relativity and its correspondence to the magnitude of gravitational wave radiation in the system of two pulsars PSR J0737-3039A/B;
• 2014 - Astronomers at the Harvard-Smithsonian Center for Astrophysics (BICEP) reported the detection of primordial gravitational waves while measuring fluctuations in the cosmic microwave background radiation. At the moment (2016), the detected fluctuations are considered not to be of relict origin, but are explained by the emission of dust in the Galaxy;
• 2016 - international LIGO team reported the detection of the gravitational wave transit event GW150914. For the first time, direct observation of interacting massive bodies in ultra-strong gravitational fields with ultra-high relative velocities (< 1,2 × R s , v/c >0.5), which made it possible to verify the correctness of general relativity with an accuracy of several post-Newtonian terms of high orders. The measured dispersion of gravitational waves does not contradict previously made measurements of the dispersion and upper bound on the mass of a hypothetical graviton (< 1,2 × 10 −22 эВ), если он в некотором гипотетическом расширении ОТО будет существовать.

Deming began the red bead experiment in his first lectures to the Japanese in 1950 to demonstrate the difference between general and special causes of variation. For many years, Deming used the same equipment to experiment with red beads. These basic devices are: a box of white and red beads in a ratio of approximately 4:1 and a rectangular piece of plastic, wood, metal, etc., usually called a spatula, in which 50 vertical depressions are made. A selection of 50 beads is achieved by dipping a spatula into the box. (Note to statisticians: I deliberately do not use the term "random sample", even though the beads may be well mixed before the spatula is dipped into them.)

The basic form of the red bead experiment demonstrated in the four-day workshops has remained relatively unchanged over the years. Volunteers from the audience are invited:

six interested workers (they do not require any special skills: they will be trained and will have to comply with all requirements without questions or complaints);

two junior inspectors (they only need to be able to count to twenty);

Chief Inspector (must be able to compare two numbers to see if they are equal or not and be able to speak loudly and clearly);

registrar (must be able to write accurately and perform simple arithmetic operations).

The workday for each worker is the process of taking a sample (50 beads) from a box using a spatula. White beads are a good product, acceptable to the consumer. Red beads are not a product

acceptable. In accordance with the requirements of the master or the wishes of senior management, the task is to prevent more than one to three red beads from entering. Workers are trained by a master (Deming), who gives precise instructions about how the work should be carried out: how to mix the beads, what should be the directions, distances, angles and level of stirring when using a spatula. To minimize variations, the procedure needs to be standardized and regulated.

Workers must follow all instructions very carefully, because the results of their work determine whether they will remain at work.

“Remember, every day you work could be your last depending on how you work. I hope you enjoy your work!”

The control process involves a lot of personnel, but it is very effective. Each worker brings completed day job to the first sub-inspector, who silently counts and writes down the number of red beads, and then goes to the second sub-inspector, who does the same. The Chief Inspector, also remaining silent, compares the two accounts. If they differ, it means an error has crept in! What's even more concerning is the fact that even if both accounts agree, they may still be wrong. However, the procedure is such that in the event of an error, the inspectors, still independently of each other, must recalculate the result. When the score matches, the chief inspector announces the result and the registrar records it on a slide projected on the screen above.

The worker returns his beads to the box - his work day is completed.

The work continues for four days. There are 24 results in total. The master constantly comments on them. He praises Al for reducing the number of red beads to four, and the audience applauds him. He berates Audrey for getting sixteen reds, and the audience laughs nervously. How can Audrey have four times as many defective beads unless she is careless and lazy? None of the other workers can remain calm either, because if Al could do four, then anyone can do it. Al is a definite "worker of the day" and will receive a bonus. But the next day, nine red beads are found on Al because he has calmed down too much. Audrey brings ten: she started off badly, but is now starting to improve, especially after a serious conversation with the master at the end of the first day. Stop! Stop the line! Ben just made seventeen reds! Let's have a meeting and try to understand what is causing the poor performance. This type of work can lead to the closure of the enterprise. At the end of the second day the master

Organization as a system

holds a serious conversation with workers. As people become more comfortable and experienced, their results should improve. Instead, following the 54 red beads received on the first day, a whopping 65 were received on the second day. Do the workers not understand their task? The goal is to get white beads, not red ones. The future looks pretty bleak. Nobody reached the goal. They should try to do better.

Depressed workers return to work. And suddenly two glimpses appear: Audrey, continuing to improve her results, reaches seven red beads; Ben is also on the right track, repeating the success of his first day of work - nine reds! However, all others perform worse. Total number red beads rise again and reach 67. The day ends without success, like the previous ones. The foreman tells the workers that if significant improvements do not occur, the plant will have to close.

The fourth day begins. We are relieved to find that things have improved thanks to Audrey, who now produces only six red beads*. But overall the day ends with 58 reds, which still worse than the first day.

Here are all the results so far: Day 1 Day 2 Day 3 Day 4 Audrey Total 16 10 7 6 39 John 9 11 12 10 42 Al 4 9 13 11 37 Carol 7 11 14 11 43 Ben 9 17 9 13 48 Ed 9 7 12 7 35 Amount per day Total 54 65 67 58 244 At this stage, the foreman decides to call on the well-known great achievement of management for help - to save the enterprise, leaving only the best workers. He fires Ben, Carol and John, three workers who made 40 or more red beads in four days, and keeps Audrey, Al and Ed, paying them a bonus and forcing them to work double shifts.

No wonder this doesn't work.

*Note to traditional statisticians: Under the standard null hypothesis, and given that Audrey received four different scores, there is a 1/4 chance that those scores got better day by day! = 1/24 = 0.024. This is a significant result at more than the 5% significance level! - Approx. auto

Chapter 6. Experiment with red beads

By observing the red bead experiment, we gain a rare advantage: we understand the system well and can be confident that it is controllable. Once we realize this, it becomes clear to us how pointless all the actions of the master (or anyone else) to influence results that are supposedly dependent on the workers, but in fact are completely determined existing system. All these actions were reactions to purely random variations.

However, suppose we lack an understanding of the system. What should we do then? We would then need to plot the data on a control chart and let it tell us about the behavior of the process. The center line on the map corresponds to the average reading, i.e. 244/24 = 10.2, so the calculation gives:

Hence, for the position of the upper and lower control boundaries we have:

10.2 + (3 x 2.8) = 18.6 and 10.2 - (3 x 2.8) = 1.8

accordingly (for similar calculations, see: “Out of the Crisis”, p. 304). The control chart is shown in Figure 17.

This map confirms what we assumed: the process is in a statistically controlled state. Variations are caused by the system. The workers are helpless: they can only give out what the system gives. The system is stable and predictable. If we do the experiment tomorrow, or the day after tomorrow, or next week, we will likely get a similar range of results.

Central

Rice. 17. Red Bead Experiment Data Control Chart

Organization as a system

Seminar participants who are committed to actively accepting the conclusions arising from the experiment with red beads can do a lot interesting observations even before Deming begins summing up the results. They see the pleasure they get from good results, and grief from the bad ones, independent of the curses and criticism of the master. They see a trend (like Audrey's tendency to significantly improve her results), they see relatively uniform results (like John's), and they see variable results (like Ben's). They see and hear the master's complaints and lamentations when his useless and meaningless instructions are not followed to the letter. They see workers being compared to each other, when in reality workers have no say in producing results: results are entirely determined by the system within which they work. And the seminar participants also see how workers lose their jobs without any fault on their part, while others receive bonuses without having any special merit (except that the system treats them more loyally).

Deming points out some obvious features of the experiment plus a few others that are less obvious. Thus, the accumulated average values ​​at the end of each of the four days are respectively:

Deming asks the audience what value the average will settle at if the experiment continues. Since the ratio of white to red beads is 4:1, it is clear to those familiar with the laws of mathematics that the answer must be 10.0. But this turns out not to be the case. This would be correct if the sampling was carried out using the random number method. But in reality it is carried out by immersing the blade in the box. This is a mechanical sampling, not a random one, for which mathematical laws apply. As further evidence, Deming cites results obtained by using four different blades over a number of years. For at least two of these, a traditional statistician would rate the results as “statistically significantly” different from 10.0. What type of sampling do we carry out in production processes? Mechanical or random? Where does all this leave those who depend only on standard statistical theory for industrial applications?

Not everything in this experiment provides an example of what not to do. There is an important positive aspect to the way the control process is organized. At first glance, it contradicts one of the ideas that Deming sometimes

Chapter 6. Experiment with red beads

considers at its seminars - and in the control process there is a division of responsibility. In fact, the contributions of each controller to the result are independent of each other; the risk of shared responsibility is reduced to the risk of consensus. This issue is discussed in more detail in Chapter 21 (see also rule 4 in the funnel and target experiments).

In both the funnel experiment (see Chapter 5) and the red bead experiment, a natural question arises: what can be done to improve things? We already know the answer. Since the system under consideration is in a state of statistical control, real improvements can only be achieved by actually changing it. They cannot be obtained by influencing the outputs, i.e. results of system operation: influencing outputs is only suitable in the presence of special causes of variation. Influencing the results is exactly what rules 2, 3 and 4 in the funnel experiment are aimed at, and all the emotional exclamations of the master in this experiment are also aimed at.

Impact on the system in order to eliminate common reasons variation is usually a more difficult task than action to eliminate special causes. Thus, in the funnel experiment, the funnel itself can be lowered or a softer cloth can be used to cover the table in order to absorb some of the movement of the ball after it falls. In the red bead experiment, somehow the proportion of red beads in the box must be reduced - by introducing improvements in upstream stages of the manufacturing process or in the supply of raw materials, or both.

Deming refers to the red bead experiment as "extremely simple." This is true. However, as in the case of the funnel experiment, the ideas conveyed are not so simple at all.

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What is a thought experiment?

A thought experiment in philosophy, physics and a number of other sciences is the form cognitive activity, where any situation is modeled not in the form of a real experiment familiar to each of us, but in the imagination. This concept was first introduced by the Austrian positivist philosopher, mechanic and physicist Ernst Mach.

Today, the term “thought experiment” is actively used by various scientists, entrepreneurs, politicians and specialists in various areas Worldwide. Some of them prefer to conduct their own thought experiments, while others give all sorts of examples, with the best examples whom we would like to introduce to you.

As the title implies, we will consider eight experiments in total.

Philosophical Zombie

Imagine a living dead man. But not ominous, but so modest, harmless, similar to ordinary person. The only thing that distinguishes him from people is that he cannot feel anything, does not have conscious experience, but is able to repeat people’s actions and reactions, for example, if he is burned with fire, he skillfully imitates pain.

If such a zombie existed, it would go against the theory of physicalism, where human perception is determined only by processes of the physical plane. The philosophical zombie also does not in any way correlate with behaviorist views, according to which any manifestations, desires and consciousness of a person are reduced to behavioral factors, and such a zombie cannot be distinguished from an ordinary person. This experiment also partially concerns the problem of artificial intelligence, because instead of a zombie there may be a notorious android capable of copying human habits.

Quantum suicide

The second experiment concerns quantum mechanics, but here it changes - from the position of an eyewitness to the position of a participant. Take for example Schrödinger's cat, who shoots himself in the head from a gun with a mechanism powered by the decay of a radioactive atom. A gun can misfire 50% of the time. , there is a collision of two quantum theories: “Copenhagen” and many-worlds.

According to the first, a cat cannot be in two states at the same time, i.e. he will either be alive or dead. But according to the second, any new attempt to shoot, as it were, divides the universe into two alternatives: in the first, the cat is alive, in the second, it is dead. However, the cat's alter ego, which remains alive, will remain unaware of its demise in a parallel reality.

The author of the experiment, Professor Max Tegmark, leans towards the theory of the multiverse. But most of experts in the field of quantum mechanics who were interviewed by Tegmark trust the “Copenhagen” quantum theory.

Poison and reward

Curtain of Ignorance

A wonderful experiment on the theme of social justice.

Example: everything that concerns social organization, entrusted certain group of people. In order for the concept they came up with to be as objective as possible, these people were deprived of knowledge about their status in society, class affiliation, IQ and others that can guarantee competitive superiority - this is all the “curtain of ignorance.”

The question is: what concept of social organization will people choose, being unable to take into account their own personal interests?

Chinese room

The man who is in a room with baskets filled with hieroglyphs. He has at his disposal a detailed manual on native language, explaining the laws of combining unusual signs. There is no need to understand the meaning of all hieroglyphs, because... Only the drawing rules apply. But in the process of working with hieroglyphs, you can create text that is no different from writing resident of China.

Behind the door of the room there are people handing the recluse cards with questions on Chinese. Our hero, taking into account the rules from the textbook, answers them - his answers do not make sense to him, but for the Chinese they are quite logical.

If we imagine the hero as a computer, the textbook as an information base, and people's messages as questions to the computer and answers to them, the experiment will show the limitations of the computer and its inability to master human thinking in the process of simply responding to initial conditions through in a programmed way.

Infinite Monkey Theorem

Based on this experiment, an abstract monkey, if it randomly hits the keys of a printing mechanism for eternity, at one point will be able to print any text initially given, for example, Shakespeare's Hamlet.

Attempts were even made to bring this experiment to life: teachers and students at the University of Plymouth raised two thousand dollars to give six macaques at the zoo a computer. A month passed, but the “test subjects” still did not achieve success - they literary heritage contains only five pages, where the letter “S” predominates. The computer was almost completely destroyed. But the experimenters themselves said that they learned a lot from their project.

You can come up with some of your own unusual thought experiments - for this you just need to turn on your head and... By the way, have you ever thought that many of us, almost all of us, mentally conduct all sorts of experiments involving, for example, ourselves, someone close to us, or even pets? Next time, when you imagine a situation, write it down on paper or even publish it - maybe your ideas will get good development.

What are the most impressive thought experiments you've come across?

Why don't aliens contact us?

There is a worm on the road and you pass by it. Does the worm know that you are intelligent? The worm has no idea about the concept of intelligence because you are much more intelligent than him. So, the worm has no idea that something intelligent has passed by it. This makes us wonder if we might have the idea that some super beings are also “passing” past us. Maybe they are not interested in us because we are too stupid for them to even think about a possible dialogue? You don’t walk past a worm with thoughts like “I wonder what he’s thinking about?” This may be one of the best explanations why aliens have not yet made contact with us. If they are watching us, they might have come to the conclusion that there are signs intelligent life not on Earth.

How the “footprints” of you and I travel throughout the Universe

Any object that has mass has a gravitational field. Thus, at the moment a child is born, its gravitational field becomes independent and begins to spread throughout space at the speed of light in the form of an ever-growing sphere.

The strength of our gravitational field weakens with distance, but never reaches zero. Thus, waves propagating to infinity touched the surface of the Sun 8.3 minutes after our birth. 5.5 hours later they reached Pluto.

After 1 year, our gravitational field expands to a sphere with a diameter of 11.8 trillion miles. After just over 4 years, the field slides across the surface of our nearest famous stars- Proxima Centauri. By age thirty, our gravitational field has expanded 300 trillion miles around us in space.

Still feeling small? What's really unsettling is that when we die, our gravitational field will continue to exist forever, endlessly spreading throughout the Universe, passing through the Andromeda galaxy millions of years later and beyond.

Pieces of everyone we have ever known, living or dead, are rushing through the depths of space right now. The gravitational fields of our most distant ancestors and everything that has ever existed rush through the Universe, forever diminishing but never truly disappearing.

What does traveling back in time look like?

What is it like to experience time travel back? At first it seems that you will simply watch everything as if in reverse, but if you think about it, it will feel completely different.

At every single moment in time, let's call it T=0, we are processing information encoded in our brain that reflects memories from the past, moments: T=-1, T=-2, T=-3, etc. as well as much fuzzier expectations and visualization of the future: T=1, 2, 3, etc.

Usually from moment T=0 we move to T=1. At this time, physical processes create in memory a record of the instant T=0, which appears in a long series of moments from the past.

Now let's assume that we instead follow back to T=-1. Do we have memories of T=0? No. There are none because we went back in time to the moment when the Universe existed at T=-1, and at that moment we had memories of T=-2 and only expectations of T=0. And if we go back to T=-2, then at that moment we will have memories of T= -3 and expectations of T=-1.

Thus, no matter how far back we go, at any given moment in time we will still remember the previous one and imagine the next one. There is no moment at which we could see the egg coming together instead of being broken. It will feel the same as moving forward.

And now the realization comes to us that we cannot move back. If every moment of moving backward feels exactly the same as every moment of moving forward, then what does that mean? Are we moving forward at all?

Solid Earth below us is a myth

On a clear night, lie down in your backyard and look up at the stars.

At first, you will feel the familiar comfort of resting on stable ground, looking up at the stars twinkling in the sky. But just think about it: we are not really “here” and the stars are not really “there”. It's all an illusion. In reality, we are “stuck” to the surface of a sphere, which is thrown in space from side to side with enormous speed. You're not just looking at a static firmament of stars, you're seeing the vastness of space almost as if you were in the cockpit of a giant spaceship.

What does traveling to a parallel universe look like?

Imagine that you are a black square on a white sheet of paper. Welcome to Flatland. You can move here absolutely freely, but only in two dimensions. There is simply no third here and there is no up and down.
But do three-dimensional objects exist here? Yes, they are. But Flatlanders like you will never see them. You can only see the plane of a three-dimensional object.

Now imagine that on the other side of a piece of paper you find someone like yourself. Can you get to the other side to say hello to your neighbor? After all, a plane separates you from him, and it seems incredible that you can penetrate to the other side, despite the fact that it is impossible to make a hole, because the third dimension does not exist.

But there is still a possibility. If the sheet were a Möbius strip, then, for example, an ant would crawl along the entire length of this sheet and return to its starting point, passing along both sides of it, but without crossing its edges.

That is, for this Flatland needs a bend. But is it acceptable? Wouldn't this make Flatland a three-dimensional space? Yes and no. The Mobius strip is three-dimensional, but like the ants on it, the inhabitants of Flatland are limited to two dimensions of a sheet of paper.

As humans, we are similar to the Flatlands in that we are limited to three dimensions and cannot travel into the fourth at will.

Imagine a Möbius strip made from our Universe in three-dimensional space, which also has a bend giving access to a parallel universe. Just like the inhabitants of Flatland, we can meet the inhabitants of “the other side of our three-dimensional universe,” that is, from a parallel universe. We may discover a universe that is dramatically different from ours.

But where is this bend? And, in general, does it exist? What are the consequences of this Möbius strip? Is it possible that this bend was created by super beings with access to the 4th dimensions, just for fun, just like we can glue a Mobius strip for ants? These are just a few of many questions...

What is it like to be blind

I am half blind, meaning I can see absolutely nothing out of my left eye. This means that I don't see anything at all. All this simply does not exist. Most people don't understand what it means to "see nothing." And when they ask this question, I usually answer like this.

Raise your hand in front of your face. Look at her. Do you see what your hand looks like right now? Keep thinking about your hand. Now put your hand behind your head. What does your hand look like now? No way. The hand that you saw in front of you is now outside your peripheral vision and is simply not there. Now imagine that your peripheral vision on the left side has decreased and you can only see half of your field of vision. That's exactly how I see it.

American educator, entrepreneur and former hedge fund analyst Sal Khan proposed a surprising and inspiring thought experiment during his 2012 MIT commencement address.

“Imagine yourself in 50 years. You have recently turned 70 and are nearing the end of your career. You're sitting on the couch, having just watched President Kardashian's holographic message.

You begin to remember your life, think about all the most important points. Think about success in your career, about whether you were able to provide for your family. But then you think about all the things you regret, all the things you wish you had done a little differently. I guess there will be such moments.

Imagine that while you are thinking about this, a genie appears out of nowhere and says: “I overheard your regrets. They're really compelling. But since you good man, I'm willing to give you a second chance if you want." You say, “Of course,” and the genie snaps his fingers.

Suddenly you will find yourself where you are sitting today. Once you feel your toned, healthy 20-year-old body, you begin to realize that this really happened. You really have a chance to do it all over again to build a career and strong relationships.”

Scientists often face a situation where it is very difficult or even simply impossible to test a particular theory experimentally. For example, when we're talking about about motion at near-light speeds or about physics in the vicinity of black holes. Then thought experiments come to the rescue. We invite you to participate in some of them.

Thought experiments are sequences of logical inferences, the purpose of which is to emphasize a certain property of a theory, formulate a reasonable counterexample, or prove some fact. In general, any proof in one form or another is a thought experiment. The main beauty of mental exercises is that they do not require any equipment and often no special knowledge (as, for example, when processing the results of LHC experiments). So make yourself comfortable, we're getting started.

Shroedinger `s cat

Perhaps the most famous thought experiment is the cat experiment (or rather, cat), proposed by Erwin Schrödinger more than 80 years ago. Let's start with the context of the experiment. At that moment quantum mechanics was just beginning its victorious march, and its unusual laws seemed unnatural. One of these laws is that quantum particles can exist in a superposition of two states: for example, simultaneously “rotating” clockwise and counterclockwise.

Experiment. Imagine a sealed box (large enough) containing a cat, a sufficient amount of air, a Geiger counter and a radioactive isotope with known time half-life Once the Geiger counter detects the decay of an atom, special mechanism breaks the ampoule with poisonous gas and the cat dies. After the half-life, the isotope decayed with a probability of 50 percent and remained intact with exactly the same probability. This means that the cat is either alive or dead - as if being in a superposition of states.

Interpretation. Schrödinger wanted to show the unnaturalness of superposition, bringing it to the point of absurdity - such large system, like a whole cat, cannot be alive and dead at the same time. It is worth noting that from the point of view of quantum mechanics, the moment when the Geiger counter is triggered by nuclear decay, a measurement occurs - interaction with a classical macroscopic object. As a result, the superposition must decay.

Interestingly, physicists are already conducting experiments similar to introducing a cat into superposition. But instead of a cat, they use other objects that are large by the standards of the microworld - for example, molecules.

Twin paradox

This thought experiment is often cited as a criticism of Einstein's theory of special relativity. It is based on the fact that when moving at near-light speeds, the flow of time in the reference frame associated with the moving object slows down.

Experiment. Imagine a distant future in which there are rockets that can travel close to the speed of light. There are two twin brothers on Earth, one of them is a traveler, and the other is a homebody. Suppose a brother traveler boarded one of these rockets and traveled on it, after which he returned. For him, at that moment, when he was flying at near-light speed relative to the Earth, time flowed more slowly than for his stay-at-home brother. This means that when he returns to Earth, he will be younger than his brother. On the other hand, his brother himself was moving at near-light speed relative to the rocket - which means that the position of both brothers is in some sense equivalent and when they meet they should again be the same age.

Interpretation. In reality, the traveler brother and the stay-at-home brother are not equivalent, so the traveler will be younger, as the thought experiment would suggest. Interestingly, this effect is also observed in real experiments: short-lived particles traveling at near-light speed seem to “live” longer due to time dilation in their frame of reference. If we try to extend this result to photons, it turns out that they actually live in stopped time.

Einstein elevator

There are several concepts of mass in physics. For example, there is gravitational mass - this is a measure of how a body enters into gravitational interaction. It is she who presses us into the sofa, armchair, subway seat or floor. There is an inertial mass - it determines how we behave in an accelerating coordinate system (it forces us to lean back in a subway train leaving the station). As you can see, the equality of these masses is not an obvious statement.

The general theory of relativity is based on the principle of equivalence - the indistinguishability of gravitational forces from pseudo-forces of inertia. One way to demonstrate this is the following experiment.

Experiment. Imagine being in a soundproof, hermetically sealed elevator car with plenty of oxygen and everything you need. But at the same time you can be anywhere in the Universe. The situation is complicated by the fact that the cabin can move, developing constant acceleration. You feel yourself being slightly pulled towards the floor of the cabin. Can you distinguish whether this is due to the fact that the cabin is located, for example, on the Moon or because the cabin is moving at an acceleration of 1/6 of the acceleration of gravity?

Interpretation. According to Einstein, no, you can’t. Therefore, for other processes and phenomena there is no difference between uniformly accelerated motion in the elevator and in the field of gravity. With some reservations, it follows that the gravitational field can be replaced by an accelerating reference frame.

Today, no one doubts the existence and materiality of gravitational waves - a year ago, the LIGO and VIRGO collaborations caught the long-awaited signal from the collision of black holes. However, at the beginning of the 20th century, after the first publication of Einstein's paper on space-time distortion waves, they were treated with skepticism. In particular, even Einstein himself at some point doubted their realism - they could turn out to be a mathematical abstraction devoid of physical meaning. To demonstrate their feasibility, Richard Feynman (anonymously) proposed the following thought experiment.

Experiment. To begin with, a gravitational wave is a wave of changes in the metric of space. In other words, it changes the distance between objects. Imagine a cane along which balls can move with very little friction. Let the cane be positioned perpendicular to the direction of motion of the gravitational wave. Then, when the wave reaches the cane, the distance between the balls first shortens and then increases, while the cane remains motionless. This means they slide and release heat into space.

Interpretation. This means that a gravitational wave carries energy and is quite real. One might assume that the cane contracts and extends along with the balls, compensating for relative motion, but, like Feynman himself, it is constrained by electrostatic forces acting between the atoms.

Laplace's Demon

The next pair of experiments is “demonic”. Let's start with the lesser-known, but no less beautiful Laplace Demon, which allows (or not) to find out the future of the Universe.

Experiment. Imagine that somewhere there is a huge, very powerful computer. So powerful that it can, taking as a starting point the state of all particles of the Universe, calculate how these states will develop (evolve). In other words, this computer can predict the future. To make it even more interesting, imagine that a computer predicts the future faster than it arrives - say, in a minute it can describe the state of all atoms in the Universe, which they will achieve two minutes from the moment the calculation begins.

Suppose we started the calculation at 00:00, waited for it to end (at 00:01) - now we have a prediction for 00:02. Let's run the second calculation, which will end at 00:02 and predict the future at 00:03. Now pay attention to the fact that the computer itself is also part of our fictional Universe. This means that at 00:01 he knows his state at the time of 00:02 - he knows the result of calculating the state of the Universe at the time of 00:03. And therefore, by repeating the same technique, we can show that the machine knows the future of the Universe at 00:04 and so on - ad infinitum.

Interpretation. It is obvious that the speed of calculation implemented in a material device cannot be infinite - therefore, it is impossible to predict the future using a computer. But there are a few important points worth noting. Firstly, the experiment prohibits Laplace's material demon - consisting of atoms. Secondly, it should be noted that Laplace's demon is possible under conditions where the lifetime of the Universe is fundamentally limited.

Maxwell's demon

And finally, Maxwell's Demon is a classic experiment from the thermodynamics course. It was introduced by James Maxwell to illustrate a way to violate the second law of thermodynamics (the one that prohibits the creation of a perpetual motion machine in one of his formulations).

Experiment. Imagine a medium-sized sealed vessel, divided inside by a partition into two parts. The partition has a small door or hatch. Next to her sits an intelligent microscopic creature - Maxwell's own demon.

Let's fill the vessel with gas at a certain temperature - for definiteness, with oxygen at room temperature. It is important to remember that temperature is a number that reflects average speed movement of gas molecules in a vessel. For example, for oxygen in our experiment this speed is 500 meters per second. But in a gas there are molecules that move faster and slower than this mark.

The demon's task is to monitor the speeds of particles flying towards the door in the partition. If a particle flying from the left half of the vessel has a speed of more than 500 meters per second, the demon will let it through by opening the door. If it is less, the particle will not fall into the right half. Conversely, if a particle from the right half of the tank has a speed of less than 500 meters per second, the demon will let it pass into the left half.

After waiting long enough, we will find that the average speed of molecules in the right half of the vessel has increased, and in the left half it has decreased, which means that the temperature in the right half has also increased. We can use this excess heat, for example, to operate a heat engine. At the same time, we did not need external energy to sort the atoms - Maxwell’s demon did all the work.

Interpretation. The main consequence of the demon's work is a decrease in the overall entropy of the system. That is, after the division of atoms into hot and cold, the measure of chaos in the state of the gas in the vessel decreases. The second law of thermodynamics strictly prohibits this for closed systems.

But in reality, the experiment with Maxwell's demon turns out to be not so paradoxical if we include the demon itself in the description of the system. He spends work opening and closing the valve, and also, and this is important, measuring the velocities of the atoms. All this compensates for the drop in gas entropy. Note that there are experiments to create analogues of Maxwell's demons.

Particularly noteworthy is the “Brownian rattle” - although it itself does not separate molecules into warm and cold, it uses chaotic Brownian motion to do work. The ratchet consists of blades and a gear, which can only rotate in one direction (it is limited by a special clamp). The blade should rotate randomly, and it will be able to make a full rotation only if its intended direction of rotation coincides with the allowed rotation of the gear. However, Richard Feynman analyzed the device in detail and explained why it does not work - the average impact of particles in the chamber will be reset to zero.

Vladimir Korolev