About the essence of spoons Physicists have come up with a way to test the reality of the Matrix

US and German physicists Silas Bean, Zohra Davoudi and Martin Savage have proposed an experimental way to test a philosophical idea known as the simulation hypothesis. According to this hypothesis, there is a possibility that we live inside a huge computer model that some posthumans launched to study their own past. Despite, let's be honest, its dubious natural scientific value, the work of Bean, Davoudi and Savage deserves detailed coverage: there is quantum chromodynamics, and philosophy, and in general - it is not every day that physicists offer to test ideas inspired by the film "The Matrix".

Nick Bostrom and his simulation

In 2003, the famous Swedish philosopher Nick Bostrom published in Philosophical Quarterly a work under the almost fantastic title “Are we all living in a computer simulation?” It should be noted that Bostrom is not some outcast living on the outskirts of modern philosophy. This is one of the most important figures of transhumanism of our time, co-founder of the World Association of Transhumanists (established in 1998, now renamed “Humanity Plus”). He is the winner of many prestigious awards, and his works on the anthropic principle have been translated into more than 100 languages.

Transhumanism is a worldview based on understanding the achievements and prospects of science, recognizing the possibility and necessity of fundamental changes in man himself with the help of advanced technologies. The goal of these changes is the elimination of suffering, aging, death, as well as strengthening the physical, mental and psychological capabilities of people.

The anthropic principle is a principle formulated in the form of the formula “We see the Universe like this, because only in such a Universe could an observer, a person, arise.”

The Theory of Everything - a hypothetical physical and mathematical theory that describes all known fundamental interactions (strong, weak, electromagnetic and gravitational)

Before moving on to the formulation of Bostrom’s main result, let’s get acquainted with some concepts (based on the critical work of Danila Medvedev “ Are we living in Nick Bostrom’s speculation? ”). Posthuman civilization (consisting of posthumans) is understood as “a civilization of the descendants of man who have changed to such an extent that they can no longer be considered human.” The main difference between this civilization and the modern one will be the incredible computing capabilities that it will have. A simulation is a program that simulates the consciousness of one or more people, perhaps even all of humanity. A historical simulation is, accordingly, a simulation of a historical process in which many simulated individuals take part.

In his work, Bostrom adheres to the concept according to which consciousness depends on intelligence (computing power), the structure of individual parts, the logical relationship between them and much more, but does not depend at all on the carrier, that is, biological tissue - the human brain. This means that consciousness can also be realized in the form of a set of electrical impulses in some computer. Considering that the work is about simulations created by post-humans, the people simulated inside the simulation (Bostrom calls them a civilization of a lower level compared to the civilization that launched the simulation) have consciousness. For them, the model will seem like reality.

To assess the theoretical feasibility of conducting this kind of simulation in principle, Bostrom conducts several assessments. Thus, to the roughest approximation, the computing power of the human brain is limited to about 1017 operations per second. In this case, the amount of information received by a person is about 108 bits per second. Based on this, Bostrom concludes that simulating the entire history of mankind would require about 1033 - 1036 operations (assuming 50 years per person and estimating the total number of all people who have existed on the planet to date at 100 billion people).

back in 2002, in Physical Review Letters If we talk about modeling the entire Universe from the time of the Big Bang to the present, and not just the history of mankind, then physicist Seth Lloyd from the Massachusetts Institute of Technology published an article in which he provided calculations of the required powers. It turned out that this would require a machine with 1090-bit memory, which would have to perform 10120 logical operations.

These numbers (both Bostrom's and Lloyd's) seem simply incredible. However, in 2000, the same Lloyd published another remarkable work - he tried to calculate the maximum power of a computer weighing 1 kilogram and volume of one cubic decimeter, based on considerations of quantum mechanics. He succeeded ( pdf ) - it turns out that this amount of matter can perform about 1050 operations per second. Therefore, based on the power of such an extreme computer, the simulation Bostrom talks about does not seem too fantastic. Lloyd even estimated the time it would take to achieve such power - provided that the power of computers continues to grow according to Moore's law (which, of course, is completely doubtful: some scientists predict that the law will cease to work in 75 years). So, this time was only 250 years.

However, let's return to Bostrom. Based on the above assessments, the Swedish philosopher not only concluded that simulation is possible, but also made a paradoxical conclusion. Bostrom states that at least one of the following three statements is true (called Bostrom's trilemma):

Humanity will die out without becoming a post-civilization;
Humanity will develop into a post-civilization, which for some reason will not be interested in modeling the past;
We're almost certainly living in a computer simulation

The last point, in short, Bostrom argues with the idea that if simulations are carried out, there will be many of them. It is logical to assume that the number of simulated people will be many orders of magnitude greater than the number of ancestors of the basic civilization who ever lived. Therefore, the probability that a randomly selected person is the subject of an experiment is almost one.

It follows from this that if we are optimists and do not believe in the extinction of humanity and, in addition, are convinced of the curiosity of our descendants, then point three is fulfilled: we are most likely living in a computer simulation. By the way, Bostrom’s work generally has many paradoxical conclusions - for example, about the likelihood of modeling people without consciousness, that is, the existence of a world in which only a few are endowed with consciousness, and the rest are “shadow zombies” (as the philosopher himself calls them ). The philosopher also interestingly discusses the ethical aspects of modeling, as well as the fact that most simulations must end someday, which means, with a probability almost equal to one, we live in a world that must end its existence (you can read more about these arguments see the partial Russian translation of the article ).

Despite their popularity, Bostrom's conclusions have repeatedly been the target of criticism. In particular, opponents point to gaps in the philosopher's argumentation, as well as the large number of hidden assumptions present in his reasoning regarding a number of fundamental issues - for example, the nature of consciousness and the potential ability of simulated individuals to become self-aware. In general, there is no clear answer to the question “Do we live in the Matrix?” one cannot expect anything from philosophers (as well as other, no less “simple” questions: what is consciousness, what is reality, etc.). So let's move on to physics.

Physicists and their approach

Bostrom does not hide the fact that his work was inspired by, among other things, science fiction films. Among them, of course, is “The Matrix” (the idea of simulation) and “13th Floor” (the idea of nested simulations)
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Some time ago, a preprint of the work of physicists from the USA and Germany Silas Bean, Zohra Davoudi and Martin Savage appeared on the website arXiv.org. These scientists decided to play the game proposed by Bostrom. They asked themselves this question: if the entire Universe is a computer simulation, is it possible to find evidence of this using physical methods? To do this, they tried to imagine how the physics of the simulated world would differ from the physics of the real world.

They took quantum chromodynamics, perhaps the most advanced physical theory currently existing, as a possible modeling tool. As for the modeling itself, they assumed that posthumans would carry it out on a spatial grid with some fairly small spatial step. It is clear that both assumptions are quite controversial: firstly, posthumans would probably prefer to use a theory of everything (which, undoubtedly, would already be at their disposal) for the simulation. Secondly, the numerical methods of posthumans should differ from ours in about the same way as a nuclear reactor differs from a stone ax. However, without these assumptions, the work of physicists would be generally impossible.

Here, by the way, it is appropriate to note that modeling processes occurring in a fixed region of space is a fairly actively developing area of computational physics. So far, of course, the progress has been small: physicists are able to simulate a piece of the world with a diameter of no more than a few (from 2.5 to 5.8) femtometers (1 femtometer is equal to 10-15 meters) with a step b = 0.1 femtometer. Nevertheless, models of this kind are of great theoretical interest. For example, they can help in calculating what happens under conditions that are unattainable in modern accelerators. Or, for example, with the help of modeling it will be possible to obtain some predictions of the properties of the vacuum and compare them with experimental data - and this, perhaps, will give physicists ideas regarding the mentioned theory of everything.

To begin, Bean, Davoudi, and Savage assessed the capabilities of the simulations. It turned out that for a fixed step of 0.1 femtometer, the size of the simulated region grows exponentially (that is, the same as the computing power of computers in Moore's law) - this is the result of extrapolation of data over the almost 20-year history of this field of research. It turns out that modeling a cubic meter of matter based on the laws of quantum chromodynamics with a step b = 0.1 femtometer should be expected in about 140 years (the indicator grows by about an order of magnitude every 10 years). Considering that the diameter of the visible Universe is about 1027 meters, if regular growth is maintained (which, as noted above, is unlikely), the simulation of the required volume can be achieved in 140 + 270 = 410 years (but this is only for a fixed parameter b). However, the scientists themselves do not provide such figures, limiting themselves to the next 140 years.

Then scientists tried to evaluate the possible limitations on the physics of such a model and discovered, frankly, interesting things. They found that in the simulated universe there should be a cutoff in the spectrum of cosmic rays at certain energies. In theory, there really is such a cliff - this is the Greisen - Zatsepin - Kuzmin limit, which is 50 exaelectronvolts. It is due to the fact that high-energy particles must interact with photons of background microwave radiation and, as a result, lose energy. Here, however, two difficulties arise. First, for this limit to be an artifact of the computer model, its spatial step must be 11 orders of magnitude smaller than b = 0.1 femtometer. Secondly, the presence of the Greisen - Zatsepin - Kuzmin limit has not yet been proven in practice. There are many contradictory results in this direction. So, according to one of them, there really is a cliff. According to others, particles with energy exceeding this limit reach the Earth’s surface, and they arrive from rather dark regions of space (that is, they are not a product of the activity of active galactic nuclei closest to us).

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However, scientists have another way to check - the distribution of high-energy cosmic rays should be anisotropic (that is, unequal in different spatial directions). This is due to the assumption that the calculations are carried out on a cubic grid - this is exactly what the grid should be, according to physicists, for reasons of isotropy of space-time. At the same time, physicists do not discuss the possibility of detecting anisotropy of radiation. It is not even clear what kind of instruments are needed for such research - are already existing instruments (the Fermi space observatory, for example) sufficient? In general, there is no clear answer to the question “Do we live in the Matrix?” One cannot expect anything from physicists either.

In conclusion

Of course, the reader may feel disappointed at this point. Like, how is it possible: I read and read, but the answer to the main question “Do we live in the Matrix?” never received it. This, however, was expected, and here's why. For philosophy, the simulation hypothesis is just one of many versions of existence. If these versions compete with each other, it is only in the minds of their supporters and opponents, that is, they are objects of faith that do not pretend to be objective.

As for physicists, very interesting news recently appeared : American professor from the University of Louisiana Rhett Allain analyzed the physical component of the game Bad Piggies from Rovio, the company that created Angry Birds. He did this precisely in order to determine the possible diameter of the green pigs from the game, if they existed in reality (the diameter, by the way, turned out to be 96 centimeters). So, the work of Silas Bean, Zohra Davoudi and Martin Savage is the same kind of exercise, only with slightly more complex objects and confusing mathematics. In general, this is nothing more than entertaining gymnastics for the mind - but, like any gymnastics, it is useful. Thanks to it, the reader now knows Bostrom's trilemma and the size of a hard drive on which information about the entire Universe can be recorded. This is interesting.