The golden foliage of the trees shone brightly. The rays of the evening sun touched the thinned tops. Light broke through the branches and staged a spectacle of bizarre figures flickering on the wall of the university "kapterka".
Sir Hamilton's pensive gaze moved slowly, watching the play of chiaroscuro. In the head of the Irish mathematician there was a real melting pot of thoughts, ideas and conclusions. He was well aware that the explanation of many phenomena with the help of Newtonian mechanics is like the play of shadows on the wall, deceptively intertwining figures and leaving many questions unanswered. “Maybe it's a wave… or maybe it's a stream of particles,” the scientist mused, “or light is a manifestation of both phenomena. Like figures woven from shadow and light.
The beginning of quantum physics
It is interesting to watch great people and try to understand how great ideas are born that change the course of evolution of all mankind. Hamilton is one of those who stood at the origins of quantum physics. Fifty years later, at the beginning of the twentieth century, many scientists were engaged in the study of elementary particles. The knowledge gained was inconsistent and uncompiled. However, the first shaky steps were taken.
Understanding the microworld at the beginning of the 20th century
In 1901, the first model of the atom was presented and its failure was shown, from the standpoint of ordinary electrodynamics. During the same period, Max Planck and Niels Bohr published many works on the nature of the atom. Despite their complete understanding of the structure of the atom did not exist.
A few years later, in 1905, the little-known German scientist Albert Einstein published a report on the possibility of the existence of a light quantum in two states - wave and corpuscular (particles). In his work, arguments were given explaining the reason for the failure of the model. However, Einstein's vision was limited by the old understanding of the model of the atom.
After numerous works by Niels Bohr and his colleagues in 1925, a new direction was born - a kind of quantum mechanics. A common expression - "quantum mechanics" appeared thirty years later.
What do we know about quanta and their quirks?
Today, quantum physics has gone far enough. Many different phenomena have been discovered. But what do we really know? The answer is presented by one modern scientist. "One can either believe in quantum physics or not understand it," is the definition. Think about it for yourself. It will suffice to mention such a phenomenon as quantum entanglement of particles. This phenomenon has plunged the scientific world into a position of complete bewilderment. Even more shocking was that the resulting paradox is incompatible with Einstein.
The effect of quantum entanglement of photons was first discussed in 1927 at the fifth Solvay Congress. A heated argument arose between Niels Bohr and Einstein. The paradox of quantum entanglement has completely changed the understanding of the essence of the material world.
It is known that all bodies consist of elementary particles. Accordingly, all the phenomena of quantum mechanics are reflected in the ordinary world. Niels Bohr said that if we do not look at the moon, then it does not exist. Einstein considered this unreasonable and believed that the object exists independently of the observer.
When studying the problems of quantum mechanics, one should understand that its mechanisms and laws are interconnected and do not obey classical physics. Let's try to understand the most controversial area - the quantum entanglement of particles.
The theory of quantum entanglement
To begin with, it is worth understanding that quantum physics is like a bottomless well in which you can find anything you want. The phenomenon of quantum entanglement at the beginning of the last century was studied by Einstein, Bohr, Maxwell, Boyle, Bell, Planck and many other physicists. Throughout the twentieth century, thousands of scientists around the world actively studied it and experimented.
The world is subject to the strict laws of physics
Why such an interest in the paradoxes of quantum mechanics? Everything is very simple: we live, obeying certain laws of the physical world. The ability to “bypass” predestination opens a magical door behind which everything becomes possible. For example, the concept of "Schrödinger's Cat" leads to the control of matter. It will also become possible to teleport information, which causes quantum entanglement. The transmission of information will become instantaneous, regardless of distance.
This issue is still under study, but has a positive trend.
Analogy and understanding
What is unique about quantum entanglement, how to understand it, and what happens with it? Let's try to figure it out. This will require some thought experiment. Imagine that you have two boxes in your hands. Each of them contains one ball with a stripe. Now we give one box to the astronaut, and he flies to Mars. As soon as you open the box and see that the stripe on the ball is horizontal, then in the other box the ball will automatically have a vertical stripe. This will be quantum entanglement expressed in simple words: one object predetermines the position of another.
However, it should be understood that this is only a superficial explanation. In order to get quantum entanglement, it is necessary that the particles have the same origin, like twins.
It is very important to understand that the experiment will be disrupted if someone before you had the opportunity to look at at least one of the objects.
Where can quantum entanglement be used?
The principle of quantum entanglement can be used to transmit information over long distances instantly. Such a conclusion contradicts Einstein's theory of relativity. It says that the maximum speed of movement is inherent only in light - three hundred thousand kilometers per second. Such transfer of information makes possible the existence of physical teleportation.
Everything in the world is information, including matter. Quantum physicists came to this conclusion. In 2008, based on a theoretical database, it was possible to see quantum entanglement with the naked eye.
This once again indicates that we are on the verge of great discoveries - movement in space and time. Time in the Universe is discrete, so instantaneous movement over vast distances makes it possible to get into different time densities (based on the hypotheses of Einstein, Bohr). Perhaps in the future it will be a reality just like the mobile phone is today.
Aether dynamics and quantum entanglement
According to some leading scientists, quantum entanglement is explained by the fact that space is filled with some kind of ether - black matter. Any elementary particle, as we know, exists in the form of a wave and a corpuscle (particle). Some scientists believe that all particles are on the "canvas" of dark energy. This is not easy to understand. Let's try to figure it out in another way - the association method.
Imagine yourself at the seaside. Light breeze and a slight breeze. See the waves? And somewhere in the distance, in the reflections of the rays of the sun, a sailboat is visible.
The ship will be our elementary particle, and the sea will be ether (dark energy).
The sea can be in motion in the form of visible waves and drops of water. In the same way, all elementary particles can be just a sea (its integral part) or a separate particle - a drop.
This is a simplified example, everything is somewhat more complicated. Particles without the presence of an observer are in the form of a wave and do not have a specific location.
The white sailboat is a distinguished object, it differs from the surface and structure of the sea water. In the same way, there are "peaks" in the ocean of energy that we can perceive as a manifestation of the forces known to us that have shaped the material part of the world.
The microworld lives by its own laws
The principle of quantum entanglement can be understood if we take into account the fact that elementary particles are in the form of waves. Without a specific location and characteristics, both particles are in an ocean of energy. At the moment the observer appears, the wave “turns” into an object accessible to touch. The second particle, observing the system of equilibrium, acquires opposite properties.
The described article is not aimed at capacious scientific descriptions of the quantum world. The ability to comprehend an ordinary person is based on the availability of understanding of the material presented.
Physics of elementary particles studies the entanglement of quantum states based on the spin (rotation) of an elementary particle.
In scientific language (simplified) - quantum entanglement is defined by different spins. In the process of observing objects, scientists saw that only two spins can exist - along and across. Oddly enough, in other positions, the particles do not “pose” to the observer.
New hypothesis - a new view of the world
The study of the microcosm - the space of elementary particles - gave rise to many hypotheses and assumptions. The effect of quantum entanglement prompted scientists to think about the existence of some kind of quantum microlattice. In their opinion, at each node - the point of intersection - there is a quantum. All energy is an integral lattice, and the manifestation and movement of particles is possible only through the nodes of the lattice.
The size of the "window" of such a grating is quite small, and measurement with modern equipment is impossible. However, in order to confirm or refute this hypothesis, scientists decided to study the motion of photons in a spatial quantum lattice. The bottom line is that a photon can move either straight or in zigzags - along the diagonal of the lattice. In the second case, having overcome a greater distance, he will spend more energy. Accordingly, it will differ from a photon moving in a straight line.
Perhaps, over time, we will learn that we live in a spatial quantum grid. Or it might turn out to be wrong. However, it is the principle of quantum entanglement that indicates the possibility of the existence of a lattice.
In simple terms, in a hypothetical spatial “cube”, the definition of one facet carries with it a clear opposite meaning of the other. This is the principle of preserving the structure of space - time.
Epilogue
To understand the magical and mysterious world of quantum physics, it is worth taking a close look at the development of science over the past five hundred years. It used to be that the Earth was flat, not spherical. The reason is obvious: if you take its shape as round, then water and people will not be able to resist.
As we can see, the problem existed in the absence of a complete vision of all acting forces. It is possible that modern science lacks a vision of all acting forces to understand quantum physics. Vision gaps give rise to a system of contradictions and paradoxes. Perhaps the magical world of quantum mechanics contains the answers to the questions posed.
How do modern theoretical physicists develop new theories that describe the world? What do they add to quantum mechanics and general relativity to build a "theory of everything"? What limitations are discussed in articles that talk about the absence of “new physics”? All these questions can be answered if you understand what is action- the object underlying all existing physical theories. In this article, I will explain what physicists understand by action, and also show how it can be used to build a real physical theory, using just a few simple assumptions about the properties of the system under consideration.
I immediately warn you: the article will contain formulas and even simple calculations. However, they can be skipped without much harm to understanding. Generally speaking, I give formulas here only for those interested readers who certainly want to figure everything out on their own.
Equations
Physics describes our world with equations that link together various physical quantities - speed, force, magnetic field strength, and so on. Almost all such equations are differential, that is, they contain not only functions that depend on quantities, but also their derivatives. For example, one of the simplest equations describing the motion of a point body contains the second derivative of its coordinate:
Here I denoted the second time derivative with two points (respectively, one point will denote the first derivative). Of course, this is Newton's second law, discovered by him at the end of the 17th century. Newton was one of the first to recognize the need to write the equations of motion in this form, and also developed the differential and integral calculus needed to solve them. Of course, most physical laws are much more complicated than Newton's second law. For example, the system of hydrodynamic equations is so complex that scientists still do not know whether it is generally solvable or not. The problem of the existence and smoothness of solutions to this system is even included in the list of “millennium problems”, and the Clay Mathematical Institute has awarded a prize of one million dollars for its solution.
But how do physicists find these differential equations? For a long time, the only source of new theories was experiment. In other words, first of all, the scientist measured several physical quantities, and only then tried to determine how they are related. For example, it was in this way that Kepler discovered the three famous laws of celestial mechanics, which later led Newton to his classical theory of gravity. It turned out that the experiment seemed to "run ahead of the theory."
In modern physics, things are arranged a little differently. Of course, experiment still plays a very important role in physics. Without experimental confirmation, any theory is just a mathematical model - a toy for the mind that has nothing to do with the real world. However, physicists now obtain equations that describe our world not by empirical generalization of experimental facts, but derive them “from first principles”, that is, based on simple assumptions about the properties of the described system (for example, space-time or electromagnetic field). Ultimately, only the parameters of the theory are determined from the experiment - arbitrary coefficients that enter into the equation derived by the theorist. At the same time, the key role in theoretical physics is played by principle of least action, first formulated by Pierre Maupertuis in the middle of the 18th century and finally generalized by William Hamilton at the beginning of the 19th century.
Action
What is an action? In the most general formulation, an action is a functional that associates the trajectories of the system (that is, functions of coordinates and time) with a certain number. The principle of least action states that true trajectory action will be minimal. To understand the meaning of these buzzwords, consider the following illustrative example, taken from the Feynman Lectures on Physics.
Suppose we want to know what trajectory a body placed in a gravitational field will move along. For simplicity, we will assume that the motion is completely described by the height x(t), that is, the body moves along a vertical line. Suppose that we only know about the motion that the body starts at the point x 1 at time t 1 and comes to a point x 2 per moment t 2 , and the total travel time is T = t 2 − t one . Consider the function L equal to the difference in kinetic energy TO and potential energy P: L = TO − P. We assume that the potential energy depends only on the coordinate of the particle x(t), and kinetic - only on its speed ẋ
(t). We also define action- functionality S, equal to the average value L for the entire journey: S = ∫ L(x, ẋ
, t) d t.
Obviously the value S will depend significantly on the shape of the trajectory x(t) - in fact, that's why we call it a functional, not a function. If the body rises too high (trajectory 2), the average potential energy will increase, and if it loops too often (trajectory 3), the kinetic energy will increase - after all, we assumed that the total time of movement is exactly equal to T, which means that the body needs to increase its speed in order to have time to go through all the turns. In fact, the functionality S reaches a minimum on some optimal trajectory, which is a segment of a parabola passing through the points x 1 and x 2 (trajectory 1). By a happy coincidence, this trajectory coincides with the trajectory predicted by Newton's second law.
Examples of paths connecting points x 1 and x 2. Gray marks the trajectory obtained by a variation of the true trajectory. The vertical direction corresponds to the axis x, horizontal - axes t
Is this a coincidence? Of course, not by accident. To show this, suppose we know the true trajectory and consider it variations. Variation δ x(t) is such an addition to the trajectory x(t), which changes its shape, but leaves the start and end points in their places (see figure). Let's see what value the action takes on trajectories that differ from the true trajectory by an infinitesimal variation. Expanding function L and calculating the integral by parts, we get that the change S proportional to the variation δ x:
Here the fact that the variation at the points x 1 and x 2 is zero - this allowed us to discard the terms that appear after integration by parts. The resulting expression is very similar to the formula for the derivative, written in terms of differentials. Indeed, the expression δ S/δ x sometimes called the variational derivative. Continuing this analogy, we conclude that with the addition of a small additive δ x to the true trajectory, the action should not change, that is, δ S= 0. Since the addition can be practically arbitrary (we fixed only its ends), this means that the integrand also vanishes. Thus, knowing the action, one can obtain a differential equation describing the motion of the system, the Euler-Lagrange equation.
Let's return to our problem with a body moving in the field of gravity. Recall that we have defined a function L as the difference between the kinetic and potential energy of the body. Substituting this expression into the Euler-Lagrange equation, we actually get Newton's second law. Indeed, our guess about the form of the function L turned out to be very successful:
It turns out that with the help of the action it is possible to write the equations of motion in a very short form, as if “packing” all the features of the system inside the function L. This in itself is interesting enough. However, the action is not just a mathematical abstraction, it has a deep physical meaning. In general, a modern theoretical physicist first of all writes out the action, and only then derives the equations of motion and investigates them. In many cases, an action for a system can be constructed by making only the simplest assumptions about its properties. Let's see how this can be done with a few examples.
Free relativistic particle
When Einstein was building the special theory of relativity (STR), he postulated a few simple statements about the properties of our spacetime. First, it is homogeneous and isotropic, that is, it does not change with finite displacements and rotations. In other words, no matter where you are - on Earth, on Jupiter, or in the Small Magellanic Cloud galaxy - at all these points, the laws of physics work the same way. In addition, you will not notice any difference if you move in a uniform straight line - this is Einstein's principle of relativity. Secondly, no body can exceed the speed of light. This leads to the fact that the usual rules for recalculating velocities and time when switching between different reference systems - Galilean transformations - need to be replaced with more correct Lorentz transformations. As a result, a truly relativistic quantity, the same in all frames of reference, becomes not the distance, but the interval - the proper time of the particle. Interval s 1 − s 2 between two given points can be found using the following formula, where c- speed of light:
As we saw in the previous part, it is enough for us to write down the action for a free particle in order to find its equation of motion. It is reasonable to assume that the action is a relativistic invariant, that is, it looks the same in different frames of reference, since the physical laws in them are the same. In addition, we would like the action to be written as simply as possible (complex expressions will be left for later). The simplest relativistic invariant that can be associated with a point particle is the length of its world line. Choosing this invariant as an action (for the dimension of the expression to be correct, we multiply it by the coefficient − mc) and varying it, we get the following equation:
Simply put, the 4-acceleration of a free relativistic particle must be equal to zero. 4-acceleration, like 4-velocity, is a generalization of the concepts of acceleration and velocity to a four-dimensional space-time. As a result, a free particle can only move along a given straight line with a constant 4-velocity. In the limit of low velocities, the change in the interval practically coincides with the change in time, and therefore the equation we obtained goes over into Newton's second law already discussed above: mẍ= 0. On the other hand, the condition of zero 4-acceleration is also fulfilled for a free particle in the general theory of relativity, only in it space-time already begins to curve and the particle will not necessarily move along a straight line even in the absence of external forces.
Electromagnetic field
As you know, the electromagnetic field manifests itself in interaction with charged bodies. Usually this interaction is described using electric and magnetic field strength vectors, which are connected by a system of four Maxwell equations. The practically symmetrical form of Maxwell's equations suggests that these fields are not independent entities - what seems to us an electric field in one frame of reference can turn into a magnetic field if we switch to another frame.
Indeed, consider a wire along which electrons run at the same and constant speed. In the frame of reference associated with electrons, there is only a constant electric field, which can be found using Coulomb's law. However, in the original frame of reference, the movement of electrons creates a constant electric current, which, in turn, induces a constant magnetic field (Biot-Savart's law). At the same time, according to the principle of relativity, in the frames of reference chosen by us, the laws of physics must coincide. This means that both electric and magnetic fields are parts of a single, more general entity.
Tensors
Before we turn to the covariant formulation of electrodynamics, it is worth saying a few words about the mathematics of special and general relativity. The most important role in these theories is played by the concept of a tensor (and in other modern theories, too, to be honest). Roughly speaking, the rank tensor ( n, m) can be thought of as ( n+m)-dimensional matrix whose components depend on coordinates and time. In addition to this, the tensor must change in a certain cunning way when moving from one reference system to another or when the coordinate grid changes. How exactly, determines the number of contravariant and covariant indices ( n and m respectively). At the same time, the tensor itself, as a physical entity, does not change under such transformations, just as the 4-vector, which is a special case of a rank 1 tensor, does not change under them.
The tensor components are numbered using indices. For convenience, superscripts and subscripts are distinguished in order to immediately see how the tensor transforms when changing coordinates or reference systems. For example, the tensor component T rank (3, 0) is written as Tαβγ , and the tensor U rank (2, 1) - as Uα β γ . According to the established tradition, the components of four-dimensional tensors are numbered in Greek letters, and three-dimensional - in Latin. However, some physicists prefer to do the opposite (for example, Landau).
In addition, for brevity, Einstein suggested not writing the sum sign "Σ" when folding tensor expressions. Convolution is the summation of a tensor over two given indices, and one of them must be "upper" (contravariant), and the other must be "lower" (covariant). For example, to calculate the trace of a matrix - the rank tensor (1, 1) - you need to collapse it over the two available indices: Tr[ A μ ν ] = Σ A μ μ = Aμ μ . You can raise and lower indices using the metric tensor: T αβ γ = T αβμ g μγ .
Finally, it is convenient to introduce an absolutely antisymmetric pseudotensor ε μνρσ - a tensor that changes sign for any permutation of the indices (for example, ε μνρσ = −ε νμρσ) and whose component ε 1234 = +1. It is also called the Levi-Civita tensor. Under rotations of the coordinate system, ε μνρσ behaves like a normal tensor, but under inversions (a change like x → −x) is converted differently.
Indeed, the vectors of the electric and magnetic fields are combined into a structure that is invariant under Lorentz transformations - that is, it does not change during the transition between different (inertial) frames of reference. This is the so-called electromagnetic field tensor Fμν . It is best to write it in the form of the following matrix:
Here, the components of the electric field are denoted by the letter E, and the components of the magnetic field - by the letter H. It is easy to see that the electromagnetic field tensor is antisymmetric, that is, its components on opposite sides of the diagonal are equal in absolute value and have opposite signs. If we want to get Maxwell's equations "from first principles", we need to write down the action of electrodynamics. To do this, we must construct the simplest scalar combination of tensor objects we have, somehow related to the field or spacetime properties.
If you think about it, we have little choice - only the field tensor can act as "building blocks" Fμν , metric tensor gμν and absolutely antisymmetric tensor ε μνρσ . Of these, you can collect only two scalar combinations, and one of them is a total derivative, that is, it can be ignored when deriving the Euler-Lagrange equations - after integration, this part will simply turn to zero. Choosing the remaining combination as an action and varying it, we get a pair of Maxwell's equations - half of the system (first line). It would seem that we missed two equations. However, we don't actually need to write out the action to derive the remaining equations - they follow directly from the antisymmetry of the tensor Fμν (second line):
Once again, we have obtained the correct equations of motion by choosing the simplest possible combination as the action. True, since we did not take into account the existence of charges in our space, we obtained equations for a free field, that is, for an electromagnetic wave. When adding charges to the theory, their influence must also be taken into account. This is done by including a 4-current vector in action.
gravity
The real triumph of the principle of least action in its time was the construction of the general theory of relativity (GR). Thanks to him, the laws of motion were first derived, which scientists could not obtain by analyzing experimental data. Or they could, but they didn't. Instead, Einstein (and Hilbert, if you will) derived the equations in terms of metrics based on assumptions about the properties of spacetime. Starting from this moment, theoretical physics began to “overtake” the experimental one.
In GR, the metric ceases to be constant (as in SRT) and begins to depend on the density of the energy placed in it. I note that it is more correct to speak about energy, and not about mass, although these two quantities are related by the relation E = mc 2 in its own frame of reference. Let me remind you that the metric sets the rules by which the distance between two points (strictly speaking, infinitely close points) is calculated. It is important that the metric does not depend on the choice of coordinate system. For example, a flat three-dimensional space can be described using a Cartesian or spherical coordinate system, but in both cases the space metric will be the same.
To write down the action for gravity, we need to build some kind of invariant from the metric, which will not change when the coordinate grid changes. The simplest such invariant is the metric determinant. However, if we only enable it, we will not get differential equation, since this expression does not contain derivatives of the metric. And if the equation is not differential, it cannot describe situations in which the metric changes over time. Therefore, we need to add the simplest invariant to the action, which contains derivatives gμν . Such an invariant is the so-called Ricci scalar R, which is obtained by convolution of the Riemann tensor Rμνρσ , which describes the curvature of space-time:
Robert Couse-Baker/flickr.com
Theory of everything
Finally, it's time to talk about the "theory of everything". This is the name of several theories that try to combine general relativity and the standard model - the two main physical theories known at the moment. Scientists make such attempts not only for aesthetic reasons (the fewer theories needed to understand the world, the better), but also for more compelling reasons.
Both GR and the Standard Model have limits of applicability, after which they cease to work. For example, general relativity predicts the existence of singularities - points at which the energy density, and hence the curvature of space-time, tends to infinity. Not only are infinities themselves unpleasant - in addition to this problem, the Standard Model states that energy cannot be localized at a point, it must be spread over some, albeit small, volume. Therefore, near the singularity, the effects of both GR and the Standard Model should be large. At the same time, general relativity has not yet been quantized, and the Standard Model is built on the assumption of a flat space-time. If we want to understand what happens around singularities, we need to develop a theory that includes both of these theories.
Bearing in mind the success of the principle of least effect in the past, scientists base all their attempts to build a new theory on it. Remember, we considered only the simplest combinations when we built the action for various theories? Then our actions were crowned with success, but this does not mean at all that the simplest action is the most correct. Generally speaking, nature does not have to adjust its laws to make our life easier.
Therefore, it is reasonable to include the following, more complex invariant quantities in action and see where this leads. In some ways, this resembles the successive approximation of a function by polynomials of ever higher degrees. The only problem here is that all such corrections come into play with some unknown coefficients that cannot be calculated theoretically. Also, since the Standard Model and general relativity still work well, these coefficients must be very small - hence difficult to determine from experiment. Numerous papers reporting on "restrictions on the new physics" are just the same aimed at determining the coefficients at higher orders of the theory. So far, they have only been able to find upper bounds.
In addition, there are approaches that introduce new, non-trivial concepts. For example, string theory suggests that the properties of our world can be described with the help of vibrations of not point, but extended objects - strings. Unfortunately, experimental confirmation of string theory has not yet been found. For example, she predicted some excitations at the accelerators, but they never appeared.
In general, it does not seem that scientists have come close to discovering a “theory of everything”. Probably, theorists still have to come up with something essentially new. However, there is no doubt that the first thing they do is write out an action for the new theory.
***
If all these arguments seemed complicated to you and you scrolled through the article without reading, here is a brief summary of the facts that were discussed in it. First, all modern physical theories in one way or another rely on the notion actions- a quantity that describes how much the system “likes” this or that trajectory of movement. Secondly, the equations of motion of the system can be obtained by looking for the trajectory on which the action takes least meaning. Thirdly, the action can be constructed using only a few elementary assumptions about the properties of the system. For example, about the fact that the laws of physics are the same in frames of reference that move at different speeds. Fourth, some of the candidates for a "theory of everything" are obtained by simply adding terms to the operation of the Standard Model and GR that violate some of the assumptions of these theories. For example, Lorentz invariance. If after reading the article you remember the above statements, that's good. And if you also understand where they come from - just wonderful.
Dmitry Trunin
The English physicist Isaac Newton published a book in which he explained the movement of objects and the principle of gravity. The "Mathematical Principles of Natural Philosophy" gave things in the world fixed places. The story goes that at the age of 23, Newton went to a garden and saw an apple fall from a tree. At that time, physicists knew that the Earth somehow attracted objects using gravity. Newton developed this idea.
According to John Conduitt, Newton's assistant, seeing an apple fall to the ground, Newton got the idea that the gravitational force "was not limited to a certain distance from the earth, but extends much further than is usually believed." According to Conduitt, Newton asked the question: why not even to the moon?
Inspired by his insights, Newton developed the law of universal gravitation, which worked equally well for apples on Earth and planets orbiting the Sun. All these objects, despite the differences, obey the same laws.
“People thought he explained everything that needed to be explained,” Barrow says. “His achievement was great.”
The problem is that Newton knew there were holes in his work.
For example, gravity does not explain how small objects are held together, since this force is not that great. Also, although Newton could explain what was going on, he could not explain how it worked. The theory was incomplete.
There was a bigger problem. Although Newton's laws explained the most common phenomena in the universe, in some cases objects violated his laws. These situations were rare and usually involved high speeds or heightened gravity, but they did happen.
One such situation was the orbit of Mercury, the planet closest to the Sun. Like any other planet, Mercury revolves around the Sun. Newton's laws could be applied to calculate the motions of the planets, but Mercury didn't want to play by the rules. More strangely, its orbit had no center. It became clear that the universal law of universal gravitation was not so universal, and not a law at all.
More than two centuries later, Albert Einstein came to the rescue with his theory of relativity. Einstein's idea, which in 2015 provided a deeper understanding of gravity.
Theory of relativity
The key idea is that space and time, which appear to be separate things, are in fact intertwined. Space has three dimensions: length, width and height. Time is the fourth dimension. All four are connected in the form of a giant space cell. If you've ever heard the phrase "space-time continuum", that's what it's all about.
Einstein's big idea was that heavy objects like planets or fast moving ones could warp spacetime. A bit like a tight trampoline: if you put something heavy on the fabric, a dip will form. Any other objects will roll down the slope towards the object in the valley. Therefore, according to Einstein, gravity attracts objects.
The idea is strange in its essence. But physicists are convinced that it is. She also explains the strange orbit of Mercury. According to the general theory of relativity, the giant mass of the Sun bends space and time around. Being the closest planet to the Sun, Mercury experiences much more curvature than other planets. The equations of general relativity describe how this curved space-time affects Mercury's orbit and allow the planet's position to be predicted.
However, despite its success, the theory of relativity is not the theory of everything, like Newton's theories. Just as Newton's theory does not work for truly massive objects, Einstein's theory does not work on the microscale. As soon as you start looking at atoms and anything smaller, matter starts to behave very strangely.
Until the end of the 19th century, the atom was considered the smallest unit of matter. Born from the Greek word "atomos", which means "indivisible", the atom, by its definition, should not be broken into smaller particles. But in the 1870s, scientists discovered particles that are 2,000 times lighter than atoms. By weighing beams of light in a vacuum tube, they found extremely light particles with a negative charge. Thus was discovered the first subatomic particle: the electron. In the next half century, scientists discovered that the atom has a compound nucleus around which electrons scurry. This nucleus is made up of two types of subatomic particles: neutrons, which have a neutral charge, and protons, which are positively charged.
But that's not all. Since then, scientists have found ways to divide matter into smaller and smaller parts, while continuing to refine our understanding of fundamental particles. By the 1960s, scientists had found dozens of elementary particles, making up a long list of the so-called particle zoo.
As far as we know, of the three components of the atom, the only fundamental particle is the electron. Neutrons and protons are divided into tiny quarks. These elementary particles obey a completely different set of laws, different from those that trees or planets obey. And these new laws - which were far less predictable - put the physicists in a bad mood.
In quantum physics, particles have no definite place: their location is a little blurry. As if each particle has a certain probability of being in a certain place. This means that the world is inherently a fundamentally undefined place. Quantum mechanics is even hard to understand. As Richard Feynman, an expert in quantum mechanics, once said, “I think I can safely say that no one understands quantum mechanics.”
Einstein, too, was concerned about the fuzziness of quantum mechanics. Despite the fact that he, in fact, partially invented it, Einstein himself never believed in quantum theory. But in their chambers - large and small - both quantum mechanics and quantum mechanics proved the right to undivided power, being extremely accurate.
Quantum mechanics has explained the structure and behavior of atoms, including why some of them are radioactive. It also underlies modern electronics. You couldn't read this article without her.
General relativity predicted the existence of black holes. Those massive stars that collapsed into themselves. Their gravitational attraction is so powerful that not even light can escape it.
The problem is that these two theories are incompatible and therefore cannot be true at the same time. General relativity says that the behavior of objects can be accurately predicted, whereas quantum mechanics says that you can only know the probability of what objects will do. It follows that there are some things that physicists have not yet described. Black holes, for example. They are massive enough that relativity theory can be applied to them, but also small enough that quantum mechanics can be applied. Unless you get close to a black hole, this incompatibility will not affect your daily life. But it has puzzled physicists for most of the past century. It is this incompatibility that makes one look for a theory of everything.
Einstein spent most of his life trying to find such a theory. Not being a fan of the randomness of quantum mechanics, he wanted to create a theory that would unify gravity and the rest of physics so that quantum oddities would remain secondary consequences.
His main goal was to make gravity work with electromagnetism. In the 1800s, physicists figured out that electrically charged particles could attract or repel each other. Because some metals are attracted by a magnet. Obviously, if there are two kinds of forces that objects can exert on each other, they can be attracted by gravity and attracted or repelled by electromagnetism.
Einstein wanted to combine these two forces into a "unified field theory". To do this, he stretched space-time into five dimensions. Along with three space and one time dimensions, he added a fifth dimension, which should be so small and curled up that we couldn't see it.
It didn't work, and Einstein spent 30 years looking for nothing. He died in 1955 and his unified field theory was not developed. But in the next decade, a serious rival for this theory emerged: string theory.
String theory
The idea behind string theory is quite simple. The basic ingredients of our world, like electrons, are not particles. These are tiny loops or "strings". It's just that because the strings are so small, they appear to be dots.
Like guitar strings, these loops are under tension. This means that they vibrate at different frequencies depending on the size. These vibrations determine what sort of "particle" each string will represent. Vibrating a string in one way will give you an electron. Others, something else. All the particles discovered in the 20th century are the same kind of strings, just vibrating differently.
It's quite difficult to immediately understand why this is a good idea. But it applies to all the forces in nature: gravity and electromagnetism, plus two more discovered in the 20th century. Strong and weak nuclear forces operate only within the tiny nuclei of atoms, so they could not be detected for a long time. A strong force holds the core together. A weak force usually does nothing, but if it gains enough strength, it breaks the nucleus apart: therefore, some atoms are radioactive.
Any theory of everything will have to explain all four. Fortunately, the two nuclear forces and electromagnetism are fully described by quantum mechanics. Each force is carried by a specialized particle. But there is not a single particle that would carry gravity.
Some physicists think that it is. And they call it "graviton". Gravitons have no mass, a special spin, and they move at the speed of light. Unfortunately, they haven't been found yet. This is where string theory comes into play. It describes a string that looks exactly like a graviton: has the correct spin, no mass, and moves at the speed of light. For the first time in history, the theory of relativity and quantum mechanics have found common ground.
In the mid-1980s, physicists were fascinated by string theory. “In 1985, we realized that string theory solved a lot of problems that had plagued people for the past 50 years,” says Barrow. But she also had problems.
First, "we don't understand what string theory is in the right detail," says Philip Candelas of the University of Oxford. "We don't have a good way to describe it."
In addition, some of the predictions look strange. While Einstein's unified field theory relies on an extra hidden dimension, the simplest forms of string theory need 26 dimensions. They are needed to link mathematics theory with what we already know about the universe.
More advanced versions, known as "superstring theories", get by with ten dimensions. But even this does not fit with the three dimensions that we observe on Earth.
“This can be dealt with by assuming that only three dimensions have expanded in our world and become large,” says Barrow. “Others are present but remain fantastically small.”
Because of these and other problems, many physicists dislike string theory. And they offer another theory: loop quantum gravity.
Loop quantum gravity
This theory does not aim to unify and include everything that is in particle physics. Instead, loop quantum gravity simply attempts to deduce a quantum theory of gravity. It is more limited than string theory, but not as cumbersome. Loop quantum gravity assumes that space-time is divided into small pieces. From afar, it seems that this is a smooth sheet, but upon closer inspection, you can see a bunch of dots connected by lines or loops. These little fibers that weave together offer an explanation for gravity. This idea is as incomprehensible as string theory, and has similar problems: there is no experimental evidence.
Why are these theories still being discussed? Maybe we just don't know enough. If big phenomena are discovered that we have never seen, we can try to understand the big picture, and fill in the missing pieces of the puzzle later.
“It's tempting to think we've discovered everything,” Barrow says. - But it would be very strange if by 2015 we had made all the necessary observations to get a theory of everything. Why should it be so?
There is another problem. These theories are difficult to test, in large part because their math is so brutal. Candelas has been trying to find a way to test string theory for years, but has never been able to.
"The main obstacle to the advancement of string theory remains the lack of development of mathematics, which should accompany physical research," says Barrow. "It's at an early stage, there's still a lot to explore."
With all this, string theory remains promising. “For years, people have been trying to integrate gravity with the rest of physics,” says Candelas. - We had theories that explained electromagnetism and other forces well, but not gravity. With string theory, we're trying to combine them."
The real problem is that the theory of everything may simply be impossible to identify.
When string theory became popular in the 1980s, there were actually five versions of it. “People started to worry,” Barrow says. “If this is the theory of everything, why are there five?” Over the next decade, physicists discovered that these theories could be converted from one to the other. They are just different ways of seeing the same thing. The result was the M-theory put forward in 1995. This is a deep version of string theory, including all earlier versions. Well, at least we are back to a unified theory. M-theory only requires 11 dimensions, which is much better than 26. However, M-theory does not offer a unified theory of everything. She offers billions of them. In total, M-theory offers us 10^500 theories, all of which will be logically consistent and capable of describing the universe.
It looks worse than useless, but many physicists believe it points to a deeper truth. Perhaps our universe is one of many, each of which is described by one of the trillions of versions of M-theory. And this gigantic collection of universes is called "".
At the beginning of time, the multiverse was like "a big foam of bubbles of all shapes and sizes," Barrow says. Each bubble then expanded and became the universe.
"We're in one of those bubbles," Barrow says. As the bubbles expanded, other bubbles could form inside them, new universes. “In the process, the geography of such a universe has become seriously complicated.”
The same physical laws operate in every bubble universe. Because in our universe everything behaves the same way. But other universes may have other laws. This leads to a strange conclusion. If string theory is indeed the best way to unify relativity and quantum mechanics, then both of them will and will not be a theory of everything at the same time.
On the one hand, string theory can give us a perfect description of our universe. But it will also inevitably lead to each of the trillions of other universes being unique. A major change in thinking will be that we stop waiting for a unified theory of everything. There can be many theories of everything, each of which will be true in its own way.
Among the two fundamental theories that explain the reality around us, quantum theory appeals to the interaction between least particles of matter, while general relativity refers to gravity and largest structures throughout the universe. Since the time of Einstein, physicists have tried to bridge the gap between these teachings, but with mixed success.
One way to reconcile gravity with quantum mechanics was to show that gravity is based on indivisible particles of matter, quanta. This principle can be compared to how the light quanta themselves, photons, represent an electromagnetic wave. Until now, scientists have not had enough data to confirm this assumption, but Antoine Tilloy(Antoine Tilloy) from the Institute of Quantum Optics. Max Planck in Garching, Germany, attempted to describe gravity with the principles of quantum mechanics. But how did he do it?
quantum world
In quantum theory, the state of a particle is described by its wave function. It, for example, allows you to calculate the probability of finding a particle at a particular point in space. Before the measurement itself, it is unclear not only where the particle is, but also whether it exists. The very fact of measurement literally creates reality by "destroying" the wave function. But quantum mechanics rarely refers to measurements, which is why it is one of the most controversial areas of physics. Remember Schrödinger's paradox: You won't be able to resolve it until you take a measurement by opening the box and finding out if the cat is alive or not.
One solution to these paradoxes is the so-called GRW model, which was developed in the late 1980s. This theory includes such a phenomenon as " outbreaks» are spontaneous collapses of the wave function of quantum systems. The result of its application is exactly the same as if the measurements were carried out without observers as such. Tilloy modified it to show how it can be used to get to the theory of gravity. In his version, the flash that destroys the wave function and thereby forces the particle to be in one place also creates a gravitational field at that moment in space-time. The larger the quantum system, the more particles it contains and the more often flashes occur, thereby creating a fluctuating gravitational field.
The most interesting thing is that the average value of these fluctuations is the same gravitational field that Newton's theory of gravity describes. This approach to unifying gravity with quantum mechanics is called semiclassical: gravity arises from quantum processes, but remains a classical force. "There is no real reason to ignore the semiclassical approach, in which gravity is classical at a fundamental level," says Tilloy.
Gravity Phenomenon
Klaus Hornberger of the University of Duisburg-Essen in Germany, who did not take part in the development of the theory, treats it with great sympathy. However, the scientist points out that before this concept forms the basis of a unified theory that unites and explains the nature of all the fundamental aspects of the world around us, it will be necessary to solve a number of tasks. For example, Tilloy's model can certainly be used to derive the Newtonian force of gravity, but its compliance with the gravitational theory still needs to be verified using mathematics.
However, the scientist himself agrees that his theory needs an evidence base. For example, he predicts that gravity will behave differently depending on the scale of the objects in question: for atoms and for supermassive black holes, the rules can be very different. Be that as it may, if tests reveal that Tillroy's model indeed reflects reality, and gravity is indeed a consequence of quantum fluctuations, then this will allow physicists to comprehend the reality around us on a qualitatively different level.
There are many places to start this discussion, and this is as good as the others: everything in our universe has the nature of particles and waves at the same time. If one could say about magic this way: "All these are waves, and only waves," that would be a wonderful poetic description of quantum physics. In fact, everything in this universe has a wave nature.
Of course, also everything in the universe has the nature of particles. Sounds weird, but it is.
Describing real objects as particles and waves at the same time would be somewhat inaccurate. Strictly speaking, the objects described by quantum physics are not particles and waves, but rather belong to the third category, which inherits the properties of waves (frequency and wavelength, along with propagation in space) and some properties of particles (they can be counted and localized to a certain degree ). This leads to a lively debate in the physics community about whether it is even correct to speak of light as a particle; not because there is a contradiction in whether light has a particle nature, but because calling photons "particles" rather than "quantum field excitations" is misleading students. However, this also applies to whether electrons can be called particles, but such disputes will remain in purely academic circles.
This "third" nature of quantum objects is reflected in the sometimes confusing language of physicists who discuss quantum phenomena. The Higgs boson was discovered as a particle at the Large Hadron Collider, but you've probably heard the phrase "Higgs field", such a delocalized thing that fills all of space. This is because under certain conditions, such as particle collision experiments, it is more appropriate to discuss excitations of the Higgs field than to characterize the particle, while under other conditions, such as general discussions of why certain particles have mass, it is more appropriate to discuss physics in terms of interactions with the quantum a field of universal proportions. They are just different languages describing the same mathematical objects.
Quantum physics is discrete
Everything in the name of physics - the word "quantum" comes from the Latin "how much" and reflects the fact that quantum models always include something that comes in discrete quantities. The energy contained in a quantum field comes in multiples of some fundamental energy. For light, this is associated with the frequency and wavelength of the light—high-frequency, short-wavelength light has a huge characteristic energy, while low-frequency, long-wavelength light has little characteristic energy.
In both cases, meanwhile, the total energy contained in a separate light field is an integer multiple of this energy - 1, 2, 14, 137 times - and there are no strange fractions like one and a half, "pi" or the square root of two. This property is also observed in discrete energy levels of atoms, and energy bands are specific - some energy values are allowed, others are not. Atomic clocks work thanks to the discreteness of quantum physics, using the frequency of light associated with the transition between two allowed states in cesium, which allows you to keep time at the level necessary for the "second jump".
Ultra-precise spectroscopy can also be used to search for things like dark matter, and remains part of the motivation for the institute's work on low-energy fundamental physics.
It's not always obvious - even some things that are quantum in principle, like blackbody radiation, are associated with continuous distributions. But upon closer examination and with the connection of a deep mathematical apparatus, quantum theory becomes even more strange.
Quantum physics is probabilistic
One of the most surprising and (at least historically) controversial aspects of quantum physics is that it is impossible to predict with certainty the outcome of a single experiment with a quantum system. When physicists predict the outcome of a particular experiment, their prediction is in the form of the probability of finding each of the particular possible outcomes, and comparisons between theory and experiment always involve deriving a probability distribution from many repeated experiments.
The mathematical description of a quantum system, as a rule, takes the form of a "wave function", represented in the equations of the Greek beech psi: Ψ. There are many discussions about what exactly the wave function is, and they have divided physicists into two camps: those who see the wave function as a real physical thing (ontic theorists), and those who believe that the wave function is solely an expression of our knowledge (or lack thereof) regardless of the underlying state of a particular quantum object (epistemic theorists).
In each class of the underlying model, the probability of finding a result is not determined directly by the wave function, but by the square of the wave function (roughly speaking, it is still the same; the wave function is a complex mathematical object (and therefore includes imaginary numbers like the square root or its negative variant), and the probability operation is a little more complicated, but "the square of the wave function" is enough to get the basic gist of the idea). This is known as the Born rule, after the German physicist Max Born, who first calculated it (in a footnote to a 1926 paper) and surprised many people with its ugly implementation. There is active work in trying to derive the Born rule from a more fundamental principle; but so far none of them has been successful, although it has generated a lot of interesting things for science.
This aspect of the theory also leads us to particles that are in many states at the same time. All we can predict is probability, and before measuring with a particular result, the system being measured is in an intermediate state - a superposition state that includes all possible probabilities. But whether the system is really in multiple states or is in one unknown depends on whether you prefer an ontic or epistemic model. Both of them lead us to the next point.
Quantum physics is non-local
The latter was not widely accepted as such, mainly because he was wrong. In a 1935 paper, along with his young colleagues Boris Podolkiy and Nathan Rosen (the EPR paper), Einstein made a clear mathematical statement of something that had been troubling him for some time, what we call "entanglement."
EPR's work claimed that quantum physics recognized the existence of systems in which measurements made at widely separated locations could be correlated so that the outcome of one determined the other. They argued that this meant that the results of measurements had to be determined in advance, by some common factor, since otherwise it would be necessary to transmit the result of one measurement to the location of another at a speed faster than the speed of light. Therefore, quantum physics must be incomplete, an approximation of a deeper theory (the “hidden local variable” theory, in which the results of individual measurements do not depend on something that is farther from the measurement site than a signal traveling at the speed of light can cover (locally), but rather is determined by some factor common to both systems in an entangled pair (hidden variable).
The whole thing was considered an incomprehensible footnote for more than 30 years, since there seemed to be no way to verify it, but in the mid-60s, the Irish physicist John Bell worked out the consequences of EPR in more detail. Bell showed that you can find circumstances under which quantum mechanics will predict correlations between remote measurements that are stronger than any possible theory like those proposed by E, P, and R. This was experimentally tested in the 70s by John Kloser and Alain Aspect in the early 80s. x - they showed that these intricate systems could not potentially be explained by any local hidden variable theory.
The most common approach to understanding this result is to assume that quantum mechanics is non-local: that the results of measurements made at a particular location can depend on the properties of a distant object in a way that cannot be explained using signals traveling at the speed of light. This, however, does not allow information to be transmitted at superluminal speed, although many attempts have been made to circumvent this limitation using quantum nonlocality.
Quantum physics is (almost always) concerned with the very small
Quantum physics has a reputation for being weird because its predictions are drastically different from our everyday experience. This is because its effects are less pronounced the larger the object - you will hardly see the wave behavior of the particles and how the wavelength decreases with increasing momentum. The wavelength of a macroscopic object like a walking dog is so ridiculously small that if you magnified every atom in a room to the size of a solar system, the wavelength of a dog would be the size of one atom in that solar system.
This means that quantum phenomena are mostly limited to the scale of atoms and fundamental particles, whose masses and accelerations are small enough that the wavelength remains so small that it cannot be observed directly. However, a lot of efforts are being made to increase the size of a system that exhibits quantum effects.
Quantum physics is not magic
The previous point quite naturally brings us to this point: however strange quantum physics may seem, it is clearly not magic. What it postulates is strange by the standards of everyday physics, but it is severely constrained by well-understood mathematical rules and principles.
So if someone comes to you with a "quantum" idea that seems impossible - infinite energy, magical healing power, impossible space engines - it's almost certainly impossible. This doesn't mean that we can't use quantum physics to do incredible things: we are constantly writing about incredible breakthroughs using quantum phenomena, and they have already quite surprised humanity, it only means that we will not go beyond the laws of thermodynamics and common sense .
If the above points are not enough for you, consider this only a useful starting point for further discussion.
