A brief history of quantum alternatives

Original author: Lee Phillips
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"Copenhagen" quantum mechanics says that reality does not exist until it is measured, so many continue to look for alternatives to this interpretation.



In 1915, Albert Einstein, with the help of his friends, developed the theory of gravity , which turned everything that we considered the very foundation of physical reality. The idea that the space we inhabited could not be perfectly described by Euclidean geometry was incomprehensible; so much so that the philosopher Immanuel Kant, in many ways a radical thinker, declared that no theory of physics can cope with it.

Later the physicist Werner Heisenberg pointed out the meaning of Kant’s mistake. The great philosopher postulated that our intuitive understanding of the ancient geometry of Euclid meant that it was the necessary foundation of physical reality. In fact, this turned out to be wrong, calling into question the whole philosophical system of Kant.

Despite a radical break with past ideas about space and time, Einstein’s theories soon merged with Newton’s ideas as part of “ classical physics ”. Humanity was forced to do this because the revolution of scientific thought was so deep that it created a bright mark in the history of science: the development of the theory of quantum physics.

What can be called a scientific revolution deeper than the general theory of relativity? What could create a tectonic shift, more powerful than the idea that space and time themselves are bent by matter?

To understand this, we must first try to understand: such is the inherent oddity inherent in quantum mechanics. As soon as we begin to feel uncomfortable in the quantum world, we will begin to understand why physicists tried to create alternatives to the CM after they appeared on the stage — alternatives that recreated the same fantastic correspondences with experiments, while preserving part of the classical core an intuitive understanding of how nature should behave.

All you know is wrong


Our deep intuitive understanding of the nature of reality arises from observation and interaction with the world around us, starting from childhood. Even before we can express this, we begin to understand the causal relationships. The cause of any event is another event that occurred. The world is predictable.

Later we become more sophisticated. We recognize that our understanding of causes is limited and we recognize the uncertainty of their consequences. Perhaps we even study probability theory and statistics and learn how to express the limits of our knowledge in mathematical form. But we believe that these are only our limitations and that, invisibly for us, nature behind the scenes continues to use the exact rules of cause and effect. When we throw a coin, only the lack of information about the movement of the coin and the air makes us say that the probability of a falling eagle is equal to one second. We assume that if we knew all the details and we had a large enough computer to perform the calculations, then we would not have to rely on probabilities.

However, such a “realistic” view of things cannot survive (and has not survived) the hard data obtained in experiments with photons and other subatomic particles. It was not physicists who, because of their stubborn intractability, decided to create a theory that contradicted our most precious intuitive sensations about reality: in fact, these are the results of experiments that stubbornly refused to correspond to any classical interpretations. The invention of quantum formalism was an act of despair — the only one that turned out to be working. If we limit ourselves by asking questions admitted by quantum theory, then we will be rewarded with the correct answers. But if we persist in trying to understand what the theory tells us, with the help of the concepts of the classical world, then we will come to confusion.

As a physics student, I saw a training demonstration that allowed me to take a quick look at the invisible weirdness of the world around us. You can repeat this experience at home, using only a flashlight or laser pointer, as well as three polarization filters (you can also use glasses from broken sunglasses with polarization). Arrange the two filters in a row, leaving a gap between them. Pass the light through this pair and rotate one filter until the light ceases to pass; the axes of their polarization became perpendicular. Now insert the third filter between the first two. You will see that the light will begin to pass through this construction: somehow adding an extra filter allows the light to pass through.

This demonstration was part of the introductory part of the course on quantum mechanics. For several weeks we were immersed in the formalism of quantum theory, from which this seemingly paradoxical behavior arises as a trivial consequence.

There are people who claim that there is no paradox here and that this behavior can be explained with the classical approach. And in a sense, they are absolutely right. But the results of the desktop demonstration, terrific students already familiar with classical physics, apparently arise from quantum formalism. And it means something.


Double-slit experiment with electrons.

Scientists of the first decades of the last century faced much more striking and inexplicable results of experiments. Often mention the experiment shown above with two slots. Carrying out this experiment with electrons or photons, we get the same results: the interference pattern, as if two waves interfering with each other appeared from two slits. This shows that light is a wave and that even particles with a mass, such as electrons, seem to behave in such conditions as waves.

But the experiment can be changed in two curious ways. First, if you slow down the frequency of emission of particles (photons, electrons, or even whole molecules) so that only one particle passes through the slots at a time, the result will not change. This should mean that the particle is somehow divided into two, passes through both slots and interacts with itself! Secondly, if you make any change to the installation, so that it fixes the gap through which the particle passes, the interference pattern disappears and is replaced by a pattern that could be expected if the particles were ordinary particles without wave properties: just two symmetric distributions, centered on each of the slots.

It was difficult to find a theory that would explain the results, and would suit everyone. It seemed that photons or electrons sometimes decided to behave like waves, and sometimes like particles, depending on what the experimenter wanted to see.

Then everything became even weirder. Technologies have evolved to the extent that we can choose what type of measurement to do afterhow the particle began its journey. The results of such experiments with a “delayed choice” remained the same. If we look to see which direction the particle has taken, the interference is destroyed. If we turn away, so to speak, the familiar interference pattern returns. Nevertheless, the particle had to “decide” whether to behave as a particle or as a wave even before passing through the slots and before creating the final configuration of the experiment.

The results of experiments with a deferred choice forced not one physicist to assume that information about the choice of the behavior of a particle or wave is transmitted back in time, from the time of choice at some time before the particle passes through the device. The fact that this assumption was discussed with complete seriousness should give you some idea of ​​how difficult it was to explain the results of experiments in the microworld with the help of a set of concepts (such as causality ) taken from our realistic world views. An explanation with a return back in time lasted until a recent moment when an experiment was conductedwith slow and cold helium atoms in a similar pattern. Atoms passed through the installation under the action of gravity only, therefore between the time of passage and the choice of the method of observing them, a considerable time passed. Although physicists sometimes describe some very fast subatomic processes as using a limited form of traveling back in time, the long duration in experiments with helium made the existence of such an explanation impossible.

What do we have left? The results of these and many other experiments are simply impossible to describe using traditional concepts based on reality: that objects exist with a certain set of properties; that if we decide not to measure a separate property, it still has some meaning. Physicists had experience with uncertainty long before the quantum revolution, but this uncertainty was of a completely different type. It was the uncertainty of knowledge , implying an unknown, but existing, level of deterministic reality by what we directly perceive.

If we discard all these concepts, so fundamental to our understanding of the world, then how do we replace them? After all, they have not just become an intuitive part of our everyday experience, but also serve as the foundation of other areas of science.

What we do not see


In the nineteenth century, determinism at the microscopic level led to the first huge success of probabilistic reasoning in physics: the kinetic theory of gases. It was based on the old idea that matter is made up of a gigantic number of simple atoms that repel each other like submicroscopic ping-pong balls. Thanks to several simple assumptions, as well as a good proportion of mathematics, which created the kinetic theory, scientists managed to derive the known laws of thermodynamics as average values ​​of the behavior of ideal atoms. The kinetic theory has shown how the phenomena we observe can arise from the average behavior of a multitude of processes that we are unable to observe directly. Nevertheless, these averaged behaviors acted in accordance with the well-known deterministic laws of classical mechanics — the whole theory was based on them.


Particles showing the Brownian motion.

Even in the twentieth century, many scientists did not believe in the reality of atoms. The turning point was Einstein’s article on Brownian motion, published in 1905. It applied statistical reasoning, which showed that the chaotic movements of pollen particles suspended in water can be explained by the bombardment of an invisible set of particles.

Einstein received his Nobel Prize not for this work, and not for another article of 1905, in which he introduced the concept of relativity E = mc 2 . The prize was awarded to him for another work published in the same year and devoted to the photo effect. This publication unintentionally launched a process that led to the collapse of our classic reality.

The award that earned Einstein an article explained a lot of mysterious results of experiments on the interaction of light and matter. It postulates that light is absorbed and emitted from matter by discrete quantities of energy called quanta . This work marked the birth of quantum physics — and this child of Einstein began to develop in a direction that irritated even his own father.

The next two decades witnessed an explosion of experimental research in the new field of atomic physics and chemistry. The electron was freed from the shackles of the atom and began to experiment directly with it. Even more strange phenomena began to appear in the results of experiments, a number of incomplete theories and models, and mathematical interpretations for describing the microworld appeared. Everything gradually began to come together, and physicists were finally able to predict the experimental results. But this required an unusual, abstract mathematical structure and a set of rules relating it to measurable aspects of nature, namely, quantum mechanics. (This story is told in a very well written book by David Lindley).

By the third decade of the twentieth century, almost all scientists accepted the reality of atoms and even smaller particles. But they represented them as invisible tiny versions of familiar objects: planets, billiard balls and grains of sand were used for comparison. Most scientists who did not belong to the small circle that created or understood the new theory assumed that it was another version of something like the kinetic theory of gases. And today, most people probably think in a similar way: atoms and other components of the microworld may have exotic properties and follow strange mathematical rules, but at least they take part in the reality we know. However, quantum mechanics claims the opposite.

One of the key figures in its development is Niels Bohr (with significant influence of Max Born and Werner Heisenberg), who was also one of the strangest figures in the history of physics. Bohr was a physicist and philosopher who tired his colleagues by uttering long, detailed, sometimes incomprehensible sentences. Although he, without a doubt, perfectly knew the theory and was known to solve several riddles at the initial stage of the study of atoms, but he often preferred to manipulate equations with leisure, aimless conversations. He insisted on the need to understand the meaning of everything. (His search for meaning was not shared by some of the other pioneers of quantum physics, because they had already begun research, confessing the “Shut up and calculate!” Approach .)


The coat of arms of Niels Bohr.

Partly inspired by the theory of physics, which he helped create, Bohr gradually began to develop its mystical side, and even added the Yin-Yang symbol to his coat of arms.

This first understanding or interpretation of quantum mechanics later became known as the “Copenhagen interpretation” after the University of Bor. It is still the standard view on quantum mechanics, even though there is no formal definition. Rather, it is a set of generally accepted practical rules relating to those parts of the theory that can be observed in the laboratory. They can be formulated in various ways; Here is one of the versions reflecting the modern understanding of the main aspects:

  • The state (position, impulse, etc.) of a system is completely determined by its “wave function” - a mathematical object that is deterministically transformed according to the equations of quantum mechanics. Wave function cannot be observed directly; however, it gives us the probability that at the time of the measurements we will find the system in a particular state. Such "systems" can be elementary particles, for example, electrons and protons, atoms, or even large molecules. In the process of measurement, the wave function and its probabilities are “tightened” to the measured value.
  • There is no “reality” other than calculating probabilities. There is no underlying layer of determinism; There are no hidden mechanisms that record what will be measured before the measurement. These probabilities do not reflect the lack of our knowledge, as in classical statistical physics, because there is nothing about which one can have knowledge. There is only probability.
  • There are fundamental limitations to what can be measured, described by uncertainty relations: certain pairs of quantities can be measured simultaneously with a certain degree of accuracy (examples are position-momentum and time-energy). It has nothing to do with the technology or methods of conducting experiments; these restrictions are part of nature and cannot be avoided.

The Copenhagen interpretation copes well with all the intricacies surrounding such phenomena as the above-described experiments with a delayed selection. There is no need to send mysterious signals traveling back in time, or create complex theories designed to preserve our ideas about reality. We just need to abandon these ideas and accept the fact that properties do not exist independently of their measurement. Values ​​become real only when they are measured, and quantum mechanics tells us that they are just probabilities of different realities.

No exit?


The consequences of quantum mechanics, along with the Copenhagen interpretation, are unintuitive, fanciful, and unacceptable metaphorically. It is the primary nature of probabilities and the destruction of deterministic causality that led Einstein to argue that God "does not play dice with the world." So why did physicists gladly accept this theory? Why can not we say that there may be deterministic "hidden parameters" that caused the probabilities of the quantum world?

The most important and immediate cause is the Bell theorem. This theorem, proved by John Stewart Bell in 1964, shows that ifthere is a layer of hidden parameters that we cannot measure, then certain experiments should produce certain results. To date, there is much evidence of extremely accurate experiments that measurements do not give such results. Logic demands to recognize that there is no unknown deterministic layer in the microcosm .

Bell's theorem can allow our experimental results and deterministic hidden parameters to coexist only under one condition: the influence of these parameters must propagate faster than the speed of light. However, such an influence cannot be a true, classical transfer of information, because the possibility of this is excluded by the special theory of relativity. As Einstein pointed out, moving information faster than the speed of light will further disrupt our understanding of causes and effects: it will allow consequences to precede causes, even at the level of the macrocosm.

Another possibility is to allow hidden parameters to transmit the ephemeral effects of quantum mechanics, which spread instantly, but does not transfer information in the classical sense. Einstein mockingly called these mysterious influences “terrible long-range action”, but it is with them that we explain the results of measurements of entangled particles. For them, the measurement of the state of a particle can tell us what the result of measuring another particle at an arbitrary distance will be. Theories that avoid the influence of Bell's theorem, assuming the existence of hidden variables that transmit some kind of instantaneous effect at a distance, are called “non-local theories of hidden parameters”. But they are the only way to make quantum mechanics more comfortable for us.


A less famous experiment with Schrödinger tube.

Freedom has its price


You should not be surprised that physicists were looking for a way out of the situation from the very first days of quantum mechanics. But how could something else be possible if Bell's theorem leaves us with no choice?

Any theorem is always based on assumptions, explicit and implicit. Bell's proof uses fairly simple mathematics and it seems that no assumptions are used that we would not accept as true. But desperately complex problems inspire people to desperate measures. Quantum theorists have sought alternatives to the Copenhagen interpretation, exploring some of these tacitly accepted assumptions - those that are rarely questioned, because no one can imagine that they are not true.

Quantum logic


One of these unexplored assumptions affects the rules of logic on which any type of reasoning, including mathematics, is based. Interpretations of quantum mechanics, changing the logic itself, trying to replace something, are called quantum logic . This field of knowledge has a respectable pedigree and originates from John von Neumann, a terrific scholar who wrote the early mathematical formulation of quantum theory. As far back as the 1930s, he showed that the mathematical structure of a theory is tied to logic, which differs from the underlying Aristotelian logic, which is the basis of classical physics. Research in this area continues to be an exotic (and delightful) field to explore; no one has yet created a fully functional, satisfactory alternative to the Copenhagen interpretation.

Although this area is very deep and rather mysterious, there are simple examples of how familiar logic badly adapts to the quantum world and how you can create an alternative to it. One of the first in the literature is a unique quantum idea of superposition of states. In the quantum world, our usual notions of reality are replaced by the wave function, which gives us the probabilities of detecting a system in various states. If a system can only be in one of two states, then before the measurements themselves are performed, it is in a state that is neither of them, or both, in another: in a superposition. A popular example of this is a thought experiment with “Schrödinger's cat,” which is considered both alive and dead, until the box in which he sits is open. Experiment is a dramatic conflict with classical mechanics and our everyday notions of reality: the “cat” requires that the system actually be in one of two possible states, and only the act of measurement reveals to us what the state was all this time.


Erwin Schrödinger

One of the possible ways to give superposition a meaning is to apply other rules of logic. In our usual logic, if the statement p (say, “the electron is in a state with an upward spin”) is false, and the statement q (“the electron is in a state with a downward spin”) is also false, then p ∨ q (where ∨ means “ or ") must also be false. This is exactly what happens with classical measurements. In quantum mechanics, p cannot be true if it has not been measured. Whether it should be considered “false” in the classical sense, or something else is another question. Similarly, q cannot be true either. However, the combination p ∨ q must be true.because such is the definition of superposition, in which an electron is located before measurement. Therefore, our quantum logic should allow p ∨ q to be true in the case when neither p nor q are true, in contrast to Aristotelian logic.

It may seem strange to rely on changing the rules of logic itself. But in this way we can lower the oddity of quantum mechanics to one or two levels, from the level of physics to the level of rules that we can use for reasoning.

Stochastic mechanics


This interpretation, or explanation of quantum mechanics, leaves the logic intact, but adds a new physical process. The modern and promising branch of stochastic mechanics began with the 1966 article by Edward Nelson, who boldly stated:

"In this article we have to show that a radical deviation from classical physics caused by the advent of quantum mechanics forty years ago was not necessary."

The main result of the article is impressive: the author derives the Schrödinger equation - the central equation of quantum mechanics - assuming that the particles are exposed to rapidly varying random force. Therefore, microscopic particles, such as electrons, exhibit something similar to the Brownian motion.. Deriving an equation, Nelson actively uses mathematics from statistical physics.

Since Nelson’s article, this field has been steadily developing and has attracted a large research community. Some of her intriguing successes are the explanation of the quantized moment of momentum (“spin”), quantum statistics, and the famous double-slit experiment . However, stochastic mechanics is still far from replacing the Copenhagen interpretation or traditional quantum mechanics. It uses what looks like a non-physical instantaneous action at a distance and it gives incorrect predictions in some types of measurements. However, her apologists do not give up. As says Nelson in parsing of this topic, “how can a theory be so correct and at the same time so erroneous?”

Pilot Wave Theory


This version of quantum mechanics returns to the very beginnings of the field. If the first piece of the quantum puzzle was put in place in 1905 by Einstein, when he explained how light is absorbed and emitted from matter in discrete quantities, then the second piece was laid in 1924 by Louis de Broglie. De Broglie stated that while light waves can behave like particles, particles like electrons can behave like waves.

The following year, de Broglie designed his own pilot-wave theory , in which matter waves observed in real physical objects are generated by the movement of particles. In a sense, this was the original interpretation of quantum mechanics, but it was soon defeated by the Copenhagen interpretation. De Broglie’s ideas were rediscovered in the 1950s by David Bom, who gave themfurther development . In this formulation, the wave function is also governed by the Schrödinger equation, but the pilot wave theory adds an equation derived from it that directly affects the motion of particles. Particles are considered to have real trajectories that exist independently of the dimensions; characteristic quantum effects, such as interference in a two-slit experiment, arise from complex trajectories followed by electrons or photons during an experiment. This interpretation recreates a large share of the behavior of the quantum world, while maintaining realism. It returns the probability back to our usual place, that is, the probability again becomes an indicator of our incomplete knowledge, and not an integral part of nature.


Louis de Broglie

A serious obstacle to the wave-pilot theory is that the particle trajectories it creates are complex and often bizarre; Another obstacle is that it requires an extraordinary non-locality, in principle, describing the motion of a particle as dependent on the state of all other particles of the Universe. However, this theory is considered by many physicists to be the most promising alternative to the Copenhagen interpretation and is being actively investigated .

An intriguing feature of the wave-pilot theory is the possibility of observing analogs of some of the microscopically predicted behaviors characteristic of the micro-level on a macroscopic scale. Experimental Videos repellent oil droplets exhibit a striking behavior in which the droplets play the role of subatomic particles, and the oil bath above which they are suspended performs some of the functions of the pilot wave.

Multiple Worlds


The "multi-world" interpretation of quantum mechanics has caused a lot of noise in the popular press. Therefore, many people, including some physicists, have acquired wrong views on this theory.

This interpretation does not insiston the creation of a new universe in the performance of each dimension, as is commonly believed. She simply takes the traditional quantum mechanics seriously as a description of our Universe and everything in it. Quantum mechanics describes a particle, for example, an electron, as existing in the superposition of all possible states; when performing a measurement, the superposition is replaced by the measured state. The multi-world view extends the idea of ​​superposition to control everything, including the measuring installation and its operators. She defends the view that to ensure integrity, the whole world must exist in a superposition.

The concept of “many worlds” refers to a superposition of states applied to the whole world; each potential state, or the Universe, already exists in a quantum-mechanical sense, in which every possible state of a subatomic particle has a potential existence. Measuring the state of a particle selects one possible result and makes it real. At the same time, the measurement selects one possible result for the Universe: the one that the experimenter obtained in this particular measurement.

Multiple worlds are considered deterministic and eliminate the need for wave function. Her critics say that she still can not get rid of the central role of probability and can not accommodate gravity.

There are many other alternative approaches to describe which we simply do not have enough space. Often they are closer to metaphysics than to physics. One of these ideas, located in the middle between science and philosophy, is overdeterminism . Although this idea has not yet been able to recreate the results of quantum mechanics, it attracts constant attention, possibly due to the reputation of its main apologist, Nobel laureate in physics, Gerard 't Hooft. Overdeterminism was supposed to be a loophole in Bell’s theorem and was actually described as possible.by Bell himself. The theory avoids the basic assumptions of Bell's theorem, considering everything in the Universe, including the choice of measurements made by the experimenter, as defined since the beginning of time. Naturally, he denies any possibility of free will. An interesting development of the theory in this area is the attempt by 't Hooft to implement his ideas by creating a model of quantum mechanics in a cellular automaton.

Metaphors of metaphysical concern


Einstein knew the word well and deeply understood nature. He left us a legacy of two colorful phrases that continue to quote to express our dissatisfaction with the relevant aspects of quantum mechanics: "eerie long-range action" and "God does not play dice with the world."

Although the Copenhagen interpretation still remains dominant, and accepts both of these phrases with calmness, the agonizing dissatisfaction they generate will continue to motivate new generations of physicists to look for alternatives. This alternative may be a further development of one of the models described here, one of those projects that we could not consider, or a completely new idea. But no one can say for sure whether one of them will gain universal recognition in the future.

About the author:Lee Phillips is a physicist and regular contributor to Ars Technica. He previously wrote about topics such as the legacy of the Fortran programming language and the one that changed the physics of Emmy Noether .

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