Quantum mechanics is the most successful scientific theory today, but it is also a "problem child", a theory full of paradoxes and mysteries that contain many things that cannot be intuitively explained. One of its "symptoms" is that the more we understand reality, the less we know how to describe reality—for example, when we ask, "What are particles?" ", many different answers can be obtained. It could even be argued that quantum mechanics shakes our view of the nature of reality, and its interpretation rises to divergences about the nature of science, such as the question "Is the natural world the opposite of our conscious existence?" "Can we understand and describe these properties?" " and other issues. Over the centuries, physicists have given different answers. For example, lee Smolin, a theoretical physicist and one of the founders of the theory of cyclic quantum gravity, gave the answer "yes", and like Einstein, they were called realists. The other faction, led by Niels Bohr, belonged to the anti-realists (which included quantum cognitiveists and operators) who had the upper hand in the development of physics in the 20th century. Obviously, this did not satisfy the realists, and Smalling wanted to construct a more realistic theory of the microscopic world.
Einstein's Unfinished Revolution: The Search for What Lies Beyond the Quantum presents two different perspectives, and the book is divided into three parts: the basic concepts of quantum mechanics; the work of post-1950s realists, such as Bohm and Bell (Whooping once pushed "Bohm Mechanics—" Quantum Theory Outside the Textbooks" ( some authors and others with new attempts. This paper expounds quantum mechanics from the perspective of information based on John Wheeler's "everything originates from qubits", and introduces the basic idea of "relational quantum mechanics".
This article is authorized from the third act of "The Truth of Quantum Mechanics: Einstein's Unfinished Revolution" (Sichuan Science and Technology Publishing House, September 2021 edition), "Alternatives to Revolution", with deletions, titles and subtitles added by editors. Go to the "Back to Park" public account and click "Read the original text" at the end of the article to purchase this book. Click "Watching" and post your thoughts to the message area, as of January 23, 2022 at 12:00 noon, we will select a message, 1 book free.
Written by Lee Smolin
Translated 丨 Wang Qiaoqi
Ultimately, we have to look for theories that promise to become the right ontology of the world. After all, the fire of desire that burns in the deepest recesses of the soul of all true physicists is to discover the nature of reality.
—Lucien Hardy
Over the past few years, research on quantum fundamentals has been active and the popularity has been on the rise. The field has been dormant for 80 years, and any physicist who wants to become an expert in this field will inevitably back off, but now, becoming an expert in the field of quantum fundamentals can finally be regarded as a good career plan. This is certainly a good thing, but most of the progress in the field today and the majority of young people are leaning towards the anti-realist side. At present, the goal of most new research in this field is not to revise quantum theory so that it is constantly perfected, but only to provide us with a new way to discuss it.
Lee Smolin
……
These advances have also deepened our understanding of how quantum theory is constructed. Hardy, for example, pioneered a new method for finding the most concise set of axioms from which the mathematical form of quantum mechanics could be derived. Of these axioms, several are simple and tell us that all the theories are correct; and one encapsulates all the weirdness of the quantum world.
At the same time, in such an environment dominated by an operationalist approach, there is little room for old-school realists who are struggling to find a complete quantum theory to explain events. Some of these realists were proponents of multi-world theory, but a small number of supporters of Bohm, a few realists developed wave function collapse theory, and even fewer tried to search for realistic versions of quantum mechanics away from these existing methods. Most of the people who study this issue are themselves experts in other fields, and some have achieved great success in their own areas of expertise, such as Stephen Adler's Note 1 and Gerardus't Hooft, winner of the 1999 Nobel Prize in Physics. We cannot fit perfectly into the field of quantum fundamentals that is already active today, mainly because our focus and ultimate goal and the theories we propose to achieve this goal cannot be expressed in operationalist language, and proficiency in this language is the hallmark of experts in quantum information theory. Even so, we have not stopped searching for a complete picture of realism in the quantum world.
I think, as Hardy said at the beginning of this chapter, many physicists prefer realistic interpretations to operationalist views, and will certainly be interested in realistic versions of quantum mechanics that overcome the shortcomings of existing methods. Part of the reason for the prevalence of the operationalist approach at this stage is that there are still fewer realistic approaches available to us and that are close to the truth.
The rest of the book deals with the future of realistic approaches to quantum physics. Before we forget about the non-realistic approach, let's take a look at whether their recent prevalence offers something to ponder.
Avoidance measurement – Everything comes from qubits
The first lesson I can learn from this is that there are many ways to describe the differences between the quantum world and the classical world to which Newtonian physics applies. If you're willing to adopt the anti-realist view of quantum mechanics, then you have a lot of options. You can choose to side with Bohr, who radically argues that science is nothing more than an extension of the common language we use to communicate the results of our experiments with each other. You can also throw yourself into the embrace of "quantum Bayesianism," a theory that wave functions are nothing more than representations of what we think in our minds, and predictions are just another way of saying gambling. You can also side with the purely operationalist point of view, that is, only the processes of preparation and measurement operations, on which the theories of pure operationalism are based.
One thing these theoretical schools have in common is that they all avoid the measurement problem, or more accurately, they all take the measurement link away from the definition, because there is no possibility of describing the observer and his observation tools in quantum states.
The central concept of some of the new theories is the idea that the world is made up of information, as we can conclude from John Wheeler's famous quote , "Everything is from the bit." The modern version of his quote is "Everything comes from qubits," where qubits are the smallest unit of quantum information and can be seen as a quantum binary choice in our previous stories about pet preferences. In practice, this model envisions that all physical quantities can be reduced to a limited number of quanta "whether or not", and that the process of time-varying evolution under rules-constraints can be understood as quantum information processing in the world of quantum computers. This means that the time-varying process of a system can be expressed as an operation that applies a series of logical operations to one or two qubits at a point in time.
John Wheeler put it this way:
The fact that everything originates from bits means that all objects in the physical world essentially have non-material sources and immaterial explanations. What we call reality comes down to the question of whether or not to be presented and the recording of instrumental reactions. In short, all matter theoretically originates from information, and this universe has the participation of all of us. [1]
When you first hear this view, you may think that the person who said it was just talking casually, but Wheeler was serious. There is a more succinct formulation of this view: "Physics involves the observer, the observer's participation produces information, and information produces physics." ”[2]
Wheeler once said, "This universe has all of us involved. He means that the universe was born out of the observation or perception we unfold on it. Yes, you can respond to this: "But before we have the power of observation or perception, we must first be born into the universe, and we must also rely on the power of the universe." Wheeler would respond, "Yes, is there anything wrong with that?" ”
What can we learn from conversations like these? Some systems with a limited number of evolutionary outcomes can be expressed in this way, and it does guide the way forward in physics, for example, the importance of entangled concepts in quantum physics can be used to come to the foreground. However, if a system involves an infinite number of evolutionary outcomes of physical variables, it is not easy to apply this model, such as electromagnetic fields. Nonetheless, this approach to quantum information that studies the foundations of quantum mechanics has had a positive impact on a variety of physics fields, from the central field of solid-state physics to the study of string theory, quantum black holes, and so on.
What definition of information is needed in the microcosm?
We should be careful to distinguish between several different concepts about the relationship between physics and information. In my opinion, some of these concepts do work, but they are trivial; others are quite radical and still need further argumentation. Let's start with the definition of information. Claude Shannon, the founder of information theory, gave a fairly useful definition of information. His definition is built within a communication framework that envisions a channel for the transmission of information from the sender to the receiver. By definition, such channels share a language that gives meaning to the symbols. After the recipient of the message receives the message, he or she understands the meaning of the message through a series of "whether it is a problem" or not. The number of these "problems" determines the amount of information transmitted.
According to this standard, only a few physical systems can be seen as a channel for the transmission of information between the sender and receiver who share a certain language. Taken as a whole, the universe is not such an information channel. The power of Shannon's definition of information is that it measures exactly how much information is transmitted in the context of semantics, that is, from the meaning of the information. According to Shannon's definition, the sender and receiver of a message share a set of semantic rules that give meaning to the message, but you don't need to master this set of rules to measure the amount of information carried by a message. If such a set of semantic rules is missing, a piece of information will not have any meaning. For example, to measure the amount of information about a piece of information, you first need to understand the language in which that information is used, such as the relative frequency of occurrence of letters, words, or phrases in communities that use that language. This information about the locale doesn't necessarily need to be encoded into every piece of information, and if you don't specify the language, the information loses the information that Shannon defines. In particular, this means that the information being conveyed must be in a language common to both the sender and receiver, and the no-rule symbols that are separated from the shared language cannot carry any information. Shannon's definition of measuring information depends on the language used in the message and various other aspects, rules that are common to both the sender and receiver of the message, but are not necessarily encoded into the message itself and are not purely physical quantities.
Understanding the intentions expressed by the speaker and the way in which meaning is conveyed is an old and difficult problem in the philosophy of language. The intractable question does not mean that the intention and meaning of the speech are not part of the world, they are indeed part of the world, but that their existence depends on the mind. The message in Shannon's definition is a measure of what happens in the world of meaning and intent. Even if we don't have a deep understanding of how the meaning and intent of information is embedded in the natural world, this definition of information is quite good.
To make it clearer, let me give you another example. After a heavy rain, I heard water droplets intermittently dripping from leaking sewer pipes. The rhythm of the dripping water may seem very irregular, but neither for me nor for anyone else, this sound of water droplets carries any information, because there is no sender, and I am not the receiver at all, so according to Shannon's definition, there is certainly no information in the droplets. In addition, we can also use the long and short intervals when the water drops to compile the Morse code to pass messages. The two situations have very different results because the former lacks the intention to convey information, while the latter has the intention to do so, and this intention is important: the information under Shannon's definition must be accompanied by the intention to convey the information. For a realist who wants to know something beyond the known world of man, the Shannon definition of information is of little use when applied to the microscopic world in which the atoms are located.2
The British anthropologist Gregory Bateson gave a less precise definition of information, calling it "the difference that brings difference" and sometimes "the difference that makes difference." This definition can be applied in physics as follows: if a change in an observable quantity leads to an observable change in the future of the physical system, then we consider that this quantity constitutes information, and according to this line of thought, almost all physical quantities have the possibility of transmitting information. This definition means that if the values of two physical quantities are related, then there is "information" between them. This is also not esoteric, after all, it does not indicate that there is an inherent interdependence between the various parts of the physical world. Moreover, we have already measured this correlation, which we have now called "information", but a name that weakens the particularity of this concept, but this does not seem to bring about a change in the original concept of the world, but is more likely to be confusing.
Computers process information according to Shannon's definition, they get an input signal from the sender of the message, and then apply some kind of algorithm to transform the input signal into an output signal for the recipient of the information to read, a process that is very personalized. Implanted algorithms are a key component of defining the computational process, however, most physical systems are not computers, and the evolution of the initial data in a physical system into subsequent data is not always explained by algorithms or a series of logical operations.
Some scholars seem to confuse these two definitions of information, and they want to describe nature as computers and the relationships between the various states of the world at different times as computational processes. I think this radical assumption is problematic.
Admittedly, it is true that some physical systems are able to achieve some degree of approximation through computational simulations, which is obviously possible. You can approximate important equations in physics, such as a series of equations in general relativity and quantum mechanics, encode them into algorithms, and run them on a digital computer. This is often a very efficient way to get an approximation of the equation, but it can only be an approximation, and it is impossible to get an accurate answer. For example, we can use digital means to capture the sound of the symphony orchestra to some extent, but this is always only an approximation, digital means can only intercept the sound within a certain frequency range, and the whole experience of listening to the symphony on the spot can never be fully presented by digital analog means. That's why there are still many audiences who are more willing to come to the symphony orchestra to play in person, and why vinyl records are still on the market because they are purely analog recordings. The same is true of physics, where "digitally simulating" Einstein's equations can be very useful, but it will never be able to encapsulate all the best of this system of equations.
Although we cannot understand physics as a whole as an information processing process, it may be said that quantum states do not represent the entire physical system, but only the system information we have. This obviously fits rule two note 3, because as soon as we get new information about the system, the wave function changes suddenly. If the wave function represents the systematic information we have, then the probabilities predicted by quantum mechanics must be regarded as subjective, gambling probabilities. We can further think of rule two as a renewal rule, that is, when the measurement action is made, our subjective probability prediction of the future experimental result will change according to rule two, which is called "quantum Bayesianism" [3].
Relational quantum theory
Another rather ingenious approach also holds that quantum states convey information between systems, the so-called "relational quantum theory." This theory falls somewhere between operationalism and some form of realism. It argues that quantum states are related to the division of the universe, the observer, and the observed, and represent the information that the observer can know about the observed. Relational quantum theory, based on the theory of quantum gravity, was born in my discussions with Louis Crane and Carlo Rovelli in the early 1990s.
Mathematicians such as Klein have previously proposed a minimalist cosmological theory - "topological field theories", and relational quantum theory is a concise mathematical description of topological field theory. These two theories do not involve any quantum description of the entire universe, and certainly do not involve describing the quantum state of the universe as a whole. The quantum states in these two theories describe the various ways in which the universe splits into two subsystems. We can understand these quantum states this way: they carry information about the quantum system on one side that an observer in one side of the subsystem can grasp.
This reminds us of Bohr's point of view. Bohr argues that quantum mechanics necessarily requires the world to be divided into two, with one part following classical mechanics and the other part following quantum mechanics, and that any process of division will produce such a result. Mathematicians such as Klein went a step further by proposing that each split of a system produces two quantum states, i.e. the two subsystems produced by the split each have a quantum state, because we have two ways of interpreting each split. Assuming that Alice lives on one side after the split and Bob lives on the other, Alice will see herself as a classical observer, measuring the "quantum Bob" on the other side; Bob's perspective is the opposite.
This type of model is very simple, but there is a question: how similar are the two perspectives? How likely is it that Alice's quantum description of Bob is the same as Bob's quantum description of Alice? Mathematicians believe that no matter how the universe splits, this answer will not change. With this as a premise, observers on both sides describe the same probability to measure certain universal properties that characterize the interconnectedness of the universe, which mathematicians call cosmic topology, which is where the name topological field theory comes from.
Klein realized that the mathematical structures involved in topological field theory could be extended to include loops of quantum gravity, so he took this model of the universe and studied it with Lovelli and me. As it turned out, Klein was quite right, but that was another story. He is also right to argue that this new mathematical approach offers a way to extend quantum mechanics to the universe as a whole, and that this approach is relational quantum theory.
Both of us were inspired and applied this method to general quantum theory, and then published the relevant results [4]. Lovelli's version is more general and well known, so I'm going to introduce his theory here. Bohr argues that quantum physicists must always think in terms of two worlds. We observers live in a world dominated by classical physics, but the atoms we study are in the quantum world, and the two worlds follow different physical rules. It is particularly important that objects in the quantum world exist in the form of superpositions, while in the world we live in, the observable properties of things can always only take definite values, and cannot be superimposed. Bohr believed that both worlds were necessary for science.
In a sense, the instruments we use to manipulate and measure atoms are at the boundary between our world and the atomic world, and Bohr emphasizes that the position of this boundary is not fixed. Different goals draw different boundaries, as long as it divides the world into two regions.
Take Schrödinger's cat experiment as an example. One way to demarcate the boundary is to think of atoms and photons as quantum systems, and Geiger counters and cats as classical systems. In this picture, atoms may exist in superpositions, but the Geiger counter will always show a definite state: either "yes" – which characterizes that it detects photons ; or "no" – which represents that it does not detect photons. However, we can also redraw this boundary and include geiger counters in the quantum world. In this way, the cat is either alive or dead, i.e. always in one of these two states, but the Geiger counter may be in a state of entanglement and superposition with atoms. Or, according to Schrödinger, we could draw the boundary on the four vertical faces of the box. In this way, cats also become part of a quantum system and may be entangled and superimposed with atoms and Geiger counters. At this point, a man named Sarah in the classical world opens the box to probe the situation, and since Sarah is a subject in the macroscopic world, we think she is always in some certain state. From her perspective, Sarah would feel like she was on the side of the classic world, so in her opinion, the cat was either dead or alive, always one or the other.
Eugene Wigner suggested that we go a step further, that we can draw Sarah into the quantum system along with the box, the cat, and the other objects in the box, while I myself, as a bystander, demarcate beyond the boundary so that I can see Sarah part of the entangled superposition. In one part of this superposition, the cat is alive and Sarah sees it alive; in the other part, the cat is dead and Sarah sees it dead.
So we have 5 ways to distinguish between the quantum world and the classical world. We use the word "quantum" here to indicate that things can be in a superposition state, while the word "classical" indicates that physical quantities can only have definite values. These seemingly different descriptions seem to contradict each other, such as when we see Sarah in a superposition, but she always feels that she is in a certain state.
According to Roveri's theory, all of these theories are correct, describing a part of the world and part of the truth. Each of them effectively describes a part of the world, defined by the demarcated borders. Is Sarah really in a superposition, or is she sure she saw a live cat or heard a cat's voice? Roveri didn't want to choose between the two. He argues that the description of physical events and processes is always related to some particular way of delineating the boundaries of the quantum world and the classical world. Roveri postulated that all ways of delineating borders were equally effective and part of a complete description of the world. In simple terms, Roveri thinks that it is true that the cat is alive in Sarah's view, and it is equally true that Sarah is in a superposition of "seeing a dead cat" and "seeing a live cat" in my opinion.
So, are there facts that are not influenced by the observer's perspective of observation? In my opinion, Lovelli's answer to this question is no. In the above example, although Sarah and I have different views on the results of the examination, we agree that she opened the box and examined the state of the cat, but whether Sarah's decision to open the box may depend on the outcome of some quantum event, such as whether an unstable atom decays. In this case, I can say that Sarah is in a superposition of the box that has been opened and the box that has not been opened, but Sara herself has either opened the box or has not opened it, and the two can only be one.
Notice that there is a faint consistency in this, as my description of Sarah does not quite contradict her own description. The key point we have to note is that all the ways of dividing boundaries divide the world into two incomplete parts. There is no perspective of the universe as a whole, that is, we cannot look at the entire universe outside the universe, nor can we have a quantum state that can describe the universe as a whole.
If relational quantum theory has a slogan, it must be "many local perspectives that define a universe." We can look at this theory from a variety of perspectives. Pragmatic operators will see every approach that divides the world in two by delineating boundaries as defining a system that can be processed with quantum mechanics. Each choice of boundary leads to a completely new description that contains all the information that an observer on one side of the classical world can grasp about the quantum system on the other side of the boundary. For these pragmatic operators, all of these quantum states contain information that the observer at each level has access to, and these hierarchies are determined by the boundaries that separate the observers, and each observer encodes in quantum states the information they have about the system on the other side of the boundary. These quantum states differ because they describe different subsystems.
From an operationalist perspective, relational quantum mechanics has something in common with Everett's original interpretation of associative states. Both describe the world in terms of conditional statements encoding correlations between different subsystems, which are established when subsystems interact, however, this is not However, this is not However, This is not However, This is not However, Lovelli's way of looking at relational quantum mechanics. In his opinion, his theory should be in line with realism, but it is not the kind of naïve realism that I expounded earlier. Roveri believes that reality is made up of a series of events through which a system on one side of the boundary acquires information about the world on the other side, so we can call Roveri a realist based on causality. In his theory, reality depends on the choice of boundaries, because certain things that are determined to occur are determined in the eyes of one observer—and certain events can be part of a superposition of another event. From this we can see that there is clearly some difference between Rovery's realism and naive realism, because in naive realism the events that make up reality are what all observers would agree that did happen.
Lovelli argues that this kind of naïve realism cannot exist in our quantum world, so he suggests that we embrace his radically different realism: the division of the world defines the observer, and the definition of reality is always relative to this division. Roveri's description is very different from Bohr's, and has been interpreted more precisely, but the logic they employ is similar, and they all believe that there can be no place for naïve realism in quantum systems.
exegesis
1. The book is mistranslated and confuses physicist Stephen L. Adler with Stephen J. Adler, former president and editor-in-chief of Reuters. - Editor's Note.
2. Here I need to make some additional notes, non-professional readers can skip this part. Some experts may object to Shannon's description of the definition of information, pointing out that the amount is equal to the negative number of entropy of that information. They would argue that entropy is an objectively existing natural physical property that (when the system is in a thermodynamic equilibrium) is constrained by the laws of thermodynamics. Since information under Shannon's definition is related to entropy, it must be objective and conform to the laws of physics. I have three things to say about this: First, the laws of thermodynamics do not constrain entropy itself, but changes in thermodynamic entropy. Second, as Carl Popper pointed out a few years ago, the statistical definition of entropy associated with Shannon's information definition is not a completely objective quantity, it depends on the choice of coarse grain, which describes the system approximately for us. In the case of a particular state, if the system can be accurately described, then its entropy must be zero, and this need to approximate the specificization brings a subjective element to the definition of entropy. The entropy of a quantum system depends on the splitting process that forms two subsystems, and we can see the existence of subjective elements in such processes. Finally, the entropy property of information is a definition, defined by the definition Shannon gave to information.
3. The book gives three rules, rule two: This law describes how the quantum state responds to the measurement operation, that is, immediately collapses into a state that can be measured with an exact value (this value is determined by the measurement operation). Rule two shows that only probabilistic descriptions can be used to predict the results of measurement operations. However, after the measurement is completed, the quantum state of the system under test changes — the measurement operation puts the system into a state corresponding to the measurement result, a process called wave function collapse. - Editor's Note
bibliography
[1] John Archibald Wheeler, “Information, Physics, Quantum: The Search for Links,” in Proceedings of the 3rd International Symposium: Foundations of Quantum Mechanics in the Light of New Technology, Tokyo, 1989, eds. Shunichi Kobayashi et al. (Tokyo: Physical Society of Japan, 1990), 354–58.
[2] John Archibald Wheeler, quoted in Paul Davies, The Goldilocks Enigma, also titled Cosmic Jackpot (Boston and New York: Houghton Mifflin, 2006), 281.
[3] Christopher A. Fuchs and Blake C. Stacey, “QBism: Quantum Theory as a Hero’s Handbook” (2016), arXiv:1612.07308.
[4] Louis Crane, “Clock and Category: Is Quantum Gravity Algebraic?,” Journal of Mathematical Physics 36, no. 11 (May 1995): 6180–93, arXiv:gr-qc/9504038; Carlo Rovelli, “Relational Quantum Mechanics,” International Journal of Theoretical Physics 35, no. 8 (August 1996): 1637–78, arXiv:quant-ph/9609002; Lee Smolin, “The Bekenstein Bound, Topological Quantum Field Theory and Pluralistic Quantum Cosmology” (1995), arXiv:gr-qc/9508064.
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