Contents

- 1 Abstract
- 2 Introduction
- 3 SI and Quantum Completeness
- 4 Quantum Theory and Language
- 5 Objective, Relative, and Universal Space
- 6 Statistics and Superposition
- 7 The Problem of Uncertainty
- 8 Quantum Non-Locality
- 9 The Two-Slit Experiment
- 10 The Motion of Objects
- 11 A New Kind of Causation
- 12 Mathematical Formulation
- 13 Conclusions
- 14 References
- 15 Notes

### Abstract

This paper illustrates, through examples[1], how quantum theory can be seen as a theory of *symbols*. Ordinary signs have classical properties but not meaning; *we* interpret their physical properties as meanings. This is because the signs are described physically. If, however, space-time is interpreted as a domain of types rather than quantities, the same sign can be seen to denote meanings. The description in terms of symbols subsumes the physical description, but goes beyond it. For example, in a semantic space-time, positions, directions, durations, and tenses have meanings. In classical physics these are described as quantities, and the same properties can be described in terms of types. In the typed description, the fact that a vector points upward instead of downward will indicate a meaning. Such meanings are already employed in computers where the up and down spins represent the bits 1 and 0. I will argue that quantum theory should view space-time semantically rather than physically. The problems of uncertainty, probability and non-locality in quantum theory are shown to be solved by adopting a semantic view. The semantic view makes some new empirical predictions, which are described here. The paper concludes by outlining the mathematical advancements needed to think of quantum phenomena semantically.

### Introduction

When we see a red light at a street intersection, the sensation is red but the knowledge is that we must stop. The same color is seen in two ways: physical and semantic, but our behavior (stopping at the red light) can only be explained on the basis of semantics. In this paper, I will connect difficulties in understanding present quantum theory to the possibility that nature has meanings.

To know these meanings, we need to interpret the properties of quantum eigenfunctions as denoting *types*. Different eigenvalue measurements on these eigenfunctions represent different kinds of meaning. This view requires us to see the space-time of signs as dealing with types rather than quantities. I call this view of quanta the *Semantic Interpretation of Quantum Theory *or SI henceforth. SI aims to interpret the current formalism in order to show that its interpretive problems arise because we attempt to describe meanings in terms of physical properties. The interpretation also aims to show why current quantum theory is incomplete. To complete the theory, I will argue, we need to treat quanta as symbols of meaning. This view changes the notion of quantum causality.

Causality in SI requires three ideas: (a) the ability to interpret physical states as meaning, and (b) the ability to express this meaning through different languages, and (c) the expression of this language to different observers or measurement instruments. The theory is incomplete in all these respects, but the incompleteness is intuitively understood when interpreted semantically. Then, we can also talk about how to *fix *the incompleteness. The von Neumann interpretation [4] of the theory applies choices to the wavefunction, but these choices themselves are not understood. The entire problem of quantum theory moves into the ‘mind’ which makes these choices. The SI instead invokes the mind in a more amenable manner by talking about meanings, languages, and speakers.

For example, the problem of probability is solved when particles are viewed as symbols in a text. If we don’t understand meanings in a text, we cannot predict the order of symbols in a text; we can at best measure symbol probabilities—e.g. that the word ‘idea’ has a greater probability of occurrence than the word ‘hoopla’. The statistical description is overcome when the observation is compared to reading the book, rather than measuring the probabilities of symbol recurrence. These new intuitions help us solve many types of quantum problems.

The physical properties of the sign (e.g., its position and direction) can be interpreted as meanings of a sign. Computers already use direction as meanings (1s and 0s) but position is still not treated semantically. If the computer disk were treated as a semantic space, then the symbols would be stored in different parts of the disk based on their meaning or types. This entails a different type of computer architecture—different from the current physical one. The semantic view requires no additional observations; however, it requires us to interpret the same observations in a new way. Quite specifically, we need to view quantum measurements as not just measurements of the five senses, but also of the mind which gives these properties meanings. Quite simply, the theory will now talk about the meaning of red light in addition to the redness of the light. This can lead us to a new type of causality—e.g., that drivers stop their cars at red lights.

### SI and Quantum Completeness

Let’s begin the discussion by pondering the question of whether current quantum theory is complete. The incompleteness of the theory can be illustrated by the fact that the theory treats the quantum as both a wave and a particle while experiments detect the quantum as a particle. In the double-slit experiment, for instance, the quantum is detected as a particle—either at the slits or at the battery of detectors. To explain the ‘interference’ pattern, however, we postulate that the quantum passes through both slits at once. In essence, the quantum goes through one slit, but quantum *theory* requires it go to through both slits. That quantum theory works with regard to statistical predictions should be seen in light of this problem—the theory is inconsistent with at least one fact from the observations.

Quantum theory involves a ‘choice’ of basis in terms of which an ensemble of particles is described. Each basis is an equivalent description of the ensemble in theory but not equivalent in terms of observations: in the position representation, for instance, a different basis implies particles arriving at different locations. The different eigenfunction bases correspond to two, three, four or more slits in the slit experiment. The choices about the number of slits are made by the experimenter and they have an empirical consequence. However, there is no counterpart of these choices in the *theory*. The theory insists that all the bases are possible, but does not explain how one of these bases becomes real. Before the wavefunction ‘collapses’ into an eigenfunction, it ‘collapses’ into an eigenfunction basis. Present quantum theory talks about the first collapse, not the second, so there is more than one type of choice involved in the act of a measurement.

The very fact that changes in the number slits alters the experimental outcome entails that the theory is describing our *observations *rather than *reality*. The reality in the case of the slit experiment is the quantum source, while the slits and the detectors are measurement apparatus. The theory describes the detector behavior but remains silent on the quantum source. To be realist, we insist that the detectors are in fact telling us about the quantum source, which is false because the change in the number of slits modifies the detector behavior. How can change in the measurement procedure change the reality? Our realist stance leads to more problems.

Since we cannot solve this problem satisfactorily, and we need a reality apart from observations, we must say that the current theory doesn’t deal in the reality but only observations. The reality is meaning and its observation is words. The same meaning can be expressed via different words, which correspond to the various eigenfunction bases. Effectively, the number of slits in experiment are selecting a language to express meaning.

This gives us the twin benefits of an observer independent reality (meaning) and an observer dependent measurement (words). The choice of slits now represents the relation between word and meaning through the choice of a *language *that maps words to meanings. Just as a number can be expressed in binary, decimal, octal, or hexadecimal systems, similarly, the reality is the number, and the measurement is the representation of that number. When we change the number of slits, we don’t alter the number; we are altering the *base *in which the number is expressed. The selection of quantum basis is akin to the selection of the base for numbers.

There is then the problem of interaction between particles. Within an ensemble of particles, every particle interacts with the other particles (this interaction is embodied in the Hamiltonian). However, between the ensembles, not every ensemble interacts with every other ensemble. There are hence two models of causal interactions—inside and outside the ensemble—in contrast to a classical system where all causal interactions are modeled as if there were no ensemble (ensembles are involved in classical statistical mechanics). The selection of source and destination of an interaction is also a choice.

Quantum theory involves choices—in fact three of them. The first choice involves the organization of particles within an ensemble, to create a semantic system—like the collection of symbols in a book. The second choice requires the selection of a language in which this meaning is expressed in words. It corresponds to the fact that meanings can be encoded in one language and deciphered in another. The third choice involves the selection of the measuring and measured systems akin to the reader who attempts to understand the symbols in a text.

### Quantum Theory and Language

If nature is symbolic, then why has classical physics worked so well at the macroscopic level? The answer to this paradox is that classical physics hasn’t worked for semantic phenomena at the macroscopic level. It has worked when we could (within limits) ignore the effects of semantics. Classical physics describes billiard balls, but does not describe books, pictures or other semantic objects, which are all macroscopic. To explain the meaning in the objects, we add a role for the mind. We claim that the meaning in the book is not in the book but in the mind. The explanation of the mind is, however, left for another day. What if the meaning derived from the book is in fact in the book itself? What if nature allows us to encode information in matter such that it is possible to speak about meanings objectively in science? This type of theory would be useful for a range of problems from the study of the mind, to semantic computing, to the study of molecules such as DNA as carriers of complex meaning.

The ‘language’ for carrying information is encoded in computers such as when up denotes 1 and down denotes 0. If we change the notion of up and down (by a coordinate transformation), the *interpretation *of that meaning would be false, which means there is a role for the observer in choosing the correct reference frame, even when the meanings are objective (as a fixed reference frame). The problem of meaning interpretation doesn’t entail that meanings cannot be objective. It just means that the observer is free to misinterpret reality.

For SI to be objective[2] there must be a *language *in nature in terms of which we can encode and interpret ordinary experiences as symbols of meaning. This language must apply to every object and it must be based on some pervasive facts about material objects. Extension in space and time meets this criterion[3]. Therefore, I will argue that we treat space-time position and direction to construct meanings. Quantum theory already has these properties in the form of momentum, angular momentum, energy, and spin, although they are treated physically. We need to only postulate that there is an objective reference frame in which nature itself encodes objective meanings.

Note that I employed the term ‘objective’ reference frame, but not a ‘universal’ reference frame. I don’t mean to say that every object in nature is encoded in the same language. I’m only saying that the experimenter who prepared the system to be measured used a particular language. So, to correctly observe reality we need to use the same reference frame—quite like two observers need to use the same language to communicate correctly—without having to commit to a universal reference frame.

We have ignored a common fact about the human world in physics, which is that we encode meanings into matter through books, pictures and other information encoding media. Is it possible that nature offers space and time as the choice of convention to encode meaning? If this is possible then meanings and languages are not just artifacts of our minds; they are also objective. This opens the study of objective meaning encoding techniques in nature, and how physical states could also be treated as meanings. It also follows that matter could be used to process meanings in semantic computing machines although these machines would still be transforming tokens[4].

### Objective, Relative, and Universal Space

The idea that we are situated in some universal space which is subjectively interpreted as a coordinate system is central to modern physics, and SI questions that assumption. I’m arguing that space or coordinate reference frames are *objective *in the sense that each object can have its own reference frame or language in which it encodes meaning. This means that another observer cannot read that reality correctly using a different reference frame, *unless *meanings are expressed in the new language. The basis selection performs this kind of translation. Meanings are objective precisely because there is a reality (wavefunction) which is expressed in many ways (basis). The wavefunction is meaning, and the basis is words.

The idea that meaning is objective simply translates into the idea that each object has its own coordinate system using which it encodes meaning and interprets the meanings encoded in other objects. This makes communication between objects possible, because we transform the meanings from one system to another. This allows us to view the current formalism as a theory of meaning, in addition to a theory of matter. In present theory, a quantum is specified by the eigenfunction Ψ but the theory derives *x *and *p *values by applying measurement operators to Ψ*. *In other words, the theory converts meanings to classical properties[5]. The theory will be different if we treated *x *and *p *of the particle as meanings. Now, we will consider causality based on the meaning in the symbols. Thus, the intended causality can work only in the objective frame; other frames will behave differently because they ‘read’ the meaning of the cause differently. ‘Intentionality’ is not a bad word anymore. It is just the objective reference frame used for encoding meaning.

We treat ordinary shapes as signs with meanings in everyday language. The form of the eigenfunction can be treated similarly. Essentially, I’m claiming that the tendency in ordinary languages to represent meanings using shapes of signs has a counterpart in nature, and nature has a language of forms[6] by which we can objectively encode information independent of human conventions, but dependent on the choice of the reference frame.

### Statistics and Superposition

There are two broad approaches to superposition—one that treats the ensemble to be in a superposed state and the other that treats the individual quantum to be in superposed state. I will consider the ensemble aspect of the problem in this section and discuss the individual superposition problem later while discussing uncertainty.

Einstein[7] believed that the wavefunction describes an *ensemble *rather than the *individual* quantum. With SI, each individual quantum is a symbol, and the ensemble of symbols must represent a complex symbol, like a book. In current quantum theory, however, when an ensemble is broken into its constituents, we end up with probabilities of finding a constituent in the whole. This is similar to trying to understand the meaning of a book by measuring word frequencies in it. The correct way to treat the ensemble is to view it as a *combination* rather than *superposition* of symbols. In a superposition, the wavefunction denotes a probability function but no reality, whereas in the combination the wavefunction denotes a complex composition of elementary parts with meaning.

Of course, frequencies give us an inkling of meanings: we might find that one ensemble is a book on physics rather than economics because ensembles employ different vocabularies. The words ‘particle’ and ‘wave’ occur frequently in a physics book rather than an economics book. But this is not sufficient because knowing the vocabulary is insufficient to knowing the exact manner in which these symbols are sequenced to create complex meanings. The problem associated with probabilities can be overcome in SI because semantics gives us the logical tools by which to *sequence* atomic meanings into complex meanings. Thus, an ensemble can also be seen as a complex meaning rather than a superposition. The difference between atomic and macroscopic worlds is that they denote elementary and complex meanings, respectively. When individual quanta denote words, then the sequence of quanta denotes sentences. If eigenvalues of individual quanta denote word meanings, then eigenvalues of sequences represent sentence meanings. SI, thus, opens up a new science of meanings with new types of laws.

### The Problem of Uncertainty

There are two reasons why position and momentum cannot be measured at once. First, position and momentum are complementary *representations *of the same wavefunction related by a Fourier transform. This corresponds to the fact that there are two types of meanings associated with each symbol—descriptive and programmatic. The position represents the descriptive meaning while momentum representation the programmatic meaning. The same symbol can be seen as a thing, a concept and as a program. The complementary relation between position and momentum implies that a concept can be used in several different ways but not arbitrary ways. For instance, the concept ‘knife’ is compatible with being used as a kitchen tool and as a weapon. But the knife cannot be used as a shirt, book or bag. Concepts and programs are related but they are not semantically identical.

Second, the uncertainty relation points to the fact that there is a difference between a *position *and a *position state*. Quantum theory deals with the *position state *rather than the position. Everyday objects such as chairs and tables too have a position state but not a definition position (because they are extended objects). To encode information, the quantum must be extended as a form. Uncertainty isn’t a problem if the quantum is a symbol.

### Quantum Non-Locality

Quantum ensembles are partitioned into a logically orthonormal basis. The basis represents a set of logically independent axioms from which complex theorems can be constructed. But, how does a quantum ‘know’ about existence of the ensemble such that the ensemble divides itself into a non-overlapping set? Particles in classical physics are *a priori *distinct and their distinctness doesn’t depend on the identity of other particles. However, the identity of a quantum depends on identities of every object in the ensemble. This property is called holism, and some have argued [6] that it means that the quanta are not distinct or separable particles. Quantum holism need not undermine the existence of individual quanta, if we treat their distinctness logically instead of ontologically. Quanta in a sense are not *ontologically *distinct particles, whose identities are forever fixed (identities are fixed in classical physics). They are instead *logically *distinct particles, whose identities are fungible, and the ensemble divides into a logically orthogonal set based on the coordinate frame or the choice of the language employed to encode meanings.

The orthonormal basis simply represents the use of semantically non-overlapping words such that we can minimize the *vocabulary *of a language, employing the minimum number of words for expressing meaning. In this scheme, if you change one word, you must alter all the words for the vocabulary to remain minimal. This coordinated change of words is called *non-locality*.

Two particle entanglements are a special case of the N-particle entanglement. In non-local experiments, spin +1/2 and -1/2 particles are separated and their measured spin states are found to be opposite. This seems bizarre if we subscribe to the idea that each quantum collapses into a state *independent* of the other quanta. With superposition, it seems that to collapse into a state that is opposite of the state of the distant particle, one quantum must signal the outcome of its measurement to the other.

For example, let’s assume that spins +1/2 and -1/2 represent the head and tail of a coin. The two particles are distinct as head and tail, and yet they are a single object. If one particle turns out to denote the head, then the other particle will automatically denote the tail. This is because the two particles are actually a single system; they are not distinct *objects*; they are only distinct *states*. The object is the complete wavefunction of the whole system.

### The Two-Slit Experiment

The mystery of 2-slit experiment is not in the 2-slits because 3, 4 or 5 slits also produce discrete eigenfunctions. The mystery is that with one slit we observe continuous detections but with multiple slits we find discrete detections. With slits, the experiment has two positions: at the slit and at the detector. Quantum experiments show that a particle passes through one slit (and has a slit-position), but the interference pattern is explained in current theory by supposing that the quantum goes through multiple slits at once. In other words, experiment shows that the quantum goes through one slit but theory needs it to go through multiple slits. We need a theory that explains observations with the quantum going through only one slit.

This is possible if we distinguish between two kinds of meanings that detector and slit positions denote. I will call these *concepts *and *distinctions. *Distinctions help us divide matter into parts. Distinctions are things in *terms of which* we understand, and concepts are ideas we understand. The number of slits is a counterpart of the idea that numbers can be expressed in binary, octal, decimal, hexadecimal and other representations. Since the quantum experiment produces ideas, the distinctions involved in this representation must also be *conceptual *distinctions. For instance, the distinction between white-black can produce a wide range of colors such as gray, dark gray, ashen, steely, pale black, etc. These concepts are the ‘values’ given against the ‘scale’ of white-black distinction, and their meaning is given in relation to the scale.

The slit experiment tells us that we can describe the same information in different ways, each time choosing a different representational basis, in analogue to the mathematical idea that we can express numbers in relation to different numerical bases. By changing the goggles through which we see nature, we create objective (and not merely subjective) effects: the locations of quanta in the 2-slit experiment change when the number of slits are altered in the experiment. This implies a dramatic shift in the scientific idea of objectivity where we think that science describes nature independent of the observer’s preferences. Quantum theory shows that there are many ways to describe nature, all consistent with reality, although each giving its unique experience. In so far as science is a study of experience, quantum theory is objective, although objects are created in the experimental context. We need to philosophically separate reality from objectivity, and reality is consistent with many kinds of objective descriptions because they all ‘work’ equally well. A single slit doesn’t create a distinction; it corresponds to the idea that we do not divide nature into parts and the universe is seen as a continuous ‘field’. Slits basically find a different way to express the same information, similar to how some meaning can be described by using different words. Different slits represent a ‘coordinate transform’ to represent the meaning in one basis or another.

### The Motion of Objects

In classical physics, a particle moves through different states without changing its identity. In quantum theory, each state represents a *different *particle. The change in quantum states is a succession of particles rather than the motion of the same particle. So, there is no difference between state and particle as in classical physics[8].

This implies that an observer can know their motion because the eigenfunction forms will change and motion is known by changes to form[9]. We know this fact somewhat intuitively: if I travel on a train from city A to B, my observations are consistent with me moving to city B or with city B moving to me. But, after the journey, I feel tired, whereas the people in the city B (who haven’t travelled) aren’t tired. This tiredness means that changes occur to my body, and I only need to observe *myself *to know that I have moved. Even though it seems that the city has moved to me, I have another observation—the experience of my own tiredness—which will rule out that alternative. In classical physics self-observation was not possible, due to point particles but in quantum theory we can observe the eigenstates and forms to enable that possibility.

SI also creates new experimental outcomes for parity inversion. For instance, if +1/2 and -1/2 spins denoted a circle and triangle respectively, then parity inversion will invert the words although not invert the meanings. If we called a circle by the word ‘bouba’ and triangle by the word ‘kiki’, after inversion, we will call circles ‘kiki’ and triangles ‘bouba’. This inversion creates semantic incongruity [3]. Semantic problems associated with parity inversion will mean that even though we invert the coordinate system, the world will not behave according to the new coordinates; it will still behave according to the old coordinate system in which the information was coded. This causal effect will make the information objective.

All these effects impinge on classical relativity in new ways: there are as many reference frames as there are objects, and the laws of nature work in each of those reference frames, but not *across *the reference frames. That is, I can observe myself in my reference frame but not another observer from my reference frame; I have to be situated in *their *reference frame to correctly observe them. This makes information an objective reality.

### A New Kind of Causation

We stop at a red light because we choose to, not because the redness of the color causes us to stop. The traffic department prepared the street light with a choice. And we need to obey traffic rules through another choice (otherwise there could be adverse consequences). We earlier saw that choice fixes the uncertainty in state, by fixing the position and momenta of the quanta (words with meanings). Choices are implied by the existence of symbols with meaning, but not explained by this relation.

To explain choices, we need to postulate a mind-body interaction between possibility and choice[10]. Making a choice changes the system state: a quantum is no longer in a superposed state of possibilities but in a definite state with a fixed position and momentum. A quantum becomes a symbol with a specific meaning and ability. Does this ‘action’ of choice have a ‘reaction’ on the observer? In other words, are choices completely free, or do they have consequences? This requires an entirely new domain of experience where choices are connected to consequences, and will require a new theory.

Quantum theory under SI tells us that objects denote meanings that combine to create complex meanings. The theory under SI also says that reality can be described through many different word ensembles (vocabularies). These constitute the *logical *possibilities of knowing reality. The transition from a possibility to a real-world reality requires a choice that selects (a) a language of words by choosing a basis of description and (b) meanings of words in that language. The choice is consistent with what is logically possible, but not defined by that logic. There is room for choice in a logically governed universe; choices select amongst things that are logically possible. The logical laws that define the domain of possibility differ from causal laws between choices and consequences.

### Mathematical Formulation

To formulate a semantic quantum theory, we require a mathematical theory in which numbers are represented as *forms*, instead of positions and lengths in space. Any tuple-set of numbers, representing an object’s properties, can be denoted by the Gödel number [5] of that tuple-set. When this Gödel number is represented as a form, the reality will represent both sensation and knowledge. Gödel used arithmetization of syntax to convert propositions into numbers. Semantics requires a geometrization where meanings are expressed as spatial forms. This geometry has to allow objectively real multitude of frames and yet there is only a single objective reality. These two contrary positions are reconciled when space and time are treated as *trees *rather than *boxes*. Each branch of the tree is a reference frame in relation to the leaves, but an object in relation to the trunk of the tree. Therefore, we can know the reference frame we are in only by going from the branch to the trunk in terms of observation.

The ascending of the perception entails that quantum theory describes a hierarchy of realities, and meanings are properties of a tree structure. We lose the meanings and reduce the world to physical properties when this hierarchy is flattened in classical physics. Thus, with this approach we can speak about a quantum world, and then explain how this world produces the classical world by converting the tree into a box. The quantum of action never becomes zero, but a classical world emerges from the quantum world by the reduction of hierarchy.

Descartes believed that matter is *res extensa *and mind is *res cogitans. *I’m claiming that extension itself can denote meanings. So, we are not stepping into a new ‘mental’ reality but describing the ‘physical’ world in a new way to incorporate meanings within matter itself. By changing the structure of space and time, and hence the geometry of nature, we demystify quantum theory.

### Conclusions

Quanta are extended forms whose eigenvalues are treated physically at present, but these same values can also be treated as meanings provided we can change the geometry of space time from a box to a tree. The coordinate frames of this tree are defined hierarchically—from root to leaves—and these frames are also the objective reality. So, there is no difference between matter and space, and yet a higher object—e.g., the branch of the leaf—denotes the reference frame for the leaf. This makes objects and reference frames *contextual *to the reality being studied. The reference frame becomes the ‘mind’ of the ‘matter’ but this same ‘mind’ is ‘matter’ for a higher frame. Ultimately, even the mind is material, but it is *conceptually *different; we can speak about ‘gross’ and ‘subtle’ matters simply by their *position *on the hierarchical tree.

### References

- Wimmel, H (1992). Quantum physics & observed reality: a critical interpretation of quantum mechanics. World Scientific. p. 2.
- Searle, John (1980), Minds, Brains and Programs, Behavioral and Brain Sciences 3 (3): 417–457.
- Einstein, A. (1936). Physics and Reality, Jean Piccard, trans. Journal of the Franklin Institute 221, p. 376.
- von Neumann, John. (1932/1955). Mathematical Foundations of Quantum Mechanics. Princeton: Princeton University Press. Translated by Robert T. Beyer.
- Nagel, Ernest and Newman, James R. (2008), Gödel’s Proof. NYU Press.
- Howard, D. (1985). Einstein on Locality and Separability. Studies in History and Philosophy of Science 16: 171-201.
- Bohr, N. (1961). Atomic Theory and Description of Nature. Cambridge: Cambridge University Press.

### Notes

[1] Current problems of quantum theory, I believe, require a revision to our view of reality. This revision will use a different part of our intuition than current physics uses. Specifically, current science employs ideas about objects whereas a new science can use intuitions about information. With informal examples, I aim to show that there are other parts of experience that can be used to re-think quantum theory problems.

[2] The key hurdle in thinking about the meanings objectively is that most of us view it subjectively as a human but not a natural phenomenon. That makes it useless to physical sciences.

[3] Material properties like mass, charge, color, etc. are known to not exist in every object. If we identify meanings with mass or color, then some objects by definition cannot have meaning.

[4] John Searle [2] argued that computers cannot hold meanings because they only use tokens. So, the ability to process meanings in machines using nothing but physical tokens means that machines can *behave *intelligently, although they may still not *experience *meanings or intelligence like humans.

[5] Bohr thought [7, p. 1] that quantum theory has to be described in terms of classical properties, which is the language of physics for all time to come.

[6] These shapes can be stationary states with a changing phase, so we can also think of the states as a vibrating membrane with a ‘sound’. Now, the shape and sound of stationary state are semantically identical.

[7] Einstein saw the ensemble view as the inability in quantum theory to describe individual particles, which is the “programmatic aim of physics” [3].

[8] The difference between state {*x*, *p*} and reality (particle) in classical physics meant that we distinguish the particle outside the theory and attribute that particle {*x*, *p*}. If {*x, p*} completely define the particle’s identity, the particle with a different {*x*, *p*} is a different particle. It follows, that particles never ‘go’ from one place to another. Instead, changing {*x*, *p*} transforms into other particles.

[9] To know changes to itself, observers must compare themselves to unchanging references and compare outcomes of such comparisons. Like ordinary measurements, form comparison too requires standards.

[10] Von Neumann’s interpretation [4] also postulated that consciousness collapses the possibility in the wavefunction. In my interpretation, this collapse fixes the words or meanings or both. Since words and meanings are not independent, the total uncertainty is lower than if position and momentum were independent.

Ashish Dalela, "Quantum Objects as Meaningful Symbols," in

*Shabda Journal*, July 4, 2023, https://journal.shabda.co/2023/07/04/quantum-objects-meaningful-symbols/.