The Semantic Interpretation of Quantum Theory

Introduction and Overview

I’m always looking to formulate new ways of describing a problem and its solution; this not only helps us understand what is missing but why the solution is necessary. This article presents a different way of understanding my Semantic Interpretation of Quantum Theory previously described at length in the book Quantum Meaning.

The Problem of Indeterminism

Quantum theory has many problems, but the problem that presents the widest gap from classical physics is that of statistical predictions. Classical physics predicted events deterministically—i.e. given the present state, you could always predict the next state using a law of nature. In quantum physics, given the present state, we cannot predict the next state deterministically, although we can predict it probabilistically. Furthermore, since we cannot predict the next event, we also cannot explain why it occurs. With the loss in predictive ability, we also lose the causal explanation.

Most physicists today suppose that the quantum problem is limited to sub-atomic particles, and the macroscopic world is indeed classical. This preferential application of quantum theory to atomic phenomena results in the notorious Measurement Problem where the macroscopic world somehow fixes the state of the atomic world. But, in fact, since the macroscopic world is only built from atomic particles, it should also be in an uncertain state. If we suppose that there is a quantum to classical transition, then at what point does this transition occur? Should we treat large molecules (with thousands of atoms in them), for example, as classical, quantum, or semi-classical systems? And when does this transition from a statistical to a deterministic world occurs?

We now know that any attempt to overcome the innate statistical nature of quantum theory by adding compensatory “hidden variables” contradicts the quantum theory. In other words, the theory as it stands today—as a theory that uses physical states to explain observations—cannot be improved, and any attempt to do so will produce contradictions. This result in quantum theory is called Bell’s Theorem.

Addressing the Indeterminism

This marks a dead end for an era of thinking that began with Newton in which all objects behaved according to their possessed properties. Now we know that the current possessed properties are inadequate, and any attempt to add new possessed properties will only produce contradictions. We must therefore find a new way of explaining the quantum phenomena, which cannot be based on possessed properties. Conceiving such properties, which are not possessed by material objects, and are yet objective, has presented great problems for physicists used to thinking of the world as material objects.

This problem, however, need not be so hard. There is another kind of property that is objective, and yet not possessed by the material objects. For example, the mass of a billiard ball is a possessed property of that ball, but whether that ball is the 5th heaviest object—within a collection of objects—is not. The latter property depends upon which other objects we are taking into consideration, to form a collection. Note that being the 5th heaviest object is also an objective fact and can be empirically verified. However, that objective fact is not a possessed property of an individual object.

Science thus far has dealt with numbers in a quantitative way, or what mathematicians call cardinal numbers (which denote size or magnitude). Such numbers can indeed be viewed as possessed properties of individual objects. In measuring such possessed properties, we always define an absolute scale of measurement. This absolute scale, however, does not describe whether the object with a mass of 5 kilograms is the first, the second, the third, the fourth, or the fifth heaviest object within a given collection because we haven’t yet defined the collection to determine the relative position.

An object can have two kinds of positions—absolute and relational. The absolute position on a mass scale can state that the mass of an object is 5 kilograms, but the relative position may state that the object is 7th in a collection. Both properties are objective, although the former is a possessed property of the object, while the latter is a property of an object defined in relation to a collection. This means that unless you take into account the object collection, the relative position of the object cannot be described.

Cardinal and Ordinal Positions

In the absolute definition of position, the object with a mass of 5 kilograms has a position of 5 on the kilogram scale. In the relational definition of position, the object with a mass of 5 kilograms could have the 1st, 2nd, 3rd, 4th, or any other position. The absolute definition of the position depends only on the object being measured, but the relational definition of the position depends on all the objects within a collection. Numbers, when used to denote the relative position, are called ordinals because they describe an order.

Current quantum theory describes measurements as cardinals but not as ordinals. In other words, it can describe the absolute positions of quantum objects, but cannot predict the relative order between them. Quantum theory thus predicts the cardinal position but not the ordinal position. The latter is an objective property too, but not a possessed property. Unlike cardinal properties which pertain to the object being measured, the ordinal properties pertain to an object, although as part of an object collection.

Describing such properties requires a new way of thinking in physics where we are describing not just cardinal but also ordinal properties. The interesting part of this problem is that if we know the ordinal properties of all objects, then we also know the cardinal properties of the collection. The reverse is not true. Order necessarily and sufficiently gives us quantities, but quantities do not necessarily and sufficiently give us order.

If the description of nature was based on order rather than quantities, then all physical properties used in quantum theory would be unnecessary. Since the order is always described in relation to a collection, collections would be fundamental too. The quantitative description of nature would a consequence of a collection and order, that explains quantities better than quantities by themselves.

The Classical-Quantum Conflict

Classical physics began by describing an individual isolated particle. When you have only one particle in the universe, only the possessed properties matter and that single particle is the standard against which its properties would be described. Such a singular particle would therefore be the first and the only particle in the universe. However, when you have a collection of particles, then you must order them after distinguishing them. This order is generally given by locating the objects in space and numbering the spatial locations through a coordinate system. Depending on how you have placed the objects in space, and how you describe this space with numbers using a coordinate system, you naturally order the objects by the coordinates. Whether the object is 1st or 25th in a collection, therefore, depends on the choice of a coordinate reference frame.

All such coordinate systems are arbitrarily chosen in classical physics. It doesn’t really matter if you call the object 1st or 25th, because we are only interested in measuring the possessed properties of the objects. The ordinal position can only be an objective property if there is a preferred way of describing each object’s position. This requires conceiving an absolute space in new ways.

Does Light Have a Speed?

This alternative conception of space requires us to relook at the ideas about arbitrary coordinate numbering systems in relativistic theories.

Let’s begin with the speed of light. The notion that light has a constant speed contradicts what is called non-locality in quantum theory in which two objects appear to interact instantaneously when the constant speed of light deems this to be impossible. A more quantum-compatible interpretation of the constant speed of light could be that light indeed takes zero time to travel, but a finite time to be absorbed. What we currently measure as the speed of light need not necessarily be the motion of the photon. It can be the time taken to absorb.

Current quantum theory tries to model causal interactions quite like classical physics where it takes particles time to travel from one position to another, but at the point of collision, the energy and momentum transfer is instantaneous. But what if light is not a classical particle, and it travels instantaneously but takes a finite time to be absorbed? Both explanations are consistent with the observations, as they attribute the delay between source and destination to motion vs. absorption. But only the latter explanation helps us solve the quantum problem.

How so? The time spent in the absorption can be attributed to the time it takes for the source and receiver to get entangled such that if the source and destination have entangled prior, then successive information transfers would be instantaneous. This would explain how quantum theory is non-local because it deals with the successive information transfers, not the time spent in entanglement. Classical physics would instead correspond to the time spent in entangling the source and receiver being erroneously attributed to energy transfer.

In other words, quantum theory remains non-local, and the locality implied by the constant speed of light is a misunderstanding of the quantum interaction, created by interpreting the finite time taken to complete a quantum transition in classical physical terms.

The time taken in energy transfer is now entirely due to the process of selecting and entangling a source and a destination. This time can vary depending on the type of information being transferred, which would be classically attributed to varying speeds of light. The difference is simply that the speed becomes zero if the source and destination have already been entangled for one type of information transfer. Thereby, we can fit classical locality and quantum non-locality in the same causal picture, and explain both using the same mechanism.

Two Kinds of Entanglement

Quantum theory requires two distinct notions of entanglement. First, there are particles within an ensemble, which are entangled due to the ensemble boundary. If one particle changes state, all other particles must change state simultaneously. Second, there are quantum systems, which are not part of the same ensemble, but interact with each other and they must be entangled before a transaction. The present quantum theory considers the first type of entanglement called non-locality, but the second kind of entanglement is described using locality. 

Why treat these two types of interactions differently? Why say that particles in a quantum ensemble are entangled non-locally while two quantum ensembles must not be so entangled and must therefore interact locally? Isn’t this simply a legacy of classical thinking that we are unable to give up? But sticking to that way of thinking creates a contradiction between classical and quantum paradigms. It is more appropriate to rethink all interactions such that we can reconcile the observations of quantum and classical phenomena in a single model of causal interaction. That is a stepping stone to solving the measurement problem and reconceiving reality in a new way.

If we attribute the time spent in a classical state change to the time it takes to get a source and receiver entangled, then we remove the first pillar underlying relativistic theories, namely that light travels and has a constant speed. Einstein interpreted the finite time taken from source to destination classically as the motion of some object in relativity, which then led to the non-locality problem in the case of quantum interactions, which he himself battled for the rest of his life. If this fact was interpreted as the time taken in entangling source and destination, then the problem of non-locality would not arise, because that time could be zero, equal to the speed of light, or more than the speed of light. Non-locality is just that scenario in which the time taken to absorb information about a change is zero.

The Speed of Light is Not Constant

Empirical evidence suggests that light doesn’t always travel at the same “speed” (I put it in quotes for reasons that will be obvious shortly). Researchers led by optical physicist Miles Padgett at the University of Glasgow have for example demonstrated that when light is given additional structure, it arrives late. The idea that light doesn’t take time in travel, but takes time in absorption offers useful alternatives.

In this alternative, the time taken to absorb depends on the information in the photon (encoded as its structure). If the structure of light is important, then a quantum interaction where light has the same energy but a different structure would not produce an identical effect. Quite specifically, they will produce different times of emission and absorption. The discrepancy would be caused by the structure, and if we knew the light’s structure, then we would describe the complete effect as a result of that structure, completely disregarding its energy.

The question is: How do we describe this structure? We could describe it in terms of possessed properties (e.g., the direction of wave vectors), as we do presently. However, that will not allow us to explain the different absorption times because, under a different coordinate system, the same structure would be described differently. For that structure to be causally relevant, we have to fix the coordinate system between the sender, light, and the receiver, and that is possible only if we say that they are part of the same system. Moving particles bring different reference frames, which undermine any role for structure. If instead there is no motion, then there is no problem because the source, receiver, and light are in the same reference frame, so the structure is easily defined between the source and receiver.

This solution, however, takes away the second premise underlying relativistic theories, namely, that each object has its own associated coordinate reference frame. Instead, the process of quantum communication between source and receiver requires that they be in the same reference frame. This is different from classical communication where the source and receiver can be in different reference frames.

Frame Equivalence is Unnecessary

We now reject all the relativistic premises: (1) the finite speed of light because it contradicts non-locality, (2) the constant speed of light because it contradicts the observed delays in light absorptions, and (3) the arbitrary coordinate system choices tied to each object.

Now, we describe the observations differently: (1) the source and the receiver are in the same coordinate frame, (2) light is not traveling at a constant speed from source to receiver, and (3) the delay between source and receiver is due to the time taken to entangle them.

Note that we haven’t discarded any observations, although we have rejected their interpretations. The finite speed of light is no longer needed because (1) the time is spent in entangling rather than traveling, (2) the entangling time depends on the structure of light, and (3) relativistic equivalence of frames doesn’t enter the explanation of observation because the source and the receiver are in the same frame.

New Forms of Causality

We can now focus on the new problem: How can a source and a receiver be put into the same reference frame prior to photon emission? In other words, how can two things far apart from each other become entangled? And why should that process take varying times?

This requires us to describe quantum reality as not in classical space, but in another space in which objects are factually not far apart. This bypasses the objection of Bell’s Theorem which demonstrated the impossibility of overcoming the causal interaction using hidden local variables, where locality is defined in terms of classical space and causality in terms of traveling particles.

It is important to set aside these objections before we consider alternate forms of causality, and it is worth noting that: (a) we are not violating experimental observations, (b) we are talking about their reinterpretations, and (c) which then open up new forms of causation.

In this alternative space, the proximity between two things (that are classically far apart) is based on ordinal properties. These properties establish the similarity between the two things. For example, if we were to order students in a class based on their grades in a subject, then students with higher grades will be similar to each other than students with lower and higher grades. These students may not necessarily live in the same neighborhood. And yet, they are more likely to interact because of their similar inclinations toward a subject.

To achieve this alternate form of causality, we have to treat each event probability as a tendency, expectation, or inclination, and then define proximities between two objects based on the similarities between these tendencies, expectations, and inclinations, rather than classical distance. In simple words, give each event probability a meaning, which then allows us to construct new forms of proximities.

What is Space?

We think that there is only one way to define space or distance between two things because we have chosen a specific way of ordering things based on our idea of motion. There are, however, other ways of ordering, which then change the distance between things. As an example, if we ordered things by their mass, two things that were previously far may become adjacent, because they have similar masses. If we then ordered things by their momentum, then two things that seemed near may become far, because they have dissimilar momenta.

The point is that two things can be proximate in one way and distant in another way. We can call these different modes of determining distances. Two things can be near in one mode and far in another mode. The distance we observe or measure is the result of picking one of the innumerable possible modes. In short, the measured distance is an effect of the choice of a specific mode of ordering.

Classical mechanics is the idea that distance must be measured in only one mode based on motion. Quantum mechanics, however, under this view, is the idea that distance can be measured in infinite modes. You just change the “axis” along which you are measuring and the same thing can be near or far. This is a new kind of quantum-compatible relativistic conception of space in which we can measure distance not merely by one property called length, but by any arbitrary property of our choosing, thereby bringing different things near or far.

The process of entanglement can now be described as the choice of how we measure distance. We normally call these “priorities”. Two observers who have the same priorities (i.e., they order things in the same way), are naturally closer and they will interact due to that proximity. Those observers who have different priorities, which means they order things differently, are naturally far and won’t interact.

The so-called ‘entanglement’ of systems is nothing other than the use of a mutually shared convention for ordering events. The problem of quantum entanglement can now be restated as the result of using shared conventions. Before information can be exchanged, the conventions must be fixed. Or rather, information is only exchanged between those systems where these conventions are already shared.

The Quantum Event Ordering Problem

The so-called ‘hidden variable’ in quantum theory is now the choice of a method of ordering that brings things nearer or farther, without changing those things themselves. This distance is not a “possessed property” in the classical sense, and it is not a property that is not in the things that we are trying to order. It is just a potentiality that can be used to order but may not be used to order always. Quite like ordinal properties are not possessed properties and yet not independent of the properties in those things likewise this new sense of proximity is in the objects and yet not fixed or objective in the sense that a different property can be evoked to create a different kind of distance.

The standard interpretation of quantum theory describes the quantum event as a consequence of a ‘collapse’, which John von Neumann called the ‘choice’ of consciousness. Since such a choice has to be made with each event, the order in quantum theory cannot be explained except by postulating an infinite succession of choices. However, this problem disappears if the event order is indicated by a system of ordering. We can analogously explain this idea as two people with similar natures, who first talk about their health, then their relationships, and then their grades. Their similar priorities themselves determine the order in which things are discussed one after another. If they were not similar, then they would not be talking to each other. So, modeling such interactions requires a similarity in their priorities.

It is not infinite choices, each being made at each moment. It is rather a system of priorities that have been chosen prior. The process of setting up a quantum experiment now involves aligning their methods of order, or their system of priorities. If we don’t know those priorities, then we think of the sequence of events as essentially being random, and model them using quantitative probabilities.

Ordering and Boundaries

In classical physics, all ordering systems are global. We call them coordinate systems. If you choose a coordinate system, then you must apply it to all objects in the universe. The entire universe must be in one coordinate system. A system of ordering things, however, need not be global. We can order some things by one criterion and other things by different criteria. The same observer can be in multiple coordinate systems at once, because those coordinate systems need not be applied to everything in the universe. They can be rather selectively applied to some things. Such coordinate systems are bounded, and their effects of interaction (based on proximity) are also bounded.

The choice of ordering is thus not just the cause of distance to something, but also the cause of selective interactions. We cannot perceive the boundary because it is dictated by the method of ordering we have chosen. The boundary that we cannot perceive, however, has effects that we can perceive. The boundary represents a causal property with empirical consequences, but you cannot measure the cause. You can, however, infer the presence of the cause by observing its effects. The choice of an ordering system is thus not measurable, and yet, its effects are measurable. If we know the cause then we can explain the observations. We can also infer the cause from the observations. But we cannot observe it. This is yet another sense in which quantum mechanics can be said to move from measurable causes to unmeasurable ones.

Hierarchical Space-Time

If we recognize such boundaries, then the universe can be segmented in many ways based on different concepts or methods of order, which gives the boundary itself an ordinal position within the larger boundary. This is what I call Hierarchical Space.

This type of space is analogous to space in everyday descriptions where the first line of an address describes a position relative to a street, the next line a street relative to a city, the next line a city relative to a country, and so forth. The divisions based on countries, cities, and streets are different methods of ordering. We use them in a specific hierarchy. Time, similarly, can be divided hierarchically into years, months, days, etc. The intuitions underlying this hierarchical space and time are fairly common, but they have been disregarded in modern science, by describing the universe in terms of a single ordering system. A hierarchical universe is not uniform, because there isn’t a single coordinate system for the entire universe. Rather, the universe is divided into smaller domains, each of which presents a different way of ordering events, within that space-time domain. So you order locations first by country, then by cities, and then by streets. You order time first by years, then by months, and then by days. This hierarchical conception of order is useful in conceiving hierarchical conceptual metrics.

Similarly, we can order things first by their mass, then by their speed, and then by temperature. By changing the methods of ordering, the distances to those things will be naturally changed, without changing those things. The difference is that the things that were previously not interacting, start interacting due to proximity created by reordering them. Since the change in the distance has an effect, therefore, the equivalence of all methods of ordering is false. However, because this change doesn’t change the objects being ordered, therefore, we could say in a classical sense that all these reference frames are equivalent. That is the difference between quantum and classical frames.

Insights into the Mind-Body Problem

The above description gives us new ways of resolving the mind-body problem. The body in question here is an object, and the mind is the space-time coordinate system that orders these objects. Changing the coordinate system automatically reorders the objects, without a causal ‘force’ affecting these objects. The interaction between space-time and matter is not due to force between Cartesian “substances” but between objective reality and varied methods of ordering it. By changing the space-time structure, we change the order of events.

The mind cannot be perceived like the objects are perceived, just as space and time cannot be perceived. However, the effects of space and time as the ordered appearance and disappearance of events can be perceived. In that sense, the mind is a concept that can be theoretically described in science, although not seen or touched. This opens science to the natural description of paranormal or psychic phenomena in which the mind controls the material world by simply changing the method of ordering things, which then reorders the events.

In current science, these coordinate systems remain in our minds and have no effect on the world. In a new science, such coordinate systems would be factual realities that change the world. The mechanisms of such interaction would now be easily explicable in scientific terms, and would no longer remain mysterious. Of course, the ability to apply our mental coordinate system to the world would still involve a specialized ability, but this ability would now involve a causal interaction between objective reality and a subjective method of ordering.

Once coordinate systems are recognized as real causal entities, a completely new kind of science that manipulates matter by changing such coordinate systems would become conceivable. Anyone who has the ability to rethink the world, and then use that thought to order the world, would also be able to change the world because he can reorder reality by the mind. This presents different levels of scientific and technological advance, although that advance depends on the development of mental capacities rather than physical instruments.

Envisioning an Alternative Science

Since the mind’s effect on the body was originally disregarded in science, inducting the mind back into the material world appears incredibly difficult, simply because the mind appears to be incompatible with the nature of the material world as currently envisioned in science.

If, however, we begin with the intuitively accessible fact that the mind can control the body although it doesn’t have full control over all aspects of the body’s functioning, then both facts can be explained by the ability or inability to reorder some realities by the mind. We can also envision the possibility of expanding this control by expanding the ability to reorder things that we previously could not.

This science will reject most of the established principles of modern science such as motion, a singular modality of measuring distances, causality through traveling particles, etc. But it will open science to completely new forms of causality controlled by the mind. Quantum theory can open the door toward an alternative science if we can accept the idea that the distance to something depends on us.