Mathematics,  Physics,  Research

The Semantic Interpretation of Quantum Theory

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 post 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 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 which 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 a 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 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 mass 5 kilograms has the position 5 on the kilogram scale. In the relational definition of position, the object with mass 5 kilogram could have the 1st, 2nd, 3rd, 4th, or any other position. The absolute definition of position depends only on the object being measured, but the relational definition of 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 the induction of 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. For example, if you have ordered the objects as first, second, third, fourth, and fifth, and these are the only objects being considered, and the objects are separated by a mass of 1 kg each, then simply by knowing the order you already know the cardinal properties of each of the objects. Thus, if you know that there are five objects, but haven’t ordered them as first, second, third, fourth, and fifth, then you don’t know the masses of the individual particles, but you know the total mass. Conversely, if you have ordered them, then you know the individual masses, and by implication the total mass. In short, if you have the order, then you know the quantity, but you have the quantities then you don’t necessarily have the order.

This gives us a glimpse into the quantum problem: any theory that describes quantities but does not describe the order must be incomplete because there are many alternative orders. If, however, you have described the order, then the cardinality is already known. In that sense, a theory that describes the order has no need for cardinal properties, although a theory that only describes quantities must always be incomplete.

If the description of nature was based on order rather than quantities, then all physical properties used in quantum theory would be unnecessary. Such properties could still be used, although their explanation and prediction would be based on ordinal properties. 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.

Classical physics held that all such coordinate systems are arbitrarily chosen. That is, 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, on an absolute scale. In other words, the focus of science on possessed properties can be restated quite simply as the arbitrary choice of coordinate systems. This arbitrary choice is now formalized in physics as the equivalence of all coordinate systems (stationary, moving, or accelerating).

The ordinal position of an object can never be an objective property if coordinate systems are arbitrary. The ordinal position would only be an objective property if there was a preferred coordinate system to describe each object’s position. That claim would in turn entail that the notion that coordinate systems are chosen arbitrarily is false.

If the missing link in quantum theory is ordinal properties, then the equivalence of all frames is also false. Indeed, the belief that coordinate systems are arbitrarily chosen would directly lead to the quantum problem. We can either have arbitrary coordinate systems or solve the quantum problem, but not both.

The arbitrary choice of coordinate systems is called General Relativity and it indeed contradicts Quantum Theory. This contradiction has presented great difficulties in their unification, which is the greatest unsolved problem in modern physics. It is not hard to see why this contradiction must exist, if we note that quantum prediction require the use of ordinal positions, while classical relativity forbids the use of ordinal positions, because they effectively entail that all coordinate system choices are indeed arbitrary.

In other words, Quantum Theory and General Relativity can never be unified, because they are based on logically contradictory assumptions. Since we cannot ignore the quantum phenomena, we must explain the premises underlying General Relativity in a new way. There are two premises underlying General Relativity: (1) the speed of light is constant, and (2) the formula describing the law of nature is the same everywhere. Both these premises have to be understood in novel way based on quantum theory.

Does Light Have a Speed?

Let’s begin with the speed of light. The notion that light has a constant and finite 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. The speed of light and quantum theory are conceptually contradictory, and when Quantum Theory and Special Relativity are unified into Quantum Field Theory, infinities are created. To resolve these infinities a new type of game called renormalization is used, which according to Encyclopedia Britannica is “… the procedure in quantum field theory by which divergent parts of a calculation, leading to nonsensical infinite results, are absorbed by redefinition into a few measurable quantities, so yielding finite answers.”

I will not discuss renormalization here, but proceed with assuming that we haven’t understood what the speed of light really means in quantum terms, although we tend to treat light as a quantum particle. The constant speed of light and quantum non-locality cannot be resolved in a single theory, and a new explanation must be found.

The quantum explanation of the constant speed of light can 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 is rather the time taken for the photon to be absorbed. Current quantum theory treats 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. What if light is not like a classical particle, and it travels instantaneously but takes a finite time to be absorbed? Both explanations are consistent with the observations, but only the latter explanation makes it possible to solve the quantum problem.

How so? The notion that light is absorbed in a finite time entails that the quantum state transition takes a finite time. This transition begins with the source and destination being entangled non-locally but the effect of this entanglement is seen after the transition is complete. In other words, quantum theory remains non-local, and the so-called locality implied by the constant speed of light is actually a misunderstanding of the quantum interaction, created by employing classical notions of causality.

Light is therefore not traveling in space and just happens to ‘collide’ with an electron, changing its state. Rather, the destination of light is already known at the source before the photon is even emitted. The source is therefore not emitting a particle randomly in space, unaware of when or where that particle will eventually land. Rather, the source emits the photon only after it has entangled with the destination, and the particle is always sent to a destination known in advance. In other words, the source of light knows its destination before it emits the photon. The transfer of this photon takes zero time, but the absorption of this photon takes a finite time, in most cases. In some cases (which are called quantum non-locality), however, the absorption also takes zero time. Such particles are called ‘entangled’ in current quantum theory, and rightly so.

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 causally and they must be entangled before the causal transaction occurs. Present quantum theory considers the first type of entanglement, which is called non-locality, but the second kind of entanglement is not adequately understood.

The time taken in the second kind of entanglement is due to the time needed to change the state of a single particle. However, if one particle’s state is changed, then all particle states (within an ensemble) must change as well. The time taken in the second change is zero. If, therefore, the entanglement in which the interaction between two systems takes time (due to the supposed ‘speed of light’) was understood as the time in readjusting the receiver, there would be no conflict between local and non-local phenomena.

The speed of light can therefore be restated as the time of absorption rather than the time of travel. This takes out the first pillar underlying General Relativity—namely that light travels and has a constant speed of travel in empty space—which Einstein coined because the delay between source and receiver was observed to always be constant (this observation has now been empirically refuted, as we will see shortly).

Einstein interpreted the finite time taken from source to destination classically as the motion of some object, thereby creating the non-locality problem (originally coined as the EPR Paradox), which he himself battled for the rest of his life. This interpretation is perhaps the greatest mistake of 20th century physics, and it is quite unnecessary. If this phenomenon was interpreted in a different way as the time taken in absorption, then the problem of non-locality, the conflict between Quantum Theory and General Relativity, and the incompleteness of Quantum Theory would itself not arise.

The Speed of Light is Not Constant

Empirical evidence now suggests that the speed of light is not constant. Researchers led by optical physicist Miles Padgett at the University of Glasgow have for example demonstrated the effect by racing photons that were identical except for their structure. The structured light consistently arrived a tad late. Unfortunately, we don’t have a good explanation for this fact today, and such variations would entail that a number of other physical constants would vary, as they depend on the speed of light. If this speed isn’t a constant, then how must it change the understanding of nature in physics? 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 structure of light because that structure encodes information beyond the energy of the photon. In other words, we cannot treat light merely as energy without a structure. We must rather understand light as something that is described more accurately by its structure. Since light is a vibration, describing this vibration itself requires assuming a coordinate reference frame, and the relation to other objects in that reference frame. If the structure of light is physically important, then a quantum interaction where light has the same energy but a different structure would not produce an identical effect. The discrepancy would be caused by the structure, and if we knew the light’s structure, we would not need to know the energy.

This takes us back to my earlier point that when science relies on order among the objects, quantitative properties such as energy become irrelevant. But there are deeper lessons too in this, which include the fact that all reference frames are not equivalent, because the source and destination of light must be put in the same frame to even describe the structural effect. The idea that the source or destination are “moving” relative to each other (and are therefore in different coordinate frames) becomes an impediment because if we make that assumption then we cannot explain the structural effect.

We are now led to a paradox. There is a sense in which two objects (source and receiver) are moving relative to each other. There is another sense in which they are in the same coordinate system. If you tie the coordinate system to the moving objects, you can never resolve this paradox. The paradox can only be solved if we say that there is a shared reference frame in which the source and destination exist, and the moving objects are not just moving relative to each other, but also relative to that reference frame. When this is realized, the second premise underlying General Relativity—namely that each object has its own associated coordinate reference frame—also disappears.

The Rejection of Frame Equivalence

We now reject all the premises that led to General Relativity: (1) the finite speed of light because it contradicts non-locality, (2) the constant speed of light because it contradicts varied delay observations, and (3) the arbitrary coordinate system choice because explanation of structure requires a shared coordinate system. Note that we haven’t rejected any observation, although we have rejected their interpretations. The finite speed of light is no longer needed if the time taken in a cause-effect is in absorption, rather than in travel. The constant speed of light is no longer needed because this absorption time depends on the structure of light. And the arbitrary coordinate system is not needed because the structure can be described only in a common reference frame.

We are now back to the quantum problem, without being encumbered by relativistic assumptions, although this problem must now be broadened to include the idea that the absorption of light takes a finite time, depending on its structure, and that this structure must be described in a shared coordinate system. Any two objects that partake in a causal interaction must therefore be placed in a shared coordinate frame. Such objects must be entangled before the energy is emitted, and therefore the light is always ‘headed’ towards a receiver known in advance. In essence, light is not a particle that collides with other material objects, depending on whichever particle happens to cross its path. Rather, light is emitted with the foreknowledge of which particle will absorb it.

New Forms of Causality

The entanglement between source and destination requires a completely different kind of causality, which is missing in current quantum theory. The succession of particles in the two-slit experiment is therefore due to a succession of entanglements between the source and the detector, and which electron will arrive at which detector is known at the time of particle emission. That particle therefore is not accidentally encountering a destination. Rather, the particle is destined to a specific detector from the start. The foresight involved in quantum theory is one key reason that makes this theory different from classical physics. But the mechanism of this foresight requires a new kind of causality.

In the classical way of thinking, if you happen to ‘accidentally’ meet someone on the road, you would try to explain this based on the past states of those objects, and the element of surprise is generally mitigated by supposing that this ‘chance’ meeting is just a ‘coincidence’. In the quantum way of thinking, you would say that the meeting was ‘destined’ and the process of its realization had begun much before the event actually occurred. Since we don’t understand what was happening before the meeting occurs, we erroneously tend to suppose that the meeting is a chance occurrence.

The randomness in quantum theory is quite like a ‘chance’ meeting with a friend. It appears as a chance event, so long as we don’t understand how a source and receiver become entangled, which then eventually manifests an event. The entanglement occurs much before the event is manifest, so we cannot ‘observe’ it empirically. Therefore, we must find new kinds of theoretical constructs to describe this new causality.

In classical physics, we are used to thinking that only the present state causes the future state. To address the quantum problems, we now need a new notion of causality in which the past (which is unobservable) creates the future. Unlike the current physical model of causality, this future is commonly called destiny. It exists in the past, but cannot be perceived. It entangles with the destinies of other objects to create future events. How this destiny is created, how it entangles with other destinies, and how the entanglement creates events, constitutes a radically different form of causality.

I will not dwell on these mechanisms here, although I have described them in other places such as Moral Materialism. The crux of that explanation is that a causal interaction has three parts: cause, effect, and consequence. In present science we only study the cause and effect, and neglect the consequence. In a new science, material interactions will produce a consequence, which remains unobservable until it entangles with other consequences to create an event. The cause of an event is the entanglement between two consequences, produced by time. The effect is the event that we observe. And the event produces a new consequence. In short, material transactions create destinies, which lie dormant and therefore unobservable. These destinies are excited into mutual entanglement by time. And that entanglement produces events.

The Quantum Understanding of Karma

This view of causality is pervasive across many Eastern philosophies, and is called karma. In Indian philosophy, there are three states of karma, called sanchita, prarabdha, and kriyamana. The term sanchita denotes the destinies that lie unentangled and therefore unobservable. The prarabdha denotes the destinies that have become entangled with other destinies due to time, and will gradually manifest observable events. The kriyamana denotes the destinies that are currently manifesting events. From these events, more sanchita is produced, which lies dormant for a long time. In this way, a cycle of actions and reactions is created in which the present becomes the past, and the past becomes the future. This view of causality is radically different than used in modern science, but it can be used to understand the problems in modern science.

When a person is born, or an experimental setup is created, sanchita becomes prarabdha: the possibilities of previous consequences have now become realizable. However, this prarabdha will only manifest gradually, in a succession of events. The reason we cannot predict these events is because we don’t know the prarabdha and how it manifests from sanchita. We just observe the events—i.e. kriyamana—and are baffled by their succession. This bafflement is ensconced in the quantum problem, and its solution is a new notion of causality in which the present events are being caused due to the consequences of the events that occurred in the distant past.

The mystical or religious aspect of this theory is how one can break the cycle of cause-effect-consequence, but it depends on a firm understanding of this cycle itself. The cycle of action and reaction is the foundation on which true religion is built, and in that sense, the foundation of religion is a scientific understanding of natural causality, not merely faith. Science pertains to the law of cause-effect-consequence while religion is how to get out of this law. In other words, the law of material nature can be overcome by performing certain types of action which have an effect, but no consequence. In so far as the effect follows the cause, this is still science. But in so far as the consequences are not created, it is religion. When religion is disconnected from an understanding of natural causality, then numerous ‘faiths’ are created. When religion is based on this causality, there is no faith, only a scientific understanding of how natural causality works, and how it can be overcome.

Can Coordinate Systems Be Physically Real?

I will now return to the quantum problem, and outline some ideas about the nature of space-time, and how the modern ideas in science must be revised to create a new notion of causality. As we have seen, causality requires pairwise entanglement of objects, and this entanglement requires us to place these interacting objects in the same coordinate systems. Objects that don’t interact, or interact pairwise in separate groups, can have different coordinate frames. I am thus not claiming that there is only one reference frame, but that whenever a causal interaction occurs, a reference frame shared between a source and receiver must be used because on this frame can we speak about structure.

The universe is therefore not arbitrary coordinate frames. Rather, there are many coordinate frames within which different pairwise interactions occur. If any object could interact with any other object, then all these objects would be in a single, fixed, and universal coordinate frame. Either way, coordinate systems are not arbitrary. Rather, they have to be defined through causal interactions in which the interacting objects use the same coordinate system. As this causality is widened, we arrive at a single universal coordinate frame. This frame represents the universal space-time.

If light is emitted from an object and then travels to another object, then the source and destination can view this transaction differently. If, however, the two systems have to be entangled before the light can be emitted or absorbed, and the effects of this emission or absorption depends on the structural relation between the two, then the source and destination must reside in the same coordinate system throughout the transaction. The use of different coordinate systems at the source or destination would fail to explain the observations, because the structure would itself be described differently.

The conventional wisdom in physics states that coordinate systems are simply our way of observing the world, and have nothing to do with the world itself. The solution to the above problems entails that we recognize this coordinate system as a physically real entity. Since the coordinate system exists in the observer, although it is not an object, recognizing the reality of coordinate systems would entail a new kind of physical entity that, although already used in physics, is not yet treated as a physically real entity. The coordinate system becomes the basis on which events are ordered. Essentially, the succession of events is nothing other than the space-time structure, and this space-time structure can be known if we know the material destinies. Since the destinies are constantly being created through actions, the space-time structure is also being created. The events in the distant future are therefore being created right now, but they will manifest much later.

Space-time is not a static entity as the currently dominant Block Universe view assumes. Rather, events in space-time produce more space-time, which appears later. When the consequences of previous actions are destroyed, the past ceases to exist materially. Until those consequences are not realized, the past is materially real. Since the future is produced from the present, it is materially real until it is realized, and becomes the present. In one sense, past, present, and future are all real. In another sense, they are all unreal. This reality and unreality creates problems for philosophers, but these problems are resolved when we take the cause-effect-consequence cycle into account.

Object Ordering and Concepts

We have seen why space-time, or the method of ordering events, is not an object (in the sense of being sensually perceivable). We have also seen above that this space-time must be materially real to create causality. I will now discuss how this material reality is distinct from the notion of material objects in current science.

Suppose that we are ordering a collection of particles based on mass. We might then label a particular object as the 5th object in a collection by mass. If the same collection were then ordered based on momentum, frequency, size, etc., the ordinal position could change. The ordinal position of an object, therefore, changes based on how we order the objects—namely based on mass, momentum, frequency, size, etc. The method of ordering objects, therefore, has an effect on the objects, namely that it changes their ordinal position. If the ordinal position presented an empirical phenomenon, then the observed order of objects would entail a preferred choice of coordinate system.

Coordinate systems are useful constructs for ordering events. And this ordering is essentially a concept which allows us to sequence the events into an order. It follows that the space-time of events—which we use to order events, but which we cannot perceive sensually—is a concept by which ordering is performed. There are innumerable coordinate frames because there are innumerable concepts by which we can order events. In one case, the order may be created by frequency, while in another by momentum. We can also have events ordered first by momentum, and then by frequency. The space-time therefore need not be described as a set of points or events, which are essentially effects of ordering. We can also describe space-time as the method of ordering.

The senses of the observer are the methods of ordering. The eye, for example, can order by color, size, form, distance, etc. The ear, similarly, will order by tone, pitch, phase, distance, etc. The skin, likewise, orders based on temperature, roughness, hardness, etc. There can be many orders between the properties measured by a sense, and orders between the use of senses themselves. For instance, we can order first by form, then by size, and then by color. Or, we can order by form, then by taste, then by touch, etc. Accordingly, the senses of the observer produce an observer-unique coordinate frame for ordering events. We can also create properties that combine two or more of the above properties.

These coordinate frames are choices of the observer and different observers can use different conceptual reference frames, each of which defines the properties in terms of which we will order objects , thereby creating different languages for describing the same world. However, when we communicate with other observers, we must use the same language. In that sense, two observers must be situated in the same coordinate frame in order to exchange information. The so-called ‘entanglement’ of systems is nothing other than the use of a shared convention for ordering events. The problem of quantum entanglement can therefore be simply defined as the use of a shared language. Before information can be exchanged, the language of exchange must be defined.

These conventions are widely employed even in current science. For example, before we can compute the gravitational effect of two masses, we must agree to describe the mass either in terms of kilograms or pounds. If Earth uses the pound standard and I use the kilogram standard, the law would only produce erroneous results. Similarly, we must agree on the definition of all physical properties, how they would be measured, and the order in which they would be measured. In classical physics, we assumed that if we hold different standards, we may not be able to communicate our results other observers, but we would still be able to do scientific experiments by ourselves. In quantum physics, we must suppose that we cannot even perform an experiment unless a shared convention of ordering facts has been previously defined because the interacting objects can be different frames. We may disagree on the ideas shared in a communication, but we must agree on the language used in communication, even to begin disagreeing with the ideas.

The Quantum Event Ordering Problem

The quantum event ordering problem can thus be reduced to a specific coordinate system choice, which can then be reduced to the concepts that are used for ordering, which can then be reduced to the methods of perception in the observers. Now, we come to a radical conclusion, which is that the order of events you perceive depends on your methods of perception. Individuals who have different methods cannot agree on the event order. Such individuals would not even be able to communicate with each other. This is no longer a description of a social fact often observed in debates where two people with radically different languages cannot communicate, but also a description of physical phenomena where object interactions depend on the use of shared conventions.

Quantum theory permits the use of different languages which is why this fact is important for quantum phenomena. For example, quantum theory allows the same wavefunction to be represented in many different bases each of which has a different event order. The meaning through such expressions can be the same, but the order in which the meaning is expressed through words can differ. The world is thus not fixed, and the observer is not just a spectator of the events that occur independent of the observer. Rather, the observer interferes with the world by choosing a coordinate frame. The ‘hidden variable’ in quantum theory is the choice of a coordinate system which is not an object or a physical property but a concept by which we organize the world in our senses and the mind.

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 natural and indicated by a coordinate system choice. In other words, quantum events occur in a particular order if they are the first, second, third, fourth, fifth events in the chosen coordinate system. The infinite choices of consciousness in the ‘collapse’ interpretation become a single choice of a coordinate system, and this choice can be objective although not an object.

As seen above, the method of ordering objects within a collection exists as a concept—namely, the properties of mass, momentum, frequency, etc. If such concepts were accorded reality in science (in the specific sense that they help us order the objects, and give them ordinal positions), then a new kind of physical entity—i.e. a concept—would be causally efficacious, because it will explain the observed event order.

Ordering and Boundaries

In classical physics, all coordinate systems are global. That is, if you choose a coordinate system, then you must apply it to all objects in the universe. A different observer can choose a different coordinate system, and order the objects differently. The choice of coordinate systems therefore has no effect on the world because multiple ways of ordering are simultaneously permitted. Since the alternative choices can conflict with each other, the existence of such a global choice entails that these choices have no physical relevance. Arbitrary choices thus naturally lead to the quantum problem, because we cannot globally choose a coordinate system and expect it to affect the entire universe.

For such choices to be causally efficacious, the scope of the coordinate system must be limited. Such choices now represent a local space-time, which orders the events locally rather than globally. To address the quantum problem, we must postulate that the space-time that orders events is local, and its effects exist within a boundary. The boundary is the limits of the local space-time, and its effects are within that boundary.

Effectively, the resolution of the quantum problem now requires the hypothesis of a new kind of physical entity—a boundary—which orders events within the boundary. The observed event order is now explained as an effect of the boundary. The boundary is therefore the cause, and the event order is the effect. The boundary is a physical entity, and yet it may not always be an observable entity—i.e. an object. The boundary therefore cannot be sensually perceived, although its effects on the sensations can be perceived. This boundary represents a local coordinate system, which can be conceived as a physical entity, although not an object in the conventional sense of particles. By changing the boundary, the event order can be objectively altered. The form of the boundary therefore represents a physical property with empirical consequences.

Hierarchical Space-Time

Once we recognize that boundaries are real physical entities, the universe can be segmented into larger and larger boundaries. The largest boundary would then order the next smaller boundaries within it, each of which will then order the subsequent smaller boundaries within each boundary, and so forth. Each such boundary will represent a concept or a method of ordering, which effectively gives the boundary itself an ordinal position within the larger boundary. This is what I call Hierarchical Space-Time.

This type of space-time is analogous to the everyday description of space-time in which the Earth is divided into countries, which are divided into states, which are divided into cities, which are divided into localities, etc. Time, similarly, is divided hierarchically into years, months, days, hours, minutes, and seconds. The intuitions underlying this hierarchical space-time therefore exist within our everyday world, although they have been disregarded in modern science, by presenting the universe uniformly. 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.

General Relativity is based on the premise that coordinate systems are fictions of our minds; that the choice of such a coordinate system presents no effect on nature. Such coordinate systems are also supposed to be global, which essentially overlooks how a coordinate system could actually affect matter. Such equivalence is also contradictory to quantum theory. By rejecting such equivalence, we can not only resolve the quantum problem, but also find a new description in which space-time is a coordinate system, which presents a definite ordering of events and is therefore physically real.

Insights into the Mind-Body Problem

The above description also presents interesting possibilities for resolving the age-old mind-body problem that Descartes created. The body in question here is material objects, 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 therefore not due to force, but due to a mathematical property of space-time in which events occur in the order given by the space-time structure, and changing this structure changes the 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, mind is a concept which can be theoretically described in science, although not seen or touched.

This also opens science to the natural description of paranormal or psychic phenomena in which the mind controls the material world by simply changing the local coordinate system, 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 physical boundaries or forms that change the world. The mechanisms of such interaction would now be easily explicable in physical 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 our internal and external coordinate systems.

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

Envisioning a New Science

The mind controls the body, and the body is then used to control the material objects. But when the mind’s control over the body is disregarded, then we falsely come to the conclusion that the world is being controlled by the body. A push-and-pull model of causality is then developed, modeled after the body’s ability to push and pull the material objects. This is what present science tries to do. Since the mind’s effect on the body was originally disregarded in science, inducting the mind back into the physical world appears incredibly difficult, simply because the mind appears incompatible with the nature of the physical world as envisioned in science. This lacuna then appears in physics itself in our inability to explain the phenomena purely based on physical properties.

If, however, we begin with the intuitively accessible fact that the mind controls the body, then finding the path for this interaction presents us with a new kind of science and technology. This science will reject most of the established principles of modern science, but it will explain how the mind controls the body, and present a new way of controlling the world through the mind. Quantum theory can be seen as a vista to this new kind of science, provided we are prepared to adopt a new way of thinking.