PhysicsEigenket 140624

A personal interpretation of quantum theory

Hypothesis: That a simple principle of logic underpins the quantum world

Under the hypothesis which I describe in this essay, measuring an entangled particle instantly causes a reality for its remote twin because the local measurement defines the reality of the remote object. Defining something is a logical action and propagates instantly. In my hypothesis I extend this "quasi-causal" action of logic so that it specifies all of reality, and not just the odd quantum particle in a measurement.

As the above example suggests (where the remote particle does not have a reality until defined ) my hypothesis is a "non-realistic" interpretation. Thus an independent external reality does not exist. The key word here is "independent". Something which we call "reality" does exist, but it is not independent of logic - and if the logic involves us, not independent of us. To promote the action of logic in this quasi-causal (or ontological) role, I give a logical meaning to the idea of observation (to be explained in due course). Observation is not the uncovering of something already real in our world. It is an event where new reality enters our world. This occurs when something makes a logical contribution to our world.

So far I have mentioned two logical actions with quasi-causal effects: definition and observation. Another is selection. I treat selecting something from an ensemble of possibilities as a quasi-causal action of logic that results in a change in reality. I also treat randomness and the throw of a die in logical terms. The face chosen by the throw of a die should not be explained in terms of forces but in terms of logic. Similarly, if something happens "at random" we should look for an explanation in terms of logic and not speculate about underlying reality.

My interpretation, therefore, is centred on logic. I call this approach "logic first" because it contrasts with the traditional "reality first" approach of science. The difference is that traditional science starts with an assumption of reality and proceeds by observation to the acquisition of knowledge about that reality. In contrast, my approach starts with logic and proceeds to create a story to be called reality. Since the story is indistinguishable from the reality, we treat the story as actually being real. The advantage of my approach is that it explains things, or provides a plausible account  of the world. The traditional scientific approach does not provide satisfactory explanations because, in that approach, the ultimate reason for things being the way we see them is "that is how they are seen to be ".

I use the term "quasi-causal" to mean "required to exist". The term is intended to convey the idea of causality but not in the traditional sense of deterministic evolution from a pre-existing reality. The traditional sense acts in the forward direction of time (and we ignore the reverse direction). In my interpretation, both directions of time are relevant. The forward direction provides traditional causality while the reverse direction provides quasi-causality. Quasi-causality cannot be observed or demonstrated but there are good reasons to accept it. (For instance, we accept that defining something sets the reality of the thing defined.) Normal scientific causality certainly can be observed and demonstrated, but it suffers from a problem: the underlying reality undergoing evolution via this causality cannot be proved to exist. We are forced to assume an underlying reality, which we do in the guise of an axiom (the fundamental axiom of science).

Thus reality, in my scheme, is not something that self-exists for us to stumble across. Rather, it comes into existence as logic dictates.

Logic acting in this quasi-causal role is well-illustrated by the Anthropic Principle, where a particular reality of the present, the existence of us humans as conscious beings, logically requires a particular reality to have existed in the past. Here, the logical action is selection. We unwittingly select a past to agree with our present existence. My hypothesis extends the Anthropic Principle into having a quasi-causal (or ontological) role in the reality of everything. Since the Anthropic Principle is referenced to people, this quasi-causal role of logic involves us humans. Picking-out humans to have a special role might seem somewhat arbitrary, but the necessity of doing this derives from the our that selects our world. If we could find some other way of defining our world without reference to humans, we might not need to make humans special. But it seems impossible to do that, and as a consequence we are forced to make special accommodation of man (in my hypothesis).


I define reality by the following principle: To be real, an object must have  a logical impact on our world. The impact must be objective and communicable to other people.

Some consequences of this definition:

- if something exists only in someone's mind, it is not real

- it is not valid to assign reality to an object solely on the basis that it exists "in itself". For instance, it is not valid to claim reality for God solely on the basis that (unknown to us) he exists in himself

- a would-be object that does not meet the definition for reality defaults to non-existence. We act as if it does not exist and make no claims for or against its reality

- when we discover a new object, the object enters reality at that moment. Thus new has an ontological rather than epistemic meaning

- it is not the case that the new object existed before it was discovered. Before it was discovered there was no evidence for it and it did not partake in the logic of our world. Thus it was not a real object of our world. It became a real object - entered existence in our world - when we discovered it

- when something has a random origin (or happens at random) it has no reality until observed. There is no contribution to the logic of our world until we know what the result is.

The Anthropic Principle

As generally understood, the Anthropic Principle purports to explain why early choices in the history of our world turned out the way they did. The explanation is that If they had turned out differently, we humans would not exist and would not be considering the question. Given the brute fact that we are considering the question, those early choices are required to have turned out the way they did.

The two components of the AP are a particular reality at the present moment (our existence) and a quasi-causal effect of that reality on the past.  Both components are problematic for scientists. In science, people are supposed to be objective observers of the world. And causation is supposed to proceed from the past to the present rather than the other way round.

Scientists (at least, the few who entertain the Anthropic Principle) typically avoid these problems by postulating a plethora of other worlds from which our world is a random selection. For me, this "Many Worlds" solution to the anthropic problem has its own problems:

(i) those other worlds are required to have the same reality as ours, conflicting with my definition of reality. Those other worlds do not have a logical impact on our world and should not be considered real by the inhabitants of our world

(ii) to say that our world is a random selection is to say that there exists a selecting agent, logically lying outside the Many Worlds, that operates randomly to choose one of the worlds to be our world. Effectively, the selecting agent surveys all the worlds in front of it and chooses one of the worlds at random to be ours.

I find the presumed existence of such a selecting agent problematic. It is a scientific "God of the gaps", something we invent to cover an awkward gap in our knowledge. I do not accept that a suitable choice of words can avoid the implied existence of such an agent - by saying that the selection "happens at random", for instance. I'm inclined to think that selection logically requires a selecting agent.  

(iii) in the scientific scheme it is not possible to define the word our which picks out our world from the others. We introduce random selection to avoid people doing the selection anthropically, but if we define our world in terms of our we are still referencing the selection to us. The problem remains if we replace our with this or any other implied reference to humans.

Instead of inventing or assuming the existence of randomness as a selection agent, I prefer to adopt the logic of the Anthropic Principle, which says that people are logically involved in the specification of reality. There is some evidence for the involvement of people. Some of the reality around us - the existence of cars and computers, for example - is logically caused by us.

In my personal interpretation of quantum theory, I extend the role of people from specifying odd bits of reality (cars and computers) to the specification of all reality. Of course, if people were defined to be real, physical objects, there would be a logical problem with having them determine real, physical objects (i.e., a category which includes themselves). So I define them a different way, in a certain logical sense which will become clear.

I generalise the Anthropic Principle (AP) in two respects. Firstly, I find it somewhat arbitrary to apply the AP only to cherry-picked events in the early history of our universe. If the Principle is to apply at all, it should to apply to the entire past. Accordingly, I accept that the exact characteristics of the world - including the way things were only a femtosecond ago - were required to be like that by the AP. The requirement actually applies to the whole of the logical past, not to events earlier than a particular time. The logical past is everything objective. Thus, in my extended version of the AP, anything we see to be objectively real is required to be the way it is because of our human existence.

My second generalisation is to expand the existence of people to the existence of people exactly as we are. The usual discussion of the AP is referenced to the existence of people as conscious beings, but in my scheme, it is referenced to everything about people, and not limited to a vague possession of consciousness. I define people in a certain logical sense that takes into account the multifaceted nature of individual persons.

One advantage of taking into account the entire make-up of a person is that it has a chance of explaining the "fine tuning" of the Big Bang. Roger Penrose says that the Anthropic Principle (referenced only to the existence of beings with consciousness) falls far short of explaining the extreme precision of the Big Bang - a short-fall of about sixty powers of ten. In my scheme, each person effectively has a deterministic link back to the Big Bang to cause it to turn out a certain way. To accommodate all these "requests", the Big Bang is required to be exceedingly particular, using up the excess freedom represented by the sixty powers of ten.

The phenomenon of belief

Although it as an objective truth that people believe things, there does not seem to be a scientific accommodation of the belief phenomenon. Scientists vaguely assume that some arrangement of a person's neurons represents - or "just is" - a particular belief entertained by the person. This implies that the essence of the person lies elsewhere of their beliefs (as the possessor of those beliefs). But the physical location of whatever defines the person has so far eluded science.

Personally, however, I believe that a person is well defined by their set of beliefs. A belief is a directed quantity (directed at the thing believed) and can be represented by a vector. The person has many such beliefs, which can be summed into a single resultant vector replacing all the subvectors. This resultant vector, being a "single thing", is a good candidate to represent the unity of a person. (This is a possible solution to the "binding problem" in neuroscience, perhaps?) Thus the essence of a person - the thing which determines their identity - is a vector in some space.

The idea that a person is defined by their beliefs is actually the monotheistic religious position. (As described here.) Although I am sympathetic to the religious approach, I do not think that approach is appropriate to a scientific description of the world. Accordingly, I borrow the idea from religion that man is defined by his beliefs and make it into a kind of axiom of my interpretation. I justify this action by the utility of the idea (explaining the binding problem, for instance) and also for the following reason. If a person is defined by their beliefs and these are summed into a resultant, then those resultants in turn can be summed into a grand resultant pointing somewhere. It seems natural to identify this direction as the world we collectively believe to exist. Thus we become justified in identifying our world with the word our, solving a potentially serious issue for Many Worlds scientific interpretations.

The "space" that belief ranges over is the totality of things that might be believed true. A person's beliefs point at a personal world that he or she believes to be real. The grand resultant of all of our beliefs points at a world in common that we believe to be real. Although we only believe the common world to be real (we do not know it for certain) we treat it as actually real because there is no way we can prove otherwise. We cannot prove our world to be different from what we believe it to be.

Although the reality that each person believes into existence (and interacts with) is merely a personal creation, each person has the conceit that their personal reality is real reality which they have knowledge of. They define this to be independent of how people see it, which means that it applies to everybody. This leads to a particularly simple explanation of human free will, as follows.

If there is a single reality applying to everybody, then, in the absence of free will, everybody should behave identically. This is a consequence of having everybody's behaviour determined by a single reality applying to all. But it is an observed fact that people do not behave identically. A person seeing someone behave differently from themselves wonders why the other person acts strangely. "When there is one invariant reality bathing everybody, the other person should see things just as I do." Eventually the person concludes that the other person possesses a mysterious "force" allowing them to defy reality.

We call this presumed force free will. Of course, the true reason that the other person is acting strangely is that he or she is interacting with a private world of their own.

(The use of the word force in connection with free will is frowned upon in scientific circles, but it does seem as if free will logically causes physical matter to be moved around. This happens when we manufacture computers and cars, for instance.)

Thus human free will is a pseudo-force arising as compensation for an erroneous view of the world, a view that says an independent world of reality exists when it does not. I picture it as similar to the Coriolis force which arises from the error of people on a rotating platform imagining that they are at rest.

The measurement problem

Each face of a 6-sided die has a reality of about 17% before the die is thrown. (For instance, if the die were used to draw an office fund but the event cancelled and the pot divvied up, each of the six participants would get a "winnings" of 17%.) After the throw, one face obtains a reality of 100% and the other faces collapse to 0%. The measurement problem is to understand how and when this change in reality occurs.

The answer, I hypothesise, is that the change in reality occurs when the outcome of the throw is registered by the participants. It does not occur when the die comes to rest on the floor or a photograph is taken. The die must be observed, or in some other way become known to the people involved.

When the winning face is observed it contributes to the logic of the world and has a real effect on things. (In my example, it decides the winner of an office sweepstake.) Before it is observed, the winning face does not contribute to the logic of the world, meaning that the reality of all of the faces remains at about 17%. In my scheme it is important to accept that the face of the die lying on the floor does not have a real value before we observe it. The face does not have a real value because it does not contribute to the logic of our world. We might imagine that it has a particular value, but that is just our imagination.

That is about all there is to it.

Some people make a problem out of this because they prefer to explain everything in terms of atomic particles and mathematics. I believe some things are better explained in terms of logic. If the throw of the die were conducted perfectly (with an absolutely fair die and an absolutely unbiased throw) the outcome would be absolutely random and could not be predicted as a matter of logic. We would have to observe the result to know what it is and have it influence us. For me, the requirement that something generated by a random process be observed before we can consider it real is part of what random means. As I said, words like random and throw have logical meanings and we must evaluate the logic to know the reality of their effects. We can picture the throw of the die in mechanical terms - the movement of its quarks perhaps - but we should not pretend that this solves the logical problem. I repeat: when something is defined as random, this means we must observe it before we get a real outcome.

So random has a logical meaning, in my scheme. The same goes with observe, believe, new, our... and so on. These words have logical meanings, which we need to respect. Problems occur when we insist that things with logical meanings be evaluated in physical terms. When we do that, we descend into a mass of complicated detail which does not give an answer but seduces us into thinking that an answer might appear if only we went a little deeper.

(As an example, a handful of soil might possess a vast amount of factual information concerning the shape of the grains and how each one is related to each other one, etc - a hugely complicated physical Truth. But the way the handful of soil enters the logic of our world might be better explained simply by seeing it as a handful of soil.)

The word observe superficially refers to eyes but of course we could use any of our senses - or even none of them - to conduct a logical observation. The only requirement is that the observation contribute to the logic of our world. It will do that if people believe a certain result has been obtained. We can imagine some occasion when the die is not observed in the normal way but for some unknown reason everybody firmly believes it was a five. That belief will be sufficient to decide the winner of the jackpot.

It seems obvious that observation is required in the case of a purely random number but it is equally true that observation is required when anything new enters our world. The word new has a logical meaning, requiring that the new object be observed (in the generalised sense of believing it to exist) before it can be said to exist in our world.

(When something cannot be said to exist, meaning its existence cannot be communicated, it defaults to non-existence. This follows from my definition of reality.)

An example of a new object entering the reality of our world might be the discovery of a new species of animal. Since evolution theory has an essential dependence on randomness, it is logically impossible to say in advance what species of animal will evolve. We have to observe the results of the evolution process to know the answer. The argument is the same as when we consider a purely random number. Just as a random number does not contribute to the logic of our world until we observe it, neither does a randomly-generated species of animal. In both cases, the default is to assume non-existence. If a random number were written on a piece of paper and never observed, we could not use it for any logical purpose in our world. We would be obliged to ignore the piece of paper and to conduct our lives as if the number on it did not exist. If some unknown animal - an animal not named or imagined in any way and not even conceived as possibly having existence - were to evolve in some environment without us knowing about it, then it, too, would have no impact on the logic of our world. Again, we would conduct our lives as if it did not exist, and the animal would default to non-existence in our world (regardless of whether the animal existed in its own world).

If we then discover the animal, it enters our world as a new contributor to our world's reality. The discovery has exactly the same logical effect as observing the winning face on a die. (Perhaps the die would need to have an infinite number of faces to be equivalent to an animal which is a total surprise.) In both cases there is no reality in our world until observation. This is an important point. As with the unobserved die lying on the floor, it is not the case that the animal exists and we later discover it. No, the unobserved animal has zero reality. It enters reality when it makes a contribution to the logic of our world, which is what it does when we see it to exist.

This is of course contrary to the scientific axiom that people are disinterested observers of reality. Scientists traditionally assume that nothing real happens when we evaluate something random or new.

If a new species of animal requires observation before it enters the reality of our world, this superficially causes a logical problem for man's own evolution. Man's evolutionary arrival requires observation before man can be said to exist, but man does not yet exist to make such observations. In my scheme, the problem is solved by defining man by his beliefs rather than by his physical arrangement. It means that man, defined by his beliefs, is domiciled in the domain of logic. Thus he is logically outside physical reality and can choose (or require to exist) whatever reality he wants. This includes the physical make-up of people, including himself. What man "wants" is determined by what he believes to exist. (As I will explain, it is his unconscious beliefs that make this determination. Further, it is the whole of mankind, including the existence of people in our future, who determine the characteristics of what we call the present.)

Although this would-be scientific accommodation of the belief phenomenon is unusual, I see similarities with the scientific accommodation of electromagnetic waves at the end of the nineteenth century. At that time, scientists insisted that waves required a medium for their propagation. But experiments suggested that a medium was not necessary, so Einstein dropped the idea. Today, our scientific preference is for an unseen world of reality to exist in itself. Our experiments suggest that a standalone world does not exist, so my personal response is to give up the idea. Doing this raises the question of how the world around us comes to exist. My hypothesis is that it is believed to exist (or believed into existence). Our world is not different from what it is believed to be.

Schroedinger's Cat

The Schroedinger Cat experiment is explained in various interpretations of quantum theory, particularly in terms of decoherence, but here is how it might be done with the hypothesis I am presenting here.

A particular feature of Schroedinger's experiment is the "steel chamber" he describes. It seems that the experiment would not work if the scientists watched a sample of radioactive material decay in the presence of some poison and an animal, even if the idealisation were made that the experimenters had no physical effect on things. What is the logical function of the steel chamber?

In my interpretation of quantum theory, the steel chamber is an idealised way of sending the animal out of our world. We set up the experiment, shut the door, and let things happen in another world. We re-admit the animal to our world by opening the door and seeing what has occurred, the animal being either alive or dead. Up to this point, there is no "paradox". The problem occurs when we imagine what the situation was inside the chamber before we opened the door. This imagining is a mistake (in my interpretation of quantum theory). The purpose of sending the animal out of our world was to let the animal evolve in some other world (its own world). But other worlds are not part of our world and it is wrong for us to imagine some of our reality taking place there. That error is at the heart of the problem.

The correct approach is to send the cat out of our world, let things happen in another world, re-introduce the cat to our world, then re-observe the cat as a new object in our world. (It does not matter if the new object is one that we have had previous experience of.) If we observe the cat alive, that just happens to be how the new object is (or how the old object now is). If it is dead, then that is a characteristic of the newly-admitted reality. Effectively, we have created a gap in the timeline of the cat as an object in our world. The cat evolved normally prior to the gap and normally afterwards. During the gap we cannot say anything about the cat because it was not a real object of our world for that period. It did not contribute to the logic of our world. Only the steel chamber, with its impenetrable walls, made a contribution during that period. The contents of the chamber were defined as not contributing to the logic of our world.

In a slightly different light, the paradox arises from us sending the cat out of our world but pretending it remains a real object in our world. We make this pretence because we like the idea of being able to see all worlds, not just our one. If there is reality elsewhere, we want to know about it, we tell ourselves. Indeed, the formulation of the Many Worlds theory is designed to do just that. It describes all possible worlds, not just our own.

In contrast, the logic of the Anthropic Principle firmly confines us to our own world, and does not admit the real existence of Many other Worlds. Only our world is real. Personally, I prefer to say that all of the Many Worlds do exist in reality, but with a reality-value of 0%. One of the world (ours) acquires a reality-value of 100% when selected by us. That is because selection, like random or throw, has a logical meaning . Traditionally, scientists have tried to explicate selection in terms of physical processes, or not to explicate it but simply say "the selection happens at random".  I think that a logical explication is better, noting that if selection changes one of the worlds from a reality-value of 0% to a reality-value of 100%, then all of the worlds prior to selection can be pictured as having the same value. That agrees with the Many Worlds theory.


In my scheme, people are defined by their (unconscious) beliefs and each person believes a private reality to exist. It is possible that when the determinism of these private realities is traced back into the past, they end up conflicting with each other. Since reality is conceived to be logical, such conflicts cannot exist. Each of us resolves the contradiction by presuming that reality has a randomness component that dissolves people's histories into unknowability. A person's deterministic history does not extend back forever but only to a point where it meets other people's histories at which point randomness appears. Thus randomness is another invention (along with free will) to preserve the notion that a self-existent reality exists. Or to preserve the notion that I am accurate in my beliefs about reality when the evidence goes against this. I note that if the world contained just one person, then whatever reality that person believed to exist would be "true" because it could not be contradicted. And it would be deterministic. Randomness is a meaningless concept when only one person exists. These considerations support the idea that randomness is our unwitting invention.

There are two components to a quantum measurement in the laboratory. One component is the setting up of an occasion for a new reality to be admitted to the world, the other is the new reality itself. In setting up the experiment we do not know what the reality will turn out be, only that it will be new. According to my definition of reality, this means that the reality of the result does not exist before the measurement. The new reality does not have a real but unknown prior value.

The actual result of the measurement is obtained when the scientists believe a certain new reality to exist. If the experiment is throwing a die, the measurement is obtained when the scientists view the up-turned face, say a 5. At the moment of observation, the reality of the 5 changes from about 17% to 100%, while the reality of each other face changes from about 17% to 0%. In accordance with my definition of reality, it is only when a change occurs to the logic of our world that the measurement is complete. This happens when the experimenters believe something. (Believe some reality to exist.) A camera photographing the die does not believe anything and does not complete the measurement.

The fine tuning of the Big Bang can be seen as our "measurement" of the Big Bang's reality. As I said, the characteristics of the Big Bang were required to be extremely particular to accommodate the reality of the future (to accommodate whatever reality people of the future determine - or believe - to be true.) Personally, I prefer to see the Big Bang as a scientific story that we make up. Since none of us is privileged to decide the story, the Big Bang tries to accommodate us all.

Not only the Big Bang but everything about the past is determined by what people believe their present realities to be. This is reflected in an ordinary quantum measurement in the laboratory. The measurement result has to agree with everybody in the future, to avoid conflicting with how people determine their particular realities at those future times. More prosaically, the reality of the future requires an earlier-in-time chain of reality to determine it, a chain of determinism extending back to the Big Bang. When people are defined by their beliefs and summed to a resultant - and all those resultants summed - then the final vector (which selects the reality of our world) encodes all of the input vectors. It is this final vector that has a deterministic chain extending back to the detailed particularity of the Big Bang.

A simple thought experiment can show that the randomness we see in the world does not exist in reality. Let us suppose that the (random) disintegration of a radioactive atom is used to decide some real event, an event occurring somewhat after the atom's disintegration. The brute reality of that (future) event determines, in a quasi-causal sense, how the radioactive disintegration must have panned out. By brute reality I mean "starting with an observed truth of the world". If we start with that observed truth, and it has a causal chain extending back to the radioactive atom, how could the disintegration have turned out differently?

Let us suppose that the atom's disintegration was used to choose an input to an experiment that finds a cure for a particular type of cancer. People in the future who, for some reason, might have expected to die from that cancer, will say, in the spirit of the Anthropic Principle, that the atom was required to disintegrate the way it did otherwise they would not exist. Other brute reality in the future would also require that particular disintegration.

Perhaps a better example is the computer determination of a new species of animal. In this thought experiment, inspired by Richard Dawkins, a computer is set up to model the machinery of biological evolution. The randomness required by evolutionary theory is modelled by a random number generator initialised by the radioactive disintegration of an atom. Let us say that the experiment is set going and eventually the output screen depicts a new species of animal, perhaps a "meringutan". (Rather like an orangutan but with 3 eyes and 5.1 ears.) Since everything about the experiment was deterministic, apart from the random seed, the brute reality of the new creature requires the seed to be what it was. Whenever the experimenters want to demonstrate their apparatus to a visitor, they set it going with that particular seed number to be sure of getting a result in a known time frame. They correctly tell the visitor that the input number was derived purely at random.

This experiment demonstrates brute reality in the present dictating how reality shall be in the past, notwithstanding that at the time we experience that past reality, we see it as random. I like to think of this in terms of the Big Bang not being completed 14 billion years ago but still going on today. Radioactive disintegrations in the present day are just the Big Bang working its way towards completion. Just as the reality believed to exist today determines an aspect of the Big Bang, as per the Anthropic Principle, so does reality in our future determine the result of random events in our present day. This sort of determination is of course quasi-causal - or "required to be that way". It is not causal in the usual forward-in-time sense.

(Interestingly, the computer simulation of biological evolution shows that the meringutan does not exist until observed. We imagine the experiment run exactly as before but instead of having experimenters watch a screen, the output is stored on video-tape. Before we view the tape, we ask ourselves whether the meringutan is depicted on it. Some will say that it is indeed depicted there - it is stored in the tape's metal particles and we only have to view the tape to prove it. Others will say that it is not depicted on the tape until we view it, because the word "it" does not reference anything until the tape is viewed. (In other words, a proper question cannot be asked about "it".) In my opinion, the latter view should prevail. The animal does not have a logical impact on our world until it is known to exist. The contrary view - that the animal, unknown to us, is depicted in the metal particles of the tape - is based on notionally seeing the animal but transferring our viewpoint back to an earlier time when we haven't seen the animal and carrying the knowledge of the animal's existence with us. It is a subterfuge we adopt because we do not like the idea of reality - the arrangement of metal particles on the tape - coming into existence upon the act of viewing the tape.)

The identity of objects

Scientists, like all of us, take it for granted that the world is divided into objects. They might have a vague doubt as to where one object ends and another one starts but they assume that the objects themselves know where the boundaries are. They might express that by saying there is a "natural" division between them. They see no problem for the practice of science.

But personally I think scientists should consider how objects get their identity. It is one of those conveniently-overlooked aspects of science like the question of how plausibility judgements fit into science. Taking things for granted could mean overlooking an important principle of science.

Einstein made a significant contribution to the solution of this problem. (The problem of what defines an object, or constitutes the "it" that allows us to talk about it as a single thing.) Around the year 1900 people thought that motion was absolute and considered it valid to ask which of two space ships moving past each other was "really" moving. Einstein invented relativity theory to put them right. I might summarise Einstein's philosophy as follows:

1. Reality is singular not plural. That is, there is a single reality concerning the movement of the space ships. It is pointless asking the space ships about this reality because they are plural.

2. Identify an object (singular) that we can ask the opinion of. In the case of the space ships, this means forming a system (singular) comprising the two ships.

3. Ask the (singular) object what the reality is concerning itself. When we ask this question of the spacecraft system, we get the following answer: "My two spacecraft are moving past each other. The question of whether one of my ships is stationary has no meaning."

And that is the philosophical essence of Special Relativity.

Einstein went on to develop General Relativity where the (singular) object is some arrangement of matter left alone to gravitate and move. Again, the important task is to ask the object what the reality is concerning itself (again, singular). It is wrong to ask an external observer about the reality. The mere mention of an external observer means that the reality under consideration consists of the internal and (a boundary with) the external.

I feel that Einstein's philosophy is relevant to the quantum measurement question, because that question also involves reality and observation. When we talk about "measurement apparatus" we use the word "it" to summarise it. We treat it as a singular object even though it is composed of plural things. We need to ask ourselves what singular thing is to be identified with the "it" that we are talking about.

The standard answer is that this is a question of philosophy which should not be asked of a physicist. Physicists know what defines the apparatus in practice. Although this is the standard answer, physicists are acutely aware of the problem in practice and put great deal of effort into avoiding a cut between a system under measurement and the apparatus doing the measuring.

I feel that avoiding a measuring apparatus cut is like pretending that there are no objects in our everyday environment (i.e., pretending that there is just one all-encompassing object). If we are going to make cuts between the classical objects that populate our everyday world, then we need a procedure for making cuts, and when we have identified that procedure, we can use it to make the cut in the case of quantum measurement apparatus.

In my scheme, objects are simply what we believe them to be. The identity of an object lies in the belief that creates it. Different people will have slightly different beliefs about the object, but since beliefs are vectors, they can be added to form a single vector pointing at the object. The object is whatever is necessary to agree with that belief. It is the same procedure used to select our world from the Many possible Worlds (but here we are just considering an object in our world). Scientists in practice follow my scheme. When they say they "know what defines the apparatus in practice" they are saying that the apparatus is what they believe it to be.

The measuring apparatus in my scheme is our beliefs. That is, our beliefs form a selection environment that determines the result. Of course, reliance on belief means having a theory of the belief phenomenon. That is currently missing from the standard scientific account.

(For the people existing at the time of the measurement, it is their beliefs that determine what is not permitted as a measurement outcome. Apart from that, anything is permitted and this leaves a random component in the result. If we consider people existing in the future - people who in some way depend on the result of the current measurement - the random component for them will be reduced. For the last person in the future, all the apparent randomness in the current measurement will have been converted into determinism.)

(The "environment" that implements selection in Darwinian evolution is also our beliefs, in my hypothesis. The theory of evolution relies on a non-random selection environment to counter the random effects of variation and lead to the production of functioning biological machines. The entire organisation of the biological world around us depends on the specification of the selection environment. What causes this environment is not explained in current science. In my scheme, the environment is a logical one - a logic that includes our beliefs. The products of evolution must be plausible - or logical - for us to see them.)

Knowledge versus belief

Scientists conduct science to obtain knowledge of reality, knowledge being defined as belief in the reality of something, the belief being justified by reality itself (i.e., by evidence). The bare notion of belief is presumed to be outside science, a matter for philosophers rather than scientists. Scientists have an intuitive feeling for what belief means and that is all that is required for the conduct of science.

This reliance on an "intuitive feeling" reminds me of the quantum measurement problem in the early years of atomic physics. A physicist (perhaps Bohr) said it was not necessary to worry about the boundary between material under investigation and the apparatus measuring it because it was obvious where the boundary was in practice!

Just as today we are more precise about that particular matter, I feel we should be the same about the scientific accommodation of belief. If we do not make a proper accommodation of this phenomenon, but continue to rely on it in via knowledge and plausibility judgements, we are logically locating the phenomenon of belief outside the objective world. It raises the possibility that our beliefs constitute a kind of "boundary condition" on the universe. If scientists want a full picture of reality they should take that possibility into account, I believe.

For me, the first step in accommodating belief would be to recognise that belief can be either justified or not justified. We call the two notions knowledge and belief respectively. In my scheme, where things are believed to exist (believed into existence) the belief must be the unjustified sort. If the belief were justified by reality, it could hardly have the role of creating it.

In my scheme it is not possible for a person to know what their own unjustified beliefs are (although they might have an unjustified belief about it). Since the person is defined by their unjustified beliefs, the beliefs cannot be objects to the person. If they were, the person would be an object to themselves, meaning that they were somehow logically outside themselves. That would be incoherent.

My next step would be to consider making the vector defining a belief into a complex quantity.  The idea behind this is that the real part might represent knowledge and the imaginary part unjustified belief. Perhaps the proportion of these components might somehow define probabilities as per the Born rule? I do not know. My feeling is that if something is non-objective, such as unjustified belief, then it should not be represented by a real variable. In the same vein, if a variable is introduced as a kind of axiom then it, too, cannot be real. An axiom cannot be analysed or explained in terms of real quantities. In the non-religious scheme I am considering here, the special role assigned to people (believing things to exist) is a kind of axiom.

To get a handle on the measurement problem, I start with the classical coin flip where the measurement result can only be Heads or Tails (H or T) with a 50/50 probability. I am attracted by the view of quantum theory that gives the basis of the theory as "continuous transformation between pure states". Therefore, in the case of the coin toss, the theory describes a continuous transformation between H and T. The transformation is a kind of rotation through the complex dimension.

(The rotation through the imaginary dimension has nothing to do with the physical rotation of the 2D coin as it is flipped through the third dimension of space. I understand, too, that although the coin flip is "classical", there is no difference from the quantum case. The atomic make-up of the coin is irrelevant to the experiment because all the action takes place in the domain of logic. In that domain, the coin is a pure 2D object, flipping is a logical action, the flipping is perfect - i.e., the odds are exactly 50/50 - and the randomness must be observed to get a real result.)

(There are a couple of reasons why I am attracted to the idea of "continuous transformation between pure states" as a good description of the basis of quantum theory. Firstly, I find a continuous transformation more aesthetic than a discrete step between the possibilities. Discrete steps appear in the standard interpretation of probability, which relates to the long-run result of identical experiments where each experiment is a discrete measurement . I prefer something along the lines of the Bayesian interpretation which has a continuous nature similar to that of rotation through the complex dimension.  Secondly, I see rotation through the complex dimension as a very natural origin of the wave phenomena that we observe.)

Moving on from the flipping of a coin, let us consider a 6-sided die, then an infinite-sided die. I picture each of these experiments as a bit of paper with a random number written on it. We must look at the paper to see what the number is. I picture a container containing all of the non-negative integers (0, 1, 2 ...). We filter a subset of numbers and observe it. In the coin-flip case, we filter the subset  (0,1) with equal weighting. For the 6-sided die we choose (1, 2, 3, 4, 5, 6), again with equal weighting. For the infinite-sided die, the subset is the entire container of numbers, and again, we do not apply any weighting factors.

In each case, the whole subset is presented to the observer. However, the observer lacks the ability to take in more than one number and sees just a single result. (The numbers might be imagined as written on top of each other - in different densities of ink if any weighting applies - but we should be careful not to claim this is the reality.) The "observer" is whoever causes one of the numbers to contribute to the reality of the common world. If a scientist were to see a number on the paper but died before communicating it to anyone, the paper would continue to have the entire subset of (virtual) numbers. There isn't a real number written on the paper until the next person sees it. The requirement for reality (I repeat) is that the number have a logical effect on our world. Whatever is written on the unobserved bit of paper cannot have an impact until seen by a member of our world. Decoherence does not decide the reality of the result because the physical environment that causes the decoherence  does not contribute to the "our" that defines our world. In my scheme, it is coherence that decides the reality - the coherence of everybody contributing to the "our". The dead scientist did not make a contribution and therefore he had no effect on our reality. (The fact that he saw the paper and died before communicating it would itself be a contribution to the logic of our world, but a different one.)

The observers seeing a real number written on the paper will explain the result as "random", because they have accounted for all the non-random factors via the filtering they have applied (their preparation of the experiment). Any number in the subset is logically compatible with their world. But future inhabitants of the world, looking back at this experiment, will have a different opinion. From their point of view, not all of the numbers in the subset can lead up to their then-current environment. For instance, if one face of the infinite-sided die were coupled to an event wiping out all of mankind, the possibility of that face appearing (while compatible with the observers at the time, who would have been obliterated) would not be compatible with observers of the future. For them, wiping out mankind fifty years ago could not have been an option, even if they can imagine it as an option for the people of the past. Applying the Anthropic Principle in this way - extended to the whole of the logical past as I have described - we reach the result that the number seen on the piece of paper is required to turn out the way it is seen to be. Or rather, is required not to be certain numbers. Some randomness can remain for the future inhabitants. It is only for the last future inhabitant of our world that all the apparent randomness of the past will disappear. Then, everything about the past will be determined. The last person will say that everything had to be that way else the present would not be exactly the way it is.

A significant aspect of these experiments is that, in looking at the paper, the observers see just one number and not a jumble of them. If we imagine that all of the numbers are there, why cannot the observers see them?

The answer appears when we scale the experiment up to encompass the whole world. Then, instead of the set of natural numbers we have the set of all possible worlds. The observers have an overriding requirement for one of those worlds to be their reality. They define reality as a single, independent and objective environment that applies to everybody. Its existence is considered to be Truth and it is intended to replace each person's subjective reality. The people insisting on this Truth - each of us individually - want their own reality to apply to everybody else but cannot enforce this. So they invent an external reality (agreeing with their personal view, of course) and claim knowledge of that independent Truth. In that way they encourage others to come around to their way of thinking.

(Since a person is defined by their beliefs, it amounts to getting other people to be them. Or to not exist if they do not want to do that. I note that an independent reality is only possible if there is more than one person.)

My personal picture is as follows. There are an infinite number of worlds "out there" all equally real and fully deterministic. None of the worlds is intrinsically "ours" and therefore the degree of reality that each possesses is 0% (i.e., they are virtual). We humans are defined by our ability to believe things into existence, so if the existence of things is determined by logic, people are accommodated in the domain of logic. (Scientists striving for a mathematical theory of everything are effectively making logic the determinant of what shall exist.) The domain of logic can be pictured as a "platform" lying outside all of the worlds. From this platform we humans unconsciously survey all of the possible worlds and choose one of them to be "ours".  We make the choice by unconsciously believing a world with particular characteristics to exist. The selected world becomes 100% real by that action, by being defined as 100% real. It was fully deterministic before selection, and keeps the determinism when selected, but we humans inject an element of (apparent) randomness into it. We do that to restore logicality in the face of an illogicality that we insist shall be present. The illogicality we insist upon - our bottom line - is that a reality shall exist independent of us saying it. We would like to avoid saying it, but that would mean proving its (independent) existence and that is something which we are unable to do.

And that is about all I can say.

Although my interpretation of quantum theory is in the nature of an hypothesis, there is some evidence in support of it. For instance, given the hypothesis, one could predict that an apparent force of free will should exist. (Resulting from us imagining an independent reality to exist when it does not.) The observed existence of this apparent force could be taken as retrospective evidence supporting  the hypothesis. Benjamin Libet's experiments on free will also support my view. According to Roger Penrose, the experiments of Libet suggest that free will is an unconscious action, and that is a necessary part of my hypothesis.

Other support comes from the general plausibility of the hypothesis. For instance, the addition of vectors is a plausible solution to the "binding problem" in neuroscience, at least philosophically. Similarly, the hypothesis gives a plausible origin for the randomness apparent in our world. (Randomness could be considered an anomaly when the Many Worlds are supposed to be deterministic.) And the hypothesis provides a plausible accommodation of the phenomenon of belief. Admittedly, the accommodation of belief is by way of an axiom, which could be considered cheating. But it is a step forward compared with not attempting any accommodation. The precision of the Big Bang also receives an explanation, as I have described. Although I have not mentioned it, I believe the idea of time also receives an insight from the hypothesis. Time can be seen as an objectification of the logic of the hypothesis. The entire evolution of the world depends on what we unconsciously believe - a subjective process. But we want an objective process. Accordingly, we invent an objective reality, some laws, and a parameter tracking the logical development of things. We call that parameter time. So time is our way of objectifying the logic of our beliefs.

The idea of "explanation" is explained by the hypothesis as a believed account. This solves a nagging problem in the philosophy of science. Traditional science cannot entertain this explanation because there is no accommodation of belief. (But in practice scientists rely on believed accounts.)

In the spirit of Karl Popper, perhaps, it might be possible to prove my hypothesis false. That could be done by proving, contrary to my hypothesis, that an independent reality does in fact exist. To do that, we would need to show that when two people agree that a certain reality exists, they both have the same thing in mind (i.e., they are agreeing about the same thing). Personally, I do not think such proof is possible - and I believe that the existence of free will proves the opposite, that people do not have the same thing in mind. Other possible evidence against the hypothesis would be finding explanations to replace those I have given here. For instance, scientists might find a way to define our world without reference to us. (In the spirit of Einstein, such a definition would need to treat our world as a single thing and not merely comprise a listing of facts pertaining to our world.) And finding another explanation of the measurement problem might obviate the need for my hypothesis. Ideally, such an explanation should be proven true and not rely on plausibility. Perhaps the best refutation of my hypothesis would be to prove that the phenomenon of belief has nothing to do with science. That could be done by finding something about our world which is true but not believed so. A lack of parallelism such as that would show that science does not rely on what people believe but takes an independent approach to the truth. (I repeat that we cannot rely on the truth of an external world being the cause of our beliefs about it, because that would cause all of us to have the same beliefs - and we do not.)

In conclusion

The hypothesis outlined here has explanatory potential and I believe it to be logically sound. My hope is that a theoretical physicist would consider developing it into a theory. There have been various suggestions for that but I am not competent to follow them through. Undoubtedly the main scientific objection to this hypothesis is the special role allotted to people, particularly given the religious associations of this idea. I recall, however, that it was not too many years ago that "non-realism" generated the same distaste. These days, however, some physicists do embrace non-realism - and some even suggest that the only self-existent "thing" is mathematics. I would agree with this last idea, provided some logical way is found to incorporate axioms and initial conditions into the mathematics (or rather, into the logical framework in which mathematics is immersed ). I have tried to do that in this essay. My hypothesis starts with the generation of gross objects as things believed to exist, the decomposition of these objects providing the particles manipulated by the mathematics. The objects believed to exist are the origin of space, and the evolution of those objects is the origin of the physical laws and of time. In that way, the generation of everything becomes a matter of logic. I like that idea because it amounts to a version of the Many (virtual) Worlds theory which has logic as the external observer selecting one of the worlds to be real.

For logical reasons (as I mentioned) it is our unconscious beliefs that select our world, and this introduces an element of subjectivity into the logic. But this is not a flaw. It is a requirement  of any theory of the world that it be not entirely objective, because the notion of objectivity requires an observer to validate it. When we have such an observer, the object observed is not everything. In my scheme the presence of a subjective element allows a comprehensive explanation of "everything". (My scheme, however, relies on the axiom that people have a logical role in the specification of what shall exist.)

Of course, the presence of a subjective element has the disadvantage that the logic cannot be known to be true. Fortunately, it is not necessary to know this so long as we believe it.