Eigenket 151109

A personal interpretation of quantum theory

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

Reality First  vs  Logic First

There are two ways of approaching the world of objects. The difference lies in how we assume objects come to be. The first way is to assume that objects define themselves. In this approach, an object is what it is in itself and there is no need for anybody to see it or know about it for it to exist. It exists in the world of Reality, regardless of whether it exists in the world known to humans. I call it the "Reality First" approach because it starts with the assumed existence of a self-existent reality, and only later proceeds to us humans finding out what that reality is.

The second approach is an assumption that some context defines an object. In other words, an object is not what it is in itself, it is how its context defines it. Heuristically, we can picture a world of elementary particles with some external context deciding where the boundaries shall lie between different things. We habitually assume that a mountain, for instance, is a real object and takes part in a "reality first" approach to the world. But where does the bottom of the mountain lie? At the level of the plain from which the mountain rises? At sea level? On the sea bed? And would it still be considered a mountain by beings on another planet whose own mountains are a thousand times higher?

We might think the mountain's reality is just a matter of our human definitions. But reality as it is in itself is supposed to be independent of humans and their whimsies. If we cannot find a definition totally independent of us - one that the mountain notionally would use for itself and thereby allow it to exist "in itself" - then the mountain is not a real object and does not exist "in itself".

The "context" approach would seem to have advantages. Certainly, when an object is distributed in some way, such as a choir or government, it is hard to remove a human context from the object's definition. But it is true even in the case of mechanical objects. Suppose a computer is analysing a scene of a car parked on the road. The computer might assume that the tyres are part of the road because they are a geometric shape like the road - circular in one case and linear in the other, but both geometrical. And the colour of the road and tyres is the same and unlike the body of the car. So the computer sees a different reality from us. Of course, we humans can program the computer so that it sees things the way we do. But doing that makes the reality depend on us. If the car is to be a real object, it must define itself without invoking observers.

Another advantage of the "context" approach is that it can solve some awkward philosophical problems in science. For instance, when reality consists of things defined by themselves, even God can be real, if he exists. There is no evidence for God, but none is needed in the Reality First approach. Evidence is human-centred, and irrelevant to a reality independent of humans. Reality is what it is in itself. If God is part of that reality, so be it. That is awkward for science. Typically we try to get around it by saying that reality is what it is in itself and how we see it. But that is not entirely coherent. Two different agents defining an object is not much different from having two different definitions of the object. Which definition is the object supposed to obey?

The "context" approach solves that problem because there is only one definition of an object in our world. It is the definition that our world gives it. Other worlds might define things differently and have a different mix of objects. But we are happy to confine ourselves to our world, and define things as they suit us. That is one of the advantages of the "context" approach. Of course, in the "reality" approach we are not allowed to define things to suit ourselves. Instead, objects are supposed to define themselves.

Since our world is an object itself, then, like the objects it contains, it is defined by an overarching context. That context is us.

In the context of our world, an object will conform to the reality we humans observe to exist. Thus the object and how we define it will always agree with each other. There is no problem about which definition the object is expected to obey.

Considering the ensemble of all possible worlds - not just ours - what might be the grand context for everything, in a "context" approach to reality? The answer is logic. The ensemble of worlds will conform to a certain logic, hopefully described by a theory of everything in the Many Worlds approach. Each individual world will conform to a logic. Having logic in charge gives us a simple and intuitive definition of reality: An object is real if it contributes to the logic of the particular world under consideration. Under this definition, God is not a reality of our world, because he does not contribute to our scientific logic. That is true even if (unknown to us) God exists in himself.

It might seem to many people that my definition of a real object - as something that contributes to the logic of our world - is commonsense, and what we already practise. Yes, it is what we already practise. But we humans have an emotional attachment to the idea that reality exists "in itself", and is independent of us and our logic. Accordingly, we shun the idea of logic defining an object and replace it with the notion that an object defines itself.

But if an object defines itself, we should not refer to our world as our world. Our references humans. Objects existing in themselves are supposed to be independent of humans. If we want a "reality first" approach to the world, we need to find some other way of defining our world, without using the word "our". But that seems impossible.

We might hope to avoid the word our, in the definition of our world, by saying the or using some other construction. But even the is an implied reference to the world we see around us, our world. And we should not refer to "the" world when there are a multitude of logically possible worlds. These problems disappear when we accept that an object is not what it is in itself, but whatever its context says it is.

I prefer the "context" approach for aesthetic reasons. First, I am uncomfortable with the idea of objects defining themselves when the world is a sea of identical, structureless, elementary particles. Electrons, for instance, are all the same and do not have an internal structure to define one versus another. For an electron to exist in reality - to have a notional self allowing it to say that it exists in itself - there needs to be some way of referring to it which does not involve us humans. But without an internal structure, one electron is identical to another. This is not a problem in the context approach. Our human context can have lots of instances of the electron. The instances are different not because there are many electrons (there is still just the one) but because the idea of many copies of it fits into our human context.

I am also uncomfortable with the basic idea of an object defining itself. (Regardless of how we might express that.) The object does not exist to do any defining. It only exists after the defining has been done.

Scientists in practice use the context approach. They might express the results of their experiments in terms of Reality, but in logical terms an experiment is just a context for seeing what exists in it. So the context comes first. The reality we observe depends not only on what the experiment produces but on what experiment we choose to conduct. Science seems to be one big context for determining what objects shall exist alongside the objects we have already accepted as existing.

It would seem scientists construct reality by their experimental contexts. But they prefer the idea that reality is independent of their constructions. They assume science finds out about reality, rather than creating it. Any given page in the scientific story is considered an approximation to how reality really is "in itself". I find it uncomfortable that scientists make such an assumption when their story is context-based. Surely a context-based definition of reality would be preferable.

So let us take the context approach. The question then is what scientific context might be the determinant of reality. Obviously the scientific context cannot be one of objects. The context is responsible for objects so cannot itself be defined by them. Objects will only come into existence when the context creates them.

If the context is not one of objects, what else could it consist of? Again, the natural choice is logic. Under Context First, logic specifies what shall exist. This is not to say that real objects exist and we learn the logic of how they came into being. No. That would be Reality First. The uncomfortable truth of Context First is that real objects do not exist. They do not exist because real means existing in itself, and that is different from existing according to a context.

For instance, if the context says an object no longer exists, then it does not. In the Reality approach, however, if the context says that the object no longer exists, the object could say to itself that it knows differently. "You say I do not exist, but I say I do. And my opinion trumps yours because I define the reality of myself."

So those are the two approaches to the world of things. I call them Reality First and Logic First, respectively. To repeat, Reality First starts with an assumption that a real world of independent things exists. Logic First starts with an assumption that a logical context comes first, then the context specifies, or determines, what objects shall be contained therein.

The world will appear to us exactly the same in both approaches. The difference is not in how things appear but in how the world of appearances came into existence. With Reality First, objects are a just-so observation. We conducted experiments to see how the world was, and that is what we saw. But with Logic First, there is a logical reason for the world appearing the way it appears. And it is not incoherent to suppose we can learn about that reason. Learning that would allow us to answer the question of why the world is the way it is and not something different. The "why" question is not addressable under Reality First.

Since a vast number of logically possible worlds could exist, we will concentrate on just one of them, our world. Since our is a reference to us humans it is likely that the logic of our world will involve us. Human involvement could be avoided if we were able to define or refer to our world without using our, but, as I said, it seems impossible.

Reality First starts with a near-infinite number of facts representing how reality is supposed to be constituted, and science is the process of finding out what those facts are. I am inclined to see such a starting point - a multitude of trivial facts - as inelegant. Originally the facts of science related to gross objects, later to molecules, then atoms, nuclei, and quarks - and now, possibly sub-quarks. It seems such analysis will never stop. There will never be a point where we will know why the world is the way it is and not something different. The ultimate reason for the impasse is that the facts describing an objective reality cannot logically include whatever it is that makes objective reality into the object it is. It is impossible for observed facts to explain the observation process.

Logic First, on the other hand, can be pictured as an infinitely sharp point rather than a collection of just-so truths scattered around. It is a sharp point because at its simplest the logic might just be that the world exists. Then that truth becomes the context for further truths, and we proceed in that way to find out why the world has to be the way it is.

(I picture the two approaches like zeros and poles in the complex plane. Reality First is like a zero and defined by all the things it is not. That is to say, it is defined by things. The contours we draw to indicate a zero extend to infinity and involve every point in the plane. But Logic First is like a pole and is located at a point. In contrast to a zero which is defined by every point in the plane, a pole defines one point absolutely. It defines itself. I am intrigued by Liouville's theorem which says the complex plane must have at least one pole - possibly at infinity - otherwise the entire plane is featureless - at least, that is my understanding. I have an image of reality, in a Reality First approach, as deriving from an infinite number of trivial features, whereas in a Logic First approach, reality derives from just one feature of infinite significance.)

Logic First has the disadvantage that we cannot obtain knowledge of reality. Knowledge of reality is out of the question when reality does not exist. The reality uncovered by science is only a story deemed true in our human context. We should not imagine that it represents anything more than that, unless we can prove differently. However, we humans are fond of the idea of knowledge and seize upon the idea that the scientific story we put together is not just a story but is Real. As someone said, "Reality is so important to us that if it didn't exist we would create it." It seems that we have done that.

But we can balance Logic First's inability to provide knowledge with its ability to explain the world. Logic First provides a trail of logic saying why the world appears the way it appears. Reality First cannot do that because it does not provide explanations. The ultimate explanation of the world in Reality terms is that "it just is". Or that we observed it and that is how it was seen to be.


Given a decision to adopt the Logic First approach, my hypothesis is that a particular logical feature connected with man sets the appearance of our world. The logical feature I have in mind is an extension of the Anthropic Principle which says that man's existence requires the past to be constituted a certain way. According to the AP, various features arising from the Big Bang were logically required to turn out the way they did, otherwise man would not exist and be reading these words. I extend the Anthropic Principle in two ways. First, I make it apply to all features of the logical past, not just the Big Bang. Second, I replace man's bare existence with man's detailed existence. It is man's extremely particular existence in whatever he calls the present moment that requires the past to be exactly as it was.

Many scientists rightly reject the Anthropic Principle. Under Reality First, it is incoherent to suppose that man's later arrival on Earth can affect the intrinsic reality of objects in the distant past. Under Logic First, however, objects of the past have no intrinsic reality but are a construction of the present. Therefore it is quite possible that man is involved in their construction. (We can see some of man's construction in the objective existence of cars and computers, for instance. I repeat that anything objective is in the logical past.)

To make this work, I need to define man in a certain logical sense rather than by neurons or other hardware. In my hypothesis, the existence of man's bodily hardware, like the rest of the world's hardware, depends on a context and that context involves man. It would be incoherent to suppose that such hardware, having been created by man, could turn around and create man.

Defining man in the logical sense that I propose allows man-the-object to be produced by evolution as commonly believed. But the brute existence of man, defined in that logical sense, cannot be explained. It is a kind of axiom, or just-so initial condition.

However, the idea of having man as an axiom has a couple of things going for it. In my hypothesis, the logic defining man has the character of a vector, and vectors can be summed to a resultant replacing the component vectors. Thus the just-so initial condition of 50 billion vectors (an assumed number for people who have ever lived or will live) can be replaced by a single vector pointing at our world. This defines the word our, and picks out our world from the ensemble of other logically possible worlds. It also makes the origin of our world a single thing, a "point". I consider this more aesthetic than the plethora of just-so scalar facts that constitute the starting conditions of Reality First.

So how do I define man? By what he believes to exist. Man's belief is a vector directed at the thing he believes to exist (or believes into existence). A person has many beliefs, all of them represented by vectors. They can be summed to a resultant vector representing the unity of the person. It is that resultant vector that defines a person. The resultants representing everybody who will live or who has lived can in turn be summed to a grand resultant. This points at the world believed to exist. It is the origin of our which picks out our world from the ensemble of all logically possible worlds.

Traditionally (under Reality First) a person's belief about something is assumed to be caused by an arrangement of the person's neurons. (Or "just is" that arrangement.) But under Logic First, belief stands alone in the domain of logic. We can associate a belief with an arrangement of neurons if we like, but the belief will not be caused that way. It remains "free". I note that under Reality First the unknown facts of reality are free to be whatever we eventually observe them to be. So both approaches have a free parameter, not just Logic First.

It is a matter of starting points. Either we assume a reality comprising a great number of facts, or we assume a logic involving man's beliefs (in my hypothesis). The ability to assume is accommodated by the second option, but not by the first. That suggests we should adopt Logic First. However, man has a preference for Reality First because it allows him to have knowledge. That is, he prefers to assume a starting point of reality. To get around the problem of being able to assume things, he assumes that his preferred starting point exists independently of his assumptions. I am inclined to think some dodgy logic lies in that, but it is avoided under Logic First

Traditionally, scientists have tried to remove human belief from their discipline and replace it with knowledge caused by evidence, caused in turn by reality. This is a reasonable approach, given a Reality First starting assumption. But it raises a couple of questions. First, if Reality is a single invariant truth, why do people have different beliefs? If we are all bathed in the same reality, it should cause all of us to believe the same. We can get around this by assuming people have "free will" to defy reality, but it is not an elegant solution. Giving Reality First a free parameter in the form of free will is not unlike making belief free under Logic First.

Second, if people's beliefs are outside science we should expect the scientific community to produce truths that, for some unknown reason, are not believed true by the scientific community. That never seems to happen. Scientists never seem to announce truths that they do not believe in. It seems odd that two independent quantities - reality and our scientific belief about it - should track each other so precisely. Perhaps we can explain it via the reality-evidence-belief chain of causation, but it brings back the problem of people being able to defy reality with their magical free will.

Under Logic First, where the logic of the world involves man's beliefs, the reason for reality and scientific belief tracking each other is simple. What scientists believe defines reality. The world is not different from what it is believed to be. (Try to prove the contrary.) The vectors representing each person are summed to a resultant pointing at the world believed to exist. Whichever direction that resultant points towards - whichever world it points at - that is the world determined to exist. We call it our world.

As a point of clarification, the beliefs that define a person must be their subjective or unconscious beliefs, and not what the person says or imagines they believe. Anything objective that we can have knowledge of or talk about is created by being believed to exist (under my hypothesis). This applies to beliefs-as-objects as much as to obvious hardware objects. It follows that the beliefs doing the creating cannot be objective. They must be subjective or unconscious. At least, they must not have the character of something factual which can be talked about. Of course, we might have some belief about our beliefs.

My hypothesis, therefore, is that man has a logical role in determining reality via his unconscious beliefs. Those beliefs are vectors and therefore capable of being summed into a resultant. The summation allows us to talk about belief as a quantity rather than a thing. The unconscious, non-objective, nature of belief stops it from being represented by a real variable in the equations of physics, but I do not rule it out from being represented by a complex variable. I will suggest an approach to this end (but I do not have sufficient knowledge of physics to carry it through to a conclusion).

The "NEV" principle

In logical arguments, the principle of "no exterior viewpoints" prohibits the introduction of a meta-viewpoint able to see the truth of a proposition that cannot be proved. The NEV principle says that the truth of the proposition must be established within the system.

Many people have an emotional attachment to a favoured "truth" and will embrace any means to establish it. If they import an outside viewpoint to do this, then according to the NEV principle they are not arguing logically and we should not accept the proposition as true.

A simple example is a religious person trying to demonstrate the truth of a religious text. The person being preached to cannot see the truth of the text, but the religious person invokes God as an exterior validating viewpoint. The argument between the two parties would be valid if both accepted the role of God, but it is invalid if one party does not.

As a more sophisticated example, suppose we take an infinite number and add 12 to it. Is the resultant number bigger? Mathematicians say no, but a non-mathematician might argue as follows.

"In reality the new number is bigger. We even know by how much: 12. It's just that we cannot prove it."

Here, the exterior viewpoint is supposed to be that of "reality" reporting the truth concerning itself. The person feels that the new number is bigger and quotes reality to support his view. But mathematicians are not concerned with what reality is or isn't. They confine themselves to what can be proved within their system. According to the NEV principle, the mathematicians are acting correctly, the non-mathematician is not.

Does an atomic particle have properties such as position, momentum, spin - even existence - before it is observed? Many scientists have an emotional attachment to the idea of an external reality and respond as follows:

"Of course the particle exists before we observe it. We might not know what spin it has before we look at it, but it has a definite spin. The same is true for position. The particle is definitely somewhere before we observe it."

But atomic experiments appear to show that a particle does not have a definite existence until it is observed. In an ideal world, people would accept this evidence. But many of us have an emotional attachment to the idea of a reality that exists independent of us. Accordingly, we contrive an external viewpoint - credulity, in this case - to support our opinion. We say of course the particle pre-exists. This invites other people to see that the alternative is not credible. A reliance on what is credible would be acceptable if credibility were accommodated within the scientific system. But it is not. Therefore, when a scientist relies on what people believe or find plausible, they are appealing to an external viewpoint and violating the NEV principle.

Many scientists now accept that atomic particles do not have a definite existence until they are measured in some way. They accommodate this apparent truth in the same way that mathematicians accommodate reality - by not concerning themselves with what is real but confining themselves to what can or cannot be proved within their system. ( "Shut up and calculate.")

However, when atomic particles are amalgamated into macroscopic objects such as trees and buildings, scientists are sometimes forced into deciding  whether or not such gross objects are real before they are observed. Since the scientists, like most of us, have an emotional attachment to a reality independent of people, they want the answer to be yes. Accordingly, they break the NEV principle and assume that there is some external viewpoint, presently unknown to them, which sees that a definite reality does exist even if not yet observed. This is faulty reasoning according to the NEV principle.

Many scientists have the same attitude to the Anthropic Principle. They have a distaste for the AP because it suggests man has a role in the creation of reality. So they invent a notional viewpoint that can see the world independently of man and thereby avoid the AP's logic. This notional viewpoint is not defined or discussed, it is just assumed. According to the NEV principle, scientists who take that approach are not acting logically.

For students at a college, it might be acceptable to quote an absent  teacher as an external viewpoint validating some proposition, but it depends on whether the teacher's viewpoint is accepted by the debaters. If it is, the teacher is effectively inside the students' logical system and it is valid to quote him or her. If the students do not respect the teacher's opinion, then it is not valid to invoke it, according to the NEV principle.

The way to avoid breaking the NEV principle is to set up your axioms and initial conditions and confine yourself to what can be proved on that basis - as mathematicians do. The NEV principle can be seen as extending the logical precision of mathematics to the rest of science.

Since breaking the NEV principle is "a bad thing", perpetrators try to hide their tracks. For instance, they might make an explicit assumption at the start of their argument, then quietly lead the audience into thinking that it was not an assumption but a statement of truth. Another popular way is to make an assertion but present it as a truth. Another is to assume a truth to be "obvious". This is particularly effective if the speaker has a high status.

If all else fails, one can resort to ridicule. Here is the current  de-facto chief expert in the quantum physics section of Physics Forums using ridicule to put his point across:

"Take for example recording a double slit experiment into computer memory. You disassemble the apparatus, even destroying its parts, and say, 10 years later, you take the ram to a computer science class.

"You then claim, since it hasn't been observed by a conscious observer,  [that the data in the ram chip isn't] real until someone reads it on a computer screen or similar. You can copy it, disseminate it, do whatever you like to it, but until a conscious observer actually views it it's not real.

"Don't be surprised if they all leave laughing their heads off, and as you leave, dejected, some nice men in white come along."  [bhobba: physicsforums.com "Busting the myth of the observer: the double slit experiment" 2014-08-14]

I urge respect for the NEV principle whenever one has an emotional attachment to an unproved proposition. Instead of introducing an exterior viewpoint to justify a position, one should either enlarge one's set of axioms or accept the default position - that the unproved proposition should not be treated as true.

As a help towards this goal, anybody tempted to introduce an exterior viewpoint should consider replacing their preferred exterior viewpoint with a deity. If they are not happy to accept God in that role, they should be equally unhappy to accept any other non-provable viewpoint. Bhobba, for instance (in the spirit of Bishop Berkeley, perhaps) could have replaced his last paragraph with "That is all nonsense, of course. God can see that the data in the RAM was real right at the start.")


In a Logic First approach to reality, where a logical context decides what shall be real, reality may be defined roughly in terms of 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 my 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 is supposed to exist "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. That is because the unseen object - which cannot be predicted in any way - does not make a contribution to the logic of our world until we know about it. It might make a logical contribution to some other world - its own, perhaps - but that is not relevant to the constituents of our who define "our" world.

The Anthropic Principle

As generally understood, the Anthropic Principle purports to explain why early events 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 in the present day, and would not be considering the question of why early events turned out that way. Given the brute fact that we are considering that 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  soft 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 who entertain the Anthropic Principle typically avoid these problems by postulating a plethora of other worlds from which our world is a random selection. But 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-status as ours. This conflicts with my definition of reality. In my hypothesis, those other worlds should not be considered real by the inhabitants of our world because those worlds do not have a logical impact on ours.

(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 chooses 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 - a scientific "God of the gaps". We invent it 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.  The assumption of an unknown external selecting agent contradicts the NEV principle. The Anthropic Principle avoids the problem by openly acknowledging 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. If we introduce random selection to avoid people doing the selection anthropically, but then define our world in terms of our, we are still referencing the selection to us, and the problem remains. The problem also 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 (albeit unwittingly). There is some evidence for the involvement of people in specifying reality. Some of it - the existence of cars and computers, for example - is logically caused by us. Why not all of it? Where is the dividing line?

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 as real, physical objects like cars and computers, there would be a logical problem with having people as the determinants of real, physical objects. That is why I define people a different way.

I generalise the Anthropic Principle 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 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. It is not limited to a vague possession of consciousness. My definition of people in terms of vectors representing unconscious beliefs 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 - the question of why the Big Bang was so improbably constituted. Roger Penrose says that the Anthropic Principle, when referenced only to the existence of beings with consciousness, falls short of explaining the extreme precision of the Big Bang by a factor 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 particular way compatible with the characteristics of the particular person. To accommodate all these "requests", the Big Bang is required to be exceedingly particular, and this uses 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. It implies that the essence of the person lies elsewhere of their beliefs, as the possessor of those beliefs. The physical location of this essence - of whatever defines the person - has so far eluded science.

But 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. A person has many beliefs and they can be summed into a single resultant vector replacing the component vectors. The resultant vector, being a single thing, is a good candidate to represent the unity of a person. (Philosophically, this might be a solution to the "binding problem" in neuroscience, perhaps.) Thus the essence of a person - the thing which determines their identity - is a vector in a 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 religion is appropriate to a scientific description of the world. Accordingly, I limit myself to borrowing the idea from religion that man is defined by his beliefs and make this a kind of axiom in my interpretation. I justify this by the utility of the idea, and also for the following reason. If a person is defined by their beliefs summed into a resultant, then those resultants (representing the 50 billion people who have ever lived or will live) can in turn be summed into a grand resultant pointing somewhere. It seems natural to identify the direction of the grand resultant as pointing at 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 (where there are a plethora of worlds and our world is a random selection from them).

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 - that would require proof) 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 actually the common reality, a supposedly independent entity applicable to everybody. Each person imagines that their belief in a private reality is actually knowledge of the public reality. This leads to a simple explanation of human free will, as follows.

If there were a single reality applying to everybody, then, in the absence of free will, everybody should behave identically. That is a consequence of every person and their behaviour being determined by a common 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, and behave just like me." They conclude that the other person possesses a mysterious "force" that allows them to defy reality.

We call that presumed force free will. Of course, the reason that the other person is acting strangely is that he or she is not bathed in a universal world but is interacting with a private world of their own.

The use of the word force in connection with free will is frowned upon in science, but it does seem as if free will logically causes physical matter to be moved around - when we manufacture computers and cars, for instance. The explanation here is that human free will is a pseudo-force arising as compensation for an erroneous view of the world, the erroneous view that an independent world of reality exists when it does not. I picture the force of free will 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 throw of 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 our world and has a real effect on things. In my example, it decides the winner of the sweepstake. Before it is observed, the winning face does not contribute to the logic of our 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 dice-throwing 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. Thus logic prevails over hardware.

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. 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 constituent 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 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 - its existence cannot be communicated - then it defaults to non-existence.)

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 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 considered a purely random number. Just as the 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 it is supposed to exist 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 would require observation before his existence could be considered a reality, 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. Man, defined by his beliefs, is domiciled in the domain of logic. Thus he is logically outside physical reality and can choose (or unwittingly 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. And, as I said, 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 all 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. Before that time, scientists resolutely insisted that waves required a medium for their propagation. When experiments suggested that a medium was not necessary for wave propagation, Einstein dropped the idea.

Today, we have a different scientific preference - that an unseen world of reality exists in itself. Our experiments suggest that such a world does not exist, and my personal response is to accept that. It raises the question of how the world around us comes to exist, and my hypothesis is that it is believed to exist (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. 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. It 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. I note 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 had 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 all those private realities is traced back into the past, they start to conflict with each other. Since reality is conceived to be logical, such conflicts cannot exist. We resolve the contradiction by assuming that reality has a randomness component that dissolves people's histories into unknowability at various points in the past. 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 when it does not. 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 an unnecessary 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 our world, the other is the new reality itself. In setting up the experiment we do not know what the reality will turn out to be, only that it will be new. According to my definition of new, 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 would determine - or believe - to be true). Personally, I see the Big Bang as part of the scientific narrative that we are making up. Since none of us is privileged to decide the narrative, 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. 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, evaluated at the death of the last person, 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 independently of us (i.e., is not really real). Let us suppose that the random disintegration of a radioactive atom is used to decide some real event occurring some time after the atom's disintegration. The brute reality of that future event determines, in a soft 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 but who were saved by the cure, 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, as championed 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 pseudorandom 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 on the screen 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 the earlier 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 soft causal, or "required to be that way". It is not causal in the usual forward-in-time sense.

(As an aside, 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, which adheres to the NEV principle, 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 that breaks the NEV principle. We do it 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 take it for granted that the world is divided into objects. They might have a doubt as to where one object ends and another one starts but they assume that the objects themselves know where their 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 more thoroughly 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. Again, the important task is to ask the object what the reality is concerning itself (again, singular). It is wrong to imagine what an external observer would say about the reality. The assumption of an external observer breaks the nev principle, and suggests that the reality under consideration includes 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 the apparatus as a singular object, notwithstanding that 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 a great deal of theoretical 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 resultant 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. Our beliefs form a selection environment that determines the result. Of course, reliance on belief means having a theory of the belief phenomenon, 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, rather than what shall occur. Apart from that, anything is permitted and this leaves an apparent 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 this selection environment. What causes it to have such beneficial characteristics is not explained in current biological science. In my scheme, the environment is a logical one - a logic that includes our beliefs. The products of evolution must have a plausible, logical, fit with what we believe to be reality. If something extremely weird were to evolve that did not fit into our reality, we would not see it. It would not exist in our world.)

Knowledge versus belief

Scientists conduct science to obtain knowledge of reality, knowledge being defined as belief in the reality of something, where the belief is 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 the belief phenomenon, but continue to rely on it via knowledge and plausibility judgements, we are logically locating the phenomenon of belief outside the objective world and violating the NEV principle. 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 - called knowledge and belief respectively. In my scheme, where things are believed to exist (believed into existence) the bare notion of belief must be the unjustified sort. If it were justified by reality, it could not have the role of creating reality.

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 the matter). The person is defined by their unjustified beliefs and therefore their beliefs cannot be objects to them. 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 in accommodating belief within science would be to consider making the vector defining a belief into a complex quantity.  The idea behind this is that the real part of the vector 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 non-religious scheme I am considering here, the special role of people - unconsciously believing things to exist - should be represented by an imaginary variable.

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 with a 50/50 probability. I am attracted by the view of quantum theory that gives the basis of quantum theory as "continuous transformation between pure states". In the case of the coin toss, the theory describes a continuous transformation between Heads and Tails. 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 discrete steps between possibilities. Discrete steps appear in the standard interpretation of quantum probability, where probability is the long-run result of identical discrete experiments. 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, coupled with Euler's formula, 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. Instead of a coin or die, it is easier to picture each experiment simply as a piece of paper with a random number written on it, and we must look at the paper to see what the number is. The piece of paper depicts a filtered subset of the non-negative integers (0, 1, 2 ...). To represent the coin-flip case, the filtered subset is  (0,1) with equal weighting. To represent the 6-sided die, the filtered subset is (1, 2, 3, 4, 5, 6), again with equal weighting. To represent the infinite-sided die, the subset is the entire container of numbers excluding 0, and again, we do not apply any weighting factors.

In each case, the whole subset is presented to the observer. However, the observer wants a single world of reality and therefore sees only a single number on the paper. (To see all the numbers at the same time would not fit into our reality, particularly in the case of a physical die.) The observer is whoever causes the number 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 on it. There isn't a real number (i.e., with 100% reality) 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 it does not reference our world. (Decoherence is only coherent in Many Worlds interpretations, in my opinion.) In my scheme, it is coherence that decides the reality - the coherence of everybody referenced by the our in our world. The dead scientist did not make a contribution and therefore had no effect on our reality. We had to wait until the next scientist saw it. (The fact that the first scientist saw the paper and died before communicating it would itself be a contribution to the logic of our world, but a different one from the revelation of a number on the paper.)

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 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, 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. It is this overriding desire for Truth to be singular that makes us see only our world. It is also why we see only a single number on the paper.

(The individual people insisting on this Truth want their own reality to apply to everybody else. They cannot enforce this so they invent an external reality - agreeing with their personal view, of course - and claim to have 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 trying to get 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, as there is no way to show a lone person that reality was different from what they believed it to be.)

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." Therefore the degree of reality that each of those real worlds possesses is 0% (i.e., they are all virtual). We humans, accommodated in the domain of logic and outside the worlds, unconsciously survey them all and choose one 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. We define it 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. The randomness accommodates the private worlds of other people, as I have described.

Ultimately, the randomness and other imperfections in our world arise from our wanting a reality to exist independent of us. We are unable to prove such a reality exists so we assert it. That is an obvious illogicality when we define reality as not needing assertion. This logical flaw permeates every aspect of our construction, causing our reality to be less than ideal.

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 support my view. According to Roger Penrose, Libet's experiments suggest that free will is an unconscious action - and that is also 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 a kind of axiom, 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. I believe the idea of time also receives an insight from the hypothesis. Time can be seen as an objectification of the logic described by my hypothesis. The entire evolution of the world tracks our unconscious beliefs, a subjective process. But we want an objective process. Accordingly, we endow our objective creation with some laws and a parameter tracking reality's logical development. We call the parameter time. Time is our way of objectifying the logic of our unconscious beliefs.

The idea of "explanation" is explained by my hypothesis as a believed account. This solves a nagging problem in the philosophy of science. Traditional science cannot entertain "believed account" as the meaning of an explanation because there is no scientific accommodation of belief, even though scientists in practice 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 my 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.) Finding another explanation of the measurement problem would be another way of avoiding 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 or logic. 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 at heart. My hope is that a theoretical physicist would consider developing it into a physical theory. There have been various suggestions for how that might be done, 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 with such an idea. I recall, however, that it was not too many years ago that "non-realism" generated the same distaste. These days, non-realism is a respectable philosophical position embraced by some physicists. Some even suggest that the only self-existent "thing" is mathematics - and that is a far cry from the solidity of physical particles.

(I would agree with reality being nothing more than mathematics if some logical way could be 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 the objects providing the particles manipulated by the mathematics. The gross objects believed to exist are the origin of the space between them, 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 in which logic is the external observer selecting one of the worlds to be real.

For logical reasons, as I said, it is our unconscious beliefs that select our world, and this introduces an element of subjectivity into the logic. But it is not a flaw. It is a requirement  of any theory of the world that it not be entirely objective. That is because the notion of objectivity requires an observer to validate it, the observer being outside the thing observed. The existence of such an observer means that the object observed is not everything. In my scheme I specifically include a subjective element (the role of man as an axiom) and this allows a comprehensive explanation of "everything".

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