Eigenket 170105

A personal interpretation of quantum theory

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

Does Reality Exist?

Possibly not. Something we call reality exists, but whether it has the credentials to be true reality is doubtful. The required credentials are self-existence and independence from man. Unfortunately, there is evidence to suggest that what we call reality does not possess those credentials. In particular, it seems to depend on man. If the evidence is confirmed, reality exists at man's unwitting behest rather than "in itself". So when defined in terms of self-existence, reality appears not to exist.

As well as the evidence seeming to implicate man, there is another problem. It concerns our logical conception of reality as a singular rather than plural entity. We conceive reality as existing in itself, a body of truth independent of man's whimsies, the sum of everything. It is what a notional viewpoint outside reality (such as an equation giving a Truly Grand Theory of Everything) would see if it could look at everything objectively.

All those concepts are singular: body of truth, sum of everything, existing in "itself", an equation, "it". Even the words reality and world are singular.

Given that that our fundamental notion of reality is singular, the question arises whether it is possible to form "the sum of everything". Until about a century ago our answer was yes. We were unable in practice to form the sum of all things (to write down a Truly Grand TOE, for instance) but it was conceptually possible. There were no logical strictures preventing it.

But in the last century or so we have discovered that forming the sum of everything is indeed impossible. This has arisen from the discovery that randomness is a fundamental component of everything. Forming the sum of everything - by looking at the objects around us and extrapolating to "all" - is not possible when there is a component of randomness in each object. It is like forming the sum of a mathematical series when the terms are ill-defined.

We might imagine that the sum of everything exists even when it is logically impossible to form it. But a mathematician would not agree. Only an incompetent mathematician would say "Of course the sum of the [ill-defined] series exists. It is all the terms added together". Likewise, a physicist might be deemed incompetent if they insisted that reality was the sum of unknowable things.

In my view, we should simply accept the scientific phenomenon of randomness and conclude that a self-existent reality does not exist. And neither do real objects, since they are part of reality. Objects might exist in a person's private view - just not in reality.

If nothing really exists, how is science to proceed? Descartes said that we can be sure of one thing: our own personal existence. I think that is still true today. Descartes might have gone off the rails immediately after his famous pronouncement, but "I exist" is still a reasonable starting point for us.

So that is roughly the starting point I adopt in this interpretation of quantum theory. Each person believes themselves to exist. But of course I need to say what I mean by person. I define a person as a viewpoint of reality. (And conversely, I treat a viewpoint of reality as a person, though not necessarily a real one.) The viewpoint I have in mind is logical rather than physical.

Defining a person in this way - as a logical viewpoint - is the closest I can get to a scientific definition of 'person'. It largely avoids mystical connotations and skirts the difficult question of how a singular entity is supposed to arise from the plurality of bodily parts that we normally associate with a person.

My definition also has the following advantage. We can identify the viewpoint of reality that we call a person as having the character of a vector. It has the enormous benefit of allowing viewpoints of reality to be added together. The vector exists in a logical context rather than in time or space. We cannot base our theory of the world on time and space when the existence of reality is in doubt. A logical context avoids this problem. My assignment of vectors does not apply to people alive at a particular moment but to everyone who has lived or will ever live - say 50 billion people.

Vectors have the useful property of being summed into a single resultant encoding all the information in the input vectors. This sum is a "single thing" and capable of defining the world as a single thing for science to examine. In this way we generate "reality" as the sum of everything. I put reality in quotes to indicate that it is not quite the way reality is customarily defined. Here, reality exists not because it exists in itself but because there is a vector pointing at it. Since this vector is not the same as any individual person's vector, it is to some extent independent of individual people. That independence makes my reality somewhat consistent with that assumed by science.

The adoption of a "philosophical" context for science might be distasteful to some scientists, but it is possible that the vector in question can be represented by a variable in an equation and thereby prove useful in conventional science. I will discuss the substance of the vector later, but its direction is easily understood. The vector points towards reality. A person's individual vector points at the reality he or she sees to exist, and the sum of those vectors points at the common reality that we see to exist.

So that is the first of two foundational principles in my personal interpretation of quantum theory: Man is implicated in reality.


The second of my two principles relates to determinism. Determinism is difficult to accommodate in current science because randomness is an established scientific phenomenon. But in my interpretation I am free to adopt determinism in the individual realities that people see to exist. The sum of those viewpoints will also be deterministic, and will point at a deterministic world in common. This trick hides randomness in the difference between people.

The trick banishes randomness but also explains why we see randomness to exist. Shortly I will describe how this works. Current science does not attempt to explain randomness but either accepts it as brute reality or attempts to explain it away. The Many Worlds conception, for instance - at least as I understand it - makes all of the worlds deterministic with our world being a random example from them. Doing that does not explain the scientific phenomenon of randomness.

My approach is equivalent to evaluating the world's randomness at the end of time. Radioactive disintegrations, for instance, are seen in terms of how they actually did turn out and not in terms of observers' puzzlement at the time the decay occurred.

So that can be considered my second foundational principle: strict determinism

The Anthropic Principle

I now make use of the Anthropic Principle. This principle gives a human-centred reason for events in the past to turn out the way they did. Unlike conventional scientists, I am permitted to make use of the Anthropic Principle because it is validated by my first axiom.

I start by generalising the Anthropic Principle, which is normally limited to cherry-picked events in the early history of our universe. My generalisation is to make it apply to the whole of the past - even to one femtosecond ago, for instance.

And normally the principle is referenced to the vague existence of mankind in the future. I generalise the Principle so that it applies to each individual person exactly as they are at all future moments. This precision is possible because the vector defining each person is capable of very detailed pointing in the space over which it ranges.

Thus my generalisation of the Anthropic Principle amounts to the following: The past needs to be exactly as it was for the present to be exactly as it is.

This is of course determinism. Man is not explicitly mentioned but is implied by the word present. The realisation that the generalised Anthropic Principle is a kind of restatement of determinism will, I hope, remove some of the distaste that scientific people have for the Principle.

My generalisation of the Anthropic Principle makes it apply to the logical past, and not to a physical past measured by time. Therefore it does not have an arbitrary definition for the past, such as earlier than one femtosecond ago. An object is put into the logical past by whatever subjective viewpoint makes the object into an object.

The Meaning of Quantum Superposition

Let us now consider the Schroedinger Cat superposition. We will conduct the experiment in Bermuda and replace the cat with a butterfly. If the box is opened and the butterfly is alive, it flaps its wings and triggers the complete extinction of man in 30 years. In 50 years, the people say "The butterfly had to die. We would not be here if it had survived." So what we thought was random turned out 50 years later to be (in a sense) "determined". I prefer to say "required to be that way by the Anthropic Principle". But it amounts to determinism when we allow cause-and-effect to be bidirectional, which is what the generalised Anthropic Principle does.

It leads to the following explanation of quantum superposition. Superposition, along with apparent randomness, is a place-holder for the future. (Or a place-holder for subsequent logical development, which avoids the mention of time.)

It is not necessary for the people to know about the butterfly or the epidemic that it would have triggered. Nor does the event need to be as momentous as the entire extinction of mankind. The people need only accept that based on logical grounds the past had to be exactly the way it was for the present to be exactly the way it is. Again, the "present" is peculiar to each person. We could say that people unwittingly select the present and that selects the past. (Actually, the past must allow each person's present to be exactly as they see it to be. Exact bi-directional determinism will not apply until the end of time.)


What is the substance of the vector that defines each person?

I have defined a person as a viewpoint of reality. However, a viewpoint is more like a scalar than a vector. We can get a vector by treating the person's viewpoint of reality as seeing reality into existence - in other words, creating reality. Thus the substance of each person's vector is their ability to create their own reality. This does not occur by physical means or conscious selection. The person merely sees a particular reality to exist, and a particular personal reality tags along. It does that because there is no way that the person can prove a "true" reality to exist that is different from the reality they see.

Of course, when a person "sees" a particular reality to exist, they could alternatively hear it or touch it or use some other sense - or none at all. It is somewhat illogical to base "the seeing of reality" on eyes or other senses when those physical organs do not yet exist. Our starting point is a collection of vectors: physical reality, including eyes and ears, follows later. ("Later" refers to a logical progression, not time.)

To avoid this illogicality we can replace seeing, hearing, and so on, with believing a certain reality to exist. The substance of the vector, therefore, is the person's belief in whatever reality they see to exist. The direction of the vector is towards whatever they believe to be true. This can be thought of as an unwitting choice of a world that the person considers "real". Due to the additive property of vectors, we can say that the reality of the real world is whatever the scientific community believes it to be. Personally I prefer not to single out any particular collection of people but instead use the passive voice: The world is not different from what it is believed to be.

To avoid logical problems, the person's belief must be subjective rather than determinable by science. If the belief were objective it could in principle be explained by a pre-existing arrangement of matter. A person defined that way could not have a role in determining pre-existing arrangements of matter. In my scheme, the person is defined by the vector associated with them, and not by their quarks and electrons.

A person has a multitude of subjective beliefs about all sorts of things. Those beliefs, being vectors, can be summed to a resultant defining the person as a unity. Those 50 billion resultants, in turn, can be summed to a grand resultant representing all of us together (past, present and future). The grand resultant points at the scientific reality of our world. It defines the reality of our world.

Thus the world is not different from what we subjectively and collectively believe it to be. That statement would appear to be true even in conventional science. It seems impossible to prove that the world is different from what we believe it to be.

"Collectively" means, in particular, that people of the future determine, or constrain, the reality of us who are alive today. This constraint appears as superposition and randomness, as I said.

The Origin of Man

Since man in my hypothesis is defined logically rather than physically, he is in a sense "outside the world" and the world is an object to him. This validates the practise of science because the world is now an object for man to study objectively. It allows man's physical appearance to be explained by evolution according to the facts as we see them to be.

But how does man-the-vector come to exist? We can avoid recourse to religion by accepting that logic is the outside viewpoint that sees the world into objectivity. And that man's beliefs are part of that logic. Doing this makes man into an unexplained initial condition. As an initial condition, this might be simpler than the plethora of apparently arbitrary facts that currently define our world.


My hypothesis is built upon man having a role in the specification of reality and on a deterministic generalisation of the Anthropic Principle. The generalisation has man setting not only the characteristics of the Big Bang but everything about his past. After the past has been defined in this way, determinism leads to the present reality being exactly as we see it.

But I make it the other way around. A person defines his or her present, rather than their unique past. They define their present according to what they unconsciously believe it to be. This in turn, by reverse determinism, specifies how their past shall be consituted. Every person does this, and the sum of those specifications leads to what we call reality.

Thus the world is not different from what it is believed to be, individually or collectively. Having the world created in this way agrees with the idea, suggested on other grounds, that reality is not a pre-existing truth for man to discover. Man creating reality might be a novel approach to truth but the appearance of reality remains exactly the same. Compared with conventional science, nothing changes except how reality comes to exist. It comes to exist from our scientific effort to construct a logically consistent story explaining us and our environment. The story describes the world we believe to exist around us, and we imagine the scientific story corresponds to an external reality. But nothing changes if we delete that last step. That is what my hypothesis is largely reducible to.

My hypothesis undoubtedly has distasteful elements from a scientific point of view. But if developed into a full theory it might provide a better understanding of atomic physics. Human belief enters my hypothesis as an initial condition, but it is not out of the question for the belief vector to be a variable amenable to manipulation in conventional physics. My layman's picture is that it could be similar to Schroedinger's Psi - something that facilitates results while remaining inscrutable itself.


My hypothesis illuminates many "niggles" in conventional science:

The nature of belief If, contrary to my hypothesis, people's beliefs originate in an external reality applicable to everybody, then we should all believe the same. That is the logical consequence of reality being in charge. The fact that we do not believe the same suggests we are not bathed in the same reality - which is my hypothesis.

My hypothesis also provides scientific accommodation of the phenomenon of belief in general. It does this by making belief part of the world's logic. Currently, science does not provide any such accommodation. Scientists vaguely assume that correct belief is caused by the world's reality, via evidence, and incorrect belief by people using their free will to disregard the evidence (or to extend the evidence unjustifiably). But the bare notion of belief is considered to be outside science. This is unsatisfactory, and not only because it introduces a quasi-magical force of free will. It is unsatisfactory because scientists use their beliefs to choose axioms and initial conditions and decide what to study, and where the cut between measuring apparatus and the world under measurement shall lie. They also use their beliefs to decide when a phenomenon is considered explained. (When they have a believed account of it.)

Free will Each person acts fully in accord with the reality they believe to exist. That reality is personal to them, but they want to believe that they have knowledge of an external reality, rather than mere belief in a private one. The "force" of free will is a compensation for inventing an external reality.

My hypothesis also explains the "irrationality problem" associated with free will. Just as it is impossible for a rational person to adopt irrationality (because that would be irrational) so too it would seem impossible for a rational ("scientific") world to proceed scientifically for a few billion years then pass control over to the irrationality of human free will. It might be possible to circumvent the logic by invoking randomness, but that would be a kind of "God-of-the-gaps" solution.

In my scheme, the irrationality of man is present from the beginning - from even before the Big Bang. My scheme also has the advantage of treating free will as a scientific phenomenon to be explained, rather than as an aberration to be explained away.

Randomness Randomness has always been an anomaly in science (as a causal agent rather than a useful assumption in statistics). It is possible to explain anything at all - even something extremely unlikely - by recourse to randomness. That hardly amounts to an explanation. And "random cause" has the appearance of an oxymoron. A cause ideally should be contrasted with randomness, not aligned with it.

My hypothesis explains the deterministic origins of randomness more-or-less as follows. Each person believes a particular reality to exist in their present. When these individual realities are extended deterministically back into the past, they start to contradict each other. The contradictions are a result of each person imagining they have knowledge of a common external reality rather than personal belief in a private one. The contradictions are resolved by having the deterministic histories merge into randomness rather than extending back without limit. Thus randomness, like free will, is a compensation for our arbitrary insistence that a common external reality shall bathe us all.

The measurement problem A measurement is complete when the scientists believe the result. A camera photographing the result does not complete the measurement because nothing is believed at that time. The photograph must be viewed by someone in our world for it to influence the logic of our world.

The "cut" between the classical and quantum worlds There is no cut. If a coin is tossed and falls on the floor, it does not have a real value until observed (assuming a 100% fair coin and perfect tossing). "Real" means taking part in the logic of our world. The unobserved coin does not do that.

The complexity problem If there were a fixed external reality for scientists to study, some evidence should have arrived by now that the scientific story was coming to an end. But science seems to be descending into bottomless complexity. Unlimited complexity is to be expected when there is no external reality, because the story we make up cannot include us who are writing it. An object cannot explain the subjective viewpoint making the object into an object.

Reality Each of us likes the idea of an external reality but proof that such a thing exists has always been lacking. Proof would involve showing that when two people agree about the existence of some external thing, they have the same mental state (i.e., they are agreeing about the same thing). Not only is such a proof probably impossible, the evidence points in the other direction. The phenomenon of free will suggests that people are not immersed in the same reality.

And it would appear that the process by which people infer the existence of an external reality is flawed. We all believe in a personal reality and since there are plural people, on the face of it we should have plural realities. (Lots of realities rather than a single Reality.) But we insist on a single Reality. The flaw arises from how we generate that singular entity. We do it by seeing a few objects and imagining that other people have the same visual experience as ourselves (although the evidence is against that). Then we extrapolate to imagined unseen objects, and form the sum. We define the sum as "everything" and call it reality.

But, as I said, this process is like an incompetent mathematician vaguely knowing the first few terms of an ill-defined series and confidently declaring that the series has a sum when they have no procedure for generating it. When confronted, the mathematician replies "Of course the series has a sum. It is all the terms added together. It is implied by the word sum."

My hypothesis does not venture beyond individual personal realities and does not conjure-up a world of self-existent things. If we want a "reality" (and it can be convenient to have such a thing) we can sum the personal realities. This sum exists because it results from summing the vectors that generate those realities.

My approach also avoids the awkward problem, in current science, of having to consider "real" things that we have no knowledge of - like a deity. There is no evidence for a deity, but if reality consists of things that exist in themselves regardless of us, then such a being exists as a scientific possibility.

Why do we like to imagine a self-existent reality? It is sometimes said that people invent a deity because they like the idea. The same could be said of reality. We like the idea of a self-existent body of truth that we can obtain knowledge of, so we invent it. As to why we like knowledge, it is because each of us wants to feel superior to others, and knowledge of a would-be universal truth seems to make us superior.

If we avoid inventing a reality and accept my hypothesis as an alternative account of the world, the world stays exactly the same as we see it today, and science carries on almost exactly as now. There is nothing to fear. One of the changes for science is that man might turn up as a boundary condition in physics. Another is that scientists will not attempt to find a physical correlate of the phenomenon of subjective belief. Perhaps the biggest change would be to our attitude regarding knowledge. Under my hypothesis, scientific knowledge would not be knowledge of a universal truth but the construction of an exterior world to match what we collectively believe. If we believed differently, reality would be different. I admit that I do not know the ramifications. I feel sure that scientists will continue to be esteemed for how good they are at writing the scientific narrative and solving human problems.

"Our" world In conventional science it is often thought that our world is a selection from all possible worlds. But how is the word "our" to be defined? If we want our world to be independent of us humans, we need to find some way of defining our world without reference to us. That would appear to be impossible. (It might be possible if we had an infinite list of facts unique to our world.) The definition is simple under my hypothesis. The single resultant vector that defines a person can be added to the vectors from everybody else to form a single grand resultant vector that points at a world of reality. That vector defines our world and provides scientific accommodation of the word "our".

The binding problem In biology (or neuroscience) there is a problem explaining how the multitude of facts pertaining to a person can be bound into a singular resultant to be identified with the "I" of the person themselves. In my hypothesis the multitude of scalar facts is replaced by a multitude of vector beliefs. Vectors have the useful property of being summed into a resultant - a single entity - that entirely replaces the components. The resultant encodes all of the information from the beliefs that make it up.

A form of the binding problem also exists for inanimate objects. When we refer to an object and use the singular case, we are summarising a bunch of quarks and electrons and distinguishing them from neighbouring bunches. How does each bunch define itself as a singular entity? It is easy for humans to make the definition (it is what my hypothesis is about) but how does the object itself do it? To put it another way, what singular entity corresponds to the singularity of the word "it" when we talk about it? If we say that the object exists "in itself", how is the word self to be defined? Current science seems to have an assumption that there are "natural" boundaries between objects, and that "we all know" what the object is even if the object cannot tell us. This lack of precision is unsatisfactory.

In my hypothesis, each person defines just one object, their world, and all other objects are formed by ever-deeper analysis of that object. Science does the same thing, drilling down from the world of reality believed to exist. An object is created the moment the scientists believe it to exist, meaning it now takes part in the world's logic whereas it didn't before. This is similar to the way a tossed coin lying on the floor obtains a real value when it is viewed and not before. The explanations are much simpler once we have man pulling the strings.

Libet's experiments on free will Benjamin Libet attached probes to a volunteer and found that the person decides to lift their arm perhaps a half second before they are conscious of making the decision. Roger Penrose explains this by the suggestion that the decision is unconscious - in line with my hypothesis.

The objectivity of our world Scientists treat our world as an object for study, but an object is only an object in relation to some logical point of view outside the object. What or where is that point of view? If it resides in the scientists, then they are logically outside the world and science should recognise that boundary condition. I am inclined to see it as incoherent if the viewpoint of reality is presumed to reside in reality itself. An object needs a (notional) subject outside itself to validate its existence as an object.

The scientific answer tends toward saying that logic is the outside viewpoint. Some body of logic, hopefully in the form of mathematically formulated truth, generates the world. My hypothesis agrees that logic is the correct answer. But I believe that the logic includes our human beliefs. Mathematical physics would seem incapable of providing a full answer if it continues to rely on axioms and initial conditions chosen according to what man believes to be a good choice.

Time and its direction Our physical equations allow for time to flow either way but we only see it moving forwards into the future (to use familiar speech). Why do our equations have an apparently unused facility to evolve in the reverse direction? The answer, according to my hypothesis, is that the reverse direction of time allows the future to "cause" the past via the generalised Anthropic Principle. I put cause in quotes to indicate that it is different from normal causation. The past is "required to be that way" rather than assembled from earlier-in-time antecedents. There might exist antecedents but it is logically impossible to know what they are at the time. They are virtual, and only get real values when the future decides.

In my hypothesis, time is a parameter tracking our beliefs. Our unconscious beliefs have a logical progression but we cannot see the progression because our beliefs are subjective. We invent time as an external parameter that we can see objectively and associate with the reality we invent.

The Second Law of Thermodynamics Roger Penrose says that if we observe the present and use our observations to deduce how conditions must have been a few moments ago (or a week or a billion years) we would decide that the past was more disordered than the present. That is because probability does not have a direction. If we think the future will be more disordered, we ought to make the same judgement about the past, judging from the present.

But if we judge from a wider view, not just from the present, we find that the past was more ordered than the present and the Big Bang exceedingly so. Where does this order come from? Under my hypothesis, the order of the Big Bang - "the precise point in phase space that was the origin of our universe" - is caused by billions of humans in the future unconsciously specifying how their deterministic personal worlds shall be constituted. The Big Bang tries to accommodate all these "requests" and ends up in a very precise spot as a result.

Entanglement If I measure an entangled twin in my laboratory, I determine its reality and simultaneously define the reality of the other twin a billion light-years away. The effect is instantaneous because defining something does not need physical propagation. This solution is only possible if we give up the idea of a pre-existing external reality, in line with my hypothesis.

Personally, I see no need to be precious about the existence of an external reality. What matters is the logic of our existence, not would-be facts presumed to be supporting the logic. Something is real if-and-only-if it contributes to the logic of our world. (Which is why God should not be considered real.) The reference to our world implicates us humans and leads to the conclusion that reality centres on us. And that is the essence of my hypothesis.



Reality First Vs Logic First An alternative treatment of the above, from a different starting point

The Religious Account of the World How monotheism introduces humans and explains reality