From Quantum Theory to Philosophical Idealism.

* * * * * * * * * * * * * *

Matthew J. Donald

The Cavendish Laboratory, JJ Thomson Avenue, Cambridge CB3 0HE, Great Britain.


home page:

* * * * * * * * * * * * * *

On 5th December 2014, I gave an after-dinner talk to fellows of Churchill College and their guests. Because I only had twenty minutes to speak, I wrote my talk out in advance. This is a lightly-edited version of that talk into which I have merged the overheads in bold type.

* * * * * * * * * * * * * *

Abstract: It is well known that quantum theory is a bit odd, and I have long been intrigued by the question of what that oddness might suggest about the nature of reality. The oddness lies in a beautiful mathematical structure, which perfectly predicts the probabilities of events, or of outcomes of measurements, but which leaves almost entirely unexplained what events or measurements are, or when they occur, or how they fit into the theory. An “interpretation” of quantum theory is an attempt to give the missing explanation. The many-minds interpretation which I have tried to develop, centres neither on events nor on measurements, but on “observations” and “observers”, and suggests indeed that “observers” or “minds” are the fundamental building blocks of reality. Carried to its logical conclusion, this leads to philosophical idealism, a way of looking at the world first put forward over three hundred years ago by Bishop Berkeley. In roughly twenty minutes for a post-prandial audience, I shall try to sketch some of the lessons I’ve learned from working on this project.

* * * * * * * * * * * * * *

Host's Introduction: Forty years ago this term, Matthew Donald was an undergraduate at Caius reading mathematics. Playing violin in a Sidney Sussex college concert, he met a viola player and singer who is now the Master of this college. After he had done Part III Maths and she had finished her PhD here, they went to Cornell, where his PhD was on mathematical models in quantum field theory. A post-doctoral year at Rockefeller University, a research fellowship at Caius, and research at the Cavendish supported by the Leverhulme Trust followed. After that, it became clear that his brilliant future was behind him while Athene’s was just beginning, so he became a house-husband and gentleman scholar. Since then, despite publishing the occasional mathematical paper on topics related to quantum information, he has mainly worked on the interpretation of quantum theory. He likes to tell people that he is interested in what quantum theory tells us about the nature of reality, but as he is about to explain, that statement is really rather disingenuous.

* * * * * * * * * * * * * *

Slides: Preamble; Bullet Points; Mathematical Quantum Theory; The Hot Big Bang; Correlations; The Interpretation of Quantum Theory; The Many-Minds Interpretation; Idealism; Characterising Observers; However; Summary; The Problem of Consciousness.

* * * * * * * * * * * * * *


When I was invited to give this talk, I decided that I wanted to tell you about the project that I have worked on for over twenty years, where I have aimed to understand what would be required to make sense at a detailed technical level of certain approaches to the interpretation of quantum theory.

So I wanted to tell you something about how I went

From Quantum Theory to Philosophical Idealism

and I needed to do it

in roughly twenty minutes

for a post-prandial audience.

This was an interesting challenge, but in due course I managed to write a talk, which began at the beginning with

what everyone knows about quantum theory (it's a bit weird and either the cat is alive or its dead)

and then went on to discuss the different views of physicists and philosophers and mathematicians and how they could be reconciled.

And then I wanted to introduce the problem of consciousness (or mind), and the peril of dualism, and how that could be avoided; either by turning to materialism, according to which the fundamental building blocks of reality are physical and material; or to philosophical idealism, according to which the fundamental building blocks of reality are mental.

And, of course, I was going to mention George Berkeley, Bishop of Cloyne who lived from 1685 to 1753, and I was going to talk about the tree in the quad problem.

This is the problem that an idealist not only has to explain the perception of a tree in a quad but also why, if everything is mental, the tree will most likely still appear to be there, whether or not one wants it to be, the next time one returns to the quad.

Berkeley thought that he had solved this problem by arguing that the tree continued to exist in the mind of a benevolent god.

After I'd discussed all that, then finally, I was ready to get on to my own quantum version of idealism and to my attempts to characterize observers and to my own suggested solution to the tree in the quad problem by using the idea of correlations of quantum probabilities.

And I wanted to end by talking about some of the consequences of idealism.

I don't think it was a bad talk, and it was probably suitable for this audience, but there was no way I could compress it into the available time.

* * * * * * * * * * * * * *

Bullet Points.

At the end of the original version of my talk, I put some Bullet Points. These expressed some of the ideas which I think of as being, roughly speaking, the lessons I've learned from this whole project. They are also ideas which I feel might be worthy of your consideration, so tonight I'm going to throw out all the background material and just look very briefly at these five points.

My first bullet point is the idea that

• Mathematical physics is a view from nowhere.

The phrase “view from nowhere” is an image which is used by the American philosopher Thomas Nagel to suggest how much scientific objectivity leaves out of human reality, but it can also be used to emphasize how, in general, the place left for humanity in what is called “fundamental” physics has become reduced to almost nothing — we're just a short-lived species on an obscure planet around a typical star in a vast array of galaxies.

I want to argue that in mathematical quantum theory it's much worse than that — we're little more than a single possible trajectory in an almost featureless continuum of possible trajectories. Moreover, being given a continuum of possibilities in quantum theory is not like being given a bunch of random numbers sufficient to determine a single physical trajectory — it's more like being given an unthrown, multi-dimensional, almost perfectly-spherical die, which we can somehow choose how to throw, and where each act of throwing will determine a single new position on the trajectory and a revised set of possibilities for how the trajectory can continue.

My second bullet point is the claim that

• A many-minds quantum version of philosphical idealism is not ruled out.

As a mathematician, I like nothing better than showing why a plausible idea has to be an impossible absurdity. This I failed to do with the many-minds idea, although I did manage I hope, at least to point to some of the problems and weaknesses of the idea.

Next comes the realization that

• The more physics we know, the less we are sure of the nature of reality.

The reason why, as David said in his introduction that I now believe that it is somewhat disingenuous to say that what I am trying to do is to find out what quantum theory tells us about the nature of reality is because the more I've studied it, the more it has become clear to me that we are free within the framework of modern physics to paint a wide range of quite radically different pictures of how reality might be and that it is not likely that anything will ever let us definitively decide between those pictures.

On the other hand, there are difficult and interesting technical issues to be solved before we can make sense of any of the possible pictures, and those are the sort of issues on which I've worked.

My fourth bullet point is rather more positive for a many-minds interpretation. It just states that

• Claims of simplicity should not ignore initial conditions.

It strikes me as silly that there is great concern raised by the standard model's 17 unknown physical constants, but very little concern about the continuously many numbers that would be needed to construct a universe in which every butterfly's wing-flappping was decided from the beginning of time. I think that the answer to this issue lies in the claim behind my first bullet point — the butterfly's wings are nowhere until they, or their consequences, come to be an observed possibility.

As a starting point to the development of a theory of mind, it would be helpful to be sure that minds exist. Recently, however, I have become both more and more convinced and more and more troubled by my final bullet points which indicates that

• Nothing we can say can show that we have minds.

Essentially this follows from what a philosopher would refer to as a rejection of functionalism, or in other words, from an argument that it is not possible to define a mind merely as a pattern of behaviour — because there are continuously many ways of defining such patterns — and that therefore there are patterns that appear under appropriate analysis to behave as much like we do as you might wish but nevertheless which do not possess minds. And if we can't believe what those patterns appear (under appropriate analysis) to be saying, why should we believe what we say ourselves?

A rejection of functionalism, by the way, encourages us to be very dubious about such ideas as achieving immortality by up-loading the wiring-diagrams of our brains into a computer, or using a Star-Trek style teleporter — even a Star-Trek style quantum teleporter.

* * * * * * * * * * * * * *

Mathematical Quantum Theory.

Let's start by looking a little more closely at the nature of mathematical quantum theory.

Mathematicians tend to believe that quantum theory is the theory of everything.

And it therefore follows that the universe and everything in it is described by a single quantum state which is referred to as “the state of the universe”.

So what is a quantum state? Well, a quantum state can be thought of as describing ranges of possibilities and the corresponding probabilities.

For example the possibilities of an electron being here or here or here, or (and, as Heisenberg told us incompatibly) going slowly, or fast, or very fast.

Now, one of the interesting things about possibilities for macroscopic objects in a low entropy universe like ours is that they tend to diverge as time passes, because microscopic fluctuations can have macroscopic effects.

For example, if this Geiger counter clicks, then the cat dies; if not it will scratch you when you open the door.

In other words, possibilities and their consequences can multiply.

* * * * * * * * * * * * * *

The Hot Big Bang.

As I'm sure you know there is plenty of evidence to show that the universe began in fire with a hot big bang 13.8 billion years ago, or so.

Shortly after that singularity, all the matter in the universe was in a state of very high temperature and density.

As a quantum state, such a state contains more-or-less every possible future with some non-zero probability.

This indeed is almost the ultimate featureless “view from nowhere”.

Like an almost perfectly spherical die, the state can be assumed to have almost no content perhaps just an initial temperature and density.

It is a blank slate on which almost anything may come to appear.

And without an analysis of “appearance”, all we have is just that blank slate.

* * * * * * * * * * * * * *


Correlations are the magic mathematical ingredient which makes this work.

The correlations between appearances which the state imposes tell us how each appearance constrains the probabilities of subsequent appearances.

A possible future considered as a whole is a history of the correlations of possible appearances.

So we can say that despite its simplicity, arbitrary patterns of correlation can be seen in the universal state.

However, those patterns do need to be seen.

And we need to understand what seeing means in this context, and, in particular, we need to know how and when “seeing” can start.

* * * * * * * * * * * * * *

The Interpretation of Quantum Theory.

This sort of question about the nature of appearance in quantum theory is precisely the kind of thing that is supposed to be tackled when one tries to develop an interpretation of quantum theory.

There are, as I want indicate by my third bullet point, many radically different ways, and even many radically different viable ways, of trying to understand quantum theory.

For each of these interpretations there is a corresponding fundamental question:

For example, if one was interested in developing a dynamical collapse model involving random patterns of particle localizations, one would ask what is an “event”?

If one was a traditionalist and a follower of Niels Bohr one would ask what is the “classical regime”?

If one was prepared to accept a non-local theory violating at least the spirit of special relativity, one could ask what are the particle trajectories and how do we experience them?

The form of the question I want to pose is what is an “observation”? and leading on from that, whose observations? and when do observations start?

* * * * * * * * * * * * * *

The Many-Minds Interpretation.

So, my twenty-year project was to try to develop the technical details of a many-minds interpretation, based on the beginnings of an outline of the idea that I had first come across in the 1957 Ph.D. thesis of Hugh Everett III, a copy of which I bought from Heffers when I was an undergraduate.

At least that was the way that I read his thesis, although others don't read it in quite the same way.

I began therefore with the ideas that all “events” in quantum theory are observations by individual “observers”

and that observers are entities with “minds”.

Then that we start as individuals from the experience of nothing and we build our own individual history as the experience of a correlated sequence of possibilities.

* * * * * * * * * * * * * *


This is a form of philosophical idealism, the notion that the fundamental building blocks of reality consists of minds and their experiences.

The universal quantum state is there in the background, as part of the definition of the probabilities of possible experiences, determining the correlations between one observation (say of a tree in a quad) and another, but essentially all of the reality lies in individually experienced histories.

For example, when we are little we won't yet have experienced anything which has told us how many planets there are. We will have experienced the sort of biological interactions which indicate that we can be almost sure that we will find evidence for biological evolution if we ever look for it — because the sort of patterns of experience we have observed by the time we are say five years old is strongly correlated in the universal quantum state with the existence of that sort of evidence, but nevertheless, it is still possible for us to be living in a solar system with six planets and so the precise number of planets is not determined.

And then we are told there are nine (or nowadays perhaps eight) and, because it is unlikely that we will be living in a society in which people will lie to children about such issues, that becomes an almost certain property of the world in which we live.

* * * * * * * * * * * * * *

Characterising Observers.

However, this is no more than the sort of airy-fairy stuff that any modern popular science writer or eighteenth century bishop with a good imagination could dream up.

My interest was rather different. I wanted to try and see what would be involved in working out whether there was any way of turning this sketchy idea into a viable theory.

And the primary thing that seemed to be required for such a theory, the thing that was necessary to turn possibilities into defined events with calculable probabilities, was some sort of technical characterisation of the notion of an observer.

The preliminary input into this task was a couple of perhaps obvious assumptions: that

I'm an observer,

And, I presume, that you are too.

But that some things, even some very complex things like cameras and trees and stellar interiors are not observers.

It turns out that characterising observers is difficult, but I believe that it is not impossible.

I have proposed an abstract (that is a mathematical) characterization which doesn't depend on any such specific biological notions, not even, for example, the existence of carbon atoms or anything like that, but merely looks for the existence of suitably continuous localized patterns of simple repetitions, with individual observer “histories” defined entirely by finite sequences of such patterns.

Note that any such characterization is a rejection of functionalism, because what matters for the existence of a mind is not the behaviour apparent to other minds (which is a circular definition if ever there was one), but whether the rules of the characterization are obeyed.

* * * * * * * * * * * * * *


This is all very well, and it is interesting that it can be done at all, however, I think I can say with considerable confidence that

any such characterization will not be unique

or beautiful

or perhaps, although it is hard to tell what one should expect in this regard, even particularly simple.

And nevertheless, in this framework, where elementary (yes-no questions) observations and the probability of sequences of such observations are the fundamental building blocks of reality,

the characterization is supposed to be a law of nature.

* * * * * * * * * * * * * *


So far, I've said a little about three of my bullet points.

I've suggested that • Mathematical physics is a view from nowhere,

I've tried to indicate what was involved in establishing my belief that

• A many-minds quantum version of philosphical idealism is not ruled out,

and, by briefly mentioning some of the range of viable alternative interpretations of quantum theory, I've begun to indicate how it might be that

• The more physics we know, the less we are sure of the nature of reality.

My fourth bullet point was that

• Claims of simplicity should not ignore initial conditions.

For an idealist, the only information is observed information, so if, as I propose, observers, are finite, limited, and defined by their observations, then at least in some sense, that reality as a whole will also be finite and limited. I may be introducing quite complicated laws to define observers, but the total complexity count is comparatively low.

I want to finish by saying just a little about the problem of consciousness, with particular reference to my final bullet point that

• Nothing we can say can show that we have minds.

* * * * * * * * * * * * * *

The Problem of Consciousness.

There are many problems to do with consciousness, but the central one is quite simply the problem of what it means to say that consciousness exists.

I used to think that the existence of consciousness was obvious — indeed, following Descartes and his “Cogito Ergo Sum” that there was no other existence which had anything like the same degree of obviousness.

But of course I would say that wouldn't I. This is a problem because it is easy to argue that my reasons for saying or thinking (taking thinking as a form of internal saying) that I think therefore I am, lies in my biological evolution as a member of a social species. Ultimately, however, this is just something which involves physical causality — it is not caused by mind, but merely by the physical structure which happens to exemplify the required type of complexity.

And here, to shortcut what I hope would otherwise be the first question, I need a little digression because talking about evolution in this way may not seem entirely consistent with an idealist philosophy in which there is no past outside the lives of individual observers. Indeed, Berkeley himself referred to the need to “think with the learned, and speak with the vulgar” when talking about similar problems. For complete consistency, therefore, I would need to discuss arguments to the effect that because of the nature of the basic physical interactions and of the universal quantum state, the most likely observers with the sort of complexity of structure which we have, would be observers who will, if they know how to look, be able to see evidence of themselves as evolved social beings.

Regardless, however, of the way that we interpret physical causality or its appearance, I claim that the existence of consciousness doesn't explain why we say that we think we are at the heart of existence.

It just puts us at the heart of existence.

And one consequence of this claim is the possibility that the best handle we have on the nature and existence of consciousness lies not in what we say about ourselves and each other, but in the difficulties we have in understanding how to make sense of quantum theory.

* * * * * * * * * * * * * *

* * * * * * * * * * * * * *

Matthew J. Donald

The Cavendish Laboratory, JJ Thomson Avenue, Cambridge CB3 0HE, Great Britain.

e-mail :

home page: