Not in any direct way. That is, it doesn’t provide an argument for the existence of God. But it does so indirectly, by providing an argument against the philosophy called materialism (or “physicalism”), which is the main intellectual opponent of belief in God in today’s world.

Materialism is an atheistic philosophy that says that all of reality is reducible to matter and its interactions. It has gained ground because many people think that it’s supported by science. They think that physics has shown the material world to be a closed system of cause and effect, sealed off from the influence of any non-physical realities — if any there be. Since our minds and thoughts obviously do affect the physical world, it would follow that they are themselves merely physical phenomena. No room for a spiritual soul or free will: for materialists we are just “machines made of meat.”

Quantum mechanics, however, throws a monkey wrench into this simple mechanical view of things. No less a figure than Eugene Wigner, a Nobel Prize winner in physics, claimed that materialism — at least with regard to the human mind — is not “logically consistent with present quantum mechanics.” And on the basis of quantum mechanics, Sir Rudolf Peierls, another great 20th-century physicist, said, “the premise that you can describe in terms of physics the whole function of a human being … including [his] knowledge, and [his] consciousness, is untenable. There is still something missing.”

How, one might ask, can quantum mechanics have anything to say about the human mind? Isn’t it about things that can be physically measured, such as particles and forces? It is; but while minds cannot be measured, it is ultimately minds that do the measuring. And that, as we shall see, is a fact that cannot be ignored in trying to make sense of quantum mechanics. If one claims that it is possible (in principle) to give a complete physical description of what goes on during a measurement — including the mind of the person who is doing the measuring — one is led into severe difficulties. This was pointed out in the 1930s by the great mathematician John von Neumann. Though I cannot go into technicalities in an essay such as this, I will try to sketch the argument.

It all begins with the fact that quantum mechanics is inherently probabilistic. Of course, even in “classical physics” (i.e. the physics that preceded quantum mechanics and that still is adequate for many purposes) one sometimes uses probabilities; but one wouldn’t have to if one had enough information. Quantum mechanics is radically different: it says that even if one had complete information about the state of a physical system, the laws of physics would typically only predict probabilities of future outcomes. These probabilities are encoded in something called the “wavefunction” of the system.

A familiar example of this is the idea of “half-life.” Radioactive nuclei are liable to “decay” into smaller nuclei and other particles. If a certain type of nucleus has a half-life of, say, an hour, it means that a nucleus of that type has a 50% chance of decaying within 1 hour, a 75% chance within two hours, and so on. The quantum mechanical equations do not (and cannot) tell you when a particular nucleus will decay, only the probability of it doing so as a function of time. This is not something peculiar to nuclei. The principles of quantum mechanics apply to all physical systems, and those principles are inherently and inescapably probabilistic.

This is where the problem begins. It is a paradoxical (but entirely logical) fact that a probability only makes sense if it is the probability of something definite. For example, to say that Jane has a 70% chance of passing the French exam only means something if at some point she takes the exam and gets a definite grade. At that point, the probability of her passing no longer remains 70%, but suddenly jumps to 100% (if she passes) or 0% (if she fails). In other words, probabilities of events that lie in between 0 and 100% must at some point jump to 0 or 100% or else they meant nothing in the first place.

This raises a thorny issue for quantum mechanics. The master equation that governs how wavefunctions change with time (the “Schrödinger equation”) does not yield probabilities that suddenly jump to 0 or 100%, but rather ones that vary smoothly and that generally remain greater than 0 and less than 100%. Radioactive nuclei are a good example. The Schrödinger equation says that the “survival probability” of a nucleus (i.e. the probability of its not having decayed) starts off at 100%, and then falls continuously, reaching 50% after one half-life, 25% after two half-lives, and so on — *but never reaching zero*. In other words, the Schrödinger equation only gives probabilities of decaying, never an actual decay! (If there were an actual decay, the survival probability should jump to 0 at that point.)

To recap: (a) Probabilities in quantum mechanics must be the probabilities of definite events. (b) When definite events happen, some probabilities should jump to 0 or 100%. However, (c) the mathematics that describes all physical processes (the Schrödinger equation) does not describe such jumps. One begins to see how one might reach the conclusion that not everything that happens is a physical process describable by the equations of physics.

So how do minds enter the picture? The traditional understanding is that the “definite events” whose probabilities one calculates in quantum mechanics are the outcomes of “measurements” or “observations” (the words are used interchangeably). If someone (traditionally called “the observer”) checks to see if, say, a nucleus has decayed (perhaps using a Geiger counter), he or she must get a definite answer: yes or no. Obviously, at that point the probability of the nucleus having decayed (or survived) should jump to 0 or 100%, because the observer then knows the result with certainty. This is just common sense. The probabilities assigned to events refer to someone’s state of knowledge: before I know the outcome of Jane’s exam I can only say that she has a 70% chance of passing; whereas after I know I must say either 0 or 100%.

Thus, the traditional view is that the probabilities in quantum mechanics — and hence the “wavefunction” that encodes them — refer to the state of knowledge of some “observer”. (In the words of the famous physicist Sir James Jeans, wavefunctions are “knowledge waves.”) An observer’s knowledge — and hence the wavefunction that encodes it — makes a discontinuous jump when he/she comes to know the outcome of a measurement (the famous “quantum jump”, traditionally called the “collapse of the wave function”). But the Schrödinger equations that describe any physical process do not give such jumps! So something must be involved when knowledge changes besides physical processes.

An obvious question is why one needs to talk about knowledge and minds at all. Couldn’t an inanimate physical device (say, a Geiger counter) carry out a “measurement”? That would run into the very problem pointed out by von Neumann: If the “observer” were just a purely physical entity, such as a Geiger counter, one could in principle write down a bigger wavefunction that described not only the thing being measured but also the observer. And, when calculated with the Schrödinger equation, that bigger wave function would not jump! Again: as long as only purely physical entities are involved, they are governed by an equation that says that the probabilities don’t jump.

That’s why, when Peierls was asked whether a machine could be an “observer,” he said no, explaining that “the quantum mechanical description is in terms of knowledge, and knowledge requires somebody who knows.” Not a purely physical thing, but a mind.

But what if one refuses to accept this conclusion, and maintains that only physical entities exist and that all observers and their minds are entirely describable by the equations of physics? Then the quantum probabilities remain in limbo, not 0 and 100% (in general) but hovering somewhere in between. They never get resolved into unique and definite outcomes, but somehow all possibilities remain always in play. One would thus be forced into what is called the “Many Worlds Interpretation” (MWI) of quantum mechanics.

In MWI, reality is divided into many branches corresponding to all the possible outcomes of all physical situations. If a probability was 70% before a measurement, it doesn’t jump to 0 or 100%; it stays 70% after the measurement, because in 70% of the branches there’s one result and in 30% there’s the other result! For example, in some branches of reality a particular nucleus has decayed — and “you” observe that it has, while in other branches it has not decayed — and “you” observe that it has not. (There are versions of “you” in every branch.) In the Many Worlds picture, you exist in a virtually infinite number of versions: in some branches of reality you are reading this article, in others you are asleep in bed, in others you have never been born. Even proponents of the Many Worlds idea admit that it sounds crazy and strains credulity.

The upshot is this: If the mathematics of quantum mechanics is right (as most fundamental physicists believe), and if materialism is right, one is forced to accept the Many Worlds Interpretation of quantum mechanics. And that is awfully heavy baggage for materialism to carry.

If, on the other hand, we accept the more traditional understanding of quantum mechanics that goes back to von Neumann, one is led by its logic (as Wigner and Peierls were) to the conclusion that not everything is just matter in motion, and that in particular there is something about the human mind that transcends matter and its laws. It then becomes possible to take seriously certain questions that materialism had ruled out of court: If the human mind transcends matter to some extent, could there not exist minds that transcend the physical universe altogether? And might there not even exist an ultimate Mind?

Discussion Summary

In my BQO essay I sought to explain in non-technical language the main issues that lead to different “interpretations” of quantum mechanics, and why they present a choice between the anti-materialist implications of the traditional Copenhagen interpretation and the bizarre and (for most people) incredible implications of the Many Worlds Interpretation (MWI).

Another way to frame the argument is in terms of the “ontological status” of wavefunctions. The most obvious thing is to think of a wavefunction as simply a straightforward description of “the world as it is”. But that is equivalent to the MWI, because generally speaking the wavefunction of a system contains a large number of branches in which the system behaves in different ways. The alternative view (adopted in the Copenhagen interpretation) is that a wavefunction is not an account of the world as it is, but of some observer’s state of knowledge of the world. That interpretation brings knowledge (and therefore mind) into the discussion as something that is as fundamental as matter, because wavefunctions themselves are fundamental to our understanding of the world.

These seem to be the only viable choices if one accepts the present formalism of quantum mechanics. The third possibility, then, is to say that this formalism needs to be changed somehow. Several commentators on my article either mentioned or proposed approaches to modifying quantum mechanics. Two well-known approaches that they mentioned were “hidden variables theories” and “objective collapse theories”. Certainly, science can never be absolutely certain that it has arrived at a final and complete description of the physical world; so it will always remain a possibility that present quantum mechanics is incomplete and that a modification of its formalism will resolve all its puzzles, paradoxes, and conundrums. However, as I explained in my responses, the present formalism of quantum mechanics has been spectacularly successful since the 1920’s in describing with astonishing precision a vast range of phenomena. It seems less likely than it once did that it will have to be modified. (Many, including one commentator on my essay, have seen the difficulty of combining present quantum mechanics with Einstein’s theory of gravity as evidence that the former will have to be modified. Superstring theory shows, however, that Einstein’s theory can be consistently “quantized”.)

Not only does the traditional interpretation of quantum mechanics have anti-materialist implications, but, as noted by more than one commentator, it is compatible with philosophical idealism (which makes mind the only fundamental reality) and even with solipsism (which makes one’s own mind the only reality). If we reject such extremes and take the view that both matter and mind are fundamental and equally real, then a question arises: how are they related to each other?

Connected with this question is a common objection made to the Copenhagen interpretation, which is that it seems to say that the minds of “observers” have a spooky influence on the physical world. In particular, the idea that “wavefunction collapse” is caused by “observations” seems to suggest that human knowers actually cause events to happen by knowing them. As one commentator pointed out, this would be a radical reversal of traditional ideas about the relation of knower and known. Indeed, the traditional interpretation of quantum mechanics strikes many people as “subjectivist”. It is questionable whether the Copenhagen Interpretation really has these “anti-realist” implications. At the very least, however, it makes problematic the question of what is “really going on when no one is looking”. In other words, if the wavefunction of a system is not a straightforward description of “the world as it is,” but just of some observer’s knowledge of it — then what WOULD a description of the world as it is look like? This is, indeed, an awkward question for the traditional interpretation to deal with — though various attempts have been made to answer it. A second problem connected with the relation between mind and matter, raised by another commentator to my essay, is how the relation between mind and brain is to be thought of. This is quite mysterious at present. A third question is what kinds of minds qualify as “observers” in the Copenhagen interpretation of quantum mechanics. One commentator asked why it would have to be only human minds. The answer is that it wouldn’t, but it seems it would have to be a mind capable of knowing the results of measurements and one not entirely describable by physics. Purely physical devices or inanimate things such as atoms and bacteria would not seem to qualify, whereas humans certainly do. Somewhere in between there is a line, but where it should be drawn is debatable.

It has long been suggested that the special role of mind in quantum mechanics as traditionally interpreted, together with the indeterminacy of the theory, may provide an opening for free will to operate in the world. Though I did not discuss this in my essay, several commentators did. Again, this is a murky and much debated subject.

Altogether, it is clear that quantum mechanics raises more philosophical questions that it solves.

Here are two “Big Questions” that it raises.

**Two New Big Questions:**

1. Does quantum indeterminacy provide an opening for free will?

2. In the context of the traditional Copenhagen interpretation of quantum mechanics, what would a complete description of the world through time, apart from what any “observer” knows about it, look like?

I enjoyed the read.

I’d first like to consider a very egocentric hybrid that can eliminate the need for MWI. Perhaps it is only “my” observation that can collapse the wavefunction and the rest of nature just follows Schoedingers Equation. This would make “me” a sort of god of some closed system, but into necessarily God. I guess that is similar to MWI but with no forks in the road.

We could also treat humanity as a collective. If our minds are together one perfectly coupled wave collapsing detector than there need only be one world, and one mind… collective free will? That would fit nicely with original sin and Christian dogma.

Dear jrd261,

What you are suggesting, namely solipsism, the idea that there is only one mind, is a perfectly consistent way of interpreting quantum mechanics. I quoted Eugene Wigner in my essay as saying, that materialism is “logically consistent with present quantum mechanics." The full quote was actually, "Solipsism may be logically consistent with present quantum mechanics, but materialism is not." In the solipsistic interpretation, there would still be "forks in the road": Each time the one observer (you) made an observation, the wavefunction would collapse, i.e. the universe would take one road at the fork.

Your other suggestion — all minds being a collective — also can be made consistent. In particular one could take the view that whenever there is a branching of the wavefunction (which happens when different parts of the wavefunction "decohere" from each other, in the technical jargon) all consciousness in the universe proceeds down just one branch. The wavefunction would continually branch, exactly as MWI says, but there would never be a situation where the same observer existed in several conscious versions in distinct branches. In this picture, the wavefunction itself is constantly branching, like train tracks; and what happens at the "collapse of the wavefunction" is not really any change in the wavefunction — all the tracks are still there — but rather all consciousness proceeds down a single track, so to speak. (What I have just described is my own speculative view of quantum mechanics, for what it's worth.)

There are different ways that mind could be imagined to come into the story. But unless mind comes in somehow at a fundamental level, then everything is just matter governed by Schrodinger's equation, and one is left with all parts of the wavefunction being equally real (even after decoherence). That is, one is left with MWI, and each observer existing in a huge number of equally real versions.

Excellent and succinct essay on the problem, Stephen! I believe I asked this naive question before but perhaps it is worthwhile to raise here again. Given the nature of quantum mechanics, many events will remain probabilistic; that is, they will never have an observer, and thus the wavefunction will never collapse and there will be no "jump". While this obviously is outside the main question, in that I am simply assuming an omniscient God, my question is: could God be the ultimate observer who can collapse any wave function? Would God's assumed omniscience preclude this (that is, would he see all wavefunctions at once and thus there would be no need for him to "turn his attention" to any particular set of quantum events), or, philosophically might it remain a possibility? I suppose one problem with this is that, while God could interact with the physical world "at a distance" in this way (which seems attractive in that one objection atheists have is how some kind of supernatural being can possibly interact with the physical world), the result would not be determined by God but rather the wavefunction could collapse either way (if there is a way for the observer to "choose" which direction the collapse goes, I've never heard of such). So God would be necessary, in this sense, for anything to happen (consistent with traditional theism), but he would still not necessarily know the outcome (clearly inconsistent with traditional theism). I realize this is nebulous but I still find some aspect of the argument compelling, in that observation of quantum events could be a way to explain God's continual interaction with our world in a way that is intellectually defensible. I would love to hear your opinion, and I apologize if you gave it previously but I forgot what you said!

As to the main point of the essay I certainly agree that QM does NOT directly prove anything about God, but does prevent, pretty clearly, it seems to me, an purely materialistic (or deterministic) worldview. It leaves open the door. The MWI is as ludicrous as any desperate attempt to square the circle is: sometimes one's instinctual resistance to the data leads one to propound ever-more improbable explanations. It seems there was a similar resistance to the Big Bang, which still exists but has become fringe, as I understand.

An interesting question is the relationship of quantum uncertainty to events in the brain (or rather, as the very fact that they are there is trivial, the outward effects on how the mind works). I don't think I've seen anything that isn't fairly silly on this,

pacePenrose. It does seem to me that QM undermines our traditional understanding of free will as much as any purely materialistic world view would. So working those issues out will be a key area–I'd love to hear any sources you know of on this topic that are worth reading.Hi Josh,

Good questions. I don’t think God (as understood in what is sometimes called “classical theism”) can play the role of an “observer” in quantum mechanics, for several reasons.

In the traditional (or “Copenhagen”) interpretation of quantum mechanics, as expounded by Wigner,

Peierls, and others, and explained in my essay, the collapse of the wavefunction corresponds to a change in the knowledge of the observer. But in classical theism, God is outside of time, and his knowledge does not change.

Another way of looking at all this is that the wavefunction gives the probability correlations between the results of one set of measurements and the results of another (usually later) set of measurements. For example, if I measure that an electron is located in a cubical box whose sides are of length L and that it has a certain energy, then that gives me an initial wavefunction that I can use to calculate the relative chances of finding various values for the electron’s position or momentum at a later time. In other words, in practice the wavefunction is a way of correlating the results

of various measurements. But, in classical theism, God does not make measurements. His knowledge is not “a posteriori” but “a priori”. That is, he does not learn about things as a result of their

happening, but rather they happen because he knows them, so speak.

The wavefunction encodes what some observer is in a position to assert about the physical world given some knowledge that he already possesses by virtue of other measurements or observations made by him.. So the observer is, practicaly by definition, some being who acquires information by means of physicallly interacting with the rest of the universe. God, however, (according

to traditional theism) does not physically interact with things in the universe, as he is not a physical entity. Physical entities cause things to happen in the universe by means of physically interacting with other entities. But God causes things in an utterly different way: by willing the reality or being of the whole universe. An analogy: a character in a novel has effects within the novel’s plot by means of acting within the plot in accordance with the internal rules of the novel. The author of the novel, on the other hand, causes things to happen as they do in the novel not by being’an actor in the plot, but by simply by conceiving of the plot (and of the rules that givern it).

As far as free will goes, and possible connection to “quantum indeterminacy”, I would suggest the relevant sections of my book “Modern Physics and Ancient Faith”.

There is something I still do not understand. My understanding is that until someone observes a quantum system, the wavefunction remains probabilistic. If God has already observed everything, because he is out of time, then there would be no uncollapsed wavefunctions. If not, however, then there must still be quantum events that even God does not know the result of, because they are logically unknowable. God can do anything that is logical, but not that which is by its nature illogical, correct? So I guess in response to your statement: "That is, he does not learn about things as a result of their happening, but rather they happen because he knows them"; I would ask, doesn't this preclude the possibility of there being

anyQM events that remain probabilistic? If all events (including, say, particle decays) happen because he knows they are going to happen (and where, and when, and how), then his very knowing would preclude any uncollapsed wavefunctions. . . and we would not have made the observations that led to the formulation of QM. Probably I missed something here. . .I guess where this my argument may go wrong is in your point that God does not "physically" interact with the physical world, but rather through his will. But in traditional theism, God can, if he wills, cause a physical event such as a flood. Though the distal cause is his "will" (and it is difficult for us to understand quite what this means), the proximal cause is rainfall, which presumably is not some special kind of supernatural precipitation but the same kind of physical rainfall we know (and this summer, wish for). So I don't quite understand why the action-at-a-distance of observation by God (or we can call it willing) could not be possible; Even in the case of the flood, there must be some interface between God's will and a physical event. If it is not collapse of wavefunctions, it is presumably something else. Am I way off base?

A problem and a possibility. The problem: Jane’s relationship to the french exam is accidental to Jane – it is the relationship which is probable, not Jane. It is easy to verbalise this relationship. In quantum physics probability is of the essence of the subject, a fact which mathematics reveals consistently and persistently. Verbalization of probability in this sense of essence, to use Aristotelian language, seems impossible to adopt within the necessary constraints of grammar and syntax. Is it possible to verbalize quantum mechanics without gross distortion of its fundamentals?

The possibility: Panentheism ‘God in the world’ finds ‘in’ difficult. If probability is of the essence of all created things then probability is at the heart of ‘in’. A creator God might therefore be said to be unchangeably committed to a probability inspired universe.

Hi Dr. Barr,

Prof Barr,

How does a many-world wavefunction know when to branch?.

That is, the measurement is supposed to be external to the wavefunction but if everything is internal, what would measurement mean anyway?.

Also, quantum mechanics was initially formulated as a theory of interaction of microscopic systems interacting with measuring devices. Now the physicists define and use wavefunctions of the entire universe. How is this extrapolation justified?. Or are they doing it as a matter of faith in atomism that all macroscopic objects are fully explainable as interactions of fundamental microscopic particles?

In Thomism, the parts are only defined with respect to the whole and can not be fully understood

without reference to the whole. This whole-part loop is called the Formal Cause of the thing.

Perhaps this is what quantum mechanics paradoxes require?

Dear Wallace,

First, the logical structure of the argument against materialism that I outlined in my essay is based on what happens when a measurement is made and how we are to understand the famous "collapse of the wavefunction" that occurs when a measurement gives one definite result. The argument is to the effect that the mind of the measurer (or "observer") cannot be completely described by wavefunctions governed by the laws of quantum physics. So, it is the mind of measurers that is in question, not the mind of God or gods. Let us therefore leave them out of the discussion.

Second, you say that we "might imagine a world with variables that look probabilistic to its inhabitants, but are not really undetermined." That is true, and it is exactly what happens in classical physics. In classical physics, all measureable quantities have definite values at all times, but because we don't know most of those values, we must use probabilities. Many physicists, including Einstein, have suggested that the same may be true in quantum mechanics, i.e. there are "hidden variables," whose values we don't know and that this is why probabilities seem to be needed in quantum mechanics. The most successful attempt to construct a hidden variables theory was made by David Bohm. While such theories can reproduce many of the successes of standard quantum mechanics, they are unable to deal with full-blown "quantum field theory." Most physicists, therefore, think the hidden variables approach is extremely unlikely to succeed.

Third, the structure of the argument I explained in the essay was not so much about the values that variables truly have, but rather about what a wavefunction means. Basically, a wavefunction is one of two things: it is either (a) a straightforward description of the world as it is, or (b) it encodes what some observer knows or is in a position to assert about the world. If it is (a), one is led perforce to the MWI. The reason is simple: The wavefunction contains many branches describing alternative histories of the world. So if the wavefunction is just "the world as it is", then such histories are really all going on at once, and that is the essence of MWI. On the other hand, if (b) is correct, then "what some observer knows" — and thus mind — enters into how our fundamental theories of physics. That is why Wigner wrote about 50 years ago

“While it may be premature to imagine that the present philosophy of quantum mechanics will remain a permanent feature of future physical theories, it will remain remarkable, in whatever way our future concepts may develop, that the very study of the external world led to the conclusion that the content of the consciousness is an ultimate reality."

Dear Vishmehr24

The branching of a wavefunction takes place, roughly speaking, when some microscopic system (e.g. a radioactive nucleus) interacts with a macroscopic system (e.g. a Geiger counter). The wavefunction has various parts describing the nucleus decaying at different times. In these different parts of the wavefunction the Geiger counter is also doing different things (because it is affected by what the nucleus does). Since a Geiger counter is made up of a huge number of

particles, a Geiger counter “doing different things” entails a huge number of particles behaving differently in the different parts of the wavefunction. That means that the different parts of the wavefunction differ very greatly from each other, and therefore they “decohere” from each other, to use the technical jargon. That means that for all practical purposes, they no longer can affect each other and are like different worlds.

In other words, the splitting apart of the branches happens whenever macroscopic objects are involved. The big question that distinguishes MWI from the traditional interpretation of quantum mechanics is whether all the branches are equally real. In MWI, they are equally real. In the traditional interpretation, they are not. E.g. if the observer sees the nucleus decay at 1 PM (because the Geiger counter clicked at 1 PM) then (according to the traditional view) that is what really happened and all the other branches of the wavefunction (for example the one where the nucleus

decayed at 5 PM) are just unrealized possibilities.

You are right that one is doing a great extrapolation in supposing that oen could (in principle) write down a wavefunction of the entire physical universe. Speaking just for myself, I see no problem in making that extrapolation. Of course one is always making similar extrapolations when doing physics. When one assumes that nature obeys universal laws, so that every electron in a piece of metal obeys the same Dirac equation, that is an extrapolation. (I think a reasonable and justified one. )

Dear Prof Barr,

Thanks for your reply but I am still not convinced that the quantum mechanical extrapolation of the wavefunction to the entire universe is of the same character as the extrapolation of homogenity of the universe such that same laws apply on Mars as on the Earth.

The quantum mechanics demands observers; the formulation is expressed in terms of measurement and measuring devices and observables. These presupposed things are external to the system described by the wavefunction. What possible meaning could be attributed to the wavefunction of the universe?

Am I correct in supposing that the measurement process has been resolved to the decoherence pheneomenon?. But decoherence is governed by Schrondinger’s equation and thus by the Copenhagen picture or principles can not be the full story. Measurement is required to break the natural evolution of the wavefunction. The decoherence, I believe, is asymptotic; the superpositions never die 100%

And you say that MWI keeps alive the possibiliies that are not realized in the Copenhagen picture. But the decoherence should give unique answer since it is just the evolution of Schrodinger’s equation. So how does MWI keep the possibilites alive?

I think I know what is bothering you, Josh. As I said in reply to Wallace Forman (in the third paragraph), it all comes down to what the wavefunction of a system is. One would like to be able to say that it is just a straightforward description of what is happening in the world, of the world as it really is, apart from what you or I know about it. That leads straight to the Many Worlds picture, because the wavefunction typically contains descriptions of many alternative branches. In the traditional or Copenhagen interpretation, one has a more modest view of what the wavefunction is: It is not simply “the world as it is”, but rather it encodes what some observers know or are in a position to assert about the world. that is why heisenberg himself said that the mathematics of quantum mechanics “represents no longer the behavior of elementary particles, but rather our knowledge of this behavior”. And it is why Rudolf peierls said, “the quantum mechanical description is in terms of knowledge.”

That raises a very important question — which, I think, is your question: What DOES describe “the world as it really is”? Even if the wavefunction does not describe it, there must be some comprehensiove and complete and accurate description of physical reality — call it the “God’s eye view of things” (even thouigh I don’t want to drag God back into the discussion).

In other words, what IS really going on when no one is looking? What if beings such as ourselves had never evolved? What about regions of the universe that no human or other sentient organism is ever going to observe or make measurements of? What about what will be happening in the universe after all life has died out? Good questions! The wimpy answer is that science cannot speak about things that cannot be observed, and what is going on in places that will never be observed is, by definition, something that cannot be observed! But that seems a pretty unsatisfactory answer. The traditional Copehagen interpretation doesn’t give an answer. I have an answer that satisfies me, and I give a very brief sketch of it in my reply to jrd261. Here I will only say that I think that even in the context of the traditional interpretation of quantum mechanics there does exist an answer to the question “what is really going on in the world even when no observers are looking”. In other words, the traditional interpretation does NOT commit one to some form of subjectivism or Berkeleyan idealism, but can be consistent with a robust philosophical “realism”. But this is a tricky business, and probably beyond what can be discussed in such a forum.

I'm curious as to your take on how the concept of retrocausality impacts your discussion. Very good article as well, thank you!

Dear Ageingcrofter,

I would agree with you that attempts to discuss mathematical subjects “verbally” (if by that is meant “natural languages” rather than mathematical symbols) can lead to distortion. This is especially the case with subatomic physics, where the concepts needed are far removed from everyday experience. For example, the idea that the wavefunction is a “vector in a Hilbert space” involves a high level of mathematical abstraction. On the other hand, it is impossible to learn either mathematics or physics without using natural language in addition to mathematical symbolism. One starts with ordinary experience, and everything one learns must be somehow connected to ordinary experience if one is to grasp it. One cannot understand complex numbers, for instance, or develop intuition about them, unless one first has some experience with ordinary counting numbers.

Dear jarruda,

If by retrocausality you mean effects coming before their causes, then this is not allowed in present theories of physics. Theories that “violate causality” are regarded as “pathological” and unrealistic.

But do you mean something else?

So I follow the thread of the argument you've made, Stephen, but it seems that you're making a probably false assumption – namely, that the universe admits nonzero probabilities of infinitely small value. One way of explaining why wave functions "jump" in some interactions but not in others would be to say that the universe can only sustain probabilities that are of a sufficiently high magnitude (because it only measures things to a finite accuracy), so that once a single wave function is tested enough times it necessarily collapses one way or the other. To make a very rough analogy, this would be along the lines of a calculator rounding 2/3 up to 0.666667: because the calculator can't display (or even really calculate) infinitely many digits, at some point it has to terminate its operations and simply decide to put a 6 or a 7 at the end. If the engine that's running the physics of our universe is only finitely powerful, it would make perfect sense for minds to be sufficient (in most cases) but unnecessary for the collapse of wave functions: minds are very complex but not

onlyminds are very complex, and eventually time alone would guarantee a wave function's collapse.Granted, this explanation isn't obvious and it leaves some things to be answered (though if you can give me a physical theory that leaves *no* questions to be answered then I'll be very impressed). But it would at least explain the data without requiring the positing either of magical properties for minds or the reality of the many worlds hypothesis, and (so far as I'm aware) it is at least plausible. We obviously know that the universe measures things very precisely indeed, but I've not read anything that would necessitate the universe measuring things infinitely precisely.

Dear larryniven,

You make an interesting suggestion, but I am not sure it can be made to work. The “collapses” of wavefunctions (i.e. jumps in probabilities) don’t only happen when the relevant probabilities are close to 0 or 1. Consider, for example, the case of a (hypothetical) radioactive nucleus that has a half-life of one hour. If the nucleus is there at noon, it has 25% chance of decaying during the interval between 1 PM and 2 PM. During that interval, the survival probability of the nucleus varies continuously between 0.5 and 0.25 (and the decay probability varies in the corresponding way). At no point in this time interval are the decay or survival probabilities that are given by the wavefunction close to 0 or 1. Typically the probabilities jump by an amount that is finite and not at all small.

Your idea that probabilities are discrete rather than continuous is nevertheless interesting to contemplate. One would have to modify the rules of quantum mechanics in a radical way for it to work, however, as those rules use mathematical operations that would not be consistent with discretized probabilities.

You wouldn’t happen to be the science fiction writer Larry Niven?

"You make an interesting suggestion, but I am not sure it can be made to work. The "collapses" of wavefunctions (i.e. jumps in probabilities) don't only happen when the relevant probabilities are close to 0 or 1."

Sure – but I didn't say that they would

onlycollapse when near 0 or 1, just that they wouldalwaysdo so. Again, think of it like it was a simulation that you were running on your own computer: you could easily write a "random" decay function so that it would have a 50% chance of decaying at time N, a 25% chance of decaying at time N+1 and so on. What you could not do is write a decay function that stays smooth indefinitely, because eventually your machine would run out of digits with which to calculate, and the probability would effectively become 0."One would have to modify the rules of quantum mechanics in a radical way for it to work, however, as those rules use mathematical operations that would not be consistent with discretized probabilities."

Really? I'd like to see some examples of what you mean by this, because I'm not at all sure that it's true. I mean, yeah, if the discrete increments were (relatively) large, we'd see something very different in the universe and the theory would never have come up. But if they were (relatively) small? I haven't done the proof yet, but I suspect we'd have to look very closely in order to notice the difference. And it's not like probability theory requires continuous distributions; in fact, most math that deals with continuous distributions is just a clever abstraction of math that deals with discrete distributions (to take an easy example, calculus is like this). So which operations would not be consistent with what I'm suggesting, exactly?

Thanks for the interesting essay. I have several questions.

1) Why do you say that the Copenhagen interpretation requires a human observer; are there other ways of understanding the Copenagen interpretation that do not require this?

2) Are Copenhagen and Many Worlds the only tenable options; what about objective collapse theory (which does not require a human observer)?

3) How do you differentiate your position from a "God of the Gaps" argument? Can't we just say that our physics models and our interpretations of them currently only incompletely describe the universe as we experience it (as has always been the case)? For example, the math that describes quantum mechanics does not cleanly mesh with general relativity, but I think the most reasonable conclusion to draw is that the math is not complete. Even if the math we currently use to describe quantum mechanics has hit something of a dead end, we already know that quantum mechanics is only an incomplete explanation of the universe. It seems strange to make so much of its quirks.

Thanks.

Dear Ethan,

Excellent questions. I will take them in the order presented.

Question 1: The traditional interpretation of quantum mechanics (also called the Copenhagen or standard interpretation) makes a distinction between the “system” being measured and the

“observer” doing the measurement. The wavefunction describes the system. The wavefunction changes in two ways: (a) When the system is left alone, its wavefunction evolves in a continuous and unique way in accordance with the Schrodinger equation. (b) When the observer makes a measurement of some observable property of the system and gets a definite result, the wavefunction

undergoes a “collapse” that reflects the result of the measurement. Unlike the Schrodinger evolution (a), the collapse (b) is sudden and unpredictable.

The problem I described in my essay is that if the observer is included completely in the system, then the wavefunction changes only in way (a) and there is no “collapse of the wavefunction”. There is thus no unique and definite outcome, but all possibilities remain in play — thus MWI.

So the question arises, what or who can play the role of “observer”? The first point — emphasised by Peierls, whom I quoted in the essay — is that the observer cannot be a purely physical entity, for if it were one could consider the larger system which comprised both the original system and the (purely

physical) observer. But then one would have the problem that the wavefunction of this larger system could collapse —- unless there were some other observer outside of IT. But then, if THAT observer is purely physical, one can expand the system yet further to include IT. An infinute regress.

So it seems that the observer has to be something that is not purely physical. Moreover, since a measuremet is only completed when the observer KNOWS the result, it seems that

the observer has to be a knower. That is why many people — such as Wigner and Peierls —- have argued that the “consciousness” or the “mind” or the “knowledge” of the observer plays an essential role.

Does the observer have to be “human”? Well, certainly humans are observers: we make measurements and get definite results. But that doesn’t mean that only human beings are observers.

Could inteligent space alliens be “observers”? Obviously, if there are any. Could chimpanzees or dogs? That depends on whether they can make measurements and whether they are completely describable by physics.

Question 2: What about objective collapse theory? Well, if one keeps to the mathematical structure of quantum mechanics as we have had it since the days of Heisenberg and Schrodinger, then there is no collapse without an observer, as explained above. (Some people — including some physicists — have the misconception that what is called “decoherence” is the same thing as wavefunction collapse. And since decoherence only requires the involvement of macroscopic systems (as I explained in answer to another person’s question) not conscious observers, they

think they have explained wavefunction collapse without invoking observers. But they are wrong.)

So, to get a collapse without an observer, one would have to change the mathematics of quantum mechanics. There have been attempts to do this. (Wigner tried, for example.) Perhaps that is

what is needed — many people have suggested that in a more complete or improved theory, all the puzzles of quantum mechanics will be resolved and wavefunction collapse will be explained. It should be noted, however, that quantum mechanics has passed hundreds of thousands of tests with stunning accuracy over the last 85 years or so. It is hard to modify it without destroying its self-consistency or its consistency with experiment. This leads us directly into question 3.

Question 3: Can’t we say that quantum mechanics is incomplete? Isn’t the difficulty of meshing it with General Relativity evidence of this? Well, many people have argued this. However,

it is believed that superstring theory is a consistent theory that incorporates both the principles of quantum mechanics and General Relativity. So that takes away a major argument’ for the inadequacy of quantum mechanics. One never knows what the future will bring in science, but right now quantum mechanics looks like it is in perfect health. It is simply not true to say “that we already know that quantum mechanics is only an incomplete explanation of the universe.” We know no such thing!

There is a bad typo in line 6 of paragraph 4 of my Reply to Mr. Blaylock. It should read that "the wavefunction of this larger system could NOT collapse"

And of course intelligent has two l's and alien has one l.

When I want to believe in something, I am quite able to use any reason whatsoever to do so. My question back to the OP is where are you going with this question? Are you paving a road and making a case to "believe in God" or what?

Dear larryniven,

I can give two examples.

First example. Suppose that a particle X has three possible "decay modes", A,B, and C, and that a "symmetry principle" makes these three decay modes equally probable. (Symmetry principles

play an important role in fundamental theories of physics.) Then the "amplitude" for X to decay in each of these modes must be EXACTLY equal to the square root of 1/3. (The "amplitudes" are what appear in the Schrodinger equation. To get the probabilities one takes the square of these amplitudes.) The exactness of the answer logically follows from two unavoidable requirements: the

probabilitiies of all outcomes must add up to 1 (100%), and the three decay amplitudes have to be equal by the symmetry principle. So, there is no way for these numbers to be "rounded off" in some high decimal place.

Second example. In the decay of an isolated radioactive nucleus, the decay amplitude and the decay probability are given EXACTLY by' an exponential function of time. This can be shown to follow

from "time tranlation invariance" of the laws of physics (a symmetry principle).

The point is that quantum probabilities follow from a precise mathematical formalism, which involves a number of fundamental principles. These probabilities cannot depart from the values

given by the formalism without violating the basic principles and assumptions of the theory.

I am not saying that your idea couldn't be true, only that for it to be true, the rules of quantum mechanics would have to be changed in a fundamental way.

"The exactness of the answer logically follows from two unavoidable requirements: the probabilitiies of all outcomes must add up to 1 (100%), and the three decay amplitudes have to be equal by the symmetry principle."

Equality is trivial in the sort of thing I'm talking about: because the system is going to have the same limitations on "memory" in every case, it'll truncate at the same place in every instance and they will be equal. (No matter how many times you divide 2 into 3 on your calculator, you'll still get .6666667.) Adding up to one is a little trickier, because the additive margin of error is not necessarily within the original margin of error – though it could be (it depends, among other things, on the additive algorithm being used). On the other hand, though, I find it awfully strange to think that the universe first generates the odds of decay and then "adds them up." That seems more like a convenient way of talking about this to make it more intuitive than a description of any real event. It has to be more plausible to say that the individual probabilities are parasitic on the fact that one of them must happen, not the other way around – or even that our talk of "outcomes having probabilities" is really shorthand for something else. But then that's entirely compatible with having a finitely powerful physics engine.

Also, like the decay thing you mention next, the power of this argument depends on evidence, does it not? I readily admit that the predictive law is infinitely exact – math is nice that way – but it begs the question to say that reality must be infinitely precise just because a predictive law that we've come up with is infinitely precise. So neither of these examples is tremendously persuasive, at least so far as I can see.

At any rate, I did about an hour's research last night and discovered that there's actually already a theory not unlike the one I'm proposing. The Penrose version of objective collapse theory evidently hypothesizes (and apologies if I'm misusing technical terms here, I'm just going for the gist) that there's a threshold amount of energy past which quantum phenomena collapse into more standard phenomena, which is not quite what I've been saying but has enough similarities to be at least analogous (e.g. energy becomes the analog of hard memory). I see that you've discussed objective collapse theories in this comment thread already, but you seem not to have addressed the Penrose variation (in that the thing about confusing decoherence with collapse seems not to apply to it). Given that this is still a live theory, even to the point of being (apparently) (semi-)endorsed by the people at Stanford's philosophy encyclopedia, and given that it's fairly close to what I've been saying, I'm beginning to feel like you gave an incomplete picture of the current state of affairs.

Hi Dr. Barr and larryniven,

I might add that if the values that the wavefunction could take on were universally discrete (at least in the way larryniven suggests), then any continuous function of the probability would inherit the discrete nature of the wavefunction. Thus the discretization ought to be manifested in macroscopic ways that can be measured (example below). To my knowledge, this has not been seen in general cases, which suggests that wavefunctions do not indeed take on only discrete values.

First, consider a Stern-Gerlach apparatus. That is, let an ensemble of electrons pass through a strong non-uniform magnetic field pointed along a given axis (call it the z-axis). Then the trajectory of the ensemble will be split in two as it passes through the field, with equal numbers of electrons in each. We label each trajectory by 'up' or 'down'. Thus electrons in one branch have 100% probability of having the property 'up', and those in the other have 100% probability of having the property 'down', and we may reasonably say that a randomly selected electron from the initial ensemble has a 50% chance of having the property 'up', and a 50% chance of having the property 'down'.

Next, pass only the 'up' ensemble through another Stern-Gerlach apparatus, but this time oriented along a different axis. Let the angle this axis makes with the first z-axis be called T. We find the initial 'up' ensemble is again split in two. We label one beam 'UP', and the other 'DOWN'. We also find that the relative number of electrons in each path depends on the angle T. In particular, it is found that the relative number of electrons in one beam is cos^2(T/2), while for the other beam it is sin^2(T/2). We may again reasonbly say that an electron randomly sampled from the beam of 'up' electrons in the middle of the apparatus has a chance of having the property 'UP' of cos^2(T/2), and a chance of 'DOWN' of sin^2(T/2).

Therefore, if the wavefunction could only take on discrete values (labeled by Pn), then the angle between the first and second apparatus can also only take on the discrete values Tn=2*arccos(sqrt(Pn)) and Tn=2*arcsin(sqrt(Pn)). While this is not impossible, this seems unlikely, and there has been no experimental evidence of it to my knowledge.

Furthermore, a Stern-Gerlach apparatus applied to atomic Sodium will split the initial ensemble into three, whereas when it is applied to atomic Beryllium that number is four. Indeed, given any positive integer N, it is in principle possible to find (or construct) an atom for which an ensemble will split into N beams. When a double-magnet apparatus is used on such ensembles, one sees the same qualitative features as with the simple electron case described above: the relative numbers of atoms in each trajectory are a continuous function of the angle T between the magnets, and these relative numbers are precisely the probabilities.

If the discretization of probability is to be universal (eg, if only probabilities of 1/10, 2/10, 3/10, … were allowed for

anysystem), then it cannot depend on the N of the atomic species being passed through the apparatus. Thus a given apparatus must be able to be oriented at all angles Tn for all possible atomic species at the same time, even if it never has anything but electron ensembles pass through it.To be self-consistent, it is therefore required that the discretized probablities are such that the discretized angles for one ensemble are in general the same as the discretized angles for another. But the function relating angles to probability is in general very complicated, with complexity increasing with N. For example, given a discretized set of probabilities (0, 1/10, 2/10, …, 1), the set of allowed angles for electrons differs from the set of allowed angles for atomic Sodium, which itself differs from the set of allowed angles for atomic Beryllium, such that if the apparatus were adjusted to say the 8th allowed angle for Beryllium while electrons were passing through, it would produce a relative abundance of 'UP' electrons that is not equal to any of (0, 1/10, 2/10, etc), which is inconsistent with the original idea that the only allowed probabilities are (0, 1/10, 2/10, etc).

While I have no proof, I suspect that the only set of probabilities that is consistent with all values of N is not discrete at all, but is continuous (or something very close to it), which leads us back to a traditional understanding of the wavefunction.

This line of thought is extremelty suggestive, especially when one considers the relatively simple nature of the Stern-Gerlach/spin problem, where there exists continuous and bounded functions relating macroscopic variables to probabilities. The analysis is likely more forbidding to discretized probability when one considers position and momentum, where the wavefunction values and the underlying operators are not in general bounded.

Dear Vishmehr,

If I understand your argument correctly, it is as follows: The collapse of the wavefunction of a system requires the observer to be outside the system. No observer (measurer) could be outside of the entire universe. Therefore, the “wavefunction of the entire universe” could never collapse. And if the wavefunction of the entire universe never collapses, one ends up with the Many Worlds interpretation.

All of that is true. It is one of the aguments that proponents of the MWI use: they say that since there ought to be a wavefunction of the entire universe, one is forced to accept MWI. Turning this around, it would seem that to reject MWI, one must also reject the possibility of a “wavefunction of the entire universe”.

This logic is all sound. I would distinguish, however, between the entire universe and the entire PHYSICAL universe. Is everything in the universe physical? According to physics, as we have understood physics for a long time, a physical system is completely characterized by some set of variables. There presumably is some set of variables that completely characterize the whole physical universe. I see no compelling reason why one could not (in principle) construct a wavefunction for the physical universe. If one considers a human observer,however, that observer would be ( in part) “outside” the description provided by that wavefunction to the extent that there is an aspect of that human being that is non-physical. In other words, there are two issues, (a) does it make sense to speak of a wavefunction of the entire physical universe, and (b) is the universe the same thing as the PHYSICAL universe? It is not clear, therefore, that accepting a wavefunction of the universe as a meaningful concept necessarily commits one to MWI.

Prof Barr,

Your solution is ingenious but leads to doubts about the physics that can be obtained from such a procedure.

If agents can not be described quantum mechanically and agents are part physical, then it leads to less confidence in the postulate of universal wavefunction.

Do you have the same degree of confidence in quantum cosmological applications as you would have on solid state?

You ask where I am going with the question.

I am simply explaining a very important line of argument that goes back to the physicists John von Neumann, Fritz London, and Edmund Bauer, and that has been accepted by many other physicists including Eugene P. Wigner and Rudolf Peierls. I think the argument presents one with three choices: (a) present quantum mechanics is wrong or incomplete in some fundamental way, (b) the Many Worlds Interpretation is right, or (c) materialism is false, at least as regards the minds of observers. Pick your poison.

Why is God mentioned in the title of the essay? The answer is simple: I was asked by the people who run Big Questions Online whether I would be willing to write an article answering the question “Does Quantum Physics Make it Easier to Believe in God?” The question was given to me, and I answered it.

I suspect that a certain line of thought may underlie your question. (I base this on your talking about how “wanting to believe something” can affect one’s reasoning.) Tell me if I am wrong. The line of thought is the follwoing: Religious people are driven not be reason but by wishful thinking. People who engage in wishful thinking bend reason to their desires and look for arguments to sustain beliefs that are actually based on completely non-rational — if not irrational — grounds. I would make several comments about this. First, the validity of an argument does not at all depend on the motives of the one making it. That is why it does not matter in science whether the person proposing a theory is a liberal, a conservative, a Marxist, a Buddhist, a Hindu, an atheist or a Christian. What matters is the strength of his arguments. The same is true in philosophy. I have co-authored research papers with colleagues whose religious, political, and philosophical ideas are diametricallly opposed to mine. For example, I have written a well known paper on the “multiverse” idea with three co-athors, one of whom is strongly atheist, and one of whom is (like me) religious. Someone who worries about the ulterior motives of the person proposing a scientific theory or philosophical theory has already betrayed reason. Second, wishful thinking is a danger to which all people are subject. Some people want to believe in God, some people want not to believe in God. Both thesm and atheism can be comforting beliefs, though in diferent ways. Third, all people have fundamental convictions and intuitions about reality that make them more disposed to accept certain conclusions and reject others. For example, one of my deepest convictions is that there is such a thing as objective moral truth. Another is that the world makes sense. To have basic presuppositions is not irrational. Indeed, one cannot be a rational person without them. Every argument requires premises.

Dear Mr. Niven,

I think you may be missing the qualifiers embedded in my previous statements. I don’t deny that a scheme such as you propose might conceivably be the correct description of the world. (Though I think it unlikely in the extreme.) All I am saying is that such a scheme is NOT standard quantum mechanics. It entails a MODIFICATION of the mathematical formalism of quantum mechanics. By the same token, Penrose is not claiming that his theory of collapse is something that is contained in our present quantum mechanical formalism; rather, he is proposing a modification of that formalism. (By the way, this is clear from the following consideration: In the standard quantum mechanical formalism, the evolutiojn of wavefunction given by the Schrodinger equation is “unitary”. The collapse of the wavefunction, on the other hand, is a non-unitary process. Thus, one must modify the equations somehow to get a collapse from them.)

You also are proposing a modification of the equations, though you apparently do not appreciate this fact. You seem to be envisioning the equations of the universe being run on a computer of some sort. (You speak of a “system” that has “memory” and that “truncates”.) In any event, the process of “truncating” numbers or mathematical expressions is a mathematical operation, just like multiplication and division. Such truncation operations are simply not a part of the mathematical formalism of quantum mechanics as we have had it since the 1920’s.

It is perfectly OK to modify a theory, as long as one remains consistent with known experimental facts. You are perfectly entitled to propose such modifications. But they ARE modifications.

I am not giving an “incomplete picture of the current state of affairs”, if by that you meant a misleading picture. (Is that what you meant?). I not only clearly stated that people have made attempts to construct objective collapse theories, but I cited Wigner’s own attempts to do so as an example. I could have mentioned Penrose’s attempt as another example. I suppose that if I do not mention every speculative attempt to modify quantum mechanics that has ever been proposed — and there have been many — you will say that I am not giving a complete account. In some trivial and sense that is true. A complete account would require a review article of several hundred pages length.

Penrose’s idea is interesting (most of his ideas are interesting); but has not attracted much of a following in the physics community. Penrose thinks that unifying quantum mechanics with General Relativity (GR) is likely to require a modification of quantum mechanics. That is one reason he thinks that wavefunction collapse will end up being explained by gravitational effects. The backstory of this is that for decades physicists were unable to find a consistent way to “quantize gravity”, and this led many people to suspect that GR would force a modification of quantum mechanics. Some still think that, but far fewer than previously, because superstring theory has demonstrated that GR can be quantized without changing the postulates of quantum mechanics.

"In any event, the process of 'truncating' numbers or mathematical expressions is a mathematical operation, just like multiplication and division. Such truncation operations are simply not a part of the mathematical formalism of quantum mechanics as we have had it since the 1920's."

As I've already conceded, it has never been a part of any physics at all, since well before the '20s. I think, however, that you're missing my point somewhat: exactness in reality is not required just because the best explanatory models that we have are exact, nor does reality have to work in the same way that our stories about it work. The "adding up" thing is a perfect example of this. Again, you seem to think that I must be wrong because (e.g.) .333… + .333… + .333… wouldn't add up to 1 under my system. But doesn't this presume something odd about reality (i.e., that the "outcomes" and their "probabilities" are, as it were, ontologically primary, and the fact that the probabilities add up to 1 is only a sort of accident)? There are ways of structuring random events so that "probability" is just a way of descriptively talking about the results or the architecture of the system, not something that's actually in the system. You should be able to appreciate this, because you're making a similar point about my usage of computer language. I fully understand that my analogy is just an analogy – that, in other words, the "systems" and "memory" and so on are more suggestive than literal. But do you understand that your various linguistic approximations (about "adding up" and so on?) are likewise just linguistic approximations? I'm beginning to doubt it.

As for my theory being a modification, I was under the impression that any additional theory would require a modification of some sort, because an explanatorily incomplete theory is one that by definition requires modification in order to become (more) complete. Positing the causal influence of "transcendent" minds, for instance, means writing a whole new set of laws that aren't causally closed, which – unless I'm very much mistaken – is also well outside the traditions of physics; along similar lines, it requires defining minds in a coherent way, which will be very difficult to do when (1) they're meant to be "transcendent" (and so, presumably, outside our capacity to study) and (2) the evidence we do have about minds is converging rapidly on the conclusion that they are just matter. Maybe, then, you're really just concerned about changing one thing as opposed to another? But in the absence of evidence to decide which thing ought to be changed, that's no more than an aesthetic consideration (i.e., you find one thing more displeasing than I do). I mean, *are* you arguing that the evidence absolutely rules out MWI or the Penrose interpretation (or any of the other alternatives that I guess are out there)? My reading of you (which, in fairness, coheres with what I read from other physicists) was that you just didn't like those other ones, in the aesthetic sense – but

that, I'm afraid, is neither something that "make[s] it easier to believe in God" (except, of course, for you personally) nor "an argument against the philosophy called materialism."I am very happy to hear from my esteemed colleague! (I should mention for the rest of the audience, that bknikolic is a theoretical physicist.) My short answer to question 1 is that I don’t think God has anything to do with the problems of how QM is to be interpreted. (I have read some of Stapp’s work, but am not familar with this aspect of his ideas.) As for 2, I don’t see how something that is entirely physical and thus described by the wavefunction of the universe could collapse the wavefunction, unless the laws of QM were modified in some way.

I appreciate the point about the brain being a hot dense system in which decoherence times are very short. Some argue from this that the brain acts in an essentially classical way. That may be so. I have my own (VERY TENTATIVE) speculative hypothesis on how wavefunction collapse is related to the mind. I say a few words about it in my answer to jrd261 above.

My basic idea, in a nutshell, is that whenever there is decoherence produced by any process anywhere in the universe, all consciousness in the universe travels down one path. { I hasten to say that I am assuming many distinct conscious beings, not some collective consciousness. I am just supposing that the consciousness of every conscious being in the universe go together down one branch of the wavefunction of the universe, at each branching.) The wavefunction of the universe keeps branching just as in MWI. But among all those branches just one path contains all consciousness. This may seem strange, in that in some other branch there are sets of degrees of freedom that look like you and me, but they have no consciousness associated with them. (In the whimsical jargon used by “philosophers of mind” nowadays, they would be “zombies”.) But this assumption violates nothing that we know empirically. There is no way to to derive (logically and mathematically) from the physical description of a system anything about whether it has consciousness associated with it. (This is connected with the well-known “problem of other minds”) Nor can we examine those other versions of us, since they are in other branches that have decohered from our branch. So the idea that all consciousness is in one branch violates nothing we know. For this idea to be consistent, one would need the decoherence time between any two branches that would look different to our senses to be shorter than the time it takes fro the brain to perform a perceptual act. (Otherwise, during the branching, when there was still significant coherence, it would be ill-defined to say that minds wer in a particular branch.) But here my idea is actually HELPED by the fact that decoherence times involving the brain are so short. The brain cannot perform any perceptual act facter than, say, a microsecond (to take a safely short time). But the decoherence times of any relevant process would be much shorter than that.

In the picture I am outlining, one has (it seems to me) the best features of both MWI and Copenhagen. It preserves the nice feature of MWI that the wavefunction changes in just one way — according to the unitary Schrodinger evolution. One never has to “saw off branches”. One can talk unambiguously about what the physical world is doing at all times: it is described by the wavefunction of the universe. But I avoid the bad feature of MWI: there is only one copy of each conscious being. I can also make sense of the “probability rule” of QM, which is somewhat problematic in MWI: The probability given by the absolute square of an amplitude is the probability that consciousness will take the corresponding branch rather than the others. Like the Copenhagen interpretation (as understood by Wigner, Peierls and others) my interpretation posits consciousness as a reality connected to, but distinct from physical entities.

I would like to discuss this further with you (off-line, it would be too hard to do it in this forum) to see if you can punch any holes in this idea. It seems to me consistent with everything we know, gives an account of wavefunction collapse, and entails no modification of the postulates of QM.

While there is much disagreement about how quantum mechanics {QM} should be interpreted, everyone agrees about what the mathematical formalism of QM is. That formalism is precise and well-defined. Everyone agree how to calculate physically measureable quantities in QM and everyone gets the same answers. Neither the MWI interpretation nor the traditional (Copenhagen) interpretation propose any modification of that formalism.

The fact that you call Penrose's idea an "interpretation" bespeaks some confusion. "Interpretations" of QM assume the standard mathematical formalism is true, and then try to make philosophical sense of it. That is to be distinguished from various suggestions for modifying the formalism, which includes Bohmian mechanics, and Penrose's idea — and your idea.

I wonder if you are reading my answers. You ask, for example, whether I am arguing that MWI or Penrose's idea is wrong. Nowhere have I argued that they are wrong. How did you get that idea? In my article, and in every subject response I have given, I have only tried to explain the alternatives. which, basically, are these: (a) The MWI interpretation, (b) the traditional interpretaion, and (c) modifying the formalism in some way. As I said in a response to another person: pick your poison.

I have argued that if the traditional interpretation is right, then materialsim is wrong, and if materialism is right then one must choose either (a) or (c). That is all I have claimed.

In my (tentatively proposed) scheme, the physical bodies of human beings would be characterized by measureable variables (e.g. the positions of particles) and these variables would be included in the wavefunction of the universe. That is, the wavefunction would provide an accurate physical description of a human being — but only a physical description. I agree with Peierls that not everything about a human being, including his knowledge and his consciousness, is describable in this way.

I should emphasize that even if my own tentaive ideas on this subject are wrong, the general discussion given in my essay is unaffected.

I thank Professor Barr for such a clear and illuminating article. He certainly keeps up the excellent standard set by his book,

Modern Physics and Ancient Faith.I begin with a question for Professor Barr. In the standard model, is the idea that taking the measurement or making the observation

causesthe wave function to collapse? So that, for example, when I check whether a certain radioactive nucleus has decayed, my observation somehow causes the nucleus to have either decayed or not decayed at the time of the observation? If this is the way it is, then human knowledge of the physical world is just as much a cause as an effect of physical reality, and the traditional understanding ofa posterioriempirical knowledge is quite wrong.Second, an observation. In a traditional theistic theology, God is, of course, the ultimate cause of all things. So, how is he the cause of the collapse of a given wave function? If some hidden variable theory were true, then we would say that God acted indirectly through the hidden variables to collapse the wave function, but Professor Barr has advised me on previous occasions that there are powerful reasons to think that hidden variable theories are untenable. If the standard model gives us the true picture of reality, and if further the idea is, as I say above, that the observer’s observation causes the wave function to collapse, then God would be acting indirectly through the observer to cause that collapse, and, presumably, with respect to wave functions for which no observations are ever made, they simply never collapse and so there is nothing there of which God needs be the cause. If the many-worlds interpretation is correct, then God is the cause of these many worlds (“O Lord my God, when I in awesome wonder, consider all the worlds thy hands have made….”), and again there is no problem.

But there is another possible interpretation of quantum mechanics, or, at least, it seems to me that there is, and I will be very interested in Professor Barr’s thoughts on it. It seems to me that a theist could say that God made physical reality such that it is accurately described by the equations of quantum mechanics (or the ultimate Grand Unified Theory, etc.). In particular, wave functions do not collapse because of “physical causes.” But, as we know from experience, wave functions do in fact collapse all the time—e.g., radioactive nuclei sometimes actually decay, etc. On the interpretation I am suggesting, God acts directly (whatever that means) on physical systems to collapse wave functions, though this direct action of his is, barring the occasional miracle (no pun intended, Steve), in accordance with the probabilities established by the equations of quantum mechanics so that the frequency distributions of events will tend strongly to confirm the equations. For example, if a certain radioactive isotope has a half-life of one hour, then every hour God causes only about half of the nuclei in a sample to decay. If this is correct, then when a human being makes an observation and sees that the wave function has collapsed, his observation in no way causes the collapse of the wave function: God has already done that. Human empirical knowledge is thus pretty much as we always thought—an effect and not a cause of physical reality. Regardless of whether observations are made, wave functions collapse when God acts to collapse them, and so there will be some—indeed, a great many—wave functions that collapse “unobserved.” Physical systems are basically never actually in superpositions because immediately, or almost immediately, collapses them. Call this the theological interpretation of quantum mechanics. What do you think, Professor Barr? Is this consistent with what physics know about the physical world?

Robert T. Miller

Hi, Robert,

The traditional interpretation (or Copenhagen interpretation, or standard interpretation) seems to be (have been) held in somewhat different form by different people. But let’s tke its defining characteristic to be that it posits a “collapse of the wavefunction” whenever a measurement gives a definite result.

I think that in the traditional interpretation one is practicaly forced to say that the wavefunction is NOT just a description of “the world as it is,” but rather that it encodes what some observer (or class of observers) knows (or is in a position to assert) about the world. If that is the case, then the observer’s observation does not NECESSARILY cause a change in extramental reality; it may only cause a change in the observer’s state of knowledge.

There is a severe difficulty in saying that the observer’s observation changes extramental reality: what if there are several observers of the same system? This is the basis of the famous “Wigner’s friend paradox”. Suppose that both Wigner and his friend (graduate student?) are waiting for a nucleus to decay. Wigner get tired and goes home for the evening, leaving his friend on watch. At 8 PM, Wigner’s friend hears the Geiger counter click. At 9 AM the next morning, Wigner arrives at the lab and asks his friend whether the nucleus has decayed, and gets the answer “yes”. One can consider Wigner’s friend as the observer, in which case the collapse happened at 8 PM. Or one can consider Wigner as the observer and his friend as part of the measuring apparatus, like the Geiger counter. Then the wavefunction collapse happens at 9 AM. Which is right? If “the wavefunction” is just the world as it objectively is, then one is caught in a dilemma. If, on the other hand, one says that the wavefunction encodes the observer’s state of knowledge, then there are two wavefunctions involved here — that encoding Wigner’s knowledge and that encoding his friend’s. The former collapses at 9 AM, the latter at 8 PM.

So, it is not clear that the traditional interpretation forces one to say that “the world as it is” is changed by an observation. It surely does force one to say that the observer’s knowledge is changed by the observation — but that is obvious anyway.

Now, that being said, I think there are some adherents of the traditional interpretation who would indeed say that the observer IS changing extramental reality just by virtue of his coming to know the result of his measurement. That, as you say, is a radical idea. But, it is far from clear that the traditional interpretation compels one to accept it. This is a very murky area!

Another thing is worth saying. Consider Schrodinger’s cat. Suppose the observer opens the box at Noon and sees that the cat is dead. The wavefunction collapses at Noon. Does that mean that the cat died at Noon according to the traditional interpretation? Not at all! The observer may decide after opening the box to do some forensic pathology on the cat: measure body temperature, insect actovity, rigor mortis, state of decomposition, etc. He may be able to infer that the cat actually died at 9 PM the night before. What to make of this? Before he opened the box, all he was in the position to assert on the basis of his past observations is that the cat had such-and-such probability of having died in such-and-such a time interval, this-and-so probability of having died in this-and-so other time interval, etc. and some probability of still being alive Then he opens the box and sees the cat dead — at that point the wavefinction collapses to “cat dead” state. Then he does his forensic tests, and the wavefunction further collapses to the “cat died at 9 PM” state.

Now, if we retreat to the modest view that the wavefunction is merely someone’s state of knowledge, and NOT “things as they are”, then how should one give a complete and objective mathematical description of reality as it is in itself? (The God’s-eye view.) That is far from clear.

Your idea, as I understand it, is to consider the wavefunction as a description of the world as it is and then say that God acts directly (in some sense) to prune away all but one branch when “wavefunction collapse” occurs. I think this is a consistent view, as long as one modifies it slightly.

If you say that the pruning happens whenever branches of the wavefunction “decohere” from each other, then I think it probably is OK. Decoherence generally happens when macroscopic objects are involved (e.g. a Geiger counter) — you don’t need the macroscopic object to be conscious or have a mind. (Of course, your idea does not need to invoke God. You can just say that some law of physics comes into play when decoherence happens and causes the unwanted branches to wither in accordance with some new equation, or modification of the Schrodinger equation. This would then be what people call an “objective collapse theory”. Whether such a theory can be found that is mathematically elegant and consistent is another question. In any event, it would be a change of the mathematical formalism of QM.) Your version would not require the mathematical formalism to be modified, but would require God to doa “manually over-ride” of the equations.

Your idea is a bit like my idea, which I explained in my answer to bknokolic above. Except that I invoke neither God nor a new law of physics. I posit what one might call a psycho-physical law, which is that all consciousness in the universe follows just one branch at any point where branches split apart and decohere. This law is probabilistic and says that which branch is followed is governed by the quantum mechanical probabilities. In this view, the wavefunction itself does not collapse, it keeps ramifying as in MWI. But consciousness selects one branch (or rather one branch is selected for it to follow, in accordance with the QM probabilities). One could look at this in two ways. (A) The wavefunction represents potentialities, not actualities. Only the branch that consciousness follows is actual. Or (B) The wavefunction, with all its branches, have merely “physical reality”. But the branch down which consciousness goes has a stronger kind of reality — call it Berkeleyan reality: a reality actually experienced by a sentient being.

Long answer. Hope it is not totally confusing.

SMB

“If, on the other hand, we accept the more traditional understanding of quantum mechanics that goes back to von Neumann, one is led by its logic (as Wigner and Peierls were) to the conclusion that not everything is just matter in motion, and that in particular there is something about the human mind that transcends matter and its laws. It then becomes possible to take seriously certain questions that materialism had ruled out of court: If the human mind transcends matter to some extent, could there not exist minds that transcend the physical universe altogether? And might there not even exist an ultimate Mind?”

Certainly it leaves the way open for that. But you could also say ‘all knowledge of phenomena is incomplete. It is simply approximative, and always will be’. In this case it is not something about ‘the human mind’ that transcends laws, but something about the nature of reality that transcends the human mind.

Traditional Philosophy of Mind argues strongly for determinism. Essentially basing this view on a Newtonian Physical analysis. A backdrop of quantum physics might not make contra-causality certain but would make determinism almost absurd. Only 'God the Father Allmighty' can have 'free will'. In a Newtonian universe all is pre-determined while in (most, as in the majority viewpoint) quantum models the possibility of being free to make choices is more likely to be the case than the opposite view.

From the perspective of the philosophical 'Mind-Body Problem' mainstrean quantum physics makes a 'dualistic' solution more or less certain. It proves the existance of the soul. Mainstream philosophers of mind regard this view as absurd, clinging as they do to any form of materialism they can find. Also, this dualism does not involve the non-material mind somehow emerging from the material brain. Rather mind and matter are both equally ontologically 'first' in the scheme of things. Mind and brain exist in tandem. And 'mind' does not simply observe matter but interacts with it, altering its nature. Mind is there from the begining. Our minds are outcrops of this Mind and we return to it. Such a 'God' is the ulltimate power in the universe but is not All Powerful in the usually understood sense. Thus solving the 'Problem of Evil'……………?

A simple example. The Young's Slits experiment 'proved' that light was composed of waves. Some time later Einstein's Photoelectric Effect experiment 'proved' that light was composed of discrete particles. Both are true yet diametrically opposite. Wave-particle duality in light is actualised as either a wave or a particle answer depending on the choice of experimental device.

There is an 'observer', a 'macroscopic measurnment device' devised by the observer and the 'observed microscopic entity'.

Could it be the case (certainly within the context of the Copenhagen Interpretation) that the above observation would point to the likelihood of 'contra-causality' at the macroscopic level?

Is the human will accordingly capable of innitiating choices? 'Free will', I would suggest, would be possible only for the God of traditional theism. Not for the Mind I postulated earlier which would be capable of choice but not infinate choice uninhibited by circumstances.

Again most mainstream Philosophy of Mind would regard the possibility of contra-causality as being absurd.

Dear Brendan,

I won’t comment on your purely theological ideas, as my concern here is only with the possible implications of quantum mechancis.

As far as free will goes, that is a distinct issue from the one that I discussed in my essay (though obviously related to it). It is one thing to argue that the traditional interpretation of QM has anti-materialist implications, and that consciousness or mind is as fundamental as matter. To argue, however, that quantum mechanics creates an opening for human free will (as many also have) is to go further.

You refer to “mainstream quantum mcehanics”. On this I will make several comments:

(1) There is no consensus among physicists on the best “interpretation” of quantum mechanics. Most physicists are dissatisfied with both the traditional Copenhagen interpretation and the Many Worlds Interpretation. Indeed, msot physicists simply ignore the issues, and among those who have thought about them, probably most would say they don’t have any idea what the right way to resolve them is. To the extent that there is a trend, it is away from Copenhagen and toward Many Worlds. Probably most quantum cosmologists favor Many Worlds. So, it is hard to speak really of what the mainstream is here.

(2) The anti-materialist conclusions drawn from the traditional interpretation of QM by Wigner, Peierls and others (which I find compelling) are not embraced by many physicists. Most are unaware of the antimaterialist argument and. those who are aware of it are not pursuaded by it. On the other hand, most also find Many Worlds hard to take. That is why the prevailing attiitude is a baffled angnosticism.

(3) The term of “wavefunction collapse” is now shied away from by many people. Nevertheless, most quantum mechanics textbooks in effect or implicitly teach the traditional interpretation, which involves wavefunction collapse, even if they may not call it that. That is, they speak as though the result obtained by a measurement is the one true state of affairs (which is the essence of wavefunction collapse and the traditional interpretation). At least, they do not teach that there are many equally real branches in which all measurement results are realized. So ,implicitly, the traditional interpretation is the way most physicists still actually have learned and teach QM and think about it, even if not explicitly aware of that fact.

(4) While the traditional interpretation logically leads to anti-materialist implications, as has been argued by Wigner, Peierls and others, that does not mean that most physicists are willing to be led by that logic.

Weak Measurements support the idea of the Wavefunciton being “real”. From what I’ve gleaned from reading papers by Yakir Aharonov (I’m not a physist) the probalistic nature is due to the fact that in most cases one is only controlling 1/2 of the Wave Function, i.e. the retarded half. If measurements are made where both the advanced and retarded waves are defined then the result is certain. Or in other words, the other half of the wave function moving backwards from the tuture completely defines the outcome.

So if one could control the boundary conditons at the beginning and end of time, then the Universe could be completely deterministic. But then how would one explain our minds from this perspective? Our free will would have to operate from that future boundary, how could that be?

—TidyTim—

I find that the most natural interpretation of quantum mechanics is idealism.

Given the success of quantum mechanics we know beyond reasonable doubt that the physical phenomena we observe are such that observations will not contradict the probabilistic rules of quantum mechanics (in the same way that on the long run the throwing of dice will not contradict the respective probabilistic rules either). But according to idealism what produces that observable order is not, say, some concrete material reality interacting with the observer’s mind to collapse the wavefunction, but rather a universal mind which directly guides and produces for us that concrete observed order. Finally, contrary to what many believe, it is not the case that according to idealism physical things do not exist. Whether apples or electrons or wavefunctions – they all exist, albeit the nature of their existence consists in being patterns present, really present, in our experience of physical phenomena.

Idealism I think very elegantly and economically solves all paradoxes of quantum mechanics, including the paradoxes related to non-locality or the paradoxes related to the Copenhagen interpretation such as “Wigner’s friend”. Indeed the idea that physical reality is basically a big wavefunction with little bubbles of collapsed regions where conscious observers happen to take a look is a weird picture to say the least.

To answer your last question first, I did not say anything about the free will to quantum mechanics in my essay. But since you ask: a scheme in which our decisions are “determined” by the future state of the universe would not contradict free will even in the strong “incompatibilist” understanding of free will. Consider the statement, “if X pulls the level for candidate Y at time T, then X chose at some t < T to do this.” That is practically an empty statement and certainly doesn’t imply that the decision at t was not free. Take an example: The current state of the universe is one where history books say that John Wilkes Booth assassinated President Lincoln. Does that tell us that the assassination that happened in 1865 was not free?

As far as Aharonov’s formulation of quantum mechanics, it does not sem to me, from what I understand of it, to give a third option between MWI and the collapse of the wavefunction. Suppose that given the initial state of a system a measurement can give more than outcome. After the measurement is seen to give one result, a question arises: Is that result the one and only true state of affairs post-measurement? Or did the other results also happen in other brancjes of reality? In the first case, one has by definition wavefunction collapse, which is a process not described by the Schrodinger equation. Thus it either has to involve some non-physical process, or the mathematical formalism has to be modified. If the other results actually do happen in other branches, then one has MWI. To the extent that Aharonov’s idea is a reformulation of standard QM it gives nothing new. If, however, like Bohmian mechanics, it is a modification of the rules of QM, then it might.