Ulrich Mohrhoff

Sri Aurobindo International Centre of Education

Pondicherry, India

Quantum theory in a nutshell The fundamental theoretical framework of contemporary

physics: quantum mechanics. The mathematical formalism of quantum mechanics:

a computational tool. Newton “framed no hypotheses.” Hume reduced causality to consistent covariation. Quantum mechanics reduces consistent covariation to

statistical correlations between measurement outcomes.It thereby allows us to calculate—on the basis of the outcomes of measurements that have been (or will be) made—the probabilities of the possible outcomes of measurements thatcan be (or could have been) made.

How do measurement outcomes influence the probabilities of measurement outcomes?

You understand this as much as anybody else!

The “measurement problem”

What earns measurements this pivotal status in a fundamental physical theory?

Under the influence of positivism, measurements came to be called “observations.”

With the discovery of special relativity in 1905, frames of reference came to be called “observers.”

Hence when quantum mechanics burst onto the scene in 1926, the obvious thing to do was to attribute the special status of measurements to the consciousness of the observer.

Today most physicists hope that measurements will eventuallybe reduced to “ordinary physical interactions.” Since quantum mechanics describes “ordinary physical interactions” in termsof correlations between the possible outcomes of measurements that may be performed on interacting systems, all that would thereby be achieved is a vicious circle.

Two lines of inquiry

From the irreducible core of quantum mechanics two different lines of inquiry proceed.

One—the fruitful one—analyzes the quantum-mechanical probability assignments in a variety of experimental contexts.

The other—a red herring—aims to interpret the theory’s mathematical symbols and relations as representing physical entities, states, or processes.

Let’s pursue the former. Suppose we want to calculate the probability of a particular

possible outcome on the basis of a particular actual outcome. We begin by imagining a possible sequence of intermediate

measurements. Then we associate with each sequence of possible outcomes

(“alternative”) a complex number called “amplitude.” Finally we use either of these rules:

Two rules

What ontologicaldifference corresponds to, or necessitates, this algorithmic difference?

Whenever Rule B applies, the distinctions we make betweenalternatives are distinctions that Nature does not make.

They correspond to nothing in the physical world. They exist solely in our minds.

Example:

The intermediate measurement is designed to answer the question: through which slit did the electron go?

Does this question have an answer even if the measurement designed to provide it is not made?

If it had an answer, this would be consistent with the predictions of Rule A rather than those of Rule B. Hence there is no answer; the question is meaningless.

The challenge is to learn to think in ways that do not lead to meaningless questions.

Meaningless questions arise from false assumptions. The false assumption, in this case, is that the electron goes either through the left slit or through the right slit. It is based on a spatial distinction that Nature does not make.

Initially there is one particle(N) heading northward and one particle (S) heading southward.

The next thing we know is that there is one particle (E) heading eastward and one particle (W) heading westward.

The intermediate measurement is designed to answer the question: which of the two alternatives took place?

In other words: which incoming particle is identical with which outgoing particle?

Does this question have an answer even if the intermediate measurement is not made?

If it has an answer, this must be consistent with the predictions of Rule A.

Another example:

Every particle is either a boson or a fermion. For bosons, the desired probability is smaller under the

conditions stipulated by Rule B than it is when calculated according to Rule A. For fermions it is larger.

Hence there is no answer. The question is meaningless. Once again the challenge is to learn to think in ways that do not

lead to meaningless questions. The false assumption, in this case, is that initially there are two

things, one moving northwards, the other southwards, and that in the end there are two things, one moving westwards, the other eastwards. Hence the meaningless question: which is which?

Here is how it can be avoided: Assume that initially there is one thing moving both

northwards and southwards, and that in the end there is one thing moving both westwards and eastwards.

Clearly, the meaningless question—which is which?—can no longer be asked. It was based on a substantial distinction that Nature does not make.

What the two examples above illustrate is that neither the spatial nor the substantial differentiation of reality goes “all the way down.”

If we go on dividing a material object, its so-called “constituents” lose their individuality. They reveal that ultimately there is only one substance, which manifests itself with different properties in different places.

By the same token, if we conceptually partition the world into smaller and smaller regions, we reach a point where the distinctions we make between regions no longer correspond to anything in the physical world.

It follows that space isn’t a self-existent (substantial) and intrinsically differentiated expanse.

If it’s an expanse that exists independently of its material content, then it is intrinsically undifferentiated; it lacks parts.In other words: ultimately there is only one place, and this is everywhere.

On the other hand, if space is intrinsically differentiated, then it isn’t a self-existent expanse. It is a set of (more or less fuzzy) spatial relations.

If space is a set of spatial relations, then the shape of a material object consists of the spatial relations between its parts. An object without parts, lacking internal spatial relations, is formless.

And while it contains—in the proper, set-theoretic sense of containment— spatial relations (including the shapes of things), space does not contain the formless relata, the so-called “ultimate constituents” of matter (which, considered out of relation to each other, are identical in the strong sense of numerical identity).

Since the early days of quantum mechanics it has been claimed that the theory is incomplete.

What is actually incomplete is the physical world. The incompleteness of the world’s substantial differentiation

rules out models that construct reality by assembling a pre-existent multitude of building blocks.

The incompleteness of the world’s spatial differentiation rules out world models that construct reality on the foundation of an intrinsically differentiated space or spacetime.

Reality is built “from the top down,” by a differentiation that does not “bottom out,” rather than “from the bottom up.”As it is said in the Rig Veda, the foundation is above.

The world thus contains exactly one substance. If we call it Brahman, we arrive at one of the most economical creation stories ever told:

In the quantum world, everything is possible, in the sense that every conceivable measurement outcome has a probability greater than zero unless it violates a conservation law.

We never have to explain why something is possible; we only need to explain why some things are not possible.

This suggests to me that the force at work in the world is an omnipotent force working under self-imposed constraints.

If this is the case, then we need not be surprised at the impossibility of explaining the quantum-mechanical correlation laws—whether by postulating underlying physical processes or by transmogrifying mathematical relations into physical processes.

There is no need to explain the working of an omnipotent force.

An omnipotent force

Sachchidananda, supermind, and mind

A distinction has to be made between mind and the original creative consciousness—supermind, to use Sri Aurobindo’s terminology.

According to the original Vedanta of the Upanishads, Brahman relates to the world in a threefold manner: as the one substance that constitutes it (sat ), as the one consciousness that contains it (chit ), and as an infinite quality/delight that expresses and

experiences itself in it (ananda ).

To the supermind, the unity of the all-constituting substance, of the all-containing consciousness, of the infinite quality/delight at the roots of existence, and of all three aspects of Brahman, is self-evident.

The creations of the supermind are primarily qualitative and infinite and only secondarily quantitative and finite. Essentially, mind is the agent of this secondary, limiting and dividing action.

When mind is used by supermind, its tendency to divide ad infinitum is checked.

This is why there are limits to the objective reality of spatial and substantial distinctions.

When mind is separated in its self-awareness from its supramental parent and left to run wild, as it is in us, it not only divides ad infinitum but also takes the resulting multiplicity for the original truth or fact.

This is why we tend to construct reality from the bottom up. It is also why we tend to be materialists, for what is

characteristic of a materialist world view is that it models reality from the bottom up, rather than from the top down.

And it is why making sense of quantum mechanics is so hard.

Mind, materialism, and quantum mechanics

Another important distinction is that between two poises of relation between supermind and the world—comprehending (vijnana ) and apprehending (prajnana ).

In the comprehending poise, the self is coextensive with the world. The subject is wherever its objects are. No distances exist between the seer and the seen. Nor is there a difference between Brahman qua all–conscious self and Brahman quaall–constituting substance.

In the apprehending poise, consciousness distantiates itself from its content. There now is a distance between the perceiver and the perceived, and objects are seen from outside, presenting their surfaces. It is in this poise that the three dimensions of space—viewer-centered depth and lateral extent—come into being.

Concomitantly, the single Self of the primary poise adopts a multitude of viewpoints within the content of its consciousness and thus effectively becomes a multitude of situated selves.

The coming into being of space

Having seen how Brahman enters into spatial relations with itself, and how the dichotomy of subject and object comes into being, we now examine the steps by which Brahman takes on the aspect of a multitude of formless relata.

It is by a multiple concentration that the one Self assumes the aspect of a multitude of selves, and it is by a multiple exclusive concentration that it loses sight—in each self—of its identity with the other selves and the Self of all selves.

The result is Avidya, which hides from us not merely our true self but a mass of subliminal influences exerted by as well as acting on us. This is the first step.

Avidya

Three main stages can be discerned in the process of creation. As said, Brahman is not only an all-constituting substance and

an all-containing consciousness but also an infinite quality/ delight that expresses and experiences itself in finite forms.

The first stage of the creative process covers the development of infinite quality into expressive ideas.

The second stage is marked by the transition from expressive idea to executive force.

The third stage consists in the creation, by the executive force, of expressive forms.

The chain of creation

There thus exists the possibility of deepening the multiple exclusive concentration to the point that the first stage of the process of creation takes place subliminally.

The result is an individual whose consciousness is centered in ideation and more or less unaware of the qualities it receives for expression.

A further deepening of the exclusive concentration, to the point that the second stage takes place subliminally, produces an individual that executes expressive ideas unconsciously.

Finally, if the multiple exclusive concentration is carried to its extreme, even the executive force falls dormant.

And since this is instrumental in the creation of individual forms, the result is an apparent multitude of formless individuals (“apparent” because by losing their individualizing properties they also lose their multiplicity).

Welcome to the physical world!

Involution

Why do the laws of physics have the particular form they do? One reason is that without it no stable matter could exist.

Specifically, the existence of objects that have spatial extent (they “occupy space”), are composed of a finite number of objects that lack spatial

extent (they do not “occupy space”), and are stable (they neither explode nor collapse as soon as they

are created),

requires the theoretical framework of physics to have exactly the form that it does.

This framework presupposes measurements, and it is eminently plausible that the existence of measurements in turn requires the validity of all well-tested physical theories: their validity is guaranteed provided that spatially extended objects are “composed” of finite numbers of objects that lack spatial extent.

This is the sole nontrivial input and the only real mystery: why are things that “occupy space” made of things that don’t?

Why the laws of physics are just so

The physical world is unique in that it is evolutionary. Here, Brahman is “playing Houdini,” imprisoning and enchaining itself as rigorously as divinely possible, challenging itself to escape, to re-discover itself, and to re-affirm its powers in what appears to be a universe of mechanical forces and random events.

Its multiple exclusive concentration allows it to enter various states of ignorance and incapacity so as to experience growth in knowledge and growth in power, the excitement of conquest and discovery, the surprise of the unknown, the challenge of opposition, the triumph of victory.

Evolution presupposes involution, and the final outcome of the process of involution is an apparent multitude of formless individuals.

The physical world has been created to set the stage for the drama of evolution, and this is why things that “occupy space” are made of finite numbers of things that don’t.

The adventure of evolution

Of all the baffling features of the quantum world, none is more baffling than the supervenience of the microscopic on the macroscopic:

molecules, atoms, and subatomic particles are what they are because of what happens or is the case in the macroscopic world, rather than the other way round, as we are wont to think.

In the micro-domain, a property exists only to the extent that its possession is indicated by—or inferable from—a macroscopic event or state of affairs (a “measurement”).

Making sense of this calls for a new paradigm. It is no longer appropriate to ask: what are the ultimate

building blocks, and how do they interact and combine? The right question to ask is: how does Brahman manifest itself

(or the world)?

To be is to be measured

Why micro supervenes on macro

The macroscopic world is the manifested world. Quantum mechanics affords us a glimpse at what lies “behind”

the manifested world, but this is not another world. Particles, atoms, and such do not inhabit a microscopic world,

nor are they the manifested world’s constituent parts or structures. They are instrumental in its manifestation.

And we cannot describe what is instrumental in the world’s manifestation except in terms of the finished product—the manifested world; hence the supervenience of the microscopic on the macroscopic.

Note, however, that the matter is not merely one of missing concepts; what is missing in the absence of measurements is attributable properties.

A detector, for example, not only serves to indicate the presence of something in a region R but also, and in the first place, to realize the property of being in R , to make it available for attribution.

We don’t expect the sensory system of a cockroach or a chipmunk to reveal the true nature of reality. Why should our sensory system be different in this regard?

The phenomenal world is a species-specific user interface. A user interface—like a computer desktop with its icons—is useful precisely because its content does not resemble what it represents.

Evolution not merely produces new species, for a new species means a new user interface, and a new user interface means a new world.

Nobody has brought this point more clearly into focus than evolutionary philosopher and cultural historian Jean Gebser, who documented the transition of human consciousness through five consecutive structures and their respective worlds: archaic, magic, mythical, mental, and integral.

An evolving world

The diminishing returns of modern science documented for example by Horgan (The End of Science ), Smolin (The Trouble with Physics ), and Woit (Not Even Wrong ) symptomize the terminal phase of the mental structure.

The mythical world is an essentially two-dimensional world of images.

The mental structure is capable of integrating images into the system of three-dimensional objects we call the “physical” or “material” world.

As this three-dimensional “coagulation” of images comes into being with the mental structure, so it fades into irrelevance with the irruption of the integral structure, which integrates all previous structures and renders the world diaphanous.

The diapheneity (“shining through”) of the Origin will concretize the whole in each part, and the mental structure’s perspectival fixation in space and time will give way to a viewpoint that is coextensive both with space and with time.

Penetrating the veil