ISIS Report 17/04/07
Beyond the Central Dogma of Physics
The universe is one manifesting itself in multiplicities that behave according
to certain mathematical rules; but this leads to paradox as soon as we think
of the underlying reality as if the multiplicities were real (see Quantum World
Coming series, Science in Society 22)
Ulrich Mohrhoff argues for the fundamental unity of nature that avoids asking what he
says are pseudo-questions
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The evolutionary paradigm
Mae-Wan Ho has written eloquently against
the Central Dogma in biology [1, 2] ( Life
After the Central Dogma of Biology series, Science in Society 24; Living with the Fluid Genome,
ISIS publication).
In physic, too, there is a Central Dogma, which I have dubbed ‘the evolutionary
paradigm’ [3, 4]. It is the notion that physics can be neatly divided into
a kinematical part, which concerns
the description of a physical system at an instant of time, and a dynamical
part, which concerns the evolution of a physical system from earlier to later
times.
The
laws of physics are correlation laws. In classical physics, states are correlated
deterministically, so earlier states can be used to predict later states (and
later states can be used to retrodict earlier states). Quantum physics correlates
measurement outcomes statistically, so earlier measurement outcomes can be
used to predict the probabilities of the possible outcomes of later measurements
(and later measurement outcomes can be used to retrodict the probabilities
of the possible outcomes of earlier measurements). Because the quantum-mechanical
correlation laws are genuinely probabilistic, they may not conform to the
evolutionary paradigm.
And
they don’t. For one thing, the time-symmetry of the laws of physics is at
odds with the unidirectionality of the evolutionary paradigm, which has its
roots in a physically unwarranted projection into the world of the way we
perceive the world [5-7]. (This casts doubt on the appropriateness of the
evolutionary paradigm even for classical physics.) For another thing, the
interpretation of a quantum state as an evolving physical state (rather than
as a mere computational device) gives rise to no end of pseudo-questions (and
gratuitous answers), such as the notorious questions of where and when and
how (and with respect to which basis) the wave function collapses [8] (see
Nature is Quantum, Really,
SiS 22).
Owing
to the Central Dogma, the wave function is widely regarded as the primary
affair. This has led to the belief that the probabilities of possible measurement
outcomes are absolute, determined
by a system’s evolving quantum state, rather than conditional, determined by actual measurement
outcomes via computational devices
called “quantum states”. Nobody has seen this more clearly than the late Asher
Peres, who insisted that, “there is no interpolating wave function giving
the ‘state of the system’ between measurements.” In dealing with quantum mechanics,
we constantly ought to remind ourselves that the state of a system between
measurements is unobservable by definition.
In
the classical limit, the quantum-mechanical probability calculus degenerates
into a classical probability calculus rather than a description of physical reality. Because the
classical calculus is trivial, in the sense that it only assigns the probabilities
0 or 1, it is possible to interpret it as representing an evolving physical
state, rather than as being an algorithm for assigning probabilities to possible
measurement outcomes. Because quantum-mechanical probabilities fill the entire
range from 0 to 1, it is not possible to think of the state vector
as representing an evolving physical state, at least not without generating
pseudo-problems and absurd solutions. The time dependence of a quantum state
is not that of an evolving physical state but the dependence of an algorithm
on the time of the measurement
to the possible outcomes of which it serves to assign probabilities.
The Central Dogma sweeps the real problem under the rug
The Central Dogma bamboozles us into believing
that to solve the so-called measurement problem “means to design an interpretation
in which measurement processes are not different in principle from ordinary
physical interactions,” as an anonymous referee once put to me. This sweeps
the real problems under the rug [5]. All we know about “ordinary physical
interactions” is through correlations between the probabilities of measurement
outcomes. The real problems are:
1. Why is the fundamental theoretical framework
of contemporary physics a probability calculus? And why are the events whose
probabilities it serves to calculate, measurements?
2. What can we conclude about Nature by analysing quantum-mechanical
probability assignments?
3. How can we rigorously define “macroscopic”?
4. Which substructure of the quantum-theoretical
‘universe of discourse’ corresponds to reality?
5. How can we understand the supervenience
of the macroscopic on the microscopic, i.e., the fact that the microworld
is what it is because of what happens in the macroworld, rather than the other
way round as we are wont to think?
The universe is objectively fuzzy
The reason why the fundamental
framework of contemporary physics is a probability calculus is an objective
fuzziness. (The proper way of defining and quantifying the objective fuzziness
of the quantum world is to assign probabilities to possible measurement outcomes
on the basis of actual outcomes.) This objective fuzziness makes possible
the existence of macroscopic objects, i.e., objects that have spatial extent
(they ‘occupy’ space), appear to be made of finite numbers of particles without
spatial extent, and are stable, i.e., they don't collapse or explode as soon
as they are created [3]. Quantum fuzziness thus is a precondition of macroscopic
objects, whose existence in turn is required for the consistency of quantum
mechanics.
Nature makes fewer distinctions than we do
The general conclusion about Nature is that
whenever quantum mechanics instructs us to calculate the probability of a
given outcome by adding the amplitudes (rather than the probabilities) of
a set of alternatives, the distinctions we make between the alternatives are
distinctions that Nature does not make;
they correspond to nothing in the real world; they exist solely in our heads.
Suppose that we perform a series of position measurements,
and that every position measurement yields exactly one outcome (i.e., each
time exactly one detector clicks). Then we have a conservation law, and we
are entitled to infer the existence of an entity which persists through time,
to think of the clicks given off by the detectors as indicating the successive
positions of this entity, to think of the behaviour of the detectors as position
measurements, and to think of the detectors as detectors. What if each time
exactly two detectors click? If there isn’t another conservation law effectively
providing the entities with identity tags, then there is no answer to the
question of which particle is which. The question is meaningless.
Now
consider a particle lacking internal relations. What is it ‘in itself’, out
of relation to its external relations? The answer is “nothing”, except possibly a substance lacking
properties. For the measurable properties of particles are either kinematical
relations such as positions or momenta, or parameters characterizing dynamical
relations such as the various kinds of charge, or they have an objective significance
independent of conventions only as dimensionless ratios.
According
to a philosophical principle, the identity of indiscernibles, A and B
are one and the same thing just in case there is no difference between A and B.
Not only is there no difference between two particles lacking internal relations
considered ‘in themselves’, but nothing real corresponds to the distinction
we make between this particle and that particle over and above the distinction between this property and that property. What follows from this is
the numerical identity of all
particles lacking internal relations, considered by themselves. If we think
of particles lacking internal relations as the ‘ultimate constituents of matter’,
then there is a clear sense in which the number of ‘ultimate constituents
of matter’ equals 1.
Thus
a quantum system is always one.
It is a single substance, the number of its ‘constituents’ simply being one
of its measurable properties. And its ‘ultimate constituents’, considered
by themselves, are identical in the strong sense of numerical identity. If
I now permit myself to think of the entire physical world as a quantum system
and ask about its constituents, I find that there is just one, a single intrinsic
substance without properties. This single substance gives rise to the totality
of more or less fuzzy spatial relations we call “space”, and it gives rise
to the corresponding apparent totality of relata we call “matter”, apparent
because the relations are self-relations.
Defining macroscopic
Whereas no object ever has a sharp position
(relative to any other object), some objects have the sharpest positions in
existence. (In a non-relativistic world this is so because the exact localization
of a particle implies an infinite momentum dispersion and hence an infinite
mean energy. In a relativistic world the attempt to produce a strictly localized
particle results instead in the production of particle-antiparticle pairs.)
The
possibility of obtaining evidence of the departure of an object from its classically
predictable position calls for detectors whose position probability distributions
are even narrower than that of the object to be probed. Such a detector is
unlikely to exist, and hence the probability of obtaining evidence of departures
from the classically predictable motion is very low. Consequently, among such
objects, there will be many of which the following is true: every
one of their indicated positions is consistent with every prediction that
can be made on the basis of previously indicated properties and a classical
law of motion. These are the objects that deserve to be
labelled ‘macroscopic’. To permit a macroscopic object to indicate a measurement
outcome, one exception has to be made: its position may change unpredictably
if and when it serves to indicate an outcome.
Quantum theory and reality
The substructure of the quantum-theoretical
‘universe of discourse’ that corresponds to reality is the macroworld, defined as the totality of relative
positions existing between macroscopic objects, ‘macroscopic positions’ for
short [9, 10].
The
reason why it is legitimate to attribute to the macroworld - not individually
to each macroscopic position but to the macroworld in its entirety - a free-standing reality, i.e., a reality independent
of anything external to it, is that, by definition, macroscopic positions
are not manifestly fuzzy. For
the supervenience of the microscopic on the macroscopic (i.e., the fact that
the microworld owes its properties to events that happen in the macroworld)
is a consequence of the fuzziness of the microworld. If all measurable quantities
were in possession of sharp values at all times, we could think of all measurements
as revealing pre-existent properties. It is the objective fuzziness of the
microworld that compels us to think of quantum measurements as creating
their outcomes rather than revealing pre-existent properties. And it is the
macroworld’s lack of manifestly fuzzy properties (i.e., the fact that, by
definition, its properties never evince their fuzziness) that permits us to
think of the macroworld as a free-standing reality.
Whence the dependence of the microworld on the macroworld?
A twenty-five centuries old paradigm thus
has passed its expiry date. It is no longer appropriate to ask, what are the
ultimate constituents, and how do they interact and combine? Ultimately there
exists One Being. Call it whatever you like. What constitutes the macroworld
is not the ‘microworld’ but the single substance without properties that,
by entering into spatial relations with itself, gives rise to both matter
and space.
The
manifested world is the macroworld. The ‘microworld’ is neither a world nor
a part of any world but instrumental
in the manifestation of the (macro)world. Quantum mechanics affords us a glimpse
‘behind’ the manifested world. But, and this is the punchline, we cannot describe
what lies behind the manifested world except in terms of the finished product,
the manifested world.
Imagine
that you experience something the like of which you have never experienced
before. How are you going to describe it? You are obliged to use words that
refer to experiences you have had. It is the same with the manifestation.
Only, in this case, it is not merely the words but the properties that are
missing. The microworld does not have
properties; it gives properties.
It is instrumental in manifesting the properties of the (macro)world.
The two other faces of reality
As said, ultimately there is a One Being.
This manifests itself, and quantum mechanics tells us how. But it does not
only manifest itself. It manifests itself to
itself. It is not only that by
which the world exists but also that for
which the world exists. In other words, it is not only the substance that
constitutes the world but also the consciousness that contains it. In addition,
that One Being is, subjectively speaking, an infinite bliss and, objectively
speaking, an infinite quality infinitely expressing and experiencing itself.
This
is the core of the ancient Indian theory of existence known as Vedanta, which
describes ultimate reality in terms of its threefold relation to the world,
as sat-chit-ananda or substance-consciousness-bliss
[11, 12].
Why
does sat-chit-ananda hide in
particles that, individually, lack spatial extent? Why does it subject their
relations to apparently self-effective laws? In this world, sat-chit-ananda is playing Houdini, imprisoning
and enchaining itself as rigorously as it can, challenging itself to escape,
to re-discover and re-affirm its powers in what seems to be a universe of
mechanical forces and random events. A multiple exclusive concentration allows
it to enter various states of ignorance and incapacity so as to experience
growth in knowledge and power, the excitement of conquest and discovery, the
surprise of the unknown, the challenge of opposition, the triumph of victory.
[13].
Because
quantum mechanics presupposes macroscopic objects, its consistency requires
the existence of macroscopic objects. And it is eminently plausible that this
in turn requires the validity of all empirically tested physical theories,
the Standard Model and general relativity [14, 15].
This
is a humbling conclusion, for it means that all empirically tested physical
theories are essentially tautological. If you want spatially extended objects
that neither explode nor collapse the moment they are formed, the validity
of these theories is a must. To be precise, their validity is guaranteed if spatially extended objects are composed
of objects that lack spatial extent. This is the sole non-trivial input and
the only real mystery. Why are things that ‘occupy space’ made of finite numbers
of things that don’t?
This,
too, can be understood. The creation of a world of unextended particles can
be seen as the final stage of an involution that has set the stage for the
adventure of evolution [12, 16, 17].
Critique of the conventional paradigm in statements made by Ho
The perspective I have presented chimes in with what Mae-Wan Ho wrote in her
Quantum World Coming
series (SiS 22) [8]: “The greatest gift of the quantum age is a truly
organic way of living and perceiving the world that will reconnect western science
to the deeply ecological and holistic knowledge systems of all indigenous cultures.
It will make us realise how urgently we need to protect and revitalize these
traditional knowledge systems as the real ‘common heritage’ of the human species.”
But I disagree with some of her statements, especially
those that are well established in both the professional and the popular literature
on the subject (and she has indeed gone on to contradict some of them in her
articles).
For
example, in Nature
is Quantum, Really (SiS
22) [18], she refers to “the weird and wonderful world of quantum systems
... in which ‘things’ are both wave and particle, and can be in two places
or multiple, contradictory states at the same time.”
A ‘thing’ is a particle only in the sense that a position
can be attributed to it, if and when, and to the extent that is measured.
The wave in question is nothing but a feature of a quantum-mechanical probability
algorithm. Interference phenomena reveal features of that algorithm, not features
of the ‘thing’. A thing can be in two places in the sense that the probability
of finding it here and the probability of finding it there are both greater
than 0; but the distinction we make between ‘the thing here’ and ‘the thing
there’ is one that Nature does not make; it corresponds to nothing in the
real world; it exists solely in our heads.
It
is misleading to say that a thing is in
a (quantum) state, though of course we often do, for a quantum state is nothing
but an algorithm giving the probabilities of the possible outcomes of possible
measurements.
In
How Not to Collapse the Wave
Function (SiS 22) [19],
Ho writes: “In the standard quantum theory, a quantum system is in a superposition
of states or in quantum entanglement, which is invariably destroyed by measurement.”
This
suggests that a superposition of states is the same as quantum entanglement.
A (pure) state plays two rôles: it can be the probability algorithm associated
with a quantum system, and it can represent a possible measurement outcome
(for the purpose of calculating its probability). When a (pure) state, which
is a vector, is written as a linear combination of other vectors, then it
is a probability algorithm, while the other vectors represent possible measurement
outcomes. Quantum entanglement is a possible feature of the state of a composite
system. Neither a superposition of quantum states nor quantum entanglement
is something that can be destroyed, inasmuch as one cannot destroy a probability
algorithm. One can only update it with newly acquired information. This typically
renders previously relevant information irrelevant.
Later
in the same article, Ho states that, “when one particle is measured to have
a certain property, then the corresponding property of the other particle
is instantaneously determined.” When one of two particles ‘in’ an entangled
state is subjected to a measurement, information is obtained that is relevant
to the probabilities of the possible outcomes of most measurements to which
the other particle may be subjected. No property of the other particle is
thereby determined. Only the probabilities of the possible outcomes of measurements
are affected.
A
related criticism can be levelled against her statement in Quantum Phases and Quantum Coherence
(SiS 22) [20]: “…why, if nature is fundamentally quantum mechanical, do we
see it predominantly as classical in our everyday life? That is because a
quantum system enters into quantum entanglement with the observer.”
Saying
that a quantum systems enters into quantum entanglement with another quantum
system is the same as saying that the appropriate algorithm for calculating
the joint probabilities of the possible outcomes of joint measurements (one
performed on each system) ceases to be a direct product of independent algorithms
(one for each system). If two quantum systems are entangled, the outcome of
a measurement performed on either system contributes to determine the probabilities
of the outcomes of most measurements that may be performed on the other system.
Hence if it were appropriate to treat a measurement apparatus (‘observer’)
as a quantum system entangled with an ‘observed’ system, there would be no
measurement. The entanglement would only make it possible to learn something
about the ‘observed’ system by subjecting the apparatus to a measurement,
which calls for another measurement apparatus, which gets entangled with the
first, and so on ad absurdum.
Ulrich
Mohrhoff teaches quantum physics in the light of Indian philosophy at Sri
Aurobindo International Centre of Education, Pondicherry, India. He is the
managing editor of AntiMatters, a recently launched online journal (http://anti-matters.org)
addressing issues in science and the humanities from non-materialistic perspectives.
His home page is http://thisquantumworld.com.
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