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Published in Emergence of New Perspective in Philosophy (UGC sponsored Seminar)
Ed.by M. Kapoor et al.(2012)
Quantum Entanglement and the Philosophy of Relations
Sisir Roy
Physics and Applied Mathematics Unit
Indian Statistical Institute, Kolkata
E-mail: sisir@isical.ac.in
ABSTRACT
Quantum entanglement is a property of a quantum state consisting of two or more quantum objects like
photons, electrons, neutrons etc. The objects producing the joint state i.e., entangled state is not separable
but makes a non-local connection between the objects separated by arbitrary distance. This connection or
so to say, the relation contains the information about the relata (here, the quantum objects) though the
relata does not necessarily need to have intrinsic properties. The metaphysics of relation in this new
perspective has been critically analyzed and compared with the views of idealist as well as realist schools
of Indian philosophy.
I. Introduction:
The remarkable progress in modern physics in twentieth century raises lot of
interest on the metaphysical aspects of quantum theory. Specifically, what it means to be a
quantum theory in a most general sense, is that the physical world is nonlocal. In other way it
can be stated as the space-like separated systems which can occupy entangled states and that it
persists as the systems separate further. The concept of entanglement plays a crucial role in
understanding quantum theory. Quantum entanglement is a property of a quantum state
consisting of two or more quantum objects like photon, electron, neutron or proton (i.e. sub-
atomic particles) in a manner such that when the state of one quantum object is altered, the other
will instantaneously change state to exactly the opposite of its partner, no matter how far these
objects are being separated. It seems that the objects making an entangled state are connected
non-locally and are non-separable. This leads us to think the entanglement as a sort of holism.
Holism is considered as a thesis which claims that the whole is more than the sum of the parts
which means two or more quantum objects when entangled can be stated as a joint state of a
quantum whole. Again the joint state of a quantum whole contains information about the related
objects. Technically speaking, the joint probability distribution associated to the joint state can
give rise to the conditional probability of the related objects but not in the reverse way. So one
can conceive of an intrinsic property of the quantum whole which does not supervene on
intrinsic properties of the parts. In other words, the intrinsic property of the quantum whole or
the relation between the quantum objects making the whole contains the information about the
relata (i.e. the quantum objects) though the relata do not necessarily need to have intrinsic
properties. Intrinsics are those qualitative properties that a thing has irrespective of whether or not there
are other contingent things, all other qualitative properties are extrinsic or relational. So characterizing
the entanglement in terms of non-separability for quantum systems is a metaphysical proposal
and a matter of philosophical arguments. In western philosophy, various theories of relations have
been discussed popularly known as medieval theories of relations. Aristotle (1) in his treatise the
Categories initiated a systematic investigation on the philosophy of relations. He suggested that whenever
two or more objects or substances are related that is to be explained by the inherent or intrinsic properties
of the relata. Aristotelian thoughts made a tremendous influence on the philosophers of middle ages on
the nature and ontological status of relations. The ontological status of relations has been discussed by
many western philosophers. Recently, Glenn (2) critically analyzed the ontological status as discussed by
Plato, Aristotle, Parmenides, Hume and Wittgenstein (S. Glenn (2000): Relations and Reality : The
Metaphysics of Parts and Wholes, Ph.D. The Dissertation, Department of Philosophy, Boston College).
The metaphysics of relations between quantum systems has been studied by Esfeld(3)
from western perspective. According to his point of view, the (quantum) entities (or the relata)
between which the relation exists; there is no need to consider the intrinsic properties of the
entities or things underlying the relations. This is in contrast to the metaphysics of individual
things which have intrinsic properties. It is worth mentioning that various schools of Indian
philosophy including Buddhist one (4) discuss the nature and the ontological status of relations
in great details. In this paper we shall discuss the views of some of those schools on metaphysics
of relations and ontological issues.
At first we shall define the concept of quantum entanglement and its characteristics in section II.
In section III the metaphysics of relations from western and eastern perspective will be critically
analyzed. Finally we discuss the comparative views on reality from quantum theory as well as
from Indian perspective.
II. Quantum Entanglement:
Quantum entanglement, also known as quantum non-local connection is a property of
quantum mechanical systems. This connection contains two or more objects. These constituent
objects are linked in such a way that it is not possible to describe the quantum state of a
constituent of that system without fully mentioning its counterparts, even if those individual parts
are spatially separated. Erwin Schrodinger coined the term “entanglement” and used it in his
three part article published in Proceedings of Cambridge Philosophical Society (5). He proposed
that entanglement arises due to the interactions of two particles (i.e. two quantum objects)
through the evolution of wave equation (popularly known as Schrodinger equation) and called
this phenomenon the characteristic trait of quantum theory. Schrodinger, also, realized that this
character, rather peculiar non-classical correlations to quantum systems, could be used to steer a
distant particle into one of a set of systems having a certain probability. Regarding entanglement
phenomena as a physical resource, beautiful and detailed discussions can be availed from the
works of Lo H.-K., Popescu, S., Spiller, T(1998)(6) or Nielson and Chung(2000)(7).
But, Einstein famously disliked this approach at first and called quantum entanglement “spooky
action at a distance” in the famous EPR debate (8). Though his belief was that someday quantum
entanglement would have been explained by future researchers in terms of certain error in
calculations, in 1982 first, then further developments established this phenomena in a concrete
manner. Aspect et al., in 1982, first showed that nonlocal interactions do occur (9).
Two quantum objects, when entangled, initially will both have an undetermined state. When one
object’s state is determined, the other’s state is instantaneously known to be the opposite, no
matter how far apart they are. Quantum theory permits that the states of quantum systems are
entangled. Instead of speaking of entangled states, one can also talk directly in terms of
entangled systems. However, since entanglement is state-dependent, it seems more appropriate to
use the notion of entangled states which in other way states that the quantum systems in question
do not have some state dependent properties each independently of one another. Examples are
position and momentum as well as spin angular momentum in any direction. Instead, there are
only correlations between the state-dependent properties of the quantum systems in question
encoded in a joint probability distribution determined by the joint state. Quantum theory does not
include any properties of each quantum system taken separately that are a supervenience basis
for these correlated probability distributions. Furthermore, these correlations – and thus
entanglement – are independent of spatio-temporal distance. Because of entanglement, quantum
physics seems to exhibit some sort of a holism. Before going into further details, let us analyze
the concept of non-separability.
Non-Separability:
Albert Einstein based his criticism of quantum theory on the principle of separability. Taking
Einstein’s criticism into account, Don Howard (10) formulates separability as the claim that
spatially separated systems possess their own, distinct physical state each and that
the joint state of two or more spatially separated systems is wholly determined by their separate
states.
In view of employing the notion of separability for a systematic characterization of quantum
entanglement, it seems reasonable to eliminate the condition of the systems being spatially
separated; for entanglement is independent of whether or not the systems whose states are
entangled are spatially separated. For instance, the spin state of the two electrons of a helium
atom in the ground state is a case of entanglement too (singlet state), although the two electrons
are not localized in such a way that they are spatially separated from one another. Furthermore,
in quantum computation, one considers the entanglement of the states of many systems which
are usually not localized in such a way that they are separated in space. Abandoning the
condition of spatial separation, one can characterize separability in this way: physical systems
have a state each in the sense that
•This state completely determines the state-dependent properties of the system and
•The joint state of two or more systems supervenes on the states of each of these systems.
The states of two or more systems are non-separable if and only if it is the joint state
of the whole that completely determines the state-dependent properties of each system and the
correlations among these systems (to the extent that these are determined at all). According to
this characterization, any case of quantum entanglement is a case of non separability, and non-
separability is the reason why quantum entanglement is a sort of holism. In any case of
quantum entanglement, only the joint state of the whole completely determines the probability
distributions of the state dependent properties of the parts by determining correlations among
these probability distributions. Quantum Theory (QT) claims that the states are entangled.
Whatever entanglement may be, it is a relation among quantum states or quantum systems. “Being
entangled with” is a property , predicated of at least two quantum systems and also it is a relational
property.
This type of relation cannot be described in the framework of the present concept of space-
time. When the state of one quantum object is altered, the other will instantaneously change state to
exactly the opposite of its partner, no matter the distance between the two. The information from one
entity of the entangled objects propagates to the other through a speed greater than the speed of light i.e.
it is acausal. The correlation or entanglement is independent of distance i.e. do not depend on the spatio-
temporal locations.
According to Ithaca interpretation of Quantum Theory (QT) (11),
The only proper subjects of physics are correlations among different parts of the physical world.
Correlations are fundamental, irreducible, and objective. They constitute the full content of physical
reality. There is no absolute state of being; there are only correlations between subsystems.
In this framework, one speaks in favour of metaphysics of relations that do not require any intrinsic
properties of the related quantum systems. At some fundamental level unconditional joint objective
probabilities have meaning, but certain conditional probabilities have no meaning because of the absence
of any objective reality. Only correlations- i.e., objective reality is associated with the joint distributions
only. From a different perspective, Rovelli(8) proposed that
Quantum states were nothing more than expressions of relations between subsystems.
Now, before going into the details of metaphysics of relations, let us discuss another concept called
Quantum teleportation in modern quantum theory.
III. Quantum Teleportation:
Different points of views regarding teleportation concepts can be identified. Among these, the
concept connected to the present work is based on the well known concept of quantum
entanglement. This phenomena can be described as an exploitation of entanglement. The general
idea is that some of the attributes or form of quantum object can be transported to a distance
without moving the matter associated to this form. This does not require any intervening
medium. This is like to scan an object in such a way so as to extract all the information from it
and then this information transported to the receiving location and used to construct the replica
of the original. According to the basic tenets of quantum theory the phenomena is like such that
as if, the state of the original object is being lost during the process of scanning. Quantum
teleportation, from the quantum entanglement point of view, can be defined as the disembodied
transport of the quantum state of a system and its correlations across the space to another system.
There, the system can be referred to any single or collective particles of matter and or energy, for
example, protons, neutrons etc, (baryons), leptons(electrons, positrons etc.), photons, atoms, ions
etc. The concept of entanglement is used in teleporting the form or the some of the attributes of
the object. Quantum teleportation has been performed in several laboratories around the world
(9). So this is not now a fiction but a physical reality.
Next, we give an overview about the characteristics of the quantum entanglement as a
relation.
IV. Metaphysics of Relations:
A metaphysical relation can grant that the things may have non-qualitative frontiers. It is now
clear from the above analysis that Quantum Entanglement can be thought of as relations having the
following characteristics:
(1) This kind of relation is not causal.
(2) It is beyond the space-time description.
(3) The relation contains the information about the relata.
(4) The relation has intrinsic property.
(5) The relata does not have intrinsic properties.
(6) Some quantum entities can be entangled although quantum theory can describe some entities which
are not entangled (product states).
(7) Since this relation is a causal and beyond space-time description, is it a mental construct ?
(8) The concept of entanglement can be used to produce teleportation of quantum objects This can be
produced even in the laboratory(ref????). So the entanglement is real but not in the sense of reality of
relata.
[[[The metaphysics of relations has been extensively discussed by various schools of Indian philosophy
including Buddhist one. Before going into the detailed discussions , let us study briefly regarding this
concept as presented by different school of metaphysics.]]]]PUT IT ABOVE THE FIRST PARAGRAPH
OF THIS SECTION
(a) Western Perspective:
The world consists of independent individual things that are embedded in space-time. These things are
individuals because
(1) They have a spatio-temporal location.
(2) They are a subject of the predication of properties each.
(3) There are some qualitative properties by means of which each of these things is distinguished from all
others (at least the spatio-temporal location is such a property)
Aristotle assumes that there is a plurality of individual things (substances) that are characterized by
intrinsic properties (forms) each.
Esfeld(3) claimed that quantum entanglement may be considered as relation which contains the
information about the relata and there is no need to consider the intrinsic properties of the relata as
claimed within the domain of western perspective.
(b) Indian Perspective
The first question needs to be discussed: what is a relation? (13) A relation connects one entity with other
entity and the basic characteristic of a relation is that it rests on two entities ( dvisthah sambandhah).
This means when it is observed that many individuals form one class, the relation (inherence) subsists
in both the class and the individuals. Symbolically speaking a relation between object a and object b is
aRb.
The next question is : is the relation is real ?
•“No” is the answer by idealists i.e., Buddhists and Advaitins.
•“Yes” is the response from realists who are conventionally identified as Nyaya-Vaisesikas and
the Mimamsakas and other pluralists.
In fact, the idealists consider the entire world as the creation of mind and so, any revelation out
of our experiences is to be termed as relation and invariably imaginary entity. The proponents of
this view i.e., Buddhists introduced the role of the mind , connected to things inherently with
language. The idealists, also, advance their argument further by introducing the role of projection
of the mind on the appearance of the existence of mind.
Nyaya-Vasesikas, Mimamsakas and other pluralists are the proponents of realist view. In the language
of realists, say Nyaya-Vaisesikas, the determinate cognition (savikalpaka-jnana) takes the vital role in
which a structure of qualifier-qualified type is revealed and consequently this structure is not possible
without the involvement of an entity called Relation.
(i) Dharmakīrti’s view :
Dharmakirti , a Buddhist scholar of around 7th century and one of the founders of Indian logic
discussed the metaphysics of relations in great depth. In one of his seven treaties of valid cognition
(Sambandhapariksa) Dharmakirti(14) made an extensive study on the analysis of relations. His
arguments can be briefly summarized in the following way:
Sambandha or Relation (R) are of two types: paratantrya (depending) and rupaslesa (close connection).
Again “dependency” can be of two types: “nispannayoh” and “anispannayoh”. He claimed that
dependency is not considered as relation since it is already nispanna.
He raised the next issue whether mixing or amalgamation between two things (rupaslesa) is a relation or
not.
In case of mixing or amalgamation two cases arise:
•If the two things are distinct, then how they can be mixed up or amalgamated , so mixing or
amalgamation can not be a relation.
•If the two things are identical then how a relation can be established since the relation must be
defined between two distinct things. So mixing or amalgamation is not a relation.
Symbolically speaking If a and b are distinct, then how can we say they are related? Now if a and b are
identical then either a or b or R exists and there is nothing like aRb. So R is not a reality.
Suppose the relation is considered only as imagination which connects a and b. Depending on this
imagination whether one can think of “kriyakarakasambandha”, This is also not possible since there is no
relation of any “karaka” with verb “kriya” and everything is momentary. So “kriyakarakasambandha”
cannot be considered as a relation between a and b.
In modern physics, Cause and effect relation is considered to be one of the pillars. It is pointed out in
“Sambandhapariksha” that cause and effect relation is not a “relation” in the sense that cause and effect
cannot exist at the same instant of time so the relation is not a reality. Now even if we consider that R
exists in case of cause and effect in a sequence not in the sense of simultaneity, then either R exists in
cause and not in the effect or the vice versa. In such case, then, how a relation exists either without b or
a respectively ?
Again, if R does not exist in the cause or the effect, then how R produces the effect in b or vice versa ?
The relation plays an important role in generating the cognition. According to realists, the ontological
reality of relation must be considered to acquire an expressible cognition. However, idealists can do away
with a relation and Dharmakirti was in favour of idealism. Since Dharmakirti wants to establish idealism
of the type of Yogacara philosophy, he has no other alternatives left than to deny all relations on the
basis of which realists will explain a qualified cognition. The assumption of the realists that cognition is
also produced by the external object cannot be accepted by the idealists. Before going into the details of
Dharmakirti’s arguments, let us discuss the views of realists.
(ii)Realist View:
Realists cannot portray the reality of this universe without accepting that the relation which appears in the
qualified cognition which are as real as the relata. Various types of relation have been researched in
detail in Navya Nyaya. This has been mentioned below(for details, ref.13) and can be classified as
follows:
(1) Samyoga and Samavaya: aRb where R is considered to be a distinct entity from a and b. Here, the
“contact” and “inherence” can be considered as particular type of relations.
(2)Svarupa : If R is neither contact nor inherence for example a causal relation implies R is the property
of being a cause or the property of being an effect , for examples : Pitr-putra bhava , guru-sisya bhava.
Navya Naiyayikas use the word “visesanata” for “svarupa” and divided “visesanata” into two types as
“daisika visesanata and “kalika visesanata”.
(3)Paryapti : Here, the relation is used to explain a cognition in which vyasajya-padartha appears existing
simultaneously in more than one locus.
(4)Kalikasambandha or Temporal Relation which is svarupasambandha and also known as “kalika
visesanata”.
The analysis of realist clearly indicates that the relation is as real as the relata in the
context of qualified cognition. Dharmakirti refuted the arguments of the realists regarding the reality of
cause and effect relation since relation presumes the existence of the relata simultaneously.
Recently, it has been argued by Ghosh(15) that Nyaya could justify in favour of admitting relation as real
in the following sense. Firstly, the relation is exposed in terms of language and the reality is beyond the
net of language. It is further argued
The Nyaya could forward the following justification in favour of admitting relation. First, relations are
disclosed in language and the real escapes the net of language. If so, is it not a sort of inconsistency on
Dharmakirti’s part to argue for unreality at the level of ontology by making a linguistic statement?
.IV. Reality:
Itacha interpretation of quantum theory commits us to realism: there are quantum systems, and they are as
quantum theory describes them, namely subject to entanglement. Furthermore, we are committed to
endorsing objective probabilities, that is, probabilities which do not simply indicate limits of our
knowledge, but which are about properties that things objectively have. Whatever entanglement may
exactly be, it is a relation among quantum systems. It is not necessary that the states of quantum systems
are entangled. Quantum theory has the means at its disposal to describe states of physical systems which
are not entangled, that is, product states. However, quantum theory describes physical systems in such a
way that entanglement is not at all exceptional, but ubiquitous.
According to Buddhist doctrine of Paticcasamuppada or dependent origination, the world we see, is
not a collection of isolated objects, but as a network of phenomena that are fundamentally
interconnected and interdependent. The Buddhist worldview, therefore, is holistic because it sees the
world as an integrated whole rather than as a dissociated collection of parts. It recognizes the fundamental
inter-dependence of all phenomena in the world. Everything is dependently connected.
It is clear from our analysis that quantum entanglement is real but not in the sense of reality of relata. We
call the reality of the relation as second order reality with respect to that of relatum.
Here, the relata are the real in the physical world and we call it as first order reality whereas the relation
(quantum entanglement) is not real in the sense of relata and we call it as second order reality.
REFERENCES
(1). Aristotle (1984) The complete works of Aristotle, J.Barues(Ed), Princeton University Press.
(2). Glen(2000) Relations and Reality: The Metaphysics of Parts and Wholes, Ph.D. The Dissertation
Department of Philosophy: Boston College.
(3). Michael Esfeld (2004) Quantum entanglement and metaphysics of relations, Studies in the History
and Philosophy of Modern Physics Vol.35B p. 601-617.
(4) G.B.J. Dreyfus(1997) Recognizing Reality, State University of New York Press.
(5). Erwin Schrodinger(1935) : Discussion of Probability Relations Between Separated Systems,
Proceedings of the Cambridge Philosophical Society Vol. 31, p 555-563; ibid .Vol. 32 (1936) p 446-
451.
(6). Lo, H.-K.,Popescu, S., Spiller, T.(1998) Introduction to Quantum Computation and
Information (Singapore: World Scientific).
(7). Nielson M.A., Chung I.L. (2000) Quantum Computation and Quantum
Information(Cambridge, Cambridge University Press).
(8) A. Einstein, B. Podolsky, N. Rosen (1935) Can Quantum-Mechanical Description of
Physical Reality be Considered Complete? , Physical Review Vol.47, p777-780.
(9). A. Aspect, P. Grangier, and G. Roger(1982) Experimental Realizations of Einstein-pdolsky-Rosen-
Bohm Gedanken experiment: A New violation of Bell’s inequalities., Physical Review Letters, Vol.
49(2), p91-94.
(10). Don Howard (1985) Einstein on Locality and Separability, Studies in History and Philosophy of
Science Vol. 16 p.171-201.
(11). N. David Mermin (1996) The Ithaca Interpretation of Quantum Mechanics: arXiv:quant-
ph/9609013
(12). Quantum teleportation experiment reference?????
(13). V.N.Jha (1990) The philosophy of relations; Sri Satguru Publications, Delhi, India.
(14). Dvarkanatha sastri, Bauddhabharati ed.(1972) Dharmakirtinibandhavali, Varanasi.
15). Raghunath Ghosh (2001) Relation as Real : A Critique of Dharmakirti; Satguru Publications, India.