Quantum Entanglement and the Philosophy of Relations - Jaina Perspective

ABSTRACT

 

Quantum entanglement is a property of a quantum state consisting of two or more microscopic 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. The concept of non-locality is a metaphysical concept. This non-local connection or quantum correlation has been experimentally verified in laboratory experiment where the distance of separation between the two such objects is over a distance more than 12 km. This connection or so to say, the relation between the two microscopic entities contains the information about the relata (here, the microscopic objects) though the relata do not necessarily need to have intrinsic properties. The metaphysics of relation has been extensively discussed by various schools of Indian Philosophy. Buddhist scholar Dharmakirti raised a lot of debate about the reality of the relations. Quantum entanglement as a relation has been critically analyzed and compared with the views of various schools of Indian philosophy with special emphasis on Jaina theory of reality. The present analysis from Jaina perspective sheds new insight on the reality of relations as envisaged in quantum theory.

 

I. Introduction:

 

The remarkable progress in modern physics in twentieth century raises lot of interest on the metaphysical aspects of quantum theory. Specifically, in dealing with the quantum theory in most general sense, the physical world is considered to be of nonlocal nature. It can also be stated as the space-like separated systems which can occupy entangled states which is able to persist even when the systems separate further. The concept of Quantum entanglement plays a crucial role in understanding quantum theory. This property i.e., quantum state consisting of two or more subatomic objects like photon, electron, neutron or proton act in such a manner so that whenever the state of one quantum object is altered, the other, instantaneously, change state to exactly the opposite of its partner, no matter how far these objects are being separated. It appears that the objects, making an entangled state, are connected non-locally and are non-separable. This phenomenon 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, in present situation, 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 (here, the two or more quantum objects) though the relata do not necessarily need to have intrinsic properties. Intrinsic properties are those qualitative properties which a thing possesses, irrespective of the presence of any other contingent things. All other qualitative properties are extrinsic or relational. So characterizing the entanglement in terms of non-separability for quantum systems turns into 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 , Wittgenstein and others.

                            

Esfeld (3)  studied in detail  the metaphysics of relations between subatomic ( quantum) systems 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 important to note that various schools of Indian philosophy, for example, different schools of ancient Hindu lineage including schools of Buddhist one (4) discuss the nature and the ontological status of relations in great details. Jaina scholars (5) critically analyzed the views of Buddhistc, Vedantic and Nyaaya approach to the reality of relation. In this paper, we shall discuss the views of some of those schools on metaphysics of relations and ontological status with special emphasis on Jaina view.

 

At first, we 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 mentioned briefly. Then we discuss and develop the comparative views on reality and relational aspects from quantum theory as well as from perspectives existing in different Indian schools, especially, emphasizing on Jain point of  views  in section IV. Finally in section V the concept of non-local relation or quantum entanglement is shown to be more transparent within Jaina perspective.

 

II. Concept of 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 which 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” for this phenomena and used it in his three part article published in Proceedings of Cambridge Philosophical Society (6). 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 as 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(7,8). 

 

But, Einstein disliked this approach at first and called quantum entanglement “spooky action at a distance” in the famous EPR debate (9). Though his belief was that someday quantum entanglement would have been explained by future researchers in terms of certain error in calculations, further developments established this phenomenon in a concrete manner. Aspect et al., in 1982, first showed that nonlocal interactions do occur (10) even in the laboratory.  

 

Two quantum objects, when entangled, initially, both will 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.  Examples for this phenomenon are position and momentum and also  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 property of a quantum system taken separately which is a supervenience basis for these correlated probability distributions. Furthermore, these correlations – and thus entanglement – are independent of spatio-temporal distance. Because of this property, i.e., entanglement, quantum physics seems to exhibit some sort of a holism. Next, let us analyze the concept of non-separability.

 

Non-Separability:

Einstein based his criticism of quantum theory on the principle of separability. Taking Einstein’s criticism into account, Don Howard (11) formulates separability as the claim which states

  •  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 (3).

 

Following this characterization, any case of quantum entanglement can be defined as a case of non-separability which, in turn, 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. In doing so, the information from one entity of the entangled objects propagates to the other through a speed greater than the speed of light(c) hence 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) (12),

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 (13) 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.

 

Quantum Teleportation:

 

In general, different views regarding teleportation concepts has been identified and discussed by various authors. Among these, the concept connected to the present work is based on the well known concept of quantum entanglement. This phenomenon 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, as if, scanning an object in such a way so as to extract all the possible information are extracted from it and then transported to the receiving location and used to construct the replica of the original. According to the basic tenets of quantum theory, 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 (14). So this is no more a fiction now but a physical reality.

 

Now, we try to give an overview about the characteristics of quantum entanglement as a relation.

 

IV. Metaphysics of Relations:

The metaphysics of relations has been extensively discussed by various schools of Indian philosophy including Buddhist  and Jaina. It is 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 relatum (i.e., single object) does not have intrinsic properties but has propensity of being emtangled.
  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 acausal and beyond space-time description,  is it a mental construct ?
  8. The concept of entanglement can be used to produce teleportation of quantum objects which can be produced even in the laboratory (14).  So, the entanglement is real.  

(a)  Western Perspective:

 

According to western perspectives, (15) the world consists of independent individual things that are embedded in space-time. These things are stated as 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 (1) assumed that there is a plurality of individual things (substances), characterized by intrinsic properties (forms) each. Esfeld(3), on the other hand,  claimed that quantum entanglement may be considered as relation containing 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 perspectives. Recently, structural realism has drawn much attention to the scientific community (16) where the concept of structure refers to some set of relations between the things or entities that they relate, called the relata. People have used the term “structural realism” to describe different approaches to the nature of the relation between things and relations. These differences all seem to be variants of three basic possibilities:

  • only relations without relata.
  •  relations, in which the things are primary and their relation is secondary.
  •  relations, in which the relation is primary while the things are secondary.

 (b) Indian Perspective

 

The nature and ontological status of relation have been widely discussed by various schools of Indian philosophy (17). Before going into the details of their analysis, one needs to discuss the basic question: what is a relation? (17) 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.

 

Now, the next question: Is the relation 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 , the Mimamsakas and Jains 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.   

 

Dharmakīrti’s view :

Dharmakirti, a Buddhist scholar of around 7th century  and one of the founders of  Buddhist logic discussed the metaphysics of relations in great depth. In one of his seven treaties of valid cognition (Sambandhapariksa), Dharmakirti(17) 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 (dependency) 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(cause and effect relation) cannot be considered as a relation between a and b.

 

Now, Cause and effect relation is considered to be one of the pillars in modern physics. 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. Let us, now, discuss the views of realists.

 

Realist View:

 

1. Realists cannot portray the reality of this universe without accepting that the relation appearing  in the qualified cognition are as real as the relata.  Navya Nyaya  have researched in detail and  classified various types of relation which can be summarized and classified as follows: (for details:  ref.(19)

2. 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. 

3. Svarupa: If R is neither contact nor inherence. A causal relation implies:  R is  the property of being a cause or the property of being an effect.  For example : Pitr-putra bhava , guru-sisya  bhava etc.

4. Navya Naiyayikas use the word visesanata for  svarupa and  divided “visesanata” into two types as  daisika visesanata  and kalika visesanata.

5. Paryapti : Here, the relation  is called Paryapti-sambandha in Navya-Nyaya.  This can be expressed over and above the inherence-relation. It is used to explain a cognition in which vyasajya-padartha appears existing simultaneously in more than one locus.

6. Kalika sambandha or Temporal Relation which is  svarupasambandha and also known as “kalika visesanata”.    

 

The analysis of realist school 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 (189that 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?

 

The Jaina view:

 

Jaina school (5), with the usual reconciliatory  metaphysical standpoint offers an approach which is intermediatory in between the extreme externalism of the Naiyayika and the equally extreme idealism of the Buddhist and Vedanta schools. Regarding reality and relational aspects a few critical points should be mentioned which contradicts directly with the different Hindu school and Budhhist schools. Following Jaina philosophy; few points need to be mentioned as follows:

 

(i) The Jaina does not believe in the existence of absolutely simple entities. A real, say, even an atom is considered as a star, present in a constellation of similar entities, which assumes various patterns, have magnitudes, determined by the internal compulsive laws and external pressure. In this manner, an infinity of relation is assumed, an internal and external, total and partial, immediate and mediate with the other phenomena of the universe. A real is, obviously, an independent existent but at the same time, a complex focus or network of relational forces, just like a knot into which the strands of such forces are woven.

(ii) Jaina school postulates the reality as a deliverance of the direct or objective experience and as a  result, the relation are posited not merely as inferable, but also as an indubitably perceptual(5).

(iii) According to Buddhists, the basis for admissibility of relation is not possible due to lack of serviceability (upakaritva, arthakriyakaritva) attributed to relation. But Jainas (for details, Pravachnadra established the fact about how the relational element is a constituent factor in making up objects. For example, if the atoms producing an object say pitcher are discrete entities as Buddhist maintain, then simply the aggregates of the atoms will not produce pitcher. In modern science one needs concept of cohesion to produce such an object. Jaina scholars emphasized that the atoms are being capable of being connected to become as concrete object. The jaina looks upon the relation resulting from the combination of the relata in it as something unique (jatyantara) in comparison with the combining relata.

(iv) Regarding “paratantryasambandha”as discussed by Dharmakirti, Pravachandra (20)  remarked that essential nature of “paratantrya” is unification of the relata not mere “dependent” as observed by Buddhist. Accordingly, Jaina view of relation is that it is an identity of differents or different terms.

 

In view of this perspective of Jaina view we will discuss the reality of  Quantum entanglement as a relation in modern physics.

 

IV. Discussion on Reality of Quantum Entanglement and Jaina view:

 

Whatever entanglement may exactly be, it is a relation among subatomic or quantum systems. It is not necessary that the states of quantum systems are entangled. In famous paper of Einstein ( known as EPR) a state of two subatomic entities are prepared by a measurement procedure : for example a singlet state of two electrons is prepared so that even the electrons are being far apart thereafter, the correlation exists hence called non-local correlation. A siniglet state is formed because of Pauli’s exclusion principle. This principle says that no two electrons can occupy the same state with same spin states. So the two electrons may be a particular state with their spins having different directions like if one in up direction along plus z-direction and then the other one along minus z-direction.

 

It is now clear that the entangle state of two electrons is not merely as aggregate of two sub-atomic entities but one needs to consider the restriction imposed by Pauli’s exclusion principle. So this is a kind of relation where we need to consider the “propensity of the relata” to form a relation called “quantum entanglement” as emphasized by Pravachandra in contrast to Buddhist view of mere dependency. Moreover, this singlet state of two electrons remains invariant under permutation or exchange of the position of two electrons though the two electrons are in different spin states in this state. This is similar to the concept of identity of differents as discussed by Pravachandra in the context of “paratantrya sambandha”.

 

V. Conclusion:

 

The concept of entanglement is used in teleporting an object from one place to another distant place without transporting it physically but its form or attribute only. Since quantum teleportation is real and can be produced in the phenomenal world, the quantum entanglement is a reality.

 

Now, following 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 a dissociated collection of parts. It recognizes the fundamental inter-dependence of all phenomena in the world, everything being dependently connected.

 

Owing to the causal relations, we gain empirical knowledge between physical things and our senses. But knowledge obtained in this way, obviously points to the intrinsic properties of physical things. The way we gain this knowledge, puts constraints:  we identify the physical properties of a system only through relations in which they enter. So to say, fundamental physical properties can be stated as describing these properties as relational. It is interesting now, to note that identity of relation does not necessarily imply the identity of intrinsic properties attached to the properties of physical things, but the way they are related to us. So, the quantum entanglement can be interpreted in terms of non- separability; we can claim that the specific relations do not need the intrinsic properties of the related systems, whereby, quantum physics, in virtue of exhibiting entanglement, offers us the arguments providing means to avoid difference between epistemology and metaphysics i.e., what is at the base level of the world are relations of quantum entanglement only. Summarizing the above arguments we emphasize that the quantum entanglement as a kind of relation which is neither in compatible with Realist view nor with Dharmakirti. Here the relation is real but not real in the sense of reality of relata.

 

The analysis of Prabhacandra is based on the distinction between the two meanings of “having parts” i.e.

(a) Physical partition and

(b) Infinite diversity or manifoldness of nature exhibiting a varied relational structure.

 

He agreed with Buddhists regarding the impartiteness of the ultimate units or atoms of nature but put forward the vital aspect of the manifold nature. For example, he suggested the fact of the infinitely manifold relatedness of an atom to the other atoms similarly located. According Jaina views an atom is not a lonely being but in a constellation of similar entities which assumes in their multitudinous determined by the laws of their internal compulsions and external pressure -

“A real is indeed an independent existent but it is also a complex focus or network of relational forces. It is as it were a knot  into which the strands of such forces are woven” 

 

It is clear from the above arguments of Prabhacandra that the quantum entanglement is a kind of relation between the two “identical subatomic entities” ( say electrons) but identity of differents since each subatomic entity has infinite diversity. This infinite diversity associated to each subatomic entity is nothing but the various attributes like “spin” states of the entity. The  spin states of the subatomic entity in the entangled state may be in different directions like x, y or z. If one entity is in up in x-direction then the other entity in the entangled state will be in down x-direction and similar happens to other directions. So even we consider the entangled state of identical sub-atomic particles like electrons we need to consider the diversity in their attributes too as emphasized by Prabhachandra in his analysis.

 

REFERENCES

(1). Aristotle (1984)  The complete works of Aristotle, J.Barues(Ed), Princeton University Press.

(2). S E Glenn (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) Y.J. Padmarajiah(2004) A comparative study of the Jaina Theories of Reality and Knowledge, Motilal Banarasidass Publishers Pvt. Ltd, Delhi.

(6). 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.

(7) Lo, H.-K.,Popescu, S., Spiller, T.(1998) Introduction to Quantum Computation and Information (Singapore: World Scientific).

(8)Nielson M.A., Chung I.L. (2000) Quantum Computation and Quantum Information (Cambridge, Cambridge University Press).

(9)  A. Einstein, B. Podolsky, N. Rosen (1935) Can Quantum-Mechanical Description of Physical Reality be Considered Complete? , Physical Review   Vol.47, p777-780.

(10) 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.

(11)Don Howard (1985) Einstein on Locality and Separability, Studies in History and Philosophy of Science Vol. 16   p.171-201.

(12).N. David Mermin (1996) The Ithaca Interpretation of Quantum Mechanics: arXiv:quant-ph/9609013

(13) Carlo Rovelli (1996) Relational Quantum Mechanics; http://arxiv.org/abs/quant-ph/9609002v2

(14) Xian-Min Jin1 et al ,(2010) Experimental free-space quantum teleportation ,Nature Photonics Vol.4 p. 376 - 381 and references there in.

(15) D. Lewis(1986) Philosophical papers, Vol.2 , Oxford University Press.

(16) John Stachel(2005) arXiv.grav-qc/0507078 v2.

(17)V.N.Jha (1990) The philosophy of relations; Sri Satguru Publications, Delhi, India.

(18)Dvarkanatha Sastri, Bauddhabharati ed.(1972) Dharmakirtinibandhavali, Varanasi.

(19) Raghunath Ghosh (2001) Relation as Real : A Critique of Dharmakirti; Satguru Publications, India.

(20)Pravachandra(1941); Prameya-Kamala-Martanda; 2nd edition; a comment on Praiksamukha-Sutra of Manikyanandi; etd. by Mahendra Kumar Shastri, Bombay.

(21) Bhatt, Govardhan P.(1989); The Basic Ways of Knowing: An In-depth Study of Kumārila's Contribution to Indian Epistemology. Delhi: Motilal Banarasidas. 

About Author: T.V.Raman Pai Chair Visiting Professor, National Institute of Advanced Studies, IISC Campus, Bangaluru – 560012 and (Former) Professor, Physics and Applied Mathematics Unit, Indian Statistical Institute, Kolkata.

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