Ladyman and Ross on Quantum-Mechanical Particles: Things, Structure and Relations (4)

Things and Structures

The most important aspect of ontic structural realist position can be expressed in the following way:

Relata (i.e., things/objects/particles/etc.) can be eliminated. Then all we will have left is relations.

James Ladyman and Don Ross ground their own philosophy by expressing Bertrand Russell's position in the following manner:

“... many philosophers have followed Russell in arguing that it is incoherent to suppose there could be individuals which don’t possess any intrinsic properties, but whose individuality is conferred by their relations to other individuals.”

Indeed that passage can be rewritten to make it more germane to Ladyman and Ross's own ontic structural realism. Thus:

It is incoherent to suppose there could be individuals (e.g., particles, etc.) which don’t possess any intrinsic properties, but whose individuality is conferred by their relations to other individuals, structures, fields, states, etc.

Thus we can ask the following question:

Does a thing/object gain its identity from its place in a structure or does it have its place in a structure because of its (prior) identity?

Indeed Ladyman and Ross state that Paul Benacerraf believed that

“an object with only a structural character could be identified with any object in the appropriate place in any exemplary structure and could not therefore be an individual”.

In other words, Benacerraf seems to have taken the position cited earlier. Namely, an object/individual has its place in a structure because of its (prior) identity. That is, an object/individual doesn't gain its (entire) identity from its place in a structure.

To elaborate on Benacerraf's position. It can be said that if structure is everything (or, at the least, if an thing/object gains its identity from its place in a structure), then any thing/object can take a place in that structure. Indeed any thing/object can take specific place x in a given structure if the individuality or identity of an object is passed onto it (as it were) by the structure it is a part of.

The problem with this (or perhaps any) form of structuralism, however, is summed up by Ladyman and Ross who state that “individuals are nothing over and above the nexus of relations in which they stand”. However, they do preface that by saying that this position – only? - applies to “individuals in the context of quantum mechanics”.

Ladyman and Ross continue by saying that “the identity or difference of places in a structure is not to be accounted for by anything other than the structure itself”. Not only that: the mathematical structuralism just discussed “provides evidence for this view”.

Despite all that, Ladyman and Ross often state that they don't actually deny the existence of entities or individuals per se. Yet it's hard to make sense of their claim that “there are objects in our metaphysics” and then go on to state that

“but they have been purged of their intrinsic natures, identity, and individuality, and they are not metaphysically fundamental”.

In other words, if you take away “intrinsic natures, identity, and individuality”, then what's left of things/objects after all that has been taken away? Only structure and/or relations? But what does that mean?

In any case, Ladyman and Ross see individuals as “abstractions from modal structure”. By “modal structure” they mean

“the relationships among phenomena events, and processes) that pertain to necessity, possibility, potentiality, and probability”.

It can easily be said that structures involve individuals and relations involve relata. At a prima facie level we can also ask:

In what way do “abstractions” involve themselves in modal realities?

Well, mathematics itself involves necessity, possibility and probability. And if structures are inherently mathematical, then structures have modal properties. All that may be true. Though what about modality as applied to the concrete world of objects, events, conditions, states, etc? What about metaphysical modality as understood by philosophers like Saul Kripke, David Lewis, D.M. Armstrong and so on?

Ladyman and Ross also quote the American philosopher of science John Stachel when he says that entities “'inherit [individuality] from the structure of relations in which they are enmeshed'”. However, saying that is a long way from saying that individuals don't exist. Even the very use of the word “inherit” surely means that it must be things which are doing the inheriting.

Now is it that Ladyman and Ross reject this position and simply deny ontological status to things/objects - full stop? Or is their position that entities inherit their individuality from the “structure of relations in which they are enmeshed” as far as they need to go? Thus it's not that Ladyman and Ross are eliminitivists about things/objects. It's simply that they have a radical philosophical take on things/objects. A take which claims that entities gain their individuality from structure. That is, before things/objects are “enmeshed” in structures, they have no intrinsic natures.

Can we go so far as to say that before things/objects are enmeshed in structures, they don't exist? Thus it's not just the nature of entities we're talking about: it's also their existence. Do entities spring into being only when they're enmeshed in structures?

This position would go against the claim (for example, of David Lewis) that objects have intrinsic natures regardless of the rest of the world.

So now we still have the following positions:

i) Things gain their natures from the structures they belong to.

ii) Things come into existence in structures.

How is i) different from saying that entities are structures? In other words, the temporal and grammatical construction of i) may seem to imply that we have an entity at time t¹ - and at t² it gains its nature from the structure it's embedded in. However, if ii) is correct, than that entity comes into existence in the structure. It doesn't only gain its nature from a structure – it comes into existence in the structure in which it's embedded.

Such abstract metaphysics is made concrete when Ladyman and Ross take the example of fermions. They cite the position that

“that fermions are not self-subsistent because they are the individuals that they are only given the relations that obtain among them”.

What's more, “[t]here is nothing to ground their individuality other than the relations into which they enter”. And, according to Ladyman and Ross, even Albert Einstein once claimed that particles don't have their own “being thus”.

Substantivalism

As just hinted at, one problem which can be raised about things/objects (as well as about Ladyman and Ross's position) can be expressed by stating two positions:

i) Things/objects have their intrinsic natures independently of the rest of the world.

ii) Things/objects can exist independently of the rest of the world.

This problem specifically arises in the context of “points of spacetime” rather than objects. (Although it may be said that they amount to the same thing.) In this case, Ladyman and Ross use the word “exist” (as in ii) above). This is also a product of two different positions: substantivalism and relationalism. Thus:

i) According to substantivalism, the “points of the spacetime manifold exist independently of the material contents of the universe”.

ii) According to relationalism, “spatio-temporal facts are about the relations between various elements of the material contents of spacetime”.

The idea that “points of the spacetime manifold exist independently of the material contents of the universe” is similar to David Lewis's take (1982) on the intrinsic properties of things. Lewis wrote:

“A thing has its intrinsic properties in virtue of the way that thing itself, and nothing else, is.”

Lewis's position (if not the substantivalist position) can be taken to its most extreme in the following statement:

Object a would still have intrinsic property P if, after the world around it disappeared, a would still have P.

In Ladyman and Ross's rendition of substantivalism, it's said that an object or point in spacetime could “exist” regardless of everything else. Could there ever be “the way that a thing itself is” regardless of everything else? That is, can object x be the way that it is regardless of its relations to other properties/objects/events/states/etc. and its place in spacetime?

Things and Relations

Ladyman and Ross provide a useful set of four positions which focus on the nature of relations and things. Thus:

i) There are only relations and no relata.

ii) There are relations in which things are primary, and their relations are secondary.

iii) There are relations in which relations are primary, while things are secondary.

iv) There are things such that any relation between them is only apparent.

At first glance one would take ontic structural realism to endorse (i) or (iii). However, if things are themselves structures (according to Ladyman and Ross), then we must settle for (i) above: “There are only relations and no relata.”

Looking at (i) to (iv) again, couldn't it be said that (ii) and (iii) amount to the same thing? In other words, how can we distinguish

(ii) There are relations in which the things are primary, and their relations are secondary.

from

(iii) There are relations in which relations are primary, while things are secondary.

Isn't this a difference which doesn't make a difference? One can still ask - in the metaphysical pictures of (ii) and (iii) - the following question:

Can things exist without relations and can relations exist without things?

That's a question of existence. Now what about natures?

One can now ask:

Can things have their natures without relations and can relations have their natures without things?

********************

To follow: 'On Quantum-Mechanical Particles: Conclusions (5)'

Ladyman and Ross on Quantum-Mechanical Particles (3)

In Every Thing Must Go: Metaphysics Naturalized, the philosophers James Ladyman and Don Ross give a clear account of the physics which underlies the problematic nature of seeing elementary particles as single things or objects. (Everything Must Go is a controversial and fairly well-known book — at least in philosophy.)

Firstly, Ladyman and Ross put the position of classical physics:

“[C]lassical physics assumed a principle of impenetrability, according to which no two particles could occupy the same spatio-temporal location. Hence, classical particles were thought to be distinguishable in virtue of each one having a trajectory in spacetime distinct from every other one.”

Clearly, in quantum mechanics (QM), many — or all — the assumptions in the classical picture are rejected. (Or, at the least, on many interpretations of QM all these assumptions are rejected.)

Take the notion of impenetrability.

Impenetrability

The “principle of impenetrability” is rejected by Ladyman and Ross.

On the classical picture, if particles are impenetrable, then that must mean that “no two particles could occupy the same spatio-temporal location”. However, if they are penetrable (or if the notion of impenetrability doesn’t make sense), then one can conclude that two particles “could occupy the same spatio-temporal location”.

Now one can immediately ask the following question:

If two particles can (or do) occupy the same spatiotemporal location, then is it correct to talk about two particles in the first place?

As a consequence of that question, the second part of the classical picture is rejected too. That second part (which follows from the first) is that

“classical particles were thought to be distinguishable in virtue of each one having a trajectory in spacetime distinct from every other one”.

Clearly, if the penetrability argument is true (i.e., two particles may occupy the same location), then each particle can’t be seen to have its own trajectory in spacetime. In other words, it will — or may — share its trajectory with another particle.

All this has the result (at least according to Ladyman and Ross) that the Leibnizian picture breaks down in the case of quantum-mechanical particles. On the other hand and according to Ladyman and Ross:

“Thus for everyday objects and for classical particles, the principle of the Identity of Indiscernibles is true [].”

So what about the notion of individuals?

Individuals

Ladyman and Ross then offer us two statements which they believe summarize the position of “standard metaphysics” on, if not particles, then on what they call “individuals”.

Take (i).

“There are individuals in spacetime whose existence is independent of each other. Facts about the identity and diversity of these individuals are determined independently of their relations to each other.”

The problem is how to take the word “independent” in the passage above.

One can accept the reality (or existence) of individuals yet also believe they that they aren’t (entirely) independent of other individuals. That is, the reality (or existence) of individuated objects and their lack of independence aren’t mutually exclusive. What’s more, one can accept the “identity and diversity of these individuals” yet also deny that such “individuals are determined independently of their relations to each other”. In other words, why does a commitment to individuals necessarily mean that one must also accept their complete independence from all other individuals (or from other events, processes, conditions, states, fields, systems, structures, etc.)?

In addition, it’s simply false that metaphysicians have accepted all that’s claimed in (i) above. Randomly, take the various monists and holists in the history of philosophy; as well as philosophers like F.H. Bradley and A.N. Whitehead. Such philosophers certainly didn’t believe that individuals are “independent of each other”.

What about Ladyman and Ross’s second statement?

They say that “standard metaphysicians assume” the following about individuals or particles:

“Each has some properties that are intrinsic to it.”

Here again what was said about claim (i) partly goes for claim (ii) as well.

Throughout the history of Western metaphysics there have been metaphysicians who’d now be classed as “anti-essentialists”. Indeed we could go back to Heraclitus (c. 535 — c. 475 BC) to find anti-essentialists (or at least to find proto anti-essentialists). In addition, we had the medieval nominalists. Come the 20th century, there’ve been many anti-essentialist metaphysicians and philosophers.

So what, in very basic terms, do essentialists (see essentialism) believe?

They believe that an individual “has some properties that are intrinsic to it”. However, here again it can be said that some/most of the ontologists who’ve (broadly speaking) accepted the bundle theory of individuals could also be classed as anti-essentialists in that they’d have denied the statement that each individual must have at least some intrinsic properties.

Discernibility and Individuality

One method for distinguishing two individuals (or two objects/particles) is basically W.V.O Quine’s reworking of Leibniz.

Quine called it “absolute discernibility”. Ladyman and Ross express his position this way:

“Quine called two objects [] absolutely discernible if there exists a formula in one variable which is true of one object and not the other.”

This is a reworking of Leibniz’s logical position (with the addition of references to “formulas”). Thus:

(x) (y) (F) (x = y ⊃. F (x) ≡ F (y).)

One obvious way in which a and b can be deemed to be “absolutely discernible” is if they “occupy different positions in space and time”.

Now for “relatively discernible” objects.

According to Ladyman and Ross,

“[m]oments in time are relatively discernible since any two always satisfy the ‘earlier than’ relation in one order only”.

This clearly makes a moment in time relational in nature (see relational theory). Or at least its relatively discernible nature is accounted for by its relational nature (i.e., “earlier than” and “later than”).

What’s just been said about time is similar to what can also be said about space (as well as about the “mathematical objects” which measure it). Ladyman and Ross write:

“An example of mathematical objects which are not absolutely discernible but are relatively discernible include the points of a one-dimensional space with an ordering relation…”

More precisely:

“[F]or any such pair of points x and y, if they are not the same point then either x > y or x < y but not both.”

In the above there’s a fusion of points in space with moments in time. Thus x and y are absolutely discernible because x is before (or “earlier than”) y or x is after (or “later than”) than y. In other words, x can’t be both earlier than and later than y (as well as vice versa) at one and the same time.

Now let’s take Ladyman and Ross’s definitions of discernibility and individuality. They write:

“The former epistemic notion concerns what enables us to tell that one thing is different from another. The latter metaphysical notion concerns whatever it is in virtue of that two things are different from one another, adding the restriction that one thing is identical with itself and not with anything else.”

At first glance, these characterisations come across as two different ways of saying the same thing. Clearly the second characterisation (“whatever it is in virtue of that two things are different from one another”) is ontological in character. The former (“what enables us to tell that one thing is different from another”) is, as Ladyman and Ross say, epistemic in character. However, don’t these two characterisations fuse? That is, in order to know “whatever it is in virtue of that two things are different from one another” one would need to employ the epistemic tools which “enable us to tell that one thing is different from another”. Thus the ontological question merges with the epistemological question (or vice versa).

We can also say that because of the spatial differences between Max Black’s two (identical) spheres (in his well-known thought experiment), sphere a and sphere b can only be classed as “weakly discernible” on Ladyman and Ross’s picture.

Ladyman and Ross make Max Black’s example more concrete (as well as scientific) by talking about two fermions (which are a mile apart) instead of spheres. According to Ladyman and Ross:

“Clearly, fermions in entangled states like the singlet state violate both absolute and relative discernibility…”

Fermions “in entangled states like the singlet state” (see singlet state) aren’t absolutely discernible because there are neither spatial nor temporal means to disentangle each fermion from other fermions. (Hence the technical term entanglement.) However, Max Black’s two spheres are also spatially indiscernible in that they’re in constant movement around a figure of eight. Thus sphere a would be continuously occupying a spatial point which had only just been occupied by sphere b — as well as vice versa. (The only way out of this would be to either literally or imaginatively freeze the movements of both spheres — though that would be unacceptable because it defeats the object of the thought-experiment.)

Fields and States

It can be seen that the notion of a field plays an important part in Ladyman and Ross’s philosophy.

The central argument is that fields and particles are intimately connected. Indeed they’re so strongly connected that a distinction between the two hardly seems warranted.

Ladyman and Ross’s position on the fields of physics can be traced back to — among others — Ernst Cassirer. (Cassirer died in 1945.) Indeed Ladyman and Ross have much to say about Cassirer. For example, they wrote the following:

“OSR [ontic structural realism] agrees with Cassirer that the field is nothing but structure. We can’t describe its nature without recourse to the mathematical structure of field theory.”

What Ladyman and Ross say about Ernst Cassirer’s position on objects is almost exactly the same as their own. Indeed it was also quantum mechanics which provided Cassirer with the motivation to reject “individual objects”. Ladyman and Ross write:

“Ernst Cassirer rejected the Aristotelian idea of individual substances on the basis of physics, and argued that the metaphysical view of the ‘material point’ as an individual object cannot be sustained in the context of field theory. He offers a structuralist conception of the field.”

One can firstly ask whether or not a commitment to the existence of objects is also automatically a commitment to “individual substances”; as well as to intrinsic (or essential) properties. (As stated earlier on in this essay.)

We can also ask whether or not these positions are equally applicable to objects in the “classical” (or macro) world.

Let’s put it this way.

Ernest Cassirer’s and Ladyman’s positions are far more acceptable when applied the the quantum world than when applied to the classical world (or to the world of experience). More precisely, all this is far easier to swallow in the “context of field theory” than it is in relation to, say, human beings (or persons), trees or cups.

There’s also the problem of distinguishing particles from the states or fields they “belong” to. Thus, in an example given by Ladyman and Ross, we can interpret a given field/particle situation in two ways:

i) A two-particle state.

ii) A single state in which two “two particles [are] interchanged”.

Since it’s difficult to decipher whether it’s a two-particle state or a single state in which two particles are interchanged, Ladyman and Ross adopt the “alternative metaphysical picture” which “abandons the idea that quantum particles are individuals”. Thus all we have are states. That means that the “positing [of] individuals plus states that are forever inaccessible to them” is deemed to be (by Ladyman and Ross) “ontologically profligate”.

Ladyman and Ross back up the idea that states are more important than individuals (or, what’s more, that there are no individuals) by referring to David Bohm’s theory. In that theory we have the following:

“The dynamics of the theory are such that the properties, like mass, charge, and so on, normally associated with particles are in fact inherent in the quantum field and not in the particles.”

In other words, mass, charge, etc. are properties of states or fields, not of individual particles. However, doesn’t this position (or reality) have the consequence that a field takes over the role of an individual (or of a collection of individuals) in any metaphysics of the quantum world? Thus does that also mean that everything that’s said about particles can now also be said about fields?

Particle Trajectories

On Bohm’s picture ( if not on Ladyman and Ross’s), “[i]t seems that the particles only have position”. Yes; surely it must be a particle (not a field) which has a position. Indeed particles also have trajectories (if probabilistically accounted for) which account for their different positions.

To Bohm (at least according to Ladyman and Ross), “trajectories are enough to individuate particles”.

It’s prima facie strange how trajectories can individuate.

Unless that means that each type of particle has a specific type of trajectory. In that case, the type trajectory tells you the type of particle involved in that trajectory.

Ladyman and Ross spot what they take to be a problem with Bohm’s position. That problem is summed up in this way:

If all we have is trajectories (as with structures), then why not dispense with particles (as individuals at least) altogether?

This is how Ladyman and Ross themselves explain their stance on Bohm’s theory:

“We may be happy that trajectories are enough to individuate particles in Bohm theory, but what will distinguish an ‘empty’ trajectory from an ‘occupied’ one?”

Here again Ladyman and Ross are basically saying that if all we’ve got are trajectories (which are part of the “structure”), then let’s stick with them and eliminate particles (as individuals) altogether.

Ladyman and Ross go into more detail on this by saying that

“[s]ince none of the physical properties ascribed to the particle will actually inhere in points of the trajectory, giving content to the claim that there is actually a ‘particle’ there would seem to require some notion of the raw stuff of the particle; in other words haecceities seem to be needed for the individuality of particles of Bohm theory too”.

If the physics of Ladyman and Ross is correct, then what they say makes sense. Positing particles seems to run free of Occam’s razor. That is, Bohm was filling the universe’s already-existing “ontological slums” with yet more superfluous entities.

One way of interpreting this is by citing two different positions. Thus:

1) The positing of particles as individuals which exist in and of themselves.

2) The positing of particles as part of package-deals which include fields, states, trajectories, structures, etc.

Then there’s Ladyman and Ross’s position.

3) If there are never particles in splendid isolation (apart from fields, states, etc.), then why see particles as individuals in the first place?

Ladyman and Ross are a little more precise as to why they endorse 3) above.

They make the metaphysical point that “haecceities seem to be needed for the individuality of particles of Bohm’s theory too” (see haecceity) . In other words, in order for particles to exist as individuals (as well as to be taken as existing as individuals), they’ll require “individual essences” (see individual essence) in order to be individuated. However, if the nature of a particle necessarily involves fields, states, other particles, trajectories, structures, etc., then it’s very hard (or impossible) to make sense of the idea that it could have an individual (or indeed any) essence.

(Can’t all this also be said about objects in the large-scale world too — that is, about human beings, tables, chairs and so on?)

In basic terms, then, all particles are parts of various package-deals. Particles simply can’t be individuated without reference to what’s called extrinsic or relational factors.

To Ladyman and Ross, this means that particles simply aren’t individuals at all.

[I can be found on Twitter here.]

Anti-Realist Positions on Quantum-Mechanical Particles (1)

The traditional view of particles can be said to have been articulated by Isaac Newton, who wrote the following:

“God in the beginning formed matter in solid, massy, hard, impenetrable, movable particles, of such sizes and figures, and with such other properties, and in such proportion to space, as most conduced to the end for which he formed them.”

As will be seen, just about everything in that quote will be discussed in this piece: the impenetrability of particles; the fact that particles are seen as things (with “sizes and figures”); the view that particles have “properties”; and Newton even hints (if only loosely) at particles being what philosophers call “individuals”.

Erwin Schrodinger, on the other hand, put a position (if 270 or or so years later) which is very much at odds with Newton's. He wrote:

“A careful analysis of the process of observation in atomic physics has shown that the subatomic particles have no meaning as isolated entities, but can only be understood as interconnections between the preparation of an experiment and the subsequent measurement.”

This is just one of many positions on subatomic particles which question their status as what philosophers call "individuals" - or even as things. Schrodinger emphasises the “interconnections between the preparation of an experiment and the subsequent measurement”. Other physicists and philosophers have stressed the various fields of physics, quantum entanglement, particles and their anti-particles, particles “swallowing” other particles, etc.

However, it's not strange that particles have been seen as particles when one looks at the scientific literature.

Take the case of the Irish physicist and Nobel laureate, Ernest Walton.

Here is a perfect case of mistaking effects for causes when it comes to particles. However, it is indeed probably the case that Walton wrote the following words for purely explanatory purposes. In any case, Walton wrote:

“Particles were coming out of the lithium, hitting the screen, and producing scintillations. They looked like stars suddenly appearing and disappearing.”

The fact is that Walton didn't see or even observe particles “coming out of the lithium, hitting the screen, and producing scintillations”. In addition, the particles wouldn't have “looked like stars”. What Walton would have seed or observed, and what would have looked like stars, were the experimental observed effects of the actions (or behaviour) of particles.

This problem is made clear in something the physicist Eric Allin Cornell once wrote:

“The postdoc explained to me how to distinguish different sorts of particles on the basis of the amounts of energy they deposited in various sorts of detectors, spark chambers, calorimeters, what have you.”

In the quote above it's made clear that it's the effects of particles that Eric Allin Cornell is talking about - not (really?) particles themselves. In other words, particles are inferred or posited from the “amounts of energy they deposited in various sorts of detectors, spark chambers, calorimeters”. Thus it can be said that (at least in this case) the particles were neither seen nor observed. In other words, they were (only?) “theoretical entities”.

What is a Particle?

Of course no one should get too fixated on the word “particle”. It's true that many physicists (as well as a fair few philosophers) get annoyed with what used to be called “conceptual analysis”. However, “particle” is the word which is used in physics - so surely that's the best place to start. After all, the place we start from is not necessarily the place we will end.

When it comes to basic definitions of the word “particle”, it is defined as “an extremely small piece of something”. In that sense, then, the particles of physics are extremely small pieces of something else. It can be said that electrons are “parts” of atoms; protons and neutrons are parts of atomic nuclei; and quarks are parts of neutrons and protons. Of course in philosophy what has been called “parthood” has been a very import subject of philosophical discussion. (We can ask what it is for X to be a part of Y. We can ask if X is an "essential" part of Y. We can also discuss the exact relation of X to Y and do so in either physical or metaphysical terms.)

The notions of an individual and of being separate are also found in definitions of the word “particle”.

Individuals

The word “individual” also throws up philosophical problems.

If an entity (or thing) is an individual, then (on some definitions at least) an individual is defined as being “single” or “separate”. That clearly doesn't work for particles - for a whole host of reasons. It's true that on some “holistic” (or “relationist”) readings, this also applies to almost all things - not only subatomic entities. After all, it can be argued that persons are intrinsically related (or connected) to not only other persons, but also to other things. On another “essentialist” level, if it weren't for my parents, I wouldn't even exist. (Thus that may be an essential relation - something Saul Kripke noted back in the early 1980.) Nonetheless, even if we accept vital (or even essential) relations, that doesn't automatically mean that an individual can't still be separate. Or, in technical speak, “relata” may still be separate from their relations and therefore still be individuals. However, in the case of particles, a clear lack of separation is fundamental to their nature.

Perhaps, in the end, this is simply a question of what the word “separate” or “separation” is taken to mean. And, if that's the case, we can simply stipulate what we take it to mean.

It's also worth noting that the situation with subatomic particles is very different to the situation with almost all other objects or things. That's because particles of a particular type are all identical in terms of their properties. Take electrons, which have the same charge, rest mass, spin, etc. This, on the surface at least, appears to violate Leibniz’s Principle of the Identity of Indiscernibles.

There are, however, ways of distinguishing electrons even though they have identical spin, mass, charge, decay rate, etc. That is, they'll still have different spatiotemporal trajectories which can't overlap. This also entails the view that each electron is impenetrable. That is, if an electron were penetrable, then it could (or would) share a spatiotemporal trajectory with another particle.

It's also the case that some philosophers (e.g., Bas van Fraassan) have individuated particles in terms of their history.

The notion of an individual can also be tied to the parallel notions of “intrinsic” and “relational” properties. Non-intrinsic properties can be “state-dependent” and therefore cashed in terms of monadic and relational properties. In other words, the state determines the properties and therefore the particle is not (or may not) be an individual. This has the result that two particles can have the same state-dependent properties. Or, in philosophical technical jargon, according to the Principle of the Identity of Indiscernibles, such particles will be identical. In any case, particles all have the same properties even when seen in a non-state-dependent context.

Of course if a physicist takes an instrumentalist line of particles, he may not care if they're deemed to be individuals or not. Indeed not many physicists use the word “individuals”, which is a philosophical term. What's more, we also have a situation of “underdetermination” here. That is, a physicist can happily accept a theory (or position) in which particles are seen as individuals or accept one that doesn't take that position. In the end, then, it may not matter to the physicist because he may see it as a difference which doesn't (really) make a difference.

Indivisibility

Another notion (or definition) that's stressed when it comes to individuals is that of indivisibility. It's of course the case that if an individual is deemed to be that which is indivisible, then that doesn't work for all particles. It works for quarks (though has been questioned). However, it doesn't work for neutrons, protons and indeed atoms. There's also the fact that some particles “turn into” other particles (though, technically, this may not be the best way of putting it). In addition, Higgs bosons are now said to provide mass to other particles (though, technically, this isn't the best way of putting it).

The very notion of indivisibility may also be problematic in a wider sense. Even if x or y were indivisible, it may still have “separate” parts or properties. After all, particles have mass, charge, spin, decay rate, etc. Yet these properties are also strongly interrelated. Nonetheless, it's the case that if a particle ceases to have that spin, mass, charge and decay rate, then, quite simply, it is no longer that particle. In that sense, then, if a particle is divided, then it's no longer the particle it was. It must therefore be indivisible.

What Physicists & Philosophers Have Said About Particles

Perhaps we should heed the words of Werner Heisenberg when he wrote following:

“Actually we need not speak of particles at all. For many experiments it is more convenient to speak of matter waves; for instance, of stationary matter waves around the atomic nucleus.... The use of 'matter waves' is convenient, for example, when dealing with the radiation emitted by the atom.”

Yet, since the wave-particle duality is essential to quantum mechanics, one can ask if Heisenberg was being literal about this. Indeed this situation is complicated even more when Heisenberg says that speaking of “matter waves” is “more convenient”. So, here at least, he appears to be taking an instrumentalist position on the nomenclature. In others words, perhaps the word “wave” is just as metaphorical, loose or ontologically suspect as the word “particle”.

The philosopher Ernan McMullin (in his 'A Case for Scientific Realism') also says that electrons “are not particles strictly speaking”. That's because

“electrons do not obey classical (Boltzman) statistics, as the familiar enduring individuals of our middle-sized world do”.

McMullin elaborates on this. He writes:

“The use of namelike terms, such as 'electron', and the apparent causal simplicity of oil-drop or cloud-track experiments, could easily mislead one into supposing that electrons are very small localized individual entities with the standard mechanical properties of mass and momentum. Yet a bound electron might more accurately be thought of as a state of the system in which it is is bound than a separate discriminable entity... What is meant by 'particle' in this instance reduces to the expression of a force characteristic of a particular field...”

Then again, some physicists have seen particles as particles. David Bohm, for example, was keen to argue that states didn't “collapse” into particles when observed. There are particles from beginning to end.

The American philosopher Ernest Nagel (in his 'The Cognitive Status of Theories') had a different (though related) take on particles. Firstly he discussed their “puzzling characteristics”. These puzzling characteristics seem to be “incompatible”. (Though the word “incompatible” isn't a synonym of “contradictory”.) More precisely, electrons are “construed to have features which make it appropriate to think of them as a system of waves”. Yet, “on the other hand”, electrons “also have traits which lead us to think of them as particles”. They are deemed to be particles because each one has “spatial location and a velocity”. However, “no determinate position and velocity can in principle be assigned simultaneously to any of them”. It is here that Nagel appears to deflate quantum mechanics. He does so by saying that

“many physicists have therefore concluded that quantum theory cannot be viewed as a statement about an 'objectively existing' domain of things and processes... On the contrary, the theory must be regarded simply as a conceptual schema or a policy for guiding and coordinating experiments”.

However, as with contemporary ontic structural realism (which will be discussed later), this deflation of quantum mechanics is far from being complete. Rather, 

“the fact that a visualizable model embodying the laws of classical physics cannot be given for quantum theory... is not an adequate ground for denying that the quantum theory does formulate the structural properties of subatomic processes”.

In other words, “every thing must go”. And when every thing has gone, all we really have left is what Nagel calls “structural properties”.

Dirac & Feynman on How Particles Behave

Instead of questioning whether or not there are particles (or, in ontic structural realist terms, whether there are “individuals”), we can emphasise “how [electrons and protons] behave, how they move”, as Paul Dirac did. This, of course, immediately raises the following point:

Surely only things (or particles) can “behave” or “move”.

That is, you can't have behaviour or movement without things/particles which display that behaviour or which move. Then again, what if it's the case that (from an anti-realist perspective) we can't get at what it is that behaves or moves. In other words, all we have is behaviour or movement.

Thus Dirac goes on to compare particles to the pieces of chess. He writes:

“I can describe the situation by comparing it to the game of chess. In chess, we have various chessmen, kings, knights, pawns and so on. If you ask what chessman is, the answer would be that it is a piece of wood, or a piece of ivory, or perhaps just a sign written on paper, or anything whatever. It does not matter. Each chessman has a characteristic way of moving and this is all that matters about it. The whole game of chess follows from this way of moving the various chessmen.”

Yet the obvious point must be made again.

Yes, chess is defined by how the pieces (to use Dirac's own terms) “behave” or “move”. Nonetheless, the chess pieces must still exist and chess can't be played without them. (I suppose there could be a purely abstract version of chess.) It's no use Dirac saying that a chess piece can be “piece of wood, or a piece of ivory” if it must still be a something – a thing. Having said that, isn't it easier to see chess as being a literally abstract game than it is to see the fundamental nature (or parts) of reality as being an abstract... something? In a certain sense, a chess game can be explained mathematically and with little physical remainder; though, surely, that isn't the case when it comes to reality or particles... Or is it?

The analogy between chess pieces and particles may break down in another way too. It's of course the case that the way chess pieces move or behave is not dependent on their being made of wood, ivory or of anything else. When it comes to particles, on the other hand, their physical nature may – or surely must - determine how they behave or move.

To put it bluntly: Dirac's position seems to be eliminativist when it comes to particles. Yet if it is eliminativist, then why speak of “particles” at all? Unless, of course, the word “particle” is simply shorthand for specific types of behaviour or movement. However, this simply raises the same question again:

What is it that behaves or moves?

Richard Feynman also had a problem with seeing particles as particles. He also hinted at the possibility that we have a wave-particle duality simply because there are no particles in the first place. (Thus there is no wave-particle duality?) He wrote:

“Things on a very small scale behave like nothing that you have any direct experience about. They do not behave like waves, they do not behave like particles, they do not behave like clouds, or billiard balls, or weights on springs, or like anything that you have ever seen.”

So perhaps there can be particles which “do not behave like particles”! However, isn't that claim hard to make sense of? In any case, like Dirac, Feynman was emphasising behaviour, not particles or things. Yet here again we can say that surely only things can behave or move. (This seems to parallel the relations-no-relata stance of ontic structural realism.)

Quantum Field Theory

If particles aren't fundamental, then what is fundamental? Lee Smolin gives an answer which is expressed in the clearest possible terms:

“If fields are not made from matter, perhaps fields are the fundamental stuff. Matter must then be made from fields.”

Of course it needs to be said that this quote expresses a conditional. Thus Smolin leave open the possibility that fields aren't fundamental. Nonetheless, these words express the huge importance of fields in physics: from Michael Faraday's electric and magnetic fields, to the Higgs field.

Indeed Smolin sees “the geometry of space as another field”. Not only that: we also have a symmetry here in that “the geometry of space is almost the same as the gravitational field”. Finally, if we take a look at the whole picture, then Smolin finishes off by saying that “[w]e have a bunch of fields all interacting with one another, all dynamical, all influencing one another”.

So we need to know what a field is.

In broad terms, in classical physics, fields were seen as global stuff or substance. Alternatively, a field is just a way of assigning properties to various spacetime points. Thus, “[i]n the case of quantum field theory”, Paul Teller tells us that

“the field quantities are not well-defined at such points (because of difficulties in defining exact locational states in quantum field theory) but are instead regarded as ‘smeared’ over space-time regions”.

Now if we turn to the more relevant idea of quantum field theory (QFT), we can say that although fields are stressed, particles aren't thereby dispensed with. QFT retains the notion of “point particles” as well as their locality. Nonetheless, such particles are deemed to be the excited states of such fields. In other words, they are “field quanta”.

Indeed the quantum-mechanical interactions of particles are seen as interactions in their corresponding (or underlying) quantum fields.

All this raises the question as to whether the word “quantum” is simply a synonym for the word “particle”.

So what is a quantum?

A quantum is the minimum amount of any physical entity (or of a physical property) which is involved in an interaction. This immediately raises a problem - at least from a philosophical point of view. In this definition, a quantum is (in basic terms) an “amount” of a “physical entity” (or of a “property”). In more technical terms, that entity (or property) can therefore be “quantized”.That means that the entity (or property) has a magnitude. That magnitude can take on certain values. Indeed it can only take on “discrete values” which are then measured in terms of integer multiples of one quantum.

Thus, here at least, there's a distinction being made between a quantum and a physical entity/thing/particle. We have an entity/thing/particle and then we have an amount (a quantum) of that entity/thing/particle. On this reading, then, an entity's quantum (value) can't be numerically identical to that entity.

Yet a photon (for example) is indeed a single quantum of light. In fact it's referred to as a "light quantum" or as a “light particle”. So here we are back to particles! It's also the case that single particles are fired in double-slit experiments - sometimes at relatively long intervals! However, are particles really fired? Of course something must be fired. Though is it the case that some thing is fired?

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See: 'Bertrand Russell on Quantum-Mechanical Particles (2)'