8 Particles

If the prop­er­ties of the microworld are what they are because of what hap­pens or is the case in the macroworld, rather than the other way around, then we cannot think of par­ti­cles, atoms, and such as the con­stituents of the macroworld. Then what con­sti­tutes the macroworld? And what is a par­ticle if it is not a con­stituent of the macroworld?

All we can know about par­ti­cles is what we can infer from cor­re­la­tions between “detector clicks.” If we per­form a series of posi­tion mea­sure­ments, and if every posi­tion mea­sure­ment yields exactly one out­come (that is, each time exactly one detector responds), then we are enti­tled to infer the exis­tence of an entity O which per­sists in time. Things get more involved as soon as each time exactly two detec­tors click. Can we infer from this the exis­tence of two per­sis­tent entities?

Pre­vi­ously we raised a sim­ilar ques­tion and con­cluded that we cannot. We cal­cu­lated the prob­a­bility with which two indis­tin­guish­able par­ti­cles scatter at right angles, and we found that the ques­tion “which of the incoming par­ti­cles is iden­tical with which of the out­going par­ti­cles?” has no answer. But a ques­tion that has no answer is meaningless.

Here as else­where, the chal­lenge is to learn to think in ways that do not lead to mean­ing­less ques­tions. Mean­ing­less ques­tions arise from wrong assump­tions. The ques­tion “Which is which?” arises because we assume that ini­tially there are two things, one moving north­ward and one moving south­ward, that in the end there are two things, one moving east­ward and one moving west­ward, and that each of these things remains iden­tical with itself.

What if we assumed instead that ini­tially there is one thing moving both north­ward and south­ward, and that in the end there is one thing moving both east­ward and west­ward? Star­tling though this assump­tion may be, it has this advan­tage that the mean­ing­less ques­tion “Which is which?” can no longer be asked. At the same time it is the con­clu­sion our inter­pre­ta­tional strategy requires us to draw, for under the con­di­tions stip­u­lated by Rule B it implies that the dis­tinc­tion we make between alter­na­tives does not cor­re­spond to any­thing in the actual world.

Thus if each time two detec­tors click, and if the ques­tion “Which of the par­ti­cles detected ear­lier is iden­tical with which of the par­ti­cles detected later?” lacks an answer, we are in the pres­ence of a single entity with the prop­erty of being in two places when­ever we check — not a system “made up” of two things but a single thing with the prop­erty of being in two places every time a posi­tion mea­sure­ment is made.

When I asked you to imagine two (exactly sim­ilar) objects in two (dif­ferent) places, I used the word “two” once too often, for if in front of you there was what looks like two exactly sim­ilar objects, it would actu­ally be one and the same object in dif­ferent places. It is, how­ever, vir­tu­ally impos­sible to create two objects that are exactly sim­ilar if they are bigger or more com­plex than an atom or mol­e­cule. With such objects the con­di­tions stip­u­lated by Rule B are never sat­is­fied. It is like­wise vir­tu­ally impos­sible to suf­fi­ciently iso­late all but the smallest objects from the rest of the world. If light of a cer­tain wave­length falls on an object, the reflected light makes it pos­sible to dis­cover the object’s loca­tion to within a wave­length. In the darkest corner of the uni­verse, were the only light is the cosmic microwave back­ground radi­a­tion, an object would still reflect light of wave­lengths in the mil­limeter range, and this would make it pos­sible to pin­point the object’s loca­tion to within a few mil­lime­ters or less. For any two objects larger than this, it will there­fore always be pos­sible to trace their respec­tive tra­jec­to­ries with suf­fi­cient pre­ci­sion to tell which is which.

Since, before quantum mechanics, it seemed always pos­sible to keep track of the iden­ti­ties of objects, it seemed always pos­sible to asso­ciate with each object a dis­tinct sub­stance. But this was com­pletely unwar­ranted, for what accounted for the apparent dis­tin­guisha­bility of things was the dis­tin­guisha­bility of their posi­tions rather than their being (let alone their being made of) dis­tinct sub­stances. Indi­vid­u­ality is strictly matter of prop­er­ties (not counting such gim­micks as the prop­erty of being “this very object”).

Hence if there is a sub­stance (that is, if the word “sub­stance” is of any use), there is exactly one sub­stance. Quantum mechanics does not permit us to inter­pose a mul­ti­tude of dis­tinct sub­stances between this one sub­stance and the mul­ti­tude of existing (“pos­sessed”) posi­tions or the mul­ti­tude of existing (“pos­sessed”) bun­dles of prop­er­ties. A phys­ical system, accord­ingly, is not made of com­po­nent sys­tems or con­stituent parts. The number of its so-​​called com­po­nents or con­stituent parts is merely one of its prop­er­ties. Whereas in a non-​​relativistic con­text this prop­erty is con­stant, in a rel­a­tivistic set­ting it can come out dif­ferent every time it is mea­sured. Hence if we permit our­selves to think of the phys­ical uni­verse as a quantum system and to ask about the number of its con­stituent sub­stances, there is just one. The rest is prop­er­ties. Quantum mechanics there­fore lends unstinting sup­port to the cen­tral idea of all truly monistic ontolo­gies: ulti­mately there is only one substance.

We arrive at the same con­clu­sion if we con­sider a fun­da­mental par­ticle “by itself,” out of rela­tion to any­thing else. What can we say about it? Apart from pointing out that it lacks a form, and that space does not con­tain it, the plain and simple answer is: nothing. For the prop­er­ties that are attrib­ut­able to fun­da­mental par­ti­cles are either rela­tional, like posi­tions and momenta, or char­ac­ter­istic of inter­ac­tions, like cou­pling para­me­ters (charges), or they have objec­tive sig­nif­i­cance inde­pen­dent of con­ven­tions only as dimen­sion­less ratios, like mass ratios. They all involve more than one particle.

According to a philo­soph­ical prin­ciple known as the Iden­tity of Indis­cernibles, what appears to be two things A and B is actu­ally one and the same thing just in case there is no dif­fer­ence between A and B. Although there is nothing so obvious that a philoso­pher cannot be found to deny it, this prin­ciple strikes me as self-​​evident. If true, it implies that all fun­da­mental par­ti­cles con­sid­ered by them­selves, out of rela­tion to any­thing else, are iden­tical in the strong sense of numer­ical iden­tity. (Numer­ical iden­tity con­trasts with qual­i­ta­tive iden­tity or exact sim­i­larity. Exam­ples of numer­ical iden­tity are (i) the evening star and the morning star, (ii) Clark Kent and Superman.)