QFT, being/non-being & Birth of Properties


What is the birth of the properties of physical objects? As we have seen, we have to enlarge the category of entities where properties can originate from, by including the quantum vacuum. To make the difference more clear, suppose that we have a region of space emptied of matter and fields. Classically, the only way to create a property inside that region is to bring in from outside an object carrying that specific property. In this sense, Netwonian physics appears as a strongly coerced theory, while relativity and quantum physics introduce different relaxations. Firstly, Newtonian physics needs to have the concept of space as existing independently of objects and with all the points easily accessed. Space and time are distinct from and exist independently of the objects (carrying properties) one chooses to populate it with. Space-time is the immense theater stage where physical processes unfold, the canvas where each dot is an event. One has, in principle, access to any of these points. General relativity shows that this does not happen if the object carrying the desired property is too massive or if we insist of making it as much as point-like – squeezing too much energy into too little space could result in the formation of a black hole. Secondly, if properties are tied to physical objects (particles or non-zero fields) as a condition along with true stochasticity as not being satisfied, then properties could appear spontaneously in vacuum, as they do not require either a real object to be attached to or a causal chain of events that would produce them.

Dynamical Casimir effect shows that there exists another way of generating properties. Note that these experiments still use the classical concept of spacetime background as in, but to explain them one needs to alter dramatically the conditions of properties as tied to physical objects and non-existence of stochasticity to accommodate the quantum-mechanical account of randomness (there exists pure randomness) and properties (properties are not intrinsically attached to objects, but are created contextually, as shown by the Kochen-Specker theorem). Let H be a Hilbert space of QM state vectors of dimension x ≥ 3. There is a set M of observables on H, containing y elements, such that the followong two assumptions are contradictory: 

(KS1) All y members of M simultaneously have values, i.e. are unambiguously mapped onto real numbers (designated, for observables ABC, …, by v(A), v(B), v(C), …).

(KS2) Values of observables conform to the following constraints:

(a) If ABC are all compatible and C = A+B, then v(C) = v(A)+v(B);(b) if ABC are all compatible and C = A·B, then v(C) = v(Av(B).

The theorem demonstrates the impossibility of a certain type of interpretation of QM in terms of hidden variables (HV) that naturally suggests itself when one begins to consider the project of interpretating QM. Because in quantum field theory the vacuum has a structure, properties can be generated at a certain point by changes of this structure, and not just by bringing them in from somewhere else. As mentioned above already, one cannot do this classically: if a property were to appear at some point in space, then classical physics would tell us that, there must be a real object that carries this property, and that there must be a causal story, enfolding in the region of space-time under consideration, which one must discover in order to have a complete description of the phenomenon. In a quantum vacuum, the structure exists as such, ready to acquire real properties, without being constructed beforehand by energy or mass previously brought in from elsewhere. By definition, the vacuum is the ground state, therefore (unless the system is metastable) there is no other lower-energy state where the system would go to if one attempts to extract energy from it. The quantum vacuum behaves, from this point of view, almost as a real material. Clearly, the ontological status of an entity that is not made of real particles but reacts to external actions does not fall straight into any of the standard philosophical categories of being/non-being.


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