What did it historically mean in physics for something to "exist"?

Question

What is the history of influential definitions of objective existence --- This Is Real, It Exists --- in physics? Where did they appear in the literature and in what context were they put forward?

Please focus on the operational definitions of physicists, but you may also discuss arguments coming from mathematicians and natural philosophers. Who were the major individuals arguing in favor of each one? What were their reasons? And what were the corresponding definitions or arguments regarding non-existence, un-reality, epiphenomenality, and of virtual objects or processes (virtual particles, virtual work, etc)?

Answer 1

To not be measured is not to have any behavior. No dynamic is induced on any other system in the universe by this object (Rosen 1978).

Objects without behavior do not exist. Their behavior is that which makes some perceptions objective not subjective things (Hutton 1794).

What is measured but not found different is double counted; it does not exist in addition to the other objects which exist (Leibniz 1686). Its whole behavior is the object, however. This is what makes it different, something other than and partly independent of everything else including its observers and the empty state (Condillac 1756). So what is not measured ... (Hutton 1794, Bohr 1928; 1934, Rosen 1978, Wheeler 1994)

Anticipating existence is not so much whether a symbol appears in a system of equations but whether the presence of one symbol somewhere being other than identity changes the result of applying one operator to another operator applied to ... in a way that builds up another operator in the system.*

Some formulations are equivalent but different in their virtual aspects. See the letters exchange between George Boole and Stanley Jevons regarding whether every object and operation arising during algebraic manipulation of an equation has and must have natural interpretation. Jevons: yes. Boole: no.)

That measurement absence is nonexistence is quite noticeable at the smallest scale, because we can and do control for any other observers at that scale.

This leads to some interesting results at the small scale regarding counterfactuals. (E.g. http://rsta.royalsocietypublishing.org/content/374/2068/20150242).

None of this should not be confused with positivism, contrary Weinberg's (1992) allegation; see Wheeler's (1994) account. Positivism or operationalism are further demands: that each specialized field of science only anticipates the existence of those objects and properties which can be measured by operations feasible or possible in that field without relying at all on any tools from any other fields. (So positivism and operationalism are just laziness codified into a method. Which is also why positivism and operationalism are sometimes popular ...)

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*Yes, people cannot directly measure primary scale particles. They are too small; but as distances get smaller ($10^{-15}$ etc) the frequencies and so the energies ($E = hv$) increase respectively. Wheeler (1971) suggested that larger particles are perturbations in the patterns of primary events in the quantum foam. This calculates out more or less correctly the lower energies we observe for the larger particles. However, measurement does not mean necessarily people measuring anything. Small objects measure other small objects, if one induces a dynamic in another. If by such constructive action we can get any of the objects in the group we suspect existence.

REFERENCES

Bohr, Niels, 1928(4), The Quantum Postulate and the Recent Development of Atomic Theory, Nature 121(15):580--590.

Bohr, Niels, 1934, Atomic Theory and the Description of Nature. Cambridge: Cambridge University Press.

Bonnot de Condillac, Etienne, 1754, Traite Des Sensations, I. London Paris: De Bure.

Boole, George; Jevons, Stanley. 1863. Letters. In 1990(6), The Correspondence Between George Boole and Stanley Jevons, History and Philosophy of Logic 12(1):15--35.

Hutton, James, 1794, An Investigation of the Principles of Knowledge, I. Edinburgh London: Strahan Cadell.

Leibnitz, Gottfried, 1686. In 1951, Selections, Philip Wiener, trans. New York, Scribner. And 1970, Philosophical Papers and Letters, Leroy Loemker, trans. Dordrecht: Reidel.

Rosen, Robert, 1978, Fundamentals of Measurement and Representation of Natural Systems. New York: North Holland.

Weinberg, Steven, 1992, Dreams of a Final Theory. New York: Pantheon.

Wheeler, John, 1971, From Atom To The Collapsing Star, Periodicita e Simmetrie nella Struttura Elementare della Materia. Torino, Bona.

Wheeler, John, 1994, At Home In The Universe. New York: American Institute of Physics.

Answer 2

Guido's answer sounds fascinating but I am not sure I follow all of it so I will provide what seems to me a more down-to-earth analysis. In some branches of modern physics like string theory, the experiment and the idea of measurability have been left in the dust, and the field is approaching mathematics in its attitude toward the existence of objects. If so, then the OP's question concerning modern theoretical physics is no different from a similar, and usual, question concerning the existence of entities in mathematics. The familiar joke cracked at the expense of these modern theories is that you would need an accelerator the size of the whole universe to confirm these theories. I am actually not even sure of that being possible :-) This does not undermine the field; it simply ranks it alongside with mathematics.