An example of the use of analogy in developing science:
"In spite of many points in which they differ, there is a profound inner similarity between the problems met with in the theory of relativity and those which are encountered in the quantum theory. In both cases we are concerned with the recognition of physical laws which lie outside the domain of our ordinary experience and which present difficulties to our accustomed forms of perception."
"The very nature of the quantum theory thus forces us to regard the space-time co-ordination and the claim of causality, the union of which characterises the classical theories, as complementary but exclusive features of the description, symbolising the idealisation of observation and definition respectively. Just as the relativity theory has taught us that the convenience of distinguishing sharply between space and time rests solely on the smallness of the velocities ordinarily met with compared to the velocity of light, we learn from the quantum theory that the appropriateness of our usual causal space-time description depends entirely upon the small value of the quantum of action as compared to the actions involved in ordinary sense perceptions."
"We have learned from the theory of relativity that the expediency of the sharp separation of space and time, required by our senses, depends merely upon the fact that the velocities commonly occurring are small compared with the velocity of light. Similarly, we may say that Planck's discovery has led us to recognise that the adequacy of our whole customary attitude, which is characterized by the demand for causality, depends solely upon the smallness of the quantum of action in comparison with the actions with which we are concerned in ordinary phenomena."
Bohr, Neils (1934) Atomic theory and the description of nature. Cambridge University Press
"Just as the general concept of relativity expresses the essential dependence of any phenomenon on the frame of reference used for its coordination in space and time, the notion of complementarity serves to symbolise the fundamental limitation, met with in atomic physics, of the objective existence of phenomena independent of their means of observation."
Neils Bohr (2010) Atomic Physics and Human Knowledge (first published 1961). Dover Publications, Inc.
"This general view can be made by way of analogy to relativity. Analogies to relativity are common but often brief in Bohr's work. With relativity we learn that any ascription of position and momentum is relative to some reference frame and that those properties are not absolute; rather, they are aspects of phenomena as they occur relative to a reference frame. Similarly, we learn something about properties in general from quantum mechanics: we learn that properties are not absolute but are aspects of phenomena as they occur in a measurement content. According to this view, complementarity is something we discover from quantum mechanical structure when we learn that there is no description of physical reality that is not measurement-frame dependent
The analogy is that measurement results are relative to a measurement context similarly to how space-time measurements are relative to an inertial frame of reference…
In relativity we might say that the space-time interval in some sense represents non-relative physical facts about the relation between two events, but that a space-time interval has different empirical meaning in different frames. Similarly we might say that the quantum state of a composite system represents non-contextual physical facts about the relation between subsystems, but that a quantum state has different empirical meaning in different measurement contexts."
Tanona, Scott (2017) Individuality and correspondence. An exploration of the history and possible future of Bohrian Quantum empiricism, in, Neils Bohr and the Philosophy of Physics. Twenty-first-century perspectives (Jan Faye & Henry J. Folse, eds.) Bloomsbury Academic: London, pp.253-288.
This is different from many of the analogies discussed on this site as (a) it is an analogy from one scientific concept to another (rather than comparing a scientific concept or phenomenon to something familiar everyday referent); (b) this is an analogy actively used in the development of the science itself, for use within the scientific community, not just for communicating scientific ideas to lay people .
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Many examples of science analogies are listed in 'Creative comparisons: Making science familiar through language. An illustrative catalogue of figurative comparisons and analogies for science concepts'. Free Download.