Thought Experiments in Science

Ai Shangzhen
Thought Experiments

Thought experiments in science are generally characterized by contrast to actual experiments: The former are conducted by engaging in an imaginative act, the latter by manipulating features of the observed world.

So if to perform an (actual) scientific experiment is to conduct an empirical test under controlled conditions with the aim of illustrating, supporting, or refuting some scientific hypothesis or theory, then to perform a scientific thought experiment is to reason about an imaginary scenario with a similar aim.

In the case of actual experiments, the theory-relevant evidence generally takes the form of data concerning the behavior of the physical world under specific conditions; in the case of thought experiments, the theory-relevant evidence generally takes the form of intuitions (or predictions) concerning such behavior.

new knowledge
new knowledge

In both instances, imagining or performing the experiment ostensibly results in new knowledge about contingent features of the natural world. The primary philosophical puzzle concerning scientific thought experiment is how (if at all) contemplation of a merely imaginary scenario can provide this.

Terminological Issues

The earliest uses of the expressions Gedankenexperiment and mit Gedanken experimentieren seem to be in the writings of the Danish Kantian Hans Christian Ă–rsted (1811) and the German polymath Georg Christoph Lichtenberg (1793) respectively.

However, contemporary use of the term stems from its apparently independent coinage by Ernst Mach, who introduced the expression Gedankenexperiment in an 1897 essay of the same name, and discussed a number of examples that have remained central to present-day discussions.

Terminological Issues
Terminological Issues

Though the historical record is a bit unclear on this point (because later editions of works often insert the word where it was not originally used), it seems to have taken roughly four decades following the publication of Mach’s essay for the term thought experiment to become widespread in scientific circles. In particular, despite his thorough knowledge of Mach’s corpus, Einstein seems not to have used the term to describe his own thinking, at least not in his written works.

Despite the absence of a specific term for the technique, the method was widely employed long before it was labeled. Contemplating imaginary cases in order to develop scientific theory was central to the practice of ancient and medieval natural philosophy, despite the apparent absence of any articulated experimental methodology.

And it played a crucial role in the development of early modern natural science. Indeed, some have argued that thought experiment was the predominant mode of scientific investigation prior to the scientific revolution.

Mermaid
characterization

This points to a certain ambiguity in the term’s application. Given the characterization offered above, it is a bit challenging to distinguish scientific thought experiment as such from scientific thought in general, because the latter largely consists in reasoning about (less or more detailed) imaginary scenarios as a way of testing or illustrating (more or less tentative) hypotheses. Indeed, nearly every exercise in a standard physics textbook would, by these criteria, count as a thought experiment.

As a matter of sociological fact, however, the expression tends to be reserved for cases where a fairly detailed scenario is contemplated in order to invoke intuitions that help to illustrate or support a specific and novel scientific hypothesis, or to refute a specific and otherwise plausible scientific hypothesis. (A parallel set of definitional and historical issues confronts the analogous term in philosophy, where the term “thought experiment” is generally used to refer to the consideration of fairly detailed, often physically unrealized, scenarios in order to invoke intuitions concerning the proper application of some concept.) Perhaps because of these definitional difficulties, philosophical discussions of scientific thought experiment have focused primarily on a small stable of canonical examples.

Examples

Among the three most widely discussed scientific thought experiments in the philosophical literature are Galileo’s refutation of the Aristotelian view that heavy bodies fall faster than light ones, Stevin’s determination of the amount of force required to prevent an object from sliding down a frictionless inclined plane, and Einstein’s demonstration of the relativity of simultaneity by consideration of the moving train. These exemplify respectively the role of scientific thought experiments in refuting, supporting, and illustrating scientific theories.

Thakana girl, Myanmar
Galileo

In Galileo’s falling body thought experiment, by which Galileo is said to have refuted the Aristotelian theory that heavier bodies fall faster than lighter ones, Galileo imagines two otherwise similar bodies of differing weights that are strapped together and dropped from a significant height.

If one accepts the Aristotelian assumption that natural speed is proportional to weight, and accepts that there is no fact of the matter about whether the strapped body is one entity or two (that is, if one accepts that entification is not physically determined), then it seems that two outcomes are predicted: on the one hand, the lighter body should slow down the heavier whereas the heavier speeds up the lighter, so the combined object should fall with a speed that lies between the natural speeds of its components; on the other hand, because the weight of the two bodies combined is greater than the weight of the heavy body alone, their combination should fall with a natural speed greater than that of the heavy body.

Galileo’s suggested resolution to the paradox is to assume that the natural speed with which a body falls is independent of its weight, that is, that “both great and small bodies ... are moved with like speeds”

Stevinus
Stevinus

In Stevin’s inclined plane thought experiment, which served as Mach’s original example of the term, Stevinus establishes the amount of force required to prevent an object from sliding down a frictionless inclined plane by imagining a connected string of beads hung across a triangular prism with a horizontal base.

Consideration of this imaginary setup convinces him that the balls are in a state of equilibrium—that is, that the chain moves neither to the left nor to the right (else, it seems, the system would be in a state of perpetual motion, for because the beads are of equal weight and hung equally along the string, if the current state is one of disequilibrium, so too would be the state into which the system moved as the result of the string sliding.)

He next imagines cutting the string at the two lower corners, so that only the beads along the two diagonal planes remain. Given that beads were in equilibrium prior to the cutting, and that the lower part of the loop exerts equal force on both sides of the string, the balls can be expected to remain in equilibrium afterwards.

Einstein
Einstein

Because the number of beads along each side is proportional to the length of the plane, and because the beads are of equal weight spaced equidistantly, it follows that two bodies on two different, inclined planes are in balance if their weights are proportional to the lengths of the two planes.

In Einstein’s moving train thought experiment, Einstein illustrates the relativity of simultaneity by imagining a situation in which there are two people, one standing at a point, call it M, along the embankment of a railroad track, the other riding on a train that is moving with respect to the embankment. He then supposes that lightning strikes the embankment at two points, A and B, which are a significant distance from one another, but equidistant from M.

From the perspective of the person standing on the bank, the two flashes occur simultaneously: that is, the ray of light that is emitted from point reaches person at exactly the same moment as the ray of light that is emitted.

moving train
moving train

But from the perspective of the person on the moving train, the two flashes are not simultaneous, because (considered with reference to the embankment) she is rushing toward the beam emitted from B, and away from the beam emitted from A. (Note that from her perspective, it is the person on the embankment who is in motion in the direction of A. Note further that neither frame of reference is privileged in any way.)

Because the speed of light is constant, the B-light will reach the passenger earlier than the A-light, so from her perspective, the two flashes are not simultaneous: the B-flash occurs first.

Einstein concludes: “We thus arrive at the important result: Events which are simultaneous with reference to the embankment are not simultaneous with respect to the train, and vice versa ... unless we are told the reference-body to which the statement of time refers, there is no meaning in a statement of the time of an event”.

Philosophical Issues

Philosophical Issues
Philosophical Issues

Philosophical discussions of scientific thought experiment have primarily focused on two related questions. The first, which may be called the “what” question, concerns what sort of knowledge one gains from the contemplation of imaginary cases: do they provide one with new knowledge about contingent features of the natural world, or do they instead provide knowledge of some other sort? The second, which might be called the “how” question, concerns the process by which such knowledge is obtained: what, if anything, is epistemically distinctive about the process of thought-experimental reasoning?

The “what” Question

A strong case can be made for the view that scientific thought experiments do not, in themselves, provide new knowledge about contingent features of the natural world: to the extent that they provide new knowledge, that knowledge concerns necessary truths.

So, for example, the reader who works through Einstein’s moving train thought experiment does not thereby gain novel knowledge of the (apparently) contingent truth that simultaneity is relative.

The Question
The Question

What one gains instead is new knowledge of the (apparently) necessary truth that, if the speed of light is constant, then simultaneity is relative, which can then be combined with one’s antecedent knowledge that the speed of light is constant in order to gain knowledge of the consequent.

Likewise in the case of Stevin: What the thought experiment reveals is not the (apparently) contingent fact that the force required to hold a ball in place along an inclined plane is inversely proportional to the length of the plane, but rather to the (apparently) necessary truth that if certain sorts of states are equilibrium states, then the force required is inversely proportional to length.

A person combines independent knowledge of this conditional with prior (empirically obtained) knowledge of statics and dynamics, and thereby gains knowledge of the consequent.

Galileo case
Galileo case

So too in the Galileo case:What the reader gains is not new knowledge of the (apparently) contingent truth that the speed at which a body falls is independent of its weight, but rather the (apparently) necessary truth that, if entification is not a physically determined matter, then natural speed is independent of weight. And one can combine this conditional knowledge with one’s empirically obtained knowledge of the antecedent to derive the conclusion.

Those who wish to challenge this position must argue that it is by engaging in this particular instance of thought-experimental reasoning that knowledge of the relevant contingent antecedent is gained.

This is least plausible in the case of illustrative thought experiments that evoke intuitions about highly theoretical properties (e.g., the Einstein case), and most plausible in the case of supportive or refutory thought experiments that evoke physical intuitions.

general information
general information

So it might be argued that it is precisely by contemplating the imaginary scenario in question that a person might come to know (the contingent fact) that the balls do not move in the Stevin example, or in the Galileo example (the contingent fact) that it is not a physically determined matter whether the strapped objects form one entity or two: though the intuitions evoked by the cases have their ultimate basis in experience (or the accumulated experience encapsulated by evolution), the general information they encapsulate was too unsystematized to count as knowledge prior to engaging in the act of directing imagining. Something like this view appears to have been held by Mach, who writes:
Unquestionably in the assumption from which Stevinus starts, that the endless chain does not move, there is contained primarily only a purely instinctive cognition. He feels at once, and we with him, that we have never observed anything like a motion of the kind referred to, that a thing of such a character does not exist.

This conviction has so much logical cogency that we accept the conclusion drawn from it respecting the law of equilibrium on the inclined plane without the thought of an objection, although the law, if presented as the simple result of an experiment, otherwise put, would appear dubious.
The “how” Question

John Norton

A number of recent discussions of thought-experimental cognition have focused on whether the structured contemplation of imaginary examples produces distinctive sorts of cognitive access to the knowledge they do give (whether or not that knowledge concerns contingent features of the natural world).

In a series of widely discussed articles, John Norton has defended a view that he calls “empiricism” according to which “thought experiments are just ordinary argumentation, disguised in some vivid picturesque or narrative form. As a result,” he contends, “they can do nothing more epistemically that can ordinary argumentation”.

On this view, knowledge obtained through scientific thought experiment is the result of inference from known premises to inductively or deductively implied conclusions: “the actual conduct of a thought experiment consists of the execution of an argument”.

natural world
natural world

Norton’s view has been widely discussed and criticized by those who hold that contemplation of well-articulated specific imaginary cases can give access to inchoate information about patterns of experience to which people lack independent propositional or conceptual access.

Some have suggested that thought experiment does this by exploiting the same cognitive mechanisms that mental models do; others have suggested that certain thought experiments work by evoking quasi-sensory intuitions, resulting in new beliefs about contingent features of the natural world that are produced not inferentially, but quasi-observationally.

Yet others have stressed other aspects of the similarities between thought experiments and actual experiments (for example, their indifference to certain sorts of changes of content but not others), contending that insofar as the latter are not arguments, neither are the former.

James Robert Brown
James Robert Brown

A final contrasting view, advanced in a series of papers and books by James Robert Brown is that in certain instances (the Galileo case being one) engaging in thought-experimental reasoning provides “a priori (though still fallible) knowledge of nature” derived through a process of what Brown terms “platonic insight”.

“Thought experiments,” he writes, “are our telescopes to see into the abstract realm”; by making use of “the mind’s eye,” they allow us to perceive the laws of nature “a priori”. The laws in question are necessary rather than contingent, involving “relations between objectively existing abstract entities”. Such a view will be appealing only to those who accept Brown’s platonist metaphysics along with its corresponding epistemology.
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