# When can a Computer Simulation act as Substitute for an Experiment? A Case-Study from Chemisty

Johannes Kästner and Eckhart Arnold

### 3.5 Experiment-likeness

The main conclusions drawn by (Goumans/Kaestner 2010) were the suggestion that “H atoms could chemisorb on PAHs in the moderately warm (100-200~K) regions of the interstellar medium, contributing to the catalytic formation of $H_2$” and that “D will chemisorb an order of magnitude slower [than protium]” (Goumans/Kaestner 2010, p. 7352). A conclusion given more implicitly was that the reaction would be too slow were it not for the tunneling process which accelerates the reaction by many orders of magnitude (depending on the temperature). Thus, when drawing conclusions the simulation results are treated like experimental results by the authors. The simulation here acts as a stand-in for an otherwise impossible experiment.

Not surprisingly, the simulation of the H-chemisorption on benzene shows many characteristics that make it appear experiment-like: Just like an experiment, the calculations provide numbers which have to be post-processed in order to obtain rates, and interpreted in order to draw conclusions. The simulation also mimics an experiment with respect to its function of hypothesis confirmation. For, the “computer experiment” could either confirm or falsify the hypothesis that tunneling contributes to $H_2$-formation in space. In the end it confirmed the hypothesis.

The process of designing or setting up the simulation also exposes analogies to experiments. While in a material experiment, the techniques of measurements have to be chosen adequately, in the simulation various approximations have to be chosen adequately. A wrong choice will result in wrong results, generally, however, no results at all, in either case. Errors in these choices can in both cases be identified by reproducing the experiment or the simulation with different parameters.

And like an experiment the simulation can be replicated. In the case of computer simulations replication means: Reimplementing the same simulation under different conditions, like, for example, under a different system environment, with different but functionally equivalent software frameworks and libraries, with different but equally well motivated approximations or with different functionals that have a comparable reliability for the problem at hand. Just like the replication of an experiment the replication of a simulation serves the purpose of reassuring the researchers that the obtained results were not merely an artifact of the idiosyncrasies of a particular set-up.

Speaking of the relation between simulations and experiments in general, we have noted earlier that there are not only many striking similarities between simulations and experiments but also some important differences (see section 2.2 above). Whether a simulation can be considered as experiment-like on the phenomenological level and, beyond that, as a viable experiment-surrogate on the epistemological level, does also depend on how relevant these differences are in a particular case.

For our example of the H-tunneling simulation we can safely draw the conclusion that the fact that the simulation is not a material experiment and does not operate directly on the target system or generate any new empirical data, does not matter in this case, because the problem of determining the H-tunneling rates can be decided by theory alone, and does not require collecting new empirical data. Of course it must be taken for granted that the theory is true.

An experiment could - at least conceivably - also reveal that quantum theory is false or, say, not valid in outer space. Such an accidental finding (in an experiment that was not intended to test the theory) is impossible with a computer simulation. But given how very well tested quantum mechanics is, this seems extremely unlikely to occur in any such experiment and one would surely first take the possibility of all sorts of experimental error into account, before starting to doubt quantum mechanics.

Thus, in the example of our case-study, materiality is not really an issue and we can therefore consider the simulation not only as experiment-like in virtue of its many similarities to experimental procedures, but also as an experiment-surrogate in the stronger epistemological sense as well. Its epistemic reliability ultimately rests on the confidence in quantum mechanics as a comprehensive background theory. Because the simulated phenomena are completely covered by quantum mechanics we can be sure that no causal factors will be missed out by basing the simulation exclusively on quantum mechanics. Apart from quantum mechanics the epistemic reliability depends also on the credibility of the justifications for the approximations and modeling techniques employed in the simulation. This, again, does not require materiality. Therefore it would be safe to label this simulation a “computer experiment” without running the danger of exaggerating its epistemic reliability.