I wrote my undergrad thesis on a topic directly pertaining to this concept, so I might be a bit of help. I looked at the American effort in the Pacific Theater, and specifically, what sort of adaptations/advancements were needed in order to overcome not only the enemy, but also the environment and geography of the region.

At the most basic level, I think you are right to a degree that it is difficult to say that war, in and of itself, speeds up technological advancement. What it certainly does do, however, is force ongoing technological advancement in certain areas. What this does is speed up innovation in certain areas, while also detracting from others.

The Office of Scientific Research and Development was extremely important in the Pacific Theater, simply due to the challenges that the Pacific region presented. At the beginning of American involvement in WWII, the US, as well as the European powers, had become extremely good at fighting in Europe. Tactical and strategic doctrine, training, even the development of armor and the concept of Combined Arms warfare was largely born out of the battlefield of the previous century in Europe. We quickly learned, however, that what had been proven effective in Europe wasn't necessarily effective on the islands of the Pacific, and that the varied environments of the Pacific introduced new endemic diseases and other problems that the Western nations weren't as proficient at adapting to initially.

The OSRD was instrumental in helping the Army and Marines overcome these challenges, and spearheaded efforts in synthesizing and mass producing Malaria medications, studying the effects of Malaria in controlled studies, developing insecticides (DDT and DEET), studying the psychiatric effects of combat (essentially the genesis of research into what we now call PTSD), and many other important projects with more wide reaching effects, including early research on the atomic bomb, guided weapons, proximity fuzes, and enhanced radar capabilities.

The OSRD only existed from 1941 until 1947, and yet had a massive impact on technological and scientific advancement. That was the result of a massive surge in funding, coordinated research across institutions, and definitive targets to advance towards. War is convenient for scientific research in that it creates extremely specific problems that need to be solved in short amounts of time. This results in more concentrated research, and shorter development periods due to the expediency of the issue. While this does slow down research in other areas, it tends to create breakthroughs in the areas pertinent to the war effort that become the basis for future research.

For further reading on the subject, here's some of the stuff that I used in my research:

Bush, Vannevar. Foreword to Irvin Stewart. Organising Scientific Research for War: The Administrative History of the Office of Scientific Research and Development. Boston 1948.

Macleod, Roy M. “‘Combat Scientists’: The Office of Scientific Research and Development and Field Service in the Pacific.” War & Society vol 11 no. 2 (October 1993): 117-134.

Macleod, Roy M. Science and the Pacific War. Boston, MA: Kluwer Academic Publishers, 2000.

Strahan, Jerry E. Andrew Jackson Higgins and the Boats that Won World War II. Baton Rouge, LA: Louisiana State University Press, 1994.

Bresnahan, Josephine C. Dangers in Paradise: The Battle Against Combat Fatigue in the Pacific War. Ph.D. dissertation, Harvard University, 1999. Ann Arbor, MI: UMI, 2000.

Mellsop, Graham W, Vasanthi Duraiappah, and Jo-Ann J Priest. 1995. "Psychiatric casualties in the Pacific during World War II: Servicemen hospitalised in a Brisbane mental hospital". Medical Journal of Australia. 163 (11-12): 619-621.

Have historians looked at whether war is responsible for technological advancements? Absolutely, and it definitely has been / is. Can historians prove that this is more the case than if society invested similar resources into non-military research? Fundamentally no.

Patents aren't a good proxy for invention in wartime for a few reasons: 1) Patenting has increased across time throughout US history, so showing a simple increase would not be enough; 2) demands of war lead to changes in how IP is handled, such as the US seizing German patents during both world wars, and lots of businesses contracting for costs + $1 for their services rather than usual profit-motive work; and 3) patents only cover a subset of invention anyway, especially if we discount classified patents that would be applicable to things like atomic weapons.

As for military money spurring invention and research, there's no question that major advances are directly attributable to military money. In fact, military funding paid for the VAST majority of US science since 1945, both in private industry and academia. The huge increases in science funding since the Second World War, mostly attributable to defense concerns, in turn enabled new kinds of science and technology such as high energy physics and computing. A very obvious branch of military-funded breakthrough is all things nuclear, which would have been an ENORMOUS risk vs. reward to build without the pressing need for war. The Manhattan Project was tremendously expensive, and aimed at a result that no one knew for certain was realistically commercially/militarily viable. It's hard to imagine nuclear reactors within decades of the 1940s without the war.

BUT

What happens if there were no world wars? We fundamentally cannot know. An educated guess would be that there's MUCH less money devoted to scientific research in the US, at least, as most science funding before the wars came from private donations and organizations like the Rockefeller or Ford Foundations, and government had a much much smaller role in science funding generally. The wars were a major stimulus for expanding the role of government in US society.

If, on the other hand, we were to imagine that there were reason for non-military competition, such as economic posturing vs. Europe or whatever else, and that money somehow WAS devoted to science, there's no reason to think that America would have seen any less invention and technological advance than during and because of the wars. Quite likely we would have no nuclear weapons, but it's impossible to know what other breakthroughs we might have had in other fields - perhaps we would be "40 years ahead" of where we are now in biological sciences and medicine.

My guess is basically that the wars were the only way to get Americans, deeply suspicious of government, to pony up the money to research, so war indirectly stimulated technology. But I don't think that's a result of the war per se.

Regarding "testing rigorously" - like I said, patents aren't an ideal proxy, but economic historians have looked at aspects of this issue. Petra Moser's work (http://www.nber.org/papers/w15598), in particular uses, increases in patenting driven by the First World War seizure of German patents to show that this led to increased patenting in those fields in future years. Other econometric analyses play with similar questions/methods. Frankly I'm really skeptical of their methods, however, mostly because economists and economic "historians" tend to completely ignore what historians are writing about their topics generally. As such, they do sophisticated difference-in-difference regressions but lack the context to situate what they're doing, and therefore are susceptible to lots of alternate explanations for their work that they don't bother addressing. Even the best of that work, which I think Moser's is pretty good, tends to just generate more questions that need answering while making really over-generalized conclusions about patenting or invention per se, rather than patenting or invention in this one particular, historical context.

Bibliography / suggested readings:

• Paul Forman, “Behind quantum electronics: National security as basis for physical research in the United States, 1940-1960,” Historical Studies in the Physical and Biological Sciences 18 (1987), p.149-229. [shorter than it looks – lots of graphs, etc.]

• Daniel J. Kevles, “Cold War and Hot Physics: Science, Security, and the American State, 1945-1956,” Historical Studies in the Physical and Biological Sciences 20 (1990), p.239-264.

• Stuart Leslie, The Cold War and American Science: The Military-Industrial-Academic Complex at MIT and Stanford.p.1-43, 233-256

• Roger Geiger, "Science, Universities, and National Defense, 1945-1970" Osiris 7 (1992) p.26-48

• Allan Needell, "Project Troy and the Cold War annexation of the social sciences." In Universities and Empire: Money and Politics in the Social Sciences during the Cold War. Edited by Christopher Simpson. New York, NY: New Press, 1998, pp. 3-38.

• John Krige, American Hegemony and the Postwar Reconstruction of Science in Europe.

• Nicholas Rasmussen, "Of 'small men,' big science and bigger business: The Second World War and biomedical research in the United States.” Minerva 40 (2002): 115-146.

• Nicholas Rasmussen, "The midcentury biophysics bubble: Hiroshima and the biological revolution in America, revisited." History of Science 35 (1997): 245-93.

• Dan O'Neill, "Alaska and the Firecracker Boys." In Bruce Hevly and John Findlay, ed., The Atomic West. (University of Washington Press): 179-200.

• Loren Graham, Science in Russia and the Soviet Union

Dick, Steven J. and Launius, Roger D., ed. Societal Impact of Spaceflight. NASA History series. (http://history.nasa.gov/sp4801-part1.pdf and http://history.nasa.gov/sp4801-part2.pdf)

• Daniel J. Kevles, The Physicists

• James Capshew and Karen Rader. "Big science: Price to the present," Osiris 7 (1992): 3-25.

• Peter Galison, "Removing Knowledge," http://www.fas.harvard.edu/~hsdept/bios/docs/Removing%20Knowledge.pdf

• Alex Wellerstein, "Patenting the Bomb: Nuclear Weapons, Intellectual Property, and Technological Control"

I'm not sure how related this is, as it more directly is about the rise of complex societies. Anthropologist Robert Carneiro formulated a theory called Carneiro's Circumscription Theory (or Carneiro's Warfare Theory). Basically, as groups come into conflict, warfare occurs. In situations where migration is not an option (they live a fertile area surrounded by a desert for example), the losers submit to the victors. As a result, the victorious group of people is forced to deal with the integration of a different culture and an influx of people. This encourages a more centralized state organization to alleviate these issues, which are solved via methods that lead to increased technological development (better irrigation, more productive farming techniques, etc.). The success of this model when applied to early civilizations varies. That's the main gist of his model.

Here's a source from the man himself: http://www.columbia.edu/itc/anthropology/v3922/pdfs/carneiro.pdf

And here's a handy image that sums it up.

http://i.imgur.com/UTqx3Ee.png

My summary may be slightly wrong in a few areas (I studied his theory briefly in a class I took last semester on early civilizations), hence why I posted something written by him as well as a diagram taken from my professor's notes.

Given the other top level post, I would argue that warfare leads to a host of problems that arise both during and post-warfare, problems that can often be alleviated through intentional technological discoveries and improvements. Though, the same can be said of many societal problems, so I wouldn't count the problems of warfare as being unique, since technological developments can occur during peacetime. As for speeding up advancement, I believe the above model indirectly sheds light on the issue, at least in the context of early civilizations.