Why the military revolution is a cause of the industrial revolution?

I'd concur that I don't think you can suggest that the 'military revolution' caused the industrial revolution. I'm not quite sure what you mean by 'military revolution' - but if you're referring to the Napoleonic system (the levee-en-masse, war paying for war, the use of war as 'politics by other means') then it's root cause is the significant paradigm shift caused by the French Revolution.

A source may help: it's old (published 1962) and... ideologically dubious (i.e. Marxist) and therefore needs to read with a questioning mind. I'm referring to Eric Hobsbawms Age of Revolution. https://www.amazon.co.uk/dp/B004JHY7R2/ref=dp-kindle-redirect?_encoding=UTF8&btkr=1

The basic argument is (if I've understood it right) that the conditions for an industrial revolution appear primarily in britain because of specific local occurrences which simply did not occur elsewhere, in China nor in Europe. However the 'launch point' is primarily only in the textile industry until the development of Railways in the 1830's, and its the railways that kick-started the development of 'heavy' metalwork industries.

Only in Britain was there, for example, a systematic process that moved workers away from the land and into the 'free' (i.e. mobile) system (the enclosure movement). There was a functioning trade system that moved raw materials (cotton from India or the Americas) to the UK and a commodity and a process that delivered increasing amounts of profits from the transformation of the raw material into manufactured goods (cotton textiles) - and a rapidly increasing population fuelled by improvements in farming (crop rotation, and above all, the potato) that provided a market for cheaper goods.

These conditions were simply not present in France - nor China. Primarily this was because the overall result of the French Revolution - which Hobsbawm lucidly notes was a middle class revolution - was the creation of a national class of petit-bourgouise, rather than a 'free' proletariat and a capitalist middle-class. What the revolution did do, in respecxt of the industrial revolution - was to emphasise those elements of the enlightment thought that applied to the middle classes. These - promotion by merit; a use for science and knowledge; discussion and democratic debate - were not too incompatible with the values of the emerging british middle classes (the Radicals) - utlitarianism, nonconformism, self-improvement.

As a result it was these strands that created the 'military revolution' I assume you mean - not the other way round.

According to Aime Cesaire you have your causation backward. It was the increasing industrialisation under capitalism which launched Europe on a series of wars all around the globe which pretty much ended with the globe under European domination, eventually this competition for territorial possession tore Europe itself apart in the two World Wars, and which allowed many colonies to throw off the shackles of colonialism (though the USA was very keen to step into Indo-China with a record, in Vietnam and Cambodia, that disabused them forever, of the notion that somehow they were the good guys) and which led to a great deal of soul-searching in Europe as to what had gone wrong in European civilisation that had caused such an enormous amount of suffering, not just in Europe, but all over the globe.

I'm not sure exactly how relevant this will be, but in the BBC documentary Empire of the Seas, it is alleged that the industrial revolution was caused by the Royal Navy, or rather the need for one.

The argument goes that in the late 1600s England needed a grand new navy to realise global ambitions. Problem was, the nation simply had no infrastructure to accomplish this. Firstly, this had to be financed. This led to the creation of the Bank of England, which acquired the financing, leading to the creation of the civil service to administer and account for all of what was required. The investment then led to the creation of cottage industries, which consolidated and evolved into industrial hubs to provide the necessary resources.

Paul Kennedy argued in The Rise and Decline of the Great Powers that Europe was criss-crossed by geographic barriers such as rivers and mountain ranges, leading to many different political entities and distinct cultures/nationalities, leading to political and military competition and technological innovation. The large empires of Asia, situated on large plains, usually with hundreds of miles between them and their rivals, on average did not have as much external competition and were more concerned with maintaining political control and social cohesion.

China and Europe may have had the same level of technology in 1500 or 1600 (and China had, then as now, many more people) but by 1800 Europe surely had pulled ahead, not only in weaponry but also in industry and political/military/financial organization.

I'm not sure it was military revolution that drives industrial revolution. There are several theories which try to explain the cause of industrial revolution. Barrington Moore, for example, proposed that it was the rise of the merchant class and the fall of feudalism which leads to mass production (which will lead again to three different political systems, but that's different story).

But to answer your question, I suppose Martin van Creveld's theory may fit. He wrote in Technology and War: From 2000 B.C. to the Present (1991) and several journals.

His basic assumption is: military revolution will always lead to a change in civilization.

It is possible because a military revolution always involves military innovations: the change in organization (the way units is arranged, leadership, etc), the change in strategy and tactics, and the most important, the change in technology. Technological innovation is often firstly used for the need of the military. Like how railroad was used in the 19th century, and internet in contemporary times. Later then it would be adapted for civilians use (which explains the link).