More than 150 leading scientists including Professor Stephen Hawking have signed a letter to the Times saying a vote to Leave the EU would be a “disaster for UK science and universities”.

We don’t propose to FactCheck Hawking’s theories on information hidden behind the event horizon of black holes, but his views on Europe are fair game, and critics say he and all the other professors are scaremongering.

The academics who signed the letter say Switzerland is now paying the price for crossing Brussels on the free movement of workers, and Britain could get the same treatment. What are the facts?

British scientist and theoretical physicist Stephen Hawking attends a launch event for a new award for science communication, called the Stephen Hawking Medal for Science Communication, in London, Britain December 16, 2015. REUTERS/Toby Melville - RTX1YYFR

The analysis

Switzerland’s relationship with the EU is sometimes held up by Eurosceptics as a model for how Britain could rebuild relations with the bloc after a Leave vote.

The Swiss managed to negotiate a number of bilateral treaties granting them partial access to the EU’s single market without becoming a member, although there are question marks over how good the deal really is.

As part of the agreement, Switzerland had to sign up to many of the key EU principles, such as the free movement of goods and people.

Relations hit the skids in February 2014 when a slim majority of voters backed a proposal by the right-wing Swiss People’s Party to introduce quotas for EU migrant workers – a breach of the free movement rule.

There were warnings of dire consequences, and some EU-watchers saw the stand-off as a kind of trial run for how the EU might treat Britain in the event of a Leave vote.

The prominent Eurosceptic Conservative MEP Daniel Hannan wrote immediately after the vote that the EU could not afford to punish Switzerland over the affair, given its importance as a trading partner.

Mr Hannan wrote: “So far… the only punishment delivered by Brussels has been, er, the deferral of some talks on cross-border sales of electricity.”

He added: “Our withdrawal from EU institutions would prompt angry speeches and vague threats and maybe some symbolic non-collaboration.”

A week later, the European Commission blocked Swiss students from participating in the EU’s Erasmus Plus student exchange programme, and froze the country out of the 80bn-euro science funding programme Horizon 2020.

Swiss universities were dismayed, warning of a long-term loss of prestige and talent as well as billions of euros in funding over several years.

European Commissioner László Andor was quick to say that this was not a case of the EU seeking to punish Switzerland over the immigration vote.

He said in a statement: “I want to make very clear that this freeze of negotiations is not a ‘punishment’ or ‘sanction’ for the expression of the Swiss electorate, but a logical consequence of the choice Switzerland itself has made, a consequence which was very well-known before. Nobody can pretend to be surprised here.”

A man plays an alp horn as a huge 80x80 metres (262x262 feet) Swiss national flag is seen on the western face of the north-eastern Swiss landmark Mount Saentis, Switzerland July 31, 2015. The flag marks the Swiss National Day. REUTERS/Arnd Wiegmann TPX IMAGES OF THE DAY - RTX1MJKJ

What would it mean for British science if this country got similar treatment ?

The Royal Society points out that British institutions have tended to do rather well from the EU science funding pot in recent years, getting more grants than any other country except Germany in 2014.

In the 2007 to 2013 financial framework, official figures suggest Britain paid in 5.4 billion euros to EU research and development funds and received 8.8 billion back.

We can’t say as a matter of certainty that Britain would be frozen out of EU science funding in the event of a Leave vote, but Brussels is firmly linking access to programmes like this with acceptance of core EU principles like free movement.

Of course, research is only a small part of the whole EU budget. And overall, Britain is a net contributor to EU coffers, a point quickly made by Professor Angus Dalgleish, a cancer specialist, Ukip election candidate and spokesman for Scientists for Britain.

Prof Dalgleish said: “The bottom line is that we put far more into Europe than we get out. Any difference we can easily make up with the money we would save.”

That sounds definitive, but really it’s the start of a complex argument about whether the EU is worth the membership fee.

Would there be a straightforward saving to the taxpayer if we left? Only if the EU really does not provide any benefits in terms of jobs, growth and trade – a massive moot point.

Boris Johnson has predicted that the UK economy will follow the path of the Nike swoosh logo after Brexit – a short downturn followed by a long uptick upwards.

The OECD’s chief economist Catherine Mann retorted: “I don’t see a tick, I see an ‘L’ shape.”

Unfortunately the economics of this are almost as complicated as string theory and FactCheck for one has not figured out a way to settle it.

Apart from the question of money, there’s the threat of a brain drain. Swiss universities said they started haemorrhaging researchers after the EU suspended it from Horizon 2020. Would British institutions encounter the same problem?

The verdict

The row over the Swiss immigration vote suggests the EU is capable of taking a tougher line than some commentators expected with countries that flout its core values.

Of course we can’t assume that Britain – a much bigger economy than Switzerland – would face exactly the same treatment.

And we should note that dark hints of Switzerland being denied access to the single market in the wake of the referendum have not come to pass.

But it seems fair to assume that if the UK denied freedom of movement to EU citizens after Brexit, we would run the risk of being shut out of things like EU-wide science funding too.

It’s true that Britain takes out more than it pays into the research pot, although the opposite is true of the EU budget as a whole: Britain is a net contributor.

Whether there would really be a saving in the long run from cancelling the subscription to Europe is probably the biggest question for neutral voters as the referendum looms.

Unfortunately, FactCheck can’t answer that one – and we don’t think anyone else can either.