Syriza's victory in the Greek general election is a hopeful moment for Europe. It shows how a radical left-wing political movement, brought together in a short time, can use the democratic system to attack three menaces: the rentier lords of jurisdiction-hopping private capital, the compromised political hacks of the traditional parties who have become their accomplices, and the panphobic haters of the populist right.

Nationalist-conservative movements, it turns out, don't have a monopoly on the anti-establishment wave. The future doesn't have to belong to Golden Dawn, Ukip, the Front National, Pegida, the Finns Party, Partij voor de Vrijheid or the Sweden Democrats. It could belong to Syriza, or Podemos, or Die Linke, or to an as-yet non-existent British movement – anti-austerity, pro-Europe – which would scoop up votes from Labour, Liberals, the Scottish National Party, Ukip and the Greens.

And these left-wing movements – so it seems now, savour it while you can – don't have to rely on street protests to get what they want. They can get it through an instrument long considered by socialist radicals to be redundant: the ballot box.

The ascent of Syriza signifies the emergence of a trans-European politics in a way the previous rise to prominence of the likes of the Front National and Ukip haven't. The eurosceptics want to push the European Union away. They want their politics to be more national. What makes Alexis Tsipras radical is not what he wants to do in Greece, but what he wants to do in Europe.

Tsipras's programme will work only if he manages to ignite the Syrizification of the entire Eurozone; if he can win the implicit support of voters in enough national elections across the continent to force Angela Merkel and her fellow pro-austerity north Europeans into the position of isolation that Greece is in now.

Greece risks ostracism and expulsion from the Eurozone if it renounces the terms of the loan ('unsustainable and will never be serviced,' Tsipras says) it got from Europe to enable it to pay off the previous loans it couldn't pay off.

The buzz in the financial world is that the risk of 'financial contagion' is low this time round, should Greece drop out of the euro. But that ignores the possibility of political contagion, on which Tsipras is staking his hopes; the idea that everything could be turned on its head and it become Germany, rather than Greece, that is pushed to make an in-out choice on the euro by an overwhelmingly anti-austerity Europe.

In an open letter to the German people published on 13 January in the business daily Handelsblatt, Tsipras laid out his argument. His complaint, he said, was not that Germany had given Greece too little money when his country was 'rescued' after its financial collapse, but that it had given too much; Europe, he said, had acted like a reckless banker who refuses to accept that he made a bad bet on a failing business, and instead of writing the loan off, lets the firm limp on, stagnating, not closing but unable to renew itself because all its profits go to paying debt instead of investment.

It is a disingenuous letter. Tsipras doesn't really think Germany gave Greece too much money; he thinks Germany and its fellow-creditors lent Greece too much, and didn't give it enough. A form of bankruptcy has always been open to Greece – quitting the Eurozone and defaulting. But Tsipras doesn't want that. He wants to stay in the Eurozone, and for Athens to be able effectively to print euros, to be allowed to break out of its austerity straitjacket and embark on a Keynesian programme of expansion.

I have sympathy for Germans clutching their heads at this. Why, they might ask, should we let the Greeks dilute our currency? To which the Greeks might answer that it is their currency too, and sometimes, when a currency becomes sluggish, a bit of dilution is what it needs. And Tsipras's demand is not as presumptuous as it sounds. There is a sense in which the bailout was a bailout of Greece's creditors – big financial institutions – rather than the country. Really what Tsipras seems to be seeking for Greece is something like the Chapter 11 bankruptcy rules that exist in America, where a company can file for protection from creditors, continue to operate, and still borrow money to rebuild.

But Tsipras is issuing a much deeper challenge than that to the existing European dispensation. He is demanding that the rich parts of the Eurozone take the same direct responsibility for the less successful, or unluckier, areas as the richer parts of Germany or France do for the poorer regions within their own countries. He is seeking the mutualisation of giving a damn from the Arctic to the Aegean.

This idea has always existed in the abstract, but Syriza's victory has given it flesh. And although it might seem Greece has no leverage, the European Central Bank's launch of quantitative easing (money-printing) is a move in Tsipras's direction. Who knows what influence a strong showing by Syriza's Spanish counterpart, Podemos, in December might have on Portugal, Ireland and Italy, and what the consequences in France might be? The European Union may yet fragment into something looser. But should it move in the opposite direction, it may not be on Angela Merkel's terms.