Even George Mitchell admits that the building blocks for a real peace process are not in place, so why expect Hamas to get involved in any way?
Hamas cannot turn towards peace - there is no partner
Now that Israel and Hamas have completed their prisoner exchange after five years of indirect contacts, many people are asking if this might be a signal that Hamas will one day drop its principled refusal to enter peace negotiations. The French president, Nicolas Sarkozy, has spoken of his hopes for new talks "even in the most difficult circumstances". There have been a few calls in Israel, although rather muted, for a new approach to Hamas after the release of Gilad Shalit.
There are good grounds to believe that the relationship between Hamas and Israel can change in ways that may help the people of Gaza. Hamas leaders are saying that the terms of the prisoner swap deal require Israel to ease its blockade of Gaza and allow the reconstruction of buildings destroyed in the war which ended in January 2009.
The government of Benjamin Netanyahu has reasons to ease the blockade. The rift with its one-time ally, Turkey, has grown so wide and so damaging that it makes sense for Mr Netanyahu to go some way to meet Ankara's demands to ease the plight of the Gazans.
The revolution in Egypt has so far been a source of anguished hand-wringing in Israel. Now a policy response is required. Popular opinion in Egypt, now more strongly expressed, views Israel in terms of its treatment of the Palestinians, so some compromise is needed from Israel on Gaza.
On the Hamas side, life has also got more complicated since the start of the Arab uprisings, with Syria, its base outside Gaza, engulfed in near civil war. Hamas's refusal to condemn the protesters outright has soured its relations with Syria and Iran. The Hamas government in Gaza seems to be having difficulty paying salaries. It needs some new friends in the Arab world.
All this suggests that there is room for some detente between Israel and Hamas. But this is a long way from saying that the Islamist group is ready to join the so-called peace process.
Hamas leaders are often asked why they do not subscribe to the Arab peace initiative, endorsed by the Arab League in 2007. This does not require recognition of Israel immediately, but only after the establishment of a Palestinian state and a just solution to the problem of Palestinian refugees.
Hamas officials have welcomed the initiative, no doubt to avoid upsetting Saudi Arabia, the original sponsor of the proposal, but never signed up. Neither has Israel accepted it, though its rejection is couched in more sophisticated language.
Senator George Mitchell, who served as President Barack Obama's special envoy for Middle East peace until May this year, was asked this week when he thought Hamas might join the negotiations.
Speaking at Chatham House in London with David Miliband, the former British foreign secretary, he drew on his experience in Northern Ireland to answer the question. In contrast to his failure in the Middle East, the senator's efforts in Northern Ireland led to agreement in 1998 on a government embracing both the Unionist and Republican communities.
He pointed out that Sinn Fein, the political wing of the Irish Republican Army (IRA), boycotted his negotiations for the first 16 months. The Republicans made the necessary concessions that enabled them to join the talks - including renouncing violence - "only when they became convinced this was a serious process that had a possible result", Mr Mitchell said.
The same goes for Hamas, he said. Once they see there is a meaningful negotiation which they cannot afford to miss, they will take the steps required to join in.
For all the failures of US diplomacy in this area, and Mr Obama's inability to stand up to the Israeli prime minister over settlement-building, Mr Mitchell is surely right on this point. The basic requirement of a meaningful negotiation is absent.
Mr Mitchell admitted that he had failed to secure commitments on three issues which he believed were the necessary foundations for a peace process: an Israeli commitment to stop settlement building on occupied land; a Palestinian commitment to stay engaged in the talks, whatever the Israelis did or said; and for Arab states to take "positive steps" towards normalisation with Israel, such as permitting trade links.
Given these three failures, it is hardly surprising that Hamas has chosen to stay out. Any reasonable observer must conclude that the talks have been at best a shadow play, at worst a distraction while the Israeli government proceeds with its settlement building.
With the current configuration of Israeli parties, no conceivable Israeli government could survive a peace agreement that was acceptable to the Palestinians. Even if there were a deal on the table, the Palestinian president, Mahmoud Abbas, lacks the authority to carry out such a historic act on behalf of his people.
Although Mr Mitchell defines himself as an optimist, his assessment of the possibilities of peacemaking in the Middle East was remarkably downbeat. Both he and Mr Miliband agreed that the regional context was a key element.
Inevitably that will require some stability. But Mr Mitchell saw a period of "revolutions, counter-revolutions and re-revolutions" before the region settles down.
It is natural to hope that the prisoner exchange might shatter the deadlock. But in time it may be remembered only for the large number of prisoners that Israel had to release to secure the return of one of its soldiers.
For the sake of the people of Gaza, it should lead to a new modus vivendi between Israel and Hamas. But as for a two-state solution, that seems as far off as ever.