Smoke rises following an Israeli airstrike in Gaza City. (Hosam Salem/AFP/GETTY IMAGES)

Egypt-watchers have wondered for months how the country's post-revolutionary, democratically elected, Muslim Brotherhood-allied government would respond to an Israeli strike on the Gaza Strip, which sits between the two countries. Now the world might find out. 

The Muslim Brotherhood has expressed sympathy for the Palestinian population under embargo in Gaza and skepticism toward Egypt's treaty with Israel. It is also more sensitive to Egyptian public opinion – which is not terribly pro-Israel – than was Hosni Mubarak's government. The Egypt-Israel relationship has remained generally stable since the Egyptian revolution, and Egypt has held up its end of the embargo, but analysts have worried that an Israeli assault on Gaza could change Cairo's calculus. So far, the fighting is limited to Hamas missiles and Israeli airstrikes, but the Israeli military has signaled its readiness to send ground troops.

Egypt has already recalled its ambassador from Israel over the Gaza strikes, something it threatened to do in August over an Israeli airstrike that killed three Egyptians. Despite rumors, Israeli officials tell Reuters they have not recalled their own ambassador. Perhaps the best-case scenario would be that Israeli-Egyptian tensions escalate no further and that Egypt, possibly with some assurances from the United States, restores full diplomatic relations with Israel.

Another possibility is something more like Turkey's response to the 2008 "Operation Cast Lead" Israeli ground invasion of Gaza, which led to a significant breakdown in Israeli-Turkish diplomatic and military cooperation -- once relatively strong for the region. Turkey, also increasingly democratic, is governed by an Islamist-leaning political party that has vocally criticized Israeli policies, particularly in Gaza. A 2010 Gaza-bound aid flotilla ended in the deaths of eight Turkish citizens and one American when it was raided by Israeli troops. The decline of Israeli-Turkish relations has not been catastrophic for Israel, but it hasn't been great news for the country, either. Turkish leaders are showing interest in Palestinian politics; Prime Minister Recep Tayyip Erdoğan was planning a trip to Gaza.

Israel's relationship with Egypt is unique, though, and includes some particularly important provisions. There's no indication that Egypt is considering lifting its embargo of Gaza, but doing so would probably deal an enormous blow to Israeli-Egyptian relations. If Egyptian President Mohamed Morsi were looking for a way to escalate his retaliation against Israel for its strikes on Gaza, this might be one way he could potentially choose to do it.

The worst-case scenario would almost certainly be Egypt walking away from the Camp David Accords, under which it has maintained its peace with Israel for three decades. This seems especially unlikely, given that President Obama has repeatedly called it a "red line." Egypt relies heavily on U.S. aid money, particularly now with its economy in such trouble. It's difficult to imagine any Egyptian government bringing such severe costs on Egypt for the benefit of Gazans.

Whatever Cairo's response, it could be significant beyond just the Gaza clash – though that's certainly significant enough on its own – by revealing something of how the new Egypt approaches Israel during moments of tension.