One of the great social experiments in American history will be launched here this week as California's intricate governmental colossus attempts, in three weeks flat, to fit itself into the limitations imposed by a two-thirds elimination of property taxes, effective July 1.

"Whatever happens, the social scientists will be writing books about it for years," predicted Assembly Republican Leader Paul Priolo as his party tried to decide on its politicalstrategy for the next three weeks.

The Jarvis - Gann amendment to the California constitution - Proposition 13 - which the voters passed Tuesday mandated the tax cut and deadline, but gave no clues about how it was supposed to be implemented.

The political decisions as to whom gets how much of what is left will fall to the legislature and the governor during the remaining days of June, and no one in state government is looking forward to the pressures that will be brought to bear.

During that fight the legislature must decide upon a formula to allocate the $4.4 billion in property tax revenue - down from $11.4 billion - that will be left to cities, counties and school districts after passage of Propostition 13 last Tuesday.

The legislature also must decide how much, if any, of the $5 billion state surplus to return to schools and local governments and work out a formula for returning it. And it also will be prodded to reach a decision on various pending proposals to reduce state spending and make still more money available locally.

At the municipal level, confusion is the order of the day. Predictions about what will happen when the new property tax limit - 1 percent of the 1975-1976 assessed valuation - takes effect range from the doomsday forecasts of San Francisco Mayor George Moscone to the sanguine outlook of Los Angeles City Treasurer Ira Reiner.

The critics of Proposition 13 talk as if we're going to have tumbleweeds blowing unmolested down the streets," Reiner said last week. "That just isn't going to happen."

The trouble is, nobody knows exactly what will happen. Modern government is so intricate, complex and expensive that there are those who fear the entire interrelated system of laws, rules, regulations and services will begin to crumble when the cash flow is cut July 1

The one thing certain is that California state government, with a $175 billion budget exceeded by only six nations in the world, is now going to be making the key decision for thousands of city, county, school and special district governments. This perhaps is the greatest irony of the Jarvis-Gann initiative, which was sold to the voters with the rhetoric of popular sovereignty and local control.

Presently, most cities and school districts have drawn up various contingency budgets for the next fiscal year and have announced cutbacks ranging from 10 to 60 percent. But most of these "budgets" are in reality public relations devices which do not take into account prospective help from the state surplus. Any real budgeting process at the local level must await a decision from the legislature.

Among the central unanswered questions that confront the California Legislature as it prepares to embark on a new era of government:

Will the huge windfall tax savings realized by big businesses under Proposition 13 create an economic spurt, as predicted by former governor Ronald Reagan and conservative economists? If a boom develops, state sales and corporation tax revenues would rise swiftly. Gov. Edmund G. (Jerry) Brown Jr. says that the businesses which profit from the Proposition 13 have a "moral obligation" to invest in California.

WIll local government employes and the unions that represent them accept firings and pay freezes without strikes or other disruptions?

Will the spirit of frugality urged both by Brown and by Republican leaders prevail at the state level, where there is now a hiring freeze? One indication that it won't came Thursday, when the California State Employers Association asked for a 125 percent pay raise totaling $300 million a year.

Can school districts, required by state law to conduct classes for 175 days a year, afford to wait until the legislature acts before cutting out their summer school program? At least five southern California districts decided last week to cancel all their summer courses.

Will the California Supreme Court, confronted with five lawsuits challenging the constitutionality of Proposition 13, issue a quick ruling? The issue is complicated by the precarious political position of Chief Justice Rose Bird, a former top aide to Brown, who faces a yes-or-no ballot confirmation vote in November.

Will local governments try to make up for lost revenue by raising old fees or charging new ones for trash collection, water services, transportation and debt service? Some city councilmen fear that in its present mood the electorate will resist any such charges by voting out incumbents who support them.

Will cities and counties reduce police and firefighting services? Polls taken for the committee which opposed Proposition 13 show that citizens are least willing to accept reductions in these services.

Los Angeles Police Chief Darryl F. Gates has warned the City Council that Mayor Thomas Bradley's proposal to lay off 1,080 officers - about one-seventh of the force - would be "catastrophic, devastating." And Los Angeles County Deputy Fire Chief Robert Simpson said last week that unless the state allows fire districts to levy their own taxes, 58 of the county's 128 fire stations will close and paramedic services will eliminated entirely.

The biggest question of all is whether the California Legislature, known for proclivity to sidetrack great issues on amall procedural questions can possibly pass the necessary legislation by the July 1 deadline.

Some politicians have likened the situation to the reapportionment crisis created by the "one man, one vote" decision of several years ago. In that instance the legislature proved unable to act and state supreme court drew the boundaries of the new legislative districts.

State Attorney General Evelle J Younger, the states chief law enforcement officer and also Brown's Republican opponent in November, has warned that he will ask the court to determine the allocation for local government if the legislature proves unable to do so.

Leaders of both parties here say they doubt the legislature will wind up a a tangle this time, as it did last summer when disputes between the Assembly and Senate killed a property tex relief measure and paved the way for Proposition 13.

Already, however, a Senate-Assembly battle appears to be developing over the question of whether the state surplus should be used primarily to bail out school districts or whether school districts, cities and counties should be aided proportionately.

And the beginnings of a partisan battle are also in the making.

State Sen. George Deukmejian of Long Beach, the Republican nominee for attorney general, said Friday that he opposed giving all of the state surplus back local government, as recommended by Brown.

Deukmejian said the mandate of the voters last Tuesday was for reduction in government spending that won't occur if the state bails out the local governments. If this happens, he said, it would simply postpone the hard decisions until 1979.

But it Sacramento, at least, the time for postponing decisions is over. During the next three weeks, everyone from the teachers to the taught, from mayors to welfare mothers, will be flocking to Sacremento for one of the greatest governmental showdowns of our times.