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Dalio, Bernanke and Summers walk into a bar...

Ray Dalio, Bridgewater Associates
Scott Mlyn | CNBC
Ray Dalio, Bridgewater Associates

A hedge fund manager, a central banker and a treasury secretary walk into a bar...

It may sound like the start to a wonky monetary policy joke, but billionaire investor Ray Dalio essentially proposed that it actually happen, given his differing views on economic growth with former Federal Reserve chairman Ben Bernanke and former Treasury Secretary Larry Summers.

"Perhaps we can have that discussion in person over a beer sometime," Dalio wrote of the proposed meeting in a private note to clients of his Bridgewater Associates, the world's largest hedge fund manager.

The actual debate is no joke: Whether the developed world is in a new era of of "secular stagnation," or permanently slower growth not tied to a regular economic cycle. Summers is a proponent of the theory, while Bernanke has argued against.

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Dalio believes tepid expansion is here to stay. "We (the United States, Europe and Japan) are in a period of secular stagnation," he wrote in the April 7 note obtained by CNBC.com.

Echoing a point he has made in previous public remarks, Dalio wrote that the Fed and other central banks have limited policy tools given already near-zero interest rates. That means less lending, and therefore less investment and lower economic growth. If interest rates stay the same, Dalio added, the economic boost from them will also taper off.

"Interest rate declines and debts increasing faster than incomes to pull demand and economic activity higher are largely a thing of the past," Dalio wrote.

Dalio's stagnation view is somewhat at odds with Bernanke.

"Does the U.S. economy face secular stagnation? I am skeptical, and the sources of my skepticism go beyond the fact that the U.S. economy looks to be well on the way to full employment today," Bernanke wrote in a recent Brookings blog post.

Bernanke has argued that there will always be profitable investments to make with very low interest rates, and that recent low growth levels were more from temporary pressures of the post-financial crisis economic cycle.

Former White House economist Summers is more in Dalio's camp on stagnation.

In a recent blog post responding to Bernanke, Summers said the "essence" of secular stagnation is "a chronic excess of saving over investment."

"If this is the case," Summers said, "monetary policy will not be able to normalize, there will be a continuing need for expanded public and private investment, and there will be a need for global coordination to assure an adequate level of demand and its appropriate distribution."

Summers believes government spending on infrastructure is a potential solution, one that Dalio wrote he supports in principal (Bernanke does, too, although he said recently it may not be satisfactory.)

Read MoreBernanke speaks: Interest rates could rise

Regardless, it's clear Dalio would relish a discussion with both men.

"It's always fascinating to explore these sorts of questions with great thinkers like Larry Summers and Ben Bernanke," Dalio wrote. "And, as a markets guy, I find it especially exciting to place bets based on that thinking. At the end of the day, the markets will provide the most objective feedback."

Bridgewater manages approximately $169 billion for institutional clients, such as sovereign wealth funds, pension plans and foundations. About 1,500 people work at the Westport, Connecticut-based firm.

Bridgewater's main hedge fund has an enviable track record of returns, including a 14.5 percent gain in the first quarter.

A spokesman declined to comment.