Did Einstein cheat?

I asked Neil Ashby, a professor of physics who works at the University of Colorado and specializes in theoretical general relativity with practical applications. "I am acquainted with Tom Van Flandern and his view," he told me. "It is incorrect to claim that no relativistic corrections are used after launch. Actually because GPS satellites are in eccentric orbits, they suffer frequency variations due to their varying speeds and varying heights above the Earth's surface. Information is transmitted down to the receivers from each satellite, which enables receivers to make a relativistic correction which accounts for these effects."

He added: "Einstein has not been 'blown off.' On the contrary, a great deal of thought has gone into the problem and all of the known special and general relativistic effects have been accounted for if they are predicted to be big enough to be important."

Other gravitation specialists, such as Charles Misner at the University of Maryland, Lawrence Mead of the University of Southern Mississippi, Clifford Will of the University of Washington in St. Louis and Steve Carlip of the University of California at Davis, confirm that special and general relativity are built into the software for GPS.

But the most interesting aspect of Van Flandern's objections to relativity bears directly on Einstein himself and his professional integrity. According to Van Flandern, Einstein cheated.

Van Flandern told the American Spectator's Washington correspondent, Tom Bethell, that he had reason to believe Einstein manipulated his field equations for one of his most momentous predictions: the advance of the perihelion of Mercury, the point in orbit where a planet is closest to the sun. Astronomers have long observed that this point, like the oval end of an ellipse drawn with a spirograph, is itself subject to motion, and over the years revolves around the sun just like the planet itself. In the case of Mercury, this effect is pronounced. It was assumed to be due to gravity and the closeness of the planet to the sun, but Newtonian theory could never predict its advance accurately. It was a classic problem by the time Einstein came along, and his general theory of relativity solved it immediately.

Too brilliantly, for some.

According to the Spectator's account, Van Flandern "asked a colleague at the University of Maryland, who as a young man had overlapped with Einstein at Princeton's Institute for Advanced Study, how, in his opinion, Einstein had arrived at the correct multiplier. This man said it was his impression that, 'knowing the answer,' Einstein had 'jiggered the arguments until they came out with the right value.'"

Curious why the source for this remarkable claim was never named, I contacted Bethell, who told me he was not given permission to name the source. Van Flandern was even more mysterious: "There's a reason," he wrote, "why that person was not quoted by name." He then suggested I send him any queries, which he could forward to this source for consideration.

Instead, I went to the University of Maryland on the Web, where a search revealed five working physicists who got their doctorates from Princeton within the decade after Einstein's death.

One of them is Carroll Alley, who received his degree in 1962. When I called him to ask about the mysterious quote, he told me he had indeed hired Van Flandern to do some work in celestial mechanics. As for knowing Einstein personally, Alley recounted how he had had the pleasure of attending the last lecture given by the great physicist before his death in 1955.

When asked about the claim that Einstein manipulated his equations to get a correct prediction, Alley, acknowledging that he was indeed the mystery man quoted in Bethell's article, told me, "That was not an accurate quote."

What he did say was that Einstein knew that Mercury's observed perihelion was 43 arc seconds per century more than predicted by Newton's theory. "A lot of people say that he didn't know it, but he did," said Alley. This is no surprise to anyone familiar with the history of astronomy or the various biographies of Einstein written by Ronald Clark, Abraham Pais and Albrecht Fvlsing.

Indeed, the burning question at the time Einstein was working on general relativity was not what the perihelion figure was, but how to account for it without making special assumptions. This is a key point, because cranks offer all sorts of counter theories that rely on nothing but special assumptions.

In short, to say that Einstein knew what the correct prediction should be and that he "jiggered" his multipliers to get it are two very different statements, the latter of which Alley disavowed in our conversation.

I contacted Van Flandern for clarification about the quote he had given to the Spectator regarding Einstein's alleged tampering. "Basically," he answered, "the choice of coefficients of potential phi in the space-time metric is arbitrary. Einstein knew the unmodeled perihelion motion of Mercury, and therefore confined his attention to metrics that predicted this quantity correctly."

I asked Carlip whether this made any sense.

"No, it makes no sense at all. Van Flandern seems to have invented a free parameter where none exists. There is one free parameter, but it's just Newton's gravitational constant, G, and is fixed completely by the requirement that the theory reduce to Newtonian gravity in the weak-field, low-velocity limit. Once you've fixed that, everything else is completely determined." According to Carlip, "Van Flandern seems to be under the impression that there are a bunch of adjustable parameters in general relativity that can be fiddled with. This is certainly not true."

"As far as I can tell," he added, "Van Flandern simply doesn't understand the Einstein field equations."

Other physicists I queried also flatly reject the notion that Einstein ever fooled with his figures. "I doubt very much that Einstein had any problem calculating [the perihelion]," wrote Ted Jacobson, a gravitation specialist at the University of Maryland. Ashby agreed, as did Lee Smolin, a specialist in general relativity at the University of Pennsylvania and author of "The Life of the Cosmos": "I have also personally checked the calculations about the perihelion of Mercury, as have I'm sure thousands of other people."

Michel Janssen and John Stachel have been working on the Einstein Papers Project at Boston University, reviewing the letters and papers of Einstein for publication in a new series. Janssen in particular worked closely on a review of Einstein's Mercury paper, and he was not amused about the accusation of fudging.

"Not to put too fine a point on it," he said, "that is crap."

Next Page: A psychosis that results in people believing that they have disproved relativity

• View blog reactions