Albert Einstein and the Ophthalmologist
Allvar Gullstrand died in 1930, one of the most recognized opthamologists who ever lived, winner of the Nobel Prize in 1911 for his work…
Allvar Gullstrand died in 1930, one of the most recognized ophthalmologists who ever lived, winner of the Nobel Prize in 1911 for his work on “dioptrics of the eye”.
Born in 1862, Gullstrand is also the only person to win the prize and also decline it, for, in 1911, the committee for the Nobel Prize in Physics suggested he receive their prize. He declined in favor of the prize in medicine. It was probably a good decision since the prominent Swede was a member of the Nobel Physics committee that year.
Although self-taught, Gullstrand was no dabbler when it came to physics or mathematics. In his work, he treated the eye like a “miniature camera”. He developed several instruments, still used today, to measure the precise parameters of the lens and cornea and, feeding these into mathematical equations, came up with an extremely accurate model of the eye.
He published this work as an Appendix in Von Helmholtz’s Treatise on Physiological Optics. It was for this work that he was offered Nobel Prizes in medicine and physics.
His mathematical acumen was not limited to optics. He was perfectly comfortable solving the Einstein equations, arriving at an exact solution, something Einstein himself had failed to achieve in his original paper in 1915.
As a long time member of the Nobel physics committee, Gullstrand was a major force against Albert Einstein receiving the Nobel himself, believing that Einstein’s relativity, for which he had become famous, was wrong. A powerful presence, he argued that relativity was so flawed and impossible to verify that Einstein should not receive the prize.
The larger physics community, however, disagreed.
By 1922, Einstein had received no less than 60 nominations for a Nobel prize, frequently for relativity but also for other contributions like Brownian motion, but the Nobel committee was biased against theoreticians. They also didn’t understand his equations.
In 1921, Gullstrand, tired of the endless nominations, wrote a secret report on Einstein’s work. Over 50 years later, the results of the committee deliberations were “declassified” and it was found that Gullstrand had found numerous “errors” and problems with Einstein’s work and declared it wrong. The committee decided not to award a prize that year, ending in a stalemate.
In 1922, Einstein was nominated again and the committee decided to award the 1921 prize to him retroactively but explicitly stated it was not for relativity. Rather, they highlighted Einstein’s other famous work on the photoelectric effect which was less conflicted and no less impressive. We owe both lasers and solar panels to it.
Today Gullstrand is not that well known outside ophthalmologist circles except for a contribution to none other than relativity: the Gullstrand-Painlevé solution to the Einstein equations.
Discovered by Painlevé and Gullstrand in 1921 and 1922 independently, both believed it actually proved relativity wrong. The reason was because it was another static, spherically symmetric solution. The first solution Schwarzschild discovered in 1916. The solution is one of the most important in all of general relativity because it can be used to describe gravity around spherical bodies like planets and stars. Almost all tests of general relativity near the Earth use this solution.
In fact, in 1922 in Paris, Painlevé met with Einstein before a committee of notable physicists where they debated the solution. Einstein found the solution baffling and ill formed and decided to reject it.
It turned out however that this solution displayed one of the most beautiful aspects of relativity, which is that everything is, well, relative. It has to do with who is measuring. The solution that Schwarzschild found, which Einstein thought was “right”, was how spherical bodies appear to a distant observer hanging out in deep space. Gullstrand and Painlevé’s (GP) solution was a solution for somebody falling into one of those bodies. So they were actually the same solution, just from different perspectives. This was not, however, discovered until 1933.
Today, the GP coordinate system is used to describe not only observers falling into planets or stars but also falling into black holes.
While Schwarzschild’s solution breaks down at the event horizon, the imaginary surface beyond which nothing can escape, the GP does not.
That makes sense. A distant observer can’t see through the event horizon, so anything beyond it is nonsense. An observer falling into the black hole, on the other hand, shouldn’t run into any blow ups at all until they hit the singularity at the center.
The GP is sometimes called the “raindrop” solution because it is as if you were a raindrop starting out in a cloud in deep space and falling towards a black hole. You can demonstrate some of the weirdness of relativity this way.
For a distant observer, as the raindrop falls towards the black hole, its velocity appears to slow down. This is because time relative to the distant observer is slowing down. At the event horizon, the raindrop velocity appears to be zero. It just disappears at that point.
For the raindrop, however, it continues to fall faster and faster as it plunges into the black hole. At the event horizon, its velocity has reached half of light speed. It continues to increase. It approaches to light speed at the singularity but at that point we don’t know what happens. Einstein’s equations break down.
Looking back from the raindrop’s perspective to the universe it has now left, having crossed the event horizon, it sees the stars compress more and more into a bright band all around its middle.
You can see this effect in this video around 30 seconds in:
The singularity, meanwhile, is hidden before it like an ever growing dark planet lying in its future. What happens when you reach it, nobody knows.
Not bad for an ophthalmologist.
Ravin JG. Gullstrand, Einstein, and the Nobel Prize. Arch Ophthalmol. 1999;117(5):670–672. doi:10.1001/archopht.117.5.670
Margo, C. E., and L. E. Harman. “Allvar Gullstrand, Albert Einstein, and a Nobel dilemma revisited.” (2012).