Einstein's Blackboard

[toucana]

Albert Einstein died on April 18th 1955 aged 76. As most of the world’s press converged on Princeton Hospital NJ where the legendary physicist had died, Ralph Morse - a photgrapher for Life Magazine - found his way over to the Institute for Advanced Studies where Einstein worked, and with the help of a bottle of whisky persuaded the superintendent to allow him into Einstein’s office to take some iconic photographs of the blackboard on the wall.

A new video by two young physicists Chris Pattison and Parth G delves into the interesting and largely unexplored topic of what was written on that blackboard ? What problem was Einstein working on the last time he picked up a piece of chalk and wrote on it ?

https://www.youtube.com/watch?v=AB_RyZzGFEg

The answers are not conclusive, some parts of the blackboard are illegible. But with the help of staff at the University of Portsmouth Institute of Cosmology & Gravitation, the videomakers suggest that Einstein was trying to rewrite the fundamental 2-dimensional Metric Tensors of General Relativity in terms of 1-dimensional Tetrad Vectors. This might well have been an attempt to produce a quantizable form of the theory of General Relativity i.e. one that could be reconciled with the theory of Quantum Mechanics. Conceiveably the basis of a theory of Quantum Gravity.

At one point the symbols on the blackboard include a sinister looking reference to ‘Killing’ which happens to be a reference to a type of expression known as a ‘Killing Vector’ (named after Wilhelm Killing). The final section of writing on the bottom right of the blackboard has a pair of tabulations labeled ’New’ and ‘Old’. The videomakers suspect that Einstein was explaining that this way of rewriting the GR field equations doesn’t really work. Certain numbers and degrees of freedom get moved around, but not in any useful way that would simplify the problem.

Edited April 1, 2023 by toucana
Edited redundant 'of' in last line

[Markus Hanke]

There’s no way to be sure that this is what he was actually working on, but it might be interesting for the reader here to know that we now do have a fully worked-out tetrad formalism for General Relativity. This is, in fact, a more general description of GR than the usual tensor formalism, because it contains additional degrees of freedom - physically, these allow for gravity to couple directly to intrinsic angular momentum (ie spin). So long as we deal with purely bosonic matter fields, this doesn’t make any difference, and the physical predictions are the same. However, in situations where we are dealing with predominantly fermionic matter fields (or a mix of bosonic and fermionic matter), this leads to the appearance of new gravitational phenomena such as spin-spin and spin-orbit coupling. Since some of these mechanisms have repulsive effects, under some circumstances this leads to predictions that differ from those of ordinary GR in major ways - for example, given the right initial and boundary conditions, it is possible to avoid the formation of singularities during gravitational collapse processes.

The trouble here is that, even though the tetrad formalism of GR is still purely classical, the extra degrees of freedom it introduces will also modify the fermionic wave equations in relativistic QM, notably the Dirac equation and the Rarita-Schwinger equation, making them non-linear. In principle at least this should be testable. In the case of the Dirac equation, there is currently no experimental evidence (that I’m aware of) to suggest such non-linear contributions do in fact exist. Of course it could just be the case that these effects are too small to be detectable yet…but still, the evidence is currently absent.