Among the fathers of quantum mechanics, Pascual Jordan is the least well-known one. Needless to say, politics is the single most important reason behind his invisibility although it is not necessarily the only one.
While he genuinely believed in the ideals of the NSDAP that he joined at some moment (not to speak about Luftwaffe and the Peenemünde rocket center where he worked as a climate scientist), he was pretty much suppressed already in the 1930s. After all, he was also unreliable for the regime due to his past collaboration with Jews such as Max Born and Wolfgang Pauli.
Mostly for political reasons, he became isolated from the research community already around 1930. But after the war, some fellow physicists declared him "rehabilitated", he became a tenured professor again, and he was also elected as a lawmaker for the most mainstream among German parties, CDU. Nevertheless, he had done pretty much all the important original technical contributions to physics before 1930 or so.
(Well, it's not quite fair because he would work on general relativity and its extensions – and on cosmology – after the war. He even worked on Kaluza-Klein theory where he realized that the 4D Newton's constant depends on the radius of the fifth dimension – surely a key insight that was heavily exploited e.g. by Arkani-Hamed, Dvali, and Dimopoulos, among many others. In 1961, together with Jürgen Ehlers, he developed the kinematic decomposition of a timelike congruence. Jordan also independently discovered or invented the Brans-Dicke theory, rarely called the JBD theory because it isn't politically correct, either.)
When it comes to science and philosophy, it's therefore much more interesting to focus on the 1920s when he was a major determinant of the evolution of physics and the 1930s when he was a maximally competent person to summarize the state of the affairs. I just watched a pretty fascinating 35-minute 2010 lecture by Don Howard, a historian and philosopher of science at Notre Dame:
Quantum Mechanics in Context: Pascual Jordan’s 1936 Anschauliche Quantentheorie in its Philosophical and Political Setting (35 minute video, main link of this blog entry)Most of the talk is dedicated to an analysis of Anschauliche Quantentheorie, his 1936 textbook on quantum mechanics that covered everything from the philosophical foundations of quantum mechanics to the "completed" status of non-relativistic quantum mechanics and to the state-of-the-art quantum field theory and nuclear physics at that time (which was still confusing and incomplete but whose birth was partly Jordan's work, too).
Howard's talk makes it look like it was an excellent text. Too bad it doesn't seem to be translated into English, a fact that has most likely political reasons as well. Maybe this suppression of the once-successful textbook – or perhaps some people's emotional desire to deliberately contradict it – is one of the major historical reasons why quantum mechanics remains so heavily misunderstood today.
The title of the book means something like "Lively/Imaginative Quantum Mechanics" and it deliberately emulates the title "Anschauliche Geometrie" by David Hilbert and Stephan Cohn-Vossen, an important book that was translated to English under the title "Geometry and the Imagination". Jordan, a fan of Hilbert, really meant to "do the same thing" as Hilbert for quantum mechanics.
Concerning research contributions, Jordan previously co-developed matrix quantum mechanics in the mid 1920s together with (his adviser) Max Born and partly in collaboration with Werner Heisenberg. He should have arguably shared the 1954 physics Nobel prize but he was probably erased because of his politics. He has invented the Jordan algebras but their utility in quantum mechanics was later found to be very limited – while pure mathematicians began to use them in other contexts.
Back to the book
But let's return to the mid 1930s and his book on quantum mechanics. Howard argues that Jordan knew very well what his philosophical roots were. It was a particular combination of traditions and emerging movements and this combination makes a lot of sense, at least up to some point.
He would endorse Ernst Mach's logical positivism (which would also inspire the creation of the Vienna Circle, a philosophical club that Jordan de facto belonged to and that used to be called the Ernst Mach Society) as well as David Hilbert's finitism in mathematics and he would argue that they're pretty much the same thing and quantum mechanics as associated with the names of Bohr and Heisenberg is showing that the same principles hold in microscopic physics, too. Well, he didn't hide that he considered himself (and Paul Dirac) to be the actual fathers of Bohr's complementarity, anyway.
Now, one must be careful about philosophies and excessive generalizations. Mindless generalization may lead you to very wrong conclusions. If a philosophy or a vague idea works in one class of questions, it doesn't necessarily work for all other questions. And indeed, I think that Jordan's vitalism ("living things are different from non-living things" and therefore "biology is more fundamental and physics is its special case"; and he even wrote positive things about telepathy!) may be an artifact of a philosophy that was extrapolated too far and too mindlessly.
However, at the level of foundations of quantum mechanics, his combined philosophy seems completely coherent and meaningful to me. Ernst Mach would emphasize that one shouldn't talk about the data we can't experimentally extract, not even in principle. Of course, Mach was far from understanding quantum mechanics but I think it is very fair to say that quantum mechanics confirmed that Mach's warnings were very important.
Jordan would also endorse Hilbert's finitism in mathematics – the idea that only objects we can completely construct exist. This is a legitimate – and perhaps my preferred – attitude to various dilemmas in set theory. Is the Axiom of Choice true? We know that we may create consistent axiomatic systems with the Axiom of Choice as well as ones with its negation. Using the finitist logic, the reason behind this ambiguity is that the only real numbers (and other objects) that "really inevitably exist" are those that may be exactly described by a finite sequence of steps or conditions. So even the proposition that the number of real numbers exceeds the number of integers shouldn't be viewed as a statement about the "actual real numbers that are out there"; instead, it is a statement about the non-existence of an "actual map" (again, fully specified by finitely many symbols) matching real numbers to integers.
The finitist philosophy indeed seems very analogous – and from a broader viewpoint, "equivalent" (as long as it makes any sense to talk about the equivalence between principles in mathematics and principles in physics) – to the logical positivism because it urges you not to think about things that objectively exist – like arbitrarily contrived real numbers or the values of observables in QM prior to the measurement – and instead, to focus on the finite propositions you can make and the most general methods you may design to find out which of them are true and which of them are false.
Howard concludes that the unifying element of all themes in Jordan's book is his opposition to materialism so in some sense, all his efforts were ideologically driven. Even though I would sometimes count myself as a materialist and I dislike research that is ideologically driven, he probably had something to say. I haven't really read the book but I would love to. ;-)