Albert Einstein: Von Ulm nach Princeton

Abstract

We introduce pentacene-doped naphthalene as a material for diamagnetic levitation, offering compelling applications in matter-wave interferometry and nuclear magnetic resonance. Pentacenedoped naphthalene offers remarkable polarizability of its nuclear spin ensemble, achieving polarization rates exceeding 80% at cryogenic temperatures with polarization lifetimes extending weeks. We design a multi-spin Stern-Gerlach-type interferometry protocol which, thanks to the homogeneous spin distribution and the absence of a preferential nuclear-spin quantization axis, avoids many of the limitations associated with materials hosting electronic spin defects, such as nanodiamonds containing NV centers. We assess the potential of our interferometer to enhance existing bounds on the free parameters of objective collapse models. Beyond matter-wave interferometry, we analyze the prospects for implementing magic angle spinning at frequencies surpassing the current standard in NMR, capitalizing on the exceptional rotational capabilities offered by levitation. Additionally, we outline a novel protocol for measuring spin ensemble polarization via the position of the nanoparticle and conduct an analysis of dominant noise sources, benchmarking the required isolation levels for various applications.

Relativizing the A Priori By Way of Reflective Judgement

“…7In a letter to Cassirer, Einstein sceptically reiterates this point: ‘Aren’t the notions of cow and donkey also a priori?’ (1924b: 201).…”

“…Commenting on the neo-Kantian movement in science, Einstein himself claimed that for Kant, ‘a priori elements could not come into conflict with any future reasonable physical theory. … If one does not consider this goal to be attainable, then one should probably not call oneself a “Kantian”’ (1924a: 500; see also Kitcher 2000: 89). Proponents derive resources from the constitutive synthetic a priori principles of understanding of the Critique of Pure Reason , which Kant takes to ground the Newtonian laws of motion: rejecting the meaning of the Kantian a priori as ‘necessary and unrevisable, true for all time’, they embrace a second sense, as ‘constituting the concept of the object of knowledge’, or establishing the conditions of possibility for a given scientific framework (Reichenbach 1920: 48; Richardson 1998: 112, 120; Friedman 2001: 72; French and Massimi 2013: 235; Heis 2014: 18–19).…”

“…In a critical review of the book Kant and Einstein , Einstein writes: ‘“Ideality” pertains to all concepts, those relating to space and time no more and no less than all the others. … In my opinion, Kant had an unfavorable influence on [scientific] development by giving spatio-temporal concepts and their relations a special position in relation to other concepts’ (1924a: 502) 7 . Because Einstein downplayed the constitutive significance of spacetime as the fixed foundation for general relativity, and instead sought a more dynamical account on which any conception of ‘space’, ‘time’ or ‘spacetime’ would ultimately prove dispensable, he rejected any role for the a priori in his own philosophy of science 8…”

“…We can take the suggestion of simultaneously constitutive and regulative principles to motivate weakening the constitutive force of general covariance. While covariance does not in fact obtain within the framework, Einstein claims that it nevertheless has ‘significant heuristic force, which has already brilliantly proven itself in the gravitational problem that has been based on it’ (1918a: 39); Ryckman (2005: 17) derives the constitutive status of the principle from this assertion of ‘heuristic force’.…”

“…At the outset, I considered Einstein’s dissatisfaction with the idea that space, time or causality would have a necessarily privileged status in establishing any possible scientific framework. The account I have sketched here offers the beginnings of a response to the demonstration over the course of the intervening centuries that developments such as ‘spacetime’ or non-Euclidean geometries are at least conceivable, and arguably even intuitable (Helmholtz 1876; Einstein 1924a, 1924b; Richardson 1998: 122), or that the categories of ‘substance’ or ‘causality’ are dispensable in the wake of new physical theories of mass, relation and probabilistic events (Reichenbach 1920: 78). In accounting for such shifts, Kant’s characterization of reflective judgement, as what is called for when the ‘particular, as such, contains something contingent with regard to the universal’ and when ‘the a priori derivation of the particular laws from the universal … is impossible’, suggests important resources for the relativized a priori theorist ( CJ , 5: 404).…”