List of Footnotes
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“[D]er Gravitationsradius des zur Messung dienenden Probekörpers (![]() ![]() ![]() |
2 | Translations from German to English: SH. | |
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“Wenn die Explosionen tatsächlich existieren und die für die Konstante ![]() ![]() ![]() ![]() |
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“Der Umstand, daß [die Plancklänge] wesentlich kleiner ist als ![]() ![]() ![]() |
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“Mir ist es bisher nicht gelungen, solchen Vertauschungs-Relationen einen vernünftigen mathematischen Sinn zuzuordnen…Fällt Ihnen oder Pauli nicht vielleicht etwas über den mathematischen Sinn solcher Vertauschungs-Relationen ein?” |
6 | The story has been told [313] that Peierls asked Pauli, Pauli passed the question on to his colleague Oppenheimer, who asked his student Hartland Snyder. However, in a 1946 letter to Pauli [289], Snyder encloses his paper without any mention of it being an answer to a question posed to him by others. | |
7 | Though the hope of a lowered Planck scale pushing quantum gravitational effects into the reach of the Large Hadron Collider seems, at the time of writing, to not have been fulfilled. | |
8 | In the classical theory, inside the horizon lies a singularity. This singularity is expected to be avoided in quantum gravity, but how that works or doesn’t work is not relevant in the following. | |
9 | An example of a different choice of basis can be found in [314]. | |
10 | The word ‘effective’ should here not be read as a technical term. | |
11 | According to the Hellinger–Toeplitz theorem, an everywhere-defined symmetric operator on a Hilbert space is necessarily bounded. Since some operators in quantum mechanics are unbounded, one is required to deal with wave functions that are not square integrable. The same consideration applies here. | |
12 | The Lorentz group has a second Casimir operator, which is the length of the Pauli–Lubanski pseudovector. It can be identified by it being a function of the angular momentum operator. | |
13 | Though it has meanwhile been shown that the fixed point behavior can be found also in the Lorentzian case [218]. |