The fine structure constant, a dimensionless physical constant, is approximately 1/137, and the astronomer Arthur Eddington conjectured in 1929 that its reciprocal was in fact precisely the integer 137, which he claimed could be "obtained by pure deduction". This conjecture was not widely adopted, and by the 1940s, the experimental values for the constant were clearly inconsistent with it (i.e. closer to 137.036).
Physicist Leon M. Lederman numbered his home near Fermilab 137 based on the significance of the number to those in his profession. Lederman expounded on the significance of the number in his book "The God Particle: If the Universe Is the Answer, What Is the Question?," noting that not only was it the inverse of the fine-structure constant, but was also related to the probability that an electron will emit or absorb a photon. He added that it also "contains the crux of electromagnetism (the electron), relativity (the velocity of light), and quantum theory (Planck's constant). It would be less unsettling if the relationship between all these important concepts turned out to be one or three or maybe a multiple of pi. But 137?” The number 137, according to Lederman, "shows up naked all over the place,” meaning that scientists on any planet in the universe using whatever units they have for charge or speed, and whatever their version of Planck’s constant may be, will all come up with 137, because it is a pure number. Lederman recalled that Richard Feynman had even suggested that all physicists put a sign in their offices with the number 137 to remind them of just how much they don’t know.
In the Bohr model, the innermost electron of an atom with Z = 137 would be orbiting (just below) the speed of light, and the next element (Z = 138) would be "impossible". Since the Bohr model does not include either quantum mechanics or special relativity, the fact that it breaks down in this regime is not surprising. However, such large atoms (if their nuclei were stable) could be expected to behave rather differently from a naive extrapolation of trends in the periodic table.
The fine structure constant of physics continues to convince esotericists that the universe has numerological fine tuning: for example the age of the universe could be considered as roughly 137 times the square of a myriad of years.
The Hebrew word קבלה (Kabbalah) takes a Gematria value of 137. Kabbalah is generally taken to mean "receiving," as evident from its root in Hebrew k-b-l (kof-beit-lamed), to "receive". Nevertheless, an additional nuance of meaning can be derived from the first appearance of its root (k-b-l) in the Torah. In Exodus 26:5 and 36:12, the root k-b-l appears to imply a state of “corresponding” rather than “receiving.” It is used to describe the “corresponding loops” which, when clasped together, enjoined the two sections of the Tabernacle’s ceiling. These loops were suspended directly over the veil that divided the Holy Place and the Holy of Holies. Symbolically, this is the threshold between the physical dimension and the utterly spiritual dimension. In other words, at the boundary line of the physical world, the number 137 emerges.