Physics Buzz has a nice article about Paul Erdos and the Erdos Number Project (mine is 6), which ends with a good question:
I for one, am wondering: who would be the Paul ErdÅs of the physics world?
It's a tough question, complicated further by the existence of really gigantic collaborations in experimental high-energy physics, where author lists can run to hundreds of people. The 511 collaborators that Erdos can boast is more impressive in math than in some fields of physics.
For something really equivalent in spirit to Erdos, you would need to look for a physicist who had a long and distinguished career, and who worked in a wide range of fields, so that they might reasonably be connected to physicists in lots of different areas. These days, that would probably mean a theorist, as experimental skills in most fields are highly specialized, and you don't get a lot of field-switching. Theoretical methods, though, are pretty similar in different fields, so you can get people who make contributions in, say, solid state physics and particle physics both.
I'm not sure who a good modern candidate would be. Within my own field of AMO physics, somebody like Peter Zoller or Paul Julienne might work, as they've done a little bit of everything. I don't know if you could easily connect them to particle physics, though. Ed Witten is the dominant figure in high-energy theory (or so it seems from the outside), but I don't know if he's a prolific collaborator.
Going back a bit, I. I. Rabi is somebody who might work, as he did important work in both atomic and nuclear physics. A lot of his connections to people were more administrative in nature than the sort of thing that would lead to co-authorship. John Wheeler is another possibility.
It's a tough question. So I'll just throw it out there: If you were going to establish an Erdos-number equivalent for physics, who would you use?
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Richard Feynmann would have to be a candidate. He was known to take sabbaticals in other fields, including a stint in biology (where, according to his memoirs, he missed out on an important discovery because he made a rookie mistake in one of his experiments).
Feynman published surprisingly few papers, by modern standards.
The answer, of course, is deterministic - you calculate the Erdos number for all physicists, using all physicists as Erdos, and choose the person who minimizes the global Erdos number - you just have to choose a metric.
Trivial N^2 calculation for small N.
In astronomy I'd hazard to guess that either Rees or Ostriker would be it, although with large collaboration a big thing, someone like Mather, who was on multiple large projects over many years, might end up being the lynchpin.
More importantly, which physicist would you let into your house and office, and entertain for a duration of their discretion, just for the privilege of working with them?
If you really want to find Paul Erdos's equivalent in physics, you can't just find somebody with a very broad network of collaborators. You need to find an influence criterion that is both natural and itself related to the individual's work. Because a significant part of the joke about Erdos numbers is that Erdos did a lot of work on graph theory.
Wheeler.
Bethe? As we all know, Alpher and Gamow have a Bethe number of 1.
I would suggest Fermi, at least as an option to be debated.
Erdos published a LOT and with lots of collaborators, so a number like 6 would be pretty high if you were a mathematician. Where is the cross-over point into physics that you used?
As for your question, there is an accepted ANTI-Erdos number for physics: Pauli.
Pauli published very few papers with a collaborator, and most of his few collaborators had similar habits. As a result, a small Pauli number is rare. In my generation, 5 or 6 is hard to beat.
And it fits the joke requirement. Exclusion.
My understanding is that when they did this for acting (i.e. looked for a Hollywood equivalent of ErdÅs), Kevin Bacon was chosen because of his location in the network, and not because of some artistic merit criterion or his range of experience. You can define a $person number of any published academic or actor. If you calculate the mean $person number for ErdÅs and Bacon then it is unusually low. So the question isn't "who would you choose?". You just try everyone (or some plausible subset to make the problem computationally managable) and pick whoever gives the lowest mean!
Well, calculating your Einstein number is already fairly popular in physics (mine is 4) although this seems to be based on a gross misunderstanding of the "number" paradigm. I think Wheeler would be a much better choice, but one would have to count people who were his students or postdocs but didn't write a paper with him as a link because his strongest influence did not always spread by coauthorship. Calculating it this way would also benefit me greatly as many of the people who invented modern quantum information theory were in his group.
@Michael Williams
Interestingly, it turns out that Kevin Bacon's connectivity,while higher than most, is far from the greatest. He's just shy of making the top 500, in fact.
http://oracleofbacon.org/center_list.php
I suggest John Bardeen. He was based in condensed matter physics, but he collaborated with people from many fields, experimentalists and theorists. He provided theoretical support for the development of transistors, then worked with 2 people with particle physics backgrounds, Cooper and Schrieffer, to work out the BCS mechanism for superconductivity. Then he worked with other theorists and experimentalists on low-dimensional phenomena.
Isaac Asimov Number: I have about 250 pages of printout, to be turned into a paper. He is the Paul Erdos of {Science Fiction UNION Biomedical Literature}. Also, Asimov is the Feynman of Science Fiction, and Feynman is the Asimov of Physics. Ask the loyal readers, and the ladies...
If we are calculating a 'Wheeler number' based on adviser/student relationships then I have a Wheeler number of 3, cause my undergrad adviser had Wheeler as his Ph.D. adviser. Makes me sound a lot more special then I am :)