The Greenberger Universes

Shortly after I entered graduate school at CCNY1 in 1970, I was invited2 to the Departmental Winetasting sponsored by Professor Danny Greenberger. I don’t remember if I had abandoned my hope of doing a thesis with him, but I sat at his table. He offered a rather startling observation for a physicist, “There are no laws of physics!” He offered two arguments which at the time I found totally convincing. With the benefit of thirty years of hindsight, I find them less so, but still sobering. The two arguments were:

I. The Greenberger Universe I: a one dimensional universe in which the physicists are always wrong about the Ultimate Question. This does not prove that there are no laws of physics. It makes them untestable3. Under rigid empiricist assumptions the two are the same. I will argue there is also a GU II, but probably not a GU III

II. The Greenberger Condition: the theoretical physics analog of the Lipschitz Condition4 of mathematics. Without The Final Theory in hand, can you know if physics is converging toward it? The Greenberger Condition circumvents this difficulty. However, the review of twentieth century theories seems to indicate that physics is not converging. This view is weakly confirmed by the Coleman Conundrum.

1My degree actually says CUNY [City University of New York], but only the philosphers and such who don’t need a lot of real estate could be housed, at reasonable cost, in the graduate center across from the main branch of the New York Public Library. Physicists of that time felt the need to do experiments, which requires lots of real estate, hence we were sequestered at the unit colleges. I was at the City College of New York in Harlem, which is why I say I have a PhD from the Edge of Hell.

2Graduate students were given a partial dispensation from the monetary contribution.

3Or could you say that GU I relegates ‘laws of physics’ to the noumenal world.

4Wikipedia and Mathworld are both rather unkind to earthlings on this point. I’ll try to amend at some point. Yet another problem with Wikipedia – vast variance in the amount of background required. Judicious use of hypertext should be equal to this problem. That is to say, a hypertext document should accomodate a broad range of readers although “document” would not accurately describe the very different experiences of different readers. Such things are, however, very hard to write so the current “document” will be subject to a similar criticism.