## The Secret of Chimpanzee Painting

Back in the early 70s there was a chimpanzee, Pablo the Chimp, who won 2nd prize in a California art show, under a pseudonym. When this came to light Pablo’s trainer was asked how the chimpanzee was, as an artist. The reporters ganged around, raised a skeptical eyebrow or three, and asked “Just how good is Pablo, *qua artist*e?”

This was before the Internet, back when if you wanted to send a message to a nearby island you had to get out your hammer and chisel, so I wasn’t able to find an exact record of the trainer’s response. But as I remember it, his response was along the lines of:

*As you might expect, Pablo has a good sense of color. And his sense of form is surprisingly good as well. His one problem is, he doesn’t know when to stop. *

*The secret of chimpanzee painting is knowing when to take the canvas away from your chimp.*

My dissertation has been a labor of love for some years now — sometimes more love, sometimes more labor — something I’ve been doing in addition to my regular consulting work. My old friend Jonathan M. Smith has been serving as an informal advisor, but primary responsibility for taking the trainer’s role has been mine. How is the inquiring chimp to know when it is time to put the canvas down slowly & back away?

I came up with three tests (there are always three tests):

- Is there a well-defined objective (is there a canvas?)
- Have we hit the objective? (is there a painting? does the arrangement of paint on the canvas show some sense of color & form?)
- Has everything not needed for one and two been stripped away (did the canvas make its escape in time?)

In the case of my dissertation, the first was relatively straightforward. The objective is to:

**Quantize time using the same rules as for space**

The second took a bit more thought: how do we know we have done that? What are the requirements? This probably merits a post in its own right, but I came up with five requirements. Is quantum time:

**Well-defined?**Can we go to any experimental situation and say what the predictions of “quantum time” are?**M****anifestly symmetric between time and space?**This is the defining condition of the project. I use the “eyeball” test: if time and space appear symmetrically in the expressions for the four dimensional Schödinger equation and kernel, then we are done. (I put this requirement second because until you have a well-defined theory, you can’t apply the eyeball test.)**Con****sistent with known experimental results?**Do we reproduce the existing predictions of the standard quantum mechanics? Or, has*quantum time*already been falsified? There are too many places where time and quantum mechanics intersect to be able to look at them all. Instead, I looked at some obvious limits and a few of the more obvious experiments (double-slit in time, time varying magnetic and electric fields, a few others).**Testable?**This is the flip side of “consistent”: you want a new theory to be consistent but not*too*consistent. (Otherwise it is merely an interpretation.) Getting a starter set of experiments together was really my answer to this requirement as well as the first and third.**Reasonably simple?**If you are willing to throw a sufficient number of epicycles at the problem, any theory can be made to work. How many epicycles is too many? There is an element of taste here, but if the second requirement — manifest symmetry between time and space — has been met, then in a certain sense*quantum time*is at least no worse than standard quantum mechanics.

The third test was the real problem (the third test is always the worst):

I started by trying to look at all the places where you might expect to see effects of quantum time: single particle, photon-particle interactions, ladder diagrams, statistical mechanics in time, particle-vacuum interactions, … Too much. Much, much, too much.

Eventually I thought to ask (thanks Jonathan!) not what are all the places you might look for quantum time, but what is **the least possible analysis needed to get to testable**?

The specific answer I came up with: stick to the single particle case & a starter set of experiments. Much more doable and, I suspect, much more readable as well.

But asking the right question — *what is the least possible analysis to get to testable? —* was really the key.

White space is good!