Quantum graininess

Everybody knows about the Heisenberg Uncertainty Principle. How much they know about it varies. Most know it as a limit to the knowledge that we can have about quantum systems. Some know it more specifically as a limit to the knowledge we can have about the value of two conjugate variables. Some can derive the uncertainty principle from other basic rules of quantum mechanics.

Last year as I first began to learn about quantum optics I was extremely surprised to learn that phase and number can be considered to be conjugate variables in a loose sense. If you know photon number perfectly you can do so only by destroying photon phase.

Anyway, the HUP shows up all over the place and becomes a problem any time you want to perform a measurement. I suppose that the question that I want to pose now is simple: when you have a nonlinear effect that manifests itself as an effect on the phase of a system that phase will have an uncertainty that corresponds to your knowledge of the number state of that system. If the phase is classically proportional to the strength of your nonlinear interaction then you might map that uncertainty onto the strength of your nonlinear interaction. From this mapping can one state an uncertainty principle for the precision with which the strength of the nonlinear interaction can be specified? It seems like if you could this might open up a way to analyze fundamental limits to your ability to make precision measurements using nonlinear optics.

So how should I get at the problem? The first way you might get at specifying the uncertainty of a quantity is by representing it as an operator and seeing what it commutes with. I think, however, that nonlinear interaction strengths are not likely to be observables but rather parameters that you can estimate using observables. So I guess that the analysis might follow one that you would use for other important but unobservable parameters like phase.

Alma's Tao

After talking about diligence and temperance Alma continues giving advice to his Shiblon in verse 11:

See that ye are not lifted up unto pride; yea, see that ye do not boast in your own wisdom, nor of your much strength.

I like that verse a lot. One thing interesting about it is how in the last phrase Alma seems to acknowledge that Shiblon has much strength even as he asks him not to boast of it. This morning I was thinking about the verse in terms of how it might help me practically in getting things done. I think there are a couple of ways.

First, it reminds me of Benjamin Franklin's autobiography. One thing he states and tries to teach is that if you want to get something good done it is wiser to get yourself out of the way. To paraphrase, he says that you can get a lot more accomplished if you aren't worried about getting the credit for accomplishing it.

But a second thing comes out of Alma's sentence and that is a matter of focus. When you want something to happen you need to look somewhere for the power to make it happen. If you are full of pride and see accomplishments primarily in terms of your own qualities of wisdom and strength then I think you are focusing on the wrong things. Because nature is much more powerful than you are you should be focusing rather on the way that things outside of you work. Your strength is local and limited. So is your wisdom. But natural laws have amazing power. If you can flow with them and make use of them then perhaps you can really get things done. Now you have something scalable.

So let me give an example: you can use your amazing powers of persuasion to sell a crummy product. You'll make some sales but only as many as you can get to happen by running around and convincing. And hopefully at some point you'll get stuck with your own reputation. Or you can sell something that is excellent enough to knock peoples socks off. In this case you still may need to start off running around finding people with knockable socks. But now, because you are acting in accordance with the way things are, you have a success that can really grow.

Hot, hot chilli

Check out this article about some chillies that blow the socks off of our habaneros.

Who should clean up the bathroom?

Okay. Here is something that is on my mind a bit.

First, I know that my primary responsibility is my family, including myself. That said, tell me this. We have about 6 billion people on the earth and all of us share some problems. How much responsibility should we each take for these shared problems? How much should we do to prevent irreversible changes to the planet? How much should we do to help cure diseases? To prevent unnecessary deaths due to innefficiencies? To feed hungry children?

Anyway, the point isn't to try and find problems. The point is to talk about responsibility and life choices. The thing is that if every person focuses only on taking care of his or her family the side effects of that inherently good and important process may do real and irrevocable damage. On the other hand 6 billion seems like a large enough number that if that group works with any kind of unity a lot could be done.

Anyway, goodnight.

Founder's Touch

I read "The Founder's Touch" this past week about Paul Galvin and the beginning of Motorola. Now that was a wild ride. Paul and his partner went all out two seperate times before Motorola ever began. Both times they landed flat on their faces, the first time shut down because they couldn't pay inventory tax and the second again because they ran out of money. Motorola was bought from the ashes of the second crash. For years after it was up and running they were up against the wire, nearly crashing and burning again several times, but this time they pulled out of it. Oddly enough I think that part of their later success was because of the tight times at the beginning. Reading the book I got the sense that they formed a very tight team. Here are just a few of my favorite quotes:

"Even small problems seem big when they are not solved. Making an effort to solve them keeps them small." P.V. Galvin

"When a man and a woman have shared the hardship that Lillian and I have shared, there are not words that can easily describe how much they come to mean to one another." P.V. Galvin

"He had a unique way of adding up a man's potential in his own mind. Someone once said of him that 'he could remember a mistake a man had made ten years before.' It was true that he could recall these episodes of error, but what he watched closely were the ways in which the man either benefited or did not benefit from the mistakes. One of his favorite sayings was, 'I don't mind a fellow who is dumb but I can't stand one who is numb.'" Petrakis quoting Galvin

"Do not fear mistakes. Wisdom is often born of such mistakes. You will know failure. Determine now to acquire the confidence required to overcome it. Reach out. . ." P.V. Galvin