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Physics question February 3, 2007

Posted by dorigo in physics.

I know there are a few theorists who visit this site periodically… If you are one of them, you might have a minute to answer a question posted by my friend Helge, on perturbations of a simple Schroedinger operator. It is at http://cow-gone-mad.blogspot.com/.



1. Helge - February 3, 2007

How, cool I am getting lots of comments now … time to write up some more stuff.

2. Carl Brannen - February 4, 2007

Your friend is working in perturbation theory, an area that has been searched very carefully for many decades by many very smart people. The effect is equivalent to the fact that when the drunk finds he has no car keys at midnight, he looks for them near the lamp posts. After a few hours of searching, he might consider the possibility that his keys aren’t in a well lit area. Eventually dawn, and sobriety, will arrive and the sun will shine on his keys.

Perturbation theory works by representing states as things that can be combined in linear superposition. It seems that linear superposition is a general property of quantum states, but it turns out that some states cannot form a linear superposition. For example, elementary particles has no states that are partly fermion and partly boson. Or partly electron and partly neutrino. But partly electron and partly muon states can and do occur. Superselection sectors.

Spinor representations of quantum states are automatically linear, density matrix representations are automatically non linear (bilinear). It’s possible to convert from one sort of representation to the other. Maybe the keys aren’t near the kets.

3. dorigo - February 4, 2007

Hi Carl,

thanks for visiting… I like your analogy, but does the sun always shine on the keys in the morning ? It could be raining 😉

I am sure Helge was happy to be getting some answers. Thanks to all who contributed.


4. Bee - February 4, 2007

this again shows us how much smarter nature is than we are. if the guy’s so drunk, he’s better off not finding the keys.

5. dorigo - February 4, 2007

Yes Bee, good point – but I have always thought, with quite a bit of cynism, that there is some kind of natural selection at work when young people kill themselves in saturday night car accidents. Those are usually not the brightest members of our species anyway…

Sorry if this insults anybody, of course I am speaking on general grounds.


6. Bee - February 5, 2007

if they would only kill themselves, you’d have a point there.

my driving teacher told me: a car is a weapon, that’s why you need a licence.

7. Carl Brannen - February 5, 2007

I think that the reason that people are disappointed by people is mostly because they set extremely high standards for each other. Humans are an intelligent animal that eat only meat that they have killed for themselves and that hunt in packs. Of the other animals that have ever existed on the planet, the humans remind me most of the raptors that played a part in the movie Jurassic Park.

The other animals are rightly terrified by humans. (I certainly am.) It’s amazing that humans are as civilized as they are. When I see thousands of them maneuvering automobiles at high rates of speed on freeways I am filled with wonder at the ability of those animals to manipulate the controls in a way that results in such a small number of “accidents”, especially when taking into consideration that the vehicles are unnatural and there has been little evolutionary pressure applied to be compatible with machines.

8. Bee - February 6, 2007

I think ‘people who are dissapointed in people’ are really dissapointed by themselves. It’s a projection as well as an avoidance.

9. dorigo - February 6, 2007

Carl, it is true, we ask ourselves too much. But pushing up standards is a way to keep us going, a little bit like what happens to the economy. The moment we stop and stare at how good we are, we might be dead.

Car accidents are collateral damage… You should not be terrified, but certainly wary. Life was a risky business for our ancestors, and the elevation of our social standing has not saved from risks. An infection does not scare us much nowadays, but a speck of anthrax or Polonium-210 has started to.

In line with the comments to my “41” post: let’s try and optimistically live this life through, fortified in our knowledge that we should not worry too much: it will be over one day.


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