Feynman's New Zealand lecture, Inca astronomy, rule and reason.

[Spinnor]

In Feynman's New Zealand lecture,



he points out how the Inca Indians were able to predict the motion of major heavenly bodies but did not understand the physics behind these motions (Let us assume that is true. We don't have, as Feynman points out, much recorded Inca history so it is possible they contemplated a sun centered solar system with planets, moons, and other stuff orbiting the sun and may have even come up with Newton's law of gravitation, big ifs).

I think Feynman pointed out that like the Incas we can predict much experiment, and like the Incas we have no picture (in the spacetime that the experiments occupy) that implies the quantum physics of nature.

Did Feynman consider such a picture tough or impossible to come up with? I think Feynman answers this question at the one hour, 8 minute mark of the video above, very tough.

Have any of our best physicists and mathematicians made any stabs at such a picture?

Any suggested reading would be welcome!

 

[Jolb]

Feynman talked a good deal about the "pictures" he and other quantum physicists use to understand quantum theory. (From "No Ordinary Genius" by Christopher Sykes, a sort of compilation of random things by and about Feynman.)

"Sometimes I wonder why it's possible to visualize or imagine reality at
all. (That sounds like a very profound philosophical question, like "Why is it possible to think?" But that's not what I really mean.) It's easy to imagine, say, the Earth as a ball with people and
things stuck on it, because we've all seen balls and can imagine one going
around the sun - it's just a proportional thing, and in the same way I can
imagine atoms in a cup of coffee, at least for elementary purposes, as
little jiggling balls. But when I am worrying about the specific
frequencies of light that are emitted in lasers or some other complicated
circumstance, then I have to use a set of pictures which are not really
very good at all - they're not good images. But what are "good images"?
Probably something you're familiar with. But suppose that little things
behave very differently than anything that was big, anything that you're
familiar with?

Animals evolved brains designed for ordinary circumstances, but if the gut
particles in the deep inner workings of things go by some other rules, and
were completely different from anything on a large scale, there would be
some kind of difficulty, and that difficulty we are in - the behavior of
things on a small scale is so fantastic, so wonderfully and marvelously
different from anything on a large scale! You can say, 'Electrons behave
like waves' - no, they don't, exactly; 'they act like particles' - no,
they don't, exactly; 'they act like a fog around the nucleus' - no, they
don't, exactly. Well, if you would like to get a clear, sharp picture of
an atom, so that you can tell correctly how it's going to behave - have a
good image of reality, in other words - I don't know how to do it, because
that image has to be mathematical. Strange! I don't understand how it is
that we can write mathematical expressions and calculate what the thing is
going to do without actually being able to picture it. It would be
something like having a computer where you put some numbers in, and the
computer can do the arithmetic to figure out what time a car will arrive
at different destinations but it cannot picture the car.

I guess my feelings would somewhat echo Feynman's: I think in order to understand quantum physics, quantum physicists use a set of pictures which are abstract mathematical pictures similar to the diagrams in math books, along with some pictures of the classic QM experiments (e.g. tunneling, double slit, stern gerlach). But it's sort of a piecemeal picture since you can't easily put it all together into one nice neat master picture of what really goes on in the full formalism of quantum theory.

 

[bhobba]

I think the issue with QM is not so much we can't get an intuitive grasp, and even 'pictures' of what's going on - I think we can. But they are different from our everyday intuition and pictures we have of the classical everyday world.

I posted in another thread how I picture QM:
Here is a way of looking at QM at a foundational level that may make it clearer. Suppose you have a system and some observational apparatus that has n possible outcomes and you associate a number with each of the outcomes. This is represented by a vector of size n with n numbers yi. To bring this out write it as Ʃyi |bi>. Now we have a problem. The |bi> are freely chosen so nature can not depend on them. We need a way to represent it that does not depend on that. The way QM gets around it is to replace the |bi> by |bi><bi| giving Ʃyi |bi><bi|. This is defined as the observable of the observational apparatus. It says to each such apparatus there is a Hermitian operator whose eigenvalues are the possible outcomes of the observation. This is the first axiom of QM. The second axiom says the expected outcome of such an observation is Tr(PR) where R is the observable of the observation and P is a positive operator of unit trace called the state of the system. This can be proven by what is known as Gleason's Theorem if we assume something called non contextuality that you can read up on if you wish. So while the second axiom is not implied by the first it is strongly suggested by it - depending on exactly what you think of non-contextuality.

The thing is its a picture in a mathematical sense based on a key idea - the outcomes of observations should be expressed in a coordinate free way. I do not think it can be done in terms of everyday pictures.

Here is another way of picturing it that brings out the essential importance of entanglement:
http://arxiv.org/abs/0911.0695

To me its not that we lack pictures - its that they are of a different sort.

Thanks
Bill