Guide Quantum Potential: Physics, Geometry and Algebra (SpringerBriefs in Physics)

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For example, string theory is shockingly good at counting how many curves of different kinds you can draw on certain varieties. Thus, we now see string theorists talking with algebraic geometers, each able to surprise the other with their insights.


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In particular, his page unpublished manuscript Pursuing Stacks , written in , made a big impression on me. At first this idea may sound just like algebraic geometry, where we use algebra to describe geometrical shapes, like curves or higher-dimensional varieties. Thanks to my work on physics, his proposal was tremendously exciting when I came across it.

It seems that until we do this, our understanding of the fundamental laws of physics is doomed to be incomplete. One reason is that quantum physics is based on algebra, while general relativity involves a lot of topology. But that suggests an avenue of attack: If we can figure out how to reduce topology to algebra, it might help us formulate a theory of quantum gravity. My physics colleagues will let out a howl here, and complain that I am oversimplifying.

So, starting in the s, I tried to understand the powerful abstract concepts that Grothendieck had invented—and by now I have partially succeeded. Some mathematicians find these concepts to be the hard part of algebraic geometry. They now seem like the easy part to me. The hard part, for me, is not these abstract concepts but the nitty-gritty details.

But there is also a lot more. A student of physics once asked a famous expert how much mathematics a physicist needs to know.

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Until last year, algebraic geometry never rose to the top of the list. What changed? I realized that algebraic geometry is connected to the relation between classical and quantum physics. Classical physics is the physics of Newton, where we imagine that we can measure everything with complete precision, at least in principle. And in classical mechanics, we assume we can measure this arrow precisely.

In quantum mechanics—a more accurate description of reality—this turns out not to be true. For example, if we know how far this arrow points in the x direction, we cannot know how far it points in the y direction. This uncertainty is too small to be noticeable for a spinning basketball, but for an electron it is important: Physicists had only a rough understanding of electrons until they took this into account.

Thank you for your interest in our all-inclusive travel package to the fourth dimension. Here are some of the most frequently asked questions we get from prospective explorers. So far, none of our clients have returned—or even sent a text—so That is, they start with the classical description of some physical system, and they want to figure out the quantum description. There is no fully general and completely systematic procedure for doing this. This should not be surprising: The two world views are so different. Community Reviews. Showing Rating details.

More filters. Sort order. Feb 06, Mark Moon rated it liked it Shelves: r , subject-physics , library-read. Neither coherent nor well-edited, but a decent guide to recent developments in de Broglie-Bohm quantum mechanics. Kaiser rated it it was amazing Feb 07, Pt Books added it Jan 14, Nitin CR added it May 15, Chris Aldrich added it May 29, Mohammad Nourbakhsh added it May 08, R marked it as to-read May 26, Brennan marked it as to-read Sep 08, There are no discussion topics on this book yet.

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Quantum Potential: Physics, Geometry and Algebra

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More filters. Sort order. Feb 06, Mark Moon rated it liked it Shelves: r , subject-physics , library-read. Neither coherent nor well-edited, but a decent guide to recent developments in de Broglie-Bohm quantum mechanics.

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