Talk:Imaginary time

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I had been under the impression that just as instants in time are conventionally made to correspond to real numbers, imaginary time was made up of instants corresponding to imaginary numbers. But this article does not mention that. Was my impression mistaken? Michael Hardy 22:08, 19 January 2006 (UTC)

I believe that you are correct; I think an inclusion of that might make the article a bit clearer. Hawking used that explanation to rebuke a naive philosopher's attacks on imaginary time as a "mathematical trick with nothing to do with the 'real world'". However, it is sort of hard to tell exactly what it means for real time to correspond to real numbers and for imaginary time to correspond to complex/imaginary numbers.

But if I'm right, then this article fails to explain the concept. Can you? Michael Hardy 23:42, 27 February 2006 (UTC)

There are two very important aspects of imaginary time that are not mentioned. 1) imaginary (or Euclidean) time corresponds to equilibrium thermodynamics: if a system is held at a temperature T, one can set time= i /( k_B T ) where i is the imaginary number 2) Making this transformation converts the Schroedinger equation , which has wave solutions into a diffusion-like equation. This is much easier to calculate with and is the basis for most numerical methods to treat quantum systems with more than 3 particles. see articles on lattice guage theory or quantum monte carlo. These two aspects are of great practical importance in our understanding of quantum systems. Comment on whether this is too technical. Ceperley 02:39, 22 May 2006 (UTC)

I would not say it's too technical if it's the simplest way to explain it. But if added to the article, it should not be as terse as that. Michael Hardy 22:46, 7 June 2006 (UTC)