After reading several of Hawkins's lectures, I have been stuck on this issue for several days. I can not seem to wrap my mind around it. I was hoping someone of this forum would be willing to explain it in Layman's terms. Thanks

After reading several of Hawkins's lectures, I have been stuck on this issue for several days. I can not seem to wrap my mind around it. I was hoping someone of this forum would be willing to explain it in Layman's terms. Thanks
Hello,
I didn`t read Hawking lectures so I don`t know his usage of imaginary time but imaginary time is standard technique in thermal quantum field theory. It is not something you need to interpret in real world just convenient formalism. It can be shown for example that Greens functions are periodic in time if we perform transfrmation where is imaginary time and real time. Therefore Greens functions in energetical representation will contain only discreete frequencies callet Matsubara frequencies.
Also for example transition amplitude between two states can be written as . We know from statistical physics that partition function (or statistic sum or whatever you call it) is where T is temperture and H Hamiltonian. So if we say that (we say that time is imaginary inverse of temperature) then we can calculate partition function as sum over expectation values of evolution operator in all states.
It can be used in relativity if you want to avoid calculations in Minkowski spacetime where and instead calculate in Euclidean space where
with . Don`t know what its good for though here as relativity isn`t my area.
To sum: imaginary time is just mathematical trick for convenient calculations.
Last edited by Gere; September 16th, 2013 at 02:20 PM.
Just like imaginary numbers that comes from negative roots!
imaginary mass comes from imaginary inertia too
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