Talk:Imaginary time

message: ::The Big Bang, for example, appears as a singularity in "regular time." But when visualized with imaginary time, the singularity is removed and the Big Bang functions like any other point in spacetime.
I don't doubt this, but it is just an incredibly interesting statement and one would like somewhere further to look on the subject that talks directly about this topic.  — Preceding unsigned comment added by 99.13.241.174 (talk) 21:18, 28 November 2012 (UTC)
thread_title: Would like Citation

message: 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)
replies: text: 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)
replies: text: 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)
thread_title: Comments by Michael Hardy

message: Does the existence of both real time and imaginary time mean that time is complex and therefore two-dimensional, at least at a quantum mechanical level? GilesW 11:19, 19 April 2007 (UTC)
replies: text: Yes. 16:28, 2 August 2010 (UTC)
replies: text: I would disagree. In theories of Relativity at least, real and imaginary times are treated as alternative interpretations or expressions of the equations. You have to choose which you want to work with and complex time cannot therefore arise. Quantum mechanics involves complex spatial expressions as well, but we treat that as an artefact of the mathematics and do not say that space is therefore six-dimensional. — Cheers, Steelpillow (Talk) 13:11, 30 October 2017 (UTC)

text:  As discussed in Talk:Complex_spacetime, considering spacetime over the complex numbers (complete field), rather than the real field is mainstream. Have a look at these recent articles on the importance of \(\mathbb{C}\) vs. \(\mathbb{R}\) (for the base field) when it comes to QM prediction results (DOI: 10.1038/s41586-021-04160-4; DOI: 10.1063/PT.6.1.20220120a) and complex-time (kime) for repeated measurement longitudinal processes (DOI: 10.1515/9783110697827; DOI: 10.1016/j.padiff.2022.100280). Iwaterpolo (talk) 15:38, 29 January 2024 (UTC)
thread_title:  Complex Time

message: This is also referred to as Euclidean time, correct?  --Starwed 04:27, 26 August 2007 (UTC)
thread_title:  Name 

message: Stephen Hawking and J. B. Hartle proposed in Physical Review D, volume=28, pages=2960ff (1983) that, under certain conditions of extremely high compression when the present universe was just beginning to expand after the "Big Bang", time may have been "imaginary" rather than "real".  The term "imaginary" as used by mathematicians and theoretical physicists does not mean "fictitious" but rather has a precise mathematical meaning often defined in the second year of secondary school algebra courses.  (One may look up imaginary number for further information.)  When time becomes "imaginary" one may replace, in any of the equations of physics, the time variable t with the quantity i τ in which i is the square root of the negative number minus one and the Greek letter tau τ represents "imaginary time".  In spite of the name "imaginary" the solutions to the equations are expected to apply to the "real" world, the universe that we inhabit.
Later, in A Brief History of Time Hawking proposed that "imaginary time" might prevail under all conditions of the universe we inhabit.  He said that under such conditions the universe would not be created at one point in time (the "Big Bang") and destroyed by collapse at a later time (the "Big Crunch") but would simply exist eternally, even though its inhabitants at certain points in its "evolution" are unable to examine it as a whole.
Regardless of the merits of this proposal, there is an important omission.  Hawking inserted "imaginary time" into Einstein's equations of general relativity or gravity, and into the quantum mechanical equations that govern the universe.  He then discussed the consequences of doing so, but he did not comment on the consequences of inserting "imaginary time" into Maxwell's equations, which govern all electromagnetic phenomena (including the wave equation that governs the propagation of light and heat).  I cannot describe the mathematical details here without going beyond the scope of this discussion page, but they may be confirmed by any physics professor who has taught a graduate course on electrodynamics, as I have.  The effect of "imaginary time" is to stop the propagation of all electromagnetic waves and to produce a universe without heat and light.  In a universe in which "imaginary time" prevails there can be no curvature in any electric field and therefore there can be no particles with electric charge like protons or electrons.  Without such particles there can be no material as we know it.  Therefore Hawking's proposed universe is apparently dark, frozen, and empty.  That is recognizably different from the universe we inhabit.
We therefore invite Professor Hawking to explain the effect of inserting "imaginary time" in Maxwell's equations.
--Origins Quester (talk) 13:47, 26 September 2011 (UTC)
thread_title:  Heat, Light, and Matter in a Universe Featuring Imaginary Time 

message: Some formatting errors have creeped into this articvle.  Can we fix it soon? Bearian (talk) 12:25, 23 September 2013 (UTC)
thread_title:  Format errors 

message: I liked the big quote from Stephen Hawking displayed on this page, but hadn't a clue where it came from. I've now found it in "The Universe In A Nutshell" p59. This kind of specific sourcing is always appreciated by those of us looking to verify Wikipedia information, so perhaps it would be a good idea to add it. Thanks.
Cjmonks (talk) 00:00, 2 May 2015 (UTC)
thread_title: Info on that Stephen Hawking quote

message: The article lead gives the impression that theories of imaginary time, e.g. in cosmology, treat it as a second time dimension, orthogonal to real time. My understanding is that this is false, it is merely an alternative formulation (or interpretation) of time in the equations of relativity. Treating spacetime as some four-dimensional manifold (which provides a solution to the equations of general relativity), we apply a metric to the general topological manifold in order to give things scale. Imaginary time is just a subtly different metric from real time, it does not change the topology of the manifold by adding an extra dimension. Nor can it be orthogonal to a time dimension which is not present. The lead needs amending accordingly. — Cheers, Steelpillow (Talk) 13:14, 30 October 2017 (UTC)
replies: text: Done. — Cheers, Steelpillow (Talk) 22:43, 1 November 2017 (UTC)
thread_title:  Real vs imaginary 

message: What the IP tries to add seemingly is related to imagination, not imaginary numbers. It is off-topic hence, even if the expression “imaginary time” in music exists. Incnis Mrsi (talk) 11:16, 6 May 2019 (UTC)
thread_title:  Music theory 

message: I am restoring the recently-reverted edit because it contains two citations and is a useful attempt to answer the clarification tag attached to some obscure jargon. That aspect deserves to stay. I am also editing it down to reduce any misplaced sense of OR. If any remaining OR is still suspected or shown, it can be dealt with as a supplementary issue. — Cheers, Steelpillow (Talk) 09:51, 9 October 2019 (UTC)
thread_title:  Green's functions 

message: The article says: In fact, the names "real" and "imaginary" for numbers are just a historical accident, much like the names "rational" and "irrational":
How was it an accident?  Rational numbers are those that can be expressed as a "ratio".
:Ratio is the Latin for "reason". Irrational originated as, and remains, a common synonym for "unreasonable". Thus, the numbers are deemed reasonable and unreasonable. We now know that is nonsense but the names have stuck. — Cheers, Steelpillow (Talk) 08:19, 21 September 2020 (UTC)
thread_title:  Rational or Irrational