Talk:Imaginary time

Would like Citation

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)

Comments by Michael Hardy

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)

An additional 'clue' that an imaginary time axis is relevant to real physics lies in relativistic formula for "distance" =√∆d² - ∆t² . If the universe is actually built on imaginary time τ ≈ i•t, then that peculiar '-' sign is there because we are [for whatever reason] using t, where squaring iτ=-t².

Complex Time

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)

Yes. 16:28, 2 August 2010 (UTC)Patsobest (talk)

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)

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)

Name

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

Please add Stephen Hawking quotation

Source : http://everythingforever.com/hawking.htm

Stephen Hawking : "...This might suggest that the so-called imaginary time is really the real time, and that what we call real time is just a figment of our imaginations. In real time, the universe has a beginning and an end at singularities that form a boundary to space-time and at which the laws of science break down. But in imaginary time, there are no singularities or boundaries. So maybe what we call imaginary time is really more basic, and what we call real is just an idea that we invent to help us describe what we think the universe is like." Softvision (talk) 12:17, 1 August 2009 (UTC)

This quote does not appear to convey useful information, and the web site you link doesn't provide a citation for it (it just says, "in a lecture paper"). If you want to include a quote from Hawking about imaginary time, by all means, but that quote should either come from a refereed journal paper he wrote about imaginary time, or from a similarly technical context. For more information, please read Wikipedia's "reliable source" policy, with special attention to the section about sources for articles about scientific topics. --Christopher Thomas (talk) 06:22, 5 August 2009 (UTC)

It's from his popular book A Brief History of Time (1990), not a technical paper; but it's been widely quoted and commented on in these books. It might be sensible to report some of the reaction to it, like the guy who says Hawking here "only adds to the confusion".

An extensive point/counterpoint about the book would probably be best left for the A Brief History of Time article. What I'm concerned with here is that the quote chosen doesn't seem to _say_ much from a technical perspective, and I'm even less certain what User:Softvision is trying to use it to say. For context, see the thread below, from Talk:Time. --Christopher Thomas (talk) 07:31, 5 August 2009 (UTC)

It is interesting, that this article is adequate, but qutation of the author of this idea is inadequate (widely quoted and commented on in these books). Quite strange. ;-) Softvision (talk) 22:15, 7 August 2009 (UTC)

Imaginary time

According to Stephen Hawking (reliable source), the time is imaginary. If time is imaginary, than according to the current SI metre unit definition, the space is imaginary. If time and space are imaginary, the speed of light is imaginary. If speed of light is imaginary, the light itself can be imaginary. If light is not imaginary, then ... Softvision (talk) 20:51, 31 July 2009 (UTC)

Please provide a page number and book/article reference. You can construct coordinate systems where time is imaginary, but I strongly suspect you're misreading Hawking's statements. --Christopher Thomas (talk) 21:02, 31 July 2009 (UTC)

Stephen Hawkings - Universe documentary + (http://everythingforever.com/hawking.htm).

Stephen Hawking:"...This might suggest that the so-called imaginary time is really the real time, and that what we call real time is just a figment of our imaginations. In real time, the universe has a beginning and an end at singularities that form a boundary to space-time and at which the laws of science break down. But in imaginary time, there are no singularities or boundaries. So maybe what we call imaginary time is really more basic, and what we call real is just an idea that we invent to help us describe what we think the universe is like."

From this it is realy not clear, what is real and what is idea, what is physical and what is imaginary. "If universe has a beginning and an end ... the laws of science break down." Is the only solution to this to preserve "beginning and an end" of the real time, and to create imaginary time ? It is possible, that I have desinterpreted the context a little bit. But, what is the meaning of imaginary time in context of the speed of light ? I have to study more this subject. I wanted to stress that time cannot be nonexisting or unreal. However, I consider the concept of imaginary time as synthetic construction and therefore unreal. I do not think that imaginary time is necessary to extend our knowledge about reality. Softvision (talk) 21:56, 31 July 2009 (UTC)

You should probably start by reading the actual refereed publications Prof. Hawking has produced. Anything shown on a TV show is dumbed down enough to be very misleading. The documentary seems to be referring to applying a different/transformed coordinate system and calling it "time" for purposes of solving the GR equations, but again, check the publications (not television documentaries) to find out what he's actually saying. --Christopher Thomas (talk) 23:42, 31 July 2009 (UTC)

..."what we call real is just an idea (figment of our imaginations)"... According to Stephen Hawking (reliable source), the real time is just an idea (figment of our imaginations) that we invent to help us. Do you think this is better ? Than according to the current SI metre unit definition the space is just an idea (figment of our imaginations) that we invent to help us... you can move forward and backward along imaginary time, just like you can move right and left in space - is this real ? Softvision (talk) 23:54, 31 July 2009 (UTC)

Christopher brings up a good point. What you're currently proposing doesn't use very good sourcing (peer-reviewed pubs are the best) and extrapolates a ton. It's also very philosophical and to me doesn't mean anything. I think that it's likely, as Christopher said, a simplification of a coordinate transformation. Awickert (talk) 00:55, 1 August 2009 (UTC)

"In mathematics and its applications, a coordinate system is a system for assigning an n-tuple of numbers or scalars to each point in an n-dimensional space." Are there any experimental proofs of the existence of other dimensions, than three space dimensions and one time dimension ? If such experimental confirmations do not exist, coordinate system assigned to the real space-time can have only four independent "numbers". To what real entity is the imaginary component of the imaginary time assigned ? If there is no real entity of imaginary time assignment, the imaginary component of the imaginary time is only unreal theoretical idea.

It is important to consider the time entity in context of the speed of light physical phenomenon. The speed of light is fundamental reality and the significant fundament of theoretical physics. The meaning of the speed of light is essentially dependent on the concept of the time. According to current SI units definitions, the time unit is fundamental independent unit. It could be very dangerous, to undermine the concept of time.

I think, that the article Imaginary time should be marked as speculative and inconsistent with the fundaments of theoretical physics and reality. This section should be moved to the Imaginary time article discussion page. Softvision (talk) 10:56, 1 August 2009 (UTC)

Firstly, if you have objections to the imaginary time article, you should bring those objections up at talk:imaginary time, not here. Secondly, the imaginary time article seems to be well-sourced and to describe topics and techniques that physicists do use and have published in detail about, so it does belong in Wikipedia. --Christopher Thomas (talk) 13:14, 1 August 2009 (UTC)

I have moved this section here from the Time article discussion. Softvision (talk) 23:14, 1 August 2009 (UTC)

Do you mean that well sourced nonsense should be presented, or propagated, as a valid information, not marked as speculative and inconsistent with the fundaments of theoretical physics and reality ? I think that there are many well sourced nonsenses. Truth and reality are the best reliable sources. Softvision (talk) 23:23, 1 August 2009 (UTC)

I mean that if it's well-sourced, it probably isn't nonsense. Please make an effort to track down the referenced publications, read them, and understand them. After that, by all means raise concerns, but you don't seem to be interested in doing this. --Christopher Thomas (talk) 06:17, 5 August 2009 (UTC)

Please, answer these questions : To what real existing dimension is the imaginary part of imaginary time assigned ? What is the meaning of the speed of light phenomenon, if "what we call real time is just an idea (figment of our imaginations)" ? Softvision (talk) 16:22, 6 August 2009 (UTC)

Energetical balance of valid experimental data confirms rapid increase of causal energy needed to create kinetic effects near the speed of light. This is most important evidence of existence and character of the causal speed limit. That means, the causal speed limit is not only the separate limit of the "light" propagation, but it has deep fundamental physical context. The speed of light phenomenon should be considered in this context. The speed of light is not conversion factor. The speed of light phenomenon is essential fundamental physical cause that should be considered completly and seriously. The meaning of the speed of light is essentially dependent on the concept of the time. According to current SI units definitions, the time unit is fundamental independent unit. It could be very dangerous, to undermine the concept of time. (already partially undermined)

"In mathematics and its applications, a coordinate system is a system for assigning an n-tuple of numbers or scalars to each point in an n-dimensional space." If the n-dimensional space is the real space-time, then you can assign as "numbers" in a coordinate system only real dimensions. Universe has three same dimensions and one specific dimension. That is the reason, why we have two types of units. There is no way to constitute the real coordinate system on one type of unit.

Solving one inconsistency in theory with another inconsistency in theory is escapade.

I think, that the article Imaginary time should be marked as speculative and inconsistent with the fundaments of theoretical physics and reality. Softvision (talk) 22:27, 7 August 2009 (UTC)

We cannot ask if a model corresponds to reality, because we have no independent test of what reality is. All we can ask is whether the predictions of the model are confirmed by observation. Models of quantum theory use imaginary numbers, and imaginary time in a fundamental way. These models are confirmed by many observations. So imaginary time is as real as anything else in physics. I just find it difficult to imagine.

Stephen Hawking —Preceding unsigned comment added by TimBowe92 (talk • contribs) 12:29, 27 November 2009 (UTC)

It seems to me that this article should be marked

I am a quite smart guy, science is somewhere between a hobby and an interest, and yet this article is all Greek to me. However, if you more well-versed individuals agree that this is as simple as it can be worded, then I trust you. Ethalehow (talk) 06:39, 6 May 2010 (UTC)

Heat, Light, and Matter in a Universe Featuring Imaginary Time

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)

Format errors

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

Info on that Stephen Hawking quote

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)cjmonks

Real vs imaginary

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)

Done. — Cheers, Steelpillow (Talk) 22:43, 1 November 2017 (UTC)

Music theory

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)

Green's functions

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)

Rational or Irrational

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)