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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)
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)
But if I'm right, then this article fails to explain the concept. Can you? Michael Hardy 23:42, 27 February 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.
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)
This is also referred to as Euclidean time, correct? -- Starwed 04:27, 26 August 2007 (UTC)
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)
Moved from Talk: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)
New material starts here. |
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
This article may be too technical for most readers to understand.(September 2010) |
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)
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)
Some formatting errors have creeped into this articvle. Can we fix it soon? Bearian ( talk) 12:25, 23 September 2013 (UTC)
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
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)
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)
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)
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".
This article is rated Stub-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | |||||||||||
|
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)
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)
But if I'm right, then this article fails to explain the concept. Can you? Michael Hardy 23:42, 27 February 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.
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)
This is also referred to as Euclidean time, correct? -- Starwed 04:27, 26 August 2007 (UTC)
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)
Moved from Talk: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)
New material starts here. |
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
This article may be too technical for most readers to understand.(September 2010) |
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)
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)
Some formatting errors have creeped into this articvle. Can we fix it soon? Bearian ( talk) 12:25, 23 September 2013 (UTC)
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
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)
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)
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)
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".