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It’s easy, relatively speaking, to develop an intuition for higher spatial dimensions, usually by induction on familiar lower-dimensional spaces. But I’m having difficulty envisioning a universe with multiple dimensions of time. Even if such a thing may not be real or possible, it seems like a good intellectual exercise. Can anyone offer an illustrative example?

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    $\begingroup$ This is very very very far off from real physics, We have only one time dimension as far as we know. Why would you try to build an intuition into this? $\endgroup$ – Prathyush Nov 3 '12 at 2:55
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    $\begingroup$ @Prathyush see Qmechanic's nice answer, which is about serious physics (+1) ;-). It is (at least up to now) not forbidden to think and talk about physics that could be valid and most relevant at higher (not yet directly experimentally accessible) energy scales and that differs from the effective physical laws we observe at our low energy "everyday scales" ! $\endgroup$ – Dilaton Nov 3 '12 at 10:48
  • $\begingroup$ I asked a similar question as a comment on a previous question. It was a rather uninformed comment, as I saw 3+1 dimensions being addressed as a matrix with diagonal elements, I only asked why not two, as opposed to one, may be negative. I got a good response, apparently a trace of zero has bad implications, so I guess a possibility left is $diag(-1,-1,1,1,1)$, but again, I'm just making this all up physics.stackexchange.com/q/13451 $\endgroup$ – Alan Rominger Nov 7 '12 at 15:40
  • $\begingroup$ I've got a kind of sub-question to piggy back on this: If everything's relative aren't people experiencing different time effects in the same universe when one is moving much faster than the other? Arent the two subjects experiencing different "times"? $\endgroup$ – Len Feb 15 '18 at 16:55
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  1. Several authors (in particular Itzhak Bars) have written papers about two-time-physics that should help build intuition for the topic.

  2. Infinitely many 'times' appear in integrable systems.

  3. F-Theory, which is a 12 dimensional theory, has been described as having extra temporal dimensions, however see Wikipedia.

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Theories can be formulated in any number of space-time dimensions. Examples of multidimensional theories:

  1. F-theory, 12d theory with two times.

  2. S-theory, 13d theory with three times.

  3. Kalitzin's relativity with r-times or even infinite-dimensional times (the latter much less developed) was studied.

Indeed, I think to remember some people tried to understand quantum mechanics in a multitemporal set-up.

In philosophy, some people studied three-dimensional time theories. These times are called time, hyparxis and eternity.

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If you are happy to focus on the intuitive without worrying about too much maths, the classic work on multiple time dimensions in physics must surely be J W Dunne's The Serial Universe - the second edition, published in 1942, is shorter and (comparatively) more readable. It was the sequel to his bestseller An Experiment with Time and elaborated on the role of the observer in modern physics. His regress of multiple time dimensions was inhabited by a similar regress of observers, thus (in retrospect) proffering a solution to the Schroedinger's Cat + Wigner's Friend regress of discrete real observers.

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  • $\begingroup$ I agree that An Experiment with Time is a fascinating book, but "Mainstream scientific opinion remains that, while Dunne was an entertaining writer, there is no scientific evidence for either dream precognition or more than one time dimension and his arguments do not convince". $\endgroup$ – PM 2Ring Feb 6 at 12:34
  • $\begingroup$ At the time, mainstream science was split. See for example Herbert Dingle's contemporary commentaries in Nature. After WWII Dunne was largely forgotten and today's mainstream scientific opinion has barely even heard of him. Suffice to say that his case at least contains some intriguing ideas. (BTW, is it not the custom here to cite Wikipedia when you quote directly from it, especially when I wrote part of your quote and added a citation in support of it? I do not post here from ignorance or prejudice!) $\endgroup$ – Guy Inchbald Feb 6 at 13:44

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