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## Main Question or Discussion Point

Just what would a universe be like if it had two time dimensions?

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Just what would a universe be like if it had two time dimensions?

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Paul Colby

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How would you generalize equations of motion? What would the action principle look like?

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OmCheeto

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hmmm....Just what would a universe be like if it had two time dimensions?

I've heard about something called "spooky at a distance".

I do not understand it at all, but from what I've heard, it seems to violate "my" notion of our one dimension of time.

Perhaps we already have two time dimensions.

hmmmm.... Perhaps this thread belongs in the sci-fi section.

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A paper by Itzhak Bars http://de.arxiv.org/abs/hep-th/9809034

And more recent results can be found at INSPIRE

I'm not sure how interesting it is but it does exist (in 12 dimensions or more)

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arivero

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For the sake of discussion, I would like to see how it works with two macroscopic time dimensions and flat space, with minkowsky product coming from the matrix diag(1,1,1,-1,-1).I'm not sure how interesting it is but it does exist (in 12 dimensions or more)

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Maybe some day I'll find the time to check it out.

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fresh_42

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Where's the problem is a macroscopic diag(1,1,1,-1,-1) world?

Maybe some day I'll find the time to check it out.

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A guess would be that consistency of dimensional reductions can do some weird things.

I'm only a little aware of the consistency of those procedures so I have to look into it on Monday since the document that might give me a hint whether more time directions mess things up is in my dorm room.

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arivero

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For a classical non-relativistic particle, it seems that instead of conditions in two extremes [a,b] in the time-line we should impose them in a circle of the time-"plane".What would the action principle look like?

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fresh_42

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Even if we get the geometry somehow explained, what about entropy?For a classical non-relativistic particle, it seems that instead of conditions in two extremes [a,b] in the time-line we should impose them in a circle of the time-"plane".

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I am not qualified to answer any of this ( not having studied this type of PDE ), but I would also be interested to hear what the mathematicians here have to say on this. My intuition tells me that things won't work out nicely if you add an extra ( macroscopic ) time dimension, but I may well be wrong. And then of course there is the option of having the extra dimension compactified.

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Fervent Freyja

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Two different universes.

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Well, for one you'd have trivially easily occurring closed timelike curves.For the sake of discussion, I would like to see how it works with two macroscopic time dimensions and flat space, with minkowsky product coming from the matrix diag(1,1,1,-1,-1).

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Demystifier

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The Cauchy problem is not well posed for such spacetime signatures. See e.g.

I am not qualified to answer any of this ( not having studied this type of PDE ), but I would also be interested to hear what the mathematicians here have to say on this. My intuition tells me that things won't work out nicely if you add an extra ( macroscopic ) time dimension, but I may well be wrong. And then of course there is the option of having the extra dimension compactified.

http://arxiv.org/abs/gr-qc/9702052

http://arxiv.org/abs/gr-qc/9901045

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I suspected that, thank you ! So the (3+1) case really does seem to have a privileged character...The Cauchy problem is not well posed for such spacetime signatures. See e.g.

http://arxiv.org/abs/gr-qc/9702052

http://arxiv.org/abs/gr-qc/9901045

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arivero

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We could try some list of priviledged D = d + t combinations. To start with, let me note the classical signatures to have susy and other stuff related to division algebras:privileged character.

R: d - t = 1

C: d - t = 2 This is our spacetime, 3-1=2

H: d - t = 4

O: d - t = 8. I think this is the 9-1 = 8 of string theory and perhaps the 10 - 2 mentioned by JorisL above

I am not sure if there is some mod8 periodicity here or the list just stops at 8.

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The Cauchy problem is solved for linear functions. See hereThe Cauchy problem is not well posed for such spacetime signatures. See e.g.

http://arxiv.org/abs/gr-qc/9702052

http://arxiv.org/abs/gr-qc/9901045

http://rspa.royalsocietypublishing.org/content/royprsa/465/2110/3023.full.pdf

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Here one impressing work as you see the mathematical beauty in it.

http://arxiv.org/abs/0804.1585

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haushofer

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Isn't that related to the fact that AdS-space can be described as being embedded in Minkowski spacetime with

A paper by Itzhak Bars http://de.arxiv.org/abs/hep-th/9809034

And more recent results can be found at INSPIRE

I'm not sure how interesting it is but it does exist (in 12 dimensions or more)

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Maybe if I can find some time in the next couple of weeks I'll look into it.

This seems like the idea that underlies the arxiv-notes I linked.

I'm not well-versed in the terminology of a "target space" so I'm not sure this would lead to the AdS group?The formalism is a simple ##Sp(2, R)## gauge theory for particles ##X^M (\tau )## (zero-branes) which arises from a basic idea as follows. ##Sp(2, R)## is the automorphism symmetry of the quantum relations ##[x, p] = i## and treats ##(x, p)## as a doublet. The idea is to turn this global symmetry of Quantum Mechanics

into a local symmetry of a theory. The 3-parameter local symmetry ##Sp(2, R)## includes ##\tau##-reparametrizations as one of its local transformations, and therefore it can be regarded as a generalization of gravity on the worldline. The ##Sp(2, R)## gauge theory is non-trivial and physically consistent only if the zero

brane has two timelike coordinates ##X^0(\tau)##, ##X^{0\prime}(\tau)## in target space, and has a global symmetry SO(d, 2), which is the Lorentz group with two times.

Neither what ##d## means in this context, from the abstract it follows that ##D## is the number of spacetime dimensions.

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ohwilleke

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Flat (in the sense of lacking height, not necessarily topologically) and timeless, or one dimensional motion in space up and down a single line with time.Just what would a universe be like if it had two time dimensions?

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Starting at event 'A', the following event 'B' could be any number of different things depending on the trajectory which an observer is travelling through the 2D time.

It would be possible to travel in a circular fashion through time, so that one could return to the exact same circumstances as 'last week' just by waiting.

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If a set of physical laws could be described at all, they would impose local or global constraints on variables over the manifold. We could, for instance, define two orthogonal time directions as "positive", and look for laws where events depend only on regions with lower values for both coordinates. An observer at any point would "remember" such a two dimensional region, rather than a trajectory. This would rule out circular causation.Starting at event 'A', the following event 'B' could be any number of different things depending on the trajectory which an observer is travelling through the 2D time.

It would be possible to travel in a circular fashion through time, so that one could return to the exact same circumstances as 'last week' just by waiting.

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ohwilleke

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Apologies for not carefully reading "two <i>time</i> dimensions" as opposed to merely two dimensions. I wouldn't have been so flip if I had read more carefully.Flat (in the sense of lacking height, not necessarily topologically) and timeless, or one dimensional motion in space up and down a single line with time.

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naima

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Haven't 3 timelike directions in a black hole?