- #1
Jupiter60
- 79
- 22
Just what would a universe be like if it had two time dimensions?
hmmm...Jupiter60 said:Just what would a universe be like if it had two time dimensions?
JorisL said:I'm not sure how interesting it is but it does exist (in 12 dimensions or more)
Where's the problem is a macroscopic diag(1,1,1,-1,-1) world?JorisL said:I have absolutely no idea, I encountered a mention of it in a master thesis (and some articles I believe).
Maybe some day I'll find the time to check it out.
Paul Colby said:What would the action principle look like?
Even if we get the geometry somehow explained, what about entropy?arivero said: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".
arivero said: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).
The Cauchy problem is not well posed for such spacetime signatures. See e.g.Markus Hanke said:From a purely mathematical point of view, having an additional time dimension would fundamentally change the form of the general wave equation, turning it into what I believe is called an "ultra-hyperbolic equation" ( correct me on this if I'm wrong ). The question then becomes how the solutions to this equation behave under a given set of initial values - for example, in a theory of electromagnetism in (3+2) dimensions, do we still get a nice, well behaved wave solution, or do we get something that evolves chaotically ? Or worse still, would we be faced with a situation where no general solution even exists ?
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.
Demystifier said: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
Markus Hanke said:privileged character.
Demystifier said: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
Isn't that related to the fact that AdS-space can be described as being embedded in Minkowski spacetime with two timelike directions? (the AdS group is SO(D-2,2) )JorisL said:The idea of two time directions is sometimes used in string theory/supergravity.
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)
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.
Jupiter60 said:Just what would a universe be like if it had two time dimensions?
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.rootone said:Starting at event 'A', the following event 'B' could be any number of different things depending on the trajectory which an observer is traveling 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.
ohwilleke said: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.
No. Black hole spacetimes are globally Lorentzian; i.e., with one timelike direction.naima said:Haven't 3 timelike directions in a black hole?
A universe with two time dimensions is a hypothetical concept in physics where time is described by two independent variables instead of the usual one. This means that events can be measured and described using two different time scales.
In a universe with two time dimensions, time would not be linear but instead have two perpendicular axes. This would mean that time would move in two different directions at the same time, making it difficult to predict and understand the behavior of objects in this universe.
In a universe with two time dimensions, the concept of causality would be disrupted. This is because events could occur simultaneously or in reverse order on the different time scales, making it challenging to determine the cause and effect relationships between them.
Life in a universe with two time dimensions would be vastly different from what we know. The laws of physics would be dramatically altered, and it is unlikely that life as we know it could exist in this type of universe.
Currently, there is no evidence to support the existence of a universe with two time dimensions. This concept is purely theoretical and is still being explored and debated by scientists. However, some theories in physics, such as string theory, suggest the possibility of multiple dimensions, including time dimensions.