Multiple Time Dimensions

[PatrickPowers]

Interesting! I don't see how you can require it be continuous. Life is often discontinuous. I'm not sure why you want this requirement.

[quickfur]

I meant continuous in the sense that no matter which time-path you take, events always have some rationalizable connection with each other. Of course, nothing inherently requires continuity... but it's just so much harder to reason about things if in going from one time step to another there are sudden discontinuous leaps -- it would break causality along certain paths and make event sequences arbitrary and difficult to reason about.

Of course, discontinuous changes may also be convenient excuses for rationalizing things like magic -- one could claim that magic is essentially the effect of somebody turning 90 degrees into the orthogonal time axis, and rewriting history in a way that causes a continuity gap.

[Secret]

Quickfur, you might be interested in this

http://chat.stackexchange.com/transcrip ... 1#26393411
Roughly 2 weeks ago, I attempt to do a back in the envelope modelling of a 2 time scenario that end up with result similar to yours. Specifically, that the history of the evolution of the system becomes dependent on the direction you are facing in the 2 time plane, but the whole thing is actually consistent (i.e. no matter which path you are going in the time plane, the system evolves without any discontinuity when it moves from one state to another)

I then asked the physics students and professors there on how to make sense of my results. They then said the hamiltonian (something that describes the evolution of the system with a linear parameter known as time) can only afford a single parameter for the evolution, thus a 2 time hamiltonian equation is meaningless

Initially, I was thinking that if the calculation works, I am going to introduce a way to change the time component of the 5-velocity (a generalisation of the 4-velocity in relativity) by allowing each time axes to dilate differently so that if the observer accelerate in some direction, it can change its 5-velocity and thus seeing (in my toy model) a energy distribution that differs from what is expected if there's only one time axis

I am pretty sure there's a way to circumvent the limitation by somehow generalising the hamiltonian to allow more than one evolution parameter.

Meanwhile there are many theoretical work done on speculating 2 time physics when I check the wikipedia article on "multiple time dimensions" and they got various results

[quickfur]

Well, of course a 2-time Hamiltonian has no meaning -- because everything we know about physics -- and therefore all the mathematical models built around it -- assumes linear time!! Obviously, if we're going to model a universe with 2 time dimensions, we're going to need a radically different model of physics from the ground up. Don't expect existing models to work without some major restructuring. I also wouldn't expect that any of what we observe in our linear-time universe would generalize to 2D time; almost all of our physical perceptions (and therefore, mental models of how the universe works) are based on linear time. Even the way physical objects interact are bound to linear time. In fact, even the very definition of an "interaction" depends on linear time (there's a state "before" the interaction, and a state "after" the interaction -- the meaning of "before" and "after" becomes ambiguous once you have 2D time).

So I wouldn't expect that the physics of a universe with 2D time would be anything even remotely resembling what we'd intuitively expect. Before we even get to physics equations and stuff, we'd have to have a pretty radical re-thinking of what "physics" even means in the context of 2D time. For example, objects would not have a single trajectory, but would fan out into a 2D plane of trajectories, a continuum of trajectories, probably all different from each other. So even the meaning of time-evolution is undermined, since there's a starting state, but the meaning of "final state" is ambiguous because there's a continuum of final states, all different from each other.