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What's the purpose of a second dimension of time in physics in layman terms?

From Wikipedia:

Speculative theories with more than one time dimension have been explored in physics. The additional dimensions may be similar to conventional time, compactified like the additional spatial dimensions in string theory or components of a complex time.

Based on the special orthogonal group $SO(10,2)$, representing the GUT spin group of the extended supersymmetry structure of M-theory, a "two-time physics" has been suggested.[1]

F-theory describes a 12-dimensional spacetime having two time dimensions, giving it the metric signature (10,2).[2]

The existence of a well-posed initial value problem for the ultrahyperbolic equation (a wave equation in more than one time dimension) demonstrates that initial data on a mixed (spacelike and timelike) hypersurface, obeying a particular nonlocal constraint, evolves deterministically in the remaining time dimension.[3]

Like other Complex number variables, complex time is two-dimensional, comprising one real time dimension and one imaginary time dimension, changing time from a real number line into a complex plane. Introducing it into Minkowski spacetime allows a generalization of Kaluza–Klein theory.[citation needed]

Now, from a layman perspective, it's difficult to understand what was said. So I am wondering if a second time dimension is something real or potentially real and what the second time dimension would imply about the nature of time, because to me it seems that this second dimension is not real and would just be used to formalize something mathematically to make the reality fit into a particular theory.

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For the benefit of the users of the Physics SE, I'll provide here the answer I came up with to this question when it was posted originally on the Philosophy SE, with some edits. I hope the experts here will provide heroyu with some useful commentary on this topic.

More information is needed here to determine what it is you wish.

To begin with, who asserts that time is two-dimensional? To a physicist, two-dimensional time represents a mathematical formalism that is sometimes useful for transforming certain physical phenomena between mathematical regimes, to make their interpretation more clear. On the other hand, to a philosopher, two-dimensional time means anything (s)he wants it to mean.

Having two dimensions of time in the physical realm would mean that in addition to being able to go forward and backward in time, you could also move sideways in time onto a different world line, then back sideways to join up again with one's original world line or any other world line in any other universe.

This means that one's sudden appearance on a new world line would occur with no history on that world line, and one's disappearance from it would then result in no future on it either. Occupants of those other universes containing those alternate world lines would also be able to pop into and out of our universe as well.

In short, sideways time allows movement into and out of every possible world line in every possible universe. Thank goodness it is impossible... But I admit that imagining it is possible would provide philosophers with a new sandbox in which to entertain themselves.

One hopes that some means would exist for keeping cats out of that sandbox...

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