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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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Niels Nielsen answers the question of multiple dimensions of time by saying, in part, "Thank god it's impossible." So my response is, and then what about Itzhak Bars? His claim is that for 4 space dimensions and 2 time dimensions you get at least the Standard Model. His depiction of how that works is that if you move circularly around the 'space' axis in the time 'plane' you move through gravitational and other states, and calls these phenomena 'shadows' in his talk -- by which I think he means projections into 4 space.

The form of the projections is that in his 4+2 model, to find a "shadow" to which a particular arrangement corresponds in 3+1, you reduce the dimensions by 1 space and 1 time dimension by applying a gauge, with the net result that for simple reductions there are 4x2 of them which he diagrams in his talk and in his paper. They are not so simple as moving to a different world line.

He has a layman accessible video on YouTube.

Several StackExchange queries have been answered by "oh that's impossible". I am responding that there is someone out there who has a theory of 4+2 geometry that bears a better response than dismissal.

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  • $\begingroup$ I don't know that there's anything wrong (or right) with the content of this answer, but it's hard to understand now because you're responding to someone and we don't know (a) who that is or (b) what they said. Can you write this as a stand-alone answer? There shouldn't be any need to reply (and you cannot be sure that whatever you're referencing in reply will still exist when your answer is read). $\endgroup$
    – Brick
    Jun 24, 2021 at 17:32
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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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What's the purpose of a second dimension of time in physics in layman terms?

In physics there are generally three possible purposes for any theoretical construct:

  1. A theoretical construct may be introduced to provide consistency with experiment. This is considered the highest and most important purpose that any theoretical construct can serve. In the case of multiple time dimensions, there is currently no experimental evidence that it explains that is not already explained by other constructs.

  2. A theoretical construct may be introduced to provide theoretical or mathematical consistency between other theoretical constructs that would otherwise conflict with each other, for example quantum field theory is such a construct which was developed largely to overcome a conflict special relativity and historical frameworks for quantum mechanics. In the case of multiple time dimensions, there is currently no outstanding conflict that it resolves.

  3. A theoretical construct may be introduced to generate professional publications. Such constructs need not be constrained by any experimental need nor solve any theoretical conflict, but can simply be "what if" type constructs. They may have no other current purpose, but it is entirely possible that at some future date they may be found to have some other purpose that was not known at the time of their development. This is the purpose of current theories of multiple time dimensions. They are simply proposed, the implications are studied, and publications are produced.

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