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This is not a question asking why our universe is 1T+3D dimensional, and hence not about how the various models such as Itzhak Bars and F theory can incoporate multiple time into a model to describe our universe. It is about the interpretation of hypothetical data that suggests of possible microscopic spatial and temporal dimensions that can be manifested in particle experiments.

If I understood correctly the prediction of string theory about higher dimensions, presence of extra spatial dimensions can be inferred from the discovery of a sequence of particles that are massive as their momentum in the extra dimension manifest as some extra energy-momentum in our 4 dimensional spacetime, and such sequence will be in a pattern e.g. 1 unit different in mass from one member to the next. because the microscopic dimensions are compactified and finite

But what about microscopic temporal dimensions (which is compatible with reality as microscopic dimensions cannot violate causality). If they are present, how will fields in them manifest within our 4 dimensional spacetime. That is, what will we expect the particles that carry information about it will behave or look like in the data?

How do we determine the type of microscopic dimension that is present if given some particle data that suggests their existence?

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    $\begingroup$ I'm not sure this is a well - posed question: we can't really detect "dimensions" in a particle experiment, we detect particles. If the detections agree with the predictions of a theory that posits extra dimensions (and not with those of theories without), then we would say that we have "detected extra dimensions". So the nature of the extra dimensions is determined by our theories, which mostly posit extra spatial dimensions, not by specific properties of the experimental data as such. $\endgroup$ – ACuriousMind Oct 11 '16 at 18:18

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