Question

Is the time complex? $t= \rho e^{i\theta}$

$$||(t,x,y,z)||^2 =\rho^2 -x^2-y^2-z^2$$

The space-time has $5$ dimensions, $2$ dimensions of time and $3$ dimensions of space.

Can we make experiments of physics ? Or is the $5$ dimensional space-time just theorical?

Comments

Experiments have already been done - time is a one-dimensional variable; it is what the watches show.

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Why should "the time" be complex? And if so, why only time? What you are proposing is a complex time-coordinate (as opposed to proper time). Under Lorentz transformation (or more general coordinate transformations) space and time coordinates are mixed up, so all coordinates would have to be complex.

It would appear you are proposing a complex time coordinate in order to obtain the $(+,-,-,-)$ signature of the metric. This appears to be rather a weak justification (and reeks of $ict$), and is not straightforward to reconcile with the mixing of space and time coordinates, as complex space coordinates may introduce sign changes in the spatial part of the metric, thus thwarting the intention to provide a reason for the signature of the metric. 

Answer 1

In order for a coordinate to be called time, one needs to make sure that everything in the Universe has a to have a well defined sequential order with respect to it, otherwise becomes problematic to define proper causal relationships. This I believe will be problematic with 2-or-higher-D "times". And if a coordinate is not related to causality, why to call it "time" in the first place? It is just another coordinate like $\vec{r}$, or spin, or anything else.