I don't think that's a good reference (and researchgate is known for questionable papers).jedishrfu said:I found this article on Relativistic Mechanics and Multiple Time Dimensions
https://www.researchgate.net/public...ivistic_mechanics_in_multiple_time_dimensions
The definition of that in the paper you referenced is that the "fifth dimension" is the Minkowski interval ##ds^2##, so if ##ds^2## is timelike, the paper says there are "two time dimensions". Which is nonsense.jedishrfu said:one question I have is what does it mean to have multiple time dimensions?
This isn't adding another time dimension. It's just picking a particular coordinate chart and assigning a special meaning to its coordinate time--in other words, LET. (Which is off limits for discussion at PF.)jedishrfu said:One possible scheme would be each object would have its own time based on its speed relative to other objects. Viewing a collection of objects then one could assign a clock to each one that represents the time that object is traversing due to its relative speed from a particular vantage point.
As an example, particles traveling from deep space to the Earth would have differing speeds and hence differing lifetimes like muons. You could model that.
No, you don't. You can't change the metric signature of spacetime by choosing coordinates. You can have a coordinate chart that has three timelike and one spacelike basis vector (in fact you can have one that has four timelike basis vectors), but that doesn't change the nature of the dimensions of spacetime. It just means you've picked a coordinate chart that will be very difficult to work with (since the metric will look very complicated in it--none of the basis vectors are orthogonal, there will be cross terms all over the place, and you won't be able to read off anything useful from the line element).jedishrfu said:Another place where multi time dimensions come into play is in faster than light frames of reference where you have three time-like dimensions and one space-like dimension.
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