I am asking this question completely out of curiosity. The other day, my roommate, by mistake, used 'Light year' as a unit of time instead of distance. When I corrected him (pedantic, much), he said the following:

"Units are relative. And according to Fourier Transforms, units can be changed so Light year is a unit of time."

That got me thinking and I read up Fourier Transforms on wikipedia but couldn't find anything about using a unit in one domain as a unit for another measurement. I do agree that units (particularly, base units are relative. eg: the meter), but does his statement make any sense?

EDIT
Thank you everyone for all the answers. It isn't so much to in it in or prove a point as it is to understand the concept better. Anyways this is his response after I showed him this thread. Any comments would be appreciated.

His response:
Nevermind, for the first time I accept I was wrong. BUT using lightyears to measure time is possible. My example didn't make sense bacause I was wrong when I meantioned that I'm still measuring dist. If you have a signal in time domain and ...take the FT, I get a signal which DOES NOT HAVE to be in frequency domain. Clarify this to the guy who posted last. Now the new signal is in a domain defined by me and so is its units. This signal although not equal to the original signal, still represents that if ya take an inverse FT. So, the idea of time will still be there. Now coming back to our case: lightyears here is not the lightyears you are used to read when dealing with distance. It represents time.


Question: Do parallel realities take precedence over time travel in the Star Trek Universe?
Answer: Since the point of diversion is in the 23rd century, it makes sense (in Star Trek physics) that any point before would be in the same universe/timeline/reality.

There are other points where various characters have travelled back in time, where the two "timelines" are the same and thus Pine's Kirk and Shatner's Kirk could meet:


The Bell Riots (and other brief spots in time where O'Brien and Kira went)
Roswell, NM
1933 America


Then again, with time travel, one could meet oneself any number of times. Kirk et al. have travelled through time so much they could have met themselves. As the same actors, even!