Time Travel and Consciousness

[Cap Heresy]

If one travels back in time, does their consciousness tag along? If not, and what travels is just a collection of cells, would the Grandfather Paradox be looked at differently?

[Strange]

If one travels back in time, does their consciousness tag along?

 

I assume so, unless they leave their brain behind!

 

But really, it depends what suits the author of the work of fiction in question. It would make an interesting plot twist if time travel were possible but impossible to experience and/or survive.