You're describing a brachistochrone trajectory. The "magic" in sci-fi isn't the drugs, it's rocket engines that are actually that efficient. If you accelerate/decel at a sustained 1 g, you can make it to Mars in about 2 days.
This is the key calculation where you realize that quick inter-planetary travel is totally within the realm of physics.
> Using Days and AU (astronomical units) we can see 3 days will get about 2.5 AU (halfway to Jupiter). 4.5 days will get you 5 AU (halfway to Saturn). 9 days will get you 20 AU (more than halfway to the Kuiper belt)
Obviously inter-stellar travel seems like a totally different matter, but actually at 1g constant acceleration it works out to about “1 year + the number of light years” to an outside observer. Less time passes for the traveler.
Invent an engine efficient enough to allow constant 1g acceleration for years at a time and humans really could become interstellar.
The best ion engines get around 200,000 Isp. If you had a 500t ship burning 1t of mass per day, you would need an Isp of ~4.5m to achieve 1g over that first day (it gets easier as you get lighter).
The theoretical limit (ejecting mass out the back at 1c) for specific impulse is 300 million.
https://space.stackexchange.com/questions/840/how-fast-will-...
I'm surprised to learn that Mars is (or can be) so "close" in terms of a sustained 1g acceleration.
High-school math, napkin, and 5 minutes later: Wow, it's only 42 hours!
Or you fire off refueling packs ahead of the trip.