If one obtains results in one area of a field (say during an MSc thesis) before deciding that one is not interested in making a career in that area, should one take the time (as a PhD student) to get make those results publishable, or is it better to focus on the new area?
Some questions might help guide you to an answer:
how important is the work you've done ? If it's not yet publishable does this mean it's not complete yet ?
Since you're not in the area, do you even know if the topic/solutions are still relevant ?
Are you proud of this work, to the point where you'd be annoyed if someone else came up with the same ideas and published them ?
How much effort will it take to make the work publishable, and how does this interfere with current work that you're doing ? I.e are you in the initial stages of a Ph.D and can spend time on this, or are you deep into your own research where the context switching might prove distracting ?
It's all about marginal utility, in other words cost/utility ratio. How much time/money/effort/coffee/.. will it take to get the stuff published vs how much you think it will benefit you? It's generally hard to estimate how much different investments will pay off in the future, but it can't really hurt you to have published articles in multiple fields. On the contrary it's generally good to show diversity in intellectual capacity and output.
Now that said, you should also consider whether or not you can work on something else during your phD. I mean maybe your supervisor is not OK with you "wasting time" on something that will not be a part of your thesis. It is actually very likely that s/he will not be very positive towards the idea. After all you are burning his/her grant money ;)
In my opinion, during a PhD it is equally important to stay focused on the main track as it is to prove, you as a student can be multidisciplinary.
Being multidisciplinary will make you sometimes more attractive on job markets. That is not always true, though, as some employers will look for more goal oriented individuals.
If however you your major is biology and your interesting findings are in physics, maybe you should let it go.