system
Given the following post, respond as if you're commenting on Reddit:
human
Would a field that reduces your inertia violate any important laws of physics?

I was thinking about some sort of energy field that reduces the inertia of a body or area. I was wondering if this would violate any laws of physics. Specifically it wouldn't change gravity, so you couldn't violate the conservation of energy by building an overbalanced wheel. 

The part I have questions about is conserving kinetic energy. It would also have to speed you up and slow you down as you turned it on and off to conserve kinetic energy. But does this fly in the face of relativity? Since as far as I know, you have different amounts of kinetic energy depending on the location of the observer, right? 

You wouldn't be able to exceed lightspeed as that would either require a field that reduced your inertia to 0, or still require infinite energy. 

So I suppose my question is would a field that reduced your inertia conserve kinetic energy if you sped up and slowed down as it increased and decreased in strength, or would that still break conservation of energy?
gpt
Reducing inertia is the same as reducing mass. So in order to conserve energy, you want KE = 1/2 mv^2 to be held constant, which means that when you reduce the mass, you have to correspondingly increase v. However you also have to conserve momentum, so you also want p = mv held constant. This is a problem. You can't have both be true at once. So yes, it would violate either conservation of energy or momentum. You can, however, fix things up, if you allow your new field to itself carry energy and momentum, and which point you are describing a process whereby some of your mass decays into vibrations in the field, just as a muon can for example decay into a less massive electron plus neutrinos.