It also applies to things like gravitational potential energy, or velocity. Climb a flight of stairs, and you gain energy. Gaining potential energy really means that you've gained mass, and so you're heavier at the top of the stairs than at the bottom. The amount that you are heavier depends on the amount of energy you gained, converted into mass. Similarly, as you gain velocity, you gain kinetic energy, which also makes you heavier. If you wave your hand in front of your face, your hand's motion causes it to gain mass. Velocity also dilates time, so time passes ever so slightly slower than for the rest of your body.
This typically only matters in a relativistic context, and doesn't impact day to day life. The difference in passage of time can be measured by an atomic clock if you put it on a rocket into space, but is otherwise insignificant. It's unlikely any scale could measure your weight-gain from climbing stairs, since the amount of energy you gain is insignificant when converted into mass. You can compute the mass gain by solving for "m" in the formula E=m*c^2, so m=E/(c^2).
The speed of light c is a really big number, and so to compute the mass you gain, you're dividing the energy by c^2, which is a much bigger number. Thus a gain to kinetic or potential energy does not noticeably affect your mass in day to day situations. Conversely, if you can convert any meaningful part of your mass into energy, then it's an absolutely tremendous amount of energy: atomic weapons.
> Gaining potential energy really means that you've gained mass
I've never heard this before. Can you link to some further explanation? Intuitively, if anything, you'd lose mass, because you're in a place now where space is less curved than where you were before.
The system composed of you + planet gains mass. You can not measure a different rest mass for yourself at either situation, so you'll probably attribute the extra mass to the planet (and the planet to you).
And yes, there's also some change due to changes in gravity. I'd expect that to be much smaller.
This typically only matters in a relativistic context, and doesn't impact day to day life. The difference in passage of time can be measured by an atomic clock if you put it on a rocket into space, but is otherwise insignificant. It's unlikely any scale could measure your weight-gain from climbing stairs, since the amount of energy you gain is insignificant when converted into mass. You can compute the mass gain by solving for "m" in the formula E=m*c^2, so m=E/(c^2).
The speed of light c is a really big number, and so to compute the mass you gain, you're dividing the energy by c^2, which is a much bigger number. Thus a gain to kinetic or potential energy does not noticeably affect your mass in day to day situations. Conversely, if you can convert any meaningful part of your mass into energy, then it's an absolutely tremendous amount of energy: atomic weapons.