[EvaH (OP)]

Jay wants to know:

I recently got into a debate at work regarding how mass can change in general relativity. In my feeble understanding of general relativity, an object with more energy bends spacetime to a greater magnitude, and so in terms of gravitation it behaves as if it has more mass. But if this is true, does it also work for potential energy - If you lift an object up you put work into it. But does it now weigh more (or perhaps more than one would expect compared with simple Newtonian gravity)?

Can you help?

[Halc]

I recently got into a debate at work regarding how mass can change in general relativity. In my feeble understanding of general relativity, an object with more energy bends spacetime to a greater magnitude, and so in terms of gravitation it behaves as if it has more mass.

It does have more mass.  Mass and energy are the same thing, so adding energy is the same as adding mass, and mass bends spacetime, so energy does as well.

But if this is true, does it also work for potential energy - If you lift an object up you put work into it.

Yes!  This is unintuitive, but if you lift an object, you have expended energy from elsewhere to the object, and it now masses more.
The energy needs to come from somewhere other than the object.  If it goes uphill due to its own kinetic energy (like a roller coaster), it is losing its own kinetic energy as it gains potential energy, and the mass is unchanged.  The lifting needs to be due to energy imparted from outside the object.

But does it now weigh more (or perhaps more than one would expect compared with simple Newtonian gravity)?

The weight doesn't go up since you've moved it away from whatever gravity well defines 'down'.  So the mass goes up a tiny bit, but the weight (gravitational force) still drops.  If you have impossibly accurate weight and mass scales (spring and balance respectively), you'd measure more more mass but less weight at the top of a building.

[Bill S]

Great answer!  My understanding was that if you imparted energy to an object, its mass would increase; but I had never considered it in that detail; especially the bit about kinetic energy.   

What about a futuristic space craft, approaching "c"?  Its mass increases vastly, but the occupants perceive no change. Is this because their mass increases proportionally, and they are unaware of it; or because mass increase is observer dependant?

Could it be reasoned that it is only inertia that increases?

[Bill S]

There's a crossover between this thread and

https://www.thenakedscientists.com/forum/index.php?topic=75609.0

I look forward to your comments there.  In the meantime, I'm having a bit of trouble getting my head round the idea of proper inertia.

In a RF in which an observer sees an object as stationary, how does inertia differ from mass?

[yor_on]

'does it also work for potential energy - If you lift an object up you put work into it. But does it now weigh more'

Use a scale, put one kg on it. Then take it into a uniformly moving orbit and weight that kg again.
Will the scale register it?
=

the rest seems perfectly correct to me. That's the reason relativity talk about light 'bending' around gravity wells. Potential energy is a relation to something, as f.ex gravity. This potential energy is though 'existing' not intrinsically noticeable. When you heat something up though it will weight more, and that's because the 'energy' you put into the object by heating  is 'intrinsically existent' as long as it is in that object.

[yor_on]

Okay halc.

Try this then :)

Get up on the Eiffel tower. Tape the scale to your feet, first weight yourself, then jump.
As you're in free fall, cast a look at the scale and tell me what you weight.
You have to be quick though.

[yor_on]

doesn't matter for potential energy as far as I get it. Potential energy belongs to a ¨'system' consisting, f.ex, of you versus 'gravity'. If you imagine yourself inside a 'black box' free falling, trying to measure that 'potential energy' by experimental means, there will be nothing to measure. I would call it a relation, the way I look at it. Heat transfers energy into the object getting heated, that's about the only thing I can think of for now actually adding to a mass, and weight. And you know it belongs to the object being heated, you just have to touch it. something belonging intrinsically is what you need to add to that mass, or an acceleration.

[yor_on]

You could of course accelerate the black box up in 'orbit', but that's not 'potential energy', at least not the way I've seen it defined. That's a equivalence to 'gravity'.
=

then again, 'energy' is 'mass'. And to get something up, accelerating against the gravity well, you will expend energy, as well as gain it in the expression of a growing mass. But if you think of the black box. putting a light bulb in the middle of its 'roof' (its center of mass if you like), you will find that it blue shift from one direction, meaning that you gain energy, but red shift from the opposite, meaning that you lose as much as you gain. So I still think it's better to look at it as a equivalence to gravity. But it is a interesting thought