Naked Science Forum
Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: EvaH on 04/12/2018 10:33:54

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?

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.

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?

What about a futuristic space craft, approaching "c"?
Doesn't need to be futuristic. You're already on a spacecraft going nearly c, in an inertial frame in which you're going nearly c. You're free to choose any frame you like.
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?
I think the correct answer is both, since they're different wordings of the same answer. It takes longer to accelerate my 4xmass stein when bending elbows, but the clock runs at 1/4th speed so I don't notice this.
Could it be reasoned that it is only inertia that increases?
Inertia and mass are functionally the same thing. 'Proper mass' is something else, and that doesn't change with speed, but then neither does proper inertia. Proper mass and proper length and such are all properties of an object in the frame in which it is at rest.

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?

In a RF in which an observer sees an object as stationary, how does inertia differ from mass?
No real difference, but the words are used differently. Perhaps somebody can correct me, but it seems that mass can be measured with a balance scale and it results in gravity and such. Inertia is a resistance to acceleration, given a certain force. But F=ma, or m=F/a, (not i=F/a) so that sounds exactly like mass also being a resistance to acceleration. I don't see the difference between the two.
Observation is unnecessary. You can just say "in the reference frame in which an object is stationary".

'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.

'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?
Depends what the scale measures. You didn't say.
If it is a weight scale, it weighs less at higher altitude. If it is in orbit (altitude or not), it weighs nothing since weight is a measure of force preventing the gravitational acceleration of an object, and there is no such force on an orbiting thing.
If it is a mass scale, it will mass trivially more from gaining potential energy from being lifted further out of the gravity will. You will need an incredibly accurate mass scale to detect the difference of lifting something a mere 150 km at 1G gravity. I compute about 1.7e7 grams of additional mass of our KG in orbit. A little more since we needed to give it a proper shove to get it in orbit in addition to what we needed to get it up there in the first place. The 1.7 figure is just a brick at the top of a 160 km building at the north pole.

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.

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.
OK, weight then.
But the OP question was about change in mass, not change in weight.
So I mass 70 kg at the base of the Eiffel tower. I get up on the top. Do I mass more or less up there (assuming no loss to sweat and such)? Answer is: it depends if I take the elevator or the stairs.
If I jump off (and ignoring friction), the mass should stay the same all the way down until just before I hit.

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.

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