[Lewis Thomson (OP)]

Tibor recently wrote into The Naked Scientists to ask this question...

"We understand that energy has mass (E=mc^2), but what about potential energy? Does it also have mass? For example, if I charge up the battery in my phone, does my phone become (fractionally) heavier?"


What do you think? Leave your answers to this battery baffler in the comments below...

[Halc]

We understand that energy has mass (E=mc^2), but what about potential energy? Does it also have mass? For example, if I charge up the battery in my phone, does my phone become (fractionally) heavier?"

E=mc˛ appies to all energy, so all else being equal (no change in fingerprints for instance), the phone masses a tiny bit more after being charged. It also masses more if you move it from downstairs to upstairs since it gains potential energy that way, but it probably weighs less upstairs since it is further from Earth. So increased mass doesn't necessarily imply increased weight.

[Tibor Molnar]

Thanks. This is the answer I was fishing for, and the aspect of the question that I thought would most interest the audience. (It's a bit of a shame that it was left out of the QotW broadcast; though I am pleased to report that Otis said he would bring it up in a future episode.)
PS: Do you know a reference that addresses this specific point?   

[Halc]

First of all, welcome to the forum. May it not be your last visit.

PS: Do you know a reference that addresses this specific point?

I hadn't used one for the above reply, but a quick search turned up this:
https://physics.stackexchange.com/questions/34421/does-the-mass-of-a-battery-change-when-charged-discharged
which contains a much more quantified answer. They calculated that an electric car gains about half a microgram when charged from empty to full. A phone would gain much less of course.

[Eternal Student]

Hi.

Do you know a reference that addresses this specific point?

    Almost exactly this question has been discussed on these websites  (all forums or Question and answer sites):
https://physics.stackexchange.com/questions/34421/does-the-mass-of-a-battery-change-when-charged-discharged
https://www.quora.com/Is-a-charged-battery-heavier-than-a-depleted-one
https://www.physicsforums.com/threads/are-charged-batteries-heavier.940974/
   Some of these have additional links to other information sources.   The theory is so widely accepted that you can sensibly take for granted that it is true - a charged mobile phone battery would have more mass than an uncharged one - but there is very little direct experimental measurement:    Most people agree that for a typical household battery like a mobile phone battery, there isn't any laboratory experiment that would reliably detect the change in mass - because the difference would be so small.   That may change in the future but at the moment that does seem to be how things are.  We do have experimental evidence for systems that absorb or release larger amounts of energy and then show a mass change - the obvious example being nuclear reactions in power stations and weapons.
     The idea of a charged battery having more mass is sufficiently accepted that it is even used as an example in some texts discussing mass-energy equivalence:
     The value of the mass of the hot brick or charged battery is greater than it was before it absorbed energy.

[Taken from:   https://plato.stanford.edu/entries/equivME/ ]

- - - - - - - - - - - - - -

A different way of thinking:  Stop worrying if some energy will show up as mass.   Instead realise that is extremely rare for there to be any mass that isn't explained as a form of energy.

    "Mass" just isn't what we thought it was about 50 years ago.   For example, the Higgs field provides a description for something that we might reasonably consider as the intrinsic mass of a particle but even this does not help very much.    The mass of most particles is far greater than the mass explained by the Higgs field.   For example, a proton has only about 1% of its mass explained by the Higgs field the remaining 99% is the consequence of other forms of energy being located or contained in the "system" that we describe as being the particle.   Most of a protons mass isn't the Higgs field mass of the 3 quarks in it,  instead it's due to the binding energy that is present when the 3 quarks are in such close proximity with each other.
     To paraphrase this, at a microscopic level, it's actually better to think that all "mass" is just "energy" of one form or another bound up in one microscopic system that we call a particle.
     Here's a short video by a slightly flamboyant presenter  (under 7 minutes) that discusses the issue:
"What the heck is mass?" - Science Asylum,  available on You Tube.

    Here's a longer video (if you have 40 minutes and a deeper interest):   
"The Concept of mass" - presented by Jim Bagshot for the Royal Institution.   Available on youtube.

Best Wishes.

[Tibor Molnar]

Thanks, everyone.
Plenty here for me to follow up... 

[Eternal Student]

Hi again.

I'm sorry about the overlap with your (@Halc) post.   You had finished and posted before I did.  I have a minor disagreement with one thing you said (and nothing much to do today except write it down here).

It also masses more if you move it from downstairs to upstairs since it gains potential energy that way...

    That is controversial, Halc.
   Gravitational potential energy is not well defined in General Relativity.   We've had some discussion about this before.   
     In the standard theory of GR, the (conventional) stress-energy tensor does not consider gravitational potential energy as a source of energy density because the position of any mass (and other forms of energy density) is already specified.   If you also added some new or extra energy density somewhere that you are considering as gravitational potential energy then you would effectively be telling the stress-energy tensor that the location of the individual masses of the system has changed TWICE over.
   For example, if you want to calculate the curvature of space due to an apple being on the surface of the earth,  as opposed to the apple being 3 metres above the surface of the earth (i.e. still on the tree),  you do not and must not put the increased gravitational potential energy into the stress energy tensor.   Instead you just replace the position of the mass of the apple with the new position, re-determine the new stress energy tensor and then re-calculate with the Einstein Field Equations to find the new curvature.   The information about the change of location of the apple is already there and available to the E.F.E. through the new stress energy tensor.   
    As it happens,  you do end up generating a new curvature which, at a distance from the earth, would look like the combined earth-apple system did just have slightly more mass now that the apple was in the tree.   Anyway the key point is that the thing we are calling the "mass" of the apple was never changed, just its position.  The E.F.E. automatically emulates the effective increase in mass of the entire earth-apple system because the stress-energy tensor supplies it with information about the new spatial location of the masses.

    Let's say all of this a different way:   When you take an apple upstairs you cannot be sure that the mass of the apple will change at all.    The entire earth-apple system has a new energy content and therefore the effective mass of that system might have changed but it isn't necessarily identified as a change in mass of the apple,  or of the earth excluding the apple.  You can only identify it in the combined system.    Specifically, if you applied a force to the apple while it was upstairs its inertia (or inertial mass) won't be any different than it was while it was downstairs.    Similarly you should be able to accelerate the earth excluding the apple without noticing a change in its inertia.  It is only when you apply a force to the entire earth-apple system that you would notice there was a change in the inertia of that entire system.    (LATE EDITING:  An even easier way to phrase this:  A 1 Kg brick still masses 1 Kg as determined by its resistance to an applied force OR by its ability to act as a source of gravitation regardless of high high up in the air you take it.   You can put the brick into a spaceship and fly it in outer space and it will still have the same properties of inerta and gravitational charge, i.e. its mass does not change).

Best Wishes.

[Halc]

Gravitational potential energy is not well defined in General Relativity.   We've had some discussion about this before.

Agreed, and I have to remember that when making seeming blanket statements like I did. Mass is frame dependent, and so is kinetic and potential energy. Mass of a rising brick goes up as 'measured' by some device at some constant potential, but if you were to measure the local mass of the brick, it doesn't change a hoot at different altitudes. This makes me wonder how one might go about measuring the mass of something that isn't local. I can't think of an obvious way to do it.  You can measure its weight with help of strings and such, but that isn't mass.

LATE EDITING:  An even easier way to phrase this:  A 1 Kg brick still masses 1 Kg as determined by its resistance to an applied force OR by its ability to act as a source of gravitation regardless of high high up in the air you take it.

That acceleration due to a force is again frame dependent. It will be measured differently depending on the potential at which the measurement is taken. Hence it being an interesting problem.

Thanks for the correction ES.

[Eternal Student]

Hi.

   It's always a pleasure to discuss something and it's not as if I had other things to do today.   Thank you for your time.

Best Wishes.

[Tibor Molnar]

Fascinating!
I think I understand the frame dependence. Is it correct to say, then, that kinetic energy is somehow "local", i.e., attributable to some object; whereas potential energy is somehow "global", attributable to a whole system?

[Halc]

Is it correct to say, then, that kinetic energy is somehow "local", i.e., attributable to some object

Under Galilean/Special relativity, KE of an object is a relation with an inertial reference frame. The object is stationary in one frame and has zero KE, but it is moving relative to another frame. This is true regardless of whether the measurement is local or not. It is position invariant. So the object's relativistic mass is frame dependent, but its proper mass is invariant.

Not so when gravitational potential is involved.  A 1 kg mass will still have a proper mass of exactly 1 kg measured locally, but if the measurement is not local, it changes.  Suppose we have an observer on the surface of a non-spinning Earth, and another way up on a tower above the first observer.  Between them a 1 kg mass goes by horizontally at say 100 km/sec as measured by an observer at the altitude of the moving mass. They'll measure different KE.  From below, the mass is moving faster than 100 km/sec and even a stationary object has a higher relativistic mass than a kg sitting right next to him.  From above, the opposite is true.
Just like in special relativity where relativistic mass is frame dependent and not attributed to (a property of) the object itself. Relative to an observer that stays with the object, it has neither kinetic nor potential energy relative to him and thus still masses exactly 1 kg.

whereas potential energy is somehow "global", attributable to a whole system?

A ES explained far better, PE is a attributed to a system, so raising a rock to a top floor adds energy to the Earth/rock system and thus the mass of that system, but it is a mistake to attribute that new mass to just the rock or the Earth. My first reply made it sound otherwise, and ES corrected that.

[Eternal Student]

Hi.
   

Is it correct to say, then, that kinetic energy is somehow "local", i.e., attributable to some object; whereas potential energy is somehow "global", attributable to a whole system?

    I think we're at risk of spending the next six hours talking about what energy is.   That has formed the title and entire scope of some threads already.  It is not a simple thing.   If you're really interested, then by all means keep asking here and/or start a new thread just for that.   However, it may be desirable to keep this short to start with:  So I'll just back away from discussing energy too much.
     In my opinion, most things we might call "potential energy" are just very vague umbrella terms for something that is really likely to be a collection of other more fundamental forms of energy if you looked carefully enough.   For example, when you stretch a rubber band we say there is "elastic potential energy" in the rubber band but if you looked at the molecular level in the rubber most of this elasticity is explained by electrostatic attraction between atoms in some long molecule and/or between molecules.   Using the term "elastic potential" is just a short way of saying "there's energy stored in the rubber band and I don't care exactly how".   
      So I don't think it's as straightforward as saying "potential energy" is always something attributable to a system instead of being a precisely located store of energy which is contained within one object.  Describing something as "potential energy" is usually just declaring some store of energy that we haven't wanted to or been able to explain with any other, possibly more fundamental forms of energy.
     I've made most of the above statements with the tacit assumption that energy is a fundamental thing that exists, that's a fair assumption for many scientists and perfectly fine for most situations.   However, I should point out that even this is not clear.   A lot of our simple understanding about energy can be shaken by results like Noether's theorem.

Best Wishes.

[Robida]

Tibor recently wrote into The Naked Scientists to ask this question...

"We understand that energy has mass (E=mc^2), but what about potential energy? Does it also have mass? For example, if I charge up the battery in my phone, does my phone become (fractionally) heavier?"


What do you think? Leave your answers to this battery baffler in the comments below...

NO. The weight of the battery does not change before and after charging, because the battery charging process is a chemical change, not a physical change, and according to the law of conservation of mass, neither matter is created nor disappeared.

[Zer0]

A hot cuppa coffee weighs more than an identical cold cuppa coffee.

P.S. - CheerZ!
☕

[Peter11]

A battery gains mass as it charges and loses mass when discharging.Mass is the stored energy.Mass is the same on the moon as on earth even though the object will weigh less on the moon it has nothing to do with weight or volume.When an object moves to close to the speed of light it gains mass which is the kenetic energy building.Every object hold energy which is its mass there are two states resting mass and mass in motion.A portion of the energy in the bigbang was converted to matter which is what we see as the universe.
One kilogram of matter holds E=(1kg)x(3x108m/sec)2=9x1016 kg m2/sec2 at rest in motion it gains more mass that would be calculated. Which was created in the bigbang and where the energy came from.Its basiclly all the potential energy in an object if it was all converted to energy at once.

[William Hardy]

No, I suppose.

[ArthurArts]

Hi folks, so I need some short and clear arguments for my physics tutor as he says the mass isn't changing. brain explosion

[Kryptid]

Hi folks, so I need some short and clear arguments for my physics tutor as he says the mass isn't changing. brain explosion

Halc's first response in this thread explains it pretty well. The mass technically does change, but it's extraordinarily small (far, far too small to be of any practical concern).

If I recall correctly, AAA batteries have around 1,000 joules of energy when fully charged (the exact amount likely varies by brand). Using E=mc², that corresponds to a mass of about 11 picograms. For perspective, the mass of a red blood cell is about 27 picograms.

[GertrudeFranklin]

So, the conclusion is that it depends on the battery, right?