## Does potential energy have mass?

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tomandlu
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### Does potential energy have mass?

I have been told in the past that all energy has an associated mass (as per [imath]M = E/C^2[/imath]). Does this apply to potential energy? Does a charged battery have more mass than an uncharged battery? Does a compressed spring have more mass than the uncompressed spring?

Curious minds want to know...
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thoughtfully
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### Re: Does potential energy have mass?

Quite so. Otherwise, Conservation of Energy would be violated.

By the way, something around 95% of the mass of everything you see is really binding/potential energy among the quarks and gluons inside atomic nuclei.

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### Re: Does potential energy have mass?

Indeed, the fact that it isn’t 100% is the odd part.
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sikyon
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### Re: Does potential energy have mass?

Consider that you know all mass has an associated energy. Therefore, this mass holds potential energy by virtue of being mass. Therefore, potential energy does result in mass!

tomandlu
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### Re: Does potential energy have mass?

sikyon wrote:Consider that you know all mass has an associated energy. Therefore, this mass holds potential energy by virtue of being mass. Therefore, potential energy does result in mass!

Yes - I just found the idea of a spring having more mass depending on its state counter-intuitive although logically consistent with the conservation of energy. Anyway, thanks again you guys...
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### Re: Does potential energy have mass?

So does that mean the mass of the attractive gravitational potential well of the earth actually makes itself lighter?
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### Re: Does potential energy have mass?

That depends on the frame of reference.

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### Re: Does potential energy have mass?

tomandlu wrote:
sikyon wrote:Consider that you know all mass has an associated energy. Therefore, this mass holds potential energy by virtue of being mass. Therefore, potential energy does result in mass!

Yes - I just found the idea of a spring having more mass depending on its state counter-intuitive although logically consistent with the conservation of energy. Anyway, thanks again you guys...

What if the “spring” is the Strong Force binding the protons and neutrons together in the nucleus of, say, a uranium atom? Does it surprise you to learn that the fissile decay products have a net mass lighter than the original uranium atom even though they have the same number of protons, neutrons, and electrons? The extra mass is entirely due to the configuration of the particles, and when that configuration changes it is released as energy.
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gmalivuk
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### Re: Does potential energy have mass?

tomandlu wrote:I just found the idea of a spring having more mass depending on its state counter-intuitive
Sure, but is it any more counterintuitive than the rest of the implications of relativity?
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KingXimana
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### Re: Does potential energy have mass?

This makes me think, Is it possible Mass is a illusion? We could just observe a certain "wave length" as matter, the "wave length" being something like energy density or some other property we haven't discovered.

The real question is am I just re-saying fact, or am I being a idiot.....

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### Re: Does potential energy have mass?

KingXimana wrote:This makes me think, Is it possible Mass is a illusion? We could just observe a certain "wave length" as matter, the "wave length" being something like energy density or some other property we haven't discovered.

The real question is am I just re-saying fact, or am I being a idiot.....

Matter has a wavelength equal to Plank's constant divided by momentum. Consequently someone did the double slit experiment with buckyballs.
http://physicsworld.com/cws/article/news/2952

I don't think that makes mass an "illusion", though.

KingXimana
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### Re: Does potential energy have mass?

I was thinking Illusion as in how our body reacts to say Visable light different then Infared but they are the same thing. Energy would be our body reacting different then to the section we call matter, when in reality matter is energy.

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### Re: Does potential energy have mass?

When we bump into something and say either "ouch, there was some solid matter there" or "get out of my way, gas" it is because we found some fermions who Pauli exclusioned with us, and someone won. We do not bump into radiation in this way because it is bosons. Neither of these care about the amount of energy present. Spin is the thing.
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### Re: Does potential energy have mass?

doogly wrote:When we bump into something and say either "ouch, there was some solid matter there" or "get out of my way, gas" it is because we found some fermions who Pauli exclusioned with us, and someone won. We do not bump into radiation in this way because it is bosons. Neither of these care about the amount of energy present. Spin is the thing.

I think electromagnetic forces win out well before Fermi-degeneracy comes into play. The bumping into the matter is more to do with exchange in momentum via these forces than the Pauli exclusion principle. At least in day to day terms, the Pauli exclusion does play a role in stopping extremely dense stars from collapsing to black holes.

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### Re: Does potential energy have mass?

Yes, that is what is commonly thought, but it turns out it is not true. Dyson showed that ordinary matter collapses without Pauli exclusion, and Lieb did some very potent work extending and adding rigor to this idea.The fact that matter occupies volume is a quantum fact.
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### Re: Does potential energy have mass?

doogly wrote:Yes, that is what is commonly thought, but it turns out it is not true. Dyson showed that ordinary matter collapses without Pauli exclusion, and Lieb did some very potent work extending and adding rigor to this idea.The fact that matter occupies volume is a quantum fact.

Ordinary matter would collapse because electrons orbiting the nucleus would all drop to the lowest energy level, the nucleus would collapse, and other weird stuff, right?

That doesn't mean that the particles that are exchanged between our hand and a chunk of metal aren't almost entirely photons, though.
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Last edited by JHVH on Fri Oct 23, 4004 BCE 6:17 pm, edited 6 times in total.

doogly
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### Re: Does potential energy have mass?

The role of pauli exclusion is obvious for atoms, but it is furthermore essential for bulk stability as well.
Perhaps you are right about about the interaction of two seperate things though. I may be overstating the role.
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### Re: Does potential energy have mass?

Has the fact that potential energy and configuration add to mass been viewed as a candidate for dark matter?

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### Re: Does potential energy have mass?

ExplodingHat wrote:So does that mean the mass of the attractive gravitational potential well of the earth actually makes itself lighter?
Let's take a spherical volume of space 1 light second across. Our observer is at a constant distance from the sphere's center. We'll start with an Earth's mass of perfectly inelastic rocks evenly distributed about this space and not moving with respect to the center/observer.

The rocks would start to fall, their kinetic energy would go up and their potential energy would drop. The mass in the sphere as a whole would remain the same.

The rocks would hit each other in the center. Being perfectly inelastic, they would stick, their kinetic energy would drop and their temperature would increase. The mass in the sphere as a whole would remain the same.

The hot thing in the center would emit black-body radiation. The mass in the sphere as a whole would drop, because now something is leaving it.

The number and type of atoms in the rock wouldn't have changed, but the mass of the whole group would have decreased. For Earth, that difference would be about 1 part in 2 billion.
Last edited by Quizatzhaderac on Tue Apr 05, 2016 2:25 pm UTC, edited 2 times in total.
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gmalivuk
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### Re: Does potential energy have mass?

I think you mean inelastic.
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### Re: Does potential energy have mass?

tomandlu wrote:Does a charged battery have more mass than an uncharged battery?

That's actually a neat party trick. Have someone hand you two equal batterys, one of them charged. To everyone's surprise, you can point out the charged battery simply by holding them!
There's no trick to it. You just take one in each hand and compare their weight. The battery that weighs 0.0000000004% more is the charged one.

Spoiler:
A typical AAA battery weighs 15g, which equals around 1.35*1015 joules. (source)
Fully charged, it stores ~1 Ah at 1.5V, which is 1.5 Wh = 5400 joules.

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### Re: Does potential energy have mass?

In bulk matter, which is what most folk are familiar with, mass is potential energy. Ninety-six to ninety-seven percent comes from the binding forces inside protons and neutrons. The rest mass of elementary particles comes from interactions with the Higgs field, in straightforward ways with the weak force bosons, and less straightforward ways, that I haven't seen an adequately accessible explanation of, for the other elementary particles.

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### Re: Does potential energy have mass?

Tub wrote:
tomandlu wrote:Does a charged battery have more mass than an uncharged battery?

That's actually a neat party trick. Have someone hand you two equal batterys, one of them charged. To everyone's surprise, you can point out the charged battery simply by holding them!
There's no trick to it. You just take one in each hand and compare their weight. The battery that weighs 0.0000000004% more is the charged one.

Way ahead of you. I did that at my kid's fifth birthday and followed up with the double-slit experiment. Then we had a cake that was exactly the circumference of the Earth's Schwarzschild radius.
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doogly
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### Re: Does potential energy have mass?

That is a really unfortunate cake.
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### Re: Does potential energy have mass?

The cake was, of course, a lie.

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### Re: Does potential energy have mass?

Tyndmyr wrote:The cake was, of course, a lie.

Yes, but a very small lie.
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### Re: Does potential energy have mass?

Tub wrote:
tomandlu wrote:Does a charged battery have more mass than an uncharged battery?

That's actually a neat party trick. Have someone hand you two equal batterys, one of them charged. To everyone's surprise, you can point out the charged battery simply by holding them!
There's no trick to it. You just take one in each hand and compare their weight. The battery that weighs 0.0000000004% more is the charged one.

Spoiler:
A typical AAA battery weighs 15g, which equals around 1.35*1015 joules. (source)
Fully charged, it stores ~1 Ah at 1.5V, which is 1.5 Wh = 5400 joules.

So, I know this was posted in jest, but there actually is a neat party trick that lets you distinguish full batteries from empty ones:

Specifically, batteries less than 50% full have a high bounce, batteries more than 75% full do not bounce, and in between the bounce height is nearly linear. Source
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### Re: Does potential energy have mass?

doogly wrote:The role of pauli exclusion is obvious for atoms, but it is furthermore essential for bulk stability as well.
Perhaps you are right about about the interaction of two seperate things though. I may be overstating the role.

I suspect I was wrong by the way.
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Last edited by JHVH on Fri Oct 23, 4004 BCE 6:17 pm, edited 6 times in total.

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### Re: Does potential energy have mass?

In my experience, fully charged dry cells are noticeably heavier than dead ones, but I believe that it is due primarily to outgassing when they discharge.

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### Re: Does potential energy have mass?

I don't think this has been touched on in this thread or the GR one, so can anyone help me with my latest confusion/question?

If potential energy has mass, then presumably this counts for gravitational potential energy. So, a 1kg object lifted a few feet will have more mass than the same object resting on the ground... but this implies that all mass has a potential energy associated with the total mass of the universe (I think), which, if I'm right in that hypothesis, sounds like it might be a significant quantity.

Moving on (still slightly related), does energy exist in a universe that has reached maximum entropy? Isn't energy always about potential, and surely such a state has no potential? But this implies that such a universe has no definable mass (since such a mass must, presumably, have potential). How could one tell the difference between a universe that has a mass of 1kg and our universe, assuming both were in a state of maximum entropy?
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### Re: Does potential energy have mass?

An important principle generally is "no double counting."

GR is all about G = T, with an 8pi if you prefer to pick units that don't make it look too too simple. G is spacetime curvature, and T is mass-energy density-stress-pressure, all rolled up into a tensor.

"Gravity" lives on the left side. You don't count Newtonian style gravitational potential energy on the right side, because that sort of thing is already on the left side. If you have some energy due to electromagnetic radiation, directly insert it into the right side all the way.

As to your second point, I don't know why you think these wouldn't exist. Like, this seems a deep misunderstanding. Let's say you have perfect gas at perfect thermal equilibrium, T. Maximum entropy. Energy is well defined, it's nkT. Right?
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### Re: Does potential energy have mass?

doogly wrote:As to your second point, I don't know why you think these wouldn't exist. Like, this seems a deep misunderstanding. Let's say you have perfect gas at perfect thermal equilibrium, T. Maximum entropy. Energy is well defined, it's nkT. Right?

Would it help explain my problem if I said I've no idea what nkT means? And I sort-of get your answer to the first part, but I'm still struggling to fit the parts together.

Hopefully to clarify, here are a series of Y/N questions with my hazarded answer in brackets (all 'Y' for ease of use). They sort-of represent a chain of thought for loose definitions of 'chain' and 'thought' (and probably 'represent' as well):

1. Does an object acquire potential energy when it is lifted? (Y)
2. Does this potential energy have mass? (Y)
3. Does the mass of the object therefore increase and decrease when it's raised and lowered? (Y)
4. Does this imply that all mass has potential energy associated with all gravity wells that the mass is currently outside of? (Y)
5. Does this potential energy have mass? (Y)
6. Does this imply that the universe gets a little less massive every time there's a meteor strike or stellar collision? (Y???)
7. If you take away half the mass in the universe, does the remaining half actually weigh less than half due to the loss of potential energy? (Y???)

I think if the answer to any of these is 'No', then my max-entropy question is, I think, irrelevant... thinking about it, I'm ignoring conservation of energy somewhere in this, but I'm still interested to see where I'm going wrong (which, I'm fairly sure, comes down to the double-accounting issue). I think my stumbling block is the third one - it probably is 'Y', but that ignores what happens next to the energy released (and its associated mass), but I'm basically guessing.
Last edited by tomandlu on Thu Mar 24, 2016 3:02 pm UTC, edited 1 time in total.
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### Re: Does potential energy have mass?

The potential energy due to gravity does not have mass, that's where you get off the chain. GR is all about gravity being "different" from other forces.

n is number of particles, k is boltzmann's constant.
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### Re: Does potential energy have mass?

doogly wrote:The potential energy due to gravity does not have mass, that's where you get off the chain. GR is all about gravity being "different" from other forces.

Ah! Many thanks - I did not know that.

n is number of particles, k is boltzmann's constant.

My confusion partly stemmed from my mistake regarding PE, M and gravity, so that's largely resolved now.

Thanks again.
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### Re: Does potential energy have mass?

tomandlu wrote:Moving on (still slightly related), does energy exist in a universe that has reached maximum entropy? Isn't energy always about potential, and surely such a state has no potential? But this implies that such a universe has no definable mass (since such a mass must, presumably, have potential). How could one tell the difference between a universe that has a mass of 1kg and our universe, assuming both were in a state of maximum entropy?
In any maximum entropy universe, experimentation is impossible.

If we took 1 cubic meter sections of both universes and stuck them next to each other in a third universe This third universe would not be at maximum entropy. There would be a potential difference between the two that could (in theory) be used to do work.
I don't know why you think these wouldn't exist. Like, this seems a deep misunderstanding. Let's say you have perfect gas at perfect thermal equilibrium, T. Maximum entropy. Energy is well defined, it's nkT. Right?
All maximum entropy systems are isomorphs of each other. Volumes of maximum entropy gas, neutronium, or plasma are only different is so far as how they interact with outside systems. Tomandlu's question was about entire universes. The energy content of a heat dead universe is still well defined, but it's an epiphenomenal quantity at that point.
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### Re: Does potential energy have mass?

Quizatzhaderac wrote:The energy content of a heat dead universe is still well defined, but it's an epiphenomenal quantity at that point.

I like that word - so it exists but it cannot affect anything? (a bit like my libido, really)
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### Re: Does potential energy have mass?

But I don't think it's true. You can have a max entropy box of N particles and a box of N_2 particles, and they are not the same. Or if you have different sized boxes. These can be distinguished.
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### Re: Does potential energy have mass?

@tomandlu: correct, epiphenomenal means it can't affect anything. As for if they exist or not, that depends on your metaphysics, but with respect to hard science, epiphenomenal things are generally considered "not even wrong".

@doogly, yes, you can distinguish many different type of boxes of maximum entropy contents if you have an external universe that contains those boxes to run the experiment in. But those boxes themselves can't contain experiments to determine anything about their own contents, because experiments require signal amplification, which requires work, which requires negentropy.

Maximum entropy systems are actually very trivial. To illustrate this (in the spoiler below) I describe how the time-evolution of a maximum entropy universe under the standard model, with the actual dimensionless constants and generalized for different values; with the major implementations of quantum gravity, and some fully generalized considerations of non-physical universes:
Spoiler:
Nothing happens
As you can see, this gives us full predictive power. If we then apply Occam's razor to a model of our universe at maximum entropy we find energy is an unnecessary entity, as we didn't need it to predict the universe's evolution.
Last edited by Quizatzhaderac on Thu Apr 06, 2017 3:29 pm UTC, edited 1 time in total.
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### Re: Does potential energy have mass?

Sure but there's still some microphysics happening to make up this statistically quite boring state.
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### Re: Does potential energy have mass?

And why does 'nothing happen' to a system at maximum entropy?

If you have a box of gas particles at max entropy, after an astronomical amount of time they'll all by chance be in one half of the box, won't they?

(Or, by definition, if they do get to all be in one side of the box, could they never have been at max entropy at any earlier stage? In which case 'max entropy' isn't relevant to real world physics?)