Mass-Energy Equivalence: Matter as Potential Energy?

[Aidyan]

I think mass as a form of potential energy and am always told that this is wrong. According to wiki: "In physics, potential energy is the energy possessed by an object because of its position relative to other objects, stresses within itself, its electric charge, or other factors." Why do this "other factors" not fit for the notion of mass itself? A spring that is stretched acquires a potential energy and increases its mass. Binding energy among nuclei and quarks makes also the mass of neutrons and protons (99% of the mass is binding energy due to the strong force). After all potential energy is also said to be 'stored energy', which fits also in my understanding of mass. So, the question is, why can't we express the mass-energy equivalence also by saying that mass is a form of potential energy?

 

[stevendaryl]

I think mass as a form of potential energy and am always told that this is wrong. According to wiki: "In physics, potential energy is the energy possessed by an object because of its position relative to other objects, stresses within itself, its electric charge, or other factors." Why do this "other factors" not fit for the notion of mass itself? A spring that is stretched acquires a potential energy and increases its mass. Binding energy among nuclei and quarks makes also the mass of neutrons and protons (99% of the mass is binding energy due to the strong force). After all potential energy is also said to be 'stored energy', which fits also in my understanding of mass. So, the question is, why can't we express the mass-energy equivalence also by saying that mass is a form of potential energy?

I would say that potential energy is reflected in the mass, but not that all mass is due to potential energy. If you compress a spring, its mass will increase by a factor $\delta m = \frac{\delta U}{c^2}$, where $\delta U$ is the increase in the potential energy in the spring.

The reason I would not say that all mass is potential energy is because elementary particles such as an electron have a mass, but don't seem to have any associated potential energy.

 

[Herman Trivilino]

The kinetic energy of the constituents of a composite body, as measured in the rest frame of the body, contributes to the mass of the body. So even if the constituents do not interact, meaning there is no potential energy associated with the collection of constituents, the collection can have mass. This is true even if those constituents are massless!

 

[PeroK]

I think mass as a form of potential energy and am always told that this is wrong. According to wiki: "In physics, potential energy is the energy possessed by an object because of its position relative to other objects, stresses within itself, its electric charge, or other factors." Why do this "other factors" not fit for the notion of mass itself? A spring that is stretched acquires a potential energy and increases its mass. Binding energy among nuclei and quarks makes also the mass of neutrons and protons (99% of the mass is binding energy due to the strong force). After all potential energy is also said to be 'stored energy', which fits also in my understanding of mass. So, the question is, why can't we express the mass-energy equivalence also by saying that mass is a form of potential energy?

The term "potential", in potential energy, has a narrow definition in physics. It doesn't mean "anything that can potentially be turned into another form of energy". Fuel (gas/petrol) isn't potential energy in this strict sense, for example.

In general, you need to be careful to learn scientific words for what they are defined to be; and not what they might be, by using the everyday meaning of a word.

 

[sweet springs]

Not only potential but all form of energy is mass.
For an example hot water is heavier than cold water of same molecule numbers. Heat energy contributes to mass.

However in daily life we use the word mass in case we do not or cannot take energy from it.
Then we may say that there energy remains as "mass form" or "potential for our use in future science".

 

[Sorcerer]

Potential energy is dependent upon choice of coordinates, is it not? But mass, as the term is used today (“rest mass”), is always the same regardless of frame of reference, right? If so, how can mass be potential energy?

 

[PeterDonis]

Potential energy is dependent upon choice of coordinates, is it not?

Not really, no. The "zero point" of potential energy can be coordinate dependent, but differences in potential energy, which are what are physically meaningful, are not.

What might be confusing you here is that potential energy is said to be energy dependent on "position", and of course "position" in the usual sense is a coordinate-dependent thing. But the "position" on which potential energy depends is not. This is a "B" level thread so the technical details of this are out of scope, but basically, for there to be a meaningful concept of "potential energy" at all in a spacetime, the spacetime has to be stationary, which means there is a particular way of splitting it up into "space" and "time" that is picked out by the spacetime geometry. The "position" on which potential energy depends is the position in the "space" that is picked out in this way, which is not coordinate-dependent.

 

[Dale]

Potential energy is dependent upon choice of coordinates, is it not? But mass, as the term is used today (“rest mass”), is always the same regardless of frame of reference, right? If so, how can mass be potential energy?

This is a little complicated. Energy is only mass, $E=mc^2$, in a reference frame where the momentum is 0. Otherwise the general relationship is $E^2/c^2-p^2=m^2 c^2$. So it is a little bit off to say that mass is energy. They are closely related, but not quite the same.

 

[hkyriazi]

Related question: does the increase in gravitational potential energy resulting from moving two masses further away from each other also, then, result in increased mass of (one or both of) the two bodies?

 

[Dale]

Related question: does the increase in gravitational potential energy resulting from moving two masses further away from each other also, then, result in increased mass of (one or both of) the two bodies?

As long as the energy came from outside the system then it does increase the mass of the system.

 

[Ibix]

As long as the energy came from outside the system then it does increase the mass of the system.

Just to add, I don't think this means that the masses of the components of the system increase.

 

[hkyriazi]

So, their individual gravitational masses (weights) haven't changed (such that a 3rd body would be more attracted to their combined "system" than the 1/r² relation would predict)?

 

[Ibix]

So, their individual gravitational masses (weights) haven't changed (such that a 3rd body would be more attracted to their combined "system" than the 1/r² relation would predict)?

Other way round. If you're far enough away to regard the two bodies as one thing then you will find a stronger gravitational pull after the separation than before. Although you do need to worry about where the energy comes from - it has to be a separate source a long way from the system, so you can separate out its gravitational effect in the "before" bit of the experiment.

If you get in among the two bodies, I'm not quite sure what you'd see. I think it depends on how you add the energy - are the bodies moving, or are they held apart by a rod, has any energy been radiated away as heat. I also think that if you've added enough energy to have a significant gravitational effect, you probably can't use straightforward Newtonian 1/r².

 

[jartsa]

So, their individual gravitational masses (weights) haven't changed (such that a 3rd body would be more attracted to their combined "system" than the 1/r² relation would predict)?

Well, let's say a tanker spacecraft delivers million tons of anti-matter into the system, this increases the gravitating mass of the system by million tons. (The system is originally made of matter)

Then million tons of matter and million tons of anti matter are converted to energy which stays in the system. This does not change the gravitating mass of the system.

Then the energy is used to lift the parts of the system away from each other. This does not change the gravitating mass of the system.(Let's say "million tons of anti-matter" means million tons of anti-matter according to an observer inside the system. Then mass increase means mass increase according to that observer.)

 

[PeroK]

So, their individual gravitational masses (weights) haven't changed (such that a 3rd body would be more attracted to their combined "system" than the 1/r² relation would predict)?

A simpler example is that the mass of a hydrogen atom (formed by one proton and one electron) is less than the mass of the constituent particles.

 

[jbriggs444]

Thanks. Just out of curiosity, is that considered to be binding energy, or rest energy, or are those terms considered to be one and the same? I'm guessing binding energy is just one part of the rest energy.

Binding energy is a deduction from the sum of the energies of the components to obtain the rest energy of the composite system.

 

[Dale]

Just to add, I don't think this means that the masses of the components of the system increase.

Correct, it is the mass of the system. Usually you can not identify the mass increase with a specific part of the system