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Does a Static EM Field Acquire Mass Due to Stored Energy?


exchemist
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3 hours ago, studiot said:

If you want a classical answer you could consider the decrease in mass due to changing a silicon atom for a boron one in a silicon lattice, since this would decrease the charge by 1,thus reducing the field slightly. Since we are then talking about a solid lattice, momentum would not be involved the simple e = mc2 would suffice.

Not sure that's a great example, as elemental silicon has a giant covalent structure, in which the bonding involves electrons in motion in orbitals shared between atoms, but no doubt one could consider changes to a purely ionic structure that would alter the energy of the lattice and thus its mass. So I do take your point.  

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58 minutes ago, exchemist said:

 

Not sure that's a great example, as elemental silicon has a giant covalent structure, in which the bonding involves electrons in motion in orbitals shared between atoms, but no doubt one could consider changes to a purely ionic structure that would alter the energy of the lattice and thus its mass. So I do take your point.  

Maybe not a great example, but I meant it as a ballpark example along the following lines.

Classically, (without QM) bonds are just links of electrostatic origin. That is the bond energy is contained in an electrostatic field of some sort between the atoms.
Si is 4 valent and B is 3 valent.
So one can measure or look up the bond energies.
And also the mass difference between a silicon atom and a boron atom.
So one can get the energy difference in substituting 1 in X silicons by a boron and reducing the bond energy by four Si-Si bonds and adding back three Si-B bonds.
However this substitution will also introduce strain energy into the lattice which will tend to zero as X tends to infinity.
 

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9 minutes ago, studiot said:

Maybe not a great example, but I meant it as a ballpark example along the following lines.

Classically, (without QM) bonds are just links of electrostatic origin. That is the bond energy is contained in an electrostatic field of some sort between the atoms.
Si is 4 valent and B is 3 valent.
So one can measure or look up the bond energies.
And also the mass difference between a silicon atom and a boron atom.
So one can get the energy difference in substituting 1 in X silicons by a boron and reducing the bond energy by four Si-Si bonds and adding back three Si-B bonds.
However this substitution will also introduce strain energy into the lattice which will tend to zero as X tends to infinity.
 

Oh I see what you mean. But as there isn't really a classical picture of covalent bonding in chemistry, it's a tiny bit artificial.    

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It may be interesting to notice that the EM contribution to mass is negligible in most macroscopic cases. If you plug in the values of \( \varepsilon_{0} \), \( c^{2} \) and assume 'typical' values for the field \( \boldsymbol{E} \) the order of Volts/metre, volumes the order of cm3, you get for this charged macroscopic object a correction to mass of its uncharged state the order of one proton mass or thereabouts.

This is, of course, due to the high value of the speed of light.

Edited by joigus
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8 hours ago, joigus said:

It may be interesting to notice that the EM contribution to mass is negligible in most macroscopic cases. If you plug in the values of ε0 , c2 and assume 'typical' values for the field E the order of Volts/metre, volumes the order of cm3, you get for this charged macroscopic object a correction to mass of its uncharged state the order of one proton mass or thereabouts.

This is, of course, due to the high value of the speed of light.

Sure. My interest in the issue was merely that I often,  when explaining E=mc² to lay people, use the example of charging and discharging a battery, to show that the formula  says mass and energy go hand in hand, rather one being converted into the other, which is what the uninitiated  frequently seem to think, probably due to the association of Einstein's formula with  the mass defect in nuclear fission. And then it struck me suddenly that, while it may seem comprehensible that an object with mass, like a battery, may  in theory gain or lose a tiny amount of mass, it is less obvious what happens to something nebulous and apparently massless, like the magnetic field of a solenoid when it is energised. So I wanted to make sure my way of explaining it covered that case as well.          

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They do "go hand in hand" ( @exchemist) but they are different nevertheless. Energy is additive, mass is not. Energy with no mass, such as light, can be added to something and that something will acquire extra mass.

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17 minutes ago, Genady said:

They do "go hand in hand" ( @exchemist) but they are different nevertheless. Energy is additive, mass is not. Energy with no mass, such as light, can be added to something and that something will acquire extra mass.

Sort of, ish. Light is not energy of course: it has energy (E=pc = νλ), which can be added to that of an entity that absorbs it, which will then gain mass according to E=mc². 

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26 minutes ago, exchemist said:

Sort of, ish. Light is not energy of course: it has energy (E=pc = νλ), which can be added to that of an entity that absorbs it, which will then gain mass according to E=mc². 

Of course. I should've said "such as that of light" or something similar. Otherwise, yes, this is what I mean.

I have a picture in mind where the light remains light, i.e. is not absorbed in a sense of being converted into something else. It will be there with no mass, but the entity will gain mass still.

Edited by Genady
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5 hours ago, Genady said:

Of course. I should've said "such as that of light" or something similar. Otherwise, yes, this is what I mean.

I have a picture in mind where the light remains light, i.e. is not absorbed in a sense of being converted into something else. It will be there with no mass, but the entity will gain mass still.

Hmm, do you mean that a glass prism gains mass if you shine a light through it? I struggle to see how that would work, I must admit.

Unless..........you mean that the coupling of the radiation to the medium "lends" some of its energy to it as it passes through, which I guess it does if its refractive index deviates from unity.   

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Just now, exchemist said:

Hmm, do you mean that a glass prism gains mass if you shine a light through it? I struggle to see how that would work, I must admit.

Unless..........you mean that the coupling of the radiation to the medium "lends" some of its energy to it as it passes through, which I guess it does if its refractive index deviates from unity.   

No, I just mean mirrors. I take a box with internal walls being mirrors, let light in, say, through a little opening. Light just bounces inside from mirror to mirror (we can close the opening to make sure it doesn't escape). The mass of the box increased.

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