Mass & energy increments a la e = mc^2

[Swamp Thing]

When we consider the mass difference between an excited atom and an atom in the ground state, is it possible (or even meaningful) to try and drill down and say exactly where the extra delta(mv^2) resides in the excited case? For instance, can we say that there are more virtual photons (or maybe more energetic virtual photons) mediating the electrostatic forces in the excited atom, as compared to the ground state one, and this is how the books are balanced?

 

[PeroK]

When we consider the mass difference between an excited atom and an atom in the ground state, is it possible (or even meaningful) to try and drill down and say exactly where the extra delta(mv^2) resides in the excited case?

The extra mass of the atom is precisely the extra potential and kinetic energy of the orbital. Note that this total mass of a hydrogen atom, for example, is less than the sum of the masses of an electron and a proton. In that sense, there is a mass deficit in an atom; not extra mass over.

For instance, can we say that there are more virtual photons (or maybe more energetic virtual photons) mediating the electrostatic forces in the excited atom, as compared to the ground state one, and this is how the books are balanced?

Virtual photons are virtual, not real. They are essentially a mathematical tool, used in certain methods of perturbation theory.

 

[Swamp Thing]

The extra mass of the atom is precisely the extra potential and kinetic energy of the orbital. Note that this total mass of a hydrogen atom, for example, is less than the sum of the masses of an electron and a proton. In that sense, there is a mass deficit in an atom; not extra mass over.

Virtual photons are virtual, not real. They are essentially a mathematical tool, used in certain methods of perturbation theory.

Then is there anything specific to which we can attribute the extra mass, or is it just somehow acquired by the whole system in some "holistic" way?

Edit: For example, take an ion that has all electrons in their lowest possible levels and another ion that has one excited electron. Presumably the excited one will show lower acceleration in an electric field, compared to the other one.. Is it possible to describe a process by which the same force results in a different acceleration, going into details of things going on within the ions?

Edit^2

Virtual photons are virtual, not real. They are essentially a mathematical tool

Would it be possible to derive a virtual mass-energy value associated with these virtual photons within such a mathematical framework? If so, it would be pretty cool if these numbers could account for the difference in acceleration as in my previous edit. The idea being analogous to a cavity with photons bouncing around being heavier than one with no photons inside, only in our case the photons are still officially virtual

 

[PeroK]

Then is there anything specific to which we can attribute the extra mass, or is it just somehow acquired by the whole system in some "holistic" way?

You are missing the key point that an excited atom has less mass that the sum of its constituent parts. You are not looking for extra mass to explain an atom's mass. You need to explain why the configuration has less mass than its constituent parts.

Moreover, mass is not just matter. The premise that mass must be attributable to material particles is the wrong starting point. Mass (as we measure it) is a combination of matter and its configuration. You need to start with that premise (that mass is not just the sum of the constituent parts).

 

[Swamp Thing]

You are missing the key point that an excited atom has less mass that the sum of its constituent parts.

I was not trying to compare the atom mass with the total mass of its component bits and bobs. I was trying to compare two atoms or ions in which at leas one electron in one atom or ion is at a higher energy level than its counterpart in the other atom or ion.

 

[PeroK]

I was not trying to compare the atom mass with the total mass of its component bits and bobs. I was trying to compare two atoms or ions in which at leas one electron in one atom or ion is at a higher energy level than its counterpart in the other atom or ion.

I understand that. But, your reasoning is based on the faulty premises that I tried to explain. It cannot be due to additional particles, because the maximum mass is when the constituent particles are independent of each other.

 

[Swamp Thing]

So if I understand correctly, when we want to calculate the acceleration of a charged bound system under a certain field, we have to plug in the equivalent mass of the binding energy manually. There is no way the exact acceleration can fall out automatically from some more fundamental electrostatic or quantum mechanical or QFT calculation?

 

[Ibix]

So if I understand correctly, when we want to calculate the acceleration of a charged bound system under a certain field, we have to plug in the equivalent mass of the binding energy manually. There is no way the exact acceleration can fall out automatically from some more fundamental electrostatic or quantum mechanical or QFT calculation?

I think the point is that an electron in free space, an electron in an atom ground state, and an electron in an excited state are three quite different things with different probability densities. And you can't take "an electron in an excited state" out of the atom and put it to one side and take the nucleus out and put it somewhere else and see what you're left with, since they only exist in the states you want to consider when they're together. So I suspect you can't trace your question further than "they're different systems".

But you might be better to ask in the quantum forum.

 

[PeroK]

So if I understand correctly, when we want to calculate the acceleration of a charged bound system under a certain field, we have to plug in the equivalent mass of the binding energy manually. There is no way the exact acceleration can fall out automatically from some more fundamental electrostatic or quantum mechanical or QFT calculation?

The mass of a system in QFT includes all the internal binding and kinetic energies. Note that both an atom and even a proton are composite particles. If you go beyond basic chemistry, the concept of mass in QFT is quite a complex subject. Hence all the fuss over the Higgs boson.

 

[PeroK]

PS in an atom, the electron is bound to the proton in a fundamental way. This is where QM is fundamentally different from classical physics. The Earth is essentially still an independent planet, regardless of the fact that it is gravitationally bound to the Sun.

The QM model of the atom is fundamentally different from a mini solar system. In a very real sense there are no independent proton and electron. Instead, there is a single bound system.