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July 26

Absorption of matter, without changing the absorber's restmass. Possible?

When a stationary system absorbs a new stationary body, the system's restmass increases by the new body's restmass.

Something similar happens when an electron absorbs light. See Wikisource: The free electrons absorb some of the ultraviolet energy that initially set them free and form an ionized layer.

However, when a stationary body collides with a moving body, the stationary body gains kinetic energy, without changing this body's restmass.

Can a moving body be absorbed by an absorber (like in the first case), but with the absorber's restmass remaining the same as before (like in the second case)? HOTmag (talk) 12:35, 26 July 2024 (UTC)

A free electron cannot absorb light. Ruslik_Zero 13:24, 26 July 2024 (UTC)

Photons caught by a trap increases its mass. As Ruslik_Zero points out, photons interacting with free electrons are not absorbed. Instead they interact elastically, but inelastic collisions are always additive increasing the invariant mass of the absorber. Modocc (talk) 14:26, 26 July 2024 (UTC)

Must the answer to the question in the title be negative?

As for free electrons absorbing light, I've struck it out, but is the book "Electronics Technician" wrong? It's quoted in Wikisource: [1]: The free electrons absorb some of the ultraviolet energy that initially set them free and form an ionized layer.

HOTmag (talk) 14:46, 26 July 2024 (UTC)

Not wrong. The electrons were bonded so the photons' energies broke them without changing their intrinsic rest masses. Modocc (talk) 15:38, 26 July 2024 (UTC)

Ok, so I've just added back the first comment about free electrons absorbing light (I've also added your clarification). Anyway, I'm still curious to know the answer to the question in the title. HOTmag (talk) 16:27, 26 July 2024 (UTC)

In Compton scattering, a free electron gains energy and momentum from a photon, but it does not "absorb" it. --Wrongfilter (talk) 16:52, 26 July 2024 (UTC)

Right, matter absorbs radiation per Quantum electrodynamics. Its rest mass increases unless the energy gets scattered elsewhere. Modocc (talk) 18:06, 26 July 2024 (UTC)

The electron's mass does not increase. --Wrongfilter (talk) 18:26, 26 July 2024 (UTC)

With Compton scattering, it cannot absorb the photon. Modocc (talk) 18:29, 26 July 2024 (UTC)

Who said it does? I'm out. --Wrongfilter (talk) 18:31, 26 July 2024 (UTC)

Sorry. I certainly did not nor did I say the electron's mass increased! And when I realized I simply repeated what you said I was going to fix that. Modocc (talk) 18:35, 26 July 2024 (UTC)

Right, the mass of the bound masses increases and with respect to electrons only their energy increases. Modocc (talk) 18:38, 26 July 2024 (UTC)

HOTmag, as I was trying to say, bound matter's rest mass increases unless the energy absorbed by it gets emitted again. Modocc (talk) 18:49, 26 July 2024 (UTC)

In general, the energy of waves are absorbed: See Absorption (acoustics) and Absorption (electromagnetic radiation). Also, all matter is thought to be comprised of matter-waves. Perhaps that helps. Modocc (talk) 19:50, 26 July 2024 (UTC)

To sum up, electrons' masses are intrinsic and elemental, but the bound rest masses of objects are not. Both absorbed light and matter can increase the latter's (bound rest masses) mass as you observed, but neither can increase the former's mass (the electron's). Thus the answer is no, absorbers do not absorb matter without increasing their rest masses unless they release it, like you noted with particle annihilation, if only because their masses are not as elemental as their constituents... Modocc (talk) 00:24, 27 July 2024 (UTC)

Let me be more clear, now without mentioning photons:

When a stationary system absorbs a new stationary body, the system's restmass increases by the new body's restmass.

However, when a stationary body collides with a moving body, the stationary body gains kinetic energy, without changing this body's restmass.

Can matter be absorbed by an absorber (like in the first case), but with the absorber's restmass remaining the same as before (like in the second case)? HOTmag (talk) 19:30, 27 July 2024 (UTC)

The first case, absorption, always adds rest mass (the second case changes the object's KE, but not its rest mass like within particle accelerators). Modocc (talk) 20:11, 27 July 2024 (UTC)

I didn't ask about the first case, i.e. about a stationary system absorbing a stationary body so that the whole system's restsmass increases, nor about the second case in which the restmass doesn't change.

I wonder, why there can be no third case, i.e, a case in which a system (whether a stationary one or a moving one) absorbs a moving body, so that the system's kinetic energy increases but the whole system's restsmass doesn't change. Is there any reasoning or explanation behind this fact of absence of such a third case? HOTmag (talk) 21:56, 27 July 2024 (UTC)

When an object is at rest its KE is zero, but conservation of energy requires that every object's total energy to be the sum of its parts. We call it rest mass and absorption(s) increases it. Modocc (talk) 22:36, 27 July 2024 (UTC)

I think the conservation of energy is not sufficient for the full explanation: Without the conservation of momentum, one can still argue, that before the absorptoin, the absorber was at rest - hence carried no kinetic energy, while the other body about to be absorbed carried some kinetic energy. After the absorption, the whole system remained surprisingly with the same mass as before, but gained the absorbed body's kinetic energy. What's wrong with that? The wrong thing is my neglecting the conservation of momentum. HOTmag (talk) 00:58, 28 July 2024 (UTC)

The absorbed body adds, at a minimum, a mass-energy equal to KE/c² to the absorber which gains its KE. In addition, for the n-body system, its rest mass and total energy is conserved and unchanged whether they are far apart or bonded together, or internalized and perhaps superimposed. To calculate their combined rest mass one simply adds up their energies in its center-of-momentum frame. In this reference frame the momentum vanishes and their total energy is therefore its rest mass. Modocc (talk) 03:25, 28 July 2024 (UTC)

As to your first sentence about adding a mass $E_{K}/c^{2}$ to the absorber: Please notice, that without the conservation of momentum, one can still argue that before the absorption, the body about to be absorbed carried a total energy $E$ that included - both an internal energy $E_{0}$ - and a kinetic energy $E_{K}$ equivalent to a mass of the size $E_{K}/c^{2}$ you've mentioned. After the absorption, the whole system remained surprisingly with the same mass as before, whereas the absorbed body's internal energy $E_{0}$ was not added to the absorber's internal energy as an addition of the size $E_{0}$, but rather the absorbed body's total energy $E$ was added to the absorber's kinetic energy as an addition of the size $E$. What's wrong with that, without assuming the consevation of momentum, which may actually be not conserved (as you can see in my following thread)?

As to your last claim that "for the n-body system, its rest mass and total energy is conserved and unchanged whether they are far apart or bonded together": AFAIK, what's conserved is the mass-energy as a whole, but the mass alone doesn't have to be conserved: Check: an electron-positron pair, becoming energy alone, without conserving the mass alone (unless one attributes mass to photons, which is a controversial and debatable possibility). HOTmag (talk) 07:11, 28 July 2024 (UTC)

Energy contributes to the rest mass. For example, the gluons' energy within the proton contributes to its overall rest mass. It's a widely accepted concept. Modocc (talk) 12:35, 28 July 2024 (UTC)

Not always. Check: an electron-positron pair, becoming energy alone, without contributing any mass to the light emitted (unless one attributes mass to photons, which is a controversial and debatable possibility). HOTmag (talk) 12:38, 28 July 2024 (UTC)

The rest mass of the 2-body system is conserved. Modocc (talk) 12:54, 28 July 2024 (UTC)

Before the electron and the positron annihilated each other and became energy, the system's rest mass was positive, but after they annihilated each other, the system became light carrying no restmass. HOTmag (talk) 13:24, 28 July 2024 (UTC)

The light carries only energy and momentum yes, but there is a center-of-momentum reference frame in which the particle-waves' momentum vanishes, but their energy, their 2-body rest mass, does not. Modocc (talk) 13:44, 28 July 2024 (UTC)

Yes, their energy does not vanish, but their 2-body restmass does vanish, once they annihilate each other and become light, which actually carries no restmass, so the energy they carried before they annihilated each other does not contribute any mass to the light emitted. HOTmag (talk) 17:19, 28 July 2024 (UTC)

Place the event in an opaque container. Both the container's total energy and momentum are unaffected because its rest mass includes the photons. Modocc (talk) 19:55, 28 July 2024 (UTC)

Yes, when a photon is absorbed it contributes to the absorber's restmass.

However, when an electron-positron pair becomes light in the free space, the pair's restmass vanishes.

This proves that restmass alone, in the free space (rather than in an opaque container), doesn't have to be conserved.

Indeed, restmass is conserved if one assumes both the conservation of energy and the conservation of momentum, but if one only assumes the conservation of energy without assuming the conservation of momentum, then one can still argue, that although any massive body about to be absorbed carries a total energy $E$ that includes - both a kinetic energy $E_{K}$ - and an internal energy $E_{0}$ equivalent to restmass, still after the absorption, the absorber remains surprisingly with the same restmass as before, whereas the absorbed body's internal energy $E_{0}$ is not added to the absorber's internal energy as an addition of the size $E_{0}$, but rather the absorbed body's total energy $E$ is added to the absorber's kinetic energy as an addition of the size $E$. What's wrong with that, without assuming the consevation of momentum, which may actually be not conserved (as you can see in my following thread)? HOTmag (talk) 22:35, 28 July 2024 (UTC)

The container need not contain free space and even if it does as a system its total energy still does not change. Think also of the atmospheric cloud. It consists of enormous numbers of massive and massless particles moving at various velocities, but it is nearly stationary to you and the clouds' total energy that can be calculated is called rest mass. Modocc (talk) 23:00, 28 July 2024 (UTC)

Yes, the container, as well as the atmospheric cloud, are systems each of which conserves the restmass. However, in my previous response I didn't talk about any container, nor about any atmospheric cloud. I only said, that "when an electron-positron pair becomes light, [not in a container nor in an atmospheric cloud, but rather] in the free space, then the pair's restmass vanishes". This proves that restmass alone, in the free space (rather than in a container or in an atmospheric cloud), doesn't have to be conserved. Then I added the crucial last paragraph in my previous response. HOTmag (talk) 06:45, 29 July 2024 (UTC)

We've had the two-photon thing before. --Wrongfilter (talk) 09:32, 29 July 2024 (UTC)

Yes, I remember, but this time I'm talking with Moddoc about an electron-positron pair, which is another issue. HOTmag (talk) 10:54, 29 July 2024 (UTC)

How many photons do you think come out of an electron-positron annihilation event? --Wrongfilter (talk) 11:13, 29 July 2024 (UTC)

2. HOTmag (talk) 12:54, 29 July 2024 (UTC)