Relativistic Mass of Sub-Atomic Particles: What Does it Mean?

[Nugatory]

A compressed spring has a greater effective (relativistic) mass than uncompressed

It has greater mass. The qualifications "effective" and "relativistic" in this context are somewhere between meaningless, potentially confusing, and just plain wrong.

Is it correct to say that it has a greater *rest* mass?

Yes, and this is equivalent to saying that it has "greater mass". The qualifier "rest" is redundant, although widely used for historical reasons.

Have particles (photons) been literally added to the spring by compressing it ?

No. Energy was added to it.

 

[Dale]

A compressed spring has a greater effective (relativistic) mass than uncompressed.

Is it correct to say that it has a greater *rest* mass? After all, all particles are at rest.

Yes, although I would say it has a greater "invariant mass" rather than "rest mass"

Have particles (photons) been literally added to the spring by compressing it ?

The rest mass of a system can be greater than the sum of the masses of the constituent particles. So it is not that there are more particles, but just the system is in a more massive configuration.

 

[1977ub]

When you are compressing a spring, does this imply that somehow in the process photonic electromagnetic energy is being absorbed by the totality of the spring particle system?

 

[Nugatory]

When you are compressing a spring, does this imply that somehow in the process photonic electromagnetic energy is being absorbed by the totality of the spring particle system?

The words "photonic electromagnetic energy" don't mean much of anything, so the question as asked doesn't have any sensible answer.

When you compress the spring you're doing work on it, and that adds energy to it. Some of that energy shows up as heat; a real (as opposed to an ideal) spring warms up from very slightly from internal friction as it flexes. Some of that energy is stored as potential energy as the atoms in the spring are pushed a bit closer to one against the electromagnetic forces that tend to hold them in place in the uncompressed spring; this energy is released when the spring is uncompressed again.

(This might be a good time to mention that photons are part of quantum electrodynamics, while special relativity is based on classical electrodynamics; there are no photons in SR and thinking about them will just confuse and mislead you. I am speaking with tongue only slightly in cheek when I say that you should do your best to forget that you ever heard the word "photon" until after you've learned SR and then ordinary non-relativistic QM.
I am not speaking with tongue in cheek when I say that whenever you find yourself tempted to say "photon" in a relativity discussion you should substitute the phrase "flash of light".)

 

[1977ub]

When potential energy is added to a system, does this imply that must arrive via some one of the fundamental particles and forces of physics? Or must it only be understood as being a feature of the "arrangement" of the molecules ?

 

[Nugatory]

When potential energy is added to a system, does this imply that must arrive via some one of the fundamental particles and forces of physics? Or must it only be understood as being a feature of the "arrangement" of the molecules ?

Generally you add potential energy to a system by moving some part of the system against some force. Lifting a weight against gravity, moving a charged particle against an electrostatic force, ...

This is all classical physics, which you need to learn and understand before you take on relativity.

 

[1977ub]

Perhaps these questions need to be in the quantum area. The nub of what I'm after is the increase in mass after potential energy increases. Is there any kind of nuts-and-bolts understanding of that. The "residual" effective mass/energy after removing mass from particles - in cases where nothing is moving, is it made of anything? In cases where potential energy increases due to moving two bodies away to increase gravitational potential, in quantum terms is the system absorbing a graviton or anything?

 

[Dale]

When potential energy is added to a system, does this imply that must arrive via some one of the fundamental particles and forces of physics? Or must it only be understood as being a feature of the "arrangement" of the molecules ?

The answer to this question doesn't really matter. If you are dealing with a system that is simple enough to be described in terms of the fundamental forces then use that. If it is a more complicated system then you approximate things until you get a tractable level of complexity and just don't worry about the fundamental level.

The nub of what I'm after is the increase in mass after potential energy increases. Is there any kind of nuts-and-bolts understanding of that.

You add two vectors and take their norm. I don't see how you can get more nuts and bolts than that. It doesn't matter if the system you are dealing with is quantum or classical. It is the same process either way.

 

[1977ub]

I can appreciate that it may not "matter" but that doesn't stop my mind from trying to analyze and model it in terms of what is here and what is there.

 

[Dale]

I can appreciate that it may not "matter" but that doesn't stop my mind from trying to analyze and model it in terms of what is here and what is there.

But you cannot accurately use QFT models until you actually learn QFT. Anything that you try to analyze about it now is done from a state of ignorance, and will be misleading at best. QFT shouldn't be done halfway, and until you are ready to do it correctly it is best to avoid it. At this level of study it will not be beneficial in any way.

In this thread in particular, you are attempting to apply QM instead of focusing on the simple classical and geometric fact that the norm of the sum of two vectors is different from the sum of the norm. A deep dive into QFT will not provide any additional insight. The resolution to your question is not quantum mechanical, it is geometrical.

 

[1977ub]

I've got something in a black box. Its mass is tested using inertia or gravitational field. Some of the things I can do to what is in there which increase effective mass are clearly a matter of *adding* *something* - say, put in some more mass, or shine some photons in. I wondered if other actions which may increase the measured mass of what is in there - such as separating the mass into two parts - also amounted to adding something to the box. If not, I can accept that.

 

[DrGreg]

I've got something in a black box. Its mass is tested using inertia or gravitational field. Some of the things I can do to what is in there which increase effective mass are clearly a matter of *adding* *something* - say, put in some more mass, or shine some photons in. I wondered if other actions which may increase the measured mass of what is in there - such as separating the mass into two parts - also amounted to adding something to the box. If not, I can accept that.

The mass of the box (i.e. the box and its contents) and the total energy of the box as measured by a frame in which the box is at rest are related by $E=mc^2$. So the only way the mass of the box can change is if energy passes through the walls of the box. Any changes within the box (e.g. conversion of potential energy to kinetic energy) cannot affect the mass of the box provided nothing is added or subtracted through the walls.

 

[1977ub]

I'm actually looking at the different ways one can open the box, do something which increases the effective mass of the box, and then closing it up. When, for example, I reach in and then move half the mass to one end and half the mass to the other end, and then close it up again, there will be a greater intertial and gravitational mass since we have increased the gravitational potential energy. Does this mean I left anything in particular in the box or no?

 

[Mister T]

The nub of what I'm after is the increase in mass after potential energy increases. Is there any kind of nuts-and-bolts understanding of that.

If the potential energy of the spring increases by $\frac{1}{2}kx^2$ then the mass of the spring increases by $\frac{1}{2}kx^2/c^2$.

This is an example of the Einstein mass-energy equivalence. You seem to be seeking some mechanism by which the energy is converted to mass, but that is a misconception. There is no conversion. The energy is mass.

 

[Nugatory]

I'm actually looking at the different ways one can open the box, do something which increases the effective mass of the box, and then closing it up. When, for example, I reach in and then move half the mass to one end and half the mass to the other end, and then close it up again, there will be a greater intertial and gravitational mass since we have increased the gravitational potential energy. Does this mean I left anything in particular in the box or no?

You added some energy to the box. Whether that counts as having "left anything in particular" or not depends on what you mean by that phrase.

 

[Mister T]

When, for example, I reach in and then move half the mass to one end and half the mass to the other end, and then close it up again, there will be a greater [...] mass since we have increased the gravitational potential energy.

You don't move mass. You move stuff, like in this case maybe you are moving matter? And if that matter is attracted to the other half of the matter in the box, then when you separate the two halves you increase the potential energy and thus the mass, since the two are equivalent.

 

[1977ub]

If I open the box and shoot light at the box, this will increase the effective mass if any of it "sticks" in some way - chemically or as heat.

 

[Dale]

Some of the things I can do to what is in there which increase effective mass are clearly a matter of *adding* *something*

Any method of increasing the mass involves adding four-momentum. Whether you call that *something* or not is semantics. The key question is whether or not four-momentum was added, not whether that four-momentum is attached to some specific thing.

 

[1977ub]

I'm focusing on where the energy has to come from as well. Presumably after I reach into the box and move the different parts of the mass to different corners, this will have taken my own chemical energy in my muscles. So this will reduce the mass-energy of my body.

 

[Nugatory]

I'm focusing on where the energy has to come from as well. Presumably after I reach into the box and move the different parts of the mass to different corners, this will have taken my own chemical energy in my muscles. So this will reduce the mass-energy of my body.

Yes, but because you aren't part of the box this reduction is irrelevant to the mass of the box.

 

[Dale]

I'm focusing on where the energy has to come from as well.

It doesn't matter where it comes from, what form it is in when it enters the box, or what it turns into within the box. That is the elegance of conservation principles ... the details do not matter.

 

[1977ub]

from wikipedia: "the mass of an atomic nucleus is less than the total mass of the protons and neutrons that make it up, but this is only true after this energy from binding has been removed in the form of a gamma ray (which in this system, carries away the mass of the energy of binding). This mass decrease is also equivalent to the energy required to break up the nucleus into individual protons and neutrons (in this case, work and mass would need to be supplied). Similarly, the mass of the solar system is slightly less than the sum of the individual masses of the sun and planets."
https://en.wikipedia.org/wiki/Mass–energy_equivalence

I'm not sure what the phrase "only true after" gamma ray has been removed. Will the mass of an intact nucleus be found to be less than the sum of the protons and neutrons ?

 

[PeterDonis]

Will the mass of an intact nucleus be found to be less than the sum of the protons and neutrons ?

Yes. The article's phrasing is clumsy. What they are trying to say is that, in order to make an intact nucleus out of a bunch of free protons and neutrons, you have to remove energy from the protons and neutrons. Gamma rays are a common way for energy to be carried off from nuclear reactions, but there is no single nuclear reaction that will make, for example, an iron-56 nucleus out of 26 free protons and 30 free neutrons; it would take a long series of reactions, some of which would have products other than gamma rays. So the article is not describing a process that actually happens; it's just trying to make a general point, and doing it in a confusing way.

 

[Ibix]

I'm not sure what the phrase "only true after" gamma ray has been removed. Will the mass of an intact nucleus be found to be less than the sum of the protons and neutrons ?

I think the article is idealising the process as

1. You have protons and neutrons.
2. You fuse them.
3. They emit a gamma ray.

Step 2 would be a nucleus in an excited state. Step 3 would be a nucleus in its ground state. Step 2 would have the same mass as the particles in step 1. Step 3 would have a lower mass as long as you let the photon escape.

As Peter says, it doesn't actually happen in three easy steps like that.

 

[Orodruin]

Of course I agree that it does not happen in easy steps as the Wiki article says. However, to pile on a bit to the question "does the nucleus have less mass than the sum of the proton and neutron masses?" a clear indication of this should be the fact that the proton mass in atomic units is 1.007u and the neutron mass 1.009u. The atomic mass unit is defined as 1/12 of the mass of a unbound neutral carbon-12 atom and clearly the mass of 6 protons and 6 neutrons is larger.

 

[Dale]

Will the mass of an intact nucleus be found to be less than the sum of the protons and neutrons ?

Yes

 

[1977ub]

Also I guess I forgot gravitational potential energy is negative - in other words, you open the box, move things from the center out to the edges of the box, then close it. It is now found to have less inertial and gravitational mass.

 

[Dale]

in other words, you open the box, move things from the center out to the edges of the box, then close it. It is now found to have less inertial and gravitational mass.

You have that backwards.

 

[1977ub]

If the solar system is found to have less mass than the individual bodies, is this not due to the gravitational potential energy of their being separated in space?

 

[PeterDonis]

If the solar system is found to have less mass than the individual bodies, is this not due to the gravitational potential energy of their being separated in space?

No, it's due to the (negative) gravitational potential energy because they are not separated a lot more in space--i.e., because they are in a bound system with a finite size that is small on cosmological scales, instead of being spread out very far away from each other.

you open the box, move things from the center out to the edges of the box, then close it. It is now found to have less inertial and gravitational mass.

No, it will have more, because the things in the box are separated by a larger distance than they were before. That means you added energy to the box in order to move them apart.

If you want to decrease the inertial and gravitational mass of the box, without removing any of the objects inside, you would need to open the box and remove energy from it, bringing the objects inside closer together (i.e., making them more tightly bound) in the process.

 

[1977ub]

No, it's due to the (negative) gravitational potential energy because they are not separated a lot more in space--i.e., because they are in a bound system with a finite size that is small on cosmological scales, instead of being spread out very far away from each other.
No, it will have more, because the things in the box are separated by a larger distance than they were before. That means you added energy to the box in order to move them apart.

If you want to decrease the inertial and gravitational mass of the box, without removing any of the objects inside, you would need to open the box and remove energy from it, bringing the objects inside closer together (i.e., making them more tightly bound) in the process.

Ok then I'm back with my nagging biases. To make things more tightly bound, does this not imply perhaps that electromagnetic energy was contributed?

Aren't all forms of potential energy related to fundamental forces?

 

[PeterDonis]

To make things more tightly bound, does this not imply perhaps that electromagnetic energy was contributed?

You don't "contribute" energy to make things more tightly bound. You take away energy. As for what form the energy taken away can take, that depends on the details of how you do it. In natural processes like the formation of stars or planetary systems, electromagnetic radiation is typically the way that energy is taken away from the system to allow it to become more tightly bound.

 

[Dale]

make things more tightly bound, does this not imply perhaps that electromagnetic energy was contributed?

It doesn't matter! It can be any form.

Aren't all forms of potential energy related to fundamental forces?

It doesn't matter.

The form of the energy is an irrelevant detail, all that matters is that it is a component of the conserved four-momentum. I feel like you are just ignoring this key fact. The whole purpose of establishing conservation laws is because once you do so you don't need to worry about the details.

 

[1977ub]

You don't "contribute" energy to make things more tightly bound. You take away energy. As for what form the energy taken away can take, that depends on the details of how you do it. In natural processes like the formation of stars or planetary systems, electromagnetic radiation is typically the way that energy is taken away from the system to allow it to become more tightly bound.

Ok. So my impression seems correct. You send electromagnetic energy into the box and it becomes warmer and heavier, or more spread out and heavier, or starts moving around and gets heavier. What ways are there to remove energy / mass from a system without particles (massive or photons) being removed?

 

[PeterDonis]

You send electromagnetic energy into the box and it becomes warmer and heavier, or more spread out and heavier, or starts moving around and gets heavier.

Yes.

What ways are there to remove energy / mass from a system without particles (massive or photons) being removed?

At the fundamental level, there are only four interactions known (electromagnetic, weak, strong, and gravitational), and only two of them give rise to radiation that can travel long distances (the weak and strong interactions are short range and don't give rise to radiation). So the only other option besides the ones you list is gravitational radiation. But gravitational radiation from almost any system will be so much weaker than electromagnetic radiation that it can be ignored for all practical purposes. (The only exceptions are the kinds of systems we have detected gravitational waves from--black hole mergers, neutron stars merging to form black holes, etc.)