Is Relativistic Mass Still Relevant in Modern Physics Discussions?

[JesseM]

Here is another source saying that the mass of a compound object (the inertial mass, presumably) is proportional to the total energy rather than just the sum of the rest masses--this one is part of the virtual visitor center of Stanford's Linear Accelerator:

In fact Einstein's relationship tells us more, it says Energy and mass are interchangeable. Or, better said, rest mass is just one form of energy. For a compound object, the mass of the composite is not just the sum of the masses of the constituents but the sum of their energies, including kinetic, potential, and mass energy.

And http://www.phy.duke.edu/courses/100/lectures/Rel_2/Rel2.html is a page from a Duke University physics course which gives an example involving an inelastic collision:

Example: An Inelastic Collision

* Consider a situation where two identical particles move toward each other along a straight line, with equal speeds. They collide and stick together.

* Conservation of momentum gives

http://www.phy.duke.edu/courses/100/lectures/Rel_2/Eq22a

from which we conclude that V = 0, so the final object is at rest.
*
* Conservation of total relativistic energy gives

http://www.phy.duke.edu/courses/100/lectures/Rel_2/Eq23

since V = 0. We thus find

http://www.phy.duke.edu/courses/100/lectures/Rel_2/Eq24

* Since \gamma > 1, this shows that the mass of the final object is larger than the sum of the original masses. The lost kinetic energy has been converted to rest energy (mass).

* The classical explanation for the loss of kinetic energy attributes it to conversion into thermal energy (heat): the final object will have a higher temperature, or more specifically a larger internal energy.

* This suggests that the mass of a compound object is a measure of its total energy content, including thermal energy and the binding energies that hold its atoms or molecules in place.

If the two colliding masses were inside a box, would you say that the inertia of the box would be different before the collision than after, since the rest mass of the combined object is higher than that of the sum of the rest masses of the objects before they collided?

 

[Aer]

You can pull excerpts from all over the internet all day long, it doesn't change the fact that there is no experimental proof that this is true.

In fact, if you have just 2 objects, 1 inside the other moving at .9c. Do we know for a fact that this kinetic energy will add to the inertia? Would this be a simple test to confirm? Show me the evidence!

 

[JesseM]

Yes I did Your reply ignores the fact that the energy of a composite object is not equal to the sum of the rest energies of all the particles making it up.

You are assuming an objects inertia will increase with an increase in energy content.

I'm not assuming it, I have posted a bunch of sources that say this.

Inertia only increases with mass, and mass is only defined as "rest mass" in physics.

...and you have no source for this, it's just your faulty understanding of what relativity says. It is simply not true that inertia only increases with increases in rest mass in relativity (if it were, then it would be just as easy to accelerate something moving at 0.999999c as it is to accelerate the same object at rest).

"Relativistic mass" is on the fringe edge of physics, in fact, it is not even mentioned in any of my physics textbooks.

That's why I keep saying that we can talk in terms of total energy rather than "relativistic mass" (although given the definitions it's trivial to go back and forth between these). The rest mass of a composite object is equal to the total energy in its center-of-mass frame divided by c^2, and the inertia of a compound object is proportional to its total energy or "rest mass". See? No need to refer to relativistic mass at all. You keep disagreeing with this, although I've now presented four reputable sources to support it and you've presented a big fat zero sources to support your claims.

 

[JesseM]

You can pull excerpts from all over the internet all day long, it doesn't change the fact that there is no experimental proof that this is true.

I doubt that it's true that there have been no experimental tests of this. But leaving that aside for now, do you agree that the theory of special relativity says that the inertia is proportional to the total energy?

 

[Aer]

Mass has the property that the mass of a compound object is the sum of the mass of the constituents, corrected for binding energy

Is this the same as your "compound object". That was from the first link I clicked on upon doing a search on google.

 

[Aer]

Your inelastic collision example assumes the kinetic energy to be converted to rest energy - it doesn't explicitly say that this is true. If the collision were to really happen, are you saying no energy would be given off upon binding together? I don't think this assumption is correct. You must prove this assumption if you want to use that example.

 

[JesseM]

Mass has the property that the mass of a compound object is the sum of the mass of the constituents, corrected for binding energy

Is this the same as your "compound object". That was from the first link I clicked on upon doing a search on google.

It's unclear whether he's talking about a compound object where the parts are in motion relative to each other, though. I'm also not sure what type of "mass" he's talking about. But I'll send him an email to ask about this.

 

[Aer]

Well he also says "m is frame-independent". I take this to mean that no matter how fast an object is moving, its mass is m - and this is true whether it is contained within another object at rest or not.

 

[Aer]

And doesn't a hot air balloon rise? OK - bad reference.

 

[JesseM]

Your inelastic collision example assumes the kinetic energy to be converted to rest energy - it doesn't explicitly say that this is true. If the collision were to really happen, are you saying no energy would be given off upon binding together?

Sure, it's probably a simplified example, but if the collision happened in a vacuum then energy couldn't escape through soundwaves, so the only other way for it to escape would be through electromagnetic radiation...I suppose the example assumes this loss is negligible. In any case, you could assume the collision happens in a sealed box with mirrored insides, so no energy would escape the box. If the rest mass of the combined object is different than the sum of the rest masses of each object before the collision (photons have zero rest mass, of course), would you say that the inertia of the box will change? Do you think that this is what the theory of relativity would predict?

 

[JesseM]

And doesn't a hot air balloon rise?

What does that have to do with it? A balloon rises because of the buoyancy force--any object in a fluid will experience an upwards force equal to the weight of the volume of fluid it displaces, so the object will rise if this is greater than its own weight.

 

[Aer]

If the rest mass of the combined object is different than the sum of the rest masses of each object before the collision (photons have zero rest mass, of course), would you say that the inertia of the box will change?

You are assuming the assertion that the rest mass of an object is a measure of the total energy of its constituents in posing that question! I'll put it this way, if an experiment was conducted as stated above and the conclusion was that the mass increased, then there would be a basis for the assertion.

Otherwise, it is just that - an assertion. There is no proof one way or the other. However, I choose to go with m being frame independent - which to me, implies the mass of a compound object will be the sum of its constituent's rest masses.

I think we should agree to leave it at that. This discussion is going to go nowhere for either of us I am afraid.

 

[Aer]

What does that have to do with it? A balloon rises because of the buoyancy force--any object in a fluid will experience an upwards force equal to the weight of the volume of fluid it displaces, so the object will rise if this is greater than its own weight.

You must have missed where I said -Bad reference-

 

[εllipse]

You can pull excerpts from all over the internet all day long, it doesn't change the fact that there is no experimental proof that this is true.

I'm surprised this topic is a source of debate. I would have thought whether or not particles weigh more as they approach the speed of light would have been addressed quite plainly by general relativity. I, however, don't know much about GR so I hope someone who knows how to work the GR equations will jump in and solve this (pervect?). If GR doesn't address this, then somebody needs to fix that. Anyway, here's a little excerpt from The Elegant Universe (page 52):

The faster something moves the more energy it has and from Einstein's formula we see that the more energy something has the more massive it becomes. Muons traveling at 99.9 percent of light speed, for example, weigh a lot more than their stationary cousins. In fact, they are about 22 times as heavy--literally.

Of course, being a layman text, Greene may be using the terms "weigh" and "heavy" very generally (as we can see he uses the term "mass" generally; he's obviously talking about relativistic mass in this text, but he doesn't specifically state so). He might not be talking about how much such things weigh in the Earth's gravitational field (although the fact that he clarifies with the word "literally" seems to indicate that he's not using the term "heavy" in a general context), but just how hard it is to push them faster. Which brings me to another point:

In fact, if you have just 2 objects, 1 inside the other moving at .9c. Do we know for a fact that this kinetic energy will add to the inertia? Would this be a simple test to confirm? Show me the evidence!

What is your explanation for why we can't accelerate particles faster than the speed of light in particle accelerators? The explanation I've heard is this: If we create a large electromagnetic field and accelerate a charged particle, its resistance to further acceleration increases. This means that we'd have to use an even stronger electromagnetic field to accelerate it by the same amount. As the speed of the particle approaches the speed of light (in our reference frame), we require more and more energy to accelerate it, and to push it to the speed of light we would require infinite energy. Why would we require more and more energy? Well, to reiterate, the particle's resistance to acceleration increases, so it takes more energy to accomplish the same amount of acceleration. What's another word for resistance to acceleration? Inertia. And, of course, gravitational mass is another word for inertial mass, and gravitational mass is what decide's a body's weight.

However, I do not know whether "inertia" and "inertial mass" are related. That seems to be the point of possible confusion to me. I hope somebody will clear this up.

And please, don't rail on me, Aer. You asked for a debate; I'm just providing the information I have available to me and hoping for some clarification.

 

[JesseM]

You are assuming the assertion that the rest mass of an object is a measure of the total energy of its constituents in posing that question! I'll put it this way, if an experiment was conducted as stated above and the conclusion was that the mass increased, then there would be a basis for the assertion.

You seem to be shifting the goalposts--originally I took you to be arguing that my and learningphysics' assertions about what the theory of relativity predicts were wrong, not that they were right but that you thought the theory itself was wrong. So once again, are you or are you not disagreeing with the assertion that the theory predicts inertia is proportional to total energy?

Incidentally, here's one piece of evidence--if you have a chemical reaction where heat is given off, the inertial mass of the products will be measured to be slightly less than the inertial mass of the reactants, and the difference in inertial mass turns out to be exactly proportional to the heat energy given off divided by c^2.

 

[JesseM]

You must have missed where I said -Bad reference-

So you were talking about your own example, rather than the webpage you linked to? I thought a "reference" meant an outside source of confirmation.

 

[Aer]

You seem to be shifting the goalposts--originally I took you to be arguing that my and learningphysic's assertions about what the theory of relativity predicts were wrong,

We clearly do not define mass to be the same thing, you say mass is M = γ * m.

I claim mass is m, not M. M is relativistic mass and is mentioned nowhere in any of my physics textbooks, why is that?

Incidentally, here's one piece of evidence--if you have a chemical reaction where heat is given off, the inertial mass of the products will be measured to be slightly less than the inertial mass of the reactants, and the difference in inertial mass turns out to be exactly proportional to the heat energy given off divided by c^2.

They lost energy in binding together - i.e. binding energy, that is no surprise.

 

[Aer]

So you were talking about your own example, rather than the webpage you linked to? I thought a "reference" meant an outside source of confirmation.

It was a joke - nevermind!

 

[Aer]

I'm surprised this topic is a source of debate.

Yes, everyone who assumes relativistic mass to be real is always surprised that relativistic mass is a source of debate.

 

[Aer]

What is your explanation for why we can't accelerate particles faster than the speed of light in particle accelerators?

Read this thread completely! I am not going to repeat myself ad infinitum

 

[JesseM]

We clearly do not define mass to be the same thing, you say mass is M = ? * m.

NO I DON'T! I've said over and over again that this issue of inertia can be phrased solely in terms of energy.

I claim mass is m, not M. M is relativistic mass and is mentioned nowhere in any of my physics textbooks, why is that?

Because most physicists prefer not to use the concept of relativistic mass (not because it's 'wrong'--any statement involving relativistic mass has an equivalent in terms of rest mass, momentum, energy, etc.--but just because it can be misleading). What does this aesthetic choice have to do with the physical question of whether inertia is proportional to total energy or not? Once again, are you or are you not disagreeing with the assertion that the theory of relativity says the inertia of a compound object is proportional to its total energy?

They lost energy in binding together - i.e. binding energy, that is no surprise.

So you agree the binding energy contributes to the inertial mass of the reactants, that their inertial mass is not solely the sum of the rest masses of all the particles involved?

 

[εllipse]

I didn't mean I'm surprised you're claiming relativistic mass is a useless concept. I meant I'm surprised that such a claim has sparked such a long debate with no clear winner. Why hasn't anybody addressed it in the context of general relativity yet? (Atleast not in the posts I've read; I admit I haven't read them all.) Shouldn't whatever general relativity states is the mass (relativistic or invariant) that decides a body's weight be the deciding factor? Or could that be interpreted in multiple ways too? I suppose it could, so the deciding factor really seems to be if there is another explanation for why we can't accelerate particles faster than the speed of light in our own reference frame and whether there is a clear relationship between inertia and inertial mass.

Actually, there is. Inertial mass is caused by a body's resistance to acceleration, so if increase in speed = increase in inertia = increase in inertial mass = increase in gravitational mass = increase in weight is correct, which it seems to be to me from the reasoning I outlined earlier, then relativistic mass would seem to atleast be related to inertial mass, if not equivalent.

 

[Aer]

are you or are you not disagreeing with the assertion that the theory of relativity says the inertia of a compound object is proportional to its total energy?

I provided you a link that stated otherwise - that is, the assertion you are making above is incorrect.

So you agree the binding energy contributes to the inertial mass of the reactants, that their inertial mass is not solely the sum of the rest masses of all the particles involved?

Where do you think binding energy comes from? It comes from the particles rest masses, not any type of kinetic or potential energy! That is fundamental.

After the objects bind, this binding energy is forever lost and thus the inertial mass of the new object is less than the combined inertial masses of the two objects before binding. Again - nothing to do with kinetic and potential energy increasing an objects inertia.

I never thought I'd have to remember concepts learned in chemistry class on a relativity forum.

 

[Aer]

Actually, there is. Inertial mass is caused by a body's resistance to acceleration, so if increase in speed = increase in inertia = increase in inertial mass = increase in gravitational mass = increase in weight is correct, which it seems to be to me from the reasoning I outlined earlier, then relativistic mass would seem to atleast be related to inertial mass, if not equivalent.

As an object is accelerating within Earth's gravitational field, if it approaches .9c, it will still accelerate all the same with the same amount of force in its own frame. (i.e. relativistic mass does not equal gravitational mass) and inertial mass = rest mass

 

[JesseM]

I provided you a link that stated otherwise - that is, the assertion you are making above is incorrect.

The link you provided was ambiguous, and I provided four links to back up what I'm saying. And as I said, I emailed the author of the page you referred to, if he ends up supporting my position will that change your mind in any way?

Where do you think binding energy comes from? It comes from the particles rest masses, not any type of kinetic or potential energy!

Huh? The binding energy is the energy it takes to pull the atoms apart, and the atoms are held together by electromagnetic forces. So, the binding energy is just the difference between the electromagnetic potential when the atoms are in the bound state vs. the electromagnetic potential when they are moved arbitrarily far apart (the system naturally stays bound because the potential energy is lower, although in some cases there may be a 'hump' in the potential where the potential becomes higher when you start to move them apart but then goes lower when they're even farther apart, so some molecules can release energy when broken apart, as described on http://www.2ndlaw.com/obstructions.html ).

 

[Aer]

The link you provided was ambiguous, and I provided four links to back up what I'm saying. And as I said, I emailed the author of the page you referred to, if he ends up supporting my position will that change your mind in any way?

I did not find it ambiguous, what part of, -mass is frame independent- is unclear. Or did you just choose to ignore that?

Huh? The binding energy is the energy it takes to pull the atoms apart,

Ahh yes, you can tell I am not a Chem person. This is true - I stated it backwards. Anyway, the binding energy still comes from the rest mass of the object that is being split. My argument was still correct in substance.

 

[JesseM]

I did not find it ambiguous, what part of, -mass is frame independent- is unclear. Or did you just choose to ignore that?

Like I said, there was also the issue of whether he was talking about a compound object where all the parts were at rest with regard to each other. Again, if he ends up supporting my position will this change your mind at all? I want a commitment in advance on this!

Ahh yes, you can tell I am not a Chem person. This is true - I stated it backwards. Anyway, the binding energy still comes from the rest mass of the object that is being split.

No, as I said it comes from the difference in potential energy between the bound state and the unbound state. The sum of the rest masses of the particles doesn't change when you split them apart.

 

[Aer]

Like I said, there was also the issue of whether he was talking about a compound object where all the parts were at rest with regard to each other. Again, if he ends up supporting my position will this change your mind at all? I want a commitment in advance on this!

Why would I make up an opinion based only on some random person's opinion? Only experimental proof will change my mind - find that.

No, as I said it comes from the difference in potential energy between the bound state and the unbound state. The sum of the rest masses of the particles doesn't change when you split them apart.

That is part of the rest mass, is it not?

 

[Aer]

From wikipedia:

Some books follow this up by stating that "mass and energy are equivalent", but this is somewhat misleading. The mass of an object, as we have defined it, is a quantity intrinsic to the object, and independent of our current frame of reference. The energy E, on the other hand, varies with the frame of reference; if the frame is moving at a high velocity relative to the object, E will be very large, simply because the object has a lot of kinetic energy in that frame. Thus, E = mc2 is not a "good" relativistic statement; it is true only in the rest frame of the object.

So doesn't this mean either the above is incorrect or "mass of a compound object is a measure of its total energy" is incorrect.

 

[Aer]

The sum of the rest masses of the particles doesn't change when you split them apart.

From wikipedia:

Because a bound system is at a lower energy level, its mass must be less than its unbound constituents. Nuclear binding energy can be computed from the difference in mass of a nucleus, and the sum of the mass of the neutrons and protons that make up the nucleus. Once this mass difference (also called the mass defect) is known, Einstein's formula (E = mc²) can then be used to compute the binding energy of any nucleus.

 

[JesseM]

Why would I make up an opinion based only on some random person's opinion? Only experimental proof will change my mind - find that.

Shifting the goalposts again. As I've said over and over, I am only asking about what the theory of relativity predicts. Surely the opinion of professional physicists should have some influence on whether you accept my claim that the theory predicts inertia is proportional to total energy, no? If all the physicists in the world claimed that the theory does predict this, would you still somehow argue that they are all wrong about what the theory "really" predicts?

That is part of the rest mass, is it not?

Uh, no, potential energy is not part of the rest mass, since I just told you the sum of rest masses doesn't change when you change the potential.

Some books follow this up by stating that "mass and energy are equivalent", but this is somewhat misleading. The mass of an object, as we have defined it, is a quantity intrinsic to the object, and independent of our current frame of reference. The energy E, on the other hand, varies with the frame of reference; if the frame is moving at a high velocity relative to the object, E will be very large, simply because the object has a lot of kinetic energy in that frame. Thus, E = mc2 is not a "good" relativistic statement; it is true only in the rest frame of the object.

Of course, I agree 100% with this. What's your point?

Because a bound system is at a lower energy level, its mass must be less than its unbound constituents. Nuclear binding energy can be computed from the difference in mass of a nucleus, and the sum of the mass of the neutrons and protons that make up the nucleus. Once this mass difference (also called the mass defect) is known, Einstein's formula (E = mc^2) can then be used to compute the binding energy of any nucleus.

Here I think they are talking about inertial mass (or gravitational mass, which would be the same), not rest mass (or you could say they are talking about the rest mass of the nucleus, but with the understanding that the 'rest mass' of a compound system is defined as its total energy divided by c^2).

 

[Aer]

Here I think they are talking about inertial mass (or gravitational mass, which would be the same), not rest mass.

Inertial mass IS rest mass

Even when you are shown to be wrong, you still claim you are right!

What other mass would they be referring to? Mass only has one definition in the equation E = mc^2 and that is inertial mass.

Here, maybe numbers will help you:

A deuteron is the nucleus of a deuterium atom, and consists of one proton and one neutron. The masses of the constituents are:

mproton = 1.007276 u (u is Atomic mass unit)
mneutron= 1.008665 u
mproton + mneutron = 1.007276 + 1.008665 = 2.015941 u

The mass of the deuteron is:

Atomic mass 2H = 2.013553 u

And if rest mass is not inertial mass, then which of the following is it?

Strictly speaking, there are three different quantities called mass:

* Inertial mass is a measure of an object's inertia: its resistance to changing its state of motion when a force is applied. An object with small inertial mass changes its motion more readily, and an object with large inertial mass does so less readily.
* Passive gravitational mass is a measure of the strength of an object's interaction with the gravitational field. Within the same gravitational field, an object with a smaller passive gravitational mass experiences a smaller force than an object with a larger passive gravitational mass. (This force is called the weight of the object. In informal usage, the word "weight" is often used synonymously with "mass", because the strength of the gravitational field is roughly constant everywhere on the surface of the Earth. In physics, the two terms are distinct: an object will have a larger weight if it is placed in a stronger gravitational field, but its passive gravitational mass remains unchanged.)
* Active gravitational mass is a measure of the strength of the gravitational field due to a particular object. For example, the gravitational field that one experiences on the Moon is weaker than that of the Earth because the Moon has less active gravitational mass.

 

[JesseM]

Inertial mass IS rest mass

For a compound system, this is only true if you define its total "rest mass" as its total energy divided by c^2. This is how physicists define things, but if you choose to make up your own idiosyncratic definition where the compound system's rest mass is just the sum of the rest mass of its parts, then inertial mass and rest mass will not be the same. And of course, if you do this, you'll be hard-pressed to explain why the reactants in a chemical reaction have a different inertial mass than the products, even though all the constituent particles are the same (as far as I know massive particles like protons, electrons and neutrons are not created or destroyed in chemical reactions--photons may be, but they have zero rest mass).

Even when you are shown to be wrong, you still claim you are right!

That source doesn't "show" that inertial mass IS rest mass, it doesn't address the issue at all--you are just making an assumption.

 

[learningphysics]

From wikipedia:

Because a bound system is at a lower energy level, its mass must be less than its unbound constituents. Nuclear binding energy can be computed from the difference in mass of a nucleus, and the sum of the mass of the neutrons and protons that make up the nucleus. Once this mass difference (also called the mass defect) is known, Einstein's formula (E = mc^2) can then be used to compute the binding energy of any nucleus.

Yes... this precisely shows that the rest mass of the nucleus is not simply the sum of the rest masses of the constituent particles. You need to take into account the energy content.

Nuclear binding energy is just one form of energy that leads to mass... it is by no means the only one.

A hydrogen atom weighs slightly less than the sum of the masses of a proton and electron. The difference in mass is due to kinetic energy, and electrostatic potential energy between the electron and proton.

 

[JesseM]

What other mass would they be referring to? Mass only has one definition in the equation E = mc^2 and that is inertial mass.

No, the m in that equation is rest mass.

Here, maybe numbers will help you:

A deuteron is the nucleus of a deuterium atom, and consists of one proton and one neutron. The masses of the constituents are:

mproton = 1.007276 u (u is Atomic mass unit)
mneutron= 1.008665 u
mproton + mneutron = 1.007276 + 1.008665 = 2.015941 u

The mass of the deuteron is:

Atomic mass 2H = 2.013553 u

What's your point? I am sure they are defining the mass of the deuteron as its total energy divided by c^2. If they were just defining its mass as the sum of the rest masses of all the particles, then why do you think its mass is not 2.015941 u, assuming you acknowledge that "binding energy" does not involve any extra particles with nonzero rest mass?

And if rest mass is not inertial mass, then which of the following is it?

Strictly speaking, there are three different quantities called mass:

* Inertial mass is a measure of an object's inertia: its resistance to changing its state of motion when a force is applied. An object with small inertial mass changes its motion more readily, and an object with large inertial mass does so less readily.
* Passive gravitational mass is a measure of the strength of an object's interaction with the gravitational field. Within the same gravitational field, an object with a smaller passive gravitational mass experiences a smaller force than an object with a larger passive gravitational mass. (This force is called the weight of the object. In informal usage, the word "weight" is often used synonymously with "mass", because the strength of the gravitational field is roughly constant everywhere on the surface of the Earth. In physics, the two terms are distinct: an object will have a larger weight if it is placed in a stronger gravitational field, but its passive gravitational mass remains unchanged.)
* Active gravitational mass is a measure of the strength of the gravitational field due to a particular object. For example, the gravitational field that one experiences on the Moon is weaker than that of the Earth because the Moon has less active gravitational mass.

This is from the wikipedia entry on mass, and they say in the section on relativity that "the quantity m has a simple physical meaning: it is the inertial mass of the object as measured in its rest frame, the frame of reference in which its velocity is zero." This definition implies that the inertial mass of the object when measured in a frame other than its rest frame will not be equal to the "m" in E=mc^2 (ie the rest mass)--and of course this is true, objects with large velocities are harder to accelerate than objects that have the same rest mass but smaller velocities, which by definition means they have different inertial masses.

 

[εllipse]

What other mass would they be referring to? Mass only has one definition in the equation E = mc^2 and that is inertial mass.

Actually, isn't the m in E=mc^2 relativistic mass (if applied to other reference frames)? I thought the invariant mass version of the equation was E^2=p^2c^2+m^2c^4.

 

[Aer]

And of course, if you do this, you'll be hard-pressed to explain why the reactants in a chemical reaction have a different inertial mass than the products, even though all the constituent particles are the same (as far as I know massive particles like protons, electrons and neutrons are not created or destroyed in chemical reactions--photons may be, but they have zero rest mass).

It takes energy to bind the proton and neutron together, no?

 

[Aer]

No, the m in that equation is rest mass.

From this page

The rest mass (m) of a particle is the mass defined by the energy of the isolated (free) particle at rest, divided by c 2 . When particle physicists use the word ``mass,'' they always mean the ``rest mass'' (m) of the object in question

 

[JesseM]

It takes energy to bind the proton and neutron together, no?

Yup, and of course this fits with my claim that the inertial mass of the deuteron is equal to its total energy divided by c^2, but it doesn't fit too well with your claim that its inertial mass is dependent only on the sum of the rest masses of its parts, and not on any other forms of energy that may be in the deuteron.

 

[Aer]

What's your point? I am sure they are defining the mass of the deuteron as its total energy divided by c^2. If they were just defining its mass as the sum of the rest masses of all the particles, then why do you think its mass is not 2.015941 u, assuming you acknowledge that "binding energy" does not involve any extra particles with nonzero rest mass?

From this page
the energy that holds a nucleus together; the difference between the sum of the masses of the individual nucleons and the actual mass of the nucleus.

So is the energy not a part of the combined system?


Sorry that I have to keep referring to authority - Chemistry is not my strong point.

 

[JesseM]

No, the m in that equation is rest mass.

From this page

The rest mass (m) of a particle is the mass defined by the energy of the isolated (free) particle at rest, divided by c 2 . When particle physicists use the word ``mass,'' they always mean the ``rest mass'' (m) of the object in question

Yes, that's exactly what I just said, m is used to mean rest mass (although again, for a compound object the rest mass is defined to be the inertial mass in the compound object's rest frame, which is equal to its total energy divided by c^2 in that frame).

 

[Aer]

Yup, and of course this fits with my claim that the inertial mass of the deuteron is equal to its total energy divided by c^2, but it doesn't fit too well with your claim that its inertial mass is dependent only on the sum of the rest masses of its parts, and not on any other forms of energy that may be in the deuteron.

Why isn't this binding energy apart of the rest mass of the system? (I think your answer is rest mass is different from inertial mass - then what is the difference, explicitly)

 

[Aer]

Yes, that's exactly what I just said, m is used to mean rest mass (although again, for a compound object the rest mass is defined to be the inertial mass in the compound object's rest frame, which is equal to its total energy divided by c^2 in that frame).

But by that definition, you have to separate each particle separately and measure it's -rest mass-

What part of isolated particle is not clear?

 

[JesseM]

From this page
the energy that holds a nucleus together; the difference between the sum of the masses of the individual nucleons and the actual mass of the nucleus.

So is the energy not a part of the combined system?

Of course it's part of the combined system, but the energy doesn't have any rest mass of its own. So this contradicts your claim that the rest mass of the combined system is just the sum of the rest masses of its parts, and supports my claim that the rest mass of the combined system is the total energy of the system divided by c^2.

 

[Aer]

Of course it's part of the combined system, but the energy doesn't have any rest mass of its own. So this contradicts your claim that the rest mass of the combined system is just the sum of the rest masses of its parts, and supports my claim that the rest mass of the combined system is the total energy of the system divided by c^2.

It doesn't support your claim! BTW - I never made any claim regarding combining masses in chemistry!

If it supported your claim, then the mass of the deutron should be LARGER than the mass of the proton and neutron combined. Because it not only contains your proton and neutron, but also binding energy - which adds to the total energy.

 

[JesseM]

Why isn't this binding energy apart of the rest mass of the system? (I think your answer is rest mass is different from inertial mass - then what is the difference, explicitly)

It is! But that's assuming you use my definition that the "rest mass" of a composite system is the total energy in the system's rest frame divided by c^2. If you want to define the rest mass of a composite system as just the sum of the rest masses of each of its parts, then instead of looking at each components energy/c^2 from the point of view of the combined system's rest frame, you have to consider each part's energy/c^2 in that part's own rest frame (ie each part's rest mass), ignoring the rest of the system. But what is the rest mass of the binding energy on its own, ignoring all the particles? That doesn't seem to make any sense, binding energy is just a difference in potential energies, how can a difference in potential energies have a rest frame?

 

[JesseM]

Yes, that's exactly what I just said, m is used to mean rest mass (although again, for a compound object the rest mass is defined to be the inertial mass in the compound object's rest frame, which is equal to its total energy divided by c^2 in that frame).

But by that definition, you have to separate each particle separately and measure it's -rest mass-

It's your definition that the rest mass of a compound system is the sum of the rest mass of it's parts, which means you have to measure each part's rest mass separately. My definition is that the compound system's rest mass is the total energy divided by c^2, and I claim that the theory of relativity predicts this is equal to its inertial mass, which you can measure just by looking at the system's resistance to acceleration in its own rest frame.

 

[Aer]

If you want to define the rest mass of a composite system as just the sum of the rest masses of each of its parts, then instead of looking at each components energy/c^2 from the point of view of the combined system's rest frame, you have to consider each part's energy/c^2 in that part's own rest frame (ie each part's rest mass), ignoring the rest of the system. But what is the rest mass of the binding energy on its own, ignoring all the particles? That doesn't seem to make any sense, binding energy is just a difference in potential energies, how can a difference in potential energies have a rest frame?

I only said this about adding together particles that were separated but contained (as in a box), NOT regarding binding particles together - which LOSE mass.

 

[Aer]

It's your definition that the rest mass of a compound system is the sum of the rest mass of it's parts, which means you have to measure each part's rest mass separately. My definition is that the compound system's rest mass is the total energy divided by c^2, and I claim that the theory of relativity predicts this is equal to its inertial mass, which you can measure just by looking at the system's resistance to acceleration in its own rest frame.

Doesn't fit too well with your binding energy argument.

 

[Aer]

It doesn't support your claim! BTW - I never made any claim regarding combining masses in chemistry!

If it supported your claim, then the mass of the deutron should be LARGER than the mass of the proton and neutron combined. Because it not only contains your proton and neutron, but also binding energy - which adds to the total energy.

Which goes back to what I said, the binding energy comes from the proton and neutron's rest mass but is still apart of the system.