Can Mass Be Transformed Into Energy?

[eoghan]

Hi there!
I've a question about special relativity: how can I transform mass in energy? I mean.. if I take an hammer and I beat a table, I transfer energy to the table, but why this energy isn't transformed in mass?
And if I have a mass, how can I transform it in energy? If I break an atom I free energy, but why can't I have energy breaking a glass or something else?

 

[mathman]

For all day to day activity involving mass-energy conversion, such as heating things up on a stove, the mass change is so small as to be essentially unmeasurable. It is only with nuclear reactions (fission, fusion, radioactive decay) or extreme accelerations (particle physics devices) that mass changes are significant.

 

[eoghan]

It is only with nuclear reactions (fission, fusion, radioactive decay) or extreme accelerations (particle physics devices) that mass changes are significant.

Why?

 

[pmb_phy]

Hi there!
I've a question about special relativity: how can I transform mass in energy? I mean.. if I take an hammer and I beat a table, I transfer energy to the table, but why this energy isn't transformed in mass?
And if I have a mass, how can I transform it in energy? If I break an atom I free energy, but why can't I have energy breaking a glass or something else?

Mass is never converted to Energy since both mass and energy are conserved quantities. Only the form of the mass can change, e.g. from proper mass to mass of motion.

Why?

The mass of a particle is a function of the particle's speed. The mass is practicly unchanged for velocities which are much less than the speed of light. But even if v = c/1000 the speed is enormous yet the mass will be about the same as the proper mass.

Pete

 

[Tachyonie]

Mass is never converted to Energy since both mass and energy are conserved quantities. Only the form of the mass can change, e.g. from proper mass to mass of motion.

I am a littlebit confused here. What happens in annihilation process then? (matter + antimatter)

 

[lbrits]

Mass is perfectly capable of being transformed into energy and vice versa. Some people confusingly talk about relativistic and rest-masses, but this is not standard practice anymore. The only "mass" a thing has is the number you get when you put it on a scale, i.e., it's rest mass (that is an relativistically invariant quantity and is therefor meaningful).

The thing that is conserved is proper four momentum p^\mu. So you may take an electron and positron and allow them to annihilate into two photons. In the rest frame of the e-p pair, you'll have

p_1^\mu = (m, 0, 0, 0)
p_2^\mu = (m, 0, 0, 0)

and afterwards, the two photons will have proper momenta, say,
p_1^{\prime \mu} = (m, m, 0, 0)
p_2^{\prime \mu} = (m, -m, 0, 0)

You'll notice that four-momentum is conserved, but the individual photons don't have mass (you can't go into a photon's rest frame).

 

[lbrits]

I realized that we hadn't actually answered the question. The reason you can't, under normal circumstances, create mass using energy is because you need a lot of energy in concentrated form. The lightest particles (ignoring neutrinos for now) are electrons, with a mass of 0.511 MeV/c^2. On the other hand, visible light comes in energy lumps of around 10eV. So you really have to have very concentrated amounts of energy. Said differently, you'd have to hit your hammer pretty hard before you created electrons.

On the other hand, there is no threshold for creating photons, since they are massless. I guess you could say the mass of a particle is the term that goes in the energy relation E = \sqrt{p^2 c^2 + m^2 c^4}. So we can create photons of arbitrarily little energy (fortunately, else all would be dark).

Coming back to my photon example, note that although the photons don't have mass, if you had the electron/positron pair in a box, and weighed the box, allowed the pair to annihilate and could somehow weigh the box again before the photons escaped, the box would weigh the same. Roughly speaking, the "net" four momentum is still \textstyle\sum p^\mu = (2m, 0, 0, 0) which is of a massive particle at rest. There is a saying that says a hot potato weighs more than a cold potato, and I hope you can see why this is the case =)

 

[dst]

On the other hand, there is no threshold for creating photons, since they are massless. I guess you could say the mass of a particle is the term that goes in the energy relation E = \sqrt{p^2 c^2 + m^2 c^4}. So we can create photons of arbitrarily little energy (fortunately, else all would be dark).

Are you sure about that? Since there is an upper bound on a photon's energy (when wavelength hits Planck length, IIRC?) then isn't there a lower bound?

 

[dst]

Mass is never converted to Energy since both mass and energy are conserved quantities. Only the form of the mass can change, e.g. from proper mass to mass of motion.

The mass of a particle is a function of the particle's speed. The mass is practicly unchanged for velocities which are much less than the speed of light. But even if v = c/1000 the speed is enormous yet the mass will be about the same as the proper mass.

Pete

Not at all, any concentrated energy has a certain mass. Chemical bonds have a characteristic mass even. I don't remember if it's experimentally verified but I imagine so.

 

[lbrits]

Are you sure about that? Since there is an upper bound on a photon's energy (when wavelength hits Planck length, IIRC?) then isn't there a lower bound?

We don't know if there's an upper bound or not, since we don't know what happens at the Planck length. Something might take over that keeps everything smooth. On the other hand, I suspect that QED behaves very non-linearly far below the Planck length anyway, so "known" physics alread takes over.

There's no reason to believe that there's a lower bound to the energy a photon can posess. Now, if the photon were placed in a box (or, the universe is of finite size), then you could only create photons with certain wavelengths, so "arbitrarily small" wouldn't be correct. But, as a theory, QED doesn't forbid arbitrarily small wavelengths and actually requires it for gauge invariance, afaik.

 

[yuiop]

Mass is perfectly capable of being transformed into energy and vice versa. Some people confusingly talk about relativistic and rest-masses, but this is not standard practice anymore. The only "mass" a thing has is the number you get when you put it on a scale, i.e., it's rest mass (that is an relativistically invariant quantity and is therefor meaningful).

Please clarify your definition of rest mass using this example:

Say we have 3 identical flywheels, A, B and C.

Flywheel A is cold and not spinning.
Flywheel B is cold and spinning.
Flywheel C is hot but not spinning.


Flywheels B and C are heavier than A when weighed on scales.
Does this mean flywheels B and C have more rest mass than flywheel A?

Is weight a good definition of mass? All 3 flywheels have zero weight far from gravity or when in freefall, but we still consider tham to have mass. Maybe a better definition of mass is the inertial definition, where the mass of a system is a measure of its resistance to being accelerated?

It could be argued that since flywheels B and C weigh more than flywheel A and require more energy to accelerate to a given linear velocity than flywheel A that they also have more inertial mass (resistance to being accelerated) than flywheel A.

When we refer to the rest mass of a system, we seem to actually mean the "rest energy" of the system as measured by an observer that measures the total momentum of the system to be zero. The "rest mass" of a system is usually quoted in terms of mc^2 which is in units of energy rather than units of mass.


Would it not be better to speak of the rest energy of a system when the system has zero linear and angular momentum relative to the observer?

 

[lbrits]

Please clarify your definition of rest mass using this example:

Say we have 3 identical flywheels, A, B and C.

Flywheel A is cold and not spinning.
Flywheel B is cold and spinning.
Flywheel C is hot but not spinning.


Flywheels B and C are heavier than A when weighed on scales.
Does this mean flywheels B and C have more rest mass than flywheel A?

Would it not be better to speak of the rest energy of a system when the system has zero linear and angular momentum relative to the observer?

I'm not too concerned with the internal details of your flywheels. When I mean "at rest" I mean we are in the rest frame, i.e., that P^i = 0. I don't mean that it isn't spinning. If you wanted to go into a frame in which it isn't spinning, then you are in an accelerating coordinate system, so you'd have other problems.

"Would it not be better to speak of the rest energy of a system when the system has zero linear and angular momentum relative to the observer?"

Usually when relativists/field theorists/whomever talk about mass they mean rest mass and in the rest frame, this is simply the rest energy. So yes, when the system has zero linear momentum. I'm going to have to say nay on the angular momentum. That isn't a good rest frame at all (different parts of your coordinate system are traveling at different speeds) =)

For particles this is all a bit overkill, but of course we need to be able to talk about bound states and stuff like that. I invite you to look at the definition of the energy momentum tensor and think of enclosing your system (potato, flywheel) in a volume. Going into the zero linear momentum frame, I believe that if you integrate T^{00} over the volume, you will get the number you read on the scale.

But when I'm in a hurry, I simply say that the mass(squared) is whatever you get on the RHS of p^\mu p_\mu.

 

[Lojzek]

Hi there!
I've a question about special relativity: how can I transform mass in energy? I mean.. if I take an hammer and I beat a table, I transfer energy to the table, but why this energy isn't transformed in mass?
And if I have a mass, how can I transform it in energy? If I break an atom I free energy, but why can't I have energy breaking a glass or something else?

If you hit a table with a hammer, then it's internal energy will increase, so mass will increase acording to E=mc^2 formula: it will be more difficult to accelerate the table after the hit, because it has more energy/mass.
However the increase of mass will be very small, since c is so large: if you hit the table with energy of 100 Joules, the mass will increase by about 10^-15 kg.
Converting mass to energy also happens in classical physics, but the change is again so small that it can be neglected. Breaking glass is not a good example: why would broken glass have less energy than undivided glass. A good example would be cooling of an object, relaxing a spring or slowing down rotation: in all these examples the mass would decrease proportionaly to decrease of energy.

 

[Lojzek]

One more thing: I think that the rest mass-energy should not be considered a new type of energy, but rather one of the known energy types (kinectic, electromagnetic, gravitationat, strong/weak nuclear), which make the system more difficult to accelerate, so the easiest way to calculate them is weighing the whole system and using E=mc^2. The only exception are indivisible particles: we can't break them apart to see which energy contributes to their mass (although it might be possible that those particles are in fact composed of smaller undiscovered particles).

 

[yuiop]

Please clarify your definition of rest mass using this example:

Say we have 3 identical flywheels, A, B and C.

Flywheel A is cold and not spinning.
Flywheel B is cold and spinning.
Flywheel C is hot but not spinning.


Flywheels B and C are heavier than A when weighed on scales.
Does this mean flywheels B and C have more rest mass than flywheel A?

Would it not be better to speak of the rest energy of a system when the system has zero linear and angular momentum relative to the observer?

I'm not too concerned with the internal details of your flywheels. When I mean "at rest" I mean we are in the rest frame, i.e., that P^i = 0. I don't mean that it isn't spinning. If you wanted to go into a frame in which it isn't spinning, then you are in an accelerating coordinate system, so you'd have other problems.

Usually when relativists/field theorists/whomever talk about mass they mean rest mass and in the rest frame, this is simply the rest energy. So yes, when the system has zero linear momentum. I'm going to have to say nay on the angular momentum. That isn't a good rest frame at all (different parts of your coordinate system are traveling at different speeds) =)

I accept your argument that we should define the rest mass of the system as one where the system has zero linear momentum but NOT zero angular momentum relative to the observer.

You seem to be agreeing that flywheels b and C have greater rest mass than flywheel A, so it appears that if we take a stationary flywheel and spin it (or heat it) we increase the the rest mass of the flywheel system. This is a little confusing because we are constantly told that rest mass can not change. I think we have to make the distinction that the rest mass always remains constant under a Lorentz transformation, but physical processes such as spinning a system or heating it can change the rest mass of the system?

 

[Dale]

I typically prefer the term "rest energy" to "rest mass" when describing systems of more than one particle. If you have an ideal gas in a stationary container, and you heat it up it will gain energy. The hot gas will have greater inertia and gravitation, but, there are the same number of particles in the gas as before (i.e. no more matter has been created). "Mass" is commonly understood to be a property of matter, while "energy" is easier to understand as a property of a system and I believe this is a source of confusion here.

A simple example is the photon pair created after anihlation of an electron and a positron. The two photons together have the same energy (converted from matter to radiation) as the original electron and positron, but does it make sense to say that together they have mass? I believe that while it is technically correct it is confusing.

 

[eoghan]

Thanks to everybody

 

[DrGreg]

I accept your argument that we should define the rest mass of the system as one where the system has zero linear momentum but NOT zero angular momentum relative to the observer.

You seem to be agreeing that flywheels b and C have greater rest mass than flywheel A, so it appears that if we take a stationary flywheel and spin it (or heat it) we increase the the rest mass of the flywheel system. This is a little confusing because we are constantly told that rest mass can not change. I think we have to make the distinction that the rest mass always remains constant under a Lorentz transformation, but physical processes such as spinning a system or heating it can change the rest mass of the system?

That is correct. "The rest mass cannot change" is not true. "The rest mass is invariant" is true. "Invariant" has a specific meaning: it means that different inertial observers calculate the same value at a particular event (location+time). It does not mean the value cannot change over time. Such a value would be described as "conserved" rather than "invariant". So rest mass is always invariant but not always conserved.

(When talking about large bodies [or a system of particles] rather than a single point particle, it's probably better to refer to "invariant mass" rather than "rest mass", to avoid any confusion over spinning or internal motion. Or you could take DaleSpam's approach and call it "rest energy".)

 

[Disgod]

You can sort of transform some mass into energy. It is possible to make a fusion reactor, but it is extremely inefficient and the amount of energy you get out of compared to how much you need to put in, is tiny.

Well I was going to give a link to a website that shows a homemade fusion device, but I can't post links yet. If you want to see the website just do a google search for "Homemade Fusion Reactor" and it should be the first link "Fusion is Easy". The website states you can't get any usable energy from the reactor, but you're still transforming some mass into energy, not much, but some.

And then as other people have said, the reason you can't transform mass into energy is that it requires huge amounts of energy to get the process started at a level you can measure, as in nuclear bomb territory. Fusion bombs are actually fueled by an fission explosion first. Fusion works because it uses highly unstable elements and then compresses them under thousands of tons of pressure to start the fusion reaction.

 

[pmb_phy]

I am a littlebit confused here. What happens in annihilation process then? (matter + antimatter)

The mass remains the same. The only thing that has changed is the sum of the proper masses. The total inertial mass (aka relativistic mass) remains constant.

Pete

 

[pmb_phy]

That is correct. "The rest mass cannot change" is not true.

Actually it is true. The rest (aka invariant) mass of a system is the total (as in sum of masses) mass of the system as measured in the zero momentum frame. It can be readily shown that if 3-momentum is conserved in all inertial frames then mass is also conserved in all inertial frames, the zero mometum frame being one such frame. In that frame the mass of the system is called the "rest mass" of the system, even in those cases when none of the particles are at rest!

Were you aware of the fact that rest mass and invariant mass are often used as synonyms?

Pete

 

[RandallB]

The mass remains the same. The only thing that has changed is the sum of the proper masses. The total inertial mass (aka relativistic mass) remains constant.

That is not quite the whole picture that Tachyonie was thinking of. There are at least three unique cases that do have real rest mass aka invariant mass changing as some mass is disappearing.
(I would not use ‘relativistic mass’ here; I’d consider that an abstract number that does change – an other issue dealing with momentum).

Those three cases include Fission Fusion and the annihilation process Tachyonie mentioned. When you have matter and anti matter particles combine the “annihilation” that results means just what is says, invariant mass in the system has disappeared. In a similar manner mass disappears in both fusion and fission reactions.
Note the atomic mass of He is less than the mass of the H atoms that fuse to make it. Thus fusion in the sun means a loss of weight from the fusion.

One of the points of Relativity is that the rule of conservation of mass is violated and that mass in not always conserved. The conservation law was replaced or better stated as “updated” to say that the net of Mass and Energy must be conserved. Thus any loss of invariant mass in a system is matched by an increase of energy in the form of massless photons.
In the case of the sun, energy that departs the local system of the sun.

 

[Antenna Guy]

In the case of the sun, energy that departs the local system of the sun.

That example lends itself well to illustrate the direction of "local time" (albeit on a macroscopic scale).

Regards,

Bill

 

[MeJennifer]

That example lends itself well to illustrate the direction of "local time"

The direction of local time?
What do you mean by that?

 

[pmb_phy]

That is not quite the whole picture that Tachyonie was thinking of.

I'm not a mind reader answer questions that are asked and the question Tachyonie asked was I am a littlebit confused here. What happens in annihilation process then? (matter + antimatter). As far as what he asked then one can only assume that he was referring to the idea that the sum of the proper masses has changed since he was responding to my comment which was

Mass is never converted to Energy since both mass and energy are conserved quantities. Only the form of the mass can change, e.g. from proper mass to mass of motion.

The question regarding whether mass can be converted to energy is question which needs to be stated more clearly. That's why I added the comment regarding the change from proper mass to mass of motion. Actually to be precise I should have referred to the sum of the proper masses. The rest mass of a system or particles is invariant and conserved. To precisely understand this assertion one must first understand what the exact meaning of rest mass of a system or particles. So let me state that now. The rest mass of a system of particles is defined as "the total energy of the system as measured in a frame of reference in which the total momentum is zero"/c². Since energy is conserved then it follows that the rest mass of the system of particles is conserved. This does not mean that the sum of the rest masses of the particles is conserved, which is probably what Tachyonie was thinking about. Since he didn't respond to my answer I assumed he either hasn't read it yet or if he did he either understood it or simply chose not to respond.

There are at least three unique cases that do have real rest mass aka invariant mass changing as some mass is disappearing.

That is impossible for a closed system. It simply can't happen. The invariant mass of a system is the magnitude of the 4-vector obtained by adding the 4-momenta of all the particles in the closed system. Since 4-momentum is conserved it follows that the invaraint mass cannot change.

(I would not use ‘relativistic mass’ here; I’d consider that an abstract number that does change – an other issue dealing with momentum).

That's your choice of course. As far as abstract, I see no reason to refer to it as such. The only thing that is measureable are kinematic quantities. Dynamics quantities are defined in terms of the measureable quantities and therefore things like 3-momentum, 4-momentum, 3-force, 3-force, invariant mass, Electric field, magnetic rield, EM field etc. are defined quantities just as relativistic mass is. Therefore there is no reason to think of relativistic mass as abstract and 3-momentum as not abstract. But as I said, its your choice as what you yourself use but I have very good reasons for using the terms as I do. I myself don't like the term but it brings home what quantity I'm speaking about since the term "mass" doesn't really mean one particular thing. When it appears in a paper or a text one can always tell by the context in which it is used, or the author explicity explains what they mean by it.

Those three cases include Fission Fusion and the annihilation process Tachyonie mentioned. When you have matter and anti matter particles combine the “annihilation” that results means just what is says, invariant mass in the system has disappeared.

That is a misconception since the invariant mass in that case is conserved. The energy measured in the zero momentum frame remains conserved and therefore the systems rest mass (aka invariant mass) is also conserved.

One of the points of Relativity is that the rule of conservation of mass is violated and that mass in not always conserved.

Whether that is true or not will depend on how one defines the the term mass. Onky if one uses the term mass to refer to the sum of the proper masses of the particles can the "mass" changes with time. However I never saw anyone use the term in that sense.

Consider how this question has been answer in Spacetime Physics - 2nd Ed., by Taylor and Wheeler. On page 248 (note that m_i as used in the text refers to the proper mass of the ith particle)

Question: Does the explosion of a 20 megaton hydrogen bomb convert 0.93 kilogram of mass into energy ?

Answer: Yes and no. The question needs to be stated more carefully. Mass of a system of expanding gases, fragments, and radiation has the same value immediately after explosion as before; mass M of a system has not changed. However, hydrogen has been transformed into helium and other nuclear transformations have taken place. In consequence the makeup of the system

M_system = Sum m_i + Sum K_i

has changed

...

Thus part of the mass of constituents has been converted into energy; but the mass of the system has not changed.

I don't see anything wrong with how the authors explain this. It is precisely correct .. which shows why this text is so good!

The conservation law was replaced or better stated as “updated” to say that the net of Mass and Energy must be conserved.

No such update has ever occured. People have misunderstood this for a very long time. The answer has always been the same. The mass of a closed system is conserved. Nothing has changed that.

Thus any loss of invariant mass in a system is matched by an increase of energy in the form of massless photons.

In case you didn't know, photons have a finite, non-zero, inertial mass. It is the proper mass that is zero for a photon. The inertial mass of a photon is m = hf/c² (h = Planck's constant and f = frequency ofthe photon). The reason it has inertial mass is because inertial mass is defined as the m in p = mv. Since a photon has momentum it also has inertial mass. Some people, like myself, use the term "mass" to refer to "inertial mass." Using it in anyother way, in my opinion, is an extremely bad idea in general. It should only be used that way when someone gets tired of saying "rest/proper mass" and wants to simply say "mass" instead. So long as its clear what it means then there is no problem. And in all cases I've read to date it has always been clear what has been meant by the term "mass." Its not always easy to see it but it can be determined by the content in which its being used.

In the case of the sun, energy that departs the local system of the sun.

When one is speaking of conservation of energy or mass one is usually referring to a closed system and as such the photons+sun is a closed system and therefore the systems mass is conserved.

I typically prefer the term "rest energy" to "rest mass" when describing systems of more than one particle.

That's a bad idea for the following reason. The rest mass of a system is not always proportional to the rest energy of the system. This is especially true for non-closed systems, such as a dielectric in an electric field in which case the dielectric becomes polarized by the field and stress is induced into the system. In such case the rest energy of the dielectric is not proportional to the rest mass of the dielectric.

Pete

 

[Antenna Guy]

The direction of local time?
What do you mean by that?

Analogous to the direction of "t" in \nabla \times E = \frac{\delta B}{\delta t} (B just happens to be [changing] in the same direction).

Regards,

Bill

 

[RandallB]

Some people, like myself, use the term "mass" to refer to "inertial mass."
Using it in any other way, in my opinion, is an extremely bad idea in general.

I don’t see how defining photons as having no intrinsic mass but real inertial mass make understanding what is happening any better than a conversion factor between mass and energy.
It is a simple idea to consider that the classical concepts concept of a conservation of mass and the conservation of energy might be violated if one was allowed to be converted into the other. It would of course require a conversion factor, in order to maintain conservation of toal mas and energy. The factor I’ve most popularly seen used in that context is “E=mc^2” hopefully you’ve heard reference to it before.
That way of thinking, that mass actually can disappear by converting into Energy, was exactly how Lisa Meitner understood and described her discovery of fission.

I believe current science accepts that there is a difference between the nature of particles of mass (neutrinos electrons quarks etc.) vs. particles of light “photons”. And a difference between the energy of “mass in motion” vs. energy in a photon. IMO the Meitner method of describing an actual conversion taking place between mass & energy, is much better at describing when those things affect each other. Less confusing than defining where “inertial mass” of zero mass particles must be included as part of “mass”.

That's your choice of course, to define the term “mass” in a way that works best for you or even the specific field of work you are in.
But that is no reason to demand that everyone else must define the term exactly as you do.

But that is just my opinion,
I’m not aware of Meitner or Taylor and Wheeler, discussing the nuances of the different perspectives.
I see each as using, thus advocating, the approach that suits them best.

 

[pmb_phy]

I don’t see how defining photons as having no intrinsic mass but real inertial mass make understanding what is happening any better than a conversion factor between mass and energy.

What helps someone understand something is dependant on the particular individual. What might help one person understand something is no guarantee that the same explanation will help someone else. We all learn in different ways. All I'm doing is providing the physics of what happens according to well extablished definitions, and concepts and theories.

The term convert in this case means to change in form. That's what is happening in the cases of matter-antimatter annihilation, fission and fusion. The mass of each system is a conserved quantity as well as being invariant. The "conversion" that is said to happen here is from one form of mass to another form of mass. In the the case of matter-antimatter annihilation rest mass and mass associated with kinetic energy is changed into mass associated with the energy of photons.

It is a simple idea to consider that the classical concepts concept of a conservation of mass and the conservation of energy might be violated if one was allowed to be converted into the other.

As I said above we need to agree on what is being referred to when the term "mass" is being used. Please state the definition of the term "mass" as you are using it.

It would of course require a conversion factor, in order to maintain conservation of toal mas and energy. The factor I’ve most popularly seen used in that context is “E=mc^2” hopefully you’ve heard reference to it before.

Yes, of course I have silly. In fact let me quote you a reference to this subject as it appeared in a physics journal the year after the A-bomb was dropped on Hiroshima. The article is Energy Transformation and the Conservation of Mass, E.F. Barker, Am. J. Phys. 14, 309-310, (1946) which concludes

It appears, in short, that the mass-energy relation, E = mc², is a universal rule and one of the most fundamental of physical laws. Any system exhibits mass exactly in proportion to its energy, and gains or loses mass when it gains or loses energy. While energy may be changed from one form to another, it is never changed into into mass, nor is mass changed into energy. They are not mutually transformable. Energy may be transferred from one system to another, either with or without change in form; mass is always transferred in the process, but is never transformed.

Another article on this subject, published in the same year, is A Relativistic Misconception, C. Roland Eddy, Science, September 1946 which reads

It is evident, from many recent writings on the atomic bomb, that a serious misconception still presistss, not only in the popular press but also in the minds of some scientists. The idea that matter and energy are interconvertable is due to a misunderstanding of Einstein's equation E = mc². This equation does not say that a mass, m, can be converted into an energy, E, but that an object of mass m contains simultaneously an energy, E.
In nuclear reactions there is never any actual change in the total mass content of the universe. For example, the fission of a nucleus of mass M into two equal fragments, each of rest mass ...
The toal mass is thus exactly equal to the initial mass. The system does not lose any mass until collisions with other particles remove kinetic energy and mass from the fission fragments, and then mass gained by the other particles is exactly equal to the mass lost by the fission fragments. Mass is not destroyed but merely dispersed, just as potential energy originally contained in the fissionable nucleus is dispersed as kinetic energy of the particles struck by the fission fragments.
...
Likewise, in the "annihilation" of a positron and electron, it can be shown (remembering that the mass of a photon is hf/c²) that the total mass of the photon or photons produced is exactly equal to the combined mass of the electron and positron "annihilated."
The law of conservation of mass still holds.

I hope that helps

But that is no reason to demand that everyone else must define the term exactly as you do.

Huh? Who said anything about demanding everyone define it as I do? I certainly never made such a request nor do I think people shouldn't make their own decision on it. However I will use whatever I believe is best way to describe something. But please don't put words into my mouth by suggesting that I'm demanding something of anyone. Especially since it is in no way true. Thanks.

Pete

 

[RandallB]

Likewise, in the "annihilation" of a positron and electron, it can be shown (remembering that the mass of a photon is hf/c2) that the total mass of the photon or photons produced is exactly equal to the combined mass of the electron and positron "annihilated."
The law of conservation of mass still holds.

I hope that helps

Who said anything about demanding ….. please don't put words into my mouth ….

(edit)
"But that is no reason to expect that everyone else should define the term exactly as you do."
[edit to my post; didn’t mean to put words in your mouth,
I’ll move the edit into the post you didn’t like if the the edit function on PF is fixed before time expires do so.]

It only helps if you accept that photons have mass.

And I don’t think it helps to declare photons have no invariant or intrinsic mass but does have “inertial mass”.

How much “inertial mass” above the intrinsic mass of normal matter might there be in a piece of normal matter?
For example if the electrons in a batch of matter being weighed collect and destroy a large # of photons by jumping up to a higher energy level does the net weight of the total matter increase due to an increase of intrinsic mass or have it only gained “inertial mass” probably become hotter but not heavier?
IMO it would weigh more which could be interpreted as converting “inertial mass” from the photons into a intrinsic mass added to the electrons and a new part of the matter being weighed. To me that is the same as converting photon energy into “real mass” just using word games to be able use a term called “mass” on both sides of the conversion.

At least I’m not aware of an item of matter being able to accumulate a from a mass that would not cause it to weigh more. I am right on that I hope.

I guess I’d rather accept that photons might have actually have invariant mass in them before fabricating massless version of “inertial mass”.

So I guess that means when I use the term mass I expect inertial masses and gravitational masses must be fundamentally the same thing both based on “invariant” “intrinsic” “rest” mass.

 

[yuiop]

Hi,

The annihilation of matter and antimatter into photons has already been mentioned. less well known is that two photons of sufficient energy can combine to form an electron and a positron. While we can accept that the rest mass of the system has not changed and that the energy of the system is conserved, there should be some term to describe the fundamental change that has occured. The electron now has a property that means it cannot be accelerated to the speed of light. We need to agree a term for the form of mass that an electron has, that does not apply to a photon. Particles like electrons are baryons because they have rest mass while photons do not, yet photons have momentum and inertial mass and a box of photons has more inertial mass than the empty box. It is easy to see that mass is used interchangeably to mean a number of different things and it would be helpful to have some clear definitions. (even though Einstein said there is no sensible definition of mass :P)

 

[pmb_phy]

(edit)
"But that is no reason to expect that everyone else should define the term exactly as you do."
[edit to my post; didn’t mean to put words in your mouth,
I’ll move the edit into the post you didn’t like if the the edit function on PF is fixed before time expires do so.]

Thank you RandallB. That is very kind of you. There is no need to edit it. Your comment here is more than sufficient for me. We all make mistakes. I more than most.

It only helps if you accept that photons have mass.

There are two definitions of the term "mass" as it is used in relativity. One refers to proper mass and the other to inertial mass. The proper mass of a photon is zero whereas the inertial mass equals E/c². Describing anything is meaningless until one defines their terms. It has very little to do with whether a photon has mass since you must first state how one is using the term "mass" and it then follows if the mass is zero or not.

And I don’t think it helps to declare photons have no invariant or intrinsic mass but does have “inertial mass”.

The terms "invariant mass etc" and "inertial mass" are well defined and have an exact meaning. Inertial mass equals p/v (which is non-zero for a photon) and invariant mass equals m = sqrt[E² - p² ] (c = 1) (which is zero for a photon).

How much “inertial mass” above the intrinsic mass of normal matter might there be in a piece of normal matter?

It depends on the speed of the (isolated) object. The inertial mass equals the proper mass (what you call "rest mass") plus the mass associated with the objects kinetic energy.

For example if the electrons in a batch of matter being weighed collect and destroy a large # of photons by jumping up to a higher energy level does the net weight of the total matter increase due to an increase of intrinsic mass or have it only gained “inertial mass” probably become hotter but not heavier?

In this case both the proper mass and the inertial mass increases. If something becomes hotter then it is due to an increase in thermal energy and any form of energy has an assciated mass. Heat an object it it weighs more.

IMO it would weigh more which could be interpreted as converting “inertial mass” from the photons into a intrinsic mass added to the electrons and a new part of the matter being weighed. To me that is the same as converting photon energy into “real mass” just using word games to be able use a term called “mass” on both sides of the conversion.

The energy of a photon is considered to be all kinetic energy. What happens here is that the mass associated with kinetic energy becomes mass associated with proper mass. This means that the kinetic energy is changed to rest energy (aka proper energy), therefore the form of the mass changes from mass(kinetic energy) to mass(rest energy).

So I guess that means when I use the term mass I expect inertial masses and gravitational masses must be fundamentally the same thing both based on “invariant” “intrinsic” “rest” mass.

What do you mean by "based on"? The equivalence principle states that inertial mass equals gravitational mass. The inertial mass of light equals the gravitational mass of that light and this mass is non-zero since light generates a gravitational field.

Pete

 

[DrGreg]

"The rest mass cannot change" is not true.

Actually it is true.

My quote has been taken out of context.

In the context of a "closed" system, e.g. a body that is not interacting in any way with anything else outside of itself, yes, I agree, the "rest" mass cannot change.

I was speaking in a more general context, in reply to post #15, to explain the difference between invariance and conservation. If you add externally-supplied energy to a body, for instance by rotating it or by heating it up, then the result is that the body's "rest" mass can increase (and in those two examples does increase).

And, because it's confusing to talk of the "rest" mass of a spinning object, I prefer to say "invariant mass" instead. The description "proper mass" would be even better, the only problem is hardly anyone seems to use it, except you!

 

[RandallB]

Thank you RandallB. There is no need to edit it.

Actually, I prefer editing things for the benefit of future readers but the edit function (we are still with edit time limit) for that post seems to be broken, no system is flawless.

The energy of a photon is considered to be all kinetic energy. What happens here is that the mass associated with kinetic energy becomes mass associated with proper mass. This means that the kinetic energy is changed to rest energy (aka proper energy), therefore the form of the mass changes from mass(kinetic energy) to mass(rest energy).

What do you mean by "based on"? The equivalence principle states that inertial mass equals gravitational mass. The inertial mass of light equals the gravitational mass of that light and this mass is non-zero since light generates a gravitational field.

But (kinetic energy) and (rest energy).are both based on both "based on” invariant mass. Both the “rest” energy of the 'invariant mass' and kinetic energy of the 'invariant mass' in motion (p^2) must be used to know total energy.
No need to make “inertial mass” an independent thing that happens to be the same as “invariant” mass in things of matter, just so that it can be named as a form of matter within a “massless” photon (i.e. zero invariant mass) .
Although, that does allow you to say something like “invariant mass” can convert into “inertial mass” only as found in massless photons; And photons can convert massless “inertial mass” into “invariant mass” when matter is created from photons.
That is what I mean by playing word games. To me it is simpler and more direct to consider energy to matter conversions, than play word games with the term 'mass'.

So call it a personal preference when I do it my way.
Granted it means considering matter as not “conserved” nor is energy “conserved”.
But I find that to be a good thing as demonstrating that Energy stored in matter can be converted into a form of energy that cannot be modified by changing the speed of photons that carry that energy. And of course can be converted back into matter requiring that the net of all Mass and Energy be conserved using a common unit of measure defined by the “exchange rate” of E=mc^2.

I don’t see what I’m saying as anything new;
I haven’t created anything not used by others long ago.
I see this as nothing more than personal preference as to how to understand the nature of the conversions, and leave it to “Tachyonie” “kev” or others to comment on what method helps them better understand matter vs. light.
Personally I think it is important to understand both view points, and I understand yours.
Maybe the way Meitner explained it as I prefer it is old fashioned, but I prefer it and I don’t expect you need to change yours.
Both views make the same points in different ways.

 

[pmb_phy]

The description "proper mass" would be even better, the only problem is hardly anyone seems to use it, except you!

Nobody uses it on the internet except me, and I'm happy that is the case.

However it occurs in the physics literature quite often. I use it so much because the term "rest mass" has a different meaning than "proper mass" even though most people don't know that. The term "rest mass" refers to the mass of an particle as measured in the frame of reference in which the object is at rest. However the inertial mass, which is proportional to the time-component of the 4-momentum, does not, in general, equal the proper mass, especially when he particle is at rest in a gravitational field. In that case the mass will be a function of the gravitational potential. Only when the gravitational potential is zero and the the speed is zero will the rest mass equal the proper mass. Even then it is ugly business to refer to the rest mass of a photon since the photon can never be at rest. It leaves a bad taste in my mouth. A little salty, tastes a bit like fish.

Best wishes

Pete

 

[yuiop]

Double cannon experiment

Imagine we have a double rail gun. It consists of a electromagnetc accelerator and a huge battery that is the power supply. It fires two projectiles of mass 1m each in opposite directions. The cannon and its power supply has a mass of 4m when fully charged and ready to fire and the total system has a mass of of 6m and a total energy of 6m using units where c=1 throughout. .

After the cannon is fired, let's say the speed of the projectiles is 0.8c each in opposite directions and the gamma factor y=1/0.6. The cannon does not move because of its anti-recoil design. The total energy of the complete system after firing is assumed to be unchanged because the total momentum of the system is zero before and after firing.

Using the relationship that Rest Mass Energy (RE) = Total Energy (TE) -Kinetic Energy (KE) , then the total KE of the system after firing is :

KE = TE - RE = (2m/0.6 + 4M) - RE

where 4M is the "new mass" of the cannon/battery assembly after firing. (4m before firing).

RE = TE - KE = 6m -(2m/0.6 + 4M - RE)

4M = 6m - 2m/0.6 = 2.667m

The cannon/battery assembly (not including projectiles) has lost about a 33% of its (inertial?) "mass" due to the depletion of the energy stored in its battery. (4m before firing, 2.667m after firing).

The invariant energy-momentum-rest mass relationship E^2-P^2=M^2 does not hold here because this a change over time rather than a simple transformation of reference frames.

Does that calculation seem correct?

[edit} Something does not seem right here, as I have the final total enrgy equal to the total kinetic energy leaving a rest mass energy of zero ??

What are correct forms of mass to describe what is happening here?

 

[yuiop]

Perhaps this is a better way to do the calculation in post #35 ?

Assuming the initial rest mass energy (RE1) of the total system (cannon+batteries+projectiles) is 6m before firing and assuming the total energy (TE) of the system does not change after firing, then the final rest mass energy of the total system after firing (RE2) is:

RE2 = TE - KE = 6m - (2m/0.6 - 2m) = 4.666m

Assuming the rest mass of the projectiles remains constant then the loss of 1.333m in rest mass energy of the system is attributed to the discharge of stored energy in the batteries?

Should the quantity I have been referring to as the "rest mass energy" of the system be formally described as the inertial, invariant or proper mass of the system?

 

[Dale]

I would simply use the conservation of the four-momentum to do this (in units where c=1):
four-momentum of system before firing: (6m,0)
four-momentum of shells after firing: (γm,±γv)
four-momentum of the gun after firing: (6m,0)-((γm,γv)+(γm,-γv)) = (6m-2γm,0)

Note that v must satisfy the condition that 6m-2γm ≥ 0

 

[yuiop]

I would simply use the conservation of the four-momentum to do this (in units where c=1):
four-momentum of system before firing: (6m,0)
four-momentum of shells after firing: (γm,±γv)
four-momentum of the gun after firing: (6m,0)-((γm,γv)+(γm,-γv)) = (6m-2γm,0)

Note that v must satisfy the condition that 6m-2γm ≥ 0

Using the values of v=0.6 and γ=1.666 in the example I gave, then

Invariant mass of the total system before firing = 6m

Invariant mass of the 2 shells before firing = 2m
Invariant mass of the 2 shells after firing = 3.333m (Inertial mass?.. Rest mass?)

Invariant mass of the gun before firing = 4m
Invariant mass of the gun after firing = 2.666m (Inertial mass?.. Rest mass?)

Invariant mass of the total system after firing = 6m

 

[Tachyonie]

I got to read your answers just now.
I asked the question because I felt that pmb_phy was telling me that you cannot convert mass into energy which to me made no sense since I always visioned mass and energy as 2 sides of the same coin as in the E=mcc formula. Now I see that I might have misunderstud.
Its important to state that my knowledge of physics is not very good, and all I know about physics of this magnitude is self-taught since I did not advance that far in school.
As far as I know I ment the invariant mass changing, not the relativistic mass.

 

[pmb_phy]

I got to read your answers just now.
I asked the question because I felt that pmb_phy was telling me that you cannot convert mass into energy which to me made no sense since I always visioned mass and energy as 2 sides of the same coin as in the E=mcc formula. Now I see that I might have misunderstud.
Its important to state that my knowledge of physics is not very good, and all I know about physics of this magnitude is self-taught since I did not advance that far in school.
As far as I know I ment the invariant mass changing, not the relativistic mass.

I think I mentioned that regardless of which mass you're referring to its conserved, for a closed system that is. And conservation of energy always refers to a closed system although some open systems may have a conserved energy.

Pete

 

[Dale]

I would simply use the conservation of the four-momentum to do this (in units where c=1):
four-momentum of system before firing: (6m,0)
four-momentum of shells after firing: (γm,±γv)
four-momentum of the gun after firing: (6m,0)-((γm,γv)+(γm,-γv)) = (6m-2γm,0)

Note that v must satisfy the condition that 6m-2γm ≥ 0

Using the values of v=0.6 and γ=1.666 in the example I gave, then

Invariant mass of the total system before firing = 6m

Invariant mass of the 2 shells before firing = 2m
Invariant mass of the 2 shells after firing = 3.333m (Inertial mass?.. Rest mass?)

Invariant mass of the gun before firing = 4m
Invariant mass of the gun after firing = 2.666m (Inertial mass?.. Rest mass?)

Invariant mass of the total system after firing = 6m

Actually, your numbers are a little off. In units where c=1 and m=1 with v=0.8 we have:
γ=1.667
invariant mass of system before firing: |(6m,0)| = |(6,0)| = 6
invariant mass of each shell after firing: |(γm,±γv)| = |(1.667,±1.333)| = 1
invariant mass of the gun after firing: |(6m-2γm,0)| = |(2.667,0)| = 2.667
invariant mass of the system after firing: |(6m-2γm,0)+(γm,γv)+(γm,-γv)| = |(6m,0)| = 6

Note that the invariant mass of the system after firing (6) is different than the sum of the invariant masses of the parts (4.667). Loosely speaking, this difference (1.333) represents the mass that was converted to energy.

 

[RandallB]

I felt that pmb_phy was telling me that you cannot convert mass into energy.
As far as I know I meant the invariant mass changing, not the relativistic mass.

Just to split hairs a bit,
I believe you did not mean to say “I meant the invariant mass changing” but rather invariant mass is “converting” to energy as it disappears into photons.
I think pmb_phy is telling you that cannot “convert” mass into the energy of a photon because the “mass” is still there as “Inertial” mass in the photon.
I disagree with that as IMO it is only to allow us keep our cake and eat it too;
Just so that a photon still have “zero” mass except for the “Inertial” mass, so the accepted standard of a massless point particle photon is retained, while defining photon “Energy” as a kinetic thing based on mass in the photon.

For me science must pick one or the other; photons either do or do not have mass period. And with the current standard being no mass IMO that means the Energy is a unique thing that can be converted from or into mass.
I suspect that is what you are thinking and IMO represents the approach and descriptions offered by many others (Meitner etc.)

Note the confusion that can from multiple versions of mass.
The DaleSpam and kev discussion on changing values of “invariant mass” for guns and bullets based on changing the relative speeds between them, badly mangles the concept of “invariant mass”.
The term “invariant” means NOT changing:
DaleSpam and kev are actually applying ideas of “Relativistic Mass”, which the modern view considers incorrect and unnecessary and does not apply to this topic of transforming mass.
Although pmb_phy and I disagree on the accepted definition of a photon, I think pmb_phy will agree that these relativistic guns and bullets of changing mass descriptions are misleading at best.

 

[Dale]

The term “invariant” means NOT changing:
DaleSpam and kev are actually applying ideas of “Relativistic Mass”, which the modern view considers incorrect and unnecessary and does not apply to this topic of transforming mass.

"Invariant" means that different reference frames agree on the quantity. I think the term you are looking for is "conserved" which means that the quantity doesn't change over time.

I was correctly using the invariant mass (the Minkowski norm of the four-momentum) and was not referring to relativistic mass (the Euclidian norm of the three-momentum divided by the speed or γ times the invariant mass for particles moving at v<c).

 

[RandallB]

The mass remains the same. The only thing that has changed is the sum of the proper masses. The total inertial mass (aka relativistic mass) remains constant.

I think pmb_phy will agree that these relativistic guns and bullets of changing mass descriptions are misleading at best.

OOPS
I suspect my assumption of agreement here is likely wrong as “relativistic mass” is somehow involved in a way that escapes me.
I also don’t see how I’ll ever reconcile the idea the before and after value of some form of mass for a gun can significantly change after the mass of a pair of bullets depart at 0.6c as the mass of the bullets themselves also change.

If anyone wishes to research these positions further; I believe my position is closest to:
(July 1989). Lev B. Okun
"The Concept of Mass". Physics Today 42 (6): 31–36.

And some of the other positions are likely closer to those of:
(Nov. 1991). T. R. Sandin
"In defense of relativistic mass". American Journal of Physics 59 (11).

I found the published papers referenced under “Mass in special relativity” on Wikipedia.

 

[yuiop]

Just to split hairs a bit,
I believe you did not mean to say “I meant the invariant mass changing” but rather invariant mass is “converting” to energy as it disappears into photons.

Equally, we can say that part of the invariant mass of the gun has been converted into the kinetic energy of the shells.

I think pmb_phy is telling you that cannot “convert” mass into the energy of a photon because the “mass” is still there as “Inertial” mass in the photon.
I disagree with that as IMO it is only to allow us keep our cake and eat it too;
Just so that a photon still have “zero” mass except for the “Inertial” mass, so the accepted standard of a massless point particle photon is retained, while defining photon “Energy” as a kinetic thing based on mass in the photon.

For me science must pick one or the other; photons either do or do not have mass period. And with the current standard being no mass IMO that means the Energy is a unique thing that can be converted from or into mass.

We can have a laser gun version of the thought experiment. A charged battery fires photons in opposite directions until the battery is depleted. The laser gun and battery will weigh less after the battery is depleted. The inertial mass of the gun has been reduced and it would require less energy to accelerate the depleted gun rather than the charged gun. Without being able to assign some form of mass to the photons we can not have a concept of invariant mass for the system as a whole. This is made clearer, if the fuel for the laser gun consists of matter and anti matter. When the the fuel of the gun is depleted, it is very clear the gun weighs less, and without assigning mass to the photons it is very clear that there is no concept of invariant mass for the system as a whole.

THis adaptation of the experiment shows that the loss of mass of the gun (in any version of the experiment) is just as as real as the loss of mass during the annhilation of matter and antimatter into photons.

I suspect that is what you are thinking and IMO represents the approach and descriptions offered by many others (Meitner etc.)

Note the confusion that can from multiple versions of mass.
The DaleSpam and kev discussion on changing values of “invariant mass” for guns and bullets based on changing the relative speeds between them, badly mangles the concept of “invariant mass”.
The term “invariant” means NOT changing:

The gun thought experiment just made clear that invariant mass is only invariant for a closed system. The total (invariant) mass of the whole system was indeed invariant before and after firing. The invariant mass of the individual parts (which are open systems) is not invariant, showing that the expression "invariant mass" can be misleading. Perhaps something along the lines of (Total Inertial mass)^2 = (Total Energy)^2 - (Total Momentum)^2 would be clearer with the understanding that the inertial mass is invariant for a closed system.

DaleSpam and kev are actually applying ideas of “Relativistic Mass”, which the modern view considers incorrect and unnecessary and does not apply to this topic of transforming mass.
Although pmb_phy and I disagree on the accepted definition of a photon, I think pmb_phy will agree that these relativistic guns and bullets of changing mass descriptions are misleading at best.

I think we can all agree that a photon has zero rest mass, and some of us agree that a photon has inertial mass allowing us to assign quantities like momentum to a photon. As mentioned earlier being able to assign inertial (relativistic) mass to a photon allows us to use the concept of invariant mass for a system that includes photons. The energy of a photon is proportional to it momentum (pc) which in turn is proportional to its frequency (hf). The inertial (relatavistic) mass of a photon can be found from mc^2 = hf --> m = hf/c^2.

I was hoping we would avoid descending into an argument about the use of relativistic mass and deliberately avoiding using that term in my previous posts for that reason. It would seem that the term "inertial mass" has crept in as the politically correct replacement for the emotive "relativistic mass". Seeing as how you have brought up the issue of relativistic mass I will quote this passage from the Physics FAQ http://math.ucr.edu/home/baez/physics/Relativity/SR/mass.html

=========================================================
A debate of the idea of relativistic mass surfaced in Physics Today in 1989 when Lev Okun wrote an article urging that relativistic mass should no longer be taught (42, June 1989, pg 31). Wolfgang Rindler responded with a letter to the editors defending its continued use (43, May 1990, pgs 13 and 115). In 1991 Tom Sandin wrote an article in the American Journal of Physics arguing very persuasively in favor of relativistic mass (59, November 1991, pg 1032). (Links are provided here, but the articles cannot be downloaded for free.)

An optimistic view would hold that it's a measure of the richness of physics that focussing on different aspects of concepts like mass produces different insights: intuition for the case of relativistic mass in special relativity, and the notion of invariance for the case of tensor language in special and general relativity. But it's also unfortunate that whereas "pro relativistic mass" physicists will happily live with both ideas, "anti relativistic mass" physicists spend a lot of time trying to have relativistic mass outlawed.

Abandoning the use of relativistic mass is often validated by quoting select physicists who are or were against the term. But real science isn't done that way. In the final analysis, the history of relativity, with its quotations from those in favour of relativistic mass and those against, has no real bearing on whether the idea itself has value. The question to be asked is not whether relativistic mass is fashionable or not, or who likes the idea and who doesn't; rather, as in any area of physics notation and language, we should always ask "Is it useful?" And relativistic mass is certainly a useful concept.

==============================================================

 

[yuiop]

The gun thought experiment just made clear that invariant mass is only invariant for a closed system. The total (invariant) mass of the whole system was indeed invariant before and after firing. The invariant mass of the individual parts (which are open systems) is not invariant, showing that the expression "invariant mass" can be misleading. Perhaps something along the lines of (Total Inertial mass)^2 = (Total Energy)^2 - (Total Momentum)^2 would be clearer with the understanding that the inertial mass is invariant for a closed system.

After some further thought, the energy equation

m_0^2c^4 = E^2 -P^2c^2

after dividing through by c^4 to get the mass equation

m_0 ^2 = m^2 - m^2v^2/c^2

can be expressed as:

(Rest Mass)^2 = (Inertial Mass)^2 - (Momentum Mass)^2

For a photon inertial mass = E/c^2 and momentum mass = p/c = hf/c^2 are equal and so the rest mass is zero.

The expression for relativistic mass (inertial mass)

m = {m_0 \over \sqrt{1-v^2/c^2}}

when applied to a photon which has rest mass m_o = 0 becomes m = 0/0 which is undetermined by this equation but can be found from m = hf/c^2.

Rest mass (also called invariant mass) has the following properties:

1) Rest mass of a particle or closed system is invariant under a Lorentz transformation.
2) Rest mass of a closed system is conserved over time.
3) Rest mass of a particle or part of a system can change over time.

Inertial mass (the mass equivalent of the total energy also called relativistic mass) has the following properties:

4) Inertial mass of a particle or closed system is not invariant under a Lorentz transformation.
5) Inertial mass of a closed system is conserved over time.
6) Inertial mass of a particle or part of a system can change over time.
7) Inertial mass of a system is related to the resistance of the system to being accelerated and is closely related to the active gravitational mass of the system.

Examples:

In the gun experiment the total momentum before and after firing is zero as the shells move in opposite directions. The total energy (and therefore the total inertial mass) of the system is conserved before and after and so is the rest mass.

In the annihilation of a proton and anti-proton, two photons are produced moving in opposite directions to conserve the zero momentum of the system. The inertial mass (total energy) and rest mass of the system as a whole is conserved. Yes.. one photon has zero rest mass, but a system comprising of only two photons moving in opposite directions has non-zero rest mass. Surprising?

In the gun experiment if we consider only the mass of the gun, then the inertial mass and the rest mass of the gun has reduced after firing. This is an example of an object losing rest mass without involving a nuclear reaction. It could be argued that this is not the true rest mass of the gun as the mass lost is due to the loss of energy of the battery. Further rest mass could be “lost” by cooling the gun. It could be argued that the mass of an object that is not at absolute zero temperature with all forms of stored potential energy removed is never representative of the “true” rest mass of the object.
Generally, the rest mass (invariant mass) of an object that is assumed in the equations, is the inertial mass (E/c^2) measured in the inertial reference frame where the object has zero linear momentum, even though it may not truly be at rest due to thermal vibrations, spin, expansion etc. In this respect “proper mass” may be a more intuitive term than rest mass for intrinsic mass.

If we examine a single particle of the proton and anti-proton annihilation, then the rest mass of the single particle is converted to momentum mass while its inertial mass is conserved, The final momentum mass is equal to the inertial mass and the final rest mass is zero because it has become a photon.

A single shell from the double gun experiment has increased momentum mass and increased inertial mass but its rest mass is conserved.

An observer co-moving with one of the shells fired from the double gun sees the inertial mass and the momentum mass of the complete system as being greater than that measured by an observer at rest with the double gun, but both observers see the same rest mass for the system as each other and before and after firing.

A spinning top that comes to rest on a table top which has dissipated its angular motion as heat to its surroundings will have less rest mass and less inertial mass than when it was spinning. Its (linear) momentum mass before and after is zero. While the rest mass of the top as a whole is considered to be less after it has stopped spinning, the "intrinsic" rest mass of the individual elements of the spinning top have not changed over time. The extra weight it had while spinning is the kinetic energy of the elements that that for all purposes "behaves" like additional inertial mass. This is more clearly seen in the example of photon that has no rest mass but has inertial mass purely due to the energy of motion. This inertial mass of the photon is real in the sense that the photon has momentum that it can impart to a massive particle in a collision and it has gravitational mass creating its own little "dent" in the curvature of spacetime.

Having said all that, I can see that only using proper mass and invariant four velocity makes the maths simpler when using tensors and I can also see the desirablity of only having mass associated with matter and treating photons as pure energy. :P

 

[Dale]

It could be argued that the mass of an object that is not at absolute zero temperature with all forms of stored potential energy removed is never representative of the “true” rest mass of the object.

Yes, I agree. That is why I prefer the term "rest energy" for any system of more than one particle. Although based on Pete's earlier post I think "proper energy" is even better. That makes it clear that you are talking about an invariant quantity and that it includes mass due to matter as well as mass due to the energy of the system.

By the way, based on your most recent post I think you understand the difference between "invariant" and "conserved", but just to be clear this paragraph:

The gun thought experiment just made clear that invariant mass is only invariant for a closed system. The total (invariant) mass of the whole system was indeed invariant before and after firing. The invariant mass of the individual parts (which are open systems) is not invariant, showing that the expression "invariant mass" can be misleading.

Should read:

The gun thought experiment just made clear that invariant mass is only conserved for a closed system. The total (invariant) mass of the whole system was indeed conserved before and after firing. The invariant mass of the individual parts (which are open systems) is not conserved, showing that the expression "invariant mass" can be misleading.

 

[pmb_phy]

Although pmb_phy and I disagree on the accepted definition of a photon, I think pmb_phy will agree that these relativistic guns and bullets of changing mass descriptions are misleading at best.

No. I do not agree. I believe just the opposite in fact.

Pete

 

[pmb_phy]

After some further thought, the energy equation

m_0^2c^4 = E^2 -P^2c^2

after dividing through by c^4 to get the mass equation

m_0 ^2 = m^2 - m^2v^2/c^2

can be expressed as:

(Rest Mass)^2 = (Inertial Mass)^2 - (Momentum Mass)^2

Perhaps this goes without saying but that is a special case of a closed system. FIf one were to calculate the "rest mass" density and assumes this is true then one is in for a big surprise. For example: Suppose that in the frame S there is a magnetic field. Examine a small element of that field. The element is small enough so that the field may be considered uniform throughout the volume. Let the magnetic field at that point be pointing in the +z direction. Now consider a frame S' which is in standard configuration with S and moving in the +x direction with respect to S. Now evaluate the mass of that volume element. This will have the value one would expect. However consider the same thing but now let the magnetic field point in the +x direction. When you transform these quantities to S' you'll find that the momentum is zero. Thus when you divide by the speed v (of frame S with respect to the zero momentum frame) then the answer you get will equal zero. Its for this reason I prefer not to use terms like "{rest mass" or use "mass" to refer to invariant mass or rest mass. Those terms pply only to special cases and are not valid in all generality. And in my opinion a definition must hold in all possible cases.

Pete

 

[RandallB]

No. I do not agree. I believe just the opposite in fact.

Yes, as you can see from post #44
where I finally came across the Okun vs. Sandin Debate / Controversy
I suspected that to be the case

I question the reasonableness of, as kev puts it, “deliberately avoiding using that term” (relativistic mass) to avoiding addressing Okun opinions when effectively using the principles of relativistic mass, in order to apply different types of mass (rest, momentum, Inertial) to account the constituent parts that make up matter and light.

I find the Sandin position to be inconsistent and confusing, which accounts for inconstant definitions of various forms of mass between practitioners, such as those where you disagree with kev. And since it seems that the total mass “Inertial Mass” is suppose to consist of “Rest Mass” plus “Momentum mass” (Thus the zero ‘rest mass’ photons have a total “Inertial Mass” consisting of “Momentum mass”) such a summary of parts should not have “properties” like the four listed by kev. It should be “Momentum mass” that would be the independent thing to have “properties” to combined with the three properties listed for “rest mass”.

Way to many inconsistencies in the definitions I’ve seen such as:

properties for “rest mass” (invariant mass)
1) Rest mass of a particle or closed system is invariant under a Lorentz transformation.
2) Rest mass of a closed system is conserved over time.
3) Rest mass of a particle or part of a system can change over time.

If this form of mass is “invariant” how does invariant mass of a particle change over time; except by acquiring additional invariant mass to change into a new and different particle; such as an electron that converts into a heavier electron able to maintain a higher energy level.

Personally as I said before I’d rather put photons on having invariant (rest) mass;
But that is not current accepted modern science.
Thus I find the Okun approach much more reasonable. That gives us massless photons carrying a pure form of energy not based on mass.
Energy that can be destructively converted (as in not conserved) into or created from invariant mass. Science becomes a task of understanding the processes of converting between those two things “invariant” masses in particles may or may not be in motion and “pure energy” contained in photons.
But can reliable use an appropriate conversion factor to “conserve” or account for the total of all mass and energy as a whole.

Works for me anyway, if the Sandin doctrine works better for you have at it.