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?