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I Is the mass defect still considered with invariant mass?

  1. Feb 8, 2017 #1
    Suppose you were to assemble a sphere of negative charges. When you are done, the rest mass of the sphere is larger than that of the negative charges because they gain energy in forming the sphere. But the invariant mass of the electrons can't change and apparently gaining energy doesn't increase their mass but their inertia. So does the concept of mass defect still hold without relativistic mass? And does the sphere have higher invariant mass than the sum of the invariant masses of the electrons?
    Thank you.
  2. jcsd
  3. Feb 8, 2017 #2


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    Yes, it does. Invariant mass is not an additive quantity. Another simple example is a pair of photons (or pulses of light) travelling in opposite directions. Separately, each has an invariant mass of zero. Taken together the combined system has a non-zero invariant mass.
  4. Feb 9, 2017 #3
    So the energy of the internal parts have some mass of their own?
  5. Feb 9, 2017 #4


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    In my opinion, you should not try to localize the extra mass. It is not associated with any specific part. It is an attribute of the system as a whole. If you insist on assigning the extra mass to something specific, you could say that the extra mass in an assembly of electrons is carried by the electrostatic field that they produce.

    If one had that pair of photons (or light pulses) moving in opposite directions, it would not be correct to divide the invariant mass equally and assign it to the individual photons. That would work for the center-of-momentum frame. But in other inertial frames of reference, the system energy would be divided in different proportions. There is no invariant fact of the matter governing the assignment of invariant mass between the two photons. If there is no invariant fact of the matter, there is no grounds to consider the assignment physically meaningful.
  6. Feb 9, 2017 #5

    Mister T

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    I would say it slightly differently. The negative charges don't gain energy. The collection of negative charges gains energy. But otherwise, yes. This is the true meaning of Einstein's mass-energy equivalence.

    Invariant mass and rest mass are two names for the same thing. Mass is a third name for that same thing. Having more than one name for the same thing is a source of confusion.

    Of course there's a mass defect. And of course it exists when you expunge relativistic mass from your vocabulary. Changing terminology doesn't change the physics.


    Confusion arises when people start talking about different kinds of mass. That is the reason for expunging relativistic mass.

    No, the energy contribution of the internal parts is some of the mass of the sphere. The notion that you can add up the mass of the constituents to get the mass of the composite body is part of the newtonian approximation. Einstein's mass-energy equivalence tells us that such a notion is false.
  7. Feb 9, 2017 #6
    Thank you for the answer. Just defining the inertial mass as non-additive does resolve a lot more issues than I thought. It also changes radically from the way I used to think of the mass, and its quite an interesting concept. Guess that's what happens when you use slightly older textbooks.

    Though I am still wondering: the argument holds for individual photons but if you were to calculate the difference in the mass of the system now minus the sum of the invariant masses of its components, couldn't you use it as the culprit for the mass defect? Say you had the electron system this time, because that's easier to work with. In assembling the electrons they must gain some energy, and even though this energy gain could differ from electron to electron, the overall energy difference should the same in every frame right? Because if it wasn't then in one system, the sphere could do more work than in another. And that would violate energy conservation because by changing frame you can gain more energy for free. So if the overall energy difference is an invariant quantity, couldn't you just call that the extra mass?

    It feels a bit strange to refer to a collection as gaining energy, but I guess that's because I'm not used to it.
    And having different names for the same thing is definitely bothersome, though I suppose it's less annoying than having to invent ten different names for all the kinds of masses you need when you use relativistic mass.

    Of course it won't but changing the terminology does mean changing the definitions. I was unsure of whether the invariant mass of the sphere would be defined as its mass in its rest frame or the sum of the constituents, even if the latter has no real use.
    And thank you for answering
  8. Feb 9, 2017 #7
    You have a misunderstanding here, energy is conserved but it's not invariant. Conserved means that in the same reference frame it is the same at any instant in time, say before and after some process. Invariant means the same in different reference frames, which energy is not. A bowling ball can do more work in a frame where it is moving than in a frame where it is at rest.
  9. Feb 9, 2017 #8
    Good point with the balling ball. I realised that the work done by or on an open system is not invariant -in a collision with two bowling balls one can gain energy in one frame but lose energy in the other. Thank you for pointing it out.
  10. Feb 9, 2017 #9
    I disagree with everybody else.

    Suppose we were to assemble a sphere of negative charges. When we are done, the rest mass of the sphere can be measured to be larger than that of all the original negative charges. Also the rest mass of one electron can be measured, that rest mass will be larger than the rest mass of one original electron.

    So the invariant mass of an electron increases when the electron gains energy, only exception is the kinetic energy. The coordinate dependent kinetic energy does not have any effect on the coordinate independent mass, and the invariant kinetic energy of an electron is always zero, so it has zero effect on invariant mass.
  11. Feb 9, 2017 #10


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    Why do you think that?
  12. Feb 9, 2017 #11

    Mister T

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    That is in fact what happens when something as simple as lifting a book from the floor to the table top happens. It is common to state that the gravitational potential energy of the book increased, but in fact what has happened is that the potential energy of the book-Earth system increased. This system is a collection of two particles, and the mass of that collection increased when the book was lifted.

    The true meaning of the Einstein mass-energy equivalence can be seen only by looking at composite bodies. That is, bodies that are a collection of particles. This is a notion obscured by the introduction of a relativistic mass.

    There is no need to have either the bothersome arrangement or the annoying one. There is only one kind of mass, the ordinary mass, and there's no need to make mention or use of any other kind of mass. That's the way almost all high energy physicists do it and it works perfectly well. You just have to realize that the role of mass is different from its role in the newtonian approximation. It is equivalent to rest energy.

    There are many physicists, some of them prominent, who advocate for having more than one kind of mass. Usually they call them rest mass and relativistic mass. Many but not all are unaware that the latter has fallen out of usage, but to become aware all they have to do is grab a college-level introductory physics textbook that was written in the last 25 years or so and look at it. Once you remove relativistic mass from your vocabulary there is no need to distinguish the two by using the adjective "rest" to refer to the other. Moreover, there is no need, for the same reason, to attach a subscript "o" to the symbol ##m##.
  13. Feb 9, 2017 #12

    Mister T

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    Reference books, including those published by organizations such as CODATA, NIST, and BIPM, list only one value for the mass of an electron. Textbooks, too. And they no longer call it the rest mass. It's simply the mass.

    There is no such thing as invariant kinetic energy.
  14. Feb 9, 2017 #13

    Momentum of a system is the sum of momentums of its parts.

    If a sphere has some extra mass, it needs some extra momentum to get it moving. The sphere can get some extra momentum by its parts getting some extra momentum. So when a part is moving with the sphere it has some extra momentum, so when the part is stopped the stopper must absorb some extra momentum. Now if we say that stopping the part and measuring the required impulse is a measurement of mass, then the measurement shows that there is some extra mass in the part.
  15. Feb 9, 2017 #14
    In the previous post I explain how one measurement of mass gives as a result an increased mass.
    There is such kinetic energy that contributes to mass, and as mass is invariant, so is the kinetic energy that contributes to mass. So I called that kinetic energy invariant kinetic energy, because it's invariant.
  16. Feb 9, 2017 #15


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    That is utterly wrong.

    Mass is the magnitude of the energy-momentum four-vector. It is invariant because any change in energy that comes from a change in reference frame is accompanied by a change in momentum that comes with the change in reference frame. Neither the kinetic energy nor the momentum are invariant. But their norm, when combined as a four-vector is.
  17. Feb 9, 2017 #16


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    I think that this is wrong. Please provide a reference.

    I don't think that this will measure mass in relativity. Do you have a reference for this?

    I am uncomfortable with this also, but consider those other points more problematic.
    Last edited: Feb 9, 2017
  18. Feb 9, 2017 #17
    Wouldn't this energy arise from the interaction of two electrons rather than just one electron? If you had two electrons in a certain configuration, you could have brought one from infinity while holding the other still, or you could have brought both from infinity and have them reach this arrangement, or you could have brought one a little from infinity and have the other move the rest of the way. There are an infinite number of ways an arrangement could be made, but the end result: that you need to give the system a certain amount of energy is the same. So the energy can be attributed to the arrangement.
    Come to think of it, this idea of energy belonging to arrangements that fields bring with them as Mister T helpfully reminded me of (Never ever thought the A-team would help with physics) makes the mass defect being attributed to the arrangement seem like a natural extension, far more than relativistic mass anyway.
  19. Feb 9, 2017 #18


    Staff: Mentor

    Careful. The externally measured mass of the Earth-book system actually does not change at all in this process. All that changes is how that mass is distributed between the parts of the system. The energy that was used to raise the book came from somewhere, and that somewhere is also part of the system, so it counts in the externally measured mass.
  20. Feb 9, 2017 #19

    Mister T

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    Why does it have to be part of the system? Can't it be external to the system?
  21. Feb 9, 2017 #20


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    If you lift the book in your hand, then the system no longer consists of only the earth and the book. It consists of the earth, the book, and you. In lifting the book, you do work. Your internal energy decreases, the gravitational potential energy of the system increases, and the total energy of the system remains constant. The masses of the earth, the book, and the system remain constant, but your mass decreases.
    The energy needed to raise the book can indeed come from outside the system. For example, you might use solar energy to boil water, and use the steam to drive an engine that lifts the book. In that case the mass of the earth-book-engine system would increase according to the solar energy that entered the system.
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