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What is the difference between mass and energy?

  1. Sep 21, 2010 #1
    since the equation, E=MC2, indicates that mass and energy are equivalent, what exactly is the difference between them? ie, how do you explain that energy can travel at C, but not matter? or is there some significant difference between matter and an object which has mass?

    also, if mass and energy are interchangeable as implied by the equation, where do all the other properties of matter come from, such as charge?

    thanks.
     
  2. jcsd
  3. Sep 21, 2010 #2
  4. Sep 21, 2010 #3
    Hi. The relation of mass, energy and momentum of a particle is m^2 = E^2/c^4 - p^2/c^2. Mass and energy are proportional only when momentum is zero.
    Regards.
     
  5. Sep 22, 2010 #4

    bcrowell

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    This only works when m is the *rest* mass, and it also doesn't work in all cases in general relativity. There is no satisfactory definition of mass or energy in GR that works in all cases. For example, GR does not have any sensible way to write down a local energy density of an electromagnetic wave.
     
  6. Sep 22, 2010 #5
    Hi.
    Mass of a single particle is scalar even in GR. RHS of Einstein equation has energy-momentum tensor T which could include electromagnetic energy-momentum. You say we cannot write down the equation? I know that gravitational energy-momentum is pseudo- or non-tensor, but it is another topic.
    Regards.
     
    Last edited: Sep 22, 2010
  7. Sep 22, 2010 #6

    bcrowell

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    The energy-momentum tensor isn't the same thing as an integrated mass. There is no general way of writing down an integrated mass that transforms like a tensor.

    Which version do you have in mind? None of them work in general. For instance, ADM and Bondi mass require asymptotic flatness.

    These are not minor technical issues. For a good discussion of why conservation laws basically don't exist in GR, see MTW, p. 457.
     
  8. Sep 22, 2010 #7
    Hi.
    I see stress energy tensor and you see integrated mass. There is no crossing argument, isn't it?
    Coming back to jnorman's original interest, it maybe helpful to show whether your integrated "mass" and integrated "energy" are independent or not.
    I say my answer to jnorman. Energy(-mementum) is expressed in tensor. Mass is its invariant.
    I learned Einstein way and Landau-Lifgarbagez way many years ago. Your teaching on recent progress will be appreciated.
    Regards.


    PS By the way, why people call gravitational energy momentum a "PSEUDO"tensor ?. I understand pseudotensor is one that change sign for inversion of axis. It does not apply this GR case. It should be called "NON"tensor, shouldn't be?
     
    Last edited: Sep 22, 2010
  9. Sep 23, 2010 #8
    Mass is a type of energy. Energy is conserved in inertial frames including in special relativity, but general relativity deals with accelerating frames.
     
  10. Sep 23, 2010 #9

    bcrowell

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    FAQ: Does special relativity apply when things are accelerating?

    Yes. There are three things you might want to do using relativity: (1) describe an object that's accelerating in flat spacetime; (2) adopt a frame of reference, in flat spacetime, that's accelerating; (3) describe curved spacetime. General relativity is only needed for #3.

    A prohibition on #1 is particularly silly. It would make SR into a trivial theory incapable of describing interactions. If you believed this, you would have to stop believing, for example, in the special-relativistic description of the Compton effect and fine structure in hydrogen; these phenomena would have to be described by some as yet undiscovered theory of quantum gravity.

    #1 often comes up in discussions of the twin paradox. A good way to see that general relativity is totally unnecessary for understanding the twin paradox is to pose a version in which the four-vector equation a=b+c represents the unaccelerated twin's world-line a and the accelerated twin's world-line consisting of displacements b and c. The accelerated twin is subjected to (theoretically) infinite accelerations at the vertices of the triangle. The triangle inequality for flat spacetime is reversed compared to the one in flat Euclidean space, so proper time |a| is greater than proper time |b|+|c|.

    #2, accelerated *frames*, is less trivial. It's for historical reasons that you'll see statements that SR can't handle accelerated frames. Einstein published special relativity in 1905, general relativity in 1915. During that ten-year period in between, nobody really knew what the boundaries of applicability of special relativity were. This uncertainty made its way into textbooks and lectures, and because of the conservative nature of education, some students are still hearing, a century later, incorrect assertions about it.

    In an accelerating frame, the equivalence principle tells us that measurements will come out the same as if there were a gravitational field. But if the spacetime is flat, describing it in an accelerating frame doesn't make it curved. (Curvature is invariant under any smooth coordinate transformation.) Thus relativity allows us to have gravitational fields in flat space --- but only for certain special configurations like uniform fields. SR is capable of operating just fine in this context. For example, Chung et al. did a high-precision test of SR in 2009 using a matter interferometer in a vertical plane, specifically in order to test whether there was any violation of Lorentz invariance in a uniform gravitational field. Their experiment is interpreted purely as a test of SR, not GR.

    Chung -- http://arxiv.org/abs/0905.1929
     
  11. Sep 23, 2010 #10
    "Difference...and... how do you explain that energy can travel at C, but not matter?"

    fundamentally, nobody knows....we have some math, and via some rules, we can describe observational results...but WHY things are they way they are is generally beyond our reach so far. As Crowell implies we can say that particles with rest mass can't travel at c....becuse it would take infinite energy to get anything moving that fast....but why things are that way we don't know.

    We don't even know exactly what mass nor energy are nor how they originate.
     
  12. Sep 23, 2010 #11

    Ich

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    I still hold that SR cannot handle accelerated frames, by definition.
    From Einstein's book:
    "The basal principle, which was the pivot of all our previous considerations, was the special principle of relativity, i.e. the principle of the physical relativity of all uniform motion. "
    So if we deal with
    -special covariance (uniform motion, inertial frames): special relativity
    -general covariance (arbitrary motion, arbitrary frames): general relativity

    AFAIK this is still the "official" definition of the theories: by their structure.
    The definition by "physical content", aka flat vs curved spacetime, is rather informal and not supported by the literature, IIRC.
     
  13. Sep 23, 2010 #12

    pervect

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    The LL pseudotensor also requires asymptotically flat space-time, at least in order to have any physical significance other than some number that results from a specific choice of coordinates.

    Wald, "General Relativity" refers to the following paper:

    http://www.springerlink.com/content/e24p661673315205/

    which demonstrates that the LL pseudotensor approach is equivalent to the Bondi mass.

     
  14. Sep 23, 2010 #13
    Thank you for information. I am a little happy to know that LL pseudotentor that I learned long time ago still survives in theoretical physics.

    Regards.
     
  15. Sep 23, 2010 #14

    Fredrik

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    The quote only supports the principle of relativity, not that non-inertial coordinate systems must be thrown out. What we get from the principle of relativity (along with some other stuff) is that spacetime is either Galilean spacetime or Minkowski spacetime. The invariance of the speed of light rules out the former. So we're left with Minkowski spacetime, which can be defined mathematically in at least three different ways: as a vector space, an affine space, or a manifold. But regardless of which of these options we choose, there's nothing that forces us to throw out non-inertial coordinate systems. In fact, it's quite unnatural to do so.
     
    Last edited: Sep 23, 2010
  16. Sep 23, 2010 #15
    I completely disagree.

    What a theory can handle or not can be established by experiments. It has nothing to do with human made definitions.

    For instance if someone develops a theory about neutron stars and it turns out to be valid for all stars then it silly to say that such a theory is only valid for neutron stars because the inventor says so.
     
  17. Sep 23, 2010 #16

    atyy

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    From a literary standpoint, why not interpret the quote to mean that special relativity cannot deal with accelerated motion?

    Hmm, reading carefully, I see you have indeed classed the twin paradox as a general relativistic problem .... really?

    General covariance (of the equations of motion) isn't the key principle of general relativity is it? It's "no prior geometry".

    Also, structurally, isn't it just that inertial frames exist? The moment we know the relationship between the laws in all inertial frames, then we automatically know the laws in accelerated frames too.
     
    Last edited: Sep 23, 2010
  18. Sep 23, 2010 #17

    bcrowell

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    Just because SR grants privileged status to certain frames, that doesn't mean that those are the only frames SR can describe.

    Newtonian mechanics considers certain frames to be privileged, e.g., a frame fixed to the earth's surface is (approximately) inertial, so it's a privileged frame. The frame of an accelerating elevator is not a privileged frame in Newtonian mechanics. The laws of Newtonian mechanics have a certain simple form in the privileged frames. Their form is different in the non-privileged frames, e.g., Newton's third law is violated by fictitious forces. Nevertheless, we can and often do use the non-privileged frames in Newtonian mechanics.

    SR classifies frames as privileged and non-privileged by exactly the same criteria as Newtonian mechanics. Exactly as in Newtonian mechanics, the laws of physics are form-invariant in different privileged frames, but have a different and more complicated form in the non-privileged frames. Exactly as in Newtonian mechanics, we can choose to use the non-privileged frames if we wish.

    GR also has privileged and non-privileged frames, but the classification is different than in Newtonian mechanics and SR. A frame fixed to the earth's surface is not a privileged frame. The privileged frames are the free-falling frames, which would have been *non*-privileged frames in Newtonian mechanics and SR. Not only is the classification different, but we have two other differences as well: (1) the laws of physics (Einstein field equations) are form-invariant across all frames, not just privileged frames; (2) frames lose much of their importance because they can no longer be defiend globally.

    I could certainly dig up authorities (probably mostly post-1950) to support my view, and I'm sure you could dig up authorities (probably mostly pre-1950) to support yours.
     
  19. Sep 24, 2010 #18
    from Jnorman

    Nobody knows that either. The Standard Model of particle physics is the best we have for strong, weak and electromagnetic forces and particles....but values are measured, experimentally determined, because nobody has a theory from which to derive such values. Why the electron? nobody knows. It appears the three forces possibly emerge from a single initial high energy state at the big bang, but why a unified force would break into the three we observe nobody really knows. And gravity remains outside that theory so far; the search to combine all forces is called grand unification and so far eludes science.

    String theory is another theory and there different vibrational patterns of fundamental strings, one dimensional particle extensions, dictated by hidden geometries of space, determine characteristics...so one vibrational pattern confers mass, another charge, yet another the graviton...and the more energetic the "mass vibration", the more mass is observed.
     
  20. Sep 24, 2010 #19

    Ich

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    Ok, so we're tied: Ich, me, myself, and I vs Fredrik, Passionflower, atyy, and bcrowell. :wink:

    I'll open a new thread for this topic, hopefully tomorrow. You may well convince me, especially if you show me a definition in a respected GR textbook that the difference between GR and SR is exactly the inclusion of ("real"=spacetime curvature) gravity.
     
  21. Sep 24, 2010 #20
    if spacetime is flat, energy is conserved, but once you have to go to another frame of reference (because of curved spacetime), energy will not be conserved — it is not invariant between frames.:zzz:
     
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