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    The conventional explanation of mass-energy equivalence is that mass is just a manifestation of energy, and that an amount m of mass can be converted into an amount E of energy by the equation E=m \gamma c^2

    Now, often this equation is just quoted as E=mc^2.
    Obviously, where \gamma \not=1 (i.e. where in a frame where the body isn't at rest), this equation is incorrect. But mass "m" is often redefined as "relativistic mass", which is really just "\gammam". In other words, "relativistic mass" is really just a function of "mass", and redifining "mass" to mean "relativistic mass" in the context of relativity is just misleading.

    "Mass" proper is a non-invariant quantity; it is the relationship between the acceleration of a body and the force applied on that body, or the relationship between the energy of a body and the speed of light. These relationships are constant and Lorentz invariant.

    But physics doesn't seem to treat it that way. Physics presents energy as the real quantity, and mass as a form of energy. And it's this that doesn't make much sense. Energy is intrinsically non-invariant; the energy an object has changes according to your rest frame. Energy is obviously less fundamental than mass; for a fundamental quantity doesn't change according to your reference frame. Mass proper doesn't change, but energy does.

    So why isn't energy viewed as a manifestation of mass? Surely this would be much more coherent?
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    I think that rest mass and rest energy are both invariant quantities. However the total relativistic mass and total energy are not invariant. I don't think its correct to say that energy is less fundamental than mass. Energy and mass are essentially two sides of the same coin.
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    (Original post by suneilr)
    I think that rest mass and rest energy are both invariant quantities. However the total relativistic mass and total energy are not invariant. I don't think its correct to say that energy is less fundamental than mass. Energy and mass are essentially two sides of the same coin.
    Rest energy? Energy is intrinsically related to velocity, though.
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    (Original post by shamrock92)
    Rest energy? Energy is intrinsically related to velocity, though.
    The energy associated with the mass. Kinetic energy associated with motion is an extra term in the total energy.

    Total energy is

    E^2 = p^2 c^2 + m^2 c^4

    p = 0 then E = mc^2 for the particle at rest.
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    (Original post by shamrock92)
    Rest energy? Energy is intrinsically related to velocity, though.
    Total energy is related to velocity as is mass. Rest mass and rest energy as the name suggests are the constant mass and energy associated with a body at rest. The rest mass/energy of an object never changes (I think).
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    (Original post by suneilr)
    Total energy is related to velocity as is mass. Rest mass and rest energy as the name suggests are the constant mass and energy associated with a body at rest. The rest mass/energy of an object never changes (I think).
    Let me re-write what the cripple wrote, since every Tom, **** and Harry likes to be smart with the equations of Energy.


    E^2 = p^2 c^2 + m_0^2 c^4

    Where m_0 is the invarient mass, or the rest mass.
    Typically what people refer to as the "relativistic mass" is what I call energy, which is the curvature of spacetime.
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    (Original post by Mehh)
    Let me re-write what the cripple wrote, since every Tom, **** and Harry likes to be smart with the equations of Energy.


    E^2 = p^2 c^2 + m_0^2 c^4

    Where m_0 is the invarient mass, or the rest mass.
    Typically what people refer to as the "relativistic mass" is what I call energy, which is the curvature of spacetime.
    (Original post by ashy)
    The energy associated with the mass. Kinetic energy associated with motion is an extra term in the total energy.

    Total energy is

    E^2 = p^2 c^2 + m^2 c^4

    p = 0 then E = mc^2 for the particle at rest.
    (Original post by suneilr)
    Total energy is related to velocity as is mass. Rest mass and rest energy as the name suggests are the constant mass and energy associated with a body at rest. The rest mass/energy of an object never changes (I think).
    Well "energy" is still non-invariant, whereas "mass" isn't. Of course, you can define a frame in which the "rest energy" is invariant. That's like saying "In any frame, p=0 in the rest frame," which is a bit of a cop out. Mass itself is still invariant in any frame, without an ad hoc specification of frame.
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    (Original post by shamrock92)
    Well "energy" is still non-invariant, whereas "mass" isn't. Of course, you can define a frame in which the "rest energy" is invariant. That's like saying "In any frame, p=0 in the rest frame," which is a bit of a cop out. Mass itself is still invariant in any frame, without an ad hoc specification of frame.

    The total energy for a mass
     E = mc^2 = \gamma m_0 c^2

    Now this will obviously tend to infinity as v tends to c. But we can interpret this by setting c as the limiting velocity for any massive body. So by the binomial theorem:

     E = m_0 c^2 \left[ 1 - \frac{v^2}{c^2} \right]^{-0.5}

    so, expanding using the binomial theorem...

     E = m_0 c^2 \left[ 1 + \frac{v^2}{2c^2} - \frac{3v^4}{8c^4} ...\right]

    Only the first term is independent of the velocity of the mass, and so will remain constant whatever the velocity of the body. This is the rest energy,  E_0 , such that
     E_0 = m_0 c^2 , linking the rest energy to rest mass


    The second term is the classical kinetic energy term, but is just a first order approximation of the relativistic expression.

    SO basically after that ramble, I am trying to say that the object will have a mass (its rest mass) that is invariant - it is constant regardless of the motion of the object. However, for an object that is moving, it possesses kinetic energy too. By Einstein's famous equation, you could say that it then has some "kinetic mass" I suppose (but I have never seen this). Instead, you say that its rest mass is invariant. I am not quite sure if that is what you were asking....

    Hope it was of some help to someone! :rolleyes:
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    (Original post by Mehh)
    Let me re-write what the cripple wrote, since every Tom, **** and Harry likes to be smart with the equations of Energy.




    Where is the invarient mass, or the rest mass.
    Typically what people refer to as the "relativistic mass" is what I call energy, which is the curvature of spacetime.
    Chinkie.

    So you basically just wrote exactly what I wrote. :tongue: The post above this one is probably the best to explain the point.
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    (Original post by ashy)
    Chinkie.

    So you basically just wrote exactly what I wrote. :tongue: The post above this one is probably the best to explain the point.
    thank you
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    (Original post by shamrock92)
    Well "energy" is still non-invariant, whereas "mass" isn't. Of course, you can define a frame in which the "rest energy" is invariant. That's like saying "In any frame, p=0 in the rest frame," which is a bit of a cop out. Mass itself is still invariant in any frame, without an ad hoc specification of frame.
    Energy is not invarient. The length of the energy-momentum 4 vector however IS invariant (by definition of the fact it IS a 4 vector).
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    No-one seems to be answering my question.

    My point is that mass is invariant whereas energy isn't. "Relativistic mass" is obviously non-invariant, but is really just a contrivance of proper mass, which is. Evidently, then, energy can't be an objective property, as its value changes according to your frame. Mass can be an objective property, as it doesn't change according to frame. So energy should be viewed as a manifestation of mass, rather than the converse.
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    (Original post by shamrock92)
    No-one seems to be answering my question.

    My point is that mass is invariant whereas energy isn't. "Relativistic mass" is obviously non-invariant, but is really just a contrivance of proper mass, which is. Evidently, then, energy can't be an objective property, as its value changes according to your frame. Mass can be an objective property, as it doesn't change according to frame. So energy should be viewed as a manifestation of mass, rather than the converse.
    Rest mass and rest energy are equivalent and are invariant.
    Total energy and relativistic mass are equivalent and are not invariant.
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    (Original post by suneilr)
    Rest mass and rest energy are equivalent and are invariant.
    Total energy and relativistic mass are equivalent and are not invariant.
    I'm aware of that. I'm not asking what the terms mean. I'm asking why energy viewed as more fundamental than mass when it isn't.
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    (Original post by shamrock92)
    I'm aware of that. I'm not asking what the terms mean. I'm asking why energy viewed as more fundamental than mass when it isn't.
    I don't believe either is viewed as more fundamental. They're both different sides of the same coin.
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    (Original post by suneilr)
    I don't believe either is viewed as more fundamental. They're both different sides of the same coin.
    I don't think that's true. Read my posts.
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    (Original post by shamrock92)
    I don't think that's true. Read my posts.
    Do you have any sources that treat one or the other as more fundamental?
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    (Original post by suneilr)
    Do you have any sources that treat one or the other as more fundamental?
    It's not really about sources; it's an idea I've had for reasons I've explained. But yes:

    http://www.unc.edu/depts/phildept/La...usEquation.pdf
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    I think what you are asking about is the concept of the symmetries of time which leads to the law of conservation of energy.
    There is no parallel concept for mass (conservation of mass is a much weaker law, one that you need to ask Chemists about).
 
 
 
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