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Thread: Energy equivalent of mass and kinetic energy.

  1. #1 Energy equivalent of mass and kinetic energy. 
    Senior Member MaxPayne's Avatar
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    As velocity increases mass of a particle increases?

    When the mass increases the total energy should also increase proportionally.

    And closer to velocity of light it should become infinite. Is this really whats that happening?(T/F)

    Also as the object's speed increases the light speed relative to the object should decrease( c - v). Hence energy should be e' = m' (c-v)^2,

    This in a way this can balance the equation keeping net energy from reaching infinity closer to speed of light.

    But as we know this isn't the case. No matter at what speed the object travels , the light speed still remains the same and light would be speeding away from it at c.
    So c-v =c...hence V should be zero relative to c.
    So either the distance of separation between photon and the object at every instance should be zero regardless of the position of the object, meaning that the photon is present everywhere???

    OR The time slows down for the object to make the time required for the object to catch up with the photon infinity?

    Okay, Now if I travel from sun trying to catch up with a photon emitted by the sun. As described earlier time will slow down for me to make the relative speed of photon 'C' with respect to me. Now another Photon from another star is coming towards me, the time should actually tick faster in order to make the relative velocity of the incoming light 'c' (relative to me). So the time is actually slowing down and ticking faster for the same 'me'. Also this is just the case of two photons, but there may be a large number of photons crisscrossing me at different directions and each one of them should influence my time differently.

    I must admit that the original question that I had in mind was different!! But I am left this..
    **Am I thinking about it the "wrong way"? Is there some element at work here, that I have overlooked?
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  2. #2  
    Administrator Markus Hanke's Avatar
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    Quote Originally Posted by MaxPayne View Post
    As velocity increases mass of a particle increases?
    No, this is a common misconception. What increases with speed is only the total energy of the particle ( also very confusingly called "relativistic mass" ), whereas its rest mass is invariant and the same for all observers, regardless of relative motion. In modern textbooks the term "relativistic mass" is now thankfully being abandoned, since it leads to too much confusion.

    And closer to velocity of light it should become infinite. Is this really whats that happening?(T/F)
    No. The rest mass remains invariant.

    Also as the object's speed increases the light speed relative to the object should decrease( c - v)
    No. Light speed is not relative to anything, it is constant and exactly c in all frames of reference; in special relativity you do not add speeds linearly, but you use the velocity addition formula.

    Hence energy should be e' = m' (c-v)^2,
    No, the formula E=mc^2 is valid only for objects at rest.

    Am I thinking about it the "wrong way"?
    I'm afraid yes, see above. You must also bear in mind that a photon is not a valid frame of reference; concepts of the form "relative to a photon", "from the photon's point of view" and such like are physically meaningless. The photon does not have a rest frame.
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    Senior Member MaxPayne's Avatar
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    No, this is a common misconception. What increases with speed is only the total energy of the particle ( also very confusingly called "relativistic mass" ), whereas its rest mass is invariant and the same for all observers, regardless of relative motion. In modern textbooks the term "relativistic mass" is now thankfully being abandoned, since it leads to too much confusion.
    No. The rest mass remains invariant.
    Uh oh, What is rest mass really? I have been made to believe that nothing in the Universe is at rest actually. Again isn't it the drag offered by the higg's field that gives mass to the body. So rest mass should be the 'force'(???) required to initiate a motion through space. If we find out mass of a 'non moving object', isn't it really the rest mass of the object relative to earth that we are calculating. Because object is moving through space with the earth at the velocity of earth. Now we can find out the rest mass of earth with respect to sun and that of sun w.r.t galactic center and so on. Now you might argue that all these velocities add up to only about say (1/100000)th of speed of light. Hence it doesn't significantly affect the rest mass of a body. So my question here is that could it be the effect of all these velocities which gives us the false sense of rest mass?
    Also please don't put up arguments like
    "rest mass is same everywhere"...coz I think we have covered that already.
    From a wider perspective the velocity of everything in the universe must be approximately the same. Over large distances the velocity of every body should be approximately be the same, i.e same as that of space expansion about it.
    Actual rest mass should be zero if there is no relative motion between an object and space? Right?!!!!!!!!!
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    Senior Member MaxPayne's Avatar
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    No. Light speed is not relative to anything, it is constant and exactly c in all frames of reference; in special relativity you do not add speeds linearly, but you use the velocity addition formula.
    No, the formula E=mc^2 is valid only for objects at rest.
    Please don't dissect the question into bits and pieces,I urge you to read the whole thing if you have the time. (I was actually explaining my thought process.)

    I'm afraid yes, see above. You must also bear in mind that a photon is not a valid frame of reference; concepts of the form "relative to a photon", "from the photon's point of view" and such like are physically meaningless. The photon does not have a rest frame.
    I agree with you! But can I use the stars emitting the photons as a valid frame of reference, in fact the photon actually has to move through space until it 'surfaces' on the star. So until it reaches the surface of the star it can used as a valid frame of reference. To such a photon I can have a relative velocity right? Same with the case of one which is emitted by the sun.

    Edit*

    Instantaneous velocity of light is still 'c' and apparent slowing down of time is because of the time lag due to series of absorption and emission of light by atoms in a medium. So yepps, you are right any which way you look at it.
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    Administrator Markus Hanke's Avatar
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    Quote Originally Posted by MaxPayne View Post
    Uh oh, What is rest mass really?
    An invariant property of a system on which all observers agree.

    I have been made to believe that nothing in the Universe is at rest actually.
    That is correct, but you can always define a frame in which the observer is at rest with respect to the object being observed. That forms a convenient rest frame.

    Again isn't it the drag offered by the higg's field that gives mass to the body.
    In a way, yes.

    If we find out mass of a 'non moving object', isn't it really the rest mass of the object relative to earth that we are calculating.
    The rest mass is the same for all observers, so it doesn't matter with respect to what and who it is being determined. The most convenient way is to do it if the observer is at relative rest to the object, so that there is no momentum component.

    So my question here is that could it be the effect of all these velocities which gives us the false sense of rest mass?
    No, because rest mass is not a frame-dependent quantity; only total energy is.

    Actual rest mass should be zero if there is no relative motion between an object and space? Right?!!!!!!!!!
    Yet it isn't.

    Please don't dissect the question into bits and pieces,I urge you to read the whole thing if you have the time. (I was actually explaining my thought process.)
    I do read the whole thing, but I can only answer one specific point at a time.

    To such a photon I can have a relative velocity right?
    No - the speed of a photon is c in all frames of reference, so how could you define your velocity relative to it ? It is not possible.
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    Senior Member MaxPayne's Avatar
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    The rest mass is the same for all observers, so it doesn't matter with respect to what and who it is being determined. The most convenient way is to do it if the observer is at relative rest to the object, so that there is no momentum component.
    No, because rest mass is not a frame-dependent quantity; only total energy is

    Any reading done by the observer is only apparent and is influenced(comparing) by it's own rest mass, so general assumption is that the rest mass is frame independent, fair enough . Unfortunately, Isn't this another chicken or egg situation.

    Also!! Shouldn't the rest mass be zero if it is frame dependent..? What do you think?

    so that there is no momentum component
    Momentum is a) mass dependent or b) rest mass dependent?
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    Administrator Markus Hanke's Avatar
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    Quote Originally Posted by MaxPayne View Post
    Unfortunately, Isn't this another chicken or egg situation.
    Not really, since mass is not influenced by the observer at all. Don't confuse mass with weight.

    Also!! Shouldn't the rest mass be zero if it is frame dependent..? What do you think?
    Why would it be zero ? I don't quite get your reasoning.

    Momentum is a) mass dependent or b) rest mass dependent?
    To me "mass" always means rest mass; I avoid the outdated notion of "relativistic mass" like the plague since it leads to much confusion. In either case, in relativity, momentum, rest mass and total energy are all connected via the relation



    Momentum is therefore a function of both rest mass and total energy.
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    Markus: No, this is a common misconception. What increases with speed is only the total energy of the particle ( also very confusingly called "relativistic mass" ), whereas its rest mass is invariant and the same for all observers, regardless of relative motion. In modern textbooks the term "relativistic mass" is now thankfully being abandoned, since it leads to too much confusion.

    cinci: This is a little confusing. The rest mass can only be observed in the rest frame of an object. Every relatively moving frame will not observe that mass. This was discovered early in the 20th century when it was found that more energetic beams of electrons took more energy to deflect. It's the reason the LHC requires superconducting magnets where the proton mass is 7000 time its rest mass.

    I know modern texts have taken to removing the phrase relativistic mass to avoid confusion but I'm not sure who was confused. Energy responds like mass because it is equivalent to mass.
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    Administrator Markus Hanke's Avatar
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    Quote Originally Posted by cincirob View Post
    I know modern texts have taken to removing the phrase relativistic mass to avoid confusion but I'm not sure who was confused. Energy responds like mass because it is equivalent to mass.
    You are welcome to continue using the concept of "relativistic mass" - it is not wrong per se, if applied correctly.

    but I'm not sure who was confused
    All those students who automatically concluded that you can turn any object into a black hole by accelerating it long enough.
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  10. #10  
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    The technically correct term for what is referred to as "relativistic mass" is "energy". However, to express energy in units of mass, one divides the energy by . Energy is the time component of the four-dimensional energy-momentum vector.

    Invariant mass (rest mass, or simply, mass) is the magnitude of the four-dimensional energy-momentum vector.

    It is worth noting that in relativity, one often adopts units such that , which simplifies expressions, but may lead to confusion for those not familiar with the convention. However, it does allow one to simply regard energy, momentum, and mass as aspects of the same notion even though traditionally they have different units.
    A tensor equation that is valid in any coordinate system is valid in every coordinate system.
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    Markus: All those students who automatically concluded that you can turn any object into a black hole by accelerating it long enough

    cinci: I've seen this argument but not from students. I've seen it from anti-relativists. Changing the terminology won't help them. :-)
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    Quote Originally Posted by cincirob View Post
    I've seen this argument but not from students. I've seen it from anti-relativists. Changing the terminology won't help them. :-)
    True enough ( though I've seen it from students plenty of times ).
    Regardless, current consensus appears to be that the concept is outdated, since most modern textbooks no longer use it. Personally I prefer it this way, but if properly done the "old way" works just fine, too.
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