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Thread: E=mc 2

  1. #1 E=mc 2 
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    Sorry, I can't get the 2 smaller but I guess you know what it refers to anyway !?

    To what it (C2) refers is what my question refers to !

    E is energy, M is mass, which are both equal, that's easy enough to understand, BUT, how would you explain what C2 is to a layman like myself ? and how does it affect the relationship between E and M ?

    BARCUD (the layman)


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  3. #2 Re: E=mc 2 
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    Quote Originally Posted by BARCUD
    Sorry, I can't get the 2 smaller but I guess you know what it refers to anyway !?

    To what it (C2) refers is what my question refers to !

    E is energy, M is mass, which are both equal, that's easy enough to understand, BUT, how would you explain what C2 is to a layman like myself ? and how does it affect the relationship between E and M ?

    BARCUD (the layman)
    C^2 is light speed squared. A huge number, yes. It would demonstrate that you only require a small amount of M to get a huge amount of E.


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    Great, thanks Q !

    Then, the more dense the matter, the more energy it has ? A black olive contains energy BUT a black hole contains a whole lot more energy ?

    Not quite sure what light (speed) particularly has to do with it though !

    BARCUD
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    That equation has more to do with particles than large solids like olives!

    Let me explain in the context of radioactive decay (so a big nucleus decays into 2 smaller ones, say). You'd find that the original (parent) nucleus has a greater mass than the 2 products (daughters).

    The equation in this case would more accurately be written as

    ∆E = ∆mc^2

    (where ∆ means a change in something). If you have a radioactive decay, you get a release of energy. This is because some of the mass is "converted" into energy during the decay. The decay products actually have a smaller mass in total than the original nucleus. The amount of energy released would be found using the equation above. Since c^2 is such a massive number, you can see how we can get loads of energy from this process. This is how nuclear fission power plants work
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    Mash, I'm almost getting it BUT what is 'radioactive decay' ?

    BARCUD
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    Quote Originally Posted by BARCUD
    Mash, I'm almost getting it BUT what is 'radioactive decay' ?

    BARCUD
    Radioactive decay happens when an unstable (i.e. radioactive) material emits an alpha particle, a beta particle, or a gamma ray and undergoes a change in its nucleus to become a different, usually more stable, isotope. It is called "decay" because over time the unstable isotope disappears and is replaced by stable isotopes.
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    Quote Originally Posted by BARCUD
    Great, thanks Q !

    Then, the more dense the matter, the more energy it has ? A black olive contains energy BUT a black hole contains a whole lot more energy ?

    Not quite sure what light (speed) particularly has to do with it though !

    BARCUD
    No. The equation is is mass, total mass and not mass density. Density has nothing to do with it. The more mass, the more energy.

    A the energy associated with a black hole is related to the total mass, and a microscopic black hole, if such exists, might well have less mass than a black olive. Black holes formed from collapsing supernovas have more energy than a black olive because stars are bigger than black olives.

    What the speed of light has to do with it is a bit more mysterious. Even Einstein failed to provide a valid derivation for that equation in his first attempts.

    Here is Wiki article with a fairly complete discussion.
    http://en.wikipedia.org/wiki/Mass-energy_equivalence
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    Quote Originally Posted by DrRocket
    Quote Originally Posted by BARCUD
    Great, thanks Q !

    Then, the more dense the matter, the more energy it has ? A black olive contains energy BUT a black hole contains a whole lot more energy ?

    Not quite sure what light (speed) particularly has to do with it though !

    BARCUD
    No. The equation is is mass, total mass and not mass density. Density has nothing to do with it. The more mass, the more energy.

    A the energy associated with a black hole is related to the total mass, and a microscopic black hole, if such exists, might well have less mass than a black olive. Black holes formed from collapsing supernovas have more energy than a black olive because stars are bigger than black olives.

    What the speed of light has to do with it is a bit more mysterious. Even Einstein failed to provide a valid derivation for that equation in his first attempts.

    Here is Wiki article with a fairly complete discussion.
    http://en.wikipedia.org/wiki/Mass-energy_equivalence
    Einstein never failed at all, if my memory serves me correctly, he took the tailor expansion of the kinetic energy of an object and came to the equation which by the way, is wrong. The equation should really be expressed as an approximation.
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    Quote Originally Posted by Mash
    (where ∆ means a change in something). If you have a radioactive decay, you get a release of energy. This is because some of the mass is "converted" into energy during the decay. The decay products actually have a smaller mass in total than the original nucleus. The amount of energy released would be found using the equation above. Since c^2 is such a massive number, you can see how we can get loads of energy from this process. This is how nuclear fission power plants work
    there is a difference between radioactive decay and nuclear fission/fusion. As far as I am aware, radioactive decay does not convert any mass into energy.
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    No radioactive decay does not convert mass to energy, the 3 types of decay, Alpha emission (emits a helium nucleus) Beta emission releases an electron after a nuetron in the nucleus has been converted to a proton, and gamma emission which I can't remember with absolute certainty. Look it up.

    Ah I see harold has already been this way...
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    Yes, and just to spin your head even move. When a neutron decays into a protonand gives OFF partcles; it increases mass. How? - Go figure. lol
    The hand of time rested on the half-hour mark, and all along that old front line of the English there came a whistling and a crying. The men of the first wave climbed up the parapets, in tumult, darkness, and the presence of death, and having done with all pleasant things, advanced across No Man's Land to begin the Battle of the Somme. - Poet John Masefield.

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    Quote Originally Posted by leohopkins
    Yes, and just to spin your head even move. When a neutron decays into a protonand gives OFF partcles; it increases mass. How? - Go figure. lol
    Nah, the mass does not significantly change. Neutrons do, actually, weigh slightly more than protons.
    "The major difference between a thing that might go wrong and a thing that cannot possibly go wrong is that when a thing that cannot possibly go wrong goes wrong it usually turns out to be impossible to get at or repair." ~ Douglas Adams
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    Quote Originally Posted by drowsy turtle
    Quote Originally Posted by leohopkins
    Yes, and just to spin your head even move. When a neutron decays into a protonand gives OFF partcles; it increases mass. How? - Go figure. lol
    Nah, the mass does not significantly change. Neutrons do, actually, weigh slightly more than protons.
    But with beta+ decay, a proton converts to a neutron by emitting a positron, neutrino and gamma ray.
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    Fair point. But then, beta + decay does not happen in naturally occuring isotopes; positron emitting substances are generally produced in a nuclear reactor.
    "The major difference between a thing that might go wrong and a thing that cannot possibly go wrong is that when a thing that cannot possibly go wrong goes wrong it usually turns out to be impossible to get at or repair." ~ Douglas Adams
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    Quote Originally Posted by drowsy turtle
    Fair point. But then, beta + decay does not happen in naturally occuring isotopes; positron emitting substances are generally produced in a nuclear reactor.
    Potassium 40 is a naturally occurring beta+ emitter, it represents 0.012% of normal Potassium samples.
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    Hmmmm. In that case I'll have to have a rethink.
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  18. #17 Re: E=mc 2 
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    Quote Originally Posted by BARCUD
    Sorry, I can't get the 2 smaller but I guess you know what it refers to anyway !?

    To what it (C2) refers is what my question refers to !

    E is energy, M is mass, which are both equal, that's easy enough to understand, BUT, how would you explain what C2 is to a layman like myself ? and how does it affect the relationship between E and M ?

    BARCUD (the layman)
    I believe the first poster was closest to answering your question, but it was put in terms that to a ''layman like yourself'' in your words, but not qouted to exact, may be a bit more confusing. Let me quickly brief the equation in a whole.



    E= energy. Everything then that has a solid mass in the universe is found to have an energy. This energy is dependant however very closely to the right-handside of the equation. (Not Einsteins originally - it was found at least three times before him... by the way)

    = is for the equivalance. The equivalance proposes that the energy has an inverse property to mass, which allows us to distinguish the axioms brought forth in E.

    M is the inverse property, whilst c is the speed of light. If the speed of light was not squared, then the ''conversion factor'' of the energy could not be able to transmutate (1). The conversion factor then needs to be squared, a process we use all the time. This sqaured factor allows us to have a massive amount of energy on one side capable of creating a matter which is a longer lived fluctuation on a much smaller, less radical sense of being, but perhaps even a being or object that has more definition than that of energy.

    (1) - This basically means that energy and mass could not be an profitable mathematical contingeancy to allow you to have a massive amount of energy from what would seem to be a very contradictory small amount of matter.
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  19. #18  
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    I think of it as:

    matter and energy are two different states of the same thing, like water and ice. One converts to the other, and back, depending.


    But: Did Oliver Heaviside come up with, not exactly, but an equivilent, idea that E=MC (squared). 20 years before Einstein?
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    But: Did Oliver Heaviside come up with, not exactly, but an equivilent, idea that E=MC (squared). 20 years before Einstein?
    No. What do you mean by an equivalent but not exactly idea that ?

    Furthermore, I should remind you that such an idea was considered practically heretical pre-Einstein.

    Einstein never failed at all, if my memory serves me correctly, he took the tailor expansion of the kinetic energy of an object and came to the equation which by the way, is wrong. The equation should really be expressed as an approximation.
    Why? The equation works perfectly well for objects at rest. In motion, of course, the equation is convenienced with the Lorentz factor, so I assume you mean that.

    Also, I should prettyy much state that the Taylor expansion has nothing to with it. He first considered the amount of energy an observer at motion would think it would have, compared it to that observed by someone at rest, realised that the entire thing should be equivalent to the kinetic energy of the object, and simply rearranged and cancelled out. The result was the above formula.
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    Quote Originally Posted by Liongold
    But: Did Oliver Heaviside come up with, not exactly, but an equivilent, idea that E=MC (squared). 20 years before Einstein?
    No. What do you mean by an equivalent but not exactly idea that ?

    Furthermore, I should remind you that such an idea was considered practically heretical pre-Einstein.

    Einstein never failed at all, if my memory serves me correctly, he took the tailor expansion of the kinetic energy of an object and came to the equation which by the way, is wrong. The equation should really be expressed as an approximation.
    Why? The equation works perfectly well for objects at rest. In motion, of course, the equation is convenienced with the Lorentz factor, so I assume you mean that.

    Also, I should prettyy much state that the Taylor expansion has nothing to with it. He first considered the amount of energy an observer at motion would think it would have, compared it to that observed by someone at rest, realised that the entire thing should be equivalent to the kinetic energy of the object, and simply rearranged and cancelled out. The result was the above formula.
    When you qoute people, make sure to point out who you are qouting, because the first qoute was not me.
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    I think the equation should be taken into consideration. Deriving that formula, you remove the part and you get:



    thus taking the tailor expansion of the sqaure root gives us:



    so that

    which derives the relation (which is an approximation)

    where it must be approximated for low velocities. If we are talking in terms of relativitic speeds, then
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    Quote Originally Posted by Vexer
    I think of it as:

    matter and energy are two different states of the same thing, like water and ice. One converts to the other, and back, depending.
    That wasn't the problem. I just thought that there was no conversion in nuclear decay.
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    Quote Originally Posted by drowsy turtle
    Quote Originally Posted by Vexer
    I think of it as:

    matter and energy are two different states of the same thing, like water and ice. One converts to the other, and back, depending.
    That wasn't the problem. I just thought that there was no conversion in nuclear decay.
    What do you mean by nuclear conversion? Do you mean energy into mass? Or mass into energy? Or both?
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    Quote Originally Posted by Manynames
    Quote Originally Posted by drowsy turtle
    Quote Originally Posted by Vexer
    I think of it as:

    matter and energy are two different states of the same thing, like water and ice. One converts to the other, and back, depending.
    That wasn't the problem. I just thought that there was no conversion in nuclear decay.
    What do you mean by nuclear conversion? Do you mean energy into mass? Or mass into energy? Or both?
    either, or both, whatever.

    Please note I mean radioactive decay, not fusion or fission.

    Anyway, ignore me, I'm dragging us off topic.
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    Quote Originally Posted by drowsy turtle
    Quote Originally Posted by Manynames
    Quote Originally Posted by drowsy turtle
    Quote Originally Posted by Vexer
    I think of it as:

    matter and energy are two different states of the same thing, like water and ice. One converts to the other, and back, depending.
    That wasn't the problem. I just thought that there was no conversion in nuclear decay.
    What do you mean by nuclear conversion? Do you mean energy into mass? Or mass into energy? Or both?
    either, or both, whatever.

    Please note I mean radioactive decay, not fusion or fission.

    Anyway, ignore me, I'm dragging us off topic.
    Well, i am not completely civil in this topic, however, you would be surprised how much the equation takes form in atomic conversions. For instance, the quarks hold more mass than what a nucleus is made of. The balance however is saved, because the missing mass is turned into an energy that binds the quarks together. This is gluon energy.
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    When you qoute people, make sure to point out who you are qouting, because the first qoute was not me.
    As you wish, Manynames. I'll make it a point to do that from now on.
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    One idea that has not been pointed out here is the arbitrariness of units. It is possible to pick a set of units such that (See Natural units) then the units for mass and energy are the same and because we would not think that there is a lot of energy in a piece of mass we would just see mass and energy as equivalent.
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    Quote Originally Posted by c186282
    One idea that has not been pointed out here is the arbitrariness of units. It is possible to pick a set of units such that (See Natural units) then the units for mass and energy are the same and because we would not think that there is a lot of energy in a piece of mass we would just see mass and energy as equivalent.
    But natural units should be kept for Planck Calculations, i feel.
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    My point is one can do any calculation in any set of units. If you always live in one set of arbitrary units your prospective on things will be come skewed.
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    One thing to point out about natural units is that the unit of mass is very, very tiny (at least for Planck units).
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    Quote Originally Posted by MagiMaster
    One thing to point out about natural units is that the unit of mass is very, very tiny (at least for Planck units).
    Yes, i pointed this out to him/her.
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    The formula in the title was discovered by Jules Henri Poincaré, a French mathmatician in the 19th century, not by Einstein as commonly assumed.
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    Quote Originally Posted by line
    The formula in the title was discovered by Jules Henri Poincaré, a French mathmatician in the 19th century, not by Einstein as commonly assumed.
    I've also pointed out the equation was not derived by Einstein first. But i also believe the equation was derived before Poincare as well. I'll need to look into that.
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    Quote Originally Posted by MagiMaster
    One thing to point out about natural units is that the unit of mass is very, very tiny (at least for Planck units).
    So? What does tiny mean? The concept of large and small are only relative to our size and fundamentally mean nothing. A physics concept of large and small may be a division between when a problem can be solved with QM or classical mechanics.
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    Quote Originally Posted by c186282
    Quote Originally Posted by MagiMaster
    One thing to point out about natural units is that the unit of mass is very, very tiny (at least for Planck units).
    So? What does tiny mean? The concept of large and small are only relative to our size and fundamentally mean nothing. A physics concept of large and small may be a division between when a problem can be solved with QM or classical mechanics.
    Look... whilst it has been known to use Planck Values on other work, such as a specialized theory of relativity, it is ALWAYS best to keep planck measurements to small origins of their use, such as Planck calculations, which work for the Planck Time and Planck Space. I will provide some calculations if you wish, but don't use them in this context when mass and energy are equivalant, when understanding how much energy you can get from a tiny bit of mass. It helps the understanding of the reader not to.
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    I realize from a practical stance that one should use a set of units that match the problem. (However, I do enjoy giving my cars gas mileage as 1.5 inverse zeta barns)

    My only point is that ones choice of units is arbitrary. The fact that we measure the speed of light in m/s and is a really big number gives one an impression that the energy received from a small amount of mass is really large. This is true in what we think of as a small amount of mass and what that amount of energy could do, but this is just our take on what is big and what is small. In the early universe or in the collisions of the LHC there is not such a discrepancy between the visualization of the masses involved and the energy involved but it is the same physics.

    Or maybe another way: The scales involved in a problem should come from the physics not the size of the numbers that carry units.


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    Quote Originally Posted by c186282
    I realize from a practical stance that one should use a set of units that match the problem. (However, I do enjoy giving my cars gas mileage as 1.5 inverse zeta barns)

    My only point is that ones choice of units is arbitrary. The fact that we measure the speed of light in m/s and is a really big number gives one an impression that the energy received from a small amount of mass is really large. This is true in what we think of as a small amount of mass and what that amount of energy could do, but this is just our take on what is big and what is small. In the early universe or in the collisions of the LHC there is not such a discrepancy between the visualization of the masses involved and the energy involved but it is the same physics.

    Or maybe another way: The scales involved in a problem should come from the physics not the size of the numbers that carry units.


    But they are not arbitrary in this case. If they where, then using Planck units would make no sense in a whole when understanding the conversion factor of . This factor is experimentally, and mindfully important.
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    Why is a kg a kg? Why is a meter about this long? (I'm holding my arms out.) Why is a Newton about this hard? (I'm pushing on the screen.) Because some French dude thought it was a good idea. (It was, I wish we used these units in my country.) But because of these choices we need a fudge factor called for


    I realize one needs to make a choice of units and then be consistent to get the correct result, I just do not what our choice of units to cloud my concept of scale.
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    Quote Originally Posted by c186282
    Why is a kg a kg? Why is a meter about this long? (I'm holding my arms out.) Why is a Newton about this hard? (I'm pushing on the screen.) Because some French dude thought it was a good idea. (It was, I wish we used these units in my country.) But because of these choices we need a fudge factor called for


    I realize one needs to make a choice of units and then be consistent to get the correct result, I just do not what our choice of units to cloud my concept of scale.
    you've lost the point... nonetheless, my attention as well.
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    Yes we have gotten of topic So I will leave you with a reference:
    Classical Electrodynamics by J.D. Jackson
    See the Appendix on Units and Dimensions
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    Quote Originally Posted by c186282
    Quote Originally Posted by MagiMaster
    One thing to point out about natural units is that the unit of mass is very, very tiny (at least for Planck units).
    So? What does tiny mean? The concept of large and small are only relative to our size and fundamentally mean nothing. A physics concept of large and small may be a division between when a problem can be solved with QM or classical mechanics.
    Not to drag this off topic further, but I wanted to respond to this myself. (So, Manynames, don't bother responding to this post. It's off topic.)

    Yes, tiny is subjective. I was just saying that while mass and energy are directly comparable in natural units (or at least the Planck units, and some similar systems of units), these units also have a unit of mass on the order of a medium grain of sand. (Actually, there's not a whole lot at that scale to compare to. :P) Also, the units of energy (in Planck units) is on the order of a lightning bolt. Not that they aren't useful, but it's just funny to think of the mass of an apple in grains of sand or mass-energy equivalent lightning bolts.
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    Liongold,

    What do you mean by an equivalent but not exactly idea that E=mc^2?

    Well, I’ve read that it is a less elegant but exactly, E=Mc 2




    (I suppose me coming back weeks later, is er, a bit week.)
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    could someone tell me if we could make a formular triangle out of e=mc^2 such as we do with speed=distance/time?
    thanks
    K.T.B
    Men speak of killing time and yet, time secretly kills them....
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  45. #44  
    Reptile Dysfunction drowsy turtle's Avatar
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    yes.
    ../ \
    ./ E \
    /m|c˛\
    "The major difference between a thing that might go wrong and a thing that cannot possibly go wrong is that when a thing that cannot possibly go wrong goes wrong it usually turns out to be impossible to get at or repair." ~ Douglas Adams
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  46. #45  
    Forum Freshman ASTROPHYSICIST137's Avatar
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    thanks.
    K.T.B
    Men speak of killing time and yet, time secretly kills them....
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  47. #46  
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    People knew since long before Einstein that if you're going to convert from units of mass to unites of energy you would need some factor of velocity^2, since it only takes some very simple dimensional analysis to figure that out. Since energy units are force * distance, and force units are mass*distance/time^2, if you want to set a mass equal to energy, you will need some factor of distance^2/time^2. Since velocity is distance/time, that means your conversion factor will be in units of velocity^2.

    Einstein's contribution was proving that this relationship actually had physical relevance to everything.
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