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A question about E=mc^2

  1. May 28, 2015 #1
    If i put c=d/t in
    E=mc2, then E=m×d2/t2

    Now take m=1kg and d=1m

    Does this mean that E is inversely proportional to time?
     
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  3. May 28, 2015 #2

    Fredrik

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    No, that would be the case if there's a constant A such that E=A/t. If there's a constant A such that E=A/t2, that we could say that E is inversely proportional to time squared. But what you found is E= md2/t2, where m is a constant and d depends on t. So md2 isn't a constant.
     
  4. May 28, 2015 #3

    PeroK

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    No, but it means that Energy has a "dimension" of ##ML^2T^{-2}##.

    Compare this with the classical equation ##KE = \frac12 mv^2##, where kinetic energy has the same dimension as above.

    Look up "dimensional analysis".
     
  5. May 28, 2015 #4
    Okay, i get your point.

    But,
    1. d=1m and one meter is always one meter. How does 1m depend on time?

    2. When d=1m and m=1kg, we get E=1/t2. What is the physical significance of this reduced equation?

    Thanks.
     
  6. May 28, 2015 #5
    Thanks for your answer.

    One more question (silly one).

    Mass is something concrete, we can see it, touch it, feel it etc.
    Speed is something abstract, we can't see it, touch it etc. apart from mass. It doesnt seem to have independent existence.

    Then, how on earth can we multiply a concrete entity with an abstract one??
     
  7. May 28, 2015 #6

    Fredrik

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    1 m doesn't depend on time, but this d is defined by d=ct. If it's not, then we're no longer talking about velocity c. So d "depends on" t in the sense that the number represented by the variable d can be calculated if you know the number represented by the variable t.

    When d=1 m, then t is (1 m)/(299792458 m/s), so what we get is
    $$E=(1~\mathrm{kg}) \frac{(1~\mathrm{m})^2}{\left(\frac{1~\mathrm{m}}{(299792458~\mathrm{m/s}}\right)^2} = (1~\mathrm{kg}) (299792458~\mathrm{m/s})^2 =(299792458)^2~\mathrm{kgm^2/s^2} =(299792458)^2~\mathrm{J}.$$
     
  8. May 28, 2015 #7

    Dale

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    You are confusing mass with matter. You can touch and feel matter. Mass is a property that systems of matter have. It also does not have an independent existence.

    Besides, there is no reason that the operation of multiplication requires "abstract" or "concrete" entities to be multiplied by themselves. The concepts of "abstract" and "concrete" don't even enter in to the operation.
     
  9. May 28, 2015 #8
    So, it means that in this equation no kind of relation between energy and time can be ever found out....is it so??
     
  10. May 28, 2015 #9
    Does it then mean that when we do mathematics ( which is something abstract), then every kind of entity, whether concrete or abstract enters the 'abstract' realm?
     
  11. May 28, 2015 #10

    Dale

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    Mathematical operations are certainly abstract, whether the quantities represented by the math are abstract or not. However, "enters the 'abstract' realm" sounds more like something that you will find in a fantasy novel than in a scientific textbook, so I don't have a direct answer to your question.
     
  12. May 28, 2015 #11

    Fredrik

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    Not necessarily. But it means that most candidates for such relations can be immediately discarded because they contradict experiments that don't contradict relativity.

    I would say that aspects of the real world are represented by abstract mathematical things in the theory.
     
  13. May 28, 2015 #12

    russ_watters

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    No we don't. The units do not disappear.
     
  14. May 28, 2015 #13
    So, can it be said that when we do science or math, we are not concerned with the 'real' things but are only bothered about their properties??
     
  15. May 28, 2015 #14
    Cant we say in simple language that when a mass of 1kg moves a distance of 1m then as per E=mc2, we have E=1/t2.

    Why not, this seems to be a sensible interpretation...
     
  16. May 28, 2015 #15

    ShayanJ

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    t can not be a variable. The point is, ## c=299792458 \ \frac m s=\frac{299792458 \ m}{1 \ s}=\frac{149896229 \ m}{.5 \ s}=\frac{59958491.6 \ m}{.2 \ s}=\dots ##

    So you can only have ## E=m(\frac{299792458}{1})^2=m(\frac{149896229}{.5})^2=m(\frac{59958491.6}{.2})^2=\dots ##.

    You're just substituting different representations of the same number c in the formula ## E=mc^2 ##! Its like getting the formula ## E_k=\frac 1 2 mv^2 ## and writing it as ## E_k=\frac{16}{32} mv^{\sqrt{4}} ##!

    EDIT:
    More clearly, if you take d=1 m, then your t is 1/c. So the representation you're using is ## E=m(\frac{1}{\frac{1}{c}})^2=m(\frac{1}{\frac{1}{299792458}})^2 \approx m(\frac{1}{3.33 \times 10^{-9}})^2 ##!!!
     
    Last edited: May 28, 2015
  17. May 29, 2015 #16

    russ_watters

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    Well, two reasons:
    1. Because the units are still there and you are pretending they aren't. The "1" has units kg-m2. The equation should read E=1 kg-m2/t2.
    2. The equation isn't describing the motion of a kilogram of mass, the piece you broke apart is describing the speed of light ("c" is the speed of light). So the 1m is the distance traveled by light in "t" time: time is a constant here, not a variable and you can't change that. So when you plug in m=1 kg, and d= 1m, t=1/300,000,000s and it all simplifies to E=9x10^16 Joules.
    Science includes the implied assumption that the observed properties are real and there is nothing else to "concern with" or not "concern with". Beyond that, you're getting into philosophy, not science.
     
    Last edited: May 29, 2015
  18. May 30, 2015 #17
    I dont get your point fully...

    1. 'c' in this equation implies that motion of mass is involved. So, why not describe the motion of a kg of mass?

    2. How is time constant here? If i put t= 2 sec, the distance gets doubled to keep the speed of light constant. So, how is time constant?
     
  19. May 30, 2015 #18
    Time constant means this ;
    c=x/t If we assume x is one then you cannot change t cause c is constant.So you are telling us E=1/t2 here you assumed x equal one.Then you assumed t =2 We cannot change time If you choose x =1.If you change time you can see easily that you are breaking fundemental physics law "Speed of light is constant"
    Here the math c=x/t you said x =1 then t=1/c.Now we found t.Its a number but you are telling it can be three or four.Thats nonsense.
     
  20. May 30, 2015 #19

    russ_watters

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    You are mistaken. C is just a universal constant, that happens to be the speed of light.
    You stated the distance was 1m, which just makes time the new constant in the equation. No matter how you change the distance, the time must change in the opposite way in order that d/t always equals C. That's why plugging-in C=d/t is just an unnecessary complication: C is always going to be the same, so there is no point in calculating it every time you do the problem.

    You really need to stop trying to break the equation. If you get to a point where you think you have, all it means is that you've confused yourself.
     
  21. May 30, 2015 #20
    I will not argue further on the time issue...
    But,
    1. if v in KE=1/2mv2 implies the motion of mass, why doesnt c in E=mc2 imply the motion of mass.

    2. What does c in this equation mean?

    Thanks, u hav been very helpful....
     
    Last edited: May 30, 2015
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