Einstein - ukupna energija je 2E = mc^2
| Scientific Paper | |
|---|---|
| Title | Einstein - ukupna energija je 2E = mc^2 |
| Author(s) | Mustafa Sprecic |
| Keywords | Einstein, Lorentz |
| Published | 2013 |
Abstract
2E = mc^2, analogno formuli 2E_k = mv^2. Tako "e se jasno vidjeti, ve" iz algebarskog zapisa, kada se radi o inercijalnom, a kada o jednakopromjenljivom kretanju materijalne ta?ke. Primjenjivo na sve brzine <img border="0" style="border: 9px none; position: relative; box-sizing: border-box; display: inline-block; height: auto; margin: 10px auto; max-width: 100%; padding: 8px; border-image-source: url(data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAAUCAMAAAC6V+0/AAAAOVBMVEUAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAD///+8yHYvAAAAEnRSTlMAAgEDBAUJBwYzCw0UChARDghnBteEAAAAhElEQVR4XnWRSxJDIQgEEx1Axd/L/Q8bKCuuyOzsohHxdZLS25LSOV2ULQdflgEiIDu9KqiIFILXXpeEx2ChXwdnKNxUGxc4dZbNfXjPufkp5H0Nwtymq/dltUIweNy9qmXt08EgydDZ6+dT+9Qh9AeGenhROFI0fPjMaCHx6uIlh9/xBSJuB3l0A/6JAAAAAElFTkSuQmCC); border-image-slice: 9; border-image-width: 9px; border-image-repeat: stretch; -webkit-border-image: url(data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAAUCAMAAAC6V+0/AAAAOVBMVEUAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAD///+8yHYvAAAAEnRSTlMAAgEDBAUJBwYzCw0UChARDghnBteEAAAAhElEQVR4XnWRSxJDIQgEEx1Axd/L/Q8bKCuuyOzsohHxdZLS25LSOV2ULQdflgEiIDu9KqiIFILXXpeEx2ChXwdnKNxUGxc4dZbNfXjPufkp5H0Nwtymq/dltUIweNy9qmXt08EgydDZ6+dT+9Qh9AeGenhROFI0fPjMaCHx6uIlh9/xBSJuB3l0A/6JAAAAAElFTkSuQmCC) 9 fill / 9px stretch;" src="http://2.bp.blogspot.com/-MWC1YnLM1sk/USi8cXLzgNI/AAAAAAAAGC4/WVdEL9Wn1Fk/s1600/brzine-v-i-c.gif" />. Ovaj post predstavlja zajedni?ku cjelinu sa postom "akceleracija".
(f-1) <img border="0" style="border: 9px none; position: relative; box-sizing: border-box; display: inline-block; height: auto; margin: 10px auto; max-width: 100%; padding: 8px; border-image-source: url(data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAAUCAMAAAC6V+0/AAAAOVBMVEUAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAD///+8yHYvAAAAEnRSTlMAAgEDBAUJBwYzCw0UChARDghnBteEAAAAhElEQVR4XnWRSxJDIQgEEx1Axd/L/Q8bKCuuyOzsohHxdZLS25LSOV2ULQdflgEiIDu9KqiIFILXXpeEx2ChXwdnKNxUGxc4dZbNfXjPufkp5H0Nwtymq/dltUIweNy9qmXt08EgydDZ6+dT+9Qh9AeGenhROFI0fPjMaCHx6uIlh9/xBSJuB3l0A/6JAAAAAElFTkSuQmCC); border-image-slice: 9; border-image-width: 9px; border-image-repeat: stretch; -webkit-border-image: url(data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAAUCAMAAAC6V+0/AAAAOVBMVEUAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAD///+8yHYvAAAAEnRSTlMAAgEDBAUJBwYzCw0UChARDghnBteEAAAAhElEQVR4XnWRSxJDIQgEEx1Axd/L/Q8bKCuuyOzsohHxdZLS25LSOV2ULQdflgEiIDu9KqiIFILXXpeEx2ChXwdnKNxUGxc4dZbNfXjPufkp5H0Nwtymq/dltUIweNy9qmXt08EgydDZ6+dT+9Qh9AeGenhROFI0fPjMaCHx6uIlh9/xBSJuB3l0A/6JAAAAAElFTkSuQmCC) 9 fill / 9px stretch;" src="http://latex.codecogs.com/gif.latex?mc^{2}-mv^{2}=mc^{2}(1-\\frac{v^{2}}{c^{2}})" /> , (f-2) <img border="0" style="border: 9px none; position: relative; box-sizing: border-box; display: inline-block; height: auto; margin: 10px auto; max-width: 100%; padding: 8px; border-image-source: url(data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAAUCAMAAAC6V+0/AAAAOVBMVEUAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAD///+8yHYvAAAAEnRSTlMAAgEDBAUJBwYzCw0UChARDghnBteEAAAAhElEQVR4XnWRSxJDIQgEEx1Axd/L/Q8bKCuuyOzsohHxdZLS25LSOV2ULQdflgEiIDu9KqiIFILXXpeEx2ChXwdnKNxUGxc4dZbNfXjPufkp5H0Nwtymq/dltUIweNy9qmXt08EgydDZ6+dT+9Qh9AeGenhROFI0fPjMaCHx6uIlh9/xBSJuB3l0A/6JAAAAAElFTkSuQmCC); border-image-slice: 9; border-image-width: 9px; border-image-repeat: stretch; -webkit-border-image: url(data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAAUCAMAAAC6V+0/AAAAOVBMVEUAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAD///+8yHYvAAAAEnRSTlMAAgEDBAUJBwYzCw0UChARDghnBteEAAAAhElEQVR4XnWRSxJDIQgEEx1Axd/L/Q8bKCuuyOzsohHxdZLS25LSOV2ULQdflgEiIDu9KqiIFILXXpeEx2ChXwdnKNxUGxc4dZbNfXjPufkp5H0Nwtymq/dltUIweNy9qmXt08EgydDZ6+dT+9Qh9AeGenhROFI0fPjMaCHx6uIlh9/xBSJuB3l0A/6JAAAAAElFTkSuQmCC) 9 fill / 9px stretch;" src="http://latex.codecogs.com/gif.latex?2E-2E_k=2E_0=2E(1-\\frac{v^{2}}{c^{2}})" /> ,
(f-3) <img border="0" style="border: 9px none; position: relative; box-sizing: border-box; display: inline-block; height: auto; margin: 10px auto; max-width: 100%; padding: 8px; border-image-source: url(data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAAUCAMAAAC6V+0/AAAAOVBMVEUAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAD///+8yHYvAAAAEnRSTlMAAgEDBAUJBwYzCw0UChARDghnBteEAAAAhElEQVR4XnWRSxJDIQgEEx1Axd/L/Q8bKCuuyOzsohHxdZLS25LSOV2ULQdflgEiIDu9KqiIFILXXpeEx2ChXwdnKNxUGxc4dZbNfXjPufkp5H0Nwtymq/dltUIweNy9qmXt08EgydDZ6+dT+9Qh9AeGenhROFI0fPjMaCHx6uIlh9/xBSJuB3l0A/6JAAAAAElFTkSuQmCC); border-image-slice: 9; border-image-width: 9px; border-image-repeat: stretch; -webkit-border-image: url(data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAAUCAMAAAC6V+0/AAAAOVBMVEUAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAD///+8yHYvAAAAEnRSTlMAAgEDBAUJBwYzCw0UChARDghnBteEAAAAhElEQVR4XnWRSxJDIQgEEx1Axd/L/Q8bKCuuyOzsohHxdZLS25LSOV2ULQdflgEiIDu9KqiIFILXXpeEx2ChXwdnKNxUGxc4dZbNfXjPufkp5H0Nwtymq/dltUIweNy9qmXt08EgydDZ6+dT+9Qh9AeGenhROFI0fPjMaCHx6uIlh9/xBSJuB3l0A/6JAAAAAElFTkSuQmCC) 9 fill / 9px stretch;" src="http://latex.codecogs.com/gif.latex?2E_0=2E'\\cdot&space;\\sqrt{1-\\frac{v^{2}}{c^{2}}}=2E\\cdot&space;(1-\\frac{v^{2}}{c^{2}})" /> (f-4)<img border="0" height="45" width="320" style="border: 9px none; position: relative; box-sizing: border-box; display: inline-block; height: auto; margin: 10px auto; max-width: 100%; padding: 8px; border-image-source: url(data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAAUCAMAAAC6V+0/AAAAOVBMVEUAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAD///+8yHYvAAAAEnRSTlMAAgEDBAUJBwYzCw0UChARDghnBteEAAAAhElEQVR4XnWRSxJDIQgEEx1Axd/L/Q8bKCuuyOzsohHxdZLS25LSOV2ULQdflgEiIDu9KqiIFILXXpeEx2ChXwdnKNxUGxc4dZbNfXjPufkp5H0Nwtymq/dltUIweNy9qmXt08EgydDZ6+dT+9Qh9AeGenhROFI0fPjMaCHx6uIlh9/xBSJuB3l0A/6JAAAAAElFTkSuQmCC); border-image-slice: 9; border-image-width: 9px; border-image-repeat: stretch; -webkit-border-image: url(data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAAUCAMAAAC6V+0/AAAAOVBMVEUAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAD///+8yHYvAAAAEnRSTlMAAgEDBAUJBwYzCw0UChARDghnBteEAAAAhElEQVR4XnWRSxJDIQgEEx1Axd/L/Q8bKCuuyOzsohHxdZLS25LSOV2ULQdflgEiIDu9KqiIFILXXpeEx2ChXwdnKNxUGxc4dZbNfXjPufkp5H0Nwtymq/dltUIweNy9qmXt08EgydDZ6+dT+9Qh9AeGenhROFI0fPjMaCHx6uIlh9/xBSJuB3l0A/6JAAAAAElFTkSuQmCC) 9 fill / 9px stretch;" src="http://latex.codecogs.com/gif.latex?\\frac{2E}{\\sqrt{1-\\frac{v^{2}}{c^{2}}}}-\\frac{2E_k}{\\sqrt{1-\\frac{v^{2}}{c^{2}}}}=\\frac{2E_0}{\\sqrt{1-\\frac{v^{2}}{c^{2}}}}={\\color{Orchid}&space;2E'}=2E\\cdot&space;\\sqrt{1-\\frac{v^{2}}{c^{2}}}" /> . Ajnštajnovo izvo?enje formule aproksimativnim putem
ve? izrazom
(kraj citata)
Uporedite izraze (f-6) i (f-7) i zapitajte se ?ta oni ta?no zna?e (po smislu i fizi?koj sadr?ini) i ko je to "zadao" da se kineti?ka energija mase m i trenutne brzine v (navodim pojam trenutne brzine, jer se iz izraza za kineti?ku energiju o?ito vidi da se radi o jednakopromjenljivom kretanju) više ne ra?una po poznatoj formuli (f-6) ve? po sasvim novoj formuli (f-7)?!
a) Veli?ina kineti?ke energije iskazana formulom <img border="0" style="border: 9px none; position: relative; box-sizing: border-box; display: inline-block; height: auto; margin: 10px auto; max-width: 100%; padding: 8px; border-image-source: url(data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAAUCAMAAAC6V+0/AAAAOVBMVEUAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAD///+8yHYvAAAAEnRSTlMAAgEDBAUJBwYzCw0UChARDghnBteEAAAAhElEQVR4XnWRSxJDIQgEEx1Axd/L/Q8bKCuuyOzsohHxdZLS25LSOV2ULQdflgEiIDu9KqiIFILXXpeEx2ChXwdnKNxUGxc4dZbNfXjPufkp5H0Nwtymq/dltUIweNy9qmXt08EgydDZ6+dT+9Qh9AeGenhROFI0fPjMaCHx6uIlh9/xBSJuB3l0A/6JAAAAAElFTkSuQmCC); border-image-slice: 9; border-image-width: 9px; border-image-repeat: stretch; -webkit-border-image: url(data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAAUCAMAAAC6V+0/AAAAOVBMVEUAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAD///+8yHYvAAAAEnRSTlMAAgEDBAUJBwYzCw0UChARDghnBteEAAAAhElEQVR4XnWRSxJDIQgEEx1Axd/L/Q8bKCuuyOzsohHxdZLS25LSOV2ULQdflgEiIDu9KqiIFILXXpeEx2ChXwdnKNxUGxc4dZbNfXjPufkp5H0Nwtymq/dltUIweNy9qmXt08EgydDZ6+dT+9Qh9AeGenhROFI0fPjMaCHx6uIlh9/xBSJuB3l0A/6JAAAAAElFTkSuQmCC) 9 fill / 9px stretch;" src="http://latex.codecogs.com/gif.latex?\\frac{mv^{2}}{2}" /> nije "zadana" veličina - ve? je eksperimentalna ?injenica.
b) Veli?ina kineti?ke energije iskazana formulom (f-7) <img border="0" style="border: 9px none; position: relative; box-sizing: border-box; display: inline-block; height: auto; margin: 10px auto; max-width: 100%; padding: 8px; border-image-source: url(data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAAUCAMAAAC6V+0/AAAAOVBMVEUAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAD///+8yHYvAAAAEnRSTlMAAgEDBAUJBwYzCw0UChARDghnBteEAAAAhElEQVR4XnWRSxJDIQgEEx1Axd/L/Q8bKCuuyOzsohHxdZLS25LSOV2ULQdflgEiIDu9KqiIFILXXpeEx2ChXwdnKNxUGxc4dZbNfXjPufkp5H0Nwtymq/dltUIweNy9qmXt08EgydDZ6+dT+9Qh9AeGenhROFI0fPjMaCHx6uIlh9/xBSJuB3l0A/6JAAAAAElFTkSuQmCC); border-image-slice: 9; border-image-width: 9px; border-image-repeat: stretch; -webkit-border-image: url(data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAAUCAMAAAC6V+0/AAAAOVBMVEUAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAD///+8yHYvAAAAEnRSTlMAAgEDBAUJBwYzCw0UChARDghnBteEAAAAhElEQVR4XnWRSxJDIQgEEx1Axd/L/Q8bKCuuyOzsohHxdZLS25LSOV2ULQdflgEiIDu9KqiIFILXXpeEx2ChXwdnKNxUGxc4dZbNfXjPufkp5H0Nwtymq/dltUIweNy9qmXt08EgydDZ6+dT+9Qh9AeGenhROFI0fPjMaCHx6uIlh9/xBSJuB3l0A/6JAAAAAElFTkSuQmCC) 9 fill / 9px stretch;" src="http://latex.codecogs.com/gif.latex?\\frac{mc^{2}}{\\sqrt{1-\\frac{v^{2}}{c^{2}}}}" /> jeste "zadana" veličina - ali nije eksperimentalna ?injenica!
Poku?ajmo odgonetnuti i ?ta ta?no zna?i ova veličina u brojniku formule (f-7). Odgonetnut "emo to pomo?u drugih Ajnštajnovih formula (f-8) i (f-5). Koristimo i formule koje mo?emo na?i u starim ud?benicima i tekstovima, koji su pisani za vrijeme dok je Ajnštajn bio jo" ?iv. Tada je bilo više odgovornosti i pa?nje u kori?tenju oznaka i simbola u formulama. Danas je u toj oblasti op?te "arenilo, tako da smisao pojedinog algebarskog iskaza u STR treba potra?iti uz pomo" specijalne policije (i nadarenih inspektora istra?itelja). U potrazi za logi?kim i fizi?kim smislom Einstein-ovih govornih, geometrijskih i algebarskih iskaza koristimo i druge Ajnštajnove tekstove i pribilje?ke sa predavanja, posebno Ajnštajnov polazni ?lanak iz 1905. god. i tekstove iz njegove knjige "Moja teorija".
Usput i da vam postavim dva pitanja postavljena na drugom mom blogu - http://kvadrivektor.blogspot.com/.
Poku?ajte (sami sebi) objasniti:
a) Zašto Albert Einstein nije uspio objasniti teoriju relativnosti svom prijatelju Emanuelu Laskeru?!
b) Zašto Emanuel Lasker nije uspio shvatiti teoriju relativnosti ?!
Emanuel Lasker (filozof i matemati?ar) za teoriju svog prijatelja (A. Einsteina) ka?e:
"teorija relativnosti kao cjelina je zabluda kao sustav opisa stvarnosti , kako u svojim metodama tako i u svojim rezultatima."
Mislim da Ajnštajn nije imao - ni u glavi, ni na jeziku, ni u fizi?koj stvarnosti, ni u algebarskim iskazima, ni u geometrijskom prikazu - jasan sadr?aj koji izla?e ?lankom iz 1905.g. Zbog toga nije uspio objasniti svoje zamisli i STR ni naju?em krugu matemati?ara i fizi?ara u svom vremenu i bli?oj okolini (Poancare, Michelson, Lasker, F. Lenard, J. ? tark, W. Pauli, H. Lorentz...). Mislim da su samo zbog toga Ajnštajnovi mentori (oni koji su mu uspjeli obezbijediti radno mjesto u patentnom zavodu, a kasnije i drugi, Laue, Minkowski, Edington,...) plasirali propagandno-psiholo?ku parolu:
Dok je va?io Ajnštajnov stav, mi?ljenje i tvrdnja: Sa pove?anjem brzine kretanja tijela pove?ava se i njegova masa po formuli:
